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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: Stick on January 08, 2013, 01:23:56 pm

Title: VCE General & Further Maths Question Thread!
Post by: Stick on January 08, 2013, 01:23:56 pm
VCE GENERAL & FURTHER MATHS Q&A THREAD

To go straight to posts from 2020, click here.

What is this thread for?
If you have general questions about the VCE General or Further Maths course or how to improve in certain areas, this is the place to ask!


Who can/will answer questions?
Everyone is welcome to contribute; even if you're unsure of yourself, providing different perspectives is incredibly valuable.

Please don't be dissuaded by the fact that you haven't finished Year 12, or didn't score as highly as others, or your advice contradicts something else you've seen on this thread, or whatever; none of this disqualifies you from helping others. And if you're worried you do have some sort of misconception, put it out there and someone else can clarify and modify your understanding! 

There'll be a whole bunch of other high-scoring students with their own wealths of wisdom to share with you, including TuteSmart tutors! So you may even get multiple answers from different people offering their insights - very cool.


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OTHER FURTHER RESOURCES

Original post.
I don't see why the Further kids have to miss out on their own question thread! Post anything you're stuck with here and we'll try our best to help you out.

It might be a good idea to sticky this thread, just like the Methods and Specialist ones.
Title: Re: VCE Further Maths Question Thread!
Post by: Lasercookie on January 08, 2013, 08:35:58 pm
It might be a good idea to sticky this thread, just like the Methods and Specialist ones.
Done.
Title: Re: VCE Further Maths Question Thread!
Post by: Professor Polonsky on January 13, 2013, 02:43:54 pm
Does anyone have any experience with Networks? I had a look over some exams and didn't seem to like it. The other two Modules are Graphs & Relations and Matrices. I'm considering taking up Number Patterns instead.
Title: Re: VCE Further Maths Question Thread!
Post by: brenden on January 13, 2013, 02:45:28 pm
Does anyone have any experience with Networks? I had a look over some exams and didn't seem to like it. The other two Modules are Graphs & Relations and Matrices. I'm considering taking up Number Patterns instead.
I'm not that great at Math but Networks is my jam.

edit: I also absolutely hated Networks until the end of exam revision when I fully understood the logic behind it. Then it was like "kewwwwwl"
Title: Re: VCE Further Maths Question Thread!
Post by: Will T on January 13, 2013, 03:19:27 pm
Yeah, the networks module is interesting, but I do not recommend it. It's quite possibly less straight forward than the other modules.
Title: Re: VCE Further Maths Question Thread!
Post by: Conic on January 13, 2013, 05:00:58 pm
Does anyone have any experience with Networks? I had a look over some exams and didn't seem to like it. The other two Modules are Graphs & Relations and Matrices. I'm considering taking up Number Patterns instead.
If you did sequences and series in GMA then would basically understand most of the module already. You'd definitely be better off doing number patterns instead of networks if that was the case.
Title: Re: VCE Further Maths Question Thread!
Post by: Professor Polonsky on January 13, 2013, 10:21:08 pm
I did, and I quite liked sequences and series.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on January 21, 2013, 12:17:01 pm
What modules is everyone doing?

I'm doing:
1) Number Patterns
2) Graphs and Relations
3) Matrices
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on January 30, 2013, 10:05:42 pm
Is it necessary to do EVERY single question in the textbook? My teacher seems to think so  ::)
Title: Re: VCE Further Maths Question Thread!
Post by: Kuchiki on January 30, 2013, 10:17:26 pm
Is it necessary to do EVERY single question in the textbook?

It's probably not necessary, but that's what I did, just to satisfy my OCD. :P
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on January 31, 2013, 06:14:45 pm
Is it necessary to do EVERY single question in the textbook? My teacher seems to think so  ::)

Last year our teacher gave us a list of "required questions to complete". It probably isn't necessary to do them all, but if you start picking and choosing, you'll probably get to a stage where you only do one question. Perhaps allocate 30 minutes where you do every second question, and if you get that done, start working through the ones you skipped until the time is up. :)
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on February 03, 2013, 01:01:36 am
What modules is everyone doing?

I'm doing:
1) Number Patterns
2) Graphs and Relations
3) Matrices

Mine are
1) Number Patterns
2) Geo & Trig
3) Networks
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on February 03, 2013, 03:50:02 pm
What modules is everyone doing?

I'm doing:
1) Number Patterns
2) Graphs and Relations
3) Matrices

Trig, linear, matrices
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on February 17, 2013, 06:15:19 pm
Can past students give some tips on how to minimise mistakes in Graphs & Relations?

I find it quite straightforward, but it is easy to slip up in linear programming (especially when writing the constraints). Any suggestions to address this issue?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on February 17, 2013, 06:34:01 pm
Practice usually helps with finding constraints. It's an issue even strong students have initially, so don't worry too much about it. What I'd be more concerned about is not forgetting to use a dashed line for certain inequalities.
Title: Re: VCE Further Maths Question Thread!
Post by: saba.ay on February 17, 2013, 06:45:13 pm
Can past students give some tips on how to minimise mistakes in Graphs & Relations?

I find it quite straightforward, but it is easy to slip up in linear programming (especially when writing the constraints). Any suggestions to address this issue?

Well, I don't know how effective this will be for you, but whenever the question provided information in worded form and asked us to create a constraint, I would check my answer by substituting random values to make sure that the constraint was right.

eg. 2012 Exam 1: Graphs and Relations q 8
at least 5 loves of white bread will be made for ever loaf of brown bread that is made
 
w= white bread made per day
b= brown bread made per day

I'd first write up my constrain: w ≥ 5b
I'd then check this by subbing in random values for b. So, if I made 1 brown bread, I'd made 5 white bread. If this matches the constraint they provided originally in words, you'd know you have the right answer.

Hope that makes sense. :P
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on February 17, 2013, 06:49:33 pm
I have my first SAC this Wednesday (my school divides the CORE Sac into Univariate and Bivariate data). Does anyone have any tips for the univariate section?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on February 17, 2013, 06:53:45 pm
Well, I don't know how effective this will be for you, but whenever the question provided information in worded form and asked us to create a constraint, I would check my answer by substituting random values to make sure that the constraint was right.

eg. 2012 Exam 1: Graphs and Relations q 8
at least 5 loves of white bread will be made for ever loaf of brown bread that is made
 
w= white bread made per day
b= brown bread made per day

I'd first write up my constrain: w ≥ 5b
I'd then check this by subbing in random values for b. So, if I made 1 brown bread, I'd made 5 white bread. If this matches the constraint they provided originally in words, you'd know you have the right answer.

Hope that makes sense. :P


Yes, heaps of kids get these wrong! If you can get your head around this, you're looking really good. :)

I have my first SAC this Wednesday (my school divides the CORE Sac into Univariate and Bivariate data). Does anyone have any tips for the univariate section?

Knowing you, you probably just need to slow down and read each question carefully.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on February 17, 2013, 06:58:04 pm
LOL Knowing me? hehe what do you mean, do I jump the gun?! :p
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on February 17, 2013, 07:01:52 pm
No, you've probably covered every single little thing in univariate data really thoroughly (just like I did). So now, just relax and make sure you don't do something stupid in your first SAC (just like I did). :P
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on February 17, 2013, 07:09:13 pm
No, you've probably covered every single little thing in univariate data really thoroughly (just like I did). So now, just relax and make sure you don't do something stupid in your first SAC (just like I did). :P

yeah that's what I'm going to focus on in the coming days. Reading some notes and flicking through my bound reference, more or less looking at the most effective approach to questions, Random Sampling,etc, etc. Eh, I hope I do well. Thanks Stick!
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on February 17, 2013, 08:14:10 pm
Random sampling hardly ever comes up. Might be something to watch out for though!
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on February 17, 2013, 08:16:28 pm
Random sampling hardly ever comes up. Might be something to watch out for though!

Our SAC for Univariate Data is primarily based on choosing a random sample and using those 24 randomly selected values to find mean, median, mode, IQR, range, standard deviation, boxplots/histogram, write a report. You also have to know why selecting a random sample is important, and show the teacher how you went about doing that :) I don't think its a major aspect when we come to the bivariate data component for our next SAC.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on February 25, 2013, 06:59:13 pm
When graphing linear inequations on the CAS, is it possible to make the non-required region shaded, instead of having the required region shaded?

Title: Re: VCE Further Maths Question Thread!
Post by: b^3 on February 25, 2013, 07:03:32 pm
Flip the inequality sign.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on March 03, 2013, 11:49:07 am
In graphs and relations, some questions ask you to deduce the form of the equation, i.e. y=kx^2

Problem is that for some equations, plotting a linear regression line, y against 1/x and y against x^2 looks EXTREMELY similar, i.e. they both look like they have a straight line, but one is not completely straight (but you can't tell if its due to the the pixel limitations of the CAS or it's actually not linear)

Is there another way to check whether the graph is linear other than observation through the CAS?
Title: Re: VCE Further Maths Question Thread!
Post by: Professor Polonsky on March 06, 2013, 12:19:20 am
Not sure why that would happen - the rate of change for a y=kx^2 graph would be increasing - i.e. the differences between the y-values will be getting bigger. The opposite should happen with y=k/x.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on March 10, 2013, 05:35:29 pm
Hi,

For linear programming when you're asked to find the point that gives maximum profit within the feasible area, and none of the extreme points actually give maximum profit, how can you identify this?

I'm referring to VCAA Exam 2 2009 question 4 on Graphs and relations.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: b^3 on March 10, 2013, 05:44:41 pm
The extreme points don't fit the situation in this case, since you can't have half a flight for the situation. So in that case you would test the integer values that lie inside the feasible region and test which of those gives a maximum instead. Always check if what you're trying and the answer result you obtain fits the situation given :P
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on March 10, 2013, 05:53:07 pm
Is it safe to say that the intersection will always give the maximum value in any objective function assuming decimals are accepted?
Title: Re: VCE Further Maths Question Thread!
Post by: Lucho23 on March 16, 2013, 03:43:03 pm
Hey,

Can you please explain clearly how to identify and what is a seasonalised and cyclic trend? I sort of get it, but I'm still a bit confused.
Title: Re: VCE Further Maths Question Thread!
Post by: Daenerys Targaryen on March 16, 2013, 04:28:34 pm
For seasonal, it reappears every Q4. Therefore if there is a max at Q1, then a max will occur at each Q4 after. Eg. Q1, Q5, Q9
Cyclic has peaks etc but it doesnt always follow the same pattern.
An example a teacher use to tell us was:
Seasonal- ice cream sales; they would peak during summer
cyclic; apple company; they release a product, lots of people buy it, they wait until there are less sales, then release their next product
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on March 16, 2013, 05:12:47 pm
For seasonal, it reappears every Q4. Therefore if there is a max at Q1, then a max will occur at each Q4 after. Eg. Q1, Q5, Q9
Cyclic has peaks etc but it doesnt always follow the same pattern.
An example a teacher use to tell us was:
Seasonal- ice cream sales; they would peak during summer
cyclic; apple company; they release a product, lots of people buy it, they wait until there are less sales, then release their next product

Does it have to be every Q4? Because if you were investigating a 36-month period, it could be at every 12th month, or, end of every year, a trough would exist..
Title: Re: VCE Further Maths Question Thread!
Post by: Daenerys Targaryen on March 16, 2013, 05:14:13 pm
Well as long as it reoccurs at the same period
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on March 16, 2013, 05:18:44 pm
Well as long as it reoccurs at the same period

Yeah I thought so :) Thanks for the clarification. Luckily my school has divided the core into 3 SACS

Sac 1 - Univariate Data
Sac 2 - Regression + Data Transformations
Sac 3 - Time Series

:) Makes the workload so much easier in terms of studying for the SAC. Then again, the modules aren't exactly long + so its best to do them in that form.
Title: Re: VCE Further Maths Question Thread!
Post by: Daenerys Targaryen on March 16, 2013, 05:22:17 pm
Wow thats soo much better!!
I had to do it all within 1 week class time. Was one massive SAC.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on March 16, 2013, 07:49:00 pm
Wow thats soo much better!!
I had to do it all within 1 week class time. Was one massive SAC.

I guess it alleviates the stress, especially because I'm doing 2 3/4s and I can focus on little bits rather than a whole chunk!
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on March 16, 2013, 08:29:09 pm
For seasonal, it reappears every Q4. Therefore if there is a max at Q1, then a max will occur at each Q4 after. Eg. Q1, Q5, Q9
Cyclic has peaks etc but it doesnt always follow the same pattern.
An example a teacher use to tell us was:
Seasonal- ice cream sales; they would peak during summer
cyclic; apple company; they release a product, lots of people buy it, they wait until there are less sales, then release their next product

Does it have to be every Q4? Because if you were investigating a 36-month period, it could be at every 12th month, or, end of every year, a trough would exist..

I don't think either of these would get you the mark in the exams. :|

The main difference between a seasonal and a cyclic trend is that in a seasonal trend, the repetition is constant and the 'cycle' is less than one year in duration. Cyclic trends are generally more varied and are more than one year in duration.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on March 17, 2013, 10:23:17 pm
Can someone explain the sliding line technique? After reading past posts, I'm still confused about how to do it :(

How would you do it for the objective function Z=60x+100y?
Title: Re: VCE Further Maths Question Thread!
Post by: Lucho23 on March 18, 2013, 09:40:47 pm
The main difference between a seasonal and a cyclic trend is that in a seasonal trend, the repetition is constant and the 'cycle' is less than one year in duration. Cyclic trends are generally more varied and are more than one year in duration.

Thanks a lot! That's what it says in our book (Essential Maths Cambridge) but my teacher sort of confused me as to how to identify and distinguish the two. This is what I initially thought it was, but I though there may be different attributes these variations would possess. Thanks heaps!
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on March 19, 2013, 06:47:23 pm
What's the difference between bar charts and frequency histograms?
Title: Re: VCE Further Maths Question Thread!
Post by: Daenerys Targaryen on March 19, 2013, 06:52:41 pm
Bar charts are seperated. Each bar is separated, where as histograms are all touching each other, there is no break
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on March 19, 2013, 06:55:55 pm
Any other differences?
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on March 19, 2013, 07:09:47 pm
Any other differences?

Bar Charts are used to display univariate categorical data, whereas Histograms are used to display univariate numerical data, when you have over 40 data values you are working with. :)

Remember, the golden rule for univariate, numerical data
If the n value is greater than or equal to 40, use a histogram.
If the n value is less than or equal to 50, use a stem plot
If the n value is less than or equal to 20, use a dot plot.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on March 19, 2013, 07:30:11 pm
cheers :D
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on March 19, 2013, 09:59:14 pm
Bar charts are seperated. Each bar is separated, where as histograms are all touching each other, there is no break

While this isn't the most important difference between the two, this is an extremely important fact to remember for your Data Analysis SAC. Lots of people 'join up' their columns when drawing their bar graphs and examiners will dock a mark because:
1) you haven't understood a fundamental difference between two very different graphs
2) you're suggesting a relationship exists between the categories in the independent variable, which is not true.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 06, 2013, 05:00:23 pm
Really basic thing i forgot how to do.
If you are applying a transformation, say x^2, what do you type in the calc to apply it to the whole column?

Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 06, 2013, 07:41:24 pm
anyone?
Title: Re: VCE Further Maths Question Thread!
Post by: Kuchiki on April 06, 2013, 07:57:18 pm
Assuming that you're using the TI-nspire... In Lists & Spreadsheet, after you've typed up a list of values in a column titled "x", go to another column and type "=x^2" in the grey box, press enter, and when it asks "Column or Variable", choose "Variable Reference". Press OK and it should come up with a list of x^2 values.
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on April 09, 2013, 04:46:47 pm
Ok I seriously am not digging chapter 7 from essentials, esp. 7E (attached)
Can someone please help with 1c? I thought I was doing it right, but my answer is completely off the answer in the textbook, which is 692,000
And also 2a please! How can I do least squares regression if there's 4 different no. of purchases?

And one more thing that's unrelated to the questions above but still bugs the crap out of me, how do I 'clear history' on lists and spreadsheets? Like I'll be doing a question and naming column A 'x' for example, and then when I open a new lists and spreadsheets, it's still defined as the previous x. My teacher said to just 'clear a-z' in the calculator page, but is there no other way?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on April 09, 2013, 04:53:04 pm
1C: Did you standardise the years in the x-axis? It says to make 1992 the number 1 and go onwards from there. Also, make sure that you determine the right number for the year 2008. You might be one number off, so quickly make a little list.

2A: Work through the the quarters (in order) of year 1, then year 2, then year 3. Don't do something silly like taking the average.

Calculator: Not sure what calculator you use, but I just stopped defining the lists because I had a similar issue. Why do you have to label them? :P
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on April 09, 2013, 05:02:41 pm
1C: Did you standardise the years in the x-axis? It says to make 1992 the number 1 and go onwards from there. Also, make sure that you determine the right number for the year 2008. You might be one number off, so quickly make a little list.
Yep I did this, but my answer was still off :S

2A: Work through the the quarters (in order) of year 1, then year 2, then year 3. Don't do something silly like taking the average.
I'm not sure what you mean by this :S

Calculator: Not sure what calculator you use, but I just stopped defining the lists because I had a similar issue. Why do you have to label them? :P
I use the grey CAS. So you don't have to label them? What do you do then, if you need to draw a graph using the data? Don't you have to name them then?

Thanks for the help :)
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on April 09, 2013, 05:14:50 pm
Yep I did this, but my answer was still off :S
I'm not sure what you mean by this :S
I use the grey CAS. So you don't have to label them? What do you do then, if you need to draw a graph using the data? Don't you have to name them then?

Thanks for the help :)

1C: Hmm... I'm not sure. Perhaps check your working out? :S

2A: Year 1 Q1, Year 1 Q2, Year 1 Q3, Year 1 Q4, Year 2 Q1...

Calculator: I was able to draw graphs without labelling the axes. I guess I can't help there. :/
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on April 10, 2013, 06:42:43 pm
And one more thing that's unrelated to the questions above but still bugs the crap out of me, how do I 'clear history' on lists and spreadsheets? Like I'll be doing a question and naming column A 'x' for example, and then when I open a new lists and spreadsheets, it's still defined as the previous x. My teacher said to just 'clear a-z' in the calculator page, but is there no other way?
Thanks
I think you may have to start a new document, I've been bugged by it also... I just try keeping my label's as unique as possible so I don't come across it twice, then I start a new document once I'm done.

1c) I got a regression of

number of students = 10.09 x year + 520.4

When standardised, 2008 is the 17th year.

And I got an answer of 691.93.

So maybe you've just messed up the decimal places somewhere? are you using exact values in the lists and spreadsheets?


Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 15, 2013, 05:40:56 pm
Hi,
I have a question where there is an upward cyclic graph.
For the first part i had to perform a 3 point moving median smoothing.

In the second part it says, 'It was suggested a 4-point moving median smoothing would be more appropriate. State a reason as to why this may be true.'

What might be an appropriate answer for this?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on April 15, 2013, 06:17:22 pm
Smoothing is more likely to reflect the cyclic trend in the data.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 16, 2013, 04:50:46 pm
Thanks,
Also would it be better to say something has an upward trend or positive trend?

There is a question that is 2 marks and asks us to comment on the features of the time series plot. Would saying that it has a positive/upward cyclic trend be enough for the 2 marks?
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 16, 2013, 06:18:42 pm
Also, this may be a silly question but does the residual value have units? (the same units as the actual value).
Title: Re: VCE Further Maths Question Thread!
Post by: brenden on April 16, 2013, 08:08:24 pm
In time series, say upward. In describing linearity from a stem plot or something, use positive.
Sounds like enough for the marks, from memory. (Can't believe how much Further has gone out of my head, I only just realised)

I need clarification on your last question.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 16, 2013, 08:13:58 pm
Thanks,
So if it says 'state the residual for the national car sales in quarter 3.'

I have figured out the residual = 4300,
do i say residual = 4300 car sales?
Title: Re: VCE Further Maths Question Thread!
Post by: brenden on April 16, 2013, 08:15:55 pm
Yeah, I think so :)
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on April 17, 2013, 06:13:31 pm
Thanks,
There is a question that is 2 marks and asks us to comment on the features of the time series plot. Would saying that it has a positive/upward cyclic trend be enough for the 2 marks?


Two marks indicates that two pieces of information are required, so yes, you have fulfilled the criteria and mark allocation with that description.
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on April 22, 2013, 08:55:18 pm
Hey what's up guys,

When analysing a percentage histogram and representing it with a box plot what's the best technique to use?
(For example, take a look at Q6 VCAA 2009 Exam 1)

Also, if a percentage histogram is bimodal, do the two 'modes' have to be exactly the same percentage/value? If not, how much variance may exist between the two until the histogram is no longer considered bimodal?

Thanks in advance! :):)
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 24, 2013, 08:06:00 pm
Hey,
In what type of time series plots would it not be appropriate to use a least squares regression line?

I have a question that wants me to say if it is appropriate to use a least squares regression line is appropriate to model an increasing seasonal trend. I know that the answer would be no, but not sure how to explain (as it's 2 marks).

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on April 24, 2013, 09:07:57 pm
Hey,
In what type of time series plots would it not be appropriate to use a least squares regression line?

I have a question that wants me to say if it is appropriate to use a least squares regression line is appropriate to model an increasing seasonal trend. I know that the answer would be no, but not sure how to explain (as it's 2 marks).

thanks

The more linear (or secular is good to use here) a trend is, the more appropriate it is to use the least squares regression line. The correlation between the time (IV) and the DV is very strong if it is linear.

So, if it is seasonal, you're looking at relatively large fluctuations, peaks and troughs, not displaying a strong correlation between IV and DV. Because least squares regression line assumes linearity and therefore a strong correlation, it would be inappropriate to use a linear model to describe the increasing trend between IV and DV.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 25, 2013, 03:21:33 pm
Oh i see. Thank you very much.

Just another thing, apparently if a graph is approximately symmetrical the mean is a better measure of centre (than the median). Why is this so?
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on April 25, 2013, 05:55:23 pm
anyone?
Title: Re: VCE Further Maths Question Thread!
Post by: Daenerys Targaryen on April 25, 2013, 06:03:41 pm
Don't know for sure but:

On a normal symmetrically distributed bell curve.
Such as the one for the 68-97% Rule (IDR the exact numbers. Awks)

But the middle section for the peak is x-bar (mean) So i guess that's why.

Don't know the exact mathematics behind it
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on April 25, 2013, 07:35:43 pm
If a distribution is symmetric, you can use either the mean or median; this is because the mean is not affected if the distribution is symmetric with no outliers. This being the case, we can use either summary statistic.
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on April 27, 2013, 10:41:13 am
I always went for the median because it works every time, regardless of the shape of the distribution. :)
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on April 27, 2013, 01:17:15 pm
I always went for the median because it works every time, regardless of the shape of the distribution. :)

Yeah the median is always more reliabile.
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on April 28, 2013, 04:02:34 pm
Hey can someone please explain how to do:
- q13 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf
- q9 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008furmath1-w.pdf

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on April 28, 2013, 05:02:55 pm
Hey can someone please explain how to do:
- q13 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf
- q9 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008furmath1-w.pdf

Thanks!
Hi,
For q13:
- Enter the data into lists and spreadsheets. Remember to let 1989 equal 1, 1990 equal 2. So your first column will have "1, 2, 3, 4"... and your second column will have the corresponding internet use percentages: "0.5, 0.6, 1.1, 1.8...."
- Perform a three median regression and find the "m" value or gradient value.
Spoiler
If your data is entered correctly, you should get a regression equation of

For q9:
- Enter the data for the weight of the fish into your calculator and find the median, so ignore the length of the fish as it is not being considered.

My answers:
Spoiler
I got D for q13 (0.45%) and C for Q9 (440g).
Title: Re: VCE Further Maths Question Thread!
Post by: memarani on April 29, 2013, 09:17:07 pm
Upon observing the results with the 5-point smoothing, a trend appears. Take the data from the 5-point moving average smoothing and fit a straight line using the least-squares method. Put the first smoothed point at t = 3 and then centre the time data. State the y-intercept and gradient. Compare this trend line with that from question 3.

i'm confused on how to centre the time data or what is meant by that, can someone please explain this to me?
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on April 30, 2013, 12:04:26 am
Upon observing the results with the 5-point smoothing, a trend appears. Take the data from the 5-point moving average smoothing and fit a straight line using the least-squares method. Put the first smoothed point at t = 3 and then centre the time data. State the y-intercept and gradient. Compare this trend line with that from question 3.

i'm confused on how to centre the time data or what is meant by that, can someone please explain this to me?

You'd only centre the data during (even number)-pt moving mean smoothing such as 2-pt, 4pt etc.
This is because when you initially find the mean, the centre of the points is not actually belonging to the original series (or original time value). We then have to 'centre' the means through finding the 2-pt moving mean again of the already smoothed values in order to allow them to line up with their original time values.
This is would be better demonstrated using a visualised table, so perhaps try drawing one out!

However, in your case of a 5-pt moving mean or any (odd number)-pt moving mean, centring would definitely not be required. Perhaps it was a trick or a typo in the question that was provided to you so don't stress!

Hope I helped :)
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on April 30, 2013, 04:55:34 pm
You'd only centre the data during (even number)-pt moving mean smoothing such as 2-pt, 4pt etc.
This is because when you initially find the mean, the centre of the points is not actually belonging to the original series (or original time value). We then have to 'centre' the means through finding the 2-pt moving mean again of the already smoothed values in order to allow them to line up with their original time values.
This is would be better demonstrated using a visualised table, so perhaps try drawing one out!

However, in your case of a 5-pt moving mean or any (odd number)-pt moving mean, centring would definitely not be required. Perhaps it was a trick or a typo in the question that was provided to you so don't stress!

Hope I helped :)

That's right. Only when you have to smooth an even number of points (i.e. you perform smoothing WITH centring for 2-moving mean and 4-moving mean. Its usually always displayed in tabular form :)
Title: Re: VCE Further Maths Question Thread!
Post by: Professor Polonsky on May 01, 2013, 04:13:35 pm
As far as I can tell, most people seem to have already finished core. Have you guys also done a module, or did you start with core?
Title: Re: VCE Further Maths Question Thread!
Post by: brenden on May 01, 2013, 04:15:10 pm
My guys have done a SAC for Matrices, and done a SAC for everything in Core except for Time Series... they're doing the Time Series SAC soon though.
Title: Re: VCE Further Maths Question Thread!
Post by: Patches on May 01, 2013, 05:54:55 pm
We did a geometry SAC, and now we're about halfway through the core.
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on May 01, 2013, 08:38:56 pm
I'm having a SAC on time series soon but there's one thing bugging me.
I find it hard to differentiate between seasonal and seasonal with trend. For example, if you're given a graph and you see that there are peaks and troughs, how do you determine if it is indeed seasonal only and not with trend or the other way around?
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on May 01, 2013, 09:53:50 pm
I'm having a SAC on time series soon but there's one thing bugging me.
I find it hard to differentiate between seasonal and seasonal with trend. For example, if you're given a graph and you see that there are peaks and troughs, how do you determine if it is indeed seasonal only and not with trend or the other way around?

You can identify a seasonal variation within in your time series data through observing its predictable and repetitive fluctuating movements.

Time series data that contain a trend have a clear overall increase or decrease over the significant period of time.

Hence a time series data with both a seasonal and trend pattern will have predictable and repetitive fluctuating movements as well as a clear overall increase or decrease over the period of time.
(Value at start of season tends to be significanly higher or lower compared to value at end of season)

Time series data with seasonal variation only will have predictable and repetitive fluctuating movements but no clear overall increase or decrease over the period of time.
(Value at start of season tends to be similar to value at end of season)

Hope I helped :)
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on May 01, 2013, 10:35:29 pm
I'm having a SAC on time series soon but there's one thing bugging me.
I find it hard to differentiate between seasonal and seasonal with trend. For example, if you're given a graph and you see that there are peaks and troughs, how do you determine if it is indeed seasonal only and not with trend or the other way around?

Okay so the first thing you need to understand is that when you're analysing a time series plot, there are two main features:
(a) Trend - increasing (upward) or decreasing downward
(b) Variation - seasonal (pattern), cyclical (pattern) or random.

Seasonal variation can easily be identified by looking at a period of one year or less and observing evidently regular fluctuations (i.e. troughs and peaks occur at consistent time intervals over the time frame under analysis.

Now its one thing to identify seasonal variation, and another to determine trend. I had a TIME SERIES SAC today and my time series plot showed a decreasing (downward) trend with seasonal variation. Just note that in order to calculate seasonal indices, you MUST have a seasonal component (i.e. seasonal variation). Just a tip if you're stuck with what type of variation you've got.

Trend can be identified two ways. Firstly, sometimes its extremely easy to see a visible trend simply by looking at the graph, usually if you have a fair few plotted points (i.e. 8 points +). However, sometimes you have insufficient points to see any visible trend, and a tip would be to simply use your calculator to find the regression line of your time series plot; if the gradient/slope is (+), you're looking at an increasing trend, and (-) slope/gradient corresponds to a decreasing downward trend. Sometimes, there is no trend. It is possible to have seasonal variation with NO trend (i.e. over many years, you're having consistency in the seasonal component and the DV does not decrease/increase over the timeframe).

If there is a trend, you can use your rule to see a visible trend simply by looking at the overall trend of the graph, or as mentioned, using your calculator. But if no trend is visible, you practically see that there is no increase/decrease in DV over the timeframe. You can also look at the raw data; if the values of the data decrease over the quarters/months/terms, etc, there is probably going to be a decreasing (downward) trend.

Hope this helped, and best of luck!
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on May 02, 2013, 07:13:31 pm
Okay so the first thing you need to understand is that when you're analysing a time series plot, there are two main features:
(a) Trend - increasing (upward) or decreasing downward
(b) Variation - seasonal (pattern), cyclical (pattern) or random.

Seasonal variation can easily be identified by looking at a period of one year or less and observing evidently regular fluctuations (i.e. troughs and peaks occur at consistent time intervals over the time frame under analysis.

Now its one thing to identify seasonal variation, and another to determine trend. I had a TIME SERIES SAC today and my time series plot showed a decreasing (downward) trend with seasonal variation. Just note that in order to calculate seasonal indices, you MUST have a seasonal component (i.e. seasonal variation). Just a tip if you're stuck with what type of variation you've got.

Trend can be identified two ways. Firstly, sometimes its extremely easy to see a visible trend simply by looking at the graph, usually if you have a fair few plotted points (i.e. 8 points +). However, sometimes you have insufficient points to see any visible trend, and a tip would be to simply use your calculator to find the regression line of your time series plot; if the gradient/slope is (+), you're looking at an increasing trend, and (-) slope/gradient corresponds to a decreasing downward trend. Sometimes, there is no trend. It is possible to have seasonal variation with NO trend (i.e. over many years, you're having consistency in the seasonal component and the DV does not decrease/increase over the timeframe).

If there is a trend, you can use your rule to see a visible trend simply by looking at the overall trend of the graph, or as mentioned, using your calculator. But if no trend is visible, you practically see that there is no increase/decrease in DV over the timeframe. You can also look at the raw data; if the values of the data decrease over the quarters/months/terms, etc, there is probably going to be a decreasing (downward) trend.

Hope this helped, and best of luck!

Thank you. That was indeed helpful.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on May 02, 2013, 11:44:09 pm
As far as I can tell, most people seem to have already finished core. Have you guys also done a module, or did you start with core?

We finished the Core: Data Analysis and we'll be staring Module One: Number Patterns next week. I think the plan is to finish everything by mid term 3; the remainder of the time will be devoted to revision for the exams.

Upcoming Number Patterns SAC will probably be in about a month from now; my teacher wants to devote a lot of time to the modules!
Title: Re: VCE Further Maths Question Thread!
Post by: Professor Polonsky on May 03, 2013, 05:06:03 pm
We've finished a module already, and just finished Chapter 3 of Maths Quest. Our SAC on data analysis is only in like 5-6 weeks, though.
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on May 03, 2013, 08:10:13 pm
Just finished the time series SAC. I think I did pretty well. Thanks for your help Yacoubb.

We're now starting on Trig.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on May 03, 2013, 11:22:01 pm
Just finished the time series SAC. I think I did pretty well. Thanks for your help Yacoubb.

We're now starting on Trig.

Glad to hear :) We're starting on Number Patterns, a weird module lol!
Title: Re: VCE Further Maths Question Thread!
Post by: Coopermoody on May 05, 2013, 08:27:42 pm
Does anyone have a technique for these type of questions?
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on May 18, 2013, 05:27:26 pm
Can someone please explain Fibonacci Sequences to me?? I'm sooo confused with how to do them on the calculator :S
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on May 20, 2013, 05:35:03 pm
Hey, I am really stuck on Question 8 and 10. I answered 8a fine and got it right but 8b doesn't make sense to me. I keep getting 5.99 and the answer is 5.53 cm.
As for Question 10, I got 10a right too but I'm also having trouble with the second part to the question.
The answer to 10b is 67.7 cm.

http://cambridge.edu.au/go/interactive_book/books/vce_further_maths/images/chapter/inline-405.gif  <-- The questions are there. 8 and 10.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on May 21, 2013, 05:10:28 pm
Can someone explain how to "comment on histograms" and "compare histograms A and B" ?

Cheers
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on May 21, 2013, 05:57:34 pm
Can someone explain how to "comment on histograms" and "compare histograms A and B" ?

Cheers

I'm pretty sure you can comment on histograms just like you would comment on a boxplot or a bar chart.

You can look at the distribution, whether it is positively or negatively skewed (or approximately symmetric). You can look at the spread of the data, for example the data in A might be spread out and the data in B may be tightly bunched up, you can comment on that and say that the histogram A shows data with a greater spread, if you have actual statistic values you should probably mention them to back up your comments (IQR, Range, Median, Mean etc...)

Other things like median, mean, can also be taken into consideration.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on May 21, 2013, 05:58:19 pm
Can someone explain how to "comment on histograms" and "compare histograms A and B" ?

Cheers

So firstly, a histogram is a great way of displaying univariate, numerical data in a really economical way, when you have more than 40 data values. When looking at histograms, you can gather four summary statistic values:

(a) Shape
(b) Centre
(c) Spread - in terms of range.
(d) Outliers (if any)

Shape:
* The shape of the histogram can be:
- Positively skewed (median < mean)
- Negatively skewed (median > mean)
- Approximately symmetric (median = mean)

Outliers:
Outliers are data values that lie a significant distance away from the main body of data under analysis. You may or may not have any outliers in the data set.

For example: The distribution of 12 pre-schoolers' head circumferences is approximately symmetric, with no apparent outliers.

Centre:
The data distribution is centered at the median value.

You find this by calculating . Sometimes, in a data set you are given, your central point of tendency (i.e. median) will be found somewhere in a particular interval. This is usually the case with continuous, numerical data.

For example: The head circumferences of the preschoolers is centered somewhere in the interval 22 - 26cm, the median value.

Spread:
Usually, when we analyse a data set, we look at spread in terms of Range (Max - Min) and IQR (Q3 - Q1). However, because we don't have enough information given to us or displayed on a histogram, we only use the Range as a measure of spread.



For example: The spread of the distribution of preschoolers' head circumferences, as measured by the range, is 12cm (30 cm - 18 cm).

So, altogether:

The distribution of head circumferences of preschoolers is approximately symmetric, with no apparent outliers. The distribution of head circumferences is centered at somewhere in the interval 22-26cm, the median value. The spread of the head circumferences, as measured by the range, is 12cm (30cm - 18cm).

_________________________________________________________________________

I think we've established that. Comparing two histograms is also easy :)

The distribution of head circumferences of preschooler boys is approximately symmetric with no apparent outliers, while the distribution of head circumferences of preeschooler girls is positively skewed with no outliers. The distribution of male preeschoolers' head circumferences is centered at a higher value than the distribution of female preschoolers' head circumferences, 25cm to 20cm, respectively. The spread of the distribution of male preschoolers' head circumferences, as measured by the range, is greater than that of spread of the distribution of female preschoolers' head circumferences, 12cm (30 - 18) to 8 cm (27-17) respectively. Overall, the head circumferences of males tend to be greater and more variable than females' head circumferences in the distribution.
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on May 21, 2013, 06:21:32 pm
Hey, I am really stuck on Question 8 and 10. I answered 8a fine and got it right but 8b doesn't make sense to me. I keep getting 5.99 and the answer is 5.53 cm.
As for Question 10, I got 10a right too but I'm also having trouble with the second part to the question.
The answer to 10b is 67.7 cm.

http://cambridge.edu.au/go/interactive_book/books/vce_further_maths/images/chapter/inline-405.gif  <-- The questions are there. 8 and 10.

Bump! I need help.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on May 21, 2013, 06:44:50 pm
Hey, I am really stuck on Question 8 and 10. I answered 8a fine and got it right but 8b doesn't make sense to me. I keep getting 5.99 and the answer is 5.53 cm.
As for Question 10, I got 10a right too but I'm also having trouble with the second part to the question.
The answer to 10b is 67.7 cm.

http://cambridge.edu.au/go/interactive_book/books/vce_further_maths/images/chapter/inline-405.gif  <-- The questions are there. 8 and 10.
Bump! I need help.
Here's my working for your questions, have the picture by your side so you know all of the angles and the side lengths that I am referring to.

Q8B, you can use the cos rule to find BD, which is 7.32633

Then use DB, the angle BCD (88 degrees) and BC to find BDC using the sine rule.







Since we know two angles inside of the triangle BCD, we can find the angle DBC.





Then use the sin rule to find CD.








_________________________________________________________________________


For Q10b.
Use the cos rule to find AB, which was 10a, AB is 87.6071.

So CB will be 43.8036, which is half of it.

Now we can find angle QBA using the transposed cos rule with 3 sides, (this angle is the same as QBC).



In this context it is like:

where BA etc. are sidelengths.





After finding QBA, which is the same angle as QBC, you can then use the cos rule with QB and BC to find CQ.








edits: fixing messy working
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on May 21, 2013, 07:26:24 pm
Here's my working for your questions, have the picture by your side so you know all of the angles and the side lengths that I am referring to.



edits: fixing messy working

Wow. Thanks for your help. Now I know why I got it wrong. I kept thinking of it as a right angle! Hahah. Thanks again. I won't get this question wrong EVER. :D
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on May 21, 2013, 08:23:15 pm
Thanks Yacouub. Will there be different expectations if the question asked to describe a boxplot? (Besides the fact that a BP provdes 5 simmaru statistics)
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on May 21, 2013, 09:11:39 pm
Thanks Yacouub. Will there be different expectations if the question asked to describe a boxplot? (Besides the fact that a BP provdes 5 simmaru statistics)

You'd be required to quote the IQR (Q3-Q1). Other than that, you wouldn't be required to state anything else.

Remember, IQR = a measure of the spread of data around the median (central) point.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on May 21, 2013, 09:24:07 pm
Hmm, what about if I'm asked to compare two distributions? How would you structure your response to make it time efficient (but still get the marks)?
Title: Re: VCE Further Maths Question Thread!
Post by: johnsmith123 on May 29, 2013, 10:30:36 pm
Hello,
Just looking for some help with these questions, for the one which isnt finished the question something like show why they chose the right option by choosing the variable loan through comparing interest.
I can do parts of both questions but i cant get the correct final answer for all parts. Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: johnsmith123 on May 29, 2013, 10:31:46 pm
 
____
Title: Re: VCE Further Maths Question Thread!
Post by: johnsmith123 on May 30, 2013, 08:54:24 pm
Also this question i know its easy i just cant work out what im doing wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on June 14, 2013, 09:25:07 pm
hi all, im in search of a further math study guide on matrices, ive searched in the notes section of the forum but there is nothing on it, i understand it it an easy section for some, but couple of bits are hard. thank you
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on June 15, 2013, 01:35:18 pm
hi all, im in search of a further math study guide on matrices, ive searched in the notes section of the forum but there is nothing on it, i understand it it an easy section for some, but couple of bits are hard. thank you

Here, this might be helpful :)

Edit: oops. Forgot the link http://www.sparknotes.com/math/algebra2/matrices/section1.rhtml
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on June 17, 2013, 06:21:48 pm
hello, cant wait to ask to my teacher so just going to ask here hehe, matrices module 6
question is

RS=T

s= 2   4         t= 0  2          find matrix r, cant find it in my book either
     1   3              2  0
Title: Re: VCE Further Maths Question Thread!
Post by: random_person on June 17, 2013, 07:09:51 pm
hello, cant wait to ask to my teacher so just going to ask here hehe, matrices module 6
question is

RS=T

s= 2   4         t= 0  2          find matrix r, cant find it in my book either
     1   3              2  0

R=T*S^-1

S^-1 = | 1.5      -2|
            | -0.05    1|

R = | 0    2 | * | 1.5      -2 |
      | 2    0 |    | -0.05    1 |

R = | -1   2  |
      |  3   -4 |
 
Important to note that R does not equal S^-1*T
Title: Re: VCE Further Maths Question Thread!
Post by: flyhighx on June 17, 2013, 08:25:19 pm
Hi,
Can someone please explain and work out this question
An equilateral triangle has altitudes of 20cm . Find the length of one side.
thanks
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on June 17, 2013, 08:31:19 pm
Hi,
Can someone please explain and work out this question
An equilateral triangle has altitudes of 20cm . Find the length of one side.
thanks

An equilateral triangle as three same sides and angles, with the angles being 60 degrees equally. For more detail, see : http://au.answers.yahoo.com/question/index?qid=20081011170708AAg8pyQ and here is a diagram to help you: http://free-test-online.com/Content/equilateral%20triangle.jpg
Title: Re: VCE Further Maths Question Thread!
Post by: ficknisher on June 25, 2013, 07:37:15 pm
Hey guys,
Wondering if anyone could help me out with this question

Q) An equilateral triangle has altitudes of length 20cm. Find the length of one side.

Im completely lost with it

Thanks for your help :)
Title: Re: VCE Further Maths Question Thread!
Post by: robo_1337 on June 26, 2013, 08:17:25 am
Read the post above yours...

An equilateral triangle as three same sides and angles, with the angles being 60 degrees equally. For more detail, see : http://au.answers.yahoo.com/question/index?qid=20081011170708AAg8pyQ and here is a diagram to help you: http://free-test-online.com/Content/equilateral%20triangle.jpg

robo
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on June 28, 2013, 02:31:06 pm
It might be a good idea to put that equilateral triangle stuff in your bound reference. Perhaps the properties of an isosceles triangle will also prove to be useful. :)
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on July 11, 2013, 07:48:28 am
How did you cope with the time constraint in the exam? Did you feel rushed for time?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 11, 2013, 01:03:17 pm
I personally didn't, but I've heard that the 'average' Further Maths student will not complete the exam on time. I believe most subject exams are made like this.

If you're fairly proficient at Maths, you should be able to finish both exams quite comfortably, although Exam 1 is generally quicker to complete than Exam 2. This is why I advise students not to rush through the paper and to take your time and do it right the first time, to minimise silly mistakes.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on July 11, 2013, 02:01:53 pm
Thanks, also, did you feel well prepared before sitting the exam? I know it was your only 3/4 so you wouldn't have had as much workload  compared to year 12.
Title: Re: VCE Further Maths Question Thread!
Post by: McFleurry on July 11, 2013, 02:23:13 pm
How did you cope with the time constraint in the exam? Did you feel rushed for time?

Thanks, also, did you feel well prepared before sitting the exam? I know it was your only 3/4 so you wouldn't have had as much workload  compared to year 12.

I know your questions are kinda directed at Stick, but here's an answer...

For exam 1 (multiple choice) I did each module+ core in 15 minutes, which would leave me 30 mins at the end. I practised doing this for all of my prac exams, but when I got to the exam, well, let's just say there was a minor freak-out... in the end I spent about 20 mins on core and 15 on each module, and left time at the end to check.
So I went in prepared to finish the exam in an hour, and didn't really... but oh, well. I suppose I wasn't really 'rushed for time' (like only having 2 mins to check), but compared to all the prac exams I did, I was a bit 'rushed'.
Exam 2...haha. When I read the question on the direction of the wind in core, I was like....ahhhhh wahhh....... for about 10 mins. But, yeah, same situation for exam 1: I had less time to check than I had originally planned to.

Unlike Stick, I did another 3/4, but I would have to say that I felt quite prepared, I guess in the end it's just a matter of nerves. The year 12s in my class obvs had other subjects, but as we finished the course just before the September break, I suppose they were quite well prepared too.

I suppose a good thing to do would be to give yourself a set amount of time on each module+core so that you don't miss out on 'easy' marks which you can get than spending loads of time on a questions worth only 2 marks. I did my exam backwards: modules first, then core as I was better at modules than core, so play to your strengths, I suppose.

Hope that helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 11, 2013, 04:38:49 pm
Thanks, also, did you feel well prepared before sitting the exam? I know it was your only 3/4 so you wouldn't have had as much workload  compared to year 12.

Hell yes. I was doing trial exams in July because that's when our class finished the course. My goal by the exams was essentially to cover every single type of question possible so that nothing could catch me out on the exams (hence the 80+ practice exams). And still, there were some questions unlike anything I'd ever seen before. XD Like McFleurry, I also had a minor panic attack in Exam 1 over six multiple choice questions - use the time provided to calm yourself down and move onto something that's a bit easier to tackle, let your subconscious work on it for a bit and come back to it later.

The extent that I went to last year in order to feel prepared is not a luxury that I have this year. I guess the major difference between Year 11 and Year 12 for me is that I really just don't have the time to go that little bit further in all my subjects and use extra supplementary material. A lot of my study is really based on doing the 'standard' thing, but doing it really thoroughly. I'm hoping my doubts will be (somewhat) addressed by the end of the term 3 holidays, when I know I'll be pumping out the trial exams.
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on July 11, 2013, 04:49:14 pm
Hell yes. I was doing trial exams in July because that's when our class finished the course. My goal by the exams was essentially to cover every single type of question possible so that nothing could catch me out on the exams (hence the 80+ practice exams). And still, there were some questions unlike anything I'd ever seen before. XD Like McFleurry, I also had a minor panic attack in Exam 1 over six multiple choice questions - use the time provided to calm yourself down and move onto something that's a bit easier to tackle, let your subconscious work on it for a bit and come back to it later.

The extent that I went to last year in order to feel prepared is not a luxury that I have this year. I guess the major difference between Year 11 and Year 12 for me is that I really just don't have the time to go that little bit further in all my subjects and use extra supplementary material. A lot of my study is really based on doing the 'standard' thing, but doing it really thoroughly. I'm hoping my doubts will be (somewhat) addressed by the end of the term 3 holidays, when I know I'll be pumping out the trial exams.
Re: practice exams, where'd the 80+ come from, or do you mean 40 sets of exam 1 and 2? Which companies did you get your exams from, and did you end up repeating any exam more than once because you ran out or?
I'm thinking of doing some practice exams for the CORE and 1st module before school starts, and I'm looking towards VCAA. I'll do them knowing that I'll actually end up doing the same questions again closer to the actual exam, but under proper, timed exam conditions (i.e. once the whole course is finished). Do you think it's okay to repeat the VCAA exams or is it better to just do other company exams now and not expose myself to the VCAA questions until later?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 11, 2013, 04:54:20 pm
I lost count in the end - my teacher just told me 80+ and that's what I've stuck with. Only now can I truly marvel at just how many resources my teacher had. Even when I thought I had run out of practice papers, he managed to find 20 more for me. :S That's not something I know my teachers this year are able to match.

The actual time you do VCAA exams is really not as big an issue as what everyone makes it out to be, because a lot of company papers (with the exception of Kilbaha >_<) are at a fairly relevant standard. As long as you make sure that you mix them up to get a variety of difficulties, you'll be fine.
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on July 11, 2013, 05:35:41 pm
I lost count in the end - my teacher just told me 80+ and that's what I've stuck with. Only now can I truly marvel at just how many resources my teacher had. Even when I thought I had run out of practice papers, he managed to find 20 more for me. :S That's not something I know my teachers this year are able to match.

The actual time you do VCAA exams is really not as big an issue as what everyone makes it out to be, because a lot of company papers (with the exception of Kilbaha >_<) are at a fairly relevant standard. As long as you make sure that you mix them up to get a variety of difficulties, you'll be fine.
Did your teacher correct these ~80 exams? Or did the come with solutions?
How did you know that you've correctly found the solution?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 11, 2013, 05:40:52 pm
Solutions were also given to me.
Title: Re: VCE Further Maths Question Thread!
Post by: McFleurry on July 11, 2013, 11:27:47 pm
Re: practice exams, where'd the 80+ come from, or do you mean 40 sets of exam 1 and 2? Which companies did you get your exams from, and did you end up repeating any exam more than once because you ran out or?
I'm thinking of doing some practice exams for the CORE and 1st module before school starts, and I'm looking towards VCAA. I'll do them knowing that I'll actually end up doing the same questions again closer to the actual exam, but under proper, timed exam conditions (i.e. once the whole course is finished). Do you think it's okay to repeat the VCAA exams or is it better to just do other company exams now and not expose myself to the VCAA questions until later?

I did the VCAA papers a few times: once in prep for sacs, once before I started to do the prac exams, and once again after I finished all the prac exams.
The prac exams were give to us: your school will most likely give some to you.
Haha...so didn't run out. In the end I stopped halfway through 2006 papers just because the questions were getting kinda repetitive... You'll know what I mean when you do a few sets of exams.
I think VCAA is really leaning towards interpretation and understanding of questions, and not so much of the 'working out' part.
My teacher said that it's best to remind yourself of what VCAA questions are like: the VCAA must cater for all students, and their questions are very well worded in comparison to some companies' papers anyway.

In the end, you are going to be doing two exams set by the VCAA, so I think it's best to do their past ones at least twice.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on July 13, 2013, 10:08:51 pm
I lost count in the end - my teacher just told me 80+ and that's what I've stuck with. Only now can I truly marvel at just how many resources my teacher had. Even when I thought I had run out of practice papers, he managed to find 20 more for me. :S That's not something I know my teachers this year are able to match.

Hey, could you clarify if this was 80 exam 1's and exam 2's (therefore 160 papers), or 40 sets? Just wonderin.
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 13, 2013, 10:43:39 pm
I'm not sure - probably the latter as it seems more reasonable. As I said, it's what my teacher told me. Either way, it's a fair amount. Don't base yourself on what I did though. Our class finished by July and was working through practice exams for a very long time.

EDIT: Alluded to the wrong option. -.- Italicised it to clear up any confusion.
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on July 13, 2013, 11:29:21 pm
i need help with question 16b in chapter 21F. Im getting the answer as $123716.47 but in the back it is $143716.47. is it me thats wrong or is it the back of the book that is wrong?

help me out cuz.

btw its financial maths.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on July 15, 2013, 05:15:50 pm
The number of GPS for smartphone will not exceed twice the number of GPS for car.

By letting c represent the number of GPS for car and s represent the number of GPS for smartphone, find this constraint.

I am not 100% sure, as i get confused by writing out this type of constraint.
Would it be:  s <(or equal to) 2c  ?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Professor Polonsky on July 15, 2013, 05:18:06 pm
Yup. s cannot be bigger than 2c. So s is either smaller than or equal to 2c.
Title: Re: VCE Further Maths Question Thread!
Post by: Planck's constant on July 15, 2013, 05:39:33 pm
i need help with question 16b in chapter 21F. Im getting the answer as $123716.47 but in the back it is $143716.47. is it me thats wrong or is it the back of the book that is wrong?

help me out cuz.

btw its financial maths.


The book answer is correct.

Total repayments = 30 x 12  x 625 = 225000
Loan = selling price - deposit = 101283.53 - 20000 = 81283.53

Interest = 225000 - 81283.53 = 143716.47
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on July 15, 2013, 06:43:12 pm
yup! just figured out i had the exact same working but made a mistake writing it on the calculator a few times i guess :'(
Thank you.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on July 19, 2013, 05:31:03 pm
Ello!

Just 2 small questions, if any of you guys can clarify this with me.
Both from a practice exam I did recently, these are both very "pedantic" sort of marks.

1 [Geometry and Trigonometry] A scale drawing of this green has 5m side lengths represented by a 10cm line.
State the scale used.

random working if anyone is interested...
Spoiler






Ok, so my answer was 50:1, I thought because they mentioned "5cm side lengths represented by a 10cm line", the larger end of the factor would go first.

The answer at the back of the book was 1:50. Am I wrong? Haha I even wrote in my book to specify that the 50 was for the green and the 1 was for the drawing.

2 [Business Maths] Calculate the total amount of interest payed on the loan.
Basically in the previous question, I'd calculated the monthly payment and given a rounded answer (to cents).
For this part, I used the exact value of the monthly payment (non rounded) and ended up being 26 cents off. In their working, they used the rounded figure.

So, technically my answer is more "exact" then theirs...? do you think VCAA allows answers like this?

What do you guys think?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 19, 2013, 06:03:49 pm
1. Yes, technically you are wrong. :( The ratio is to be stated with the map value on the left.

2. This is a serious contradictory flaw of the Further Maths study design and it was something I contacted the chief examiner about, because most solutions (even theirs) use rounded answers in this module, despite their consistent reminder to students to not use rounded answers unless specified to do so. -.- As a result, rounding was explained in more depth in the 2012 assessment report. To answer your question, what you did was the right thing. :)
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on July 19, 2013, 06:10:17 pm
1. Yes, technically you are wrong. :( The ratio is to be stated with the map value on the left.
Thanks for your response Stick :P

Ok, so just to clarify, the 1, should always be to the left of the ratio? So it should always be presented as 1:x? Just making sure haha, these are the marks I don't want to lose =)
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 19, 2013, 06:20:09 pm
Remember that it might not always be a 1. The rule is that the number that represents the map value goes on the left, unless the question indicates otherwise. 
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on July 20, 2013, 11:28:31 am
Hi,
Just had a linear sac, and there was a m.c question which i wasn't quite sure about.

Mr Newcomer and Mrs latecomer leave the car park at the same time. If Mr newcomer arrives at the car park at 10:00 am, and Mrs latecomer is charged $24, what is the latest time Mrs latecomer can arrive at the car park?

There was graph in the question, although i can't upload a pic of it as the file is to big, so i will write it out.
- After 0 minutes up until 60 minutes the charge is $10.
- After 60 minutes up until 120 minutes the charge is $24.
- After 120 minutes the charge is $35.

a) 10:01 am
b) 10:59 am
c) 11:01 am
d) 11:59 am
e) the same time as Mr Newcomer
Title: Re: VCE Further Maths Question Thread!
Post by: robo_1337 on July 20, 2013, 12:28:34 pm
answer is d) 11:59
Title: Re: VCE Further Maths Question Thread!
Post by: Smileyyy on July 20, 2013, 03:02:36 pm

Just had a linear sac, and there was a m.c question which i wasn't quite sure about.


Was that you final sac because we haven't even started that chapter yet, and also because it's our last
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on July 20, 2013, 03:19:36 pm
Hi,
Just had a linear sac, and there was a m.c question which i wasn't quite sure about.

Mr Newcomer and Mrs latecomer leave the car park at the same time. If Mr newcomer arrives at the car park at 10:00 am, and Mrs latecomer is charged $24, what is the latest time Mrs latecomer can arrive at the car park?

There was graph in the question, although i can't upload a pic of it as the file is to big, so i will write it out.
- After 0 minutes up until 60 minutes the charge is $10.
- After 60 minutes up until 120 minutes the charge is $24.
- After 120 minutes the charge is $35.

a) 10:01 am
b) 10:59 am
c) 11:01 am
d) 11:59 am
e) the same time as Mr Newcomer

Both Mr Newcomer and Mrs Latecomer arrive at the same time. If Mr. Newcomer arrives at 10AM, and Mrs. Latecomer pays $24, that means she would have had to have been there between 1 and 2 hours (excluding 2 hours) after 10 (i.e. 11:59). Hence, the answer is D.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on July 20, 2013, 05:49:55 pm
Both Mr Newcomer and Mrs Latecomer arrive at the same time. If Mr. Newcomer arrives at 10AM, and Mrs. Latecomer pays $24, that means she would have had to have been there between 1 and 2 hours (excluding 2 hours) after 10 (i.e. 11:59). Hence, the answer is D.

ok, but where did it say they arrived at the same time. It only said that they left at the same time.
Title: Re: VCE Further Maths Question Thread!
Post by: BubbleWrapMan on July 20, 2013, 06:28:26 pm
The answer is "61 minutes before she leaves". There isn't enough info.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on July 20, 2013, 06:49:32 pm
ok, but where did it say they arrived at the same time. It only said that they left at the same time.

Sorry I meant left - I misread that part of the question.
Title: Re: VCE Further Maths Question Thread!
Post by: tomrox356 on July 23, 2013, 10:18:32 pm
Does anybody know how i can get my hands on copious amounts of further exams? not the VCAA ones as i already have them but all the other ones from various companies?
for instance a link to download exams? or where can i find them???
Please help!
cheers :)
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on July 23, 2013, 10:23:20 pm
Does anybody know how i can get my hands on copious amounts of further exams? not the VCAA ones as i already have them but all the other ones from various companies?
for instance a link to download exams? or where can i find them???
Please help!
cheers :)

I recommend going to itute.com Although some of the links appear to be broken, most of them are pretty accessible.
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on July 23, 2013, 10:32:32 pm
Hi guys

I need help with VCAA 2006 Exam 2 question (Mod 3) Question 3b.
Now I'm fine with normal inequalities but I have trouble understanding what it means when they use the words a is at least twice as b.

For example if y represents the number of dogs clipped and x the number of dogs washed, explain how would one get the inequality of y>/(greater than or equal to) 2x
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on July 23, 2013, 10:44:40 pm
Quote
Now I'm fine with normal inequalities but I have trouble understanding what it means when they use the words a is at least twice as b.


'At least' means that it must either be greater than or equal to.

So, if the number of dogs clipped is at least twice the number of dogs washed
x = number of dogs washed
y = number of dogs clipped

y is at least 2 x
y must be either equal to or greater than 2x

y>(greater than or equal to) 2x
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on July 24, 2013, 09:42:17 am


'At least' means that it must either be greater than or equal to.

So, if the number of dogs clipped is at least twice the number of dogs washed
x = number of dogs washed
y = number of dogs clipped

y is at least 2 x
y must be either equal to or greater than 2x

y>(greater than or equal to) 2x
thanks for that. I get it now but I think I'll have to read the question four times before I really get the hang of it.
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on July 24, 2013, 10:28:44 pm
These come with practice. Check your answer using a test point. :)
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on July 27, 2013, 08:45:12 pm
Guys I hate chapter 14 from the Essentials textbook for geometry and trigonometry :@ :@ :@
I'm struggling with it so much! I'd probably have to say this the chapter that I've struggled with the most thus far in further, and it's really annoying me!
Here's the questions I need help with:
- Ex 14a: I don't understand bearings! :S q7, 16, 19
- Ex 14b: Is there a difference between due north (/S/W/E) and north (/S/W/E)?? q1d, 2f, 5, 6, 8, 9, 11, 12
- Ex 14c: How the hell do I work with contour maps?!?! q2

Sorry I know there's a lot but I've got a test coming up on monday or tuesday and I need to have these clarified or I'm basically screwed :S

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on August 05, 2013, 05:59:24 pm
i need help:

Question one:
equipment is brought for $13000. In 5 years time it will depreciate in value to $4000. Assuming it depreciates by the straight line method, it depreciates annually by how much?

Question two:
equipment is brought for $2250. If for every use it depreciates by 0.08 cents, how many uses will it take to depreciate it to a value of $1000?
Title: Re: VCE Further Maths Question Thread!
Post by: RKTR on August 05, 2013, 07:31:57 pm
i need help:

Question one:
equipment is brought for $13000. In 5 years time it will depreciate in value to $4000. Assuming it depreciates by the straight line method, it depreciates annually by how much?

Question two:
equipment is brought for $2250. If for every use it depreciates by 0.08 cents, how many uses will it take to depreciate it to a value of $1000?
total depreciation = 13000-4000=9000
annual=9000/5=1800

depreciation=2250-1000=1250
depreciation per use =0.08
number of uses =1250/0.08 =15625 uses
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on August 05, 2013, 07:34:39 pm
total depreciation = 13000-4000=9000
annual=9000/5=1800

depreciation=2250-1000=1250
depreciation per use =0.08
number of uses =1250/0.08 =15625 uses

I got the same answer for question 1. but for question two i think by 0.08 cents, it means $0.0008. Just clarify this part.
Thank you friend.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on August 05, 2013, 09:54:45 pm
In linear programming, when do we use points within the feasible region as opposed to the vertices of the feasible region? I mean, I was stumped when I looked at a question in Checkpoints like that, and especially because I've never come across it.

On the bright side, 1 SAC left for Further (well, practically 2, but my Graphs+Relations SAC will be finished early next week). Then its on to practice exams!
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on August 05, 2013, 09:58:29 pm
In linear programming, when do we use points within the feasible region as opposed to the vertices of the feasible region? I mean, I was stumped when I looked at a question in Checkpoints like that, and especially because I've never come across it.

On the bright side, 1 SAC left for Further (well, practically 2, but my Graphs+Relations SAC will be finished early next week). Then its on to practice exams!

This is really common (it came up last year). Basically, you use points within the feasible region if the vertices don't give integer values and you're dealing with discrete variables. I hated these questions because you have to trial a lot of points, so it's time consuming.
Title: Re: VCE Further Maths Question Thread!
Post by: RKTR on August 05, 2013, 11:53:58 pm
I got the same answer for question 1. but for question two i think by 0.08 cents, it means $0.0008. Just clarify this part.
Thank you friend.
oops i didnt look at that part carefully
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on August 06, 2013, 07:23:57 am
This is really common (it came up last year). Basically, you use points within the feasible region if the vertices don't give integer values and you're dealing with discrete variables. I hated these questions because you have to trial a lot of points, so it's time consuming.

Okay then, thanks! Luckily I've come across it now before my SAC and the exam!
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on August 08, 2013, 06:43:59 pm
Is 33 degrees an acceptable alternate of 033 degrees for a bearing?
Title: Re: VCE Further Maths Question Thread!
Post by: ashoni on August 08, 2013, 06:57:13 pm
Asking a question for a friend of mine :)

From a point, A, due north of a tower, the angle of elevation to the top of the tower is 45◦.
From a point, B, 100 m on a bearing of 120◦ from A, the angle of elevation is 26◦. Find the
height of the tower.
Title: Re: VCE Further Maths Question Thread!
Post by: RKTR on August 08, 2013, 08:34:04 pm
Asking a question for a friend of mine :)

From a point, A, due north of a tower, the angle of elevation to the top of the tower is 45◦.
From a point, B, 100 m on a bearing of 120◦ from A, the angle of elevation is 26◦. Find the
height of the tower.
form a triangle ..the three vertices are A,B and top of tower ..

length of A to top of tower = height/ sin45
length of B to top of tower=height/sin 26
length AB=100m
angle between A to top and AB is 60
let height =x

use cosine rule to solve for x
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on August 08, 2013, 08:56:19 pm
Is 33 degrees an acceptable alternate of 033 degrees for a bearing?

033 is safer.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on August 08, 2013, 10:11:25 pm
033 is safer.
People from my school have claimed that they were penalised for not including a 0. I don't see the difference between 033 and 33 anyway. 0 is null.
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on August 09, 2013, 04:49:44 pm
People from my school have claimed that they were penalised for not including a 0. I don't see the difference between 033 and 33 anyway. 0 is null.

A convention of bearings is that they include three digits.
Title: Re: VCE Further Maths Question Thread!
Post by: DetteAmelie on August 09, 2013, 07:39:39 pm
Okay guys, I'm stuck on this question. :(
http://oi42.tinypic.com/vq5lhy.jpg

Never mind :) I've done it.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 13, 2013, 09:42:47 pm
People from my school have claimed that they were penalised for not including a 0. I don't see the difference between 033 and 33 anyway. 0 is null.
The Study Design refers to "three figure bearings". Writing 033 meets this requirement.
Title: Re: VCE Further Maths Question Thread!
Post by: kevinnguyen on August 13, 2013, 10:33:17 pm
linear programming having trouble with constaints and which inequalite to use ? please help my sac is tomorrow
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on August 13, 2013, 11:16:42 pm
linear programming having trouble with constaints and which inequalite to use ? please help my sac is tomorrow

if the question tells you 'no more than', this alludes to it being a (less than or equal to) inequality sign.
if the question tells you 'at least', this alludes to it being a (greater than or equal to) inequality sign.
if the question tells you 'more than'or 'less than', you use the normal < or > signs.

Remember that a solid line is used for (greater/less than or equal to), and a broken line is used for < or > inequalities.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on August 14, 2013, 05:15:47 pm
The Study Design refers to "three figure bearings". Writing 033 meets this requirement.
Haha now I'm worried about this a little.

Is writing this enough?



I generally keep all my bearings in true? I hope that's sufficient o.o
Title: Re: VCE Further Maths Question Thread!
Post by: robo_1337 on August 14, 2013, 06:13:14 pm
Haha now I'm worried about this a little.

Is writing this enough?



I generally keep all my bearings in true? I hope that's sufficient o.o

Well how many figures do you have? 2
The study design specifically mentions needing 3 figures
therefore not sufficient
:|
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on August 15, 2013, 11:55:34 am
Just a question regarding constraints in linear graphing:

If the point is a decimal and the situation you're talking about involves whole numbers, do you round up or round down?

Eg. If the point is (21.6, 12.3)

Cheers
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on August 15, 2013, 05:08:55 pm
It depends on what the variables actually are. In most practical cases, you'll be rounding down as the items are discrete. However, when simply dealing with numbers, you'll round to the nearest integer. Check the question too, since it may specify what to do. :)
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on August 20, 2013, 06:37:09 pm
Hi,
If a 1 mark question stated, 'Give one reason why a dummy activity may be used in a network,"

Would, " A dummy activity may be used in a network to ensure that all predecessor activities are properly accounted for," be sufficient for the mark?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on August 25, 2013, 09:18:10 pm
Asking a question for a friend of mine :)

From a point, A, due north of a tower, the angle of elevation to the top of the tower is 45◦.
From a point, B, 100 m on a bearing of 120◦ from A, the angle of elevation is 26◦. Find the
height of the tower.

can someone help with this question?
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on August 25, 2013, 10:31:14 pm
can someone help with this question?

I tried roughly sketching it out first. I've attached the bird's eye view and side views of the scenario to help.
If you follow my sketch:

Let height of tower = x metres
Let horizontal length from tower to B = y metres

As angle of elevation to top of tower from A is 45 degrees, we know horizontal distance from tower to A is also x metres (equal to height of tower).

As angle of elevation to top of tower from B is 26 degrees, we can use SOHCAHTOA to calculate that:
tan(26) = x/y
Transpose to find y in terms of x:
y = x/tan(26)

Use cosine rule on triangle (bird's eye view) to determine value of x:
y^2 = x^2 + 100^2 – 2(x)(100)cos(60)
(x/tan(26))^2 = x^2 + 100^2 – 2(x)(100)cos(60)

Solve for x using CAS:
x = 42.40, -73.61

x must be 42.4 metres as x > 0
Thus height of tower being x, is 42.4 metres tall.

Hope I helped! :)
P.S. Sorry for the dodgy drawing!

Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on August 26, 2013, 03:56:38 pm
thanks! that helped a lot  :)
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on September 01, 2013, 01:58:30 pm
Hi,

I need help with this question.

I have been given the matrix q and the matrix qrx and the question asks me to solve for x. How would I do this? I know that I have to use the inverse somewhere but if X and R are unsolved, how would I do this?

Here's the actual question.

Given Q  (2x2) no from left to right, first row then second is -2,4,3 and -2. and QRX is (2x1) top to bottom -24 and 32.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 01, 2013, 09:31:24 pm
Hi,

I need help with this question.

I have been given the matrix q and the matrix qrx and the question asks me to solve for x. How would I do this? I know that I have to use the inverse somewhere but if X and R are unsolved, how would I do this?

Here's the actual question.

Given Q  (2x2) no from left to right, first row then second is -2,4,3 and -2. and QRX is (2x1) top to bottom -24 and 32.

What answer did you get?

I did a method but I don't know if my answer is right
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on September 01, 2013, 10:36:04 pm
Hi,

I need help with this question.

I have been given the matrix q and the matrix qrx and the question asks me to solve for x. How would I do this? I know that I have to use the inverse somewhere but if X and R are unsolved, how would I do this?

Here's the actual question.

Given Q  (2x2) no from left to right, first row then second is -2,4,3 and -2. and QRX is (2x1) top to bottom -24 and 32.

i dont get what you are asking. is this question in the vcaa exams or essentials further book?
Title: Re: VCE Further Maths Question Thread!
Post by: Insa on September 17, 2013, 12:32:25 am
Hey guys :D Could anyone please help me with question in relation to networks? Thank you.
Title: Re: VCE Further Maths Question Thread!
Post by: RKTR on September 17, 2013, 05:13:20 pm
E won a match. the opponent who lost to E also only won a match. therefore E must have defeated A.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on September 18, 2013, 01:15:06 pm
Do we need to connect the dots on a time series if we plot one? Or can we leave them disconnected?
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on September 18, 2013, 09:17:26 pm
Connect them together.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 19, 2013, 07:49:30 pm
Would the following explanations be appropriate (they're for linear regression): i've just used example figures.

Coefficient of determination
87.56% of the variation in arm span can be explained by variation in height.

Describing a relationship:
From the scatterplot, it can be seen that there is a strong, negative linear relationship between number of errors on a test and the period of time spent studying, with no outliers.

Gradient:
On average, the final weight of Jane decreases by 1.44kg for every additional day spent working out.

Y-intercept:
On average, Jane's final weight at the start of the weight-loss program, is 96kg.

^ Are these templates for such questions okay? Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on September 19, 2013, 07:59:14 pm
They look good to me.

The only thing that i might've added is for the Coefficient of determination you could also say in the next sentence, "12.46% of the variation in arm span can be explained by other factors such as ......."

Not sure if it's necessary though.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 19, 2013, 08:26:28 pm
They look good to me.

The only thing that i might've added is for the Coefficient of determination you could also say in the next sentence, "12.46% of the variation in arm span can be explained by other factors such as ......."

Not sure if it's necessary though.

Nah. Checked assessment reports and none have an extra statement regarding causality. I think it would be fair to mention the remaining %age attributed to causality if a question required you to do so.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on September 19, 2013, 08:59:50 pm
Y-intercept:
On average, Jane's final weight at the start of the weight-loss program, is 96kg.

^ Are these templates for such questions okay? Thanks!
Wow, never seen a question asking to describe the y-intercept of a graph like that, but nonetheless could be useful to set out how you want to answer a question.
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on September 19, 2013, 09:09:44 pm
Would the following explanations be appropriate (they're for linear regression): i've just used example figures.

Coefficient of determination
87.56% of the variation in arm span can be explained by variation in height.

Describing a relationship:
From the scatterplot, it can be seen that there is a strong, negative linear relationship between number of errors on a test and the period of time spent studying, with no outliers.

Gradient:
On average, the final weight of Jane decreases by 1.44kg for every additional day spent working out.

Y-intercept:
On average, Jane's final weight at the start of the weight-loss program, is 96kg.

^ Are these templates for such questions okay? Thanks!

If you don't like the term 'on average', you can use 'expected' for the gradient and y-intercept (I preferred and used these):

Gradient: The final weight of Jane is expected to decrease by 1.44kg for every increase in days working out by 1.

y-intercept: When Jane spends no days working out, the final weight is expected to be 96kg.

Wow, never seen a question asking to describe the y-intercept of a graph like that, but nonetheless could be useful to set out how you want to answer a question.

This is actually really important.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 19, 2013, 09:16:12 pm
If you don't like the term 'on average', you can use 'expected' for the gradient and y-intercept (I preferred and used these):

Gradient: The final weight of Jane is expected to decrease by 1.44kg for every increase in days working out by 1.

y-intercept: When Jane spends no days working out, the final weight is expected to be 96kg.

This is actually really important.

Ah okay thanks :) Just realised I had these written in my bound reference! Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Mandy360 on September 20, 2013, 01:26:00 pm
Just a quick questions relating to the further core, I got this in a practice exam and had no idea how to work it out:
"A set of bivariate data involves the independent variable x. The mean of x is 31.38 and the standard deviation is 5.38.
The other variable is y and the mean of y is 19.46 and the standard deviation is 5.46.
Pearson's correlation coefficient is -0.813.
The least squares regression line for this data would have an equation closest to:"

A) y=45.4-0.8x
B) y=0.8+43.2x
C) y=9.9-0.8x
D) y=0.8+9.6x
E) y=44.6-0.8x

The know the answer couldn't be B or C and apparently it is A but how do I work it out?
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 20, 2013, 02:56:56 pm
Just a quick questions relating to the further core, I got this in a practice exam and had no idea how to work it out:
"A set of bivariate data involves the independent variable x. The mean of x is 31.38 and the standard deviation is 5.38.
The other variable is y and the mean of y is 19.46 and the standard deviation is 5.46.
Pearson's correlation coefficient is -0.813.
The least squares regression line for this data would have an equation closest to:"

A) y=45.4-0.8x
B) y=0.8+43.2x
C) y=9.9-0.8x
D) y=0.8+9.6x
E) y=44.6-0.8x

The know the answer couldn't be B or C and apparently it is A but how do I work it out?

The equation of a least squares regression line is y = a + bx

a is the y-intercept. This can be found by doing:

a = (mean of y) - b x (mean of x).

b is the gradient. This can be found by:

        (correlation coefficient) x (standard deviation of y)
   b=  __________________________________________
               (standard deviation of x).

So substitute the given values:

b = (-0.831 x 5.46) / 5.38 = -0.8

a = 19.46 - (-0.8 x 31.38) = 45.92

Closest answer is A
Title: Re: VCE Further Maths Question Thread!
Post by: Mandy360 on September 21, 2013, 12:34:32 pm
Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on September 22, 2013, 10:44:22 pm
Hi,
In Matrices, if you are trying to find for example the number of people living in Town A after 3 years (against the number of people living in Town B, where there originally 100 in each town), so you calculate s(3) = T^3 * s(0), and say this comes to a matrix where there is exactly 95.5 living in town A and 105.5 living in Town B, how do you round?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 22, 2013, 11:12:09 pm
Hi,
In Matrices, if you are trying to find for example the number of people living in Town A after 3 years (against the number of people living in Town B, where there originally 100 in each town), so you calculate s(3) = T^3 * s(0), and say this comes to a matrix where there is exactly 95.5 living in town A and 105.5 living in Town B, how do you round?

thanks

You usually round up either way, even if the total should equal 200.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on September 23, 2013, 01:59:53 am
Hi can someone work out this Number Patterns question and provide the working out? Will be grateful.


The sum of the first three terms of a geometric series is 57 while the infinite sum is 81.
The common ratio is
A. 1/3
B. 2/3
C. 1
D. 3/2
E. 12
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on September 23, 2013, 08:27:20 am
Hi can someone work out this Number Patterns question and provide the working out? Will be grateful.


The sum of the first three terms of a geometric series is 57 while the infinite sum is 81.
The common ratio is
A. 1/3
B. 2/3
C. 1
D. 3/2
E. 12

Set up two equations:

1: Sum to Infinity -



2: Sum of 3 terms -



Solve these two equation simultaneously, for further just use your calculator.

and
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on September 23, 2013, 01:31:33 pm
Set up two equations:

1: Sum to Infinity -



2: Sum of 3 terms -



Solve these two equation simultaneously, for further just use your calculator.

and
Thanks a lot.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on September 23, 2013, 02:40:26 pm
I hoped that it didnt come to this, but i just am attempting to do practice exams on the modules i did at the start of the year matrices and networks, im all good with graphs and relations because i just completed it last week at school lol, however if i have forgotten around 50% of the module should i go over it again or just attempt practice exams and try and find the example in the textbook? OMFG its annoying when this happens
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on September 23, 2013, 03:11:42 pm
For questions such as "The top of a two metre section of a 5 metre cone is removed. After the top is removed, the percentage of the total volume remaining is:

I know to calculate it you need to do 1- (2/5)^3 which is essentially entire thing minus top, but I was wondering why we can't do (3/5)^3 which would be bottom bit only and gives a different answer?
Title: Re: VCE Further Maths Question Thread!
Post by: b^3 on September 23, 2013, 03:35:07 pm
The volume that you have remaining is not a cone, (since we are dealing with a cone and not an inverted cone). That's why you need to look at the full cone, and the cone that we have removed from the top, leaving what we have left.
(http://i1082.photobucket.com/albums/j373/mclaren200800/cones_zpsf3ec887b.png)
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on September 23, 2013, 05:28:00 pm
I hoped that it didnt come to this, but i just am attempting to do practice exams on the modules i did at the start of the year matrices and networks, im all good with graphs and relations because i just completed it last week at school lol, however if i have forgotten around 50% of the module should i go over it again or just attempt practice exams and try and find the example in the textbook? OMFG its annoying when this happens
I would go an try some challenging questions from your textbook related to your module, a refresher to the module, and then reinforce that revision with practice exams (which I personally think is good for trying different types of questions). If you do go and just attempt practice exams you may just end not learning as effectively if your foundation of the module isn't too strong, that's just what I think, find out what works best and stick with it and you'll remember the modules in no time =p
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on September 23, 2013, 05:32:04 pm
Haha cheers mate, i am trying that now for matrices, it really helps doing questions, but then i go into my trial exam booklet i got from tsfx and its like WHY DO YOU MAKE THE EXAMS SO HARD LOL
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on September 23, 2013, 07:48:09 pm
I've probably asked this question before somewhere, but now that I've finished the further course and it's the holidays, I might as well ask again. Do you think it's stupid to self-learn a module? I did business maths, and while it wasn't the worst module, I definitely struggled trying to identify what some questions were asking me, leading to confusion and marks lost. I've always wanted to study matrices, and I'm willing to spend some time these holidays on teaching myself matrices. I'm already familiar with basic concepts, with transition matrices being the main thing I need to properly learn. I'm also thinking of going to connect education for further, so if I do decide to study matrices instead I'll be going for matrices instead of business maths and using those notes to help me. Do you guys think this is a good idea? I just don't wanna risk majorly screwing up on the actual VCAA exam, which I feel will happen if I do business maths (because I've lost quite a number of marks in this module while doing past VCAA exams, and I can't afford for that to actually happen in the exam!)

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on September 23, 2013, 08:52:49 pm
I've probably asked this question before somewhere, but now that I've finished the further course and it's the holidays, I might as well ask again. Do you think it's stupid to self-learn a module? I did business maths, and while it wasn't the worst module, I definitely struggled trying to identify what some questions were asking me, leading to confusion and marks lost. I've always wanted to study matrices, and I'm willing to spend some time these holidays on teaching myself matrices. I'm already familiar with basic concepts, with transition matrices being the main thing I need to properly learn. I'm also thinking of going to connect education for further, so if I do decide to study matrices instead I'll be going for matrices instead of business maths and using those notes to help me. Do you guys think this is a good idea? I just don't wanna risk majorly screwing up on the actual VCAA exam, which I feel will happen if I do business maths (because I've lost quite a number of marks in this module while doing past VCAA exams, and I can't afford for that to actually happen in the exam!)

Thanks :)
Haha, it always seems to be matrices that people want to switch into. =p

Here's my opinion (my personal thoughts on changing module). It almost seems like you've answered your own question - you yourself seem to be sure that you can do better in matrices than in business math and if that's the case then go for it. If you decide to learn another module - be fully committed and get heaps of practice in.

But (there's a but!) there's things you have to take into consideration:
- Getting help from teachers: if you pick matrices, there's a very good chance that teachers won't know anything about it. Of course there's AN here, but it may be more inconvenient.
- The amount of time you spend learning this module could be far less than what you spent learning business maths - you may not have enough time to go through a module as in depth as you could with the limited time available before exam's now, you had many weeks in class - now you have to cram it over a shorter amount of time. You've probably had a SAC for business math and tests for business math.
- There are always going to be tough questions in every module, there has to be in order to separate students, so even though you may have issues with some business math questions there's a good chance you'll have issues with some matrices questions as well. The start of the module always looks simple, then it builds and it's only until you get started on a question when you see how hard it may be.

Anyway that's my opinion, other's may have different feelings towards this.
All the best!
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on September 24, 2013, 03:04:01 pm
Can someone please help me with this question?
Title: Re: VCE Further Maths Question Thread!
Post by: Patches on September 24, 2013, 03:34:11 pm
I've probably asked this question before somewhere, but now that I've finished the further course and it's the holidays, I might as well ask again. Do you think it's stupid to self-learn a module? I did business maths, and while it wasn't the worst module, I definitely struggled trying to identify what some questions were asking me, leading to confusion and marks lost. I've always wanted to study matrices, and I'm willing to spend some time these holidays on teaching myself matrices. I'm already familiar with basic concepts, with transition matrices being the main thing I need to properly learn. I'm also thinking of going to connect education for further, so if I do decide to study matrices instead I'll be going for matrices instead of business maths and using those notes to help me. Do you guys think this is a good idea? I just don't wanna risk majorly screwing up on the actual VCAA exam, which I feel will happen if I do business maths (because I've lost quite a number of marks in this module while doing past VCAA exams, and I can't afford for that to actually happen in the exam!)

Thanks :)

Matrices is very very easy, if you do methods it's pretty much just basic multiplication and simplified Markov chains.
Title: Re: VCE Further Maths Question Thread!
Post by: robo_1337 on September 24, 2013, 04:21:04 pm
Can someone please help me with this question?

I would say answer A.

We can see the median is roughly 22, and we know that about 68% of all variables lie within +/- 1 standard deviation. You can immediately cross out answers C-E as they are too far away from the median. Then out of A and B, A seemed the most likely.
Title: Re: VCE Further Maths Question Thread!
Post by: Kuchiki on September 24, 2013, 09:40:03 pm
I would say answer A.

We can see the median is roughly 22, and we know that about 68% of all variables lie within +/- 1 standard deviation. You can immediately cross out answers C-E as they are too far away from the median. Then out of A and B, A seemed the most likely.

Yeah, I agree with answer A.

It's because most of the values in a normal distribution lie within 3 standard deviations of the mean, and since the values in this case seem to end at 20 and 24, and the mean appears to be 22, we can approximate 3 standard deviations to be equal to 2 (22-20 = 24-22 = 2). Therefore, one standard deviation is equal to 2/3 (roughly 0.67). And then, since 68% lies within one standard deviation of the mean, subtract the standard deviation from the mean to get the lower boundary (22-0.67 = 21.33) and add it to the mean to get the upper boundary (22+0.67 = 22.67), so you get 21.33 to 22.67.
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on September 24, 2013, 09:43:29 pm
A lot of the questions I've been doing for matrices ask me to 'evaluate' the matrix. This is in the essentials text book thus far in ch26. Is this something that'll be asked in the VCAA exam as well or just something the book wants us to do for the sake of it?
Title: Re: VCE Further Maths Question Thread!
Post by: jeanweasley on September 24, 2013, 10:41:02 pm
Hi if someone can help me to understand the answers and how to get there for the following questions from the VCAA exam, I'd be extremely grateful. The worked solutions are on Itute by the way. I know I'm going to look like an idiot since I've got a long list of what I don't understand but I think it's better to ask than just keep quiet so no judging. hahah. (I'm an arts kid so anything maths related is not my forte.)

VCAA 2010 Exam 1

Geo & Trig
Question 6 I got the first part 7.106 but I don't get how  they got the value for TM.
Question 7 I didn't know how to solve this. I think it was because I was looking for another measurement. Can someone explain how they got 38.8 degrees?
Question 9 Why is the volume of water in the cylinder equal to the volume of water in the cone?

Question 8 in graphs in relations I forgot how to do this. Can someone refresh my mind?

VCAA 2011 Exam 1

Geo & Trig

Question 7 Why is QC double PB? Is there any other method of solving this? Would similar triangles work?
Question 8 Why is x/0.8? I know the addition part but I don't know how they got 0.5818.
Question 9 Again I thought that I needed another measurement. Didn't think it was similar triangles. How did they conclude that?

Question 9 in graphs and relations Why is it 5x-5y? Why does it have to be the same gradient as AB? How do you work the gradient for this?

Finally if you have any suggestions on how I can understand questions better, feel free to shoot them at me. (:
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on September 25, 2013, 11:04:50 am
Yeah, I agree with answer A.

It's because most of the values in a normal distribution lie within 3 standard deviations of the mean, and since the values in this case seem to end at 20 and 24, and the mean appears to be 22, we can approximate 3 standard deviations to be equal to 2 (22-20 = 24-22 = 2). Therefore, one standard deviation is equal to 2/3 (roughly 0.67). And then, since 68% lies within one standard deviation of the mean, subtract the standard deviation from the mean to get the lower boundary (22-0.67 = 21.33) and add it to the mean to get the upper boundary (22+0.67 = 22.67), so you get 21.33 to 22.67.

Thanks for the help, but just to clarify something, don't all values lie within 4 standard deviations of the mean? so why approximate 3?
And there's a formula for predicting the standard deviation in the essentials textbook; Sx=Range/4, in this case it equals 1.
Are we meant to use this formula? o_o
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on September 25, 2013, 11:08:06 am
99.7% of the data lie within 3 standard deviations of the mean, we approximate 3 because it accounts for almost all of the values
Title: Re: VCE Further Maths Question Thread!
Post by: Kuchiki on September 25, 2013, 11:16:12 am
Thanks for the help, but just to clarify something, don't all values lie within 4 standard deviations of the mean? so why approximate 3?
And there's a formula for predicting the standard deviation in the essentials textbook; Sx=Range/4, in this case it equals 1.
Are we meant to use this formula? o_o

I dunno, I've never heard of that formula before (I used the Maths Quest textbook).

Regarding the standard deviation, I don't think there's a specific number of standard deviations where all values lie within (correct me if I'm wrong), but yeah, as abcdqdxD said, 99.7% lies within 3, and that's pretty close to 100%. Since the question says "About 68%...", using this approximation should be fine.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on September 25, 2013, 06:40:54 pm
In Core,
If you are asked to describe the shape, would you say for example: positively skewed with a possible outlier    -   if you know it isn't an outlier, do you still say 'possible', and likewise if you know it is an outlier?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on September 25, 2013, 07:29:13 pm
Is the answer to this B or A?
Title: Re: VCE Further Maths Question Thread!
Post by: BasicAcid on September 25, 2013, 07:47:55 pm
B as it says the first year it's $100,000 so we know the second is $108,000 third is $116,640 etc fourth is $125,971.2 etc... 13th is over $250,000
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 25, 2013, 09:10:44 pm
B as it says the first year it's $100,000 so we know the second is $108,000 third is $116,640 etc fourth is $125,971.2 etc... 13th is over $250,000

The question asks after how many years. The twelfth year is actually 13 years later. Hence, The answer is A.

After one year = t2.
Hence, after twelve years = t13

Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on September 25, 2013, 09:13:46 pm
I say A. Similar reasoning to Yaccoub.

Spoiler
t1 (first year): $100000
t2 (second year): $108000 [note: this is after one year (one year after the first)]
t3 (third year): $116640 [this is after two years]
...
t11 (eleventh year): $215892 [after 10 years]
t12 (twelth year): $233164 [after 11 years]
t13 (thirteenth year): $251817

Yes t13 is the first term above $250000, but even though it's the 13th year, it is only 12 years after the first year, and thus the answer is A.

These are the sort of questions that I get really annoyed at, they don't follow the common "n-1" formula's. I often find them a little trickier.

Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on September 25, 2013, 09:51:33 pm
yeah the answers says B (heffernan 2003 btw) so i wasn't too sure, thanks for the help:)
Title: Re: VCE Further Maths Question Thread!
Post by: sam.utute on September 26, 2013, 12:26:12 am
In Core,
If you are asked to describe the shape, would you say for example: positively skewed with a possible outlier    -   if you know it isn't an outlier, do you still say 'possible', and likewise if you know it is an outlier?

thanks

Use outlier where appropriate. If you're not sure/cannot calculate if it's an outlier, than try using "extreme values" instead.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on September 26, 2013, 07:23:49 am
doesn't "possible outlier" suggest that it may not be an outlier?
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 26, 2013, 07:38:39 am
In Core,
If you are asked to describe the shape, would you say for example: positively skewed with a possible outlier    -   if you know it isn't an outlier, do you still say 'possible', and likewise if you know it is an outlier?

thanks

If you can actually load your data onto the calculator and get a boxplot, it'll actually show whether an upper our lower outlier exists.

So, you'd say (if outliers present)
The distribution is positively skewed with an apparent outlier.

OR

if no outliers are present:
The distribution is positively skewed with no apparent oulier.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 26, 2013, 07:42:50 am
doesn't "possible outlier" suggest that it may not be an outlier?

I'd use this for stem-and-leaf plots.
Title: Re: VCE Further Maths Question Thread!
Post by: sam.utute on September 26, 2013, 09:45:01 am
If you can actually load your data onto the calculator and get a boxplot, it'll actually show whether an upper our lower outlier exists.

So, you'd say (if outliers present)
The distribution is positively skewed with an apparent outlier.

OR

if no outliers are present:
The distribution is positively skewed with no apparent oulier.

That would take up too much time in my opinion. Obviously, depends on how fast your are, but my guess is the average student won't have time to input data onto their calculator.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on September 26, 2013, 10:08:48 am
That would take up too much time in my opinion. Obviously, depends on how fast your are, but my guess is the average student won't have time to input data onto their calculator.

Depends really on how you're given the data. If it's a stem and leaf plot, then mentioning that there are 'possible outliers' would probably do. But if you were given a histogram or box plot, the outlier is usually visible.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on September 26, 2013, 12:35:53 pm
Guys just doing Networks, and this question is one that i always hate, Constructing a network

(http://i39.tinypic.com/jgi8wg.jpg)

those are the questions
but i never understand how to set out the vertices and where and how long to draw the edges,
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on September 26, 2013, 01:51:19 pm
Guys just doing Networks, and this question is one that i always hate, Constructing a network

(http://i39.tinypic.com/jgi8wg.jpg)

those are the questions
but i never understand how to set out the vertices and where and how long to draw the edges,

I'm guessing your talking about Q14?

If so, this was how I did it last year in Further:
1. Space out all of your Vertices (The Numbered Dots).
2. Go row-by-row and then match the number from the row with the corresponding number in the column. If it has a number "2" then you need to have to lines connecting the two Vertices.
You just have to be careful not to double up or add unnecessary ones, unless it has a number more than 1.

The setting out of where you put your Vertices is not an issue, and neither is the length of your Edges. What the examiners look for is that you can read the Matrix and match the lines with the two numbers. e.g. In Q14b, For Row 5 Column 3, there is a number two. That means that you have to have one line connecting the Vertices of 3 and 5, and then make another line again to show that you recognised there was 2 lines required.

I had to draw it out, but I'm not sure how to upload a Picture onto here. =/
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on September 26, 2013, 04:11:41 pm
haha damn you couldnt post the pic, what ya needa do is to go on tinypic through google and upload the photo and then just use the IMG link after you upload it and copy and paste it here, i have a few more pics to upload as i am struggling them with aswell lol.

thanks bro
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on September 26, 2013, 04:40:32 pm
haha damn you couldnt post the pic, what ya needa do is to go on tinypic through google and upload the photo and then just use the IMG link after you upload it and copy and paste it here, i have a few more pics to upload as i am struggling them with aswell lol.

thanks bro

Alright, I made a really rough drawing out of it, but I'll re draw it and make it neater and easier to understand. :) I'll have it posted within the next 45 Minutes. I'll do it now. :)

Feel free to post the other Questions as well, and I'll try and help as much I can. :)
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on September 26, 2013, 04:58:08 pm
hehe, ive got another question when drawing a network, from a Matrix representation, are you allowed to have edges crossing each other when drawing it out,

 I have B->M thats one edges then it goes P->K which looks like a big X, is this allowed, i thought edges were not allowed to cross when drawing out networks?, because if they are allowed to cross i am gonna be pissed thinking all this time you were not allowed too
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on September 26, 2013, 04:59:32 pm
haha damn you couldnt post the pic, what ya needa do is to go on tinypic through google and upload the photo and then just use the IMG link after you upload it and copy and paste it here, i have a few more pics to upload as i am struggling them with aswell lol.

thanks bro


YAY! It works. :) Let me know if you have a question about my Diagram. It's really rough, so hopefully you can still read it. :)

(http://i39.tinypic.com/168gc2s.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on September 26, 2013, 05:01:44 pm
hehe, ive got another question when drawing a network, from a Matrix representation, are you allowed to have edges crossing each other when drawing it out,

 I have B->M thats one edges then it goes P->K which looks like a big X, is this allowed, i thought edges were not allowed to cross when drawing out networks?, because if they are allowed to cross i am gonna be pissed thinking all this time you were not allowed too

Yes you are allowed to have the Edges crossing over each other, but make sure that its clearly shown where each line is connecting with the Vertices
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on September 26, 2013, 05:15:17 pm
Wat the heck?, i was so convinced they were not allowed to cross and i didnt even know you were allowed to hack Vertices 2 go around 3 and end up joining to 4, this is why i had so much difficulty with this module, omfg omfg.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on September 26, 2013, 06:44:22 pm
Wat the heck?, i was so convinced they were not allowed to cross and i didnt even know you were allowed to hack Vertices 2 go around 3 and end up joining to 4, this is why i had so much difficulty with this module, omfg omfg.

HAHA! Fair enough.

You are allowed to cross over and go around Vertices. The setup of your diagram doesn't matter, as long as all the information is presented and can easily be followed. :)
Title: Re: VCE Further Maths Question Thread!
Post by: plato on September 26, 2013, 09:10:04 pm
Hi if someone can help me to understand the answers and how to get there for the following questions from the VCAA exam, I'd be extremely grateful. The worked solutions are on Itute by the way. I know I'm going to look like an idiot since I've got a long list of what I don't understand but I think it's better to ask than just keep quiet so no judging. hahah. (I'm an arts kid so anything maths related is not my forte.)

VCAA 2010 Exam 1

Geo & Trig
Question 6 I got the first part 7.106 but I don't get how  they got the value for TM.
Draw a triangle DTM where DT = 7.106 and DM = 5.5 since M is the midpoint of DC which is 11 long. Now, if you can calculate the angle TDM, you could use the cosine rule on triangle DTM.
Angle ATM + Angle ADT = 90 degrees. So, if you calculate the angle ADT using tan(ADT) = , you can then find Angle TDM and hence the length of side TM.



Question 7 I didn't know how to solve this. I think it was because I was looking for another measurement. Can someone explain how they got 38.8 degrees?
Angle CBD is on the right triangle CBD where CD id the side opposite angle CBD and CB is the adjacent side. Therefore you could use tan(angle CBD) = .
To do this, you must calculate the length BC from the right triangle ABC using the given angle and the given length AB.


Question 9 Why is the volume of water in the cylinder equal to the volume of water in the cone?
When full, the volume of water in the cylinder = where r = 30 and h = 24. This gives a volume of 22619.46…
If this is water is all poured into the cylinder, the water will reach a certain height, assuming that the cylinder is high enough and the water does not overflow. Use the formula for the volume of a cylinder to find the depth (or height) of water. Since you know the values of V, r and , solve the resulting equation.


Question 8 in graphs in relations I forgot how to do this. Can someone refresh my mind?
Let’s use a letter “w” replace for the time being. You can then think of the equation being like .
If we were to draw a graph of , we would have a vertical axis labeled “y” and a horizontal axis labeled “w”. On such a graph, if “y” = 27, then “w” would equal 9.
So look for such a graph among the five present, remembering that “w” really stands for . The graphs A, B, C and D all have (or “w”) on the horizontal axis but only graph A has a point where “y” = 27 when “w” or = 9.



VCAA 2011 Exam 1

Geo & Trig

Question 7 Why is QC double PB? Is there any other method of solving this? Would similar triangles work?
Triangles AQC and APB are similar. Since the length AC in the larger triangle is double the length of the corresponding side AB in the smaller triangle, then all lengths in the larger triangle will be double the corresponding length in the smaller triangle.

Question 8 Why is x/0.8? I know the addition part but I don't know how they got 0.5818.
You need to first identify similar TRIANGLES rather than similar trapeziums. Do this by taking a horizontal line from P across to cross the line TU at a point we’ll call V and then continue to meet the line TU at right angles at a point we’ll call W. You now have two similar triangles PVU and PXS to which you can apply similar triangle ratios. You cannot apply such ratios to similar trapeziums.

Question 9 Again I thought that I needed another measurement. Didn't think it was similar triangles. How did they conclude that?
Angles ABD and ACB are equal. Both triangles ABD and ACB share the same angle at point A. Since these two triangles have a pair of equal angles, then they must have all three angles equal and the triangles must similar. It is now a matter of seeing that side BD = 24cm on triangle ABD is opposite to angle A and must correspond with side BC = 40cm on triangle ABC.
Therefore, each side of larger triangle is times larger than the corresponding side of the small triangle and its area must be times that of the smaller one.


Question 9 in graphs and relations Why is it 5x-5y? Why does it have to be the same gradient as AB? How do you work the gradient for this?
It is not 5x-5y .
The answer is (E) M = 5x + 5y. This line will have the same gradient as AB with a gradient of -1.
By rearrangement,  M – 5x = 5y and so which is a straight line with a gradient of -1 and a y intercept of . We need the maximum value of (greatest y-intercept of a line that touches any and all points of the feasible region along the line AB.


Finally if you have any suggestions on how I can understand questions better, feel free to shoot them at me. (:
Practice, practice and practice. Not only in doing many questions but trying to figure out how what you have learnt can relate to the question at hand.
Title: Re: VCE Further Maths Question Thread!
Post by: Conic on September 26, 2013, 09:47:19 pm
You need to first identify similar TRIANGLES rather than similar trapeziums. Do this by taking a horizontal line from P across to cross the line TU at a point we’ll call V and then continue to meet the line TU at right angles at a point we’ll call W. You now have two similar triangles PVU and PXS to which you can apply similar triangle ratios. You cannot apply such ratios to similar trapeziums.
You can't use the trapeziums because they aren't similar, not because similar trapeziums can't be used. In this case the trapeziums both share the same angles, but the ratios of the sides aren't equal, hence they aren't similar.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on September 26, 2013, 09:49:03 pm
Wat the heck?, i was so convinced they were not allowed to cross and i didnt even know you were allowed to hack Vertices 2 go around 3 and end up joining to 4, this is why i had so much difficulty with this module, omfg omfg.
I feel your frustration.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on September 30, 2013, 08:59:26 pm
Business Maths - Do we round up to keep a situation logical or round down numerically?

For example:
The number of years required for $9,000 to double in value when invested at 6.3% compound interest, where interest is paid monthly is closest to -
A: 8
B: 9
C: 10
D: 11
E: 12

So I chose E. Solving for n in the compound interest formula will give you n=132.374 [months]. Converting this to years will give 11.0312 years. If only 11 years past, there will be slightly less than 18,000 so therefore there has to be 12 years for there to be 18,000.

So, in a VCAA exam, should I be rounding up or down? I know they are written a lot better than a lot of other companies, so how should I go about it logically? (Kilbaha said I was wrong in this particular question, I've had a few Neap like this which I've gotten wrong because they rounded down.)
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on September 30, 2013, 09:32:32 pm
I think your reasoning is right, and what I used to do last year.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on October 01, 2013, 11:50:11 am
Hi Guys, is it possible to get assistance for question 9
please, thank you

(http://i44.tinypic.com/24weyyv.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: sam.utute on October 01, 2013, 12:00:58 pm
Business Maths - Do we round up to keep a situation logical or round down numerically?

For example:
The number of years required for $9,000 to double in value when invested at 6.3% compound interest, where interest is paid monthly is closest to -
A: 8
B: 9
C: 10
D: 11
E: 12

So I chose E. Solving for n in the compound interest formula will give you n=132.374 [months]. Converting this to years will give 11.0312 years. If only 11 years past, there will be slightly less than 18,000 so therefore there has to be 12 years for there to be 18,000.

So, in a VCAA exam, should I be rounding up or down? I know they are written a lot better than a lot of other companies, so how should I go about it logically? (Kilbaha said I was wrong in this particular question, I've had a few Neap like this which I've gotten wrong because they rounded down.)

I always rounded up (I'm pretty sure VCAA also expects you to round up).
Title: Re: VCE Further Maths Question Thread!
Post by: Conic on October 01, 2013, 12:07:22 pm
If you multiply the matrices you get:



so 3a+12=3b+12 and a+6=4-b. You can simplify these to get a+b=-2 and a-b=0, which is B.
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on October 02, 2013, 08:18:37 pm
Hey,
Hope you guys are having a great break!

This is from NEAP 2006 Exam 2.
I'm stuck on the proceeding questions b & c:

b. It has been determined that the relationship between deficit and week number is non-linear. One of the managers has also stated that a relationship of the form d=kt^2 will not be successful either. Do you agree with this? Give reasons.

c. The same manager believes that the relationship is of the form d=k/t. Plot a straight line to show that this is true and thus determine the value of k. Label the axes.

I don't understand question b. I don't know how to obtain the k value in c. Concise and detailed explanations would be much appreciated.
Thanks in advance!  :D
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on October 02, 2013, 08:26:59 pm
B. Plot the deficit against the time squared and see if you get a nice linear result or not.

C. Same method as B (except use the reciprocal of each time number) and use your calculator's regression function to find k.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 02, 2013, 09:33:46 pm
Can someone please have a look at q6?

I think the exam/solutions are wrong

There appears to be two correct answers in C and D.

Correct me if I'm wrong :P
Title: Re: VCE Further Maths Question Thread!
Post by: unfamila on October 02, 2013, 10:45:29 pm
The answer looks to be both unless there was an earlier question which showed all of the constraints, then you could cancel out D.
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on October 03, 2013, 05:07:38 pm
Hey I was just looking through the key knowledge in the further study design for Core and I saw this dot point: Random numbers and their use to draw simple random samples from a population -
 display, appropriately summarise and describe these samples.
. What exactly does it refer to and how would it crop up in a question?
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 03, 2013, 05:37:50 pm
Hey I was just looking through the key knowledge in the further study design for Core and I saw this dot point: Random numbers and their use to draw simple random samples from a population -
 display, appropriately summarise and describe these samples.
. What exactly does it refer to and how would it crop up in a question?

I've done around 22 exams and I've never seen this examined (on practice exams anyway)
Title: Re: VCE Further Maths Question Thread!
Post by: robo_1337 on October 03, 2013, 06:17:45 pm
Part of our SAC was on it, using the random integer function on the CAS to select a random sample of provided data and summarizing it
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on October 03, 2013, 07:35:51 pm
Hey what do you guys think about doing the VCAA exams pre-2006? I was thinking of doing those as well, since they're VCAA standard as well. For anyone that's already done further did you do these exams or just do other company exams? Also, do you think it's worth re-doing the VCAA exams? I'm doing/have done some VCAA exams already, from 2009-2012 and I was thinking of re-doing them closer to the exams under strict timed conditions and all. Is that a good idea or should I just expose myself to new exams instead?
Thanks :D
Title: Re: VCE Further Maths Question Thread!
Post by: brenden on October 03, 2013, 07:37:26 pm
Hey what do you guys think about doing the VCAA exams pre-2006? I was thinking of doing those as well, since they're VCAA standard as well. For anyone that's already done further did you do these exams or just do other company exams? Also, do you think it's worth re-doing the VCAA exams? I'm doing/have done some VCAA exams already, from 2009-2012 and I was thinking of re-doing them closer to the exams under strict timed conditions and all. Is that a good idea or should I just expose myself to new exams instead?
Thanks :D
I started at 2006 and worked my way up to 2011 and that was enough. I did a minimal amount of company but I think if you learn from exams properly you'll have near no improvement to make by the time you're done with the VCAA ones and a few company ones. (Why did you start at 2009?)
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on October 03, 2013, 07:42:12 pm
Fair enough :).. I started doing that in reverse so maybe that wasn't a good idea. I stopped at 2009 because I was doing from 2012 backwards in preparation for my internal exam at the end of the term.
Title: Re: VCE Further Maths Question Thread!
Post by: simba on October 03, 2013, 07:56:53 pm
Hmm I think last year for I only did 2006-2011 papers for further (but I had checkpoints which has some older study design questions in it too!) All of them I did in exam conditions (god knows why!)
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 03, 2013, 08:20:17 pm
Fair enough :).. I started doing that in reverse so maybe that wasn't a good idea. I stopped at 2009 because I was doing from 2012 backwards in preparation for my internal exam at the end of the term.

Usually its best to use the 2012 exam as your last exam before you walk into the actual exam, and do it under exam conditions. =/

How long ago did you do the 2012 and 2011 Exams?
Title: Re: VCE Further Maths Question Thread!
Post by: vashappenin on October 03, 2013, 08:24:30 pm
Lol yeah I know.. my bad haha. Nah I did them like during the last week of term 3 so it wasn't that recent.. I'm sure if I do them again at the end I won't remember much at all :)
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 04, 2013, 05:25:36 pm
Could someone please explain what constitutes surface area?

I get a bit confused when the shape has a top removed etc, does surface area only count the 'outside' of the shape?

Another scenario was when water is filled in a cylinder with its top removed, what would constitute "internal surface area" in this case?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on October 04, 2013, 06:24:23 pm
Generally speaking, VCAA would probably be really explicit about it if it ever came up in their exams. The only instance where the inside has been included is for a pool type question where you're required to calculate the amount of tiling to tile the inside of the pool. In these questions though, you don't need to do the outside.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on October 05, 2013, 03:24:16 pm
Hi all, This relates to matrices on 2012 exam 2 last question 3)

here is the question, the question is at the bottom of the image. its really getting annoying to realise the last question is always the hardest lmfao.


(http://i43.tinypic.com/27wyq34.jpg)

Title: Re: VCE Further Maths Question Thread!
Post by: mishamigo on October 05, 2013, 03:42:14 pm
Would you just work out the workers for each job, then add them?
Ie. 70% of A stay at A. 70% of 100 is 70 people. 80% of O stay at O- 160 people, etc. then add them all up!
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 05, 2013, 03:54:09 pm
Hi all, This relates to matrices on 2012 exam 2 last question 3)

here is the question, the question is at the bottom of the image. its really getting annoying to realise the last question is always the hardest lmfao.


(http://i43.tinypic.com/27wyq34.jpg)



Okay:
* A - 70% stay in their job
* O - 80% stay in their job
* P - 90% stay in their job

Then you look at the Initial State, and multiply the according percentage by the number of employees in that role, and add the figures. :)

(70% x 100) + (80% x 200) + (90% x 50)
= 70+160+45
= 275

Therefore, 275 staff members will stay in their role.
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on October 06, 2013, 04:08:13 pm
When we are asked for a difference equation, how do we know when the initial value is t1, or t0?
For example

for this question i got, t(n+1)=0.95(tn)+30,000 t0=200,000
Title: Re: VCE Further Maths Question Thread!
Post by: wholeT on October 06, 2013, 06:12:48 pm
For exam 2, is it required to show full workings + full worded sentences?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 06, 2013, 06:28:14 pm
When we are asked for a difference equation, how do we know when the initial value is t1, or t0?
For example

for this question i got, t(n+1)=0.95(tn)+30,000 t0=200,000

Pretty much I find the given information is the start of a sequence (like the first week, or first hour) then it will be t1. If the information gives information before a sequence takes place (like "initially" or "at the start") then it will be t0 - so in the question you showed, I would use t0.
Have a look at what I wrote here a few months ago:
Spoiler
Just expanding on what Horacio said:
I like to just write down next to the question if the term they are giving you is like the first term of the sequence or the initial term before the sequence starts.

For example, from a VCAA exam a question was:

"A crystal measured 12cm in length at the beginning of a chemistry experiment. Each day it increased in length by 3%, the length after 14 days of growth is?"

I write down that initally the length is 12cm before any days have past, so the equation will be:
Spoiler
Personally for this question, I wrote next to the question "after 1 day of growth, it will 12.36".

as you want the growth to happen 14 times (after 14 days), so in this case you don't use "n-1" as the 12cm is like the initial term before the first day of growth.


An example of the case in which you use "n-1" is:

"In the first month, the gardeners worked 625 hours. In the second month, the gardeners worked 500 hours. How many hours did they work in the fifth month.

Now we know the first term of the sequence is 625, so we have to use "n-1" or else we will generate a sequence after the first month. I wrote next to the wording there.

Hopefully that made some sense, I get so annoyed by the wording we get in some of the questions like "during", "after", "more". Or the questions when they want you to find how much "n" until one sequence reaches over a certain value.

For exam 2, is it required to show full workings + full worded sentences?
For questions worth more than 1 mark, appropriate working out should be shown. If the question is one mark, then a correct answer will suffice (but working out is always useful).
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 06, 2013, 10:27:36 pm
When we are asked for a difference equation, how do we know when the initial value is t1, or t0?
For example

for this question i got, t(n+1)=0.95(tn)+30,000 t0=200,000
I get it from reading the question. It's really tricky, especially when they say "at the end of the 8th day", "at the beginning of the 11th day".
I got the same answer as you. I think by 'initially' they mean immediately, before any years have been completed, therefore I think t0 = 200000
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on October 08, 2013, 07:35:37 pm
Hi guys this relates to module 6 - matrices
could i  get a solution to this please.

(http://i39.tinypic.com/34nodjk.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: KevinooBz on October 08, 2013, 07:54:13 pm
Hi guys this relates to module 6 - matrices
could i  get a solution to this please.

(http://i39.tinypic.com/34nodjk.jpg)
All you need to find is the number of people who are expected to change their votes. 25% of the people who initially plan to vote for Rob say they are going to change their vote and 24% of the people who initially plan to vote for Anna will also change their vote. Rob has 5692 voters initially, but 25% will change and vote for Anna. Anna has 3450 votes initially, but 24% will change and vote for Rob. So in total, the number of people who change their vote is (0.25  x 5692) + (0.24 x 3450) = 2251.
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 08, 2013, 08:32:32 pm
Pretty much I find the given information is the start of a sequence (like the first week, or first hour) then it will be t1. If the information gives information before a sequence takes place (like "initially" or "at the start") then it will be t0 - so in the question you showed, I would use t0.
Have a look at what I wrote here a few months ago:
Spoiler
For questions worth more than 1 mark, appropriate working out should be shown. If the question is one mark, then a correct answer will suffice (but working out is always useful).

Did I mention I love you? I love you. Always been confused with the t0/t1 rubbish, and it's been the crux of where I go paranoid when I do further number patterns. I love you man.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 08, 2013, 09:19:44 pm
Hey guys :)

Is anyone going to check their MC answers online on Friday Nov 1 after the exam. I have no idea whether I want to or not. I feel like its going to just kill me if I find I've made a multitude of errors, and ruin it for me, and that if I don't look up the answers, I'm going to CONSTANTLY be worried.

I was thinking of maybe checking one of the exams (possibly checking answers for exam 1). If I do well, it will be a MASSIVE confidence boost for exam 2; it sort of works out both ways.

Inputs would be great :)
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 08, 2013, 09:29:01 pm
Hey guys :)

Is anyone going to check their MC answers online on Friday Nov 1 after the exam. I have no idea whether I want to or not. I feel like its going to just kill me if I find I've made a multitude of errors, and ruin it for me, and that if I don't look up the answers, I'm going to CONSTANTLY be worried.

I was thinking of maybe checking one of the exams (possibly checking answers for exam 1). If I do well, it will be a MASSIVE confidence boost for exam 2; it sort of works out both ways.

Inputs would be great :)

Oh definitely - even if I don't do too well, there's a sense of panic that would give me the motivation to study just a bit more to consolidate knowledge. Negative reaction, you know?
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 08, 2013, 11:26:39 pm
I checked it after completing Exam 1. But the one mistake that one of my friends made, was wasting time circling it on the booklet that you get to keep as well as the MC Sheet at the same time. He should have done the whole exam first, and then copied it out, not at the same time - Otherwise you are wasting time and will not finish. He ended up guessing about 2 or 3 at the end (which isn't too bad), but its still costly marks. =/

So do the whole exam first, and if you have time at the end, then copy it over to your question booklet. :)

For those wondering how you can mark your Exam 1 (Multiple Choice Exam), the Solutions for each exam will usually be up on iTute on the night of the exam (So on the Friday at night), or within 24 hours of Exam 1 being finished. They are done by teachers, so they COULD also be wrong - Usually not dramatically wrong though.:)
Title: Re: VCE Further Maths Question Thread!
Post by: Kuchiki on October 09, 2013, 01:56:44 am
I checked it after completing Exam 1. But the one mistake that one of my friends made, was wasting time circling it on the booklet that you get to keep as well as the MC Sheet at the same time. He should have done the whole exam first, and then copied it out, not at the same time - Otherwise you are wasting time and will not finish. He ended up guessing about 2 or 3 at the end (which isn't too bad), but its still costly marks. =/

So do the whole exam first, and if you have time at the end, then copy it over to your question booklet. :)

Hmm, I disagree with this. I think it is best to circle the answers on both the question booklet and the multiple-choice sheet as you go (unless you're neatly and artistically drawing circles in your question booklet, I don't see this as "wasting" much time). And then, at the end, even if you have just a few minutes left, you can quickly go through your question booklet and make sure that your answers match up, because working out the right answer in the question booklet but then accidentally shading in the wrong answer in the multiple-choice sheet would be an awful mistake to make in the exam.

As for the question of whether to check your answers online, I think it really depends on the kind of person you are. I personally didn't do it because knowing any of my mistakes in an exam would have just caused me to dwell on them and distracted me from my later exams, but if you really believe that it would motivate you to do better, then go ahead.
Title: Re: VCE Further Maths Question Thread!
Post by: unfamila on October 09, 2013, 10:47:08 pm
This is probably a really easy question, but how to you work out the std deviation from a histogram. Do i just count the percentages from around the median up to 68% and take an educated estimate?
For example Q3-  http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf
Also in Q2- Looking off the box plot it looks as though the IQR is 2, is there a mathematical approach to getting 2.7
Thank you in advance
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on October 09, 2013, 11:54:29 pm
for question 3. i did it by counting the number of bars till the one in the middle, because it is a normal standard curve, and dividing it by 2. thus two columns represented one STDev. its supposed to be an approximate.

for question 2. the Q3 is 181.5 by observation and Q1 is 179. thus IQR is 2.5. This is why the option of 2.7 is not really close to the other options because again its an approximate.

For both of these until unless you calculate the number of ovens for each temperature (this would also be approximate as y-scale isn't clear), and work out the STDev and IQR through that, i'm not aware of any other method that could be used that is learnt in further maths. 
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 10, 2013, 08:46:49 am
This is probably a really easy question, but how to you work out the std deviation from a histogram. Do i just count the percentages from around the median up to 68% and take an educated estimate?
For example Q3-  http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf
Also in Q2- Looking off the box plot it looks as though the IQR is 2, is there a mathematical approach to getting 2.7
Thank you in advance

Range divided by 6. You see, this method could only be applied if your data distribution was approximately symmetric with no extreme values (or outliers).
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 10, 2013, 11:30:28 pm
Hello, I have a few questions:

1. Number Patterns
i) For the difference equation tn+1 = 2tn - 1, if t4=5, then t3=       (my answer was 5, just unsure whether it is 1)

2. Networks
i) Would you include dummy activities in part of the critical activity? e.g A - B - C - d1- E
ii) Would you include dummy activities as a predecessor? e.g A - B - d1 - H

Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 10, 2013, 11:53:18 pm
Hello, I have a few questions:

1. Number Patterns
i) For the difference equation tn+1 = 2tn - 1, if t4=5, then t3=       (my answer was 5, just unsure whether it is 1)


t4 = 2t3 - 1
5 = 2t3 - 1
(5+1)/2 = t3
t3 = 3.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 11, 2013, 12:59:47 am
Oh thanks, lol wow I just realised that I did 2-1 so it was 5 = 1-t3 wasnt paying attention.. forgot it was 2 x t3  not 2 + t3

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 11, 2013, 07:31:06 pm
Is there a reason why the answer's E instead of A? Is it because Adjacency matrixes count degrees? I thought it was only for edges.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 11, 2013, 09:38:11 pm
Is there a reason why the answer's E instead of A? Is it because Adjacency matrixes count degrees? I thought it was only for edges.

Loops count as 2, not 1. It's because you can go clockwise (which counts as one), and anti-clockwise (which also counts as one). But I remember my teacher last year saying something about Loops counting as 1. =/ Looking at the font, it I'm guessing its a past VCAA Exam question - what year is it from?
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 11, 2013, 10:38:42 pm
Loops count as 2, not 1. It's because you can go clockwise (which counts as one), and anti-clockwise (which also counts as one). But I remember my teacher last year saying something about Loops counting as 1. =/ Looking at the font, it I'm guessing its a past VCAA Exam question - what year is it from?

Great, now I feel mentally challenged. It's from Kilbaha 2011 exam 1.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 11, 2013, 10:53:58 pm
Great, now I feel mentally challenged. It's from Kilbaha 2011 exam 1.

Sorry. I'll try and find out more and get back to you. I'll ask my Further teacher from last year and see how it worked. :)
Title: Re: VCE Further Maths Question Thread!
Post by: yazza on October 12, 2013, 10:44:03 am
Can anyone take me through question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf

and can someone show me how shelley was right in question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007furmath1.pdf
Title: Re: VCE Further Maths Question Thread!
Post by: KevinooBz on October 12, 2013, 11:26:35 am
Can anyone take me through question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf

and can someone show me how shelley was right in question 9 for geo and trig
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007furmath1.pdf
Spoiler
You'll need to calculate the height of a triangle with the length 4m (the pole) given, and the base which is the midpoint of MN to T. So firstly, you have all the lengths of the triangle so you use the cosine rule to find the angle you want. In this case, you want angle NMT, so cos(NMT)=6^2 + 4^2 - 5^2 / 2 x 6 x 4. NMT = cos^-1(9/16) = 55.7711. Now you can work out the length of T to the midpoint of MN. sin(55.7711)= x/4. x= 4sin(55.7711)= 3.3072. Last step is finding the height, so you can use Pythagoras' theorem. sqrt(4^2 - (3.3072)^2)= 2.25 = 2.3
With the next question, hopefully you did the diagram correctly. The length of 1/2NP is given by cos(35) = x/4 -> x=4cos(35) -> 1/2NP = 4cos(35). NP is 2 times 1/2NP, so you get 2 x 4 x cos(35). If you need a diagram for both questions, I could make one later if you can't make sense of the numbers.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 13, 2013, 07:41:45 pm
A square pyramid has a volume of 25m^3 (with a height of 3m).
The square pyramid is filled with foam insulation to a depth of one metre.
What percentage of the original roof space is now filled with foam insulation? Write your answer correct to the nearest whole number.

Thank you
edit; height is actually 3m ._.
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on October 13, 2013, 08:04:54 pm
This is a similar figures question. The second pyramid is the entire pyramid minus the foamed volume. Once you see this it is a routine question. These are quite common to keep practicing them. :)
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 13, 2013, 08:07:10 pm
Hi thank you, can you please guide me through it I've never seen one of these questions before o.O
Title: Re: VCE Further Maths Question Thread!
Post by: #J.Procrastinator on October 13, 2013, 08:10:33 pm
A square pyramid has a volume of 25m^3 (with a height of 3m).
The square pyramid is filled with foam insulation to a depth of one metre.
What percentage of the original roof space is now filled with foam insulation? Write your answer correct to the nearest whole number.

Thank you
edit; height is actually 3m ._.

Firstly, find the length of one side of the base (Use 25m^3):

Volume of square base pyramid is 1/3 l^2 times its height: 1/3 x l^2 x 3 = 25
                                                                                              l^2 = 25
                                                                                              length = 5 metres

Now, use ratios to find the length of one side, where the foam reaches 1 metre:       Small : Large       Small : Large
                                                                                                                  length ratio:   x     :    5      =     2     :    3
                                                                                                                                                x/5        =        2/3
                                                                                                                                                    x = 2/3 x 5
                                                                                                                                                    x = 10/3 (leave this as a fraction for more accurate results)


Now find the volume of the smaller square base pyramid on top. Because the foam reaches 1 metre, the height of the top pyramid is 3-1= 2 metres. Use this to find its volume: V= 1/3 x (10/3)^2 x 2 = 7.4 metres^3 approx.

From the initial 25 m^3, take away the 7.4m^3 to get the volume of the bottom half of the pyramid (which is what you want- with the foam insulation):  25-7.4= 17.6 metres cubed


Finally, put this value over the original volume and multiply by 100 to get the volume that the roof space is filled with insulation. That is,

17.6/ 25 x 100= 70.4%

BUT WRITE ANSWER TO THE NEAREST WHOLE NUMBER. Hence, 70% ! Hope this is correct :)
                                                                                                                                                 
                                       
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on October 13, 2013, 08:13:54 pm
I'm on my iPad right now so this isn't going to work too well, but I'll try anyway. :)

So you have a pyramid of height 3m and this "smaller" pyramid of height 2m. That gives you a k value of 2/3. Cube that (for volume) and you'll get 8/27.

So 8/27 of the pyramid is not filled up with foam. That means that 19/27 of the pyramid has been filled with foam. (19/27)*100 = 70% to the nearest whole number.

Maybe you'll see this a bit better with a diagram too. I hope this helps, and I'm sorry that my help has been a bit limited.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 13, 2013, 08:18:12 pm
I appreciate your post, I just found out a solution on the VCAA website though, still thx.
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 13, 2013, 11:09:16 pm
quick question: Are Itute practice exams meant to be a kick in the face, similar to the Kilbaha ones?
Another one: Is it best to revisit some previously done exams, or best if you find/do other ones and struggle with them?
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 13, 2013, 11:11:43 pm
quick question: Are Itute practice exams meant to be a kick in the face, similar to the Kilbaha ones?
Another one: Is it best to revisit some previously done exams, or best if you find/do other ones and struggle with them?

Yeah, iTute ones are a bit hard, especially for Geometry and Trig.

Yes, you should revisit past exams that you have already done, and re-do the questions you got wrong. Anything that you're still getting wrong should be revised thoroughly and may be added to your bound reference.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 13, 2013, 11:13:37 pm
I haven't made and don't plan to make a bound reference. Is this an issue for me? I really, really don't think I need one.
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 13, 2013, 11:15:15 pm
Yeah, iTute ones are a bit hard, especially for Geometry and Trig.

Yes, you should revisit past exams that you have already done, and re-do the questions you got wrong. Anything that you're still getting wrong should be revised thoroughly and may be added to your bound reference.

Is it normal to struggle over their core questions as well? These Itute ones, golly they hurt my pride.

Redoing questions I've got wrong, thanks for the tips on that one. Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 13, 2013, 11:16:50 pm
I haven't made and don't plan to make a bound reference. Is this an issue for me? I really, really don't think I need one.

For Methods, its not really a big thing to have a reference, because I never look at it. However, for Further you will probably need to look at it.

What three modules are you doing?
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 13, 2013, 11:23:34 pm
Is it normal to struggle over their core questions as well? These Itute ones, golly they hurt my pride.

Redoing questions I've got wrong, thanks for the tips on that one. Thanks.

I did Further last year, so its a bit hard to remember. I don't think Core was too bad. The Core questions are definitely challenging, but possible to do. :)

No worries. :) Personally, I wouldn't waste time on questions that you got wrong because of a simple error or mistake made. Try and concentrate on the questions you got wrong because you didn't understand them.

Doing Further (or any 3/4 subject) in Year 11, is very useful. Obviously aim to get the highest mark you can, but just remember its a learning experience. Take from it things that you can improve on in Year 12. A 35 for me wasn't what I was expecting, but I saw no point in dreading over it. Instead, I thought about the positive side of it, and learnt better ways of approaching and studying for exams. :) Sorry, this paragraph is off-topic from your questions, but I thought I'd mention it. :)
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 13, 2013, 11:25:13 pm
For Methods, its not really a big thing to have a reference, because I never look at it. However, for Further you will probably need to look at it.

What three modules are you doing?
Geo/Trig, Number Patterns, Networks
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 13, 2013, 11:33:22 pm
Geo/Trig, Number Patterns, Networks

Okay. Similar to me, instead of Number Patterns, I did Matrices.

At this stage, I don't want to say that you should MAKE your own Notes Book. I would have recommended this to be done on the holidays.

What I would suggest, is to print off some Notes, may be your teacher's ones if they do Notes on Powerpoint or something, or may be get some from the AN Resources page. Read through them and make sure you know what's where. You don't want to go to the exam and waste time flicking through your your bound refernce to find something. Make sure that you have all the rules for Geo and Trig, such as the sine rule, cos rule, etc.

If you don't want to do that, then may be have a notes book with all the important rules, and CAS Functions, and also put in examples of questions that you get wrong and may be think that you would need to refer to an example when doing another similar question.

At the end of the day, it comes down to how confident you are feeling as well. For me, I couldn't go in without a Notes Book, knowing how much content was in Geo and Trig.

After doing some Practice Exams so far, have you had to look at your Notes to find something?
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 14, 2013, 12:13:11 am
Nope.. never had to look at my textbook. I know all the number patterns formulas and same with trig (unless there are more that I haven't encountered yet). With networks.. there aren't really any formulas its mainly just applying logic. Oh I know where everything is in the textbook.

I should be ok without a bound reference.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 14, 2013, 12:20:12 am
Nope.. never had to look at my textbook. I know all the number patterns formulas and same with trig (unless there are more that I haven't encountered yet). With networks.. there aren't really any formulas its mainly just applying logic. Oh I know where everything is in the textbook.

I should be ok without a bound reference.

Have you memorised the circle of data transformations for the core? I suggest take your textbook in just in case.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 14, 2013, 12:38:56 am
Yeah I can apply them all well. I'm definitely taking my textbook, of course, I'm just uncertain about bound references. I tried making one but it's really, really.. really..... untidy, I think I'd spend majority of the time looking for formulas than actually applying them, so I think I'll probably just stick to my textbook.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 14, 2013, 07:19:52 am
Okay then. If you're confident, then that's the main thing.

Taking in your textbook shouldn't be a problem.
Title: Re: VCE Further Maths Question Thread!
Post by: sam.utute on October 14, 2013, 08:32:53 am
Yeah I can apply them all well. I'm definitely taking my textbook, of course, I'm just uncertain about bound references. I tried making one but it's really, really.. really..... untidy, I think I'd spend majority of the time looking for formulas than actually applying them, so I think I'll probably just stick to my textbook.

My bound reference had a whole bunch of VCAA questions and solutions in it - I went through and saved all of the VCAA questions I got wrong and inserted them into my bound reference. When you've done about 100 practice exams, you'll realise that VCAA tends to ask questions in a similar format; and so having the difficult past VCAA questions in my reference was really reassuring.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 14, 2013, 06:38:06 pm
Thanks sam.utute

I'm on my iPad right now so this isn't going to work too well, but I'll try anyway. :)

So you have a pyramid of height 3m and this "smaller" pyramid of height 2m. That gives you a k value of 2/3. Cube that (for volume) and you'll get 8/27.

So 8/27 of the pyramid is not filled up with foam. That means that 19/27 of the pyramid has been filled with foam. (19/27)*100 = 70% to the nearest whole number.

Maybe you'll see this a bit better with a diagram too. I hope this helps, and I'm sorry that my help has been a bit limited.
My teacher said its 30%.. but I really don't think so, I (and another classmate) worked it out to be 70% too.
Title: Re: VCE Further Maths Question Thread!
Post by: Stick on October 14, 2013, 09:36:13 pm
^ I think your teacher has accidentally done how much has been unfilled, given that their answer is the exact opposite of our one.

Also, in regards to bound references, I'm sure you're going to need your bell curve at some point. I don't know of a single person yet who hasn't needed to consult this at some stage during the exams.
Title: Re: VCE Further Maths Question Thread!
Post by: Insa on October 15, 2013, 01:15:59 am
Hey guys,

Could anyone please help me? :D I am having trouble determining whether a graph is bipartite or not. For example in the question below. Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on October 15, 2013, 08:53:13 pm
Could someone please help with 2c? Is it the 8th or 7th year?
Help much appreciated~
Title: Re: VCE Further Maths Question Thread!
Post by: robo_1337 on October 15, 2013, 09:17:07 pm
I had during 1996, as the result for the start of 1997 was 22106.81
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 15, 2013, 10:28:08 pm
I had during 1996, as the result for the start of 1997 was 22106.81

Out of curiousity, is it actually acceptable to say that?
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 15, 2013, 11:12:17 pm
Its only a 1 marker, no explanation is required, just year 1997.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on October 18, 2013, 05:53:28 pm
Hi,
To express: "For every eight x, there at least ten y" as an inequality,
would it be:

8x >(or equal to) 10y  ?

i showed my teacher this, and she seems to think that it is 8x < (or equal to) 10y.

Thanks


Title: Re: VCE Further Maths Question Thread!
Post by: tum1106 on October 19, 2013, 06:35:23 pm
Hey guys I've got a question!

I want to know how do you guys go over your mistakes and make sure you don't make the same ones again? (Silly question I know). I've been doing a number of practice exams and I find that it's always bearings and contour maps (trig) are the areas that I need to work on. Do you guys a) keep doing more exams b) look at the textbook  c) do more questions from other resources e.g. Checkpoints, A+ notes and focus on those areas

I've been schooling for 13 years and I still don't know how to study properly....sigh  :(
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 19, 2013, 06:41:23 pm
Hey guys I've got a question!

I want to know how do you guys go over your mistakes and make sure you don't make the same ones again? (Silly question I know). I've been doing a number of practice exams and I find that it's always bearings and contour maps (trig) are the areas that I need to work on. Do you guys a) keep doing more exams b) look at the textbook  c) do more questions from other resources e.g. Checkpoints, A+ notes and focus on those areas

I've been schooling for 13 years and I still don't know how to study properly....sigh  :(

Well, I usually look at the solutions (after I've done the exam), and then check how to see the correct way of doing the question. I then repeat it straight away (Without looking at the solutions) and see whether or not I get it correct. If not, I keep repeating this process until its correct.

If you already know your exact weaknesses, then try do some more extra questions specific to just Bearings and Contour Maps. Ask your teacher for some extra worksheets/questions that cover these topics.
Title: Re: VCE Further Maths Question Thread!
Post by: #J.Procrastinator on October 19, 2013, 07:11:18 pm
Hey guys I've got a question!

I want to know how do you guys go over your mistakes and make sure you don't make the same ones again? (Silly question I know). I've been doing a number of practice exams and I find that it's always bearings and contour maps (trig) are the areas that I need to work on. Do you guys a) keep doing more exams b) look at the textbook  c) do more questions from other resources e.g. Checkpoints, A+ notes and focus on those areas

I've been schooling for 13 years and I still don't know how to study properly....sigh  :(

Don't worry, you're not alone! What I do, is try to redo the question again by consulting the textbook. If I can't seem to figure it out then I'll check out the solutions and learn from it.

If you struggle with bearings and contour maps then go back to your textbook and focus on those areas, specifically parts of contour maps or bearings that you struggle with. For example, how to calculate the average slope from A to D etc.. Look at the processes and don't skip any steps!

If it's still not absorbing in and you find that you're still making mistakes, cut those questions out and stick them into your further book with the correct solutions marked in red. This way, in the exam you can refer to these examples and make sure that you won't do the same mistakes again. :)
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on October 20, 2013, 12:53:47 pm
When the question does not specify to round to x decimal places, it is appropriate to just round to 4 decimal places?

And for exam 2 questions regarding a discrete amount (eg, people), are we meant to round up/down according to the closest value?

Take for example, 63.2 students = 63 students
                             63.6 students = 64 students
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 20, 2013, 01:00:02 pm
Can I get some clarification on this question?

I used 2 different methods and got different answers.

Question: A right angle triangular prism has a volume of 160cm^3. A second right angle triangular prism is made with the same width, twice the height and three times the length of the prism shown. Find the volume of the second prism.

Method 1:

0.5*h*w*l=160
hwl=320

new prism: 2h*w*3l=6hwl 
6*hwl=960cm^3     (which is the correct answer)

Method 2:

Original            New
let h=16           h=32
let w=10          w=10
let l = 2            l=6

Original volume=160

New volume = 32*10*6 = 1920cm^3

Why doesn't the 2nd method work?

Cheers
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 20, 2013, 01:08:04 pm
Can I get some clarification on this question?

I used 2 different methods and got different answers.

Question: A right angle triangular prism has a volume of 160cm^3. A second right angle triangular prism is made with the same width, twice the height and three times the length of the prism shown. Find the volume of the second prism.

Method 1:

0.5*h*w*l=160
hwl=320

new prism: 2h*w*3l=6hwl 
6*hwl=960cm^3     (which is the correct answer)

Method 2:

Original            New
let h=16           h=32
let w=10          w=10
let l = 2            l=6

Original volume=160

New volume = 32*10*6 = 1920cm^3

Why doesn't the 2nd method work?

Cheers
0.5 * 32 * 10 * 6 = 960cm^3
Title: Re: VCE Further Maths Question Thread!
Post by: RKTR on October 20, 2013, 01:12:33 pm
you also forgot the 0.5 in your method 1

hwl is 320

your new volume is 0.5 x 2h x w x 3l
                               3 x  hwl = 960 cm^3 

6hwl is 1920.. just pointing out..
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 20, 2013, 01:16:00 pm
Ah yes, silly me. Cheers.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on October 22, 2013, 11:24:57 pm
Hi,
To express: "For every eight x, there at least ten y" as an inequality,
would it be:

8x >(or equal to) 10y  ?

i showed my teacher this, and she seems to think that it is 8x < (or equal to) 10y.

Thanks



See Linear Graphs Question
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on October 26, 2013, 08:13:34 pm
how do you do Q4 of core for VCAA 2008 EXAM1
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008furmath1-w.pdf

i got D. because the IQR = 90-20= 70 and the median = 35. thus median is half of the IQR.

Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 26, 2013, 08:15:27 pm
how do you do Q4 of core for VCAA 2008 EXAM1
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008furmath1-w.pdf

i got D. because the IQR = 90-20= 70 and the median = 35. thus median is half of the IQR.

Yeah I got D as well; never quite understood why it couldn't have been a right answer..
Title: Re: VCE Further Maths Question Thread!
Post by: soNasty on October 26, 2013, 08:17:47 pm
hello can someone please help me with either of these questions on the 2011 neap trial exam thats posted online?
here's the link http://www.neap.com.au/pdf/errata/errataTEFMU34Ex1_QA_2011.pdf
question 4 and 5 in number patterns.
cheers!
Title: Re: VCE Further Maths Question Thread!
Post by: KevinooBz on October 26, 2013, 08:38:30 pm
Yeah I got D as well; never quite understood why it couldn't have been a right answer..
I'll demonstrate why that is wrong through an example. Take the numbers 1, 3, 4, 5, 7, 8, 10. Median is 5, Q1 is 3 and Q3 is 8. IQR=5 => IQR/2=2.5
2.5=/=5
Median=/=IQR/2
Furthermore, the median isn't the average of Q1 and Q3 e.g. in this case that would be 5.5 which clearly isn't the median. The median is the 50%ile value, but that does not necessarily mean that it's half the IQR or the average of Q1 and Q3. You can also look at skewed boxplots if you want to visualise this.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 26, 2013, 08:40:28 pm
I'll demonstrate why that is wrong through an example. Take the numbers 1, 3, 4, 5, 7, 8, 10. Median is 5, Q1 is 3 and Q3 is 8. IQR=5 => IQR/2=2.5
2.5=/=5
Median=/=IQR/2
Furthermore, the median isn't the average of Q1 and Q3 e.g. in this case that would be 5.5 which clearly isn't the median. The median is the 50%ile value, but that does not necessarily mean that it's half the IQR or the average of Q1 and Q3. You can also look at skewed boxplots if you want to visualise this.

Yeah I was thinking on the lines of skewing and how this affected it. I think because it's positively skewed, A would be a more appropriate answer.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 26, 2013, 09:54:41 pm
Yeah I got D as well; never quite understood why it couldn't have been a right answer..
The mean is affected by extreme values and therefore will be much higher than the median in this situation. There are 7 outliers which will all push the mean up, while the median would stay lower.

I guess D is feasible, but they want something conclusive. I don't think from a box plot we can conclude that it is exactly half of the interquartile range, it could be every so slightly off (35.5 seconds) and therefore D would be false. The scale makes it hard to see the specific times and also, time is a continous variable: the questions use "closest to" as it's impossible for us to determine an exact value, therefore we can find what's looks close to the IQR but it may not actually be.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 26, 2013, 09:57:49 pm
The mean is affected by extreme values and therefore will be much higher than the median in this situation. There are 7 outliers which will all push the mean up, while the median would stay lower.

I guess D is feasible, but they want something conclusive. I don't think from a box plot we can conclude that it is exactly half of the interquartile range, it could be every so slightly off (35.5 seconds) and therefore D would be false. The scale makes it hard to see the specific times and also, time is a continous variable: the questions use "closest to" as it's impossible for us to determine an exact value, therefore we can find what's looks close to the IQR but it may not actually be.

Yeah, fair enough. I guess going with the most conclusive answer all the time should do the trick.
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 27, 2013, 02:28:47 pm
Hi.
When both the cosine and sine rule are applicable, which rule should be favoured?
I was doing the vcaa 2012 exam 2 section for Geo/Trig, question 4d and the assessors report included the sine rule and got the answer 43.118 although the cosine rule can still be applied. Does it matter which one is used?
REPORT: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2012/fm2_assessrep12.pdf
EXAM: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2012/2012furmath2-w.pdf
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 27, 2013, 02:37:53 pm
It appears that the question required the application of BOTH the sin rule and cos rule..
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 27, 2013, 02:40:15 pm
It appears that the question required the application of BOTH the sin rule and cos rule..
Yeah. True. I didn't explain it properly, I mean the second part of the question to get the angle.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 27, 2013, 02:49:01 pm
I think you will still get the marks if your working out is correct
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on October 27, 2013, 05:10:08 pm
FOR THE CORE

Question states: IF the deaseasonalised number of ice creams sold in summer is 431, then the actual summer sales is closet to? the seasonal index for summer is 1.34

i got for this answer 578, answer is 532, why?
322
431
446
532
578
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on October 27, 2013, 05:26:02 pm
I dont see how it can be 532
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 27, 2013, 05:45:16 pm
578 is correct unless you got the seasonal index wrong
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on October 27, 2013, 10:54:26 pm
'Show that'

What's the difference between 'showing' in comparison to just calculating the answer as per usual with working out? How in depth do we have to 'show' how we received our answer?

Fankz guyz  :-*
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 27, 2013, 11:32:35 pm
The working out that led you to getting the answer.
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on October 28, 2013, 10:12:29 am
question 5 in business maths : http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf

how do you tell if its reducing balance depreciation or flat rate deprecation?
Spoiler
the way i interpreted the question was that the server depreciated by 20% of its original value each year.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 28, 2013, 03:54:59 pm
question 5 in business maths : http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf

how do you tell if its reducing balance depreciation or flat rate deprecation?
Spoiler
the way i interpreted the question was that the server depreciated by 20% of its original value each year.

I didn't do Business Maths as a Module in Further last year, but with my Accounting knowledge, I can explain that as each year progresses, the value decreases, right? So thats the reason why you calculate the Depreciation Expense for the CARRYING value of the File Server in each particular year, and NOT the ORIGINAL/HISTORICAL Cost of it.

So when it says "of its value", it means the Carrying Value of it after each year and you Depreciate it off the Carrying Value and not the Historical Cost.

Hope this helps a bit. :)
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on October 28, 2013, 04:49:53 pm
thanks bud
Title: Re: VCE Further Maths Question Thread!
Post by: hardworker on October 28, 2013, 08:42:11 pm
Hi does anyone know how to do the final network question n the 2012 vcaa exam 1 cause its doing my head in. Please help me, cause i feel like my heads gonna explode?
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 28, 2013, 08:51:50 pm
Hi does anyone know how to do the final network question n the 2012 vcaa exam 1 cause its doing my head in. Please help me, cause i feel like my heads gonna explode?

To achieve minimum number of days Lisa starts activity D after activity A is completed by John, then she does activity E. By the time activity E is completed, total number of days taken is 3+7+6=16

Then 16+5=21. Therefore D is correct. :)
Title: Re: VCE Further Maths Question Thread!
Post by: hardworker on October 28, 2013, 08:53:38 pm
To achieve minimum number of days Lisa starts activity D after activity A is completed by John, then she does activity E. By the time activity E is completed, total number of days taken is 3+7+6=16

Then 16+5=21. Therefore D is correct. :)


but what about ken why dont you add activity B?
Title: Re: VCE Further Maths Question Thread!
Post by: Green on October 29, 2013, 09:47:53 am
I dont understand question 2007 exam 1 linesr graphs  if maximum vlue of z occurs at thrle pploint (100,0)
Title: Re: VCE Further Maths Question Thread!
Post by: KevinooBz on October 29, 2013, 10:10:24 am
I dont understand question 2007 exam 1 linesr graphs  if maximum vlue of z occurs at thrle pploint (100,0)
if you sub that point into the objective function Z=200. Now you need to test for possible values of k where (100,0) gives the maximum Z value. If k=1, Z=2x + y. Subbing all the co ordinates in you get that Z is still the maximum at (100,0). When k=2, Z=2x + 2y. If you sub in (100,0) and (50,50) you get 200. You only want one maximum at (100,0) so k must be 1.
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on October 29, 2013, 11:07:32 am
Hey cuties,

Let's say I'm given quarterly seasonal indices for rainfall in mm of Summer, Autumn, Spring & Winter.
In terms of describing a seasonal index of ... for Summer, what would you guys use?

The rainfall in Summer is typically:

VCAA 2005 Ex1 q11: '% above the yearly average'
VCAA 2009 q4c: '% above the average for the four seasons of the year'

Most of the commercial papers I've done: '% above the seasonal average'
Essentials Textbook: '% higher than the quarterly average'

I'm a tad confused. Are they all the same/different? Anyone know/have evidence as to what VCAA expects?

Hope you understand the question.
Thanks A LOT!!! :)
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 29, 2013, 12:04:59 pm
Hey cuties,

Let's say I'm given quarterly seasonal indices for rainfall in mm of Summer, Autumn, Spring & Winter.
In terms of describing a seasonal index of ... for Summer, what would you guys use?

The rainfall in Summer is typically:

VCAA 2005 Ex1 q11: '% above the yearly average'
VCAA 2009 q4c: '% above the average for the four seasons of the year'

Most of the commercial papers I've done: '% above the seasonal average'
Essentials Textbook: '% higher than the quarterly average'

I'm a tad confused. Are they all the same/different? Anyone know/have evidence as to what VCAA expects?

Hope you understand the question.
Thanks A LOT!!! :)

For me, what I do is look at the context. For questions involving 4 seasons, I'll mention seasonal average. For questions Jan-Feb, I talk about the yearly average. Its really not a big deal, just make sure that you are clear about it though!

Hope this helped
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 29, 2013, 12:09:00 pm
For questions Jan-Feb, I talk about the yearly average.
Monthly average?
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 29, 2013, 12:14:27 pm
Monthly average?

Oops; probably the worst time to make a mistake. Yeah I meant monthly average haha. Thanks for that!

To avoid confusion, just go with seasonal average. Because irrespective of what you're dealing with, it'll be a season.

So for 1.5 for ice-cream sales in December:
Ice cream sales in December are 50% greater than the average seasonal ice-cream sales.
Title: Re: VCE Further Maths Question Thread!
Post by: aestheticatar on October 29, 2013, 01:26:05 pm
Thanks Yacoubb and Zealous! :) But then how come VCAA used 'yearly average' in 2005... Is that correct aswell?

Hi, Have a question about seasonal indices.


'Given that the seasonal indices for winter and autumn are 1.41 and 0.92 respectively, then it is reasonable to conclude that'

D) Autumn sales are 8% less than yearly average

E) Winter sales are approximately 35% of the yearly sales

I thought that D would have been the answer, although the solutions say that E is correct,

with explanation:
Winter sales =
(1.41/4)×100=35.25%

I thought it would've been D, as I have an explanation in my book that says if the seasonal index is 0.92, it indicates a performance of 8% below the average.

Thanks

And I've that question aswell, then I saw the VCAA papers so I was like, what? :(
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on October 29, 2013, 01:47:04 pm
Thanks Yacoubb and Zealous! :) But then how come VCAA used 'yearly average' in 2005... Is that correct aswell?

And I've that question aswell, then I saw the VCAA papers so I was like, what? :(

And there was one question with seasonal index 0.8, to correct for seasonality
(D) increase by 20%
(E) increase by 25%

Answer is E. How?!
Title: Re: VCE Further Maths Question Thread!
Post by: Patches on October 29, 2013, 01:56:49 pm
You need to add .20 to get to 1, so .2 is 25% of .8
Title: Re: VCE Further Maths Question Thread!
Post by: Green on October 29, 2013, 02:06:13 pm
when you smooth data for example exam 1 2006 question
use 2 point smoothing moving mean
 do you suppose take values each side of 2006 or do you take 2007 and 2008?

Title: Re: VCE Further Maths Question Thread!
Post by: Patches on October 29, 2013, 02:10:42 pm
For 2006, you'd get the mean of 2005 and 2006, and the mean of 2006 and 2007.
Then find the mean of those two means for the value for 2006.
Title: Re: VCE Further Maths Question Thread!
Post by: Green on October 29, 2013, 02:23:28 pm
say i was doong it for medium do i the same?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 29, 2013, 02:28:02 pm
And there was one question with seasonal index 0.8, to correct for seasonality
(D) increase by 20%
(E) increase by 25%

Answer is E. How?!
1/0.8 = 1.25 Therefore 25% increase.

There is a big difference between dividing by 0.8 and multiplying by 1.2.
Title: Re: VCE Further Maths Question Thread!
Post by: Green on October 29, 2013, 03:37:42 pm
Trouble smoothing median question 4 please explain?
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 29, 2013, 04:42:01 pm
Trouble smoothing median question 4 please explain?
Question 4 is about a time series plot.
Question 6 is about the median. What I did was:

Since it's about time period 5, you are going to want the mean from 4,5,6,7 which is 25 and 3,4,5,6 which is 19.5. To smooth them, 25+19.5 / 2 = 22.25 = C

You get the median from 2 values behind the time period and 1 value behind the time period.
Title: Re: VCE Further Maths Question Thread!
Post by: Green on October 29, 2013, 05:05:48 pm
thanks, but why do you use 2 behind and one above? since it is say median why do you.use mean smoothing?
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 29, 2013, 05:49:34 pm
thanks, but why do you use 2 behind and one above? since it is say median why do you.use mean smoothing?
I did it from 1 below and 2 below.
I used the median.
Median of 95,0,31,8 is 19.5
Median of 0,31,8,19 is 25
= 22.25
Title: Re: VCE Further Maths Question Thread!
Post by: sjayne on October 29, 2013, 09:20:57 pm
for the vcaa 2012 exam 2 how do you do question 1dii?
The answer divides 168 by 6 which equals 28 months and then uses the sum equation.
My question is, why is it 168/6? Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on October 29, 2013, 09:22:30 pm
As the common difference is -6, thus it can only reduce by 6 a certain amount of times until it reaches 0.
Title: Re: VCE Further Maths Question Thread!
Post by: sjayne on October 29, 2013, 09:28:46 pm
aaah that makes sense!! Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 29, 2013, 09:45:49 pm
Yeah, when you see after 18 months you should immediately think total. So its pretty much the total minus the 18 months and that's what has not been sold yet.
Title: Re: VCE Further Maths Question Thread!
Post by: duhherro on October 30, 2013, 07:51:19 pm


And for VCAA 2011 Ex 1 Networks,
Q7)
Is the question just asking how much can the person talk without actually interfering with the main job (critical path)?


could anyone explain to me the answer for networks on Q4 c of 2011 exam 2 vcaa? A bit question on what it wants me to do...



And for minimum monthly balances, lets say you have a bank statement over more than just one month, when you need to calculate the interest earned at each month, the smallest principal amount carries over into the next month right ? So you use that value twice again?


Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: nikeets on October 30, 2013, 07:57:21 pm
In networks, when there are loops, it equals 1 from say A to A (point A has the loop), not 2? There was confusion with this at school. Thanks!  8)
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 30, 2013, 09:55:40 pm
In networks, when there are loops, it equals 1 from say A to A (point A has the loop), not 2? There was confusion with this at school. Thanks!  8)
A loop in an adjacency matrix is recorded as 1!
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 30, 2013, 10:57:49 pm
In networks, when there are loops, it equals 1 from say A to A (point A has the loop), not 2? There was confusion with this at school. Thanks!  8)

A loop in an adjacency matrix is recorded as 1!

This.

The chief examiner published a note to all teachers last year, and our teachers made sure that we were made aware of this as well.

Loops count as 1 vertex in the matrix form. :)
Title: Re: VCE Further Maths Question Thread!
Post by: duhherro on October 31, 2013, 01:14:09 am
Also for 2012 Vcaa ex 1)

Module 4)
Q9) How would you know to pick between A or C?

And module 5)
Q9) Why can't you just do B E H? After B is done, then so can E be done, then H > finish? Because after B is done, that allows D to be completed then simply H can be done too?
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 31, 2013, 09:08:22 am
Does anyone know how to solve the median here? I know it's a tad embarrassing, but isn't it supposed to be 500 (6th point) + 450 (7th point)/2 =475? The answer says it's 440 with 430+450.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 31, 2013, 09:12:40 am
Also for 2012 Vcaa ex 1)

And module 5)
Q9) Why can't you just do B E H? After B is done, then so can E be done, then H > finish? Because after B is done, that allows D to be completed then simply H can be done too?


To achieve minimum number of days Lisa starts activity D after activity A is completed by John, then she does activity E. By the time activity E is completed, total number of days taken is 3+7+6=

Then 16+5=21. Therefore D is correct. 

Does anyone know how to solve the median here? I know it's a tad embarrassing, but isn't it supposed to be 500 (6th point) + 450 (7th point)/2 =475? The answer says it's 440 with 430+450.


Cort, you have to write out all the numbers in order from lowest to highest and then find the middle of the 6th and 7th values.
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on October 31, 2013, 09:22:38 am

To achieve minimum number of days Lisa starts activity D after activity A is completed by John, then she does activity E. By the time activity E is completed, total number of days taken is 3+7+6=

Then 16+5=21. Therefore D is correct.
 

Cort, you have to write out all the numbers in order from lowest to highest and then find the middle of the 6th and 7th values.

Just read that I had to find the median OF the dependent variables, bloody oath.

Cheers mate.
Title: Re: VCE Further Maths Question Thread!
Post by: fieldjus on October 31, 2013, 09:39:49 am
Hi guys just wondering, if I ace both further maths exams do I get a 50?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 31, 2013, 10:03:56 am
Also for 2012 Vcaa ex 1)

Module 4)
Q9) How would you know to pick between A or C?

Sorry, couldn't answer your question before as I was on my phone.

I didn't study Business Maths as a module, but I think its that last value on the x-axis (8) where Option A has a balance on the loan for a small amount, whereas in Option C, the balance is on 0 for 8 months. :)

Thats the only difference I can see.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 31, 2013, 10:08:16 am
Hi guys just wondering, if I ace both further maths exams do I get a 50?

Thanks

It depends on your SAC Scores and Ranking, as well as how well the rest of the state goes. If they smash the exams like you do, then its not always possible if they have a better rank in their cohort and better SAC Scores.

But you will never know until everyone sits the Exam. So just do the best you can, and your results will show it. :)
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 31, 2013, 10:09:48 am

Q9) How would you know to pick between A or C?
 

Option C shows the balance being completely payed of after the 8th month.
But this is not the case.

If you do not make a payment, the balance of the loan is going to stay higher than if you made the payment, and interest will be added on top of a higher value (and therefore more interest will be added). Even though a double payment has been made, there's still an extra bit of interest which has been added by the month in which no payment was made. So the loan will keep dropping but will not be fully paid out at the end of the 8 month period - therefore A.
Title: Re: VCE Further Maths Question Thread!
Post by: unfamila on October 31, 2013, 10:21:19 am
If there's a box plot with an outlier; and the question asks for the 5 point summary, do i include it as the max/min value or the end of the whisker?
 ;)
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 31, 2013, 10:22:23 am
If there's a box plot with an outlier; and the question asks for the 5 point summary, do i include it as the max/min value or the end of the whisker?
 ;)

Yep, even though it may be an outlier, it is still part of the data, and can definitely be a minimum or maximum (or in between, depending on how many outliers there are).
Title: Re: VCE Further Maths Question Thread!
Post by: unfamila on October 31, 2013, 10:56:54 am
Thankyou ;D
My exam coordinator said yesterday further starts at 9am. This is a mistake right? It starts at 3pm yeah?
Title: Re: VCE Further Maths Question Thread!
Post by: #J.Procrastinator on October 31, 2013, 11:16:00 am
Thankyou ;D
My exam coordinator said yesterday further starts at 9am. This is a mistake right? It starts at 3pm yeah?

Yep further starts at 3pm. I have my psychology exam at 9 am tomorrow. Best of luck for further tomorrow! :)
Title: Re: VCE Further Maths Question Thread!
Post by: duhherro on October 31, 2013, 12:00:08 pm
Thanks Damoz and Zealous, I'm still a bit confused on the network question with Lisa etc, how come she needs to do ABDH ? rather than just continue onwards with ADH then?
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on October 31, 2013, 12:19:19 pm
Hey,

for anyone who is doing networks,
is maximum reduction time -
- the maximum number of days an activity can be reduced by,
or the maximum number of days an activity can be reduced to ?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Patches on October 31, 2013, 12:35:08 pm
Depends on the question. Some will say x can be reduced by 3 hours, some others will say y can be reduced to 3 hours. It'll be pretty clear which applies, I would think.
Title: Re: VCE Further Maths Question Thread!
Post by: jimmy22 on October 31, 2013, 03:22:58 pm
Hi,
What is the main thing to look for when trying to see if a time series has cyclic trend?
thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Huntyy on October 31, 2013, 04:07:08 pm
Range divided by 6. You see, this method could only be applied if your data distribution was approximately symmetric with no extreme values (or outliers).

Just did this question myself and got it wrong. So the range is 16 from the histogram, if you divide that by 6 you get a standard deviation of 2.33 which would be rounded to option b (incorrect answer) rather than the correct answer, c. Also why do you divide the range by six, is it something to do with the number of columns? Which is 14 in total?

Please help, thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Patches on October 31, 2013, 04:19:19 pm
Dividing the range by four or six to find the standard deviation only works if it's completely symmetrical - definitely would not do it in the exam. Just put the values into your calculator and calculate it there.
Title: Re: VCE Further Maths Question Thread!
Post by: tae on October 31, 2013, 04:25:39 pm
For business maths.. struggling with reducing balance q's. :( From VCAA 2008.

Question 8
A loan of $300 000 is taken out to finance a new business venture.
The loan is to be repaid fully over twenty years with quarterly payments of $6727.80.
Interest is calculated quarterly on the reducing balance.
The annual interest rate for this loan is closest to:
A. 4.1%
B. 6.5%
C. 7.3%
D. 19.5%
E. 26.7%

Answer is B :\
Title: Re: VCE Further Maths Question Thread!
Post by: plato on October 31, 2013, 04:33:15 pm
For business maths.. struggling with reducing balance q's. :( From VCAA 2008.

Question 8
A loan of $300 000 is taken out to finance a new business venture.
The loan is to be repaid fully over twenty years with quarterly payments of $6727.80.
Interest is calculated quarterly on the reducing balance.
The annual interest rate for this loan is closest to:
A. 4.1%
B. 6.5%
C. 7.3%
D. 19.5%
E. 26.7%

Use your TVM with:

N = 80 (20 lots o 4 quarters)
I% = ?? (the interest rate you want to find)
PV = 300000 (positive as money comes to you)
PMT = -6727.80 (negative cos you have to pay it out)
FV = 0 (nothing left to pay after 20 years)
P/Y = 4 (number of payments per year)
C/Y = 4 (number of interest calculations per year)
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 31, 2013, 04:37:28 pm
Got a quick question =)

VCAA FM2011 Exam 1
Geometry and Trigonometry Q9
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath1-w.pdf Page 18

How can we be sure that triangles ABC and ABD are the similar triangles? or a better question: is there some way we can completely disprove the triangles ABC and BCD are similar (given we are given one angle and one side length)?
It does make sense that ABC and ABD would be similar, but when you look at BCD, with a bit of flipping etc. you can get a triangle that looks very similar to ABD, which sort of led me on the wrong track.
Title: Re: VCE Further Maths Question Thread!
Post by: serendipity21 on October 31, 2013, 04:42:42 pm
Can someone please help me with this question? Crashing questions are my weakness :(
Title: Re: VCE Further Maths Question Thread!
Post by: plato on October 31, 2013, 04:48:14 pm
Got a quick question =)

VCAA FM2011 Exam 1
Geometry and Trigonometry Q9
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath1-w.pdf Page 18

How can we be sure that triangles ABC and ABD are the similar triangles? or a better question: is there some way we can completely disprove the triangles ABC and BCD are similar (given we are given one angle and one side length)?
It does make sense that ABC and ABD would be similar, but when you look at BCD, with a bit of flipping etc. you can get a triangle that looks very similar to ABD, which sort of led me on the wrong track.


Angle ABD = angle ACB = theta
The angle at A is common to triangles ABC and ABD
ie angle ABD = angle ABC
Now that the two triangles ABC and ABD have two angles in common, it must mean that the third angle is also the same for each triangle.
ie angle ADB = angle ABC

With three angles in common, these triangles must then be similar.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 31, 2013, 05:01:27 pm
Angle ABD = angle ACB = theta
The angle at A is common to triangles ABC and ABD
ie angle ABD = angle ABC
Now that the two triangles ABC and ABD have two angles in common, it must mean that the third angle is also the same for each triangle.
ie angle ADB = angle ABC

With three angles in common, these triangles must then be similar.
Awesome! thanks plato.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on October 31, 2013, 05:26:12 pm
Can someone please help me with this question? Crashing questions are my weakness :(

There are five paths.
BGIJ - 17
BDFJ - 18
BDCEHJ - 19
AFJ - 14
ACEHJ - 15

You could assume you cannot reduce J to zero but, if you could, it means every one of these paths is reduced by one and the critical path would be 18 long.

You need to reduce an activity on the critical path, BDCEHJ.
You can only reduce one of C, E or H by one hour, otherwise you make BDFJ become a critical path of 18 which means only a one hour reduction.

D cannot be reduced below zero and so you must reduce B which will also reduce paths BGIJ, BDFJ and BDCEHJ. But you cannot reduce these paths to be less than 15 which, if you did, is where ACEHJ would become the single, new critical path (and also activity B would disappear with zero time).

So – reducing B (and the project) by four hours will make two critical paths, ACEHJ and BDCEHJ, both 15 hours long. This is a four hour reduction and the answer is D.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on October 31, 2013, 06:40:33 pm
Hey everybody, could i please get help with this exam

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

Q2) Graphs and relations about Mike's Hike, i dont understand the whole question

Thank you.
Title: Re: VCE Further Maths Question Thread!
Post by: serendipity21 on October 31, 2013, 06:57:34 pm
There are five paths.
BGIJ - 17
BDFJ - 18
BDCEHJ - 19
AFJ - 14
ACEHJ - 15

You could assume you cannot reduce J to zero but, if you could, it means every one of these paths is reduced by one and the critical path would be 18 long.

You need to reduce an activity on the critical path, BDCEHJ.
You can only reduce one of C, E or H by one hour, otherwise you make BDFJ become a critical path of 18 which means only a one hour reduction.

D cannot be reduced below zero and so you must reduce B which will also reduce paths BGIJ, BDFJ and BDCEHJ. But you cannot reduce these paths to be less than 15 which, if you did, is where ACEHJ would become the single, new critical path (and also activity B would disappear with zero time).

So – reducing B (and the project) by four hours will make two critical paths, ACEHJ and BDCEHJ, both 15 hours long. This is a four hour reduction and the answer is D.

Plato you are amazing! Explained it better than my teacher!

Thank you so much! :D
Title: Re: VCE Further Maths Question Thread!
Post by: serendipity21 on October 31, 2013, 08:26:56 pm
Hey everybody, could i please get help with this exam

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

Q2) Graphs and relations about Mike's Hike, i dont understand the whole question

Thank you.

Hey everybody, could i please get help with this exam

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

Q2) Graphs and relations about Mike's Hike, i dont understand the whole question

Thank you.

Hi tcstudent!
The graph is showing the distance Mike travels. During the hours where the graph is in a slope he's travelling at a constant speed, and where the graph is just a horizontal line he is stationary (as his distance is not changing.

a) Average speed is given by the total distance he travels/total time taken.
He travels 16km in 7 hours so, 16/7=2.3 km/h

b) The equation with the variables they want you to find is the equation of the second slope (between 3 to 7 hours).
You can use simultaneous equations to solve this.
The variables from the graph are t (for the x axis) and d for the y axis, (as the equation is in the form y=mx+c). So pick two points on the line, say (5,13) and (3,10) and sub them in to the equation. (Pick clear points so you don't have to estimate).
The two equations I got from these points are:
13=a5+b  and 10=a3+b. Plug them in to your CAS and you get a=3/2 and b=11/2 which in decimals are 1.5 and 5.5.

c) I made a mistake with this one first time I did it.
Sketching the line for the distance traveled by Katie first is a good thing to do. This also helps with the next question!
The line intersects Michael's line at t=2. Therefore they meet at 2 hours.
However just to be super careful incase it's not like 2.1 or something, double check in the exam if you have time!
Use the equation for the first slope in Michael travels (d=5t, get the five from the rise/run of the line) and make it equal the the equation for Katies distance travelled.
Plug in 5t=-3t+16 into the cas to get t=2 hrs.

d) As you can see from the lines on the graph, the distance between Michael and Katie becomes 3km somewhere between 1-2 hours until they finally meet at 2.
So since the distance is the y value here, makes Katies distance-Michael's=3 to find t when their distance apart is 3
-3t+16-5t=3
solve on CAS, t=1.625
After two when they're moving away from each other, you can see just from the graph that at t=3, Katie is at 7km and Michael is at 10km from his destination, difference of 3km.
So they are only 3km near each other from t=1.625 and t=3
3-1.625=1.38 km

Hope that helps! :)
Title: Re: VCE Further Maths Question Thread!
Post by: Colokid on October 31, 2013, 09:02:19 pm
help with this question please  :)
Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on October 31, 2013, 09:21:47 pm
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf
Networks, Q6
How is the cut 23? I thought 5 was going in the opposite direction.
Title: Re: VCE Further Maths Question Thread!
Post by: Damoz.G on October 31, 2013, 09:26:58 pm
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf
Networks, Q6
How is the cut 23? I thought 5 was going in the opposite direction.

Gotta be careful with that Question, because you have to look at the previous bit before it on the 6. The "6" has to go somewhere, so it has to go down the 5 and then move towards the right hand side. However, with the 8, the previous 11 can go through either the 5 or 2 so there are other alternatives as opposed to the 8.

Therefore, you omit the 8, but include the 5. Does that help?
Title: Re: VCE Further Maths Question Thread!
Post by: jpf299 on October 31, 2013, 09:46:31 pm
need help for core
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf

Q7 and 8 please :)
Title: Re: VCE Further Maths Question Thread!
Post by: pumpkinbread on October 31, 2013, 09:49:37 pm
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf

Number patterns, question 8.

How is it A? I thought if r>1 the graph should be positive?

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: serendipity21 on October 31, 2013, 09:55:00 pm
need help for core
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf

Q7 and 8 please :)

need help for core
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf

Q7 and 8 please :)

Question 7:
We can see that the relationship between the variables is positive-immediately cancelling out options D and E.
The dots are close to one another and in a completely straight line, so it cannot be A as a 0.98 shows a strong relationship.
0.23 is no relationship, but there is some sort of relationship between the variables, the dots aren't totally random in their placement! So that leaves us with B :)

Question 8:
Cancel E straight away as foot length is the x variable, not the y.
Pick 2 clear points that are on the line. For eg. (30,180) and (34,185) and get the gradient of the line using rise/run method ie y2-y1/x2-x1.

Get the c value (cause the line will be in the form y=mx+c) by subbing in another point say (28,177)
Title: Re: VCE Further Maths Question Thread!
Post by: jpf299 on October 31, 2013, 10:00:49 pm
Question 7:
We can see that the relationship between the variables is positive-immediately cancelling out options D and E.
The dots are close to one another and in a completely straight line, so it cannot be A as a 0.98 shows a strong relationship.
0.23 is no relationship, but there is some sort of relationship between the variables, the dots aren't totally random in their placement! So that leaves us with B :)

Question 8:
Cancel E straight away as foot length is the x variable, not the y.
Pick 2 clear points that are on the line. For eg. (30,180) and (34,185) and get the gradient of the line using rise/run method ie y2-y1/x2-x1.

Get the c value (cause the line will be in the form y=mx+c) by subbing in another point say (28,177)


thank you so much! i always overthink the question
Title: Re: VCE Further Maths Question Thread!
Post by: plato on October 31, 2013, 10:01:37 pm
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath1-w.pdf

Number patterns, question 8.

How is it A? I thought if r>1 the graph should be positive?

Thanks :)

If the first term is a negative and it is multiplied by a positive number greater than 1, the result is a greater negative. Therefor the graph must decrease as n increases.

Maybe you are you confusing r (common ratio) with r (correlation coefficient).
Title: Re: VCE Further Maths Question Thread!
Post by: pumpkinbread on October 31, 2013, 10:28:11 pm
If the first term is a negative and it is multiplied by a positive number greater than 1, the result is a greater negative. Therefor the graph must decrease as n increases.

Maybe you are you confusing r (common ratio) with r (correlation coefficient).

Oh man yeah I was. Thanks so much :)
Title: Re: VCE Further Maths Question Thread!
Post by: duhherro on October 31, 2013, 10:43:28 pm
Argh , still confused on Q9 of 2012 Ex 1 Networks.

Title: Re: VCE Further Maths Question Thread!
Post by: lala1911 on November 01, 2013, 12:19:20 am
There are five paths.
BGIJ - 17
BDFJ - 18
BDCEHJ - 19
AFJ - 14
ACEHJ - 15

You could assume you cannot reduce J to zero but, if you could, it means every one of these paths is reduced by one and the critical path would be 18 long.

You need to reduce an activity on the critical path, BDCEHJ.
You can only reduce one of C, E or H by one hour, otherwise you make BDFJ become a critical path of 18 which means only a one hour reduction.

D cannot be reduced below zero and so you must reduce B which will also reduce paths BGIJ, BDFJ and BDCEHJ. But you cannot reduce these paths to be less than 15 which, if you did, is where ACEHJ would become the single, new critical path (and also activity B would disappear with zero time).

So – reducing B (and the project) by four hours will make two critical paths, ACEHJ and BDCEHJ, both 15 hours long. This is a four hour reduction and the answer is D.
Such a great explanation. Thank you.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 01, 2013, 09:41:00 am
Argh , still confused on Q9 of 2012 Ex 1 Networks.


Time  Activity   Person
0-3         A      John
3-10       D      Lisa can start D when A finishes.

0-6         B      Ken can start B at 0.
                      He cannot start C until he finishes B at 6
                      Lisa cannot start E until she finishes D at 10

6-10      C      Ken has finished B and can start C at 6

10-16    E      Lisa has finished D and can start E at 10

10 -15   F      John can start F when Ken finishes C at 10

G can be done by anyone available when C finishes at 10. Lisa is busy with D and John is busy with F. So Ken can do G finishing at 17.

H can be done by anybody available when all of D, E and F have finished. Of these three, the last to finish is E at 16 and John or Lisa are available. Then H can finish at 21.

So, earliest finish of the entire project is 21 (D)
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on November 02, 2013, 10:31:16 am
hey can someone tell me when to use each sort of graphical display, such as stemplots, boxplots etc.
Title: Re: VCE Further Maths Question Thread!
Post by: ricebubbles123 on November 02, 2013, 01:21:24 pm
is this statement correct? If a graph can be rearranged to be planar, it is planar?

Thanks for the help
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on November 02, 2013, 02:00:31 pm
is this statement correct? If a graph can be rearranged to be planar, it is planar?

Thanks for the help

yeeeeeeah.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on November 02, 2013, 02:12:55 pm
i dont understand how this question is 4 hours, i got it wrong when i did it in timed  conditions, then i went and did it after i finished and got 5, i took the maximum time which is 19, minus by the minimum which is 14 = 5''

(http://i41.tinypic.com/2njvzug.jpg)

heres pic, apparently its D-4 hours
Title: Re: VCE Further Maths Question Thread!
Post by: Patches on November 02, 2013, 04:26:49 pm
You can't reduce the duration of an activity to 0, only to one hour/day/whatever - I think that's your problem.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 02, 2013, 04:32:04 pm
i dont understand how this question is 4 hours, i got it wrong when i did it in timed  conditions, then i went and did it after i finished and got 5, i took the maximum time which is 19, minus by the minimum which is 14 = 5''

(http://i41.tinypic.com/2njvzug.jpg)

heres pic, apparently its D-4 hours

See  the following  Further Question Thread!

***EDIT - Corrected the URL
Title: Re: VCE Further Maths Question Thread!
Post by: Green on November 02, 2013, 06:55:45 pm
how do you suppose solve part c and part d on calculator 2006 vcaa exam 2 squence and series question 3 please
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 02, 2013, 08:47:25 pm
The easiest way to solve these is with the Sequence function on the calculator.

***EDIT - For question d, solve the equation where S(n+1) = S(n)
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on November 03, 2013, 11:41:12 am
If we are given a sequence, tn= -3n+44, and the first term is not given.
Would 44 be the first term or 41?
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 03, 2013, 12:04:02 pm
There is obviously room for ambiguity here. In a sequence that does not refer to t(n+1) or t(n-1), then assume n will start at one rather than zero.
Your first term would be t(1) = a = 41
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on November 03, 2013, 12:22:28 pm
There is obviously room for ambiguity here. In a sequence that does not refer to t(n+1) or t(n-1), then assume n will start at one rather than zero.
Your first term would be t(1) = a = 41

Yeah thanks, i think the initial term would be 44.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 03, 2013, 01:24:23 pm
If tn=-3n+44 and the first term = t1=a, then

   t1=-3x1 + 44 = 41

And, since a = 41 and also tn = a +(n-1)d, then
  -3n+44 = 41 + (n-1)d
  -3n + 3 = (n-1)d
  (n - 1) x -3 = (n-1)d   and so d = -3

The sequence described by tn=-3n+44 is an arithmetic sequence where a = 41 and d = -3
Title: Re: VCE Further Maths Question Thread!
Post by: itsalmostover on November 03, 2013, 02:15:39 pm
If we are told to find the proportion of x after n days, and we end up with a matrix such as:
   _               _
  |   590.18...  |
  |   410.43...  |
  |_ 499.39..._|

Say we started off with 1500 in total at the beginning, rounding to the nearest whole number would only give 590+410+499=1499.

In this case, should we round up the value with the highest decimal so that 410 becomes 411, and we once again have a total of 1500?

Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on November 03, 2013, 02:26:12 pm
If we are told to find the proportion of x after n days, and we end up with a matrix such as:
   _               _
  |   590.18...  |
  |   410.43...  |
  |_ 499.39..._|

Say we started off with 1500 in total at the beginning, rounding to the nearest whole number would only give 590+410+499=1499.

In this case, should we round up the value with the highest decimal so that 410 becomes 411, and we once again have a total of 1500?

Because this is a closed system matrix problem, you must ALWAYS have 1500. Thus, you can choose to round up any of the elements (I'd go with the one closest to being rounded up (e.g. 410.43 over 499.39 because .43 is closer to .5 than .39 is). But, on the exam, its highly unlikely that there will be something like this (or so I've heard from Further Maths lectures I've attended).
Title: Re: VCE Further Maths Question Thread!
Post by: duhherro on November 03, 2013, 03:48:13 pm
when asked to draw a regression line, do you need to only draw at where the points start and end of the original data ? Or are you meant to extend it so it hits the Y-axis and goes further  than the most furthest x-value on the plot?

And If anyone has MAV 2012 exam 2, how do you get Q3)a) of core? I just did a statistics table and used the given linear regression to get my y-values then i just applied reciprocal on those y-values and then sketched the new regression. Or am I meant to simply look at the given graph and its data and just insert in calc with plain eye?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on November 03, 2013, 04:10:15 pm
And If anyone has MAV 2012 exam 2, how do you get Q3)a) of core? I just did a statistics table and used the given linear regression to get my y-values then i just applied reciprocal on those y-values and then sketched the new regression. Or am I meant to simply look at the given graph and its data and just insert in calc with plain eye?
The data was given in Question 2. So take all the BMI values and find the reciprocal of each one, then fit a linear regression line to the sleep time and 1/BMI.

when asked to draw a regression line, do you need to only draw at where the points start and end of the original data ? Or are you meant to extend it so it hits the Y-axis and goes further  than the most furthest x-value on the plot?
Plot it like you're drawing a linear line. So you can extend (extrapolate) the line past the data given.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on November 03, 2013, 04:17:10 pm
Hi tcstudent!
The graph is showing the distance Mike travels. During the hours where the graph is in a slope he's travelling at a constant speed, and where the graph is just a horizontal line he is stationary (as his distance is not changing.

a) Average speed is given by the total distance he travels/total time taken.
He travels 16km in 7 hours so, 16/7=2.3 km/h

b) The equation with the variables they want you to find is the equation of the second slope (between 3 to 7 hours).
You can use simultaneous equations to solve this.
The variables from the graph are t (for the x axis) and d for the y axis, (as the equation is in the form y=mx+c). So pick two points on the line, say (5,13) and (3,10) and sub them in to the equation. (Pick clear points so you don't have to estimate).
The two equations I got from these points are:
13=a5+b  and 10=a3+b. Plug them in to your CAS and you get a=3/2 and b=11/2 which in decimals are 1.5 and 5.5.

c) I made a mistake with this one first time I did it.
Sketching the line for the distance traveled by Katie first is a good thing to do. This also helps with the next question!
The line intersects Michael's line at t=2. Therefore they meet at 2 hours.
However just to be super careful incase it's not like 2.1 or something, double check in the exam if you have time!
Use the equation for the first slope in Michael travels (d=5t, get the five from the rise/run of the line) and make it equal the the equation for Katies distance travelled.
Plug in 5t=-3t+16 into the cas to get t=2 hrs.

d) As you can see from the lines on the graph, the distance between Michael and Katie becomes 3km somewhere between 1-2 hours until they finally meet at 2.
So since the distance is the y value here, makes Katies distance-Michael's=3 to find t when their distance apart is 3
-3t+16-5t=3
solve on CAS, t=1.625
After two when they're moving away from each other, you can see just from the graph that at t=3, Katie is at 7km and Michael is at 10km from his destination, difference of 3km.
So they are only 3km near each other from t=1.625 and t=3
3-1.625=1.38 km

Hope that helps! :)


thank you, however i still don't understand question D about the radio transmitters to talk to each other.
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on November 03, 2013, 04:26:09 pm
Hey guys 2012 Exam 2 , Question 2B about some stupid weather LOl here is the question

(http://i43.tinypic.com/242bv39.jpg)

Question B

Title: Re: VCE Further Maths Question Thread!
Post by: duhherro on November 03, 2013, 04:31:12 pm
The data was given in Question 2. So take all the BMI values and find the reciprocal of each one, then fit a linear regression line to the sleep time and 1/BMI.
Plot it like you're drawing a linear line. So you can extend (extrapolate) the line past the data given.


Thanks! And there will always be a range of answers given due to reading variables right?
Title: Re: VCE Further Maths Question Thread!
Post by: Cort on November 03, 2013, 04:36:06 pm
Hey guys 2012 Exam 2 , Question 2B about some stupid weather LOl here is the question

(http://i43.tinypic.com/242bv39.jpg)

Question B

Hope it wasn't too confusing. I didn't even understand the question at all the first time I did it.
Title: Re: VCE Further Maths Question Thread!
Post by: lolipopper on November 03, 2013, 05:05:05 pm
Business Maths question:

Question 7:
Greta and Sean have taken out a reducing balance loan of $340 000 at a fixed interest rate of 9% per annum calculated monthly. They make monthly repayments of $P so that in 5 years time they will owe just $80 000 on their loan.
The value of P is

A.   7 057.84
B.   8 118.51
C.   10 382.01
D.   11 024.84
E.   36 129.62

Suggested Answer:
Using TVM solver we have
N=60
I%=9
PV=340,000
PMT=?
FV=80,000
P/Y=12
C/Y=12
Their monthly payment is $8 118.51 therefore B.

My concern: should not the FV (amount owing) be -80,000 when put into TVM? Im getting $5996.17
Title: Re: VCE Further Maths Question Thread!
Post by: tcstudent on November 03, 2013, 05:52:20 pm
Hope it wasn't too confusing. I didn't even understand the question at all the first time I did it.

yea man for me very confusion, it must be due to me being overwhelmed by exams.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on November 03, 2013, 08:38:55 pm
Hey guys 2012 Exam 2 , Question 2B about some stupid weather LOl here is the question

(http://i43.tinypic.com/242bv39.jpg)

Question B

The first thing you're told is that there are 8 wind speeds.

We know that Q1 = min (in this case) =2
We know that Q3 = max(in this case) = 4

So, you get:

2, __, __, __, __, __, __, 4.

Then, we're told the median is 3.5. Because we have 8 values, the position of the median will be the 4.5th. That is, the average of the 4th and 5th value should equal the median, which in this case is 3.5. So, if 3+4/2 = 3.5, we can fairy say that term 4= 3 and term 5=4.

So:

2, __, __, 3, 4, ___, __, 4.

Now, you know that your Q1 = 2.
So, your (2nd + 3rd term)/2 = 2.
Thus, 2+2/2 = 2. So terms 2 and 3 are 2.

So:

2, 2, 2, 3, 4, __, __, 4.

Now, Q3 is 4.
4+4/2 = 4. Hence, terms 6 and 7 are 4.

Your answer:

2, 2, 2, 3, 4, 4, 4, 4.

^ Hope this helped.

:) To check, I'd put those data entries into my calculator & construct a boxplot, from which I'd then check to see whether I was right or wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: duhherro on November 03, 2013, 08:58:37 pm
Btw guys for Business maths Q3)c)ii) on exam 2 of 2012... is it a perpetuity question? I just treated it continuing the previous question, so there would be 4 years left to pay it all up .
Title: Re: VCE Further Maths Question Thread!
Post by: Daenerys Targaryen on February 09, 2014, 09:28:07 am
You get your regression line by what ever means, and use that equation. Then sub in 370, then 201 and so on. And you just solve for the rate - which is rate i assume
Title: Re: VCE Further Maths Question Thread!
Post by: popoy111 on February 22, 2014, 05:43:04 pm
I am currently doing business related maths. I own both textbooks of MAths quest and essentials but i find maths quest to be way to long. Just want to know which one you think addresses business related mathematics better?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on February 22, 2014, 10:56:59 pm
I am currently doing business related maths. I own both textbooks of MAths quest and essentials but i find maths quest to be way to long. Just want to know which one you think addresses business related mathematics better?
Isn't Business Maths in Maths Quest like ... 2 chapters? I don't think it is extremely long, just plan out how much you want to do when, and you should get it done.

If your school uses Maths Quest for a textbook, it might be worth sticking to it as your teachers might be more accustomed to using that textbook if you end up requiring assistance. Also, Maths Quest seems to be better for the theory and concept stuff, while Essentials may provide harder questions.
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on February 23, 2014, 07:06:07 pm
Hi guys, when a question asks to plot the values, do you just put the points on the graph or do you drew a line through them?
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on February 23, 2014, 07:15:17 pm
Hi guys, when a question asks to plot the values, do you just put the points on the graph or do you drew a line through them?

For a scatter plot, you only put the values on the graph. You fit a regression line on the graph when they ask you to "fit a regression line on the graph".
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on February 23, 2014, 07:17:23 pm
For a scatter plot, you only put the values on the graph. You fit a regression line on the graph when they ask you to "fit a regression line on the graph".

Thanks but I meant for Module 3, Graphs and Relations!
Title: Re: VCE Further Maths Question Thread!
Post by: spectroscopy on February 27, 2014, 11:10:20 pm
Is there a way to find out when a matrix becomes a steady state??
as S1=TSo and S3=t^3 So    and thus Sn=T^n So
is there a way to find out at what value of n the steady state appears?
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on February 28, 2014, 06:19:17 pm
why is the answer C? i square rooted the answer and it doesn't work because then you need imaginary numbers, so i took the square root and i got E
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on February 28, 2014, 07:01:38 pm
Is there a way to find out when a matrix becomes a steady state??
as S1=TSo and S3=t^3 So    and thus Sn=T^n So
is there a way to find out at what value of n the steady state appears?

For this we use the "trial and error method"
You have to show that two-three consecutive values of n yield a steady result, then the ans will be the initial value of n.

^Using my phone, so cant show a proper example. Hope it helps
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on February 28, 2014, 07:28:34 pm
why is the answer C? i square rooted the answer and it doesn't work because then you need imaginary numbers, so i took the square root and i got E

The coefficient of determination is r^2. You are given r, so square it (find r^2) and pick the option that matches.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on February 28, 2014, 09:21:10 pm
@Stick, dude im retarted. I didnt even read the question right haha that it asked for r^2, read it as it asked for, r, wow haha. Thanks for clarifying ahhahah! This is embarrassing
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on March 03, 2014, 08:38:46 pm
Hi guys, VCAA 2007 q2 graphs and relations, shouldn't the graph have an open circle at s=0?
Title: Re: VCE Further Maths Question Thread!
Post by: Professor Polonsky on March 03, 2014, 09:27:16 pm
Technically yes, but it seems like they marked both as correct (probably so to not trip so many people up with it).
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on March 04, 2014, 08:27:05 am
Hey, for 2008 VCAA q3, graphs and relations when they say between 80 and 150, does that mean inclusive of 80/150. I think it should work if 80 and 150 were included but the word "between" seems to imply otherwise.
Title: Re: VCE Further Maths Question Thread!
Post by: PsychoT on March 04, 2014, 07:57:47 pm
What does it mean by a "unique solution" in Matricies? Only thing stumping me for my SAC tomorrow.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on March 04, 2014, 08:40:09 pm
All the questions recently have been about modules I didn't do.. sigh o.o
Title: Re: VCE Further Maths Question Thread!
Post by: PsychoT on March 04, 2014, 09:05:21 pm
All the questions recently have been about modules I didn't do.. sigh o.o

What modules did you do?
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on March 05, 2014, 06:45:04 pm
can someone help me on this one, i have entered them in list 1 and 2 respectively and done lin reg, but my equation is different to that of the back of book. Can someone outline the steps
Title: Re: VCE Further Maths Question Thread!
Post by: byCrypt on March 05, 2014, 10:40:20 pm
can someone help me on this one, i have entered them in list 1 and 2 respectively and done lin reg, but my equation is different to that of the back of book. Can someone outline the steps

x is the independent variable and y is the dependent. After entering the 2 lists, then make sure you put x on the x-axis and y on the y-axis. I got D. y=7.5+0.5x
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on March 06, 2014, 07:49:24 am
thats exactly what i did, exept putting x on x-axis and y  on the y. I'm not sure how to do that, is it already set that way? I have casioclasspad 330
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on March 06, 2014, 09:34:12 am
thats exactly what i did, exept putting x on x-axis and y  on the y. I'm not sure how to do that, is it already set that way? I have casioclasspad 330
I don't know how to use the classpad, but I found these instructions in the textbook on how to calculate the regression line using the casio  classpad. I added in that question because the instruction relate to it, use this as somewhat of a template for answering your question :)

Title: Re: VCE Further Maths Question Thread!
Post by: Anchy on March 11, 2014, 07:07:16 pm
Hey, I've attached a question below and was wondering why the answer is E (1588)

Thanks. :)
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on March 11, 2014, 10:18:53 pm
Hey, I've attached a question below and was wondering why the answer is E (1588)

Thanks. :)
The seasonal index for Quarter 3 is actually 1.6 
4-(0.65+1.1+0.65) = 1.6
Now you just divide the sales value by the SI ---> 2540/1.6 = 1587.5 = 1588 :)

arrggg those silly mistakes right!  >:(
Title: Re: VCE Further Maths Question Thread!
Post by: Anchy on March 11, 2014, 11:13:45 pm
The seasonal index for Quarter 3 is actually 1.6 
4-(0.65+1.1+0.65) = 1.6
Now you just divide the sales value by the SI ---> 2540/1.6 = 1587.5 = 1588 :)

arrggg those silly mistakes right!  >:(

Haha yeah, frustrating! Thanks for that.

I've got another question.

Average no. of children per family in Denmark = 1.4
Standard deviation for the number of children per family in Denmark = 0.3

Assuming the data is normally distributed, what percentage have less than two children?

I've got my answer as 97.5%, however the answer says its 98.5%. Is that a typo or am i looking at it wrong?


Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on March 11, 2014, 11:24:24 pm
Haha yeah, frustrating! Thanks for that.

I've got another question.

Average no. of children per family in Denmark = 1.4
Standard deviation per family in Denmark is 0.3

Assuming the data is normally distributed, what percentage have less than two children?

I've got my answer as 97.5%, however the answer says its 98.5%. Is that a typo or am i looking at it wrong?

I got 97.5% as well, pretty sure that's a typo, even if the SD was moved one more to the right, it would not equal 98.5%, but hey the 7 and 8 are pretty close to each other on the keyboard :P
I'd say you are doing it right.
Title: Re: VCE Further Maths Question Thread!
Post by: Fusuy on March 12, 2014, 05:51:41 pm
Hey Guys; I have my first SAC next week Monday on Univariate and Bivariate Data (Half of the Core), just wondering if anyone has resources like practice SACs or Tests i could work through for preparation. Thank  :D
Title: Re: VCE Further Maths Question Thread!
Post by: Anchy on March 12, 2014, 06:58:35 pm
What's the difference between a seasonal trend and a cyclic trend? :|
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on March 12, 2014, 11:25:01 pm
What's the difference between a seasonal trend and a cyclic trend? :|

Well the essential difference is that a seasonal trend, as the name implies, display a specific pattern periodically (regular, predictable intervals). e.g ice-cream sales shoot up during summer.
But for Cyclic trends, the timing/patterns are a lot less predicable but you can see a pattern. e.g for the share price of Samsung phones, there will be a peak right when Samsung releases a new product but then it will slowly decrease.
So:
Seasonal --> pattern is regular and predicable (i.e showing the same pattern periodically)
Cyclic --> pattern is less predictable (i.e shows the same or similar pattern but not at the same moment every time, a peak may show up in march one year but august the next)

Hope that helped you somewhat :)
Title: Re: VCE Further Maths Question Thread!
Post by: 2014year12 on March 16, 2014, 01:04:16 pm
Can someone help me out with this question I'm a little confused....
Thanks in advance!
Title: Re: VCE Further Maths Question Thread!
Post by: The Brightest Witch on March 16, 2014, 02:02:45 pm
Can someone help me out with this question I'm a little confused....
Thanks in advance!

I keep getting $3, is that what's happening to you?
Title: Re: VCE Further Maths Question Thread!
Post by: 2014year12 on March 16, 2014, 02:15:45 pm
I keep getting $3, is that what's happening to you?
I have no clue how to do it to be honest haha! How do you go about it?
The answer is D ($2.75) though if that helps? That is the closest to $3 I guess?
Title: Re: VCE Further Maths Question Thread!
Post by: The Brightest Witch on March 16, 2014, 02:20:24 pm
I have no clue how to do it to be honest haha! How do you go about it?
The answer is D ($2.75) though if that helps? That is the closest to $3 I guess?

Ok so first I used the points (100,170) and (0,20) to get the gradient which was 1.5, and I'm pretty sure the y-intercept is 20, so my equation was C=1.5n+20.

So I subbed in 80 for n to get the cost of making of 80 apple pies, which was $140.

Then since they made a profit of $100, they would have to have sold those pies for $100 more than what it cost to make them, so they sold them for $240.

Then I divided $240 by 80 to get $3 per pie, and it looks nothing like any of the answers D:
Title: Re: VCE Further Maths Question Thread!
Post by: 2014year12 on March 16, 2014, 02:49:36 pm
Ok so first I used the points (100,170) and (0,20) to get the gradient which was 1.5, and I'm pretty sure the y-intercept is 20, so my equation was C=1.5n+20.

So I subbed in 80 for n to get the cost of making of 80 apple pies, which was $140.

Then since they made a profit of $100, they would have to have sold those pies for $100 more than what it cost to make them, so they sold them for $240.

Then I divided $240 by 80 to get $3 per pie, and it looks nothing like any of the answers D:

I think that is correct, the book is just being stupid again don't worry haha!
Thanks for your help :)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on March 16, 2014, 06:33:19 pm
i know the 1/y reciprocal transformation is in the form 1/y=a+bx

i was doing doing part C and my equation was 1/y= 0.006+1x (1/y=0.006+x) and the answer has it as 1/y=x, i know the 0.006 is negligible but isn't the answer incorrect?
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on March 17, 2014, 10:03:42 am
i know the 1/y reciprocal transformation is in the form 1/y=a+bx

i was doing doing part C and my equation was 1/y= 0.006+1x (1/y=0.006+x) and the answer has it as 1/y=x, i know the 0.006 is negligible but isn't the answer incorrect?

0.006 is such a small number that it hardly makes a difference. If you were to still use 0.006 in your equation it won't make a different in your answer (unless you round to 3 decimal places). But in terms of VCAA exam, stick with your answer :)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on March 19, 2014, 03:55:32 pm
just a quick question in regards to residual plots. Say i did a x^2 transformation, i have x values in list one , y list 2, x^2 list 3 and residual values list 4 (casio class pad). When i do my residual plot, do i use my original x values or the new x^2 values and my residual values? i think you use original x? not sure, my residual plot always looks different to that of back of book when i try both variations
Title: Re: VCE Further Maths Question Thread!
Post by: The Brightest Witch on March 19, 2014, 08:50:19 pm
just a quick question in regards to residual plots. Say i did a x^2 transformation, i have x values in list one , y list 2, x^2 list 3 and residual values list 4 (casio class pad). When i do my residual plot, do i use my original x values or the new x^2 values and my residual values? i think you use original x? not sure, my residual plot always looks different to that of back of book when i try both variations

Well you do your residual plot at first to 'show' that the data is curved and not linear, so you use the original x list.

But then I guess if you wanted to look at the residual plot for your transformed data, you could do one using x^2 or whatever which i do sometimes just to look at it for my own understanding, but yeah, the original is the one you're meant to use :)
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on March 21, 2014, 11:20:09 pm
When they ask you to find residual values without given a table of x & y values and only the graph, is there a faster way to figure out residuals without having to create a table of values and go from there? It takes me a long time and reading off the graph can be really inaccurate as well...
Also, is log10(y) and transformations the same thing?
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on March 22, 2014, 12:59:08 am
The only other way I can see you calculating the residuals without  reading from the graph is if the question also gives you a set of actual values. Which you would then use to create a regression line. From there its simply the case of
residual value = actual value - predicted value
Though I am quite sure you won't be asked to determine the residual from the graph alone, especially if its hard to make out the points (I haven't crossed any questions that do this...well at least none come to mind).

And no they are not the same.
A log10(y) is called a log transformation whereas a 1/y is called a reciprocal transformation.
Basically they serve the same purpose, its just that the reciprocal transformation compresses the data to an even greater extent than the log transformation.

hope that cleared some things up somewhat :)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on March 22, 2014, 10:38:25 am
do we need to know about how the log function works, ie. log10^etc.... the base etc.. , how we do in methods. Bit far-fetched for further though ahha
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on March 22, 2014, 12:04:57 pm
Nope as far as further maths is concerned, the use of the log transformation and knowing that it compresses your data values is about as far as it goes. Though that's for the core, my school only did number patters, business and matrices and we didn't touch logs after the core but I can't say the same for the other modules which I didn't do. But I highly doubt you need to know about the logarithms to the extent in methods, just the basics i'd say.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on March 22, 2014, 01:43:54 pm
Our further teacher is also a spesh teacher at our school, he said it wasn't needed, but he did give us a quick recap incase the exam asked for y=.... and not logy=.....

just getting rid of log and putting it to the base of 10 or something like that.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on March 22, 2014, 05:22:47 pm
kinda like getting rid of the squared in
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on March 22, 2014, 07:09:49 pm
The only other way I can see you calculating the residuals without  reading from the graph is if the question also gives you a set of actual values. Which you would then use to create a regression line. From there its simply the case of
residual value = actual value - predicted value
Though I am quite sure you won't be asked to determine the residual from the graph alone, especially if its hard to make out the points (I haven't crossed any questions that do this...well at least none come to mind).

And no they are not the same.
A log10(y) is called a log transformation whereas a 1/y is called a reciprocal transformation.
Basically they serve the same purpose, its just that the reciprocal transformation compresses the data to an even greater extent than the log transformation.

hope that cleared some things up somewhat :)
Cheers MagicGeko, it was a multiple choice question for my practice test and it was really hard to accurately pinpoint the co-ordinates of all the points :/ but looking through practice exam questions they all supplied a table of values :). When you are asked to use 3 median method and given a table of values, do you have to reorder the points so they're lowest to highest? Also, how/what do you analyse for percentaged segmented bar charts in order to get full marks?
Title: Re: VCE Further Maths Question Thread!
Post by: The Brightest Witch on March 23, 2014, 02:12:09 pm
When you are asked to use 3 median method and given a table of values, do you have to reorder the points so they're lowest to highest?

Yep! You reconstruct the table so that the x-values are from lowest to highest, but still have their corresponding y-values (so their y-values move with them). Then in each of your 3 sections separately, you order your y-values from lowest to highest. Finally, you get a median x-value and a median y-value from each of the 3 sections :)

In the example below, our 3 points are: (3.5,8.5) , (7,4) , and (11,7.5).
Title: Re: VCE Further Maths Question Thread!
Post by: lilellanii on March 24, 2014, 07:36:20 pm
Hey Guys :3

Just wondering, when describing a seasonal trend, would you mention values?  Or just like, when there are peaks and troughs?

Thanks xx
Title: Re: VCE Further Maths Question Thread!
Post by: Sense on April 07, 2014, 11:32:26 pm
When you're making a box plot from a frequency table that has classes (100- ,200-, 300-) instead of specific numbers, do you use the middle number like 100- would be 150 ?
Title: Re: VCE Further Maths Question Thread!
Post by: Sense on April 08, 2014, 12:16:40 pm
Anyone ?
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on April 08, 2014, 01:15:29 pm
When you're making a box plot from a frequency table that has classes (100- ,200-, 300-) instead of specific numbers, do you use the middle number like 100- would be 150 ?
You have to estimate the 5 point summaries. This is a good video showing you what to do
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 08, 2014, 04:00:06 pm
how do we find the linear regression formula from a graph/scatterplot?
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on April 08, 2014, 04:31:12 pm
how do we find the linear regression formula from a graph/scatterplot?

Write down the x and y co ordinates of each points of your scatterplot/graph. Then put it in the CAS--> list and spreadsheets then linear regression line.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 08, 2014, 04:46:51 pm
I've tried that before didn't get similar to the one with data.
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on April 08, 2014, 04:48:48 pm
Can you post a picture and i'll try to do it?
Title: Re: VCE Further Maths Question Thread!
Post by: Sense on April 08, 2014, 05:00:35 pm
You have to estimate the 5 point summaries.

Okay, so if I'm using this table and it asks me to find the min-q1-median-q3-max of the high dosage group, would I just use the median ( ( Median = x) of the interval or the actual interval (Median = x - x)
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on April 08, 2014, 07:31:51 pm
Okay, so if I'm using this table and it asks me to find the min-q1-median-q3-max of the high dosage group, would I just use the median ( ( Median = x) of the interval or the actual interval (Median = x - x)
i reckon you use the midpoint of the intervals. I don't know if i'm doing it right but.. i think the median is (226+1)th number, 113.5th number, so its the 800- gram interval? And for Q1, its (113.5+1)th number, 57.25th number, so its 700- gram interval? And for Q3, its (113.5+1)th number, so 57.25th number but ABOVE the median, so its still in the 800- gram interval? Min=600- and max=1000-. i dont even know. What is the answer though?
Title: Re: VCE Further Maths Question Thread!
Post by: bellaellaella on April 15, 2014, 01:02:39 pm
Is the height of something considered to be numerical or categorical data?
Title: Re: VCE Further Maths Question Thread!
Post by: Sense on April 15, 2014, 01:04:50 pm

Is the height of something considered to be numerical or categorical data?

Most likely numerical. It could be categorical if it was short, normal and tall or something but most of the time it's in cm
Title: Re: VCE Further Maths Question Thread!
Post by: bellaellaella on April 15, 2014, 01:09:12 pm
Most likely numerical. It could be categorical if it was short, normal and tall or something but most of the time it's in cm

So if it's in cms it's discrete numerical data?
Title: Re: VCE Further Maths Question Thread!
Post by: Sense on April 15, 2014, 02:16:00 pm
Nah, continuous. Cm don't have to be a whole number they could be 178.8586589754798548
Title: Re: VCE Further Maths Question Thread!
Post by: bellaellaella on April 15, 2014, 02:17:43 pm
Nah, continuous. Cm doesn't have to be a whole number it could be 178.8586589754798548

What if we're given values that do not have decimals?
My teacher said that shoe size is categorical data so now I'm just so confused
Title: Re: VCE Further Maths Question Thread!
Post by: Sense on April 15, 2014, 02:32:01 pm
I'm pretty sure if it's cm it will still be continuous even if they only have whole numbers

Yeah, a lot of teachers say different answers for shoe size, but it can be either, large medium small or in numbers. If they don't state which one it is in the question then they are wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: bellaellaella on April 15, 2014, 02:53:10 pm
I'm pretty sure if it's cm it will still be continuous even if they only have whole numbers

Yeah, a lot of teachers say different answers for shoe size, but it can be either, large medium small or in numbers. If they don't state which one it is in the question then they are wrong.

And I thought further would be my easiest subject....boy was I wrong
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on April 15, 2014, 03:59:42 pm
And I thought further would be my easiest subject....boy was I wrong
Discrete:
If we're given shoe sizes like 6, 6.5, 7, 7.5, 8, 8.5, 9 and so on... This is discrete data as our shoe sizes can only take these values (they cannot be in between).

All of the data in this table here is discrete: http://www.zangle.com.au/wp-content/uploads/2012/05/womanssizeshoes3.png (some quick googling)

Continuous:
If we were to measure our shoes to see their physical length in centimetres, this would be continuous. My shoe is not going to be 22.51cm, but rather 22.516367219cm... and so on in decimal places. The number of decimal places is limited by our recording equipment, what we use to measure the length.

Categorical vs Numerical:
The two examples above are numerical pieces of data. As Sense was saying before, if we expressed our shoe size as not a number but as a category (such as small, medium, large, extra large) ...  then we'd have categorical data.

Hopefully that helps clear some things up.
Title: Re: VCE Further Maths Question Thread!
Post by: Yacoubb on April 15, 2014, 07:27:25 pm
And I thought further would be my easiest subject....boy was I wrong

Don't worry! I think every Further student starts off thinking they're going to score 40+ with little difficulty. Most learn that this is not the case. Further is about perfection - if you don't perfect your work for Further, and minimise your errors, scoring high is not really possible. Good luck to you all though - just remember not to underestimate this subject.
Title: Re: VCE Further Maths Question Thread!
Post by: bellaellaella on April 16, 2014, 05:13:34 pm
Don't worry! I think every Further student starts off thinking they're going to score 40+ with little difficulty. Most learn that this is not the case. Further is about perfection - if you don't perfect your work for Further, and minimise your errors, scoring high is not really possible. Good luck to you all though - just remember not to underestimate this subject.

That's exactly why I'm trying to get my head around it while it's still relatively early days
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 16, 2014, 05:15:55 pm
That's exactly why I'm trying to get my head around it while it's still relatively early days

Don't worry! I think every Further student starts off thinking they're going to score 40+ with little difficulty. Most learn that this is not the case. Further is about perfection - if you don't perfect your work for Further, and minimise your errors, scoring high is not really possible. Good luck to you all though - just remember not to underestimate this subject.

exactly the same here, all those little tricks
Title: Re: VCE Further Maths Question Thread!
Post by: That_Guy18 on April 17, 2014, 11:29:00 am
Hi guys. This is my first ever post here so, I'm kinda new.
I've recently been given a practice sac from my teacher and I'm stuck on a question that requires us to comment on the shape, centre and spread of a boxplot. If someone could detail what needs to be said in each of those three it'd be much appreciated. Thank you.
Title: Re: VCE Further Maths Question Thread!
Post by: bellaellaella on April 17, 2014, 11:38:37 am
Hi guys. This is my first ever post here so, I'm kinda new.
I've recently been given a practice sac from my teacher and I'm stuck on a question that requires us to comment on the shape, centre and spread of a boxplot. If someone could detail what needs to be said in each of those three it'd be much appreciated. Thank you.

I'm pretty sure the shape is about the distribution/skew (normally distributed, positive of negative skew), the centre is the median and spread should be range (highest minus lowest value)
Maybe wait for someone else to post but that's how I've been doing it.

What textbook are you using?
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on April 17, 2014, 11:50:02 am
I forgot my bound book at school! Basically,I had a little guide as to how to comment. Yeah, shape is about skewedness but remember the centre is median. Spread could be range, iqr, or standard deviation. There was a really good post by yacoubb on another thread about this and his way is really detailed and should ensure you get full marks.
Link here: Describing a Histogram's SHAPE, CENTRE, SPREAD
Title: Re: VCE Further Maths Question Thread!
Post by: That_Guy18 on April 17, 2014, 12:44:06 pm
bellabella, I'm using Maths Quest 12, 4th Edition
~v, thanks a lot for the link, it really helped  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Michael Scofield on April 17, 2014, 03:40:03 pm
Hey guys, I was wondering if someone could help me with the question attached.
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on April 17, 2014, 04:12:33 pm
Hey guys, I was wondering if someone could help me with the question attached.

Use this formula:
For y=a+bx, b=rS(y)/S(x), a=mean(Y)-mean(x)b
Where r is correlation coeff and S is standard deviation. So all you need to do is to sub the given values in.

So u should get b=-0.67, a=9.16. Therefore, the ans is A
Title: Re: VCE Further Maths Question Thread!
Post by: Michael Scofield on April 17, 2014, 04:36:00 pm
Use this formula:
For y=a+bx, b=rS(y)/S(x), a=mean(Y)-mean(x)b
Where r is correlation coeff and S is standard deviation. So all you need to do is to sub the given values in.

So u should get b=-0.67, a=9.16. Therefore, the ans is A

Thanks a lot man!
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 19, 2014, 11:20:18 am
just a quick question - i calculated my lower fence at it was 26%. the lowest score in a maths test out of a class was 26, is this considered an outlier, or does it have to be below 26?

also what are some good resources to do when you have 3 more weeks until your sac and you've finished everything you have? I've done about 12 practice sacs , a+ , checkpoints all textbook questions don't know what to do to occupy myself for the next few weeks.

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on April 19, 2014, 04:23:41 pm
just a quick question - i calculated my lower fence at it was 26%. the lowest score in a maths test out of a class was 26, is this considered an outlier, or does it have to be below 26?

also what are some good resources to do when you have 3 more weeks until your sac and you've finished everything you have? I've done about 12 practice sacs , a+ , checkpoints all textbook questions don't know what to do to occupy myself for the next few weeks.

thanks
Lower fence? Um.. i never heard of that lol. To see if 26 is an outlier, you must use the forumula Q1-(1.5xIQR)< x<Q3+(1.5xIQR). Just because the lowest value is 26 doesn't mean it's an outlier. To find out outlier, you must have all the other information (Q1, IQR,Q3). You should get two numbers that x must be between, if 26 isn't between the two numbers then it is an outlier.
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on April 19, 2014, 04:56:05 pm
just a quick question - i calculated my lower fence at it was 26%. the lowest score in a maths test out of a class was 26, is this considered an outlier, or does it have to be below 26?

also what are some good resources to do when you have 3 more weeks until your sac and you've finished everything you have? I've done about 12 practice sacs , a+ , checkpoints all textbook questions don't know what to do to occupy myself for the next few weeks.

thanks

I had forgotten this so had alook at my last yr notes.

So if the value is spot on the lower/upper fence then it is not counted as an outlier. In ur case, 26 is not an outlier, however  any value below that is an outlier.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 19, 2014, 07:14:38 pm
ok it makes sense, because its a 'fence' anything higher/lower is outlier.

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: The Brightest Witch on April 21, 2014, 10:45:29 am
Lower fence? Um.. i never heard of that lol. To see if 26 is an outlier, you must use the forumula Q1-(1.5xIQR)< x<Q3+(1.5xIQR). Just because the lowest value is 26 doesn't mean it's an outlier. To find out outlier, you must have all the other information (Q1, IQR,Q3). You should get two numbers that x must be between, if 26 isn't between the two numbers then it is an outlier.

Lower fence is just what one of the textbooks calls the Q1-(1.5xIQR) value and upper fence is what they call the Q3+(1.5xIQR) value :)
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on April 22, 2014, 12:19:23 pm
also what are some good resources to do when you have 3 more weeks until your sac and you've finished everything you have? I've done about 12 practice sacs , a+ , checkpoints all textbook questions don't know what to do to occupy myself for the next few weeks.

thanks

Perhaps do questions from another textbook? When I did further, I normally ran out of resources, so I had 2 textbooks to keep me occupied. You don't have to buy another textbook, just simply borrowing it from your local library should suffice :)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 22, 2014, 04:14:41 pm
our librarys not the best, i have asked for the maths quest one and they didnt have it, only the ones our school uses really.
Title: Re: VCE Further Maths Question Thread!
Post by: calphanso on April 22, 2014, 07:46:55 pm
This is a trigonometry question from the 2011 Further Maths Exam 1. When I solve the question, i keep on getting B, but the answers happens to be C. Could anyone offer me some insight on how I might be able to solve it?

Edit, The answer is B, I was looking at the wrong answers...my bad..thanks for the help everybody...
Title: Re: VCE Further Maths Question Thread!
Post by: Conic on April 22, 2014, 09:04:57 pm
The assessment report says it's B:
(http://i.imgur.com/MVKIDXi.png)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 26, 2014, 03:42:11 pm
for the data, –1, 0, 3, 5, 7 the range is 8 either way you work it out, but in the further if the lowest data was -8, can the highest-(-)lowest change it to a positive sign?
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on April 26, 2014, 03:51:54 pm
for the data, –1, 0, 3, 5, 7 the range is 8 either way you work it out, but in the further if the lowest data was -8, can the highest-(-)lowest change it to a positive sign?

Ok lets try. 7-(-8)=15. Therefore it does change to positive.
Is this what you were trying to find out?
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on April 26, 2014, 05:59:12 pm
Yea, i knew that, but it was just the way of thinking about it since you can't have a negative range. All good, thanks  ;D
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on April 26, 2014, 06:03:57 pm
Yea, i knew that, but it was just the way of thinking about it since you can't have a negative range. All good, thanks  ;D

Think of it like this: if , then . So long as you got the min/max right, it's not possible to have a negative range :)
Title: Re: VCE Further Maths Question Thread!
Post by: Snorlax on April 29, 2014, 08:09:31 pm
I seem to be a little confused.
Are the 5 summary statistics different to the 5 number summary?
5 summary statistics: median, IQR, Range, Mode, Mean
5 number summary: Sample min, Q1, median, Q3, sample max

Is this correct?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on April 29, 2014, 09:33:07 pm
I seem to be a little confused.
Are the 5 summary statistics different to the 5 number summary?
5 summary statistics: median, IQR, Range, Mode, Mean
5 number summary: Sample min, Q1, median, Q3, sample max

Is this correct?

Thanks
If I was asked for a 5 number summary, I'd be looking for the min, Q1, median, Q3 and max. Then the questions following may ask you to calculate other values.

The median, IQR, range, mode and mean are measures of central tendancy and spread. I don't think you'll be asked for "5 summary statistics" in that form.
Title: Re: VCE Further Maths Question Thread!
Post by: mixedtears on April 30, 2014, 08:49:52 pm
For example: Australia: 450
Iraq: 360
Iran:210
Sudan: 380

Were the GDP. The question is calculate the GDP of a country that would be considered to have a GDP in the top 2.5%.
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on April 30, 2014, 09:36:25 pm
calculate the GDP of a country that would be considered to have a GDP in the top 2.5%

compare z scores of two countries

can anyone help me with these questions? we were just given random data and those question.
(for the 1st one) some people told me to use the bell curve. like, mean+2s others told me to rearrange the z score?
Top 2.5% means 2 standard deviations away from the mean, z score of 2. The z score corresponds to the standard deviation, so if you have a z score of 1.5, it is +1.5s. Tbh, im not sure if i answered your question when i dont really know what you're asking. 
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on May 01, 2014, 07:50:09 pm
how to use the z score to compare data?

for example the question says to compare of australia (-1.04) to the distribution of GDP

I saw all the GDP of other countries in your post but do you have a 'mean'. It only works when you have a mean because z score is x-mean/standard deviation. -1.04 means 1.04 standard deviations below the mean.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 05, 2014, 02:32:37 pm
if you've done all the work there is, and your sac is in less then a week do you suggest reading over you bound book etc?

Also between the SACS (because CORE sac is over 5-6 periods) what do i do in between for revision, do i do anything at all? since our teacher takes our bound book as well, personally what did you guys do?

Thank you :)
Title: Re: VCE Further Maths Question Thread!
Post by: kx4y on May 05, 2014, 06:30:11 pm
Hi, are there any SAC practice exams that have more difficult questions out there?
I have a SAC on time series coming up and I've finished the revision from my Essentials textbook and related questions from the  2006-2013 VCAA practice exams. I found the questions in both of these resources to be quite easy. Just wondering if there are any more challenging resources that I could use to prepare for my SAC?
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on May 05, 2014, 09:48:51 pm
Um.. you should probably look for company practise exams, like insight, neap, itute, MAV etc. But you should probably keep those for the end of year exams so you have alot to do. By the looks of it, seems like you did heaps already, you should be fine. 
Title: Re: VCE Further Maths Question Thread!
Post by: bellaellaella on May 06, 2014, 05:26:13 pm
How would you answer a question when asked to describe the features of a scatterplot?
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 06, 2014, 07:34:55 pm
Form, strength, outliers, direction
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 06, 2014, 07:35:14 pm
 between the SACS (because CORE sac is over 5-6 periods) what do i do in between for revision, do i do anything at all? since our teacher takes our bound book as well, personally what did you guys do?
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on May 10, 2014, 07:37:53 pm
When doing transition matrices, how do you find initial state if it isn't given to you but the transition matrix is???
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 11, 2014, 05:26:19 pm
You must be given one state matrix, otherwise the transition matrix is of no use.
For example, if you are given S3, you can work forwards and find S4 by
S4 = TxS3

If you wanted to start at S3 and go backwards to find S2, you need the inverse of the transition matrix
ie  S2 = T-1xS3

If you wanted to start at S3 and work back to the initial state matrix S0, you can use
S0 = T-3xS3
Title: Re: Frustrating GEO + Trig. help! + General Assistance
Post by: plato on May 14, 2014, 09:58:14 am
I am sorry that you have been so frustrated by the trig module. One good thing about the subject is the choices that are available, except in the Core.

Your hard work appears to have not paid off for you and this leads to a couple of options you may want to consider.  First up, did you fully understand the fundamentals of bearings or the sine and cos rules or has your hard work been directed toward attempting lots of questions wherte you eventually found the correct answer? Unless you have a commitment to, and a process for, gaining complete understanding of the fundamentals of any of the mathematical concepts, you may revisit your frustrations in other topics and modules.

Have you asked your teacher for advice or extra assistance? Are there catch-up classes available at your school? If your confidence in trigonometry has been fully shot, then a good tutor should be able to help you if that is an affordable option.

Another possible alternative could require even more personal determination and hard work, but could be more effective in the long run. You do not have to only study the modules that your school has selected! Discuss this with your teacher! While the Core is compulsory, you can do any three modules you like in either of the two end of year exams. Your school does not get to see what modules you attempt.

If trigonometry is too hard to recover and there is to be no more SACs this year that include trigonometry, you could look at another independently studying a module that your school is not doing.

The Networks module may be the easiest to work on independently for someone whose forte is not mathematics. If your school already includes this module, then you could look forward to greater success in this module. But you must put every effort into complete understanding of every concept within one day of it being introduced in class. Ask questions of your teacher and utilise the fantastic help available in this forum. Look up the great many posts that already exist and where you could find really useful explanations.

Another module that you could find quicker to grasp is Matrices. This does depend a lot on applying matrices on the calculator but, once you have understood what they are, this could be a good option for you.

One final point. You say that Further Maths is a potential pre-requisite for you. Does this mean you must get an "S" or is there a minimum score you may need? If you only need an "S", did you know you do not have to sit either of the two exams and you only need to satisfactorily complete the coursework at school. Discuss this with your teacher if the situation conmtinues to distress you.

I hope you have greater success and reassurance along whichever path you choose to take.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 18, 2014, 07:23:34 pm
Could someone please tell me how i would go about doing these questions
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 19, 2014, 05:45:26 pm
please  :(
Title: Re: VCE Further Maths Question Thread!
Post by: Paulrus on May 19, 2014, 06:15:06 pm
disclaimer, i haven't started geo and trig yet (going off year 11 knowledge here), so could be wrong
basically to find how far O is from the chord, you want to find the measurements of that triangle within the circle.
if the radius is 14cm, we know that the distance from A to O is 14cm. and chord AB is 4cm, but we only want half of that (from A to the middle). so we know the measurements of the triangle are 14cm and 4cm. using pythag, you calculate 142-42, which gives you 180. the square root of 180 is 13.416407865, so the chord should be 13.42cm away from O.

i'm about to eat but i'll do the other ones and edit this post after i get back lol
Title: Re: VCE Further Maths Question Thread!
Post by: Duyyy11 on May 19, 2014, 06:27:08 pm
disclaimer, i haven't started geo and trig yet (going off year 11 knowledge here), so could be wrong
basically to find how far O is from the chord, you want to find the measurements of that triangle within the circle.
if the radius is 14cm, we know that the distance from A to O is 14cm. and chord AB is 4cm, but we only want half of that (from A to the middle). so we know the measurements of the triangle are 14cm and 4cm. using pythag, you calculate 142-42, which gives you 180. the square root of 180 is 13.416407865, so the chord should be 13.42cm away from O.

i'm about to eat but i'll do the other ones and edit this post after i get back lol


So very very close!

You said yourself, we only want half of cord AB which is 4cm, therefore we want 2cm2.

Therfore we have 142-22 which equals 192. Square root 192 would give you 13.86 or 13.9 depending on the amount of decimals you want!

Hope I helped!
Title: Re: VCE Further Maths Question Thread!
Post by: Paulrus on May 19, 2014, 07:21:55 pm
oh whoops, i really need to proofread my posts. yeah, that should have been 22, thank you for that :P

as for question 13 a:
i'm going to use a lot of decimal values for each number here just for the sake of being more accurate, hopefully it doesn't make it more confusing
your calculator tell you that 8 square root 2 is equivalent to 11.3137. you can find that out just by typing it into your calculator and pressing CTRL+Enter. that lets you split the square into two triangles with the diagonal of 11.3137 acting as the hypotenuse. we know that a2+b2=c2, and because it's taken from a square we know that both a and b will be the same. so basically a2+b2 will equal 11.31372, which is 127.99980769.
127.99980769 divided by 2 is 63.999903845, which is both our a2 and b2 cos they're the same. remember that we need to square root these to find the length of the sides, so we end up with 7.99999399031.

now we can put the triangles back together, and we're left with a square that has sides of 7.9999939901cm. we want to find the area of the square, which has the formula of length2. so you take the value we found for the length of the side, and square it, which will give you 63.999903845. if you round up, that means the square will have an area of 64cm2.

hopefully that helped! tbh i think i might have used more steps than necessary, but i looked over it and i'm pretty sure that should get you the right answer. i'm not sure which textbook you're using but if you check the answers section i think it should hopefully be right haha. using that you should be able to solve 13b as well, cos it's basically the same question. if this explanation is too confusing i can try rephrase some of it  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on May 19, 2014, 07:44:29 pm
oh whoops, i really need to proofread my posts. yeah, that should have been 22, thank you for that :P

as for question 13 a:
i'm going to use a lot of decimal values for each number here just for the sake of being more accurate, hopefully it doesn't make it more confusing
your calculator tell you that 8 square root 2 is equivalent to 11.3137. you can find that out just by typing it into your calculator and pressing CTRL+Enter. that lets you split the square into two triangles with the diagonal of 11.3137 acting as the hypotenuse. we know that a2+b2=c2, and because it's taken from a square we know that both a and b will be the same. so basically a2+b2 will equal 11.31372, which is 127.99980769.
127.99980769 divided by 2 is 63.999903845, which is both our a2 and b2 cos they're the same. remember that we need to square root these to find the length of the sides, so we end up with 7.99999399031.

now we can put the triangles back together, and we're left with a square that has sides of 7.9999939901cm. we want to find the area of the square, which has the formula of length2. so you take the value we found for the length of the side, and square it, which will give you 63.999903845. if you round up, that means the square will have an area of 64cm2.

hopefully that helped! tbh i think i might have used more steps than necessary, but i looked over it and i'm pretty sure that should get you the right answer. i'm not sure which textbook you're using but if you check the answers section i think it should hopefully be right haha. using that you should be able to solve 13b as well, cos it's basically the same question. if this explanation is too confusing i can try rephrase some of it  :)

For Q 13 a and b, I think it's easier to use this method:
We know that the lengths of a square are equal, thus a diagonal cut would leave us with an isosceles triangle.
For part a), the diagonal length represents the hypotenuse, and we know that the hypotenuse is always sqrt(2) x one of the lengths of the sides.
That means that the two other sides must be 8 cm each.
Therefore you can figure out the area of the square by multiplying 8 by 8 = 64 cm squared. Or calculating the area of the triangle and doubling it. So half base x height will leave us with 4 x 8 = 32 cm squared, times 2 = 64 cm squared.

Part b) is essentially using the same concept.
We can use the above rule to find out the side lengths, however, I think it's easier to just use Pythagorean's theorem.
So we know that we have a square cut diagonally with the cut measuring 8 cm.
That means we're left right an isosceles right angled triangle.
From a2 + b2 = c2
We know that x2 + x2 = 82
Therefore 2x2 = 64
x2 = 32
x = sqrt(32)

And to find the area of the square, it's simple l x w.
so sqrt(32) times sqrt(32) = 32 cm2
Hopefully I didn't make this more confusing, but I think that's how they're trying to make you work it out. Hope it helps.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 19, 2014, 10:16:57 pm
When doing transition matrices, how do you find initial state if it isn't given to you but the transition matrix is???

Here's the question attached:
Further Question Thread!

I assume you mean question 7.
Although you are not given an initial state matrix, you are told that there were 2800 birds nesting at site C in 2008.
The transition matrix states that 20% of these birds will nest at site A in 2009. This is the transition matrix element (1, 3)
So 20% of 2800 = 560 Answer A
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on May 24, 2014, 05:48:39 pm
When a question asks to 'plot' points, do you draw a line through the points or not?
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on May 24, 2014, 06:57:20 pm
When a question asks to 'plot' points, do you draw a line through the points or not?
No, you literally only 'plot' points on the graph. When they ask eg.'add a line of best fit' or 'sketch linear regression line' then you draw a line through the points with the given equation or line of best fit by eye. Read the questions carefully and if they want to fit a line in, they'll tell you.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 24, 2014, 10:20:27 pm
could someone please help me with these two.

10 A and B
13A


Answers

10 A) 192 m2
10 B) 160 m3

13A) 892.70 cm2


im probably asking for too much :(, thanks to anyone who can help :)
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on May 24, 2014, 11:01:04 pm
Not sure how to explain it well, so I'll just show my working out I guess?

10 a)
First we'll do the bottom (shaded shape)
Front = 5x2 = 10. x2 because there's one at the back as well. 20.
Side = 2x10 = 20 x2 because there's one on the other side. 40.
Base = 5x10 = 50.
Now for the top.
Calculate the area of both triangles.
1/2 base x height. 0.5x3x4 = 6. x2 because there's 2 = 12.
Now the sides are both different.
So 4x10 = 40.
and 3x10 = 30.

Add them altogether; = 192 cm2

10 b) The volume of the bottom shaded area is 5x2x10 = 100cm3
The volume of the top is half base x height x length
1.5x4x10 = 50cm3

Add them both together = 160cm3

13a) Hopefully you can bear with me here.
We'll do the top first (half cylinder).
The area of both the front and back semi-cirlces add to equal just a normal circle.
So pi*r2 = pix52 = 78.54
Now for the half round shape around the cylinder;
We need the circumference (2*pi*r) of the circle x the length and then divide by 2, since it's only half.
so 2 x pi x 5 x 20 = ..., then divide this answer by 2.
= 314.16
Now for the bottom shaded area.
10x5x2 = 100 (both front and back)
5x20x2 = 200 (both sides)
10x20 = 200 (base)

Add them altogether = 892.70 cm3

Hope this helps.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 25, 2014, 10:24:03 am
Thanks very much :)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 25, 2014, 12:34:46 pm
With 10a, how did you get a base of 3?

and with 10b, how did you get 1.5 x 4 x 10. if its half base x height.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on May 25, 2014, 01:39:25 pm
For 10a, If you look at the triangles tilting your head right, you can see that 3 becomes the base and 4 is now the height.
We have to do this because we are unable to calculate the other side of the triangle because we don't know if it's a right angled triangle (even though it looks like one), so we can't be sure that Pythagorean's theorem can be used.

10b,  The volume is half base x height x length.
The area is only half base x height.
So using 3 as the base of the triangle again, halving it gives us 1.5
Now we times this by the height (4), then again by the length (10.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 25, 2014, 02:21:44 pm
alright, thanks for that :)

still unsurehow 3 is base when i tilt my head to the right. to see from right hand side view
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 27, 2014, 10:10:38 pm
hows this done
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on May 27, 2014, 10:21:12 pm
hows this done



Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 27, 2014, 11:03:14 pm




sweet, thanks heaps!

did the scale factor of 1/2 come from 50/100?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on May 28, 2014, 08:19:21 am
or was it, x for the bigger cone and 1/2x for the smaller one therefore scale factor 1/2
Title: Re: VCE Further Maths Question Thread!
Post by: 2014year12 on May 28, 2014, 05:09:43 pm
Can someone please explain question 1. d)
I can't figure out how to get those answers?
I got the mean to be 4.4 and the standard deviation to be 3.9??
Thanks in advance!
(Picture attached)
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on May 28, 2014, 06:24:26 pm
Can someone please explain question 1. d)
I can't figure out how to get those answers?
I got the mean to be 4.4 and the standard deviation to be 3.9??
Thanks in advance!
(Picture attached)

Can help in regards to the mean. You are not taking into account that these are intervals, not just values.

First, we need to get the mid-point of each interval.

Code: [Select]
Upper Bound = greater value of the range
Lower Bound = lower value of the range

(e.g. 100-200 where 200 is the upper bound, and 100 is the lower bound)



Now we find the frequency multiplied by the mid-point of each interval (this is required to calculate the mean soon)

Once you have done this, the mean is calculated like so:



I have attached a worked example of your question, in regards to this.
Title: Re: VCE Further Maths Question Thread!
Post by: jayzeek on May 30, 2014, 08:45:55 pm
Hey guys! just found this forum on a whim and was wondering if anyone could help.

Was doing the 2013 geo module and am completely stumped by question 5.
http://imgur.com/yicZ8jO
Anyone mind walking me through it?

EDIT: Answer is C BTW! :D
Title: Re: VCE Further Maths Question Thread!
Post by: Conic on May 30, 2014, 08:51:04 pm
4km is 4,000m, which is 400,000cm. So on the map the length is (400,000cm)/50,000=8cm.
Title: Re: VCE Further Maths Question Thread!
Post by: jayzeek on May 30, 2014, 08:59:55 pm
4km is 4,000m, which is 400,000cm. So on the map the length is (400,000cm)/50,000=8cm.
Thanks, but I'm still a little puzzled, I believe I have been taught calculating contour map distance wrong because I was led to believe you just simply times the distance by the number to the right in the scale. So what I was doing was

50,000 x 4 = 200,000
200,000 / 100,000 (convert into cm from km)
= 2cm

Clearly this is wrong, should I be employing a formula that uses ratios?
Title: Re: VCE Further Maths Question Thread!
Post by: Conic on May 30, 2014, 11:32:32 pm
I would use ratios because they give it to you as a ratio. They give you the ratio as 1:50,000. This means that distances in real life are 50,000 times greater than on the map. So to scale real world distances down we need to divide by 50,000, because we know they are 50,000 times greater than they are on the map. So the 400,000cm real world distance becomes 8cm on the map.

"50,000 x 4 = 200,000
200,000 / 100,000 (convert into cm from km)
= 2cm"

In your first step you are scaling a number in km upwards, so the result should be in km. In your second step you are dividing a number in km to convert to cm, but the number in cm should be larger, as you can fit a lot of cm in a km. It is probably easier and more accurate to break it down and do it step by step than by using a formula.
Title: Re: VCE Further Maths Question Thread!
Post by: jayzeek on May 31, 2014, 12:55:37 pm
Okay that does clear things up, thank you! :D
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on June 01, 2014, 08:30:35 pm
Couldn't the answer be either D or E considering they are interchangeable?
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 05, 2014, 05:09:04 pm
how is Q9 drawn? i know the math, but when i drew it and tried to figure it out it didnt get the answer.

with Q13, how do i do it?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 05, 2014, 05:23:06 pm
another few questions, im stuck on how i do question 14 and 15.

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on June 05, 2014, 07:37:57 pm
how is Q9 drawn? i know the math, but when i drew it and tried to figure it out it didnt get the answer.

with Q13, how do i do it?

thanks
The diagram for 9 even though it's a bit dodgy.
Also, i think for question 15, from the top of my head it's using either the sine or cosine rule. I think you have 3 angles and a side (30cm) 105, 37.5, 37.5 (??). Im not up to the trigonometry module just yet and this is all the things i remember last year, so i might be wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 05, 2014, 07:57:38 pm
The diagram for 9 even though it's a bit dodgy.
Also, i think for question 15, from the top of my head it's using either the sine or cosine rule. I think you have 3 angles and a side (30cm) 105, 37.5, 37.5 (??). Im not up to the trigonometry module just yet and this is all the things i remember last year, so i might be wrong.

Thanks!

Its cosine, but im not sure how to apply it here..

Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 07, 2014, 01:09:46 pm
how do you draw this? if you want to figure it out as well its 110m.

Ive tried different drawings best ive got is 116m...
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on June 07, 2014, 01:33:49 pm
how do you draw this? if you want to figure it out as well its 110m.

Ive tried different drawings best ive got is 116m...

(http://i1282.photobucket.com/albums/a531/Ovazealous/triangle_zps63f5fe09.png)
(O=bottom of the triangle)

Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 07, 2014, 10:06:57 pm
Thanks for that Z :)

BTW, how is angle ABT 80 degrees?
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 08, 2014, 01:56:21 pm
an equlateral triangle has altitudes of length 20cm. Find the length of one side.

I would've suspected 20cm, due to equilateral, but answer is 23.09, can someone draw a diagram and how me how its done?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Conic on June 08, 2014, 02:06:09 pm
(http://i.imgur.com/7o4z2HH.png)
Let x be the length of the sides.

Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 09, 2014, 05:11:31 pm
stuck on this for ages :(

someone help please
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on June 09, 2014, 06:04:40 pm
stuck on this for ages :(

someone help please

If AO' is 6 cm then, BO' is also 6 cm. same with AO and BO. So Now you have two triangles and you know all the side lengths. Therefore you use cosine rule to find AO'B ans AOB.

Hope that helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 09, 2014, 06:13:12 pm
I'll have a try. What's a chord? And do I need to worry about it in this q?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on June 09, 2014, 06:27:14 pm
I'll have a try. What's a chord? And do I need to worry about it in this q?

Thanks

A cord is just a line connecting to points. They say there is a cord/line between A and B.

Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 09, 2014, 07:20:06 pm
got it right, thanks :)

Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 10, 2014, 06:32:18 pm
how do i do these 2? i dont think i got the diagram right.

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on June 10, 2014, 07:17:29 pm
how do i do these 2? i dont think i got the diagram right.

thanks

I have attached the solutions. For the second one, we can also use the cosine rule for finding angles to find angle KLM, as we have all three sides known.

Hope it helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 10, 2014, 08:20:49 pm
Thanks for that Thorium :)

i also had these, how do i do 17a, i figured out 17b (after looking at answers for value of a).

And also 2d and 2e.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on June 10, 2014, 09:25:29 pm
Thanks for that Thorium :)

i also had these, how do i do 17a, i figured out 17b (after looking at answers for value of a).

And also 2d and 2e.

Thanks

I had a go with question 17a, i have attached the solution.
Title: Re: VCE Further Maths Question Thread!
Post by: Thorium on June 10, 2014, 09:35:07 pm
I had a go with question 17a, i have attached the solution.

Here is the solution for 2d-e, sorry for late reply.
Title: Re: VCE Further Maths Question Thread!
Post by: Einstein on June 12, 2014, 09:26:32 pm
thanks! how about this?
Title: Re: VCE Further Maths Question Thread!
Post by: 99.96 plz on June 15, 2014, 02:33:44 pm
Can someone help me with part b.

Thanks.

HINT: SOH CAH TOA
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on July 01, 2014, 05:27:44 pm
Questions:
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 03, 2014, 07:46:15 pm
Im having one problem with matrices, and if you could clarify it that would be great. In the book they say the inverse is as stated in the attachment (the diagonal is switched and the remaining 2 elements are multiplied by -1), but then a few pages later it goes on about finding/determining the inverse using the 1/det(A) etc, would we just switch the diagonals like before and go on from their?.. could you tell me whats happening here?

Also, when a question asks, find the inverse of this/ or show A^-1A=I etc, which way do we use when determining the inverse?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 03, 2014, 07:55:09 pm
It might seem weird at first, but they've used that method in the first question. The determinant of the matrix they've given is 2*5 - 3*3 = 1, which gives us:



(forgive the bad notation, AN doesn't seem to handle [ and ] that well)

So, you don't really have two different methods, it's actually the one mentioned in the second picture. So, always use the method in the second picture if it's a 2x2. If you have a higher order matrix, find the inverse using your CAS.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on July 03, 2014, 08:20:25 pm
Questions:

Because I'm not sure what CAS you use, I'll just use the annuities formula instead of TVM solver or Finance Solver. Just substituting values in and solving for the unknown is sufficient for all of these questions - make sure you write down all the information out so you know what information you have, and what information you need to find.

(have a look at your textbook for what each pronumeral represents, and this formula is pretty long!)

9c First we need to find out the value of the balance after the next 15 years if we are investing money each month. So . Basically, our growth factor (r) is which turns the percentage (7.2%) into a decimal, and also takes into account that we are dealing in months (hence why we multiply by 12). Our n value is because we have 15 years worth of 12 months, so we end up with 180 compounding periods.



So after 15 years, there will be $387038 available for retirement. Now we have to workout how much money we can take out of the $387038 each month, given we are going to take it out for 20 years and that the balance is compounding monthly at 8% p.a.





. So $3237 can be taken out every month in retirement each month because of the investment. Last step is to multiply that by twelve, because the question wants you to find the annual salary, which will be $3237x12=$38848.The annual salary in retirement will be $38848. (hopefully that's correct, it's been like ages since I did business maths!)

____________________________

I don't have time to go through all the questions, but I'll leave some advice here. If you can get good at using TVM solver or Finance Solver on your CAS, these questions will be much much easier. I used the method above of using the formula to check my answers during the exam because I had extra time, and I have shown that method as I'm not too sure on what calculator you use. For the rest of the questions you've sent, first write down all the information you've been given, then find the unknown using the formula or your CAS software. The hardest step is just taking in the information and picking out what is key to solving the question. You won't get many questions with multiple steps like the one above. Hopefully this helps! if you still need help with those last questions, post back here and I'll try get back to you.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 03, 2014, 09:36:22 pm
It might seem weird at first, but they've used that method in the first question. The determinant of the matrix they've given is 2*5 - 3*3 = 1, which gives us:



(forgive the bad notation, AN doesn't seem to handle [ and ] that well)

So, you don't really have two different methods, it's actually the one mentioned in the second picture. So, always use the method in the second picture if it's a 2x2. If you have a higher order matrix, find the inverse using your CAS.

Alright, that clears it up, so would you suggest always using the second option (only option) instead of the diagonal is switched and the remaining 2 elements are multiplied by -1, because the detminant will be different in cases?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 03, 2014, 09:48:08 pm
I think you misunderstand - the determinant method includes the switching.

For any matrix A,

For a 2x2 matrix , this can be simplified to
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 05, 2014, 03:10:17 pm
Any help on 5b and 7a would be awesome! Thanks

answer:
5b: x=5w-250
7a: c = 0.2n + 175
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 05, 2014, 03:48:18 pm
5b.

When x increases, so does w, so . But, when x = 0, w = 50, so there's some pesky constant in there, giving us . Subbing in the next point, we get So, we get . Now, there's one small issue with this relationship - whenever we write a relationship, we like to put it in the form of "what we see = what we control", but we've got this around the other way (which I did just because it was easier to do). So, solving for x, we get

7a.

This time they tell us the formula, so this works very much in our favour! C = an + b. Subbing in the four values they gave us, we get . Now, we just need to solve these simultaneous equations to find a and b. You can do this by CAS, but if you want to do it by hand, here's how I would:

Solve both equations for b:


Now, let both equations equal each other and solve for a.



Now, sub this into either of the equations to find b.



So, the answer is (I'm thinking the 0.2 is a mistake on the book's part, because I did double check this on a calculator)
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 05, 2014, 04:58:34 pm
Thanks Euler!!, i sent a message to you off how i got 0.2 and my method of working it out, my method is wrong as im subbing cost for n, but it still yielded the correct answer thats why i was abit iffy with how to do it.

I also had these two questions, how do you do them? Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 05, 2014, 05:26:15 pm
7. Firstly, let's give them each a pronumeral to make things easier. The best way to do it is first initial = pronumeral.

Next, interpret the words to be maths, one step at a time, and write it all down as you go along.
"The sum of Anne's mark and David's mark is 42". So, a + d = 42
"Sheila has twice as many marks as David". So, s = 2d
"The sum of Anne's an Sheila's marks is 52". So, a + s = 52

You're not expected to do this by hand at methods level, so I'd assume the same for further, but here's a way to anyway:


So, Anne got 32 marks, David got 10 marks and Sheila got 20 marks.

8 is on the way, but dinner be calling. (maybe someone will beat me to it, hahah :P)

EDIT:

8. So, we know that the mixture costs $6 per kilogram, and we need 60 kilograms, so all up we have 360 = ?a + ?b - where ? is the costs of the actual herbs a and b. So, this gives us 5a + 8b = 360. We also know that the mixture of a and b will give us 60 kg, so a + b = 60. We now have our simultaneous equations and are ready to go:



So, you need 40kg of herb A and 20kg of herb B.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 06, 2014, 01:43:53 pm
thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on July 07, 2014, 08:44:25 pm
Hi could I have some assistance please with transition matrices, thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on July 07, 2014, 08:45:58 pm
These questions trouble me.
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on July 07, 2014, 09:12:51 pm
Help with this question is also needed
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 07, 2014, 09:21:48 pm
For this, I'm going to introduce a notation you're probably not aware of, which comes from the methods curriculum - is the probability of A if you already know that B has happened. We can then put this into a matrix equation like so:



Remembering this whole set up can be a little annoying, so here's some tips - first, for the two column matrices, the one on the far right will always be the state before the one on the initial left, and the matrix in the middle is the transition matrix. To remember how we laid out the transition matrix, for , X will be whatever is in the left most matrix in the same row, and Y will be whatever you'd get if you multiplied the matrices out. If you can find another way which works for you, use that - the best way to remember this is whatever way works for you! :)

Now, to interpret this question. It says that 10% of the wagons that were at point A ended at point B - this means that . It also says that 8% of the wagons that started at point B ended at point A, this means that . So, this gives us the following matrix equation:



Now, here's something cool - the columns of any transition matrix MUST add up to one. Using this information, we can now complete the transition matrix, giving us:



Now, for part b, we're told that initially 125 wagons were at each starting point. So, we can now plug this into the far-right matrix (also called the initial state matrix, for this reason):


(note: if you know anything about probabilities, you'll know that they must be between 0 and 1. Don't worry, though - what I'm doing here is perfectly fine if you change those "Pr"s to "n"s like I did above - and it still works! ;) )

However, using this transition matrix only counts for one week, so in truth we actually have to apply it twice to get two weeks like the question wants us to. Using a CAS, this gives us:



So, 130 carts are at point A and 120 carts are at point B.

Part c is the same principle, but we don't have whole numbers to work with. So, we know that 40% start at point A, and that columns must add up to 100%, so we get:


But once again - the use of one transition matrix only counts for one week, and this questions wants to know about 6 weeks, so we have to use it 6 times, giving us:



Plugging this into the CAS, we get:



So, 51% of the carriages will be at point A, and 49% of the carriages will be at point B.
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on July 07, 2014, 10:10:33 pm
For this, I'm going to introduce a notation you're probably not aware of, which comes from the methods curriculum - is the probability of A if you already know that B has happened. We can then put this into a matrix equation like so:



Remembering this whole set up can be a little annoying, so here's some tips - first, for the two column matrices, the one on the far right will always be the state before the one on the initial left, and the matrix in the middle is the transition matrix. To remember how we laid out the transition matrix, for , X will be whatever is in the left most matrix in the same row, and Y will be whatever you'd get if you multiplied the matrices out. If you can find another way which works for you, use that - the best way to remember this is whatever way works for you! :)

Now, to interpret this question. It says that 10% of the wagons that were at point A ended at point B - this means that . It also says that 8% of the wagons that started at point B ended at point A, this means that . So, this gives us the following matrix equation:



Now, here's something cool - the columns of any transition matrix MUST add up to one. Using this information, we can now complete the transition matrix, giving us:



Now, for part b, we're told that initially 125 wagons were at each starting point. So, we can now plug this into the far-right matrix (also called the initial state matrix, for this reason):


(note: if you know anything about probabilities, you'll know that they must be between 0 and 1. Don't worry, though - what I'm doing here is perfectly fine if you change those "Pr"s to "n"s like I did above - and it still works! ;) )

However, using this transition matrix only counts for one week, so in truth we actually have to apply it twice to get two weeks like the question wants us to. Using a CAS, this gives us:



So, 130 carts are at point A and 120 carts are at point B.

Part c is the same principle, but we don't have whole numbers to work with. So, we know that 40% start at point A, and that columns must add up to 100%, so we get:


But once again - the use of one transition matrix only counts for one week, and this questions wants to know about 6 weeks, so we have to use it 6 times, giving us:



Plugging this into the CAS, we get:



So, 51% of the carriages will be at point A, and 49% of the carriages will be at point B.
Legend! Thanks so much I will look at this great explanation soon thank you so much :)
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on July 07, 2014, 10:11:50 pm
Anyone able to assist?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 08, 2014, 03:07:38 pm
looking for some help on this one, answer is d
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 08, 2014, 03:35:56 pm
looking for some help on this one, answer is d

break-even analysis (module 3) help with review question
This was actually answered a couple of years ago - and I'm with Stick, I reckon the answer should be $3. I'm guessing you're meant to do something along the lines of "it's not there - D is closest, I'll pick that"? Pretty stupid, though...
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 08, 2014, 03:41:16 pm
I saw that thread, i didnt understand it? she said to produce 80 apple pies it cost $140
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 08, 2014, 03:57:45 pm
I'm assuming that's a typo, because she supplied the correct points, and gave the correct relationship between cost of making an apple pie and number of apple pies made. If she used a numpad, 4 and 7 are right next to each other, so it makes sense.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 08, 2014, 04:53:45 pm
could you please tell me how you'd work it out, i dont understand how the other thread did it? thanks, im working ahead as well
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 08, 2014, 05:43:09 pm
nvm i got it

First find cost of making 80 pies.

C = mn +c where c = 20 (y-int)
C = mn + 20

m = (170 - 20) / (100 - 0)
m = 150/100 = 1.5

Cost = 1.5n + 20
when n = 80, C = 140

PROFIT = REVENUE - COST
100 = R - 140
R = 240

Revenue from selling 80 pies is $240
Divide by 80 to get selling price of one pie.
240/80 = 3.00
Closest answer is D.
Title: Re: VCE Further Maths Question Thread!
Post by: lilellanii on July 12, 2014, 08:53:44 pm
Hello (:
Is there anyone who can give me advice on how to cut/crash efficiently in the networks module? The Essentials textbook only skims through it... Any help would be really appreciated. Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on July 13, 2014, 05:42:25 pm
Hey how do you answer questions that end in decimal places but don't specify how many decimal places to answer it to, for example if the predicted number of passengers on a plane is 199.483 (answer from least sq reg line). Would you say 199 passengers, or round to 2dp?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on July 13, 2014, 05:52:46 pm
Hey how do you answer questions that end in decimal places but don't specify how many decimal places to answer it to, for example if the predicted number of passengers on a plane is 199.483 (answer from least sq reg line). Would you say 199 passengers, or round to 2dp?

Well... when it comes to stuff like that, just look to common sense. Are you really going to have a 0.483 of a person?
If it HAS to be whole, round to the nearest whole.
If it ISN'T always whole, round to 2dp or as specified.
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on July 13, 2014, 07:19:19 pm
Well... when it comes to stuff like that, just look to common sense. Are you really going to have a 0.483 of a person?
If it HAS to be whole, round to the nearest whole.
If it ISN'T always whole, round to 2dp or as specified.
Thank you! would that be the same for calculating the mean of the data?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on July 13, 2014, 09:24:21 pm
Yes, it's the same units for the mean.
Overall: Just remember to check your units, then apply common sense.
It shouldn't be much harder than that.  :P
(I checked the decimal place thing a few weeks back. Unless specified and it doesn't HAVE to be whole e.g. time, it's typically 2 dp for the final answer, EXCEPT in the case you're doing an r or r^2 value. Or at least, that's what I recall... hm.)
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on July 13, 2014, 09:36:59 pm
Thank you again, :) you have no idea how long this has been troubling me!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on July 13, 2014, 10:26:11 pm
No worries. Oh and to clarify my last post, r and r^2 values should actually be 4 dp, unless something states otherwise.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on July 14, 2014, 12:50:12 am
A mean value, or a predicted value, can be a decimal. For instance, the average household size in Australia in 2011 was 2.6 people. (Ref: http://www.aifs.gov.au/institute/info/charts/households/#havsize)

When an answer should be a whole number, then do NOT just automatically round to the nearest whole number. Read the question to see if it tells you what to do. Look for phrases such as "at least" or "more than" or "no more than" or "fewer than". Sometimes you may have to round an answer like 146.34 up while at other at other times you would round it down.

If the answer to a question is truly a decimal, you can expect the question to dictate the number of decimal places required unless the decimal number is exact. An answer of 4.6250000000 must be written as 4.625 unless there is an instruction to round off to a stated number of decimal places. An answer of 4.6250423897761............ etc would have the required number of decimal places dictated in the question.

The value of r and r2 should be rounded as dictated by the question. While this has often been four decimal places, you must check this each time.
Title: Re: VCE Further Maths Question Thread!
Post by: spectroscopy on July 20, 2014, 04:01:16 pm
yo i got a linear question
a herbalist wishes to prepare a mixture from two herbs, A and B. The mixture costs $6 per kilogram. If herb A costs $5 per kilogram and herb B costs $8 per kilogram, and 60 kilograms of mixture is to be prepared, how many kilograms of each herb should be used?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 20, 2014, 04:05:00 pm
http://www.atarnotes.com/forum/index.php?topic=142314.msg761176.msg#761176

This question has already been answered in the link above. :)
Title: Re: VCE Further Maths Question Thread!
Post by: spectroscopy on July 20, 2014, 04:05:44 pm
Re: Further Question Thread!

This question has already been answered in the link above. :)
oh cheers !
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 20, 2014, 09:28:16 pm
you probably dont need the question for this. But with transition matrix why, (when the formula is Sn = T^nSo) if its 4th week dont you do T to the power of 4 and not 3. I remember my teacher saying something about this in class but i didnt listen, cause i was doing something else, but doing checkpoints i havent seen this come up.

Title: Re: VCE Further Maths Question Thread!
Post by: plato on July 20, 2014, 11:38:38 pm
Define Sn as the nth state matrix.

When the initial state matrix is labelled S0 , it occurs at n = 0.
The second term is then, S1, is at n = 1 and is given by
S1 = TS0
and continuing,
S2 = TS1=T2S0
etc
and so Sn =TnS0

BUT, if the initial state matrix is labelled S1, which occurs at n = 1,
then S2 = TS1
and continuing,
S3 = TS2=T2S1
etc
and so Sn =Tn-1S1

Can you see what would happen if the initial state matrix was labelled S2014 ?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 21, 2014, 04:00:06 pm
heres the question, it said initially so i assumed no time had elapsed
Title: Re: VCE Further Maths Question Thread!
Post by: plato on July 23, 2014, 10:23:38 pm
I would call the initial state matrix S0 for this question, although there is a discrepancy between the numbers for the Airstart and Airfleet customers between the question and the answer.

I think the answer to the question should be
Sn = Tn x S0
where Sn is the state matrix after n transitions.
and the relevant matrices for T and S0 substituted.

The answer given is only the calculation that would produce S1, the state after the first transition.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on July 24, 2014, 06:43:18 pm
is the answer wrong here? i got c
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on July 24, 2014, 10:36:18 pm
It's C, answers wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on July 28, 2014, 04:35:22 pm
Whoever wrote the answers switched A and B around, hehe
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on August 02, 2014, 11:44:39 pm
Business Maths Question - help appreciated.

James and Jamie have just finished repaying a 5 year, $8000 reducing balance loan.
During the first year interest was debited monthly at 8.5% p.a.; during the next 2 years the rate fell to 8% p.a. but rose to 8.3% p.a. for the remaining period of the loan.
Before signing their contract James and Jamie were also given the option of fixing the interest rate at 8.25% p.a. (debited monthly) for the term of the loan.
By considering the total amount of interest that they paid, determine whether James and Jamie made the right decision in choosing the variable interest rate for the loan rather than the fixed rate.

Answers
Fixed: Interest = $1790.20
Variable: Interest = $1784.51 so correct decision is the variable, by $5.69
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on August 03, 2014, 02:54:46 pm
Business Maths Question - help appreciated.

James and Jamie have just finished repaying a 5 year, $8000 reducing balance loan.
During the first year interest was debited monthly at 8.5% p.a.; during the next 2 years the rate fell to 8% p.a. but rose to 8.3% p.a. for the remaining period of the loan.
Before signing their contract James and Jamie were also given the option of fixing the interest rate at 8.25% p.a. (debited monthly) for the term of the loan.
By considering the total amount of interest that they paid, determine whether James and Jamie made the right decision in choosing the variable interest rate for the loan rather than the fixed rate.

Answers
Fixed: Interest = $1790.20
Variable: Interest = $1784.51 so correct decision is the variable, by $5.69

First of all, this is a ridiculously long question. It's highly unlikely you'll get a question this difficult in the exam unless I've taken a really long approach (haven't done business maths in ages....) The finance solver entries work off each other, so take your time looking through what I've changed in each calculation.

Let's first calculate the amount of interest using the fixed rate of interest, then calculate the interest using the variable interest rate.

Fixed Interest Rate (using Finance Solver for Ti-nspire): We need to find the monthly payment, so input all the given information.
n=60 (5 years multiplied by 12 months per year)
I=8.25
Pv=8000
Fv=0
Ppy=12
Pmt=-163.17

To find out how much interest we are paying, multiply the payment by the amount of payments and subtract the value of the loan:
Interest (fixed rate)= 163.17x60-8000=1790.20

So using the fixed interest rate, we pay $1790.20 interest.

Variable Interest Rate: We again need to find the monthly payment, but we need to split this loan up into three different sections. 1: Interest of 8.5% for 1 year. 2: Interest of 8% for 2 years. 3: Interest of 8.3% for 2 years.
1a: first find the payment if the interest stayed at 8.5% for five years.
n=60
I=8.5
Pv=8000
Fv=0
Ppy=12
Pmt=-164.1323

1b: find the future value if that payment lasted only one year.
n=12
I=8.5
Pv=8000
Ppy=12
Pmt=-164.1323
Fv=6658.9675

2a: find the payment for the next four years with interest rate 8% if the payments went for all the years.
n=48
I=8
Pv=6658.9675
Fv=0
Ppy=12
Pmt=-162.5649

2b: find the future value if the $162.56 payment only lasted 2 years.
n=24
I=8.5
Pv=6658.9675
Ppy=12
Pmt=-162.56
Fv=3594.3973

3: find the final payment to complete the loan (2 years) at 8.3%.
n=24
I=8.3
Pv=3594.3973
Fv=0
Ppy=12
Pmt=-163.0571

So how much interest does he pay for the 5 year loan with the variable interest rate?
164.1323 x 12 + 162.5649 x 24 + 163.0571 x 24 - 8000 = 1784.52

Fixed Interest: 1790.20
Variable Interest: 1784.52
So they save $5.68 by choosing the Variable Interest loan and hence it was the right decision.

Note: I got a slightly different answer (1 cent) because of the large amount of calculations, so I think they rounded in between steps.

Hope that helps!
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on August 04, 2014, 08:30:34 pm
?
Title: Re: VCE Further Maths Question Thread!
Post by: PsychoT on August 04, 2014, 09:45:18 pm
?

Using Finance Solver:

N= 5x12 = 60 (interest debited monthly, solving for value after 5 years)
I= 12% (just the interest rate)
PV= 65000 (the amount of the loan, positive value as you are receiving the money, would be negative if you are making an investment, etc, giving it away for a fixed period of time)
Pmt= -715.71 (regular payments, negative as you are paying them)
FV= ____ (the amount of the principle left to be repaid after the 5 years)
PpY= 12 (amount of compounding periods per year, as it's monthly, value is 12 in both PpY and CpY)
CpY= 12

Don't have my calculator, but if you solve for the future value, that's what will still be owing after 5 years.
Title: Re: VCE Further Maths Question Thread!
Post by: NeedHelpWithStudy on August 05, 2014, 10:13:06 pm
Help with Attached question please. Don't know how to do it.
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on August 06, 2014, 07:05:45 pm
I'm not sure if I'm allowed to post here for questions that aren't math ones in a sense, but just wondering, when our sac marks are rounded, do they take the total of all our sac marks, proportionate it to a mark out of 100, then round, or do they round the mark of each sac to out of 20 or out of 40 for each sac separately? hope it makes sense :)
Title: Re: VCE Further Maths Question Thread!
Post by: PsychoT on August 06, 2014, 09:07:22 pm
I'm not sure if I'm allowed to post here for questions that aren't math ones in a sense, but just wondering, when our sac marks are rounded, do they take the total of all our sac marks, proportionate it to a mark out of 100, then round, or do they round the mark of each sac to out of 20 or out of 40 for each sac separately? hope it makes sense :)

I think they round each sac to out of 20 or 40, at least that's what they do at my school.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 06, 2014, 09:11:25 pm
Im pretty sure that they take the mark out of 20,40 etc and record it, then get a mark out of 100 after adding everything and send the proportion out of 100 to VCAA
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on August 06, 2014, 09:33:19 pm
I'm not sure if I'm allowed to post here for questions that aren't math ones in a sense, but just wondering, when our sac marks are rounded, do they take the total of all our sac marks, proportionate it to a mark out of 100, then round, or do they round the mark of each sac to out of 20 or out of 40 for each sac separately? hope it makes sense :)

It depends what each SAC is worth. Refer to the study design for assistance.

For unit 3, you do 2 SACs - an application task and an analysis task. The application task is worth (15+20+5)/60, and the analysis task is worth (15+5)/60. Your actual percentage is multiplied by this weightings, added together, and multiplied by the overall unit 3 SAC weighting of 20%.

For unit 4, you do two analysis SACs, and both are worth (7+8+5)/40. So, your actual percentage is multiplied by these weightings again, added together, and multiplied by by the overall unit 4 SAC weighting of 20%.

Then, those two final marks are added together, and that's your SAC contribution.



Why is finding the SAC contribution this tedious? Because VCAA has nothing better to do than crunch random numbers for thousands of students. I'm not quite sure how the schools submit your marks, it might be a SAC-by-SAC submission to make it easier on VCAA.
Title: Re: VCE Further Maths Question Thread!
Post by: Stressedyear11here on August 07, 2014, 09:36:39 pm
Hi,
Can a line of regression tell us if there is a relationship between two variables?

The scatter plot shows no relationship, and the regression line gradient is about 2, and r = 2.0

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on August 07, 2014, 11:37:26 pm
Hi,
Can a line of regression tell us if there is a relationship between two variables?

The scatter plot shows no relationship, and the regression line gradient is about 2, and r = 2.0

Thanks :)

The regression line is used to estimate the linear relationship between two variables.

The gradient of the regression line is not relevant in determining the strength of the relationship- what is relevant is how well the line fits the data, which is usually measured by r^2. r is always between -1 and 1, so I'm not sure how you got r = 2.0.

The scatter plot usually gives you a reasonably good idea of how strong the (linear) relationship is. Once you have found the correct value for r (and r^2), you will probably find that it is close to zero.
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on August 08, 2014, 06:26:00 pm
Thanks everyone! I think I get it, I asked my teacher and apparently we just round it off for each sac, where the application task mark becomes a mark out of 20, and the data one is out of 40 :)
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 09, 2014, 08:11:37 pm
The cost($C)of renting a car is given by C =an+b where:
n is the number of kilometers travelled
a is the cost per kilometres travelled and
b is a fixed cost

For a person travelling 200 km, the cost of car rental is $430. For a person travelling 315 km, the cost of car rental is $660. The values of a and b are:
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on August 09, 2014, 08:16:29 pm
This is an example of simultaneous equations. For person 1, and for person 2, . By substitution, . Substituting that into the equation for person 1, .
Title: Re: VCE Further Maths Question Thread!
Post by: engton1796 on August 11, 2014, 07:37:57 pm
Question relating to trigonometry and geometry.

The following diagram shows a cross-sectional view of a beehive with its regular hexagonal compartments. 
Only shows one triangle within a hexagonal compartment and the base at 10mm
Determine the value of an interior angle of each hexagonal compartment,  as shown in the diagram.

I put down 360/6 = 60 degrees,  but this was marked wrong.  How do you calculate this the right way?
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on August 12, 2014, 03:32:55 pm
Can someone help with this problem please? Ones in black pen thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on August 12, 2014, 07:51:01 pm
Question relating to trigonometry and geometry.

The following diagram shows a cross-sectional view of a beehive with its regular hexagonal compartments. 
Only shows one triangle within a hexagonal compartment and the base at 10mm
Determine the value of an interior angle of each hexagonal compartment,  as shown in the diagram.

I put down 360/6 = 60 degrees,  but this was marked wrong.  How do you calculate this the right way?

I'd have to see the diagram to be absolutely sure, because if you have a regular hexagon, that's right.
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on August 13, 2014, 09:51:00 pm
Hi guys,

I worked out the right answer by using the sin rule, where the unknown (hypotenuse) is root 2 x over sin 60, the 'opposite' is x giving you E (if you let x initially be RT). However, considering that this could be 2 right-angled triangles, why can't you let x denote RT. Then from this you get RQ being root 2 x. As SR would also be x, then couldn't you use pythag to get SQ. However, this doesn't give you the same answer as the above (the correct one). Why not?

Hope this made sense! 
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 13, 2014, 10:15:22 pm
Can someone help with this problem please? Ones in black pen thanks!
These should both be done with a TVM app on your calculator.
On the  TiNspire, it is called a Finance Solver (Menu-8)
On the Classpad, it is called Compound interest (Menu-Financial)
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 13, 2014, 11:11:00 pm
Hi guys,

I worked out the right answer by using the sin rule, where the unknown (hypotenuse) is root 2 x over sin 60, the 'opposite' is x giving you E (if you let x initially be RT). However, considering that this could be 2 right-angled triangles, why can't you let x denote RT. Then from this you get RQ being root 2 x. As SR would also be x, then couldn't you use pythag to get SQ. However, this doesn't give you the same answer as the above (the correct one). Why not?

Hope this made sense! 
First up, don't worry about using x. Just let RT = 1 unit long.
The problem is that SR does not equal 1 (or x in your case)

Because angle RQT = 45 degrees, QT = 1 unit
By Pythagoras,

In triangle SRQ, angle SQR = 30 degrees because angle PQR = 90 and angle PQS = 60.

Then
So 
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on August 14, 2014, 09:18:30 pm
Hey guys,

Not sure how to answer this, e.g. for 12 a)i I get 360 m, answer is 362m.
Isn't it just 2/2.4 = 300/x, or is this an oversimplification of the problem?
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on August 14, 2014, 09:22:31 pm
Hey guys,

Not sure how to answer this, e.g. for 12 a)i I get 360 m, answer is 362m.
Isn't it just 2/2.4 = 300/x, or is this an oversimplification of the problem?

I asked my teacher about this one, we did it a couple of times and in the end she told me it was an error from the book... but i did get 360m over and over again.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 15, 2014, 11:41:17 pm
Hey guys,

Not sure how to answer this, e.g. for 12 a)i I get 360 m, answer is 362m.
Isn't it just 2/2.4 = 300/x, or is this an oversimplification of the problem?

The view 300m from the window is 302m from where the girl is standing. If you use this distance, the answer is 362.
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on August 17, 2014, 03:22:49 pm
Hi guys,

If this is all the information that is given, would you be able to work out ST or not? Or do they have to give you angle SQT? Could you for example make a triangle PST and work it out from there?


Title: Re: VCE Further Maths Question Thread!
Post by: InsaneMDot on August 17, 2014, 04:55:04 pm
Hi guys,

If this is all the information that is given, would you be able to work out ST or not? Or do they have to give you angle SQT? Could you for example make a triangle PST and work it out from there?

I think since angles SQP and TQP are 90 degrees, SQT has to be 90 degrees?
So a pythagoras calculator should work.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on August 17, 2014, 05:04:30 pm
I think since angles SQP and TQP are 90 degrees, SQT has to be 90 degrees?
So a pythagoras calculator should work.

Nope - we're working three dimensions here, and so the angle SQT could be anything.

I've been racking my brain, and I can't find a plausible way to find the length ST using knowledge from high school geometry. You sure there's nothing else there?
Title: Re: VCE Further Maths Question Thread!
Post by: Zlatan on August 17, 2014, 05:12:34 pm
Nope - we're working three dimensions here, and so the angle SQT could be anything.


Could you explain how you know that pythag would not work in this situation ?? :)

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on August 17, 2014, 05:22:27 pm
Pythag only works for right handed triangles.

We don't have any of the angles for either the triangle SQT or the triangle SPT, so we cannot confirm that they're right-angled triangles, and so we cannot use Pythag. Using Pythagoras *could* work, but we don't have enough information about the situation to know if it will work.
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on August 17, 2014, 07:04:03 pm
It was just something I was wondering about :)
But could this problem we tackled with higher maths skills? Intrigued what the answer would be.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on August 17, 2014, 07:12:19 pm
I haven't tried it at all, but I suspect that you could use linear algebra.

If you turn each line-segment into a vector, then this layout as we see would exist in . From this, we can see that QP is the result of QS cross QT. If you define Q as the origin of our vector space, you can then set QS as (a, b, c), QT as (d, e, f) and QP as (0, 0, g), you could then use the varying vectors/line segments to find a, b, c, d, e, f and g, and then you would be able to find the angle SQT, which would mean you can use the cosine rule to find ST or simply find the length of the vector ST from basic vector addition.

Might not have enough information though - this is all conjecture, I haven't actually tried to evaluate it, nor do I have the time to try. :P
Title: Re: VCE Further Maths Question Thread!
Post by: engton1796 on August 17, 2014, 10:28:31 pm
I'd have to see the diagram to be absolutely sure, because if you have a regular hexagon, that's right.

Here.  My teacher,  as you can see,  didn't give me a mark.  The use of this 60 degree angle in other questions made my other questions correct but not this?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on August 17, 2014, 10:31:56 pm
I would interpret an interior angle to be the angle contained inside the hexagon at the point A, or the point B. For a regular hexagon, the interior angle is actually 120 degrees, as the sum of all interior angles is 720 degrees, and 720/6=120.
Title: Re: VCE Further Maths Question Thread!
Post by: SarahLoria on August 25, 2014, 05:54:53 pm
Hey guys, I have a question I am having some difficulties with in Business Maths. If anyone could help that would be great!

Question:
Joel invests $55,000 into an annuity at 7.8% interest compounding annually. After the interest has been added each year he plans to withdraw $6000 from this account to travel.

a) Using this formula A=PR^n - (Q(R^n-1))/R-1 (Reducing balance - annuities formula)
    State the Q and R values.

b) How many trips would Joel be able to take before the balance in the account falls below $39,000?

c) How many trips can Joel make from this investment?
Title: Re: VCE Further Maths Question Thread!
Post by: clidedescope on August 25, 2014, 08:26:48 pm
Hey guys. A question in my textbook about business mathematics has been bugging me and causing me quite a bit of stress. I've tried solving it the way the textbook says, but I keep on getting the wrong answer according to the book, so I figure it's either the example it used being wrong (I followed it exactly), or the answer itself. Two teachers have given me two different solutions too. Any insight would be great, because the SAC is getting closer and I am beginning to worry.

(http://i61.tinypic.com/2ljoxdu.png)
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 26, 2014, 10:57:35 pm
Quote

Question:
Joel invests $55,000 into an annuity at 7.8% interest compounding annually. After the interest has been added each year he plans to withdraw $6000 from this account to travel.

a) Using this formula A=PR^n - (Q(R^n-1))/R-1 (Reducing balance - annuities formula)
    State the Q and R values.

b) How many trips would Joel be able to take before the balance in the account falls below $39,000?

c) How many trips can Joel make from this investment?
Where did you get this question?

A couple of VCAA examiners reports have said that this annuities formula has not been in the syllabus for more than eight years. Forget the first part of the question and use TVM solver for any compound interest or annuity question.

Read the reports from VCAA as they can help you with other difficulties in business maths.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 26, 2014, 11:13:46 pm
Hey guys. A question in my textbook about business mathematics has been bugging me and causing me quite a bit of stress. I've tried solving it the way the textbook says, but I keep on getting the wrong answer according to the book, so I figure it's either the example it used being wrong (I followed it exactly), or the answer itself. Two teachers have given me two different solutions too. Any insight would be great, because the SAC is getting closer and I am beginning to worry.

(http://i61.tinypic.com/2ljoxdu.png)

It may happen in real life but I don't think there has been a further question like this. From what I can see, exam questions have all calculated and paid interest at the same time.

The $1241.37 balance on 19 May is an example of the reason you could get different answers. Is the interest for this day based on this balance or on the $445.82 balance that was there on this same day one second before the salary was deposited?

I don't think VCAA would risk having something this complicated on an exam.
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on August 28, 2014, 11:16:30 am
?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 29, 2014, 05:33:42 pm
for q8, answers A, but how did they get w is greater than or equal to 5b that doesnt make sense to me in this context.

i thought it would be 5w is greater than or equal to b??

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on August 29, 2014, 05:46:15 pm
For each loaf of brown bread made, you have at least five loaves of white bread made.

So take the number of loaves of brown bread (b), multiply it by five (5b). The number of loaves (w) is greater than equal to this number, so w >= 5b.

5w >= b would mean that for each loaf of white bread made, you have at most five loaves of brown bread.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 29, 2014, 05:48:50 pm
i know what you did but i dont get how that makes sense?

why do you multiply it by 5?

5w >= b would mean that at least 5 white loafs would be made for each brown?
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on August 29, 2014, 06:29:06 pm
i know what you did but i dont get how that makes sense?

why do you multiply it by 5?

5w >= b would mean that at least 5 white loafs would be made for each brown?

Look at it this way. In your example, 5w >= b, if you set w = 1, what are the possible values for b?

b, the number of brown loaves, can be equal to 5w = 5, or it can be smaller, so 4, 3, 2, 1, or 0. If w = 2, then b is less than or equal to 10.

So you can see that for each white loaf made there can be at most five brown loaves.

Now if w >= 5b, set b = 1. Then w >= 5. If b = 2, w >= 10. So for each brown loaf made, you must have at least five white loaves.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 29, 2014, 06:47:33 pm
ok that clears it up but with  w >= 5b if we sub 1 we get w>= 5 however it says atleast so wouldnt it need to be w <= 5 or am i thinking of it wrong?
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on August 29, 2014, 07:01:26 pm
ok that clears it up but with  w >= 5b if we sub 1 we get w>= 5 however it says atleast so wouldnt it need to be w <= 5 or am i thinking of it wrong?

>= means "at least". w >= 5b means w is at least five times b.

For every loaf of brown bread you must have at least five loaves of whit ebread.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 29, 2014, 09:51:40 pm
alright i get everything, i just dont get why you times the other letter by what your supposed (in my mind) to times the first letter by. if i have at least 5 loafs white bread for 1 brown wouldnt it be 5w >= b i just dont get why its 5b cause thats 5 brown?
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 29, 2014, 10:01:38 pm
There is an explanation for a similar problem on last year's VCAA Examination Report.

Look at their explanation of the solution to 4b in Graphs and relations at
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2013/FM2_examrep13.pdf
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on August 29, 2014, 10:18:48 pm
alright i get everything, i just dont get why you times the other letter by what your supposed (in my mind) to times the first letter by. if i have at least 5 loafs white bread for 1 brown wouldnt it be 5w >= b i just dont get why its 5b cause thats 5 brown?

It's not easy to get your head around the first time you see it. It might help to replace the inequality sign with an equals, and forget about 'w' and 'b'. Read out in words what each equation is telling you and it may be easier. Check out plato's link, it's the same idea.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 29, 2014, 11:07:04 pm
thanks for that guys, made it quite clear now!

Can anyone explain how/where the second table was source from (attached)


Question: At least two unpowered sites (y) were needed for every powered site (x).  (incase needed)
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on August 29, 2014, 11:10:44 pm
That is just saying that each value of (x,y) in that table satisfies the inequality .

For example, if x = 1 and y = 2, then y >= 2x

if x = 2 and y = 5, then y >= 2x

if x = 3 and y = 10, then y >= 2x

etc, etc.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 29, 2014, 11:43:26 pm
Thanks finally understood this. Last thing is, why is it >= and not <= eg y...2x in the ... Part?
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on August 29, 2014, 11:48:07 pm
In each line, the y-values (2, 5, 10) are greater than or equal to twice the x values (1, 2, 3).

We say when either or . In each case in that table, either y>2x or y = 2x. So we can say that .
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on August 30, 2014, 01:28:12 pm
thanks
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on September 06, 2014, 06:28:24 pm
How do you sketch a objective functions? for example C = 10x + 5y, with other inequalities such as x >= 0,, y >= 0,, x + y >= 8 ....

do we treat it as an equation to graph? or is it an inequality some how? (objective function)

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on September 06, 2014, 07:02:52 pm
How do you sketch a objective functions? for example C = 10x + 5y, with other inequalities such as x >= 0,, y >= 0,, x + y >= 8 ....

do we treat it as an equation to graph? or is it an inequality some how? (objective function)

thanks

The equation defines a plane contained somewhere in the x, y and C axis. Now, can you remember the name of the thing you draw graphs on with an x and y axis? If you guessed Cartesian plane, and then realised you have a problem, you're right.

So, the equation would actually involve colouring in the whole Cartesian plane in front of you. However, the other inequalities fix this - if we have those other constraints, then the objective function will only be defined in the intersection of those other constraints.
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on September 06, 2014, 10:43:08 pm
Hi guys, need help.
How can you tell when the two coincide for the first time using numbers?
The answer is at the 24th bar.
I used my CAS to calculate each sequence up to their 24th bar, and when looking at the two numbers from either sequence I didn't see any relevance.

Thanks in advance.
Title: Re: VCE Further Maths Question Thread!
Post by: Jono_CP on September 07, 2014, 12:52:33 am
Any Business Maths resources which will help me reach agonisingly close to a pass but with dignity for my SAC on Friday???????????????
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on September 07, 2014, 12:20:22 pm
Hi guys, need help.
How can you tell when the two coincide for the first time using numbers?
The answer is at the 24th bar.
I used my CAS to calculate each sequence up to their 24th bar, and when looking at the two numbers from either sequence I didn't see any relevance.

Thanks in advance.

Okay, so the question is a rather confusing one - let's just differentiate what each part means and change the symbols up a bit:

We'll let be the sequence we use for the crash cymbals, and be the sequence we use for the timpani rolls. Now, refers to the how much the instrument has already sounded - i.e., the th sound. Now, the value that and take on are the bar in which the sound occurs.

So, what we want is to find the first point when , and whatever value that is is our answer. Now, we note that must be a multiple of three, since we start with 3 and keep doubling it, whereas is an arithmetic sequence, and so could take any value. So, we will take , and keep calculating values until we have a multiple of three, and that should be our answer. We will then double check this against , since not every multiple of three will appear:




And so, we see that both sequences first take on the same value of 24, which is the bar that they first play together. The fact that they are at different positions only means that the cymbals have sounded more than the timpani at the time of this co-incision.
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on September 14, 2014, 02:26:35 pm
Number patterns question. Solutions provided.
Can someone explain to me how they got they answer b = 5?

Also, their solutions figure out a = 0.90 by doing another method.
Is it acceptable to use the information that 'a' is found by "reducing usage deficit by 10% compared with the prev month", therefore a = 1 - (10/100) = 0.90?

Thanks in advance.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on September 17, 2014, 12:15:40 am
Number patterns question. Solutions provided.
Can someone explain to me how they got they answer b = 5?

Also, their solutions figure out a = 0.90 by doing another method.
Is it acceptable to use the information that 'a' is found by "reducing usage deficit by 10% compared with the prev month", therefore a = 1 - (10/100) = 0.90?

Thanks in advance.
Is there more information prior to this question? There seems to something missing, aside from the possible cause of Elmo's sex change during the question.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on September 20, 2014, 06:22:55 pm
in a similar triangles question, if two lines are parallel what does this tell us and how can this tell us when solving the question?

Like with this question, i know how to do it, but being parallel does it help me in any way? does it mean i can/can't do a certain method ?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on September 20, 2014, 09:57:12 pm
in a similar triangles question, if two lines are parallel what does this tell us and how can this tell us when solving the question?

Like with this question, i know how to do it, but being parallel does it help me in any way? does it mean i can/can't do a certain method ?

Thanks

The lines being parallel confirm that the bottom two corners of both triangles are the same.
Without that being said, the angles could have easily been different and thus, not similar.

If you want me to be more detailed about this answer, just say so and I'll try to explain it better.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on September 20, 2014, 09:59:56 pm
thanks for that!! is their anything else you could add please?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on September 20, 2014, 10:40:38 pm
thanks for that!! is their anything else you could add please?

thanks

Recall that triangles have 180 degrees' worth of internal angles.
There is already one common angle at the top.
The final two angles are thus: 180 - top angle.
If they were not parallel, the four remaining angles could be anything, such as in the ways seen in the picture attached, and still be accurate. (I exaggerated some, by the way. I also apologise for my lack of ruler usage and decent to poor drawing skills.) You wouldn't be sure that they're similar, as they would no longer be guaranteed to be corresponding angles. (It won't satisfy similarity rules like SAS or AAA.)

Despite this, it is not always going to be the case; in other cases, it could be an alternate angle pair, co-interior pair or vertically opposite pair. You must memorise these for the exam.

Reminder that nearly all diagrams are not to scale and perhaps not even to proportion, so don't heavily rely on the diagram being accurate to the nth degree, unless necessary, such as in contour maps.

If you are unsure about corresponding angles or parallel lines and the related angles, reread your theory notes or textbook.
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on September 24, 2014, 04:39:42 pm
Is it possible to calculate outliers using this formula (where o is potential outliers)
o < mean - 2*standard deviations and o > mean + 2 standard deviations?
I saw this in an Insight paper and just wanted to confirm it :)
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on September 24, 2014, 10:30:38 pm
Is it possible to calculate outliers using this formula (where o is potential outliers)
o < mean - 2*standard deviations and o > mean + 2 standard deviations?
I saw this in an Insight paper and just wanted to confirm it :)

This is a method that I personally don't like for several reasons, and VCAA don't mention it in the study design (although, they don't talk much about outliers). However, it is listed in textbooks, and it is something that you certainly could do, so I'd just up to use the normal IQR method wherever possible, but then use the 2s method if given no other option.
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on September 26, 2014, 07:50:59 pm
Does anyone have a table or know where to find a good summary of the best way to display numerical and categorical data?

Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on October 03, 2014, 05:44:02 pm
Hi guys, apparently the answer is E… I don't get why?

Also does correspond mean the same thing as correlate in the context of explaining the relationship between x and y?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 03, 2014, 06:23:28 pm
Hi guys, apparently the answer is E… I don't get why?

Also does correspond mean the same thing as correlate in the context of explaining the relationship between x and y?

Well, they've given you a residual plot graph. For a linear correlation between to variables, 'x' and 'y', the residuals should be evenly spaced above and below the x-axis. That is, the linear regression line y=mx+c overestimates some 'y' values and also underestimates some 'y' values, leaving residuals.

In the graph they've given, the residuals aren't evenly spaced and there appears to be a pattern in the graph - almost like a quadratic. Because of this pattern, we can't confirm that there is a linear relationship between the variables.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 03, 2014, 07:09:14 pm
just a general question. when doing a two way frequency table do you do percentages down a column or across? what does each tell us, say the variables were males and females and overweight , underweight
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on October 03, 2014, 07:31:14 pm
Well, they've given you a residual plot graph. For a linear correlation between to variables, 'x' and 'y', the residuals should be evenly spaced above and below the x-axis. That is, the linear regression line y=mx+c overestimates some 'y' values and also underestimates some 'y' values, leaving residuals.

In the graph they've given, the residuals aren't evenly spaced and there appears to be a pattern in the graph - almost like a quadratic. Because of this pattern, we can't confirm that there is a linear relationship between the variables.

Oh man, so silly of me! Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 04, 2014, 03:38:26 pm
can someone help me with these. It's further but i dont find many people reply to questions on that, but this seems semi methods related. Say i've been given a question like this, what would be the steps to solve it?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 04, 2014, 03:45:39 pm
so the equation of the graph given is y = x^2/5

then do i go trial and error with the given graphs A-E? so the answer is D this is because when i sub the values in they give me the right y value. e.g. the equation is y = x^2/5 so if i look at D its, y= (5)^2/5 = 5 and the point is 5,5 which has been satisfied. is this the best approach?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 04, 2014, 03:51:16 pm
so the equation of the graph given is y = x^2/5

then do i go trial and error with the given graphs A-E? so the answer is D this is because when i sub the values in they give me the right y value. e.g. the equation is y = x^2/5 so if i look at D its, y= (5)^2/5 = 5 and the point is 5,5 which has been satisfied. is this the best approach?
Yep, that approach is fine. So convert the graph into an equation, then see which of the options fits the equation. Though, it's highly unlikely you'll get a question like this on a further exam.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 04, 2014, 04:16:55 pm
it was in the 2012 one http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2012/2012furmath1-w.pdf

Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 04, 2014, 04:20:12 pm
best to worst / easiest to hardest further exams we should be doing??

I get the general vibe heffernan is on par with VCAA, MAV a bit harder, Engage is under VCAA, kilbaha dont bother, NEAP only if you have time, Insight if you want etc?
Title: Re: VCE Further Maths Question Thread!
Post by: demand&supply on October 08, 2014, 06:37:42 pm
Can someone please tell me how to do this question??? (VCCA 2013 Exam 1, Module 2)

Question 8
There are four telecommunications towers in a city. The towers are called Grey Tower, Black Tower, Silver
Tower and White Tower.
Grey Tower is 10 km due west of Black Tower.
Silver Tower is 10 km from Grey Tower on a bearing of 300°.
White Tower is 10 km due north of Silver Tower.
Correct to the nearest degree, the bearing of Black Tower from White Tower is
A. 051°
B. 129°
C. 141°
D. 309°
E. 321°
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 08, 2014, 07:19:15 pm
Can someone please tell me how to do this question??? (VCCA 2013 Exam 1, Module 2)

Question 8
There are four telecommunications towers in a city. The towers are called Grey Tower, Black Tower, Silver
Tower and White Tower.
Grey Tower is 10 km due west of Black Tower.
Silver Tower is 10 km from Grey Tower on a bearing of 300°.
White Tower is 10 km due north of Silver Tower.
Correct to the nearest degree, the bearing of Black Tower from White Tower is
A. 051°
B. 129°
C. 141°
D. 309°
E. 321°

Here you go mate, hope it helps! :D

https://drive.google.com/folderview?id=0B4jDYm8MQMIFMFIxa2ZDdWhrY0U&usp=sharing
Title: Re: VCE Further Maths Question Thread!
Post by: demand&supply on October 08, 2014, 08:25:52 pm
oh i see now thanks  ;D
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on October 09, 2014, 09:06:35 pm
Hi guys
When a question asks you to comment on the shape, centre and spread of a distribution (3 marks), where would outliers fall under? Would you mention it under 'shape' or 'spread'?

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Sunshine98 on October 09, 2014, 09:21:43 pm
Hi guys
When a question asks you to comment on the shape, centre and spread of a distribution (3 marks), where would outliers fall under? Would you mention it under 'shape' or 'spread'?

Thanks :)

Shape
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on October 09, 2014, 09:29:37 pm
Hi guys,

This is a question from 2008 Insight paper (Matrices). My question is: is this right? Isn't the total profit calculated per store rather than per fruit pack? (Also there is an error for the profit for bulk, it is meant to say 52.80-33.00)

Title: Re: VCE Further Maths Question Thread!
Post by: demand&supply on October 09, 2014, 10:04:19 pm
Does anyone have solutions to the NEAP 2014 Trials (both papers)? My school didn't supply any...
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 10, 2014, 05:28:41 pm
Hi guys,

This is a question from 2008 Insight paper (Matrices). My question is: is this right? Isn't the total profit calculated per store rather than per fruit pack? (Also there is an error for the profit for bulk, it is meant to say 52.80-33.00)

hey mate, i've done insight 2008 and i can confirm that the solutions are incorrect - you can figure out pretty obviously why by looking at the actual multiplication they present in the solutions
if ive misunderstood your question  then im sorry, but the solutions are definatly wrong
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 11, 2014, 01:52:29 pm
does anyone know how to fill in the table and how they got those values??

heres all necessary info attached. where  b = 6,000
k = 30,000 and m=20
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 11, 2014, 01:53:01 pm
and
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on October 11, 2014, 01:58:48 pm
does anyone know how to fill in the table and how they got those values??

heres all necessary info attached. where  b = 6,000
k = 30,000 and m=20
You fill in the table by getting it to equal 5000 pairs of shoes. It says they need to make 5000 shoes per week, but they only make in the first 3, week(production) 1000 pairs,then they lack 4000 (deficit) as they don't reach the target of 5000. The second week, they only make 3000, they lack 2000 to get to target of 5000. For week 3, they make 3667, they lack 1333 to get to target of 5000. not really clear explanation but i hope you get it.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 11, 2014, 02:19:42 pm
oh yeah that makes sense, thats really easy then haha. i completely didnt even notice that!! thanks haha, that mark was the only one i lost and i was like wtf is this, haha all good now, cheers :)
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on October 11, 2014, 02:30:40 pm
oh yeah that makes sense, thats really easy then haha. i completely didnt even notice that!! thanks haha, that mark was the only one i lost and i was like wtf is this, haha all good now, cheers :)
Yeah just read the question carefully as it says "until capacity of 5000 shoes per week is reached".I have no idea how they got k and m as well.
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on October 11, 2014, 04:58:31 pm
Hi guys,

A bit confused with this question - Kilbaha 2014, Graphs & Relations.

I thought the answer is D because as the y-axis is in litres (not bath level) wouldn't the volume remain unchanged even after the child is placed in the bath? Kilbaha states that the answer is B as it will shoot up when the child is placed in, but we haven't actually added any extra water? :S

For the second attached qn, I interpreted "from 2005 and including 2005" as t=0 and hence 2020, as t=15. The answer requires t=16. Does anyone have tips on interpreting things like this, I seem to muck up dates and things like that :(

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Sunshine98 on October 11, 2014, 06:20:25 pm
Hi guys,

A bit confused with this question - Kilbaha 2014, Graphs & Relations.

I thought the answer is D because as the y-axis is in litres (not bath level) wouldn't the volume remain unchanged even after the child is placed in the bath? Kilbaha states that the answer is B as it will shoot up when the child is placed in, but we haven't actually added any extra water? :S

For the second attached qn, I interpreted "from 2005 and including 2005" as t=0 and hence 2020, as t=15. The answer requires t=16. Does anyone have tips on interpreting things like this, I seem to muck up dates and things like that :(

Thanks :)
For the first question, I think that putting aside the  volume rise that ur confused with , that the gradients of the first  line segments are incorrect for option d. This because the line segment doesn't become less steep(there is only a slight difference, which isn't really emphasised ) when the lady opens it 'partially' it still seems to be going at the same rate as the hot water which was 'fully' open . Thus ,putting aside  that volume rise option d , cannot be the right answer, so that only leaves you with b as that option has a distinctive change in the slope , from when the tap is open 'fully' and 'partially'.
I hope that helped. And ur right about the question being confusing because of  y axis having volume , not bath level .
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on October 11, 2014, 10:21:02 pm
Hi guys,

A bit confused with this question - Kilbaha 2014, Graphs & Relations.

I thought the answer is D because as the y-axis is in litres (not bath level) wouldn't the volume remain unchanged even after the child is placed in the bath? Kilbaha states that the answer is B as it will shoot up when the child is placed in, but we haven't actually added any extra water? :S

For the second attached qn, I interpreted "from 2005 and including 2005" as t=0 and hence 2020, as t=15. The answer requires t=16. Does anyone have tips on interpreting things like this, I seem to muck up dates and things like that :(

Thanks :)
For question 2, cliche but the only way to minimize that mistake is to read carefully. it says "including 2005" so you count 2005 as t=1. Just make sure when they say including, you count from there.
Title: Re: VCE Further Maths Question Thread!
Post by: engton1796 on October 13, 2014, 01:50:36 am
Matrices multiple-choice question.  Half an hour later...  still can't work it out.

If A =  |  1  4  1 |        and X =  |  p |        and AX = |  b  |         then,
          |  2  -3 0 |                      | q  |                        | 2a |
           | 1  0  0  |                      |  r |                        |  a  |

A.  r = b - a
B.  r = a - b
C.  r = -1
D.  r = 1
E.  r = a + b
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 13, 2014, 07:35:50 am
with q6, idk what they did, i got C personally

with q4 i got B, i dont know where the 4 x 6 came from? the question didnt make much sense to me there was something missing i think?
- i didnt do 1/2 lol
Title: Re: VCE Further Maths Question Thread!
Post by: Sunshine98 on October 13, 2014, 07:54:58 am
Matrices multiple-choice question.  Half an hour later...  still can't work it out.

If A =  |  1  4  1 |        and X =  |  p |        and AX = |  b  |         then,
          |  2  -3 0 |                      | q  |                        | 2a |
           | 1  0  0  |                      |  r |                        |  a  |

A.  r = b - a
B.  r = a - b
C.  r = -1
D.  r = 1
E.  r = a + b
The way I would go about the question is by using the simultaneous equation's techniques in matrices. Since u haven't actually said which is the answer I'm not sure if the way I did it is correct.
Firstly , my answer was option a, so if that's not the answer disregard my explanation.
So what I did is I acted as if my unknown were in matrix x (which it is ) , so the question itself does A*X=AX , to find X I did the inverse of A multiplied by the product matrix AX, so A -1*AX , this would give u the value of X .
Input in calculator and answer is the third value in the 3*1 matrix , which for me was b-1a which is equivalent to b-a ,meaning that the answer is a
 I hope that helps.
As I said , if my answer was incorrect plz disregard it , and tell me so we can figure out how to actually do the question.
Title: Re: VCE Further Maths Question Thread!
Post by: Sunshine98 on October 13, 2014, 08:04:06 am
with q6, idk what they did, i got C personally

with q4 i got B, i dont know where the 4 x 6 came from? the question didnt make much sense to me there was something missing i think?
- i didnt do 1/2 lol
Wow , q6 is baffling , I  got the same answer , I don't understand .
Which trial is it from ?
Also ,it reminds me of a VCAA question which was similar, however, the answer in the multiple choice were intervals so instead of having the exact value it said 'between 10 and 15' so I don't think they'll ask such a question, now.
But I am going to ask my teacher, u should too, its better safe than sorry.
Title: Re: VCE Further Maths Question Thread!
Post by: benobrien on October 13, 2014, 11:46:45 am
I dont think VCAA will ask for such specificity.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 13, 2014, 06:38:32 pm
Wow , q6 is baffling , I  got the same answer , I don't understand .
Which trial is it from ?
Also ,it reminds me of a VCAA question which was similar, however, the answer in the multiple choice were intervals so instead of having the exact value it said 'between 10 and 15' so I don't think they'll ask such a question, now.
But I am going to ask my teacher, u should too, its better safe than sorry.


tell me how it goes :) and what she/he says.

it was a mav one 2008/2009 off the top of my head
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 13, 2014, 07:12:35 pm
with q6, idk what they did, i got C personally

with q4 i got B, i dont know where the 4 x 6 came from? the question didnt make much sense to me there was something missing i think?
- i didnt do 1/2 lol

If you still are confused about Q4 I can help. Q6 looks a bit wonky and yeah, answers for that are pretty self-explanatory.

Let C = running total of perimeter or some shiznit like that.

Since we know the radius and the circumference of a circle: We get

Since the circumference in this question is 1/4 of a circle then So that covers the outside perimeter.

Now for the inside. We know on each side there is 12cm of wire. Bringing the total Now all is left is the inside line.

Using Pythagoras: 

Now adding the previous C:   

Thought I might aswell do it completely worked out for whatever reason. Your question was directed at the 6x4, so that comes from the perimeter on each side of the shape. It's actually 12x2 in my working but they left it as 6x4.


Edit: Does anyone have any 2014 further maths trial exams? My school doesn't give us any aside from like 2008-2012 and all of which I've completed. If anyone can throw a dog a bone I'd greatly appreciate it.
Title: Re: VCE Further Maths Question Thread!
Post by: engton1796 on October 13, 2014, 11:42:36 pm
The way I would go about the question is by using the simultaneous equation's techniques in matrices. Since u haven't actually said which is the answer I'm not sure if the way I did it is correct.
Firstly , my answer was option a, so if that's not the answer disregard my explanation.
So what I did is I acted as if my unknown were in matrix x (which it is ) , so the question itself does A*X=AX , to find X I did the inverse of A multiplied by the product matrix AX, so A -1*AX , this would give u the value of X .
Input in calculator and answer is the third value in the 3*1 matrix , which for me was b-1a which is equivalent to b-a ,meaning that the answer is a
 I hope that helps.
As I said , if my answer was incorrect plz disregard it , and tell me so we can figure out how to actually do the question.

Thanks for the reply.  Your answer was indeed correct as I found out today, so your explanation would be on the money. 
Just one more problem I had. 
When reading your explanation, you mentioned multiplying the inverse of A by the product matrix of AX.  I went ahead and multiplied the two, substituting "b" with a random 1, "a" with 2 and "2a" with 4.  I got 2, 0 and -1 for X.  How did you figure out the answer was A instead of A or D?  For A, b-a / 2-1 = 1  and then for D, a+b / -1+2 = 1, so I got the same answer.
Title: Re: VCE Further Maths Question Thread!
Post by: Sunshine98 on October 14, 2014, 05:11:33 pm
Thanks for the reply.  Your answer was indeed correct as I found out today, so your explanation would be on the money. 
Just one more problem I had. 
When reading your explanation, you mentioned multiplying the inverse of A by the product matrix of AX.  I went ahead and multiplied the two, substituting "b" with a random 1, "a" with 2 and "2a" with 4.  I got 2, 0 and -1 for X.  How did you figure out the answer was A instead of A or D?  For A, b-a / 2-1 = 1  and then for D, a+b / -1+2 = 1, so I got the same answer.
There is no need to  substitute numbers , in fact you simply place the matrix calculations  into ur CAS and it will give you the expression , which is option a .There is no need to over complicate the question (I should take my own advice some times, as I too have a tendency to do such  )
anyways I hope that helps  :)
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 17, 2014, 04:28:46 pm
why is this a straight line? (the cross section)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 17, 2014, 08:34:04 pm
why is this a straight line? (the cross section)

I would assume that this is because your intervals are almost completely equal themselves and the height is constantly increasing by 2 metres, so your cross section would be almost perfectly linear (almost, as it still deviates slightly from the bumps here and there).

However, I would require the assistance of others to clarify this, before saying that's correct. (i.e. Somebody please check this. I am not saying this is completely right, so don't take my word for it until it's said to be right by somebody else as well. )
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 17, 2014, 09:02:29 pm
How do you differentiate between options A and C?
The answer is A, but I chose C as the balance of the loan reaches near 0 assuming that it has been paid off?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 17, 2014, 09:20:05 pm
why is this a straight line? (the cross section)
Technically, the line shouldn't be a 'straight' line, as the gaps in between the 2m intervals are not the same in length.
However the assessor's report did say they accepted answers with little variance from a straight line. So assuming you didn't have substantial changes in height you were awarded full marks.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 17, 2014, 09:45:39 pm
ah yes thought so, i thought there wold be some slight rigid movements.

however i dont get the concept why it is a straight line at all?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 17, 2014, 10:00:10 pm
why have they said it has reached 60m? it in within the 50m contour line
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 17, 2014, 10:08:46 pm
why have they said it has reached 60m? it in within the 50m contour line
I presume that the information before the question would have stated Z to be 60m high.
If not, technically speaking the line could read 59.99m and not reach the 60m mark in which the interval of 60m would not be shown on the map.
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 17, 2014, 10:22:22 pm
How do you differentiate between options A and C?
The answer is A, but I chose C as the balance of the loan reaches near 0 assuming that it has been paid off?

Thanks

Edit; also question 3 from the VCAA 2010 exam 1 (MC)
I've never seen a question stated like that before, how exactly do we calculate the standard deviation?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 17, 2014, 10:49:51 pm
it doesnt mention anything along those lines?

so how do you know it reaches 59.99?
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 17, 2014, 10:59:33 pm
it doesnt mention anything along those lines?

so how do you know it reaches 59.99?
I don't.
However the height can reach anywhere up to 59.99, as long as it doesn't reach 60.
So if your cross section has the highest peak above 50m, but below 60m you'll be awarded marks.
It doesn't need to look exactly like the diagram as long as the interval heights are correct and the steepness of the lines are also correct.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 17, 2014, 11:30:22 pm
how did you know it has to be more then 50? the maximum height is 50 isnt it? so it has a somewhat turning point at 50m?

could you response to my earlier comments about why its a straight line? and not a contour line like a concave shape kinda, please/

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: IntelxD on October 18, 2014, 06:09:31 pm
How do you differentiate between options A and C?
The answer is A, but I chose C as the balance of the loan reaches near 0 assuming that it has been paid off?

Thanks

If Peter hadn't missed the fourth payment than you would have been correct to assume that the balance of the loan reaches 0 at the end of 8-month period. However, as he misses the fourth payment, the amount of interest he pays over the duration of the loan increases. Therefore he does not fully pay off the loan at the end of the 8-month period as he initially predicted.

Imagine 7% interest on $500 and 7% interest on $400. The interest on the sum of $500 is greater. This is what happens in this scenario. As he doesn't reduce the principal of the loan for a month, the interest accrued is greater than what it normally should be and therefore he doesn't fully repay the loan within the period he had initially planned. Thus the answer is A and not C.

If you need any further clarification please let me know.

Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 18, 2014, 08:58:55 pm
If Peter hadn't missed the fourth payment than you would have been correct to assume that the balance of the loan reaches 0 at the end of 8-month period. However, as he misses the fourth payment, the amount of interest he pays over the duration of the loan increases. Therefore he does not fully pay off the loan at the end of the 8-month period as he initially predicted.

Imagine 7% interest on $500 and 7% interest on $400. The interest on the sum of $500 is greater. This is what happens in this scenario. As he doesn't reduce the principal of the loan for a month, the interest accrued is greater than what it normally should be and therefore he doesn't fully repay the loan within the period he had initially planned. Thus the answer is A and not C.

If you need any further clarification please let me know.
Got it, makes sense.
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 18, 2014, 09:04:31 pm
What is the question asking us to do?
I'm finding the shortest distance (the pole will be perpendicular to the wall) at which it will hit when it falls.
By doing this I obtain answer E, however the answer is C.
So I think I may be misinterpreting the question.

Thanks in advance.

;also question 3 from the VCAA 2010 exam 1 (MC)
I've never seen a question stated like that before, how exactly do we calculate the standard deviation?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 18, 2014, 09:57:58 pm
What is the question asking us to do?
I'm finding the shortest distance (the pole will be perpendicular to the wall) at which it will hit when it falls.
By doing this I obtain answer E, however the answer is C.
So I think I may be misinterpreting the question.

Thanks in advance.

;also question 3 from the VCAA 2010 exam 1 (MC)
I've never seen a question stated like that before, how exactly do we calculate the standard deviation?

This one's a doosy - if you don't quite get what I'm saying, tell me and I'll re-explain with pictures.

You're right in that the maximum height will be then the poll falls the shortest distance. When we know the shortest this distance, we can use this to find the height via pythag.

So, the first thing you need to do is find this distance. The way I did this was to use the cosine-rule to find either angle made by the wall and the lines leading to the pole. With that, I used sin(x)=O/H to find the perpendicular distance between the pole and the wall. After that, I used c^2=a^2+b^2 to find the height, so in numbers:

Solve(5^2=6^2+4^2-2*4*6*cos(x),x), x=0.9734 (I will call this x for ease)
sin(x)=O/4 ---> 4*sin(x)=3.307 (hence O)
4^2-O^2=5.0625
sqrt(5.0625) = 2.25, closest answer is 2.3 (C)

For your standard deviation one, simply take approximate percentages from the mean and add them up. The mean (from the box-and-whisker plot) is 180. So, I add the two bars either side together, and get 40. I add the next two, and get 68. From this, I would assume that one standard deviation from the mean is 2 degrees. To confirm, I keep doing this until I hit 95% (or close to it, since guestimating the y-axis). If I hit 95% after another 2 degrees, then using the 68-95-99.7% rule, I would say that the standard deviation is 2 degrees.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 18, 2014, 10:02:58 pm
What is the question asking us to do?
I'm finding the shortest distance (the pole will be perpendicular to the wall) at which it will hit when it falls.
By doing this I obtain answer E, however the answer is C.
So I think I may be misinterpreting the question.

(http://i1282.photobucket.com/albums/a531/Ovazealous/furtherr_zpsf743d7cb.png)

First we need to find the red distance such that AT and MN are perpendicular which is the distance AT on the diagram.

We can do that if we can find out angle NMT first, then use angle NMT to find AT. Use the cos rule:



Now using angle NMT we want to find AT:



Now have a look at the blue triangle which is vertical (not on the floor), we can imagine the hypotenuse of this triangle to be the pole dropping, and we want ATP to form a triangle for the pole to fall and touch the wall. We'd get a triangle with hypotenuse 4m and on shorter end of 4.8379.

We can use pythagoras to find the height from A to P if P is lying on the wall.



Hence the answer is C.

Beaten by EulerFan! Just note that Euler's calculator is in radians - so don't freak out at x=0.9734.

Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 18, 2014, 10:46:26 pm
i think someone wanted question 8 of 2013 exam 1, so here it is

https://drive.google.com/folderview?id=0B4jDYm8MQMIFMFIxa2ZDdWhrY0U&usp=drive_web
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 18, 2014, 11:39:41 pm
can someone tell me their answer for d (ii). i got 83% however answer has 17%. If i do area of the insignia/top its 17% but it asks for whats not covered so 100-17 = 83%

A of insignia 16.6, which is needed in the calc
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 18, 2014, 11:51:13 pm
and technically speaking, shouldnt the answer is c be raised to the second power (the transition matrix)

answer has raised to 1
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 19, 2014, 04:27:07 pm
struggling with this question
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 19, 2014, 04:46:29 pm
struggling with this question

Looks like a further question so I'll give it a shot. I'm sure there's a way to do this considering one side is exactly twice the length of the other but I decided to do it the long way.

My thought process:
1.Find length AC using cosine rule
2. Use sine rule to find angle BAC
3. Since angle A is the same in both ABC and ABE we can then use it to deduce angle ABE (angle B)

1.  So using cos rule:

2.  Using sine rule:

                               

3. Due to triangle ABE being right angled we can say:

might not be right - I was expecting an integer due to the integer lengths of AB and BC. Did it another way and got Not sure if I have a rounding error somewhere but I'm confused now
Title: Re: VCE Further Maths Question Thread!
Post by: dyskontent on October 19, 2014, 04:50:04 pm
struggling with this question

Let Angle ABE =



Solve for
=52.656
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 20, 2014, 10:56:50 am
thanks guys. also had this question bth q3 and q4, idk if im doing something stupid but i dont know how the answers are C and D respectively
Title: Re: VCE Further Maths Question Thread!
Post by: BLACKCATT on October 20, 2014, 12:35:17 pm
Pretty sure that is a further question, and it's not in current study design anymore (from like year 2000? lol).
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 20, 2014, 01:24:46 pm
yeah i just found that out, thanks :)

btw can someone help me out with these sort of questions, i know how to find the equations, but if it asks us when t=4, for example, why cant we allocate 2 or 1.9999 to the first equation and then the remaining, either 2 or 2.01 etc to the second one, why do we sub the 4 into the second one? because there is different speeds (in this case) for the two equations, it was in the graphs and relations module if you wanted to know http://www.vcaa.vic.edu.au/Documents/exams/mathematics/03fmexam2.pdf

thanks

[Moderator Action] Split from Methods board and moved to Further. LiquidPaperz please keep your Further questions over here!
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 21, 2014, 02:21:31 pm
I believe this question was asked by someone else, but they never received an answer.
Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 21, 2014, 08:36:46 pm
@ The person who asked the question which Billion has posted:
I believe this question was asked by someone else, but they never received an answer.
Thanks.
The y-axis just seems to be mislabeled (perhaps due to the fickle nature of computers). Count the boxes (1 box = 1 delivery) and use that to find the median. Tedious, but that's about all I can suggest.

If you're still unsure...
Spoiler
The total adds up to 49 deliveries.
Median should be th term. (Please excuse that type of notation.) Therefore, 25th value.
The 25th value is in the 3rd category or the 10-15 one. This eliminates option E.
Note that this is a histogram, where the categories are continuous...
which means that we use the mid-point of this category. i.e. midpoint of 10 and 15 = 12.5
I believe the answer you are looking for is C.

Please correct me if I am wrong, as I can't recall everything at the moment and have left my reference book elsewhere.

Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 21, 2014, 08:46:24 pm
@ The person who asked the question which Billion has posted:The y-axis just seems to be mislabeled (perhaps due to the fickle nature of computers). Count the boxes (1 box = 1 delivery) and use that to find the median. Tedious, but that's about all I can suggest.

If you're still unsure...
Spoiler
The total adds up to 49 deliveries.
Median should be th term. (Please excuse that type of notation.) Therefore, 25th value.
The 25th value is in the 3rd category or the 10-15 one. This eliminates option E.
Note that this is a histogram, where the categories are continuous...
which means that we use the mid-point of this category. i.e. midpoint of 10 and 15 = 12.5
I believe the answer you are looking for is C.

Please correct me if I am wrong, as I can't recall everything at the moment and have left my reference book elsewhere.
Hey, thanks for taking the time to answer the question.
However I too, got C. But the solutions say B.
(I did this practice exam today, and I remember the question was asked before, but can't find out if someone figured it out)

The solutions are attached, it talks about stuff from units 1 and 2 (I didn't do those units). However it switches mid-sentence and says the mean is $11, would that be the problem?
Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 21, 2014, 08:49:10 pm
I'm fairly sure this question is on a page previous somewhere haha, someone answered it iirc? Anyhow I remember how to do yet I remember people condemning it for such specificity.

I believe the answer is B, if not please ignore this.

Total deliveries = 49 therefore median = 25th value.

If we count from the left hand side of the graph, the 25th value occurs in the 10-15 region. This is where people were saying it shouldn't require this type of working out;
 
So counting from the left hand side, we get to 23 before it enters the 10-15 region. This means there is 2 points of data left over before we find the 'true' median.

Therefore since there is 10 values in the 10-15 region we can (much to my disgust) say

which = 1. So we can conclude it is 1 dollar into the 10-15 region. Hence 11$.

edit: just restating that I seriously doubt vcaa would do a question like that - seems way too uhh, confusing?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 22, 2014, 07:17:55 pm
how do you know AM = AN do the 45 degree angles always mean this?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 22, 2014, 08:26:53 pm
how do you know AM = AN do the 45 degree angles always mean this?

Well yes - provided there is also a right angle. The triangle has a right angle and a 45 degree angle which means it is a right angled isosceles triangle - two sides of equal length and one hypotenuse. It might be worthwhile looking up the conditions for special types of triangles, it can be super useful in exams.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 22, 2014, 10:15:19 pm
is there anything specific youd have a link to Zealous?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Snorlax on October 24, 2014, 04:27:06 pm
Both these questions are from the VCAA 2013 E1 (Module 3)
Q7) I would like to know a method for questions like these.
(http://puu.sh/cokFY/0b75576691.png)

Q8) Don't understand it at all...
(http://puu.sh/cokKR/eb95b3b0e5.png)
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 24, 2014, 06:22:16 pm
Q7:  So we have to find the constant. We know it's already H versus 1/d^2.

If we consider that then we have to find the relationship between , where k is the unknown.

Soooo, they give us the point (0.44, 25.7). Remember if they give you information like this - you're usually going to have to use it.
In this case we can consider that 25.7 is unaltered (as there is no transformation on the y axis)
But with 0.44 it is ALREADY altered ()

Therefore to find the relationship it becomes

Subbing in values :                  

Now we have to put it back into the relationship. HOWEVER be careful as we have to put it into
Therefore answer is A. Not sure if I explained this adequately.
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 24, 2014, 11:53:28 pm
Hi, I got the correct answer, however the assessor's report says there was a "relatively routine computation"
I calculated the correct answer by extending the triangle. Is there another, more efficient method?
Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 25, 2014, 11:10:11 am
with the corner principle for graphs and relations, if they are all integers - say for a given context - is their ANY possible way to maximise the  objective function from points within. eg. if corners are 1,8    6,2    and    1,2     , is there any way it can be 4,3 for example?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 25, 2014, 11:12:36 am
Hi, I got the correct answer, however the assessor's report says there was a "relatively routine computation"
I calculated the correct answer by extending the triangle. Is there another, more efficient method?
Thanks.

Hey man, this is how i do it, i dont think there is another simple way

you like the colours haha? :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 25, 2014, 02:49:31 pm
with the corner principle for graphs and relations, if they are all integers - say for a given context - is their ANY possible way to maximise the  objective function from points within. eg. if corners are 1,8    6,2    and    1,2     , is there any way it can be 4,3 for example?

It depends on the situation. If they are on the same linear function, then it might and if not, it probably won't.
My notes say, and I quote this from my wonderful Further teacher, "If there are multiple minimal costs, there will be solutions on the same line that have the same minimal cost."
BUT... you must note the situation and the points on the line before you can go around using this information.
It's hard to explain without an example, so if you could supply one, that would be greatly appreciated.  :D
Title: Re: VCE Further Maths Question Thread!
Post by: Billion on October 25, 2014, 02:55:54 pm
Hey man, this is how i do it, i dont think there is another simple way

you like the colours haha? :)
Yeah, that's the same way I did.
I just thought the assessors report was hinting at another method.
Thanks, and yes, the colours are great!
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 25, 2014, 06:39:24 pm
Is it just me or did anyone find 2011 exam 2 quite hard? Geo and trig, matrices and graphs

I've been getting around 98/100 then got 91/100 and lost all marks on exam 2
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 25, 2014, 06:51:54 pm
Is it just me or did anyone find 2011 exam 2 quite hard? Geo and trig, matrices and graphs

I've been getting around 98/100 then got 91/100 and lost all marks on exam 2

Where did you lose your marks on it for? Perhaps you can separate it out and analyze your faults - make sure they never happen again. Looking over it I remember the lighthouse similar triangle question really was a bit tough.

Looking at the grade distributions. The A+ cutoff for 2011 exam 2 was ~84.2%, compared to an A+ cutoff of 85% last year. And then compared to 88% in 2012. So I guess you can conclude it was marginally harder than 2012 however compared to last years it was relatively the same. Maybe you did it in the wrong mindset haha, some exams I do I find I need to break and just get in the right head space.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 25, 2014, 08:13:30 pm
Where did you lose your marks on it for? Perhaps you can separate it out and analyze your faults - make sure they never happen again. Looking over it I remember the lighthouse similar triangle question really was a bit tough.

Looking at the grade distributions. The A+ cutoff for 2011 exam 2 was ~84.2%, compared to an A+ cutoff of 85% last year. And then compared to 88% in 2012. So I guess you can conclude it was marginally harder than 2012 however compared to last years it was relatively the same. Maybe you did it in the wrong mindset haha, some exams I do I find I need to break and just get in the right head space.

yeah i think that may have been it, ive just been doing heaps of exams lately, and 4th exam 2 of the day as well so i was fried haha.

would you be able to explain to me last question of graphs and relations http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

why they subtracted the equations and made it equal 3

cheers man
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 25, 2014, 08:15:35 pm
where do you get the info about A+ cutoffs etc
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 25, 2014, 08:30:00 pm
where do you get the info about A+ cutoffs etc

The grade distributions.
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 26, 2014, 09:00:41 am
i dont want to make another thread for this - but how many exams has everyone done ??
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 26, 2014, 09:01:39 am
i dont want to make another thread for this - but how many exams has everyone done ??

94 exams so far, yourself?
- ill be stopping exams tomorrow night so i can read over my notes and relax before the exam
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 26, 2014, 09:42:26 am
yeah i think that may have been it, ive just been doing heaps of exams lately, and 4th exam 2 of the day as well so i was fried haha.

would you be able to explain to me last question of graphs and relations http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

why they subtracted the equations and made it equal 3

cheers man

Okay so this question. They're asking you to find WHEN they're 3km apart. To do this we can create an equation to find the distance between them. We can do this by subtracting the equation of Michael's Journey from Katie's journey. It's kinda hard to really articulate without printing this out and doing it via hand but I chucked them into CAS and found I have to use Michael's first journey equation.

We can conclude that if we subtract the distance of Michael's first journey from Katie's journey we will have an equation for the distance apart.

So dissecting this you can see we are subtracting the distance of Michael's first journey from Katie's journey and then equating it to 3 (Trying to find when the distance between is equal to 3)


BUT All we have found is when they are first 3km apart - now we need to find when they are last 3km apart. Now if you were to draw Katie's journey onto the graph given you'd see it is approximately 3km away at t=3. So we know it is approximately at t=3. To confirm we are going to have to subtract Katie's journey from the journey of Michael (This time it is rather easy as he's not moving so d=10 is the equation).
 
Dissecting this you can see we subtracted Katie's journey from the journey of Michael at t=3. Solving this:


So we can conclude they were first 3km away at 1.625km, They continued to get closer and closer and finally were 3km seperated again at 3km. So for 3-1.625 their radio transmitters would work.



Not gonna lie - this was a wierd question, first time I've seen something like this in a further exam. I guess it shows that only 3% of people got full marks for question 2.


In response to the post above I have done about 25 or 26 or something exams. Planning on doing another 5-10 in the time between English and Further.
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 26, 2014, 10:41:30 am
94 exams so far, yourself?
- ill be stopping exams tomorrow night so i can read over my notes and relax before the exam

as of this post 101, should be 106 when all done (the joys of being a year 11)
i don't really think it was worth it tbh
if anyone is interested i can post a full list of the exams i have done as well as the ones which i thought were actually worth doing?
seeing that you've done 94 is making feel better about my self now that i know im not the only one.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 26, 2014, 10:50:29 am
as of this post 101, should be 106 when all done (the joys of being a year 11)
i don't really think it was worth it tbh
if anyone is interested i can post a full list of the exams i have done as well as the ones which i thought were actually worth doing?
seeing that you've done 94 is making feel better about my self now that i know im not the only one.


yeah would you be able to put a list together?

i honestly reckon i should've capped it to around 50 or so, but then again year 11 advantages hahah :)

btw just a quick question, if you look at the attached. Say this question asked, what is the total revenue of the 203 hot chocolates, would i sub 203 into the second revenue one, or sub 200 in the first and 3 in the second

also questions like, mark has a  fixed cost of 1000 and $10 for the first days, and $20 for every day after, find the equation that shows cost a after 10 days, how do we do this?

cheers
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 26, 2014, 10:58:55 am
yeah would you be able to put a list together?

i honestly reckon i should've capped it to around 50 or so, but then again year 11 advantages hahah :)

btw just a quick question, if you look at the attached. Say this question asked, what is the total revenue of the 203 hot chocolates, would i sub 203 into the second revenue one, or sub 200 in the first and 3 in the second

also questions like, mark has a  fixed cost of 1000 and $10 for the first days, and $20 for every day after, find the equation that shows cost a after 10 days, how do we do this?

cheers
theres no attachment, try again? or pop me an email with the attachment

https://docs.google.com/document/d/1pYDO-7qCchz4XUaQetMT0ga2X7kdhRJ8Tee2BaeGNeE/edit?usp=sharing
this is also the order i did them in
a little bit of information about how i went about it:
our school did networks, graphs and relations and matrices
i did number patterns in gma and quickly ditched networks after the sac
i dropped marks on 3/5 sacs (2 on bivariate, 4 on networks, 1 on matrices), but other people dropped more (networks lol), meaning i finished as number 1

i finished the course over easter, then finished it again in the winter holidays. i did 1 paper a day starting day 1 of term 3.
would i recommend doing the same? definitely not.  id only do vcaa, mav and select papers from neap if i was to do it again - personally i do not think i got any benefit from doing more than 50 papers (20 would have been suffice), and it doesnt look like i will finish with a 50 so it has been a bit of a waste)
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 26, 2014, 11:17:13 am
theres no attachment, try again? or pop me an email with the attachment

https://docs.google.com/document/d/1pYDO-7qCchz4XUaQetMT0ga2X7kdhRJ8Tee2BaeGNeE/edit?usp=sharing
this is also the order i did them in
a little bit of information about how i went about it:
our school did networks, graphs and relations and matrices
i did number patterns in gma and quickly ditched networks after the sac
i dropped marks on 3/5 sacs (2 on bivariate, 4 on networks, 1 on matrices), but other people dropped more (networks lol), meaning i finished as number 1

i finished the course over easter, then finished it again in the winter holidays. i did 1 paper a day starting day 1 of term 3.
would i recommend doing the same? definitely not.  id only do vcaa, mav and select papers from neap if i was to do it again.

Damnnnn. That's impressive. Both of you. If my school had offered further in year 11 I would've definitely done it. Feel so emasculated only having done like 25. I do maybe one every two or three days - I find them so damn repetitive ugh. Plus I've done all the commercial ones offered by my school - maybe excluding 1 or 2. But yeah I've done like 35 methods in total, 35 physics in total - coupled with like 15 singular essays. Oh the joys of year 12.

Also Liquid you didn't attach anything =/
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 26, 2014, 11:25:42 am
Damnnnn. That's impressive. Both of you. If my school had offered further in year 11 I would've definitely done it. Feel so emasculated only having done like 25. I do maybe one every two or three days - I find them so damn repetitive ugh. Plus I've done all the commercial ones offered by my school - maybe excluding 1 or 2. But yeah I've done like 35 methods in total, 35 physics in total - coupled with like 15 singular essays. Oh the joys of year 12.

Also Liquid you didn't attach anything =/

yup, no way it would have been possible in year 12
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 26, 2014, 03:07:26 pm
attached it sorry - forgot about it.

and anyone want to explain the last graphs and relations question, http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

i dont know why they minused the two equations and made it equal 3?
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on October 26, 2014, 03:22:32 pm
Both these questions are from the VCAA 2013 E1 (Module 3)

Q8) Don't understand it at all...
(http://puu.sh/cokKR/eb95b3b0e5.png)

First of all I have no idea how you guys do that cool looking math font, but hopefully I can show my working clear enough!

Personally I did this one by first finding the points, "M" and "N" which were (45,25) and (20,50). Then, I took out A and E because they had negatives.

Then, I moved down the list of options: B,C,D and subbed in their given values for "a" and "b", (so for example for B, I wrote Z=15x +15y) Then, I subbed in the points M, into that equation, to get an answer for Z, which ended up to equal 1050. Then I subbed in the points for N, into the equation to get 1050. Since both give the same answer, I concluded B is correct.

FOr safety I did the same process for C and D, just in case they also gave the same answer when the points were subbed in, but they didn't. :)
Let me know if I was clear or not, cause theres a high% chance it wasn't!
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 26, 2014, 03:50:33 pm
attached it sorry - forgot about it.

and anyone want to explain the last graphs and relations question, http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

i dont know why they minused the two equations and made it equal 3?

Okay so this question. They're asking you to find WHEN they're 3km apart. To do this we can create an equation to find the distance between them. We can do this by subtracting the equation of Michael's Journey from Katie's journey. It's kinda hard to really articulate without printing this out and doing it via hand but I chucked them into CAS and found I have to use Michael's first journey equation.

We can conclude that if we subtract the distance of Michael's first journey from Katie's journey we will have an equation for the distance apart.

So dissecting this you can see we are subtracting the distance of Michael's first journey from Katie's journey and then equating it to 3 (Trying to find when the distance between is equal to 3)


BUT All we have found is when they are first 3km apart - now we need to find when they are last 3km apart. Now if you were to draw Katie's journey onto the graph given you'd see it is approximately 3km away at t=3. So we know it is approximately at t=3. To confirm we are going to have to subtract Katie's journey from the journey of Michael (This time it is rather easy as he's not moving so d=10 is the equation).
 
Dissecting this you can see we subtracted Katie's journey from the journey of Michael at t=3. Solving this:


So we can conclude they were first 3km away at 1.625km, They continued to get closer and closer and finally were 3km seperated again at 3km. So for 3-1.625 their radio transmitters would work.



Not gonna lie - this was a wierd question, first time I've seen something like this in a further exam. I guess it shows that only 3% of people got full marks for question 2.




Did it on last page.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 26, 2014, 04:11:40 pm
thanks for that.

However i dont under the process of minusing both equations, ive never come across this before, as ive only had to make them equal each other or simultaneously solve.What does minusing the equations tell us? and what does minusing michael - kate and kate - michael represent?

and making it equal to 3, would this tell us when y is equal to 3?
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 26, 2014, 04:44:16 pm
you are effectively finding at what times they are 3 km apart
so the difference in distance = 3
that is to say: distance of m minus distance of k = 3
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on October 26, 2014, 10:45:47 pm
When using random samples in exam 2, do we write CAS speak to show the working out? As in first I'd allocate each sample a number, then could I say
Menu, Prob …..?

Also, how strict are they with marking wrong working if the answer is correct, for example in last years exam for Question 4b, I thought the points were (3,13.6) and (13,21.7), and then used gradient formula to get 0.8. However the exam report read the graph's second point as (13,21.8). Since when rounded to 1dp, the answers are the same, would I get the marK?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 26, 2014, 10:57:59 pm
When using random samples in exam 2, do we write CAS speak to show the working out? As in first I'd allocate each sample a number, then could I say
Menu, Prob …..?

NEVER use "CAS speak". Ever. Not once. Don't even do it as a last resort. Don't do it in practice even though you'll do better in the exam. Just don't. Just write that you've used your CAS as an intermediate between steps. Or, write full working out, but then just use your CAS to evaluate it.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 27, 2014, 07:19:41 pm
why is abd and dcb not similar?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 27, 2014, 08:25:22 pm
why is abd and dcb not similar?
Only one angle is the same - you have no proof they both have another angle the same, so you cannot say that they are similar.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 27, 2014, 10:05:12 pm
ok that makes sense.

just a few more questions in the course
1) if its not a transition matrix what makes it different to a transition matrix, other then columns adding to 1? can it be raised to a power for steady state? etc..
2) what essentially does Sx mean other then the spread around mean, is there anything too add? how can it be affected?
3) a quick question, if you look at the attached. Say this question asked, what is the total revenue of the 203 hot chocolates, would i sub 203 into the second revenue one, or sub 200 in the first and 3 in the second
4) also questions like, mark has a  fixed cost of 1000 and $10 for the first days, and $20 for every day after, find the equation that shows cost a after 10 days, how do we do this?


Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 28, 2014, 05:36:17 pm
ok that makes sense.

just a few more questions in the course
1) if its not a transition matrix what makes it different to a transition matrix, other then columns adding to 1? can it be raised to a power for steady state? etc..
2) what essentially does Sx mean other then the spread around mean, is there anything too add? how can it be affected?
3) a quick question, if you look at the attached. Say this question asked, what is the total revenue of the 203 hot chocolates, would i sub 203 into the second revenue one, or sub 200 in the first and 3 in the second
4) also questions like, mark has a  fixed cost of 1000 and $10 for the first days, and $20 for every day after, find the equation that shows cost a after 10 days, how do we do this?

re: 3
200 into first equation then every one after 200 (so the remaining 3) sub into second equation
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 28, 2014, 06:40:02 pm
Are you sure, because I've seen some answers that say otherwise, and some that say what you say, so conflicting views
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 28, 2014, 07:52:20 pm
and how does this work??

how can you square it?
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 28, 2014, 08:36:52 pm
and also this. why dont we use m = y2-y1/x2-x1 this seem to work all the time?

Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 28, 2014, 08:37:16 pm
and how does this work??

how can you square it?

First line is from the fact that they're similar triangles (I'd need to see the triangles to explain why), the second line is just a cross multiplication of the first line.

and also this. why dont we use m = y2-y1/x2-x1 this seem to work all the time?

They are doing this - just in different words.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 28, 2014, 08:59:34 pm
heres the triangles, do you mind shoing me how they can be flipped etc so they are in same positions

with the spped/ d/t
i use the m = y2 ....

0,0   and    15,6    gets me a gradient of 6/15 = 0.4, not 24?

edit: dw figured out the 24km/hr part didnt see axis had min
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 28, 2014, 09:15:58 pm
heres the triangles, do you mind shoing me how they can be flipped etc so they are in same positions

with the spped/ d/t
i use the m = y2 ....

0,0   and    15,6    gets me a gradient of 6/15 = 0.4, not 24?

edit: dw figured out the 24km/hr part didnt see axis had min

They are similar because the angle BDC is present in both triangles. Then, from the initial information, angle CBD=BAC. So, both triangles have two angles the same, and must be similar. You can get them in the same position by flipping the triangle BCD down (that is, the edge BD in triangle BCD is the same edge as AD in triangle ABD).

For the next question, you've got the wrong units - the gradient of the graph is in km/min, however the question wants the units in km/hour. You need to change the 15 from minutes to hours.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 28, 2014, 09:52:57 pm
thanks euler!

just a question, could you please clarify this again

First line is from the fact that they're similar triangles (I'd need to see the triangles to explain why), the second line is just a cross multiplication of the first line.


thanks
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 28, 2014, 09:57:36 pm
thanks euler!

just a question, could you please clarify this again

thanks

Because the triangles are similar, . Redraw the triangle BCD (after flipping it) next to triangle ABD to see why.

Then, multiply the denominators you, and you get:
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 29, 2014, 04:03:31 pm
can someone provide me with the reasons we smooth data? reduce all variation? seasonal only? etcc
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 29, 2014, 04:16:39 pm
can someone provide me with the reasons we smooth data? reduce all variation? seasonal only? etcc

We smooth data so we can easily see the trends that would otherwise be hidden.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 29, 2014, 05:58:59 pm
can someone give me a constraint for this and tell me why its that.

i originally got 3g is less then or equal to p, this is wrong
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 29, 2014, 06:02:17 pm
can someone give me a constraint for this and tell me why its that.

i originally got 3g is less then or equal to p, this is wrong

??? I think you forgot to attach a link as to what you are referring to.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 29, 2014, 06:16:41 pm
yeap sorry!!
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 29, 2014, 06:37:13 pm
yeap sorry!!

So, what we have here is that we don't want some number (x) of the glassware (g) to not exceed some number (y) of the plastic (p). So, our inequality is:

x*g ? y*p

So, the first part is finding x and y. It says in the question that the number of units of g must not exceed 3 times the number of units of p. In a crude sense, this means we have:



Dividing by "number of units", we have g ? 3p

Now, we just need to pick up our inequality from the words. Our gs must not EXCEED the 3ps, so g cannot be greater than 3p. This gives us:



Of course, writing like this is something VCAA doesn't like - so we take the opposite of a strict non-inequality, and get the opposite non-strict inequality.



On opposite symbols:

Strict ----> non-strict (and vice versa)
Less than -----> greater than (and vice versa)
Title: Re: VCE Further Maths Question Thread!
Post by: ETTH96 on October 29, 2014, 08:43:10 pm
Help please!
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on October 29, 2014, 08:46:07 pm
Could someone help with Q3? I got E, from tan^-1(226/210)
Title: Re: VCE Further Maths Question Thread!
Post by: engton1796 on October 29, 2014, 08:49:27 pm
Got a Multiple Choice question I couldn't figure out.

A regular pentagon, ABCDE, has all sides equal to 8cm.  The length of EC is closest to:  (The triangle is at the top half of the pentagon, thus forming a triangle with 8cm on the left and right upper sides)

A: 13cm
B: 16cm
C: 17cm
D: 22cm
E: 26cm

I got the right answer but later figured out I mistakenly used Pythagoras, so now idk.  Thanks heaps  :)
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 29, 2014, 08:49:57 pm
Help please!

Seasonal Index = Value for quarter, so the rainfall in Spring / Quarterly average, so addition of the rainfall for each season divided by four.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 29, 2014, 08:59:00 pm
Could someone help with Q3? I got E, from tan^-1(226/210)

Angle of depression = angle of elevation (Z-rule), so just find the angle of elevation (it's intuitively easier to find).

However, note that Jill's angle of elevation is the same as Jack's - so, on the off-chance you got the last question wrong, let's use Jill's information:



So, the answer is E.


Got a Multiple Choice question I couldn't figure out.

A regular pentagon, ABCDE, has all sides equal to 8cm.  The length of EC is closest to:  (The triangle is at the top half of the pentagon, thus forming a triangle with 8cm on the left and right upper sides)

A: 13cm
B: 16cm
C: 17cm
D: 22cm
E: 26cm

I got the right answer but later figured out I mistakenly used Pythagoras, so now idk.  Thanks heaps  :)

We have a regular pentagon with all sides equal - so, all angles must be the same. Since the angles in a pentagon all add up to 540 degrees, we then divide by 5 to find that each angle is 108 degrees.

Now that we know that, we can use the cosine rule (as we have the length of two sides and the angle inbetween). This gives us a length of 12.9 cm, which approximates to A.
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 29, 2014, 09:08:48 pm
Spoiler
Help please!

Seasonal index = Actual value/Yearly mean.  Yearly mean =

Thus seasonal index =


Could someone help with Q3? I got E, from tan^-1(226/210)


That seems correct to me. Am I missing something?

Got a Multiple Choice question I couldn't figure out.

A regular pentagon, ABCDE, has all sides equal to 8cm.  The length of EC is closest to:  (The triangle is at the top half of the pentagon, thus forming a triangle with 8cm on the left and right upper sides)


I got the right answer but later figured out I mistakenly used Pythagoras, so now idk.  Thanks heaps  :)

So this is what I did; disregard if the answer is not A :D

Looking at it we have an isosceles triangle with 8cm as the identical sides. So therefore if we can deduce the included angle then we can use the cosine rule to deduce the opposite side length.
 
Considering the sum of angles in a pentagon is 540 then we can do;  Concluding that each angle is 108 degrees within the pentagon

Therefore we now have a triangle with two side lengths of 8, and an included angle of 108. Time to apply cosine rule:


Dam looks like everyone beat me to them all. Whatever I got good practice out of it.
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on October 29, 2014, 09:13:31 pm
Thanks guys! I got one more if you guys wanted to help, its from the engage free exam, I tried to use the gradient to find b and c, which gave me answer D in the end, but that doesn't work because c-b=5.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 29, 2014, 09:19:13 pm
Thanks guys! I got one more if you guys wanted to help, its from the engage free exam, I tried to use the gradient to find b and c, which gave me answer D in the end, but that doesn't work because c-b=5.

IMMEDIATELY dump c and d, since the subtraction won't give 5.

So, we're stuck with a or b. Well, distance is the same at times b and c, so equate and solve:


So, the answer is a.

Dam looks like everyone beat me to them all. Whatever I got good practice out of it.
This is exactly the attitude to have! ;)
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on October 29, 2014, 09:26:15 pm
IMMEDIATELY dump c and d, since the subtraction won't give 5.

So, we're stuck with a or b. Well, distance is the same at times b and c, so equate and solve:


So, the answer is a.


Thank you!! copy and pasted right in my ref book!
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 29, 2014, 09:35:34 pm
Thank you!! copy and pasted right in my ref book!

Wait...you still have room in your reference book?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 29, 2014, 09:36:46 pm
Wait...you still have room in your reference book?

I had over 100 blank pages in mine when I walked into both my methods and specialist exams - and by that, I do mean 100 pages each. :P
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on October 29, 2014, 09:41:01 pm
Wait...you still have room in your reference book?

Two books stuck together!
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 29, 2014, 09:56:52 pm
I had over 100 blank pages in mine when I walked into both my methods and specialist exams - and by that, I do mean 100 pages each. :P

I'm similar to this. Currently only have ~24 pages in my further, and about ~35 in my methods reference book. Don't even know what else to put in 'em, probably more beneficial if I just spam practice exams.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 29, 2014, 11:07:24 pm
my bound books about 600 pages, about 3-4 books together stuck by gaffa / electrical tape lol
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 30, 2014, 08:20:06 am
my bound books about 600 pages, about 3-4 books together stuck by gaffa / electrical tape lol

Jeeez. Wouldn't expect anything less from you though lol. How's everyone preparing? I'm gonna do recent VCAA exam 1s today and then read over assessor reports tomorrow. My best subject is coming to an end :(
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 08:38:27 am
Yeah similar however everything today, I don't want to touch further tomorrow

Do you know what we have to write in for exam 1 and 2??
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 10:11:54 am
can someone help me with part c?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 01:16:02 pm
and is there any quick way of doing these questions?
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on October 30, 2014, 01:22:22 pm
Hi guys

With univariate statistics on the CAS calculator we are able to construct a boxplot by typing the numbers into the List & Spreadsheets under some variable e.g. 'a' and going to Graph and Statistics. I was just wondering if it was possible/how can we construct a box plot if they give us the univariate statistics and frequency so we now have columns 'a' and 'b.'

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: darklight on October 30, 2014, 02:53:30 pm
Another question - 2012 MAV Exam 1

I thought that the way to work out these question was similar to 2011 VCAA - so you do (for Labour for example) 0.2 + 0.2 = 0.4 * 300 (initial) to work out how many people change and then do the same thing for the 2 others, giving you D not C…
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 30, 2014, 03:42:39 pm
Another question - 2012 MAV Exam 1

I thought that the way to work out these question was similar to 2011 VCAA - so you do (for Labour for example) 0.2 + 0.2 = 0.4 * 300 (initial) to work out how many people change and then do the same thing for the 2 others, giving you D not C…

I used my calculator to work out the number of votes for each party on election day.

Next: 300-210 = 90
          250-200 = 50
          140-100 = 40

Next: 90+50+40 = 180

Therefore 180 votes were changed by election day, so the answer is C.
         
Title: Re: VCE Further Maths Question Thread!
Post by: Saikyo on October 30, 2014, 04:33:53 pm
Can anyone explain to me Question 8 Networks section on VCAA 2013 Exam 1? I don't understand the assessor's report explanation.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 06:24:30 pm
i think i have asked this before. But if it is not a transition matrix what makes it different to a transition matrix other then columns adding to 1. is their still a steady state solution with a non transition matrix? what else is not a feature..

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Sunshine98 on October 30, 2014, 06:34:58 pm
i think i have asked this before. But if it is not a transition matrix what makes it different to a transition matrix other then columns adding to 1. is their still a steady state solution with a non transition matrix? what else is not a feature..

thanks
I don't entirely understand your question but a transition matrix must be :
1- square
2- add up to one , as u mentioned
3- include proportions( as in it has to be in decimals, which must equal to one  )
4- it should be able to be used in predictions
I think that's it , u probably already know all this , but nonetheless I hope that I helped
Oh and to the second part of ur question , no I don't think any other matrix will give a steady state - it only makes sense that way , well at least I was never told so .
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 30, 2014, 06:48:17 pm
Another question - 2012 MAV Exam 1

I thought that the way to work out these question was similar to 2011 VCAA - so you do (for Labour for example) 0.2 + 0.2 = 0.4 * 300 (initial) to work out how many people change and then do the same thing for the 2 others, giving you D not C…

hey mate, ive done this exam and i had the same answer as you
id say the solutions are wrong
it comes down to how you interpret what a vote changing is. you and i interpreted as someone switching to another party
i think they think of it like a swing??
off the top of my head i cant think of a time vcaa has asked this type of question but ill have a looksee

tldr you are correct solutions are wrong
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 06:52:49 pm
well if you look in the matrices section of this exam http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath2-w.pdf

they give a matrix G, not a transition matrix, but it seems to have a steady state (in response to part D), hows this possible?
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 30, 2014, 07:07:19 pm
well if you look in the matrices section of this exam http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath2-w.pdf

they give a matrix G, not a transition matrix, but it seems to have a steady state (in response to part D), hows this possible?

It is still a transition matrix. Since the columns don't add up to 1 it means the total amount of people attending will increase or decrease. Whereas if it were 1 then the total amount of people would remain the same.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 07:28:51 pm
dont transition matrix columns have to equal 1?

or what ive learnt all year, the day before the exam gone through the window?
Title: Re: VCE Further Maths Question Thread!
Post by: Sunshine98 on October 30, 2014, 07:53:12 pm
well if you look in the matrices section of this exam http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010furmath2-w.pdf

they give a matrix G, not a transition matrix, but it seems to have a steady state (in response to part D), hows this possible?
Whoops never realised that , so now I'm confused ??????
I don't understand myanacondadont , what do u mean by increase and decrease dosent it always increase and decrease regardless ?
Title: Re: VCE Further Maths Question Thread!
Post by: vididid on October 30, 2014, 08:18:24 pm
hey guys,

so I've heard if you square the one step dominance you get either the two step or the final dominance? is this true?
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 30, 2014, 08:45:58 pm
hey guys,

so I've heard if you square the one step dominance you get either the two step or the final dominance? is this true?

1 step to the power n gives n step dominance
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 09:56:34 pm
just a quick year 7 question. If a question says this is in $'000s, does this mean something that is 17.3, is in fact 173 000 ? or 173 00 ? just a bit unsure. And how are we meant to enter it and express is, in the 173000 form or 17.3 form ? this was on one of the vcaa exams in the past so just clearing up on it.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 30, 2014, 10:02:21 pm
just a quick year 7 question. If a question says this is in $'000s, does this mean something that is 17.3, is in fact 173 000 ? or 173 00 ? just a bit unsure. And how are we meant to enter it and express is, in the 173000 form or 17.3 form ? this was on one of the vcaa exams in the past so just clearing up on it.
Well, the question would be saying that the numbers given are in thousands, so 17.3 would correspond to 17,300.

I think.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 30, 2014, 10:11:10 pm
is 000 thousands or hundreds? 0 units, 00 tens, 000 hundreds?
Title: Re: VCE Further Maths Question Thread!
Post by: rpcod on October 30, 2014, 10:23:52 pm
I just wanted to know, do I have to do the same modules on both further exams??
or must i complete the same set of modules on both exams.
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on October 30, 2014, 10:44:58 pm
I just wanted to know, do I have to do the same modules on both further exams??
or must i complete the same set of modules on both exams.

As far as I know, no you do not need to complete the same modules for both exams, but I would not reccomend spending time deciding which modules to compelte during the reading period, that will not be a very effective use of your time. But, to answer your question, as long as you complete the compulsory Core component, whichever three modules you then choose to complete is up to you, keeping in mind that for exam 1 you only have enough space to put answers for three modules (plus core) on the answer sheet and in exam 2 they will only mark the core section plus the first three modules you have completed, so there is no point doing any more than 3.
Title: Re: VCE Further Maths Question Thread!
Post by: redcracker on October 31, 2014, 08:42:03 am
I used my calculator to work out the number of votes for each party on election day.

Next: 300-210 = 90
          250-200 = 50
          140-100 = 40

Next: 90+50+40 = 180

Therefore 180 votes were changed by election day, so the answer is C.
         

this is wrong
Title: Re: VCE Further Maths Question Thread!
Post by: cliffebe on October 31, 2014, 09:12:47 am
Does any know if you can use your calculator during reading time?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 31, 2014, 09:18:36 am
Does any know if you can use your calculator during reading time?
You cannot. This should also be highlighted before the exam begins.
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 31, 2014, 09:51:14 am
How's everyone going? It's almost here - I just finished my last Further practice exam 1 EVER, aside from the real thing (duh).

I wrote down some things I usually forget to do when doing practice exams at home because it's not exam conditions but here they are (I wrote them down in my reference book and hope to do all for every question today).



Good luck everyone! Remember we have 2 exams, you can make up your mistakes on exam 1 by doing super well on exam 2!

Title: Re: VCE Further Maths Question Thread!
Post by: brenden on October 31, 2014, 10:03:35 am
Goes with out saying - someone remember to come home and scan a copy of their answer book (your highlighted answers don't matter)... That way a few of us can confirm the answers for all of the modules and get an answer set up :).

Title: Re: VCE Further Maths Question Thread!
Post by: vididid on October 31, 2014, 10:06:00 am
is core weighted more or are they all weighted up equally?
Title: Re: VCE Further Maths Question Thread!
Post by: benobrien on October 31, 2014, 10:16:18 am
Goes with out saying - someone remember to come home and scan a copy of their answer book (your highlighted answers don't matter)... That way a few of us can confirm the answers for all of the modules and get an answer set up :).

So nervous and excited at the same time to basically know how I went when I get home...  :o
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 31, 2014, 10:43:01 am
are we allowed to look at our summary book during reading time?
Title: Re: VCE Further Maths Question Thread!
Post by: vididid on October 31, 2014, 10:48:26 am
are we allowed to look at our summary book during reading time?

yes, just don't touch a pen or your calculator
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 31, 2014, 10:51:43 am
alright thanks. quick question, i know how to solve this by finding all the equations, vertex points etc, but ive been seeing you can just use the gradient, can someone tell me how this is done?

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: cliffebe on October 31, 2014, 11:20:13 am
Sorry, stupid question but I just want to be sure

are we allowed to take in 2 calculators?
Title: Re: VCE Further Maths Question Thread!
Post by: cwiddicombe on October 31, 2014, 11:21:26 am
Sorry, stupid question but I just want to be sure

are we allowed to take in 2 calculators?

Pretty sure you can take in a graphics (CAS) and a scientific calculator.
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 31, 2014, 11:54:10 am
alright thanks. quick question, i know how to solve this by finding all the equations, vertex points etc, but ive been seeing you can just use the gradient, can someone tell me how this is done?

thanks
I only solve them through finding vertices then seeing which fits. I don't think you can use gradient?? Well if you can, stick to what you know! good luck mate!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 31, 2014, 11:58:07 am
Sorry, stupid question but I just want to be sure

are we allowed to take in 2 calculators?
Pretty sure you can take in a graphics (CAS) and a scientific calculator.

This is true, but reminder that this will take up more space on your table.
I have taken this excerpt from VCAA's website (http://www.vcaa.vic.edu.au/Pages/vce/exams/authorisedmaterials.aspx):
"Further Mathematics Examination 1:
-one approved graphics or CAS calculator or CAS software and one scientific calculator
-one bound reference that may be annotated

Further Mathematics Examination 2:
-one approved graphics or CAS calculator or CAS software and one scientific calculator
-one bound reference that may be annotated"
Title: Re: VCE Further Maths Question Thread!
Post by: cliffebe on October 31, 2014, 12:07:14 pm
This is true, but reminder that this will take up more space on your table.
I have taken this excerpt from VCAA's website (http://www.vcaa.vic.edu.au/Pages/vce/exams/authorisedmaterials.aspx):
"Further Mathematics Examination 1:
-one approved graphics or CAS calculator or CAS software and one scientific calculator
-one bound reference that may be annotated

Further Mathematics Examination 2:
-one approved graphics or CAS calculator or CAS software and one scientific calculator
-one bound reference that may be annotated"

So does that mean one or the other?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 31, 2014, 12:09:04 pm
So does that mean one or the other?

No, but I can see why you'd be confused. You're allowed to bring one of the first three as well as one scientific calculator.
Title: Re: VCE Further Maths Question Thread!
Post by: abcdqdxD on October 31, 2014, 01:30:20 pm
you can bring both the CAS and a scientific calculator
Title: Re: VCE Further Maths Question Thread!
Post by: rpcod on October 31, 2014, 05:46:37 pm
In the exam can u choose any three modules plus core, or are they set school by school on which modules you must complete?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 31, 2014, 05:54:33 pm
Woo! Exam 1 down, Exam 2 to go. I won't say much more at the moment, in case it's too raw for you all.
(I have a copy of the exam, but we'll discuss this via message.)

In the exam can u choose any three modules plus core, or are they set school by school on which modules you must complete?

Aside from core, which is compulsory for every Further student, it doesn't matter which 3 modules you choose, as long as you complete four sections by the end e.g. core and Modules 1, 2 and 6.
Furthermore, the three that you choose don't necessarily have to select the three modules your school did.
That is, you may choose to complete core and the first three modules, rather than doing modules 1, 2 and 4, the ones your school did.
Title: Re: VCE Further Maths Question Thread!
Post by: rpcod on October 31, 2014, 06:02:46 pm
Is it possible for anyone to upload the exam with suggested answers?

Although I should give it time, I know we're all eagerly worried about the exam...  :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 31, 2014, 06:27:25 pm
Is it possible for anyone to upload the exam with suggested answers?

Although I should give it time, I know we're all eagerly worried about the exam...  :)

Haha... I'm sorry, but I can only tell you what I got.
I can also scan my annotations in the exam, if you would like, but we'd have to discuss this elsewhere.
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 31, 2014, 07:15:22 pm
for core, the categorical data question q4, is the answer 3 or 4?
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 31, 2014, 07:16:45 pm
for core, the categorical data question q4, is the answer 3 or 4?

What were the variables again?
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on October 31, 2014, 07:17:06 pm
for core, the categorical data question q4, is the answer 3 or 4?
3. Sex, type of car and postcode.
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 31, 2014, 07:18:36 pm
3. Sex, type of car and postcode.

Shit, i said two, didn't know Postcode was categorical.
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on October 31, 2014, 07:19:54 pm
Shit, i said two, didn't know Postcode was categorical.

One of many. I also did this :(
Title: Re: VCE Further Maths Question Thread!
Post by: LiquidPaperz on October 31, 2014, 07:20:43 pm
what wll i be looking at with rank 3, exam 1 37/40 - 2 really stupid mis read questions - and 60/60 exam 2? study score..
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on October 31, 2014, 07:21:57 pm
One of many. I also did this :(

At least we have learnt from our mistake.
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on October 31, 2014, 07:30:02 pm
what wll i be looking at with rank 3, exam 1 37/40 - 2 really stupid mis read questions - and 60/60 exam 2? study score..
Mid to low 40's, depending on the cohort strength and cutoffs for exam 1
Title: Re: VCE Further Maths Question Thread!
Post by: stevie.lowe28 on October 31, 2014, 09:51:02 pm
Can someone help me with matrices question 6 from the multie choice exam?
Title: Re: VCE Further Maths Question Thread!
Post by: QTPi on October 31, 2014, 10:38:19 pm
Can someone help me with matrices question 6 from the multie choice exam?
(i) referred to the number of the row, (j) referred to the number of the column and when the 2 numbers were added they would equal to the number it was representing, for example row 1 coloumn 1 should be representing the number 2 as 1 plus 1 clearly equals 2, as well row 3 column  2 would be 5 as 2 plus 3 equal 5. I hope that helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: rudytay on November 01, 2014, 04:02:10 pm
I got a 38/40 on exam 1. How many marks can I afford to drop on exam 2 to get a 40+ SS?
 8)
Title: Re: VCE Further Maths Question Thread!
Post by: abcdefg9999 on November 01, 2014, 05:38:02 pm
Of 2014 exam 1, is D a correct answer for question 9 of number patterns?
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on November 01, 2014, 05:41:37 pm
Ok, for exam 2, when we are dealing with questions that have a) b) c) d), in Geometry and Trig, if we find the answer to say question a) which gives an answer of root 2, but wants it to one decimal place, so we write 1.4 cm, then if in the next part b) they ask us to calculate something that requires that length, do we use 1.4 (the answer to part a but rounded to 1 dp) or do we keep using root 2? For example in the TSSM 2014 exam paper it seems they have used the rounded answer for further calculations instead of the actual answer.

Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 01, 2014, 05:56:23 pm
Ok, for exam 2, when we are dealing with questions that have a) b) c) d), in Geometry and Trig, if we find the answer to say question a) which gives an answer of root 2, but wants it to one decimal place, so we write 1.4 cm, then if in the next part b) they ask us to calculate something that requires that length, do we use 1.4 (the answer to part a but rounded to 1 dp) or do we keep using root 2? For example in the TSSM 2014 exam paper it seems they have used the rounded answer for further calculations instead of the actual answer.
If it says "using your answer from part a, find..." Then you would use the rounded answer, exactly as it is written above. Otherwise always use the exact answer, such as root 2.
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on November 01, 2014, 06:33:17 pm
Thanks, and What about in a show that question? because people who don't get it will have to use the rounded answer?
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 01, 2014, 06:39:05 pm
Thanks, and What about in a show that question? because people who don't get it will have to use the rounded answer?
If it's a show that question then I would say use that, because technically you have been given the exact length by the exam writers, so you should use that in any calculations you do.
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on November 01, 2014, 06:51:38 pm
Thank you! I have one more question if it isn't too much of a bother! If they ask us for the mode of a set of data values, but there is a maximum frequency for two data values, do we say both of those values are the mode, and/or state the data is bimodal? What if there are 3 data values with the same maximum frequency? Or would we say there is no mode?
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 01, 2014, 06:54:51 pm
Thank you! I have one more question if it isn't too much of a bother! If they ask us for the mode of a set of data values, but there is a maximum frequency for two data values, do we say both of those values are the mode, and/or state the data is bimodal? What if there are 3 data values with the same maximum frequency? Or would we say there is no mode?
List all of the values that are equal most frequent, if there is more than one then list more than one. Not necessary to say that it is bimodal, but you wouldn't lose marks by doing so.
Title: Re: VCE Further Maths Question Thread!
Post by: Splash-Tackle-Flail on November 01, 2014, 06:59:01 pm
Thank you very much!
Title: Re: VCE Further Maths Question Thread!
Post by: aejays on November 01, 2014, 09:25:45 pm
Hey guys, just a few questions about nit picky ways to lose marks:

When we're required to give rounded answers, do we first have to indicate something like x = 35.235... ≈ 35.24
or can we just say  x = 35.24 and do we actually need to use '≈' ?

For 'show that' questions, do we need to write formulas out?

'Approximately symmetric' and 'normal distribution' mean the same thing right?
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on November 01, 2014, 09:32:36 pm
When we're required to give rounded answers, do we first have to indicate something like x = 35.235... ≈ 35.24
or can we just say  x = 35.24 and do we actually need to use '≈' ?
No need to show the approximation symbol. They won't be picking on you for that sort of stuff. Just make your final answer very clear with an underline or box.

For 'show that' questions, do we need to write formulas out?
"Show that" questions: show a crazy amount of working out to be safe. Don't risk showing too little, you won't be penalised for showing too much working out. So if it's geometry using the cos rule to find a longer length, show each step of the working out (use less calculator). See http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath2-w.pdf Geometry and Trig Q3a,b for some "show that" questions (not sure if they're in other modules); then see the assessment report to see what steps were necessary.

'Approximately symmetric' and 'normal distribution' mean the same thing right?
Yep. They both refer to bell curves in further.
Title: Re: VCE Further Maths Question Thread!
Post by: Zues on November 01, 2014, 10:13:08 pm
just a question say i found the answer to length AD to be 37.44 and answer says to nearest metre so i write 37m. In the next question it ask me to find BX, and to find BX i need to use AD, do i use the 37.44 or 37?
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 01, 2014, 10:22:50 pm
just a question say i found the answer to length AD to be 37.44 and answer says to nearest metre so i write 37m. In the next question it ask me to find BX, and to find BX i need to use AD, do i use the 37.44 or 37?

Unless it clearly says "using your answer from above" use the exact answer, not the rounded answer.
Title: Re: VCE Further Maths Question Thread!
Post by: Samueling on November 01, 2014, 10:29:23 pm
On the 2012 Vcaa further maths exam 2,
On the core section, question 4a.
I got (ws3.00pm)^2 = 3.3 + 0.5 x ws9.00am.
However, it's wrong. The answer is: (ws3.00pm)^2 = 3.4 + 6.6 x ws9.00am.
I triple checked the variable that i placed in my CAS, however i still got it wrong....
someone please explain!

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: doomdestroyer on November 01, 2014, 10:37:15 pm
On the 2012 Vcaa further maths exam 2,
On the core section, question 4a.
I got (ws3.00pm)^2 = 3.3 + 0.5 x ws9.00am.
However, it's wrong. The answer is: (ws3.00pm)^2 = 3.4 + 6.6 x ws9.00am.
I triple checked the variable that i placed in my CAS, however i still got it wrong....
someone please explain!

Thanks :)

I know what you have done wrong, quite a silly mistake, but it happens. When selecting "Calc" and "Linear Reg" make sure the correct list for the transformed variable is selected, the answer you got is from the normal variable not the transformed variable.
Title: Re: VCE Further Maths Question Thread!
Post by: Samueling on November 01, 2014, 11:26:53 pm
I know what you have done wrong, quite a silly mistake, but it happens. When selecting "Calc" and "Linear Reg" make sure the correct list for the transformed variable is selected, the answer you got is from the normal variable not the transformed variable.

ahhhhhhhh..... No wonder its (ws3.00)^2
thank youu :)
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on November 02, 2014, 10:51:10 am
When describing graphs is there only 3 things we have to fulfill? Those being direction (positive/negative), strength (moderate,strong,weak) and type (linear etc) ?

And if they don't fall into a type we just describe what we see? e.g Y decreases from x = 1 to x = 5, and at which it remains steady until x = 15...etc?

What other worded questions could they ask us?
Title: Re: VCE Further Maths Question Thread!
Post by: footyal9 on November 02, 2014, 12:50:43 pm
I dropped 3.5 marks in my sacs out of 80, I'm equal second in my cohort the top 4 are two marks apart most people will be aiming for 30-35 and there are 8ish out of 70 kids aiming for 40 most should get it, is that a strong cohort? I aced multiple choice if I ace short answer what could I expect to get? Any chance of a 50?
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 02, 2014, 12:59:30 pm
I dropped 3.5 marks in my sacs out of 80, I'm equal second in my cohort the top 4 are two marks apart most people will be aiming for 30-35 and there are 8ish out of 70 kids aiming for 40 most should get it, is that a strong cohort? I aced multiple choice if I ace short answer what could I expect to get? Any chance of a 50?
Dropping 3.5/80 is a low-mid range A+, so chances of a 50 would be slim, but high 40's is still very achievable.
Title: Re: VCE Further Maths Question Thread!
Post by: ~V on November 02, 2014, 04:58:57 pm
How do you know when to round up or down? because in a matrices module, it was 331.25 but they rounded down, this was about trouts so you can't have .25 of a trout. Another question in the graphs and relations module, was referring to students, 42.22, i rounded it down to 42 but the answer was 43... help!
EDIT: Never mind, not an issue anymore.
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 02, 2014, 05:19:51 pm
How do you know when to round up or down? because in a matrices module, it was 331.25 but they rounded down, this was about trouts so you can't have .25 of a trout. Another question in the graphs and relations module, was referring to students, 42.22, i rounded it to 43 but the answer was 42... help!
General rule is when the decimal is below .5, you round down, if it's 0.5 or greater you round up.
Title: Re: VCE Further Maths Question Thread!
Post by: Sam_4331 on November 03, 2014, 11:40:01 am
does anyone have answers for exam 2, will they be put online today?
Title: Re: VCE Further Maths Question Thread!
Post by: cevap on November 03, 2014, 11:58:04 am
I just did the exam 2 and was talking to a friend of mine and we were comparing answers, for exam 1 we both got the same 39/40 but in exam 2 for most questions we were identical except for 1 mark, i am rank 1 while the friend is rank 3, will this 1 mark allow them to get a better study score (im not 100% that it is only 1 mark they could have lost some more or i could have) but i was wondering if rank could help me stay in 1st position in terms of study score.
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: forchina on November 03, 2014, 12:02:58 pm
Does anybody remember if for 3c where they ask max amount of tomatoes to ensure no loss, did they ask you to round to nearest whole kilograms? I don't recall reading that part so i left the answer as 15.2
Title: Re: VCE Further Maths Question Thread!
Post by: myanacondadont on November 03, 2014, 12:08:02 pm
Does anybody remember if for 3c where they ask max amount of tomatoes to ensure no loss, did they ask you to round to nearest whole kilograms? I don't recall reading that part so i left the answer as 15.2

Ahah I can't remember but I rounded my answer as 15. Shiiiiit.
Title: Re: VCE Further Maths Question Thread!
Post by: lokzo on November 03, 2014, 12:23:04 pm
Will someone be uploading exam 2? + Solutions?
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 03, 2014, 12:44:32 pm
Will someone be uploading exam 2? + Solutions?
They're up, in the exam discussion forum.
Further Maths Exam 2- Tentative Solutions
Title: Re: VCE Further Maths Question Thread!
Post by: alan3152 on November 04, 2014, 07:49:20 pm
What SS can I get for:
SAC: 99.7/100 (Rank 1) (Average cohort about 80people)
Exam 1: 38/40
Exam 2: 57/60
Title: Re: VCE Further Maths Question Thread!
Post by: Dan1995 on November 04, 2014, 07:57:24 pm
What SS can I get for:
SAC: 99.7/100 (Rank 1) (Average cohort about 80people)
Exam 1: 38/40
Exam 2: 57/60
Please note there is a separate thread dedicated to this in the exam discussion forum.

I'd say mid/low 40's
Title: Re: VCE Further Maths Question Thread!
Post by: AirLandBus on December 02, 2014, 09:20:37 pm
Can anyone confirm wether or not the values of 58 and 60 are outliers or not. The textbook says they are but i dont think they as the upper fence is 61, thus there inside it and not considered outliers.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on December 03, 2014, 12:52:01 am
Can anyone confirm wether or not the values of 58 and 60 are outliers or not. The textbook says they are but i dont think they as the upper fence is 61, thus there inside it and not considered outliers.

Is there any other information for this question?
Title: Re: VCE Further Maths Question Thread!
Post by: AirLandBus on December 03, 2014, 09:10:20 am
Is there any other information for this question?

Yep. This bad boy.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on December 03, 2014, 10:54:57 am
Only explanation I can come up with is that we can estimate the standard deviation to be approximately 5 or 7.5, and those data points fall further than 2 standard deviations away from the mean.

However, this method of approximated is not in the study design, and the 2 standard deviation (while mentioned in Heinemann...) is ALSO not mentioned in the study design as a way of finding outliers. So, I think your book's made an oopsie, as I can confirm you're using the IQR method properly to find the upper bound.
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on December 16, 2014, 06:17:09 pm
Can someone please explain how to do part viii of this question!?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on December 16, 2014, 06:22:57 pm
Can someone please explain how to do part viii of this question!?

A nice logic question. If you aren't familiar with the 68-95-99.7% rule, refer to this picture. You'll see that 95% of values fall between two standard deviations of the mean, and so 5% are outside those two standard deviations. By symmetry, we know that either "tail-end" should have 2.5% each. Now, we want to know the score such that 97.5% will score higher than it - so we need to start counting from those tail ends. So, we start with the 2.5% after 3 standard deviations. Then, we add the 95% from the above diagram, and we'll get 97.5% (alternatively, you could've added each segment - ie, gone to +1 sd, then 0, -1sd, -2sd).

So, 97.5% of people will score ABOVE 2 sd below the mean, which is 100-2(15)=100-30=70.
Title: Re: VCE Further Maths Question Thread!
Post by: cosine on December 16, 2014, 06:44:53 pm
omfg eulerfan, you're HERE aswell........ everywhere i go!  :P
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on December 16, 2014, 06:46:31 pm
A nice logic question. If you aren't familiar with the 68-95-99.7% rule, refer to this picture. You'll see that 95% of values fall between two standard deviations of the mean, and so 5% are outside those two standard deviations. By symmetry, we know that either "tail-end" should have 2.5% each. Now, we want to know the score such that 97.5% will score higher than it - so we need to start counting from those tail ends. So, we start with the 2.5% after 3 standard deviations. Then, we add the 95% from the above diagram, and we'll get 97.5% (alternatively, you could've added each segment - ie, gone to +1 sd, then 0, -1sd, -2sd).

So, 97.5% of people will score ABOVE 2 sd below the mean, which is 100-2(15)=100-30=70.
Left the question for a while and came back to it....omg I can't believe how simple the question was yet I didn't get it haha! Thanks heaps for the explanation as well EulerFan!
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on December 16, 2014, 06:48:04 pm
omfg eulerfan, you're HERE aswell........ everywhere i go!  :P

(http://i.imgur.com/CKi9aMl.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on January 08, 2015, 08:00:17 pm
Hey can someone please show me where they get the seasonal index of 1.30 from in part 2 of example 12. Background info to the question is in the other attachment. Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Mellyboo on January 28, 2015, 04:48:13 pm
Hey can someone please show me where they get the seasonal index of 1.30 from in part 2 of example 12. Background info to the question is in the other attachment. Thanks!

Hey there, looks like you need more information, perhaps before example 11.
Title: Re: VCE Further Maths Question Thread!
Post by: belle123 on January 29, 2015, 10:04:36 pm
This may seem like a stupid question but, for the bound reference, can i use a book with a spiral spine if it does not have perforated pages??

Just want to make sure I'm doing it right from the start

Thanks  :o
Title: Re: VCE Further Maths Question Thread!
Post by: Mellyboo on January 29, 2015, 10:07:07 pm
This may seem like a stupid question but, for the bound reference, can i use a book with a spiral spine if it does not have perforated pages??

Just want to make sure I'm doing it right from the start

Thanks  :o

Yes!
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on January 29, 2015, 10:07:22 pm
This may seem like a stupid question but, for the bound reference, can i use a book with a spiral spine if it does not have perforated pages??

Just want to make sure I'm doing it right from the start

Thanks  :o

Yep - you could use a bunch of A4 pages held together by some intense duct-taping if you wanted. ;) As long as it has a single spine, is of A4 size or smaller and the binding is permanent, you're fine.
Title: Re: VCE Further Maths Question Thread!
Post by: Mellyboo on January 29, 2015, 10:11:23 pm
Make sure you don't tab the pages. I was told that as long as they can't be removed that I could have them. Unfortunately, they wouldn't have any of that and I was forced to cut mine off, minutes before go time.  >:(
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on February 09, 2015, 06:21:39 pm
A table of values for against is as shown.


Given that , find values of and .

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on February 10, 2015, 02:08:35 am
A table of values for against is as shown.


Given that , find values of and .

Thanks!

When y=4.2, x=1, so:

y=kx^n ===> 4.2=k(1^n) ===> k=4.2

Welp, that was easy. Now, when x=2, y=33.6:

33.6=4.2(2^n) ===> 2^n=8 ===> 2^n=2^3 ===> n=3

So, n=3 and k=4.2
Note that the last step might prove tricky for the average Further student - solving 33.6=4.2(2^n) with a CAS is absolutely fine. You could also solve it using a simultaneous equation solver on your CAS, but mine didn't like that for whatever reason, so you might get a similar issue.
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on February 11, 2015, 02:03:02 pm
When y=4.2, x=1, so:

y=kx^n ===> 4.2=k(1^n) ===> k=4.2

Welp, that was easy. Now, when x=2, y=33.6:

33.6=4.2(2^n) ===> 2^n=8 ===> 2^n=2^3 ===> n=3

So, n=3 and k=4.2
Note that the last step might prove tricky for the average Further student - solving 33.6=4.2(2^n) with a CAS is absolutely fine. You could also solve it using a simultaneous equation solver on your CAS, but mine didn't like that for whatever reason, so you might get a similar issue.

Yea thanks. I tried to do simultaneous equations on my CAS but I got an "argument error". Cheers.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on February 11, 2015, 11:55:08 pm
Make sure you don't tab the pages. I was told that as long as they can't be removed that I could have them. Unfortunately, they wouldn't have any of that and I was forced to cut mine off, minutes before go time.  >:(

That's actually incorrect. You can have them as long as it:
So, if you have a page cut a sliver (that's the size of the tab - so probably an inch or so) to add the permanent tab, that's actually fine. It's also fine if you cut your A4 sheets down, so that the side is your tab or cutting corners for a "layered" effect. Colour-coding's good too, provided it follows the rules on the link above.

I did the bottom right one last year and that was absolutely fine. To show you what's allowed visually, see the attached image.
Spoiler
For people who don't have 20-20 vision, the sheets say:
  • Top left: Your average sheet of paper
  • Top right: The cut corner (+ highlight) for layered effect
  • Bottom left: The cutout tab
  • Bottom right: The measured cut with permanent sticky tab (The yellow sheet's the sticky tab.)
You probably can't see it, but I've actually ruled lines and cut them, so the page is still A4 when closed.

The sticky tabs I've got here are kind of like labels, but 'fold-able' tab version (see image).
Title: Re: VCE Further Maths Question Thread!
Post by: aaziz17 on February 12, 2015, 08:01:12 pm
Keep getting C answers says D can someone explain
Title: Re: VCE Further Maths Question Thread!
Post by: Cogglesnatch Cuttlefish on February 12, 2015, 08:35:18 pm
Keep getting C answers says D can someone explain
Spotted:
Striped:
So the question is asking for the year when the number of striped is twice the number of spotted. Thus, equate them as so:

Solve for n;
Title: Re: VCE Further Maths Question Thread!
Post by: aaziz17 on February 12, 2015, 09:55:11 pm
Spotted:
Striped:
So the question is asking for the year when the number of striped is twice the number of spotted. Thus, equate them as so:

Solve for n;
i was using the sum equation thats why i  was a bit confused. Cheers for clearing that up for me
Title: Re: VCE Further Maths Question Thread!
Post by: Cosec on February 15, 2015, 06:16:54 pm
Can somebody answer this in a SAC style answer so i know whats required.
When is it not appropriate to set up an Ordered Stem and Leaf Plot for a data set?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on February 15, 2015, 06:32:55 pm
Can somebody answer this in a SAC style answer so i know whats required.
When is it not appropriate to set up an Ordered Stem and Leaf Plot for a data set?
When the data isn't numerical.
Title: Re: VCE Further Maths Question Thread!
Post by: Cosec on February 15, 2015, 06:34:16 pm
When the data isn't numerical.

 How reliable are these z scores for interpretive purposes?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on February 15, 2015, 08:28:17 pm
How reliable are these z scores for interpretive purposes?

A z score will tell you how many standard deviations away from the mean something is, from this you can use the 68-95-99.7% rule to discuss the reliability of the statistic/whether that piece of data is "normal", etc.
Title: Re: VCE Further Maths Question Thread!
Post by: Cosec on February 16, 2015, 08:07:19 pm
Can someone confirm the skewness of these two box plots for me?
And is the outlier included in the range? Or do i do two ranges in my report. one with the outlier and one without?

Image:  http://imgur.com/dnZEKnc
Title: Re: VCE Further Maths Question Thread!
Post by: Davos on February 16, 2015, 10:08:32 pm
I believe the first box plot is positively skewed because most of the data is found at the beginning of the plot. The second box plot should be approximately symmetrical as the data is evenly distributed throughout the plot. The outlier is included in the range calculations
Title: Re: VCE Further Maths Question Thread!
Post by: Cosec on February 16, 2015, 10:21:06 pm
I believe the first box plot is positively skewed because most of the data is found at the beginning of the plot. The second box plot should be approximately symmetrical as the data is evenly distributed throughout the plot. The outlier is included in the range calculations

Would the first (blue) one be negatively skewed, how so would it be positively skewed?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on February 17, 2015, 07:08:14 am
Would the first (blue) one be negatively skewed, how so would it be positively skewed?
Because the median drifts to the positive side of the IQR.
Title: Re: VCE Further Maths Question Thread!
Post by: Cosec on February 17, 2015, 08:02:25 am
Because the median drifts to the positive side of the IQR.

If the median is on the right-er hand side from the middle within the IQR, wouldnt it then be negatively skewed?
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on February 19, 2015, 07:24:46 pm
Currently in class we are doing the Geometry and Trigonometry module.
I didnt quite understand how to do this textbook (Maths Quest) question (based on the sine rule)

The answers :

a.)129.1 degrees
b.) 68km

Thanks! :)
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on March 02, 2015, 04:36:09 pm
Question:
The number of goals scored by the gal attack each week for a netball team would be best represented in a:
a) histogram
b) frequency diagram
c) frequency polygon
d) pie chart
3) cumulative frequency graph

What is the difference between options a), b) and c)?
(a) is correct
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on March 02, 2015, 08:10:04 pm
Question:
The number of goals scored by the gal attack each week for a netball team would be best represented in a:
a) histogram
b) frequency diagram
c) frequency polygon
d) pie chart
3) cumulative frequency graph

What is the difference between options a), b) and c)?
(a) is correct
a) implies continuous data
b) implies discrete data
c) is used to give a shape to the data.

a) is correct because, since we're working in time, we have continuous data, so we use a histogram. (before someone jumps in with "but we're using discrete time!!", it's still considered as continuous data) You should be familiar with the difference between discrete and continuous data, and what graphs imply which. If you're not, say you're not, because I know that most textbooks do a pretty poor job of teaching it. :)

Currently in class we are doing the Geometry and Trigonometry module.
I didnt quite understand how to do this textbook (Maths Quest) question (based on the sine rule)

The answers :

a.)129.1 degrees
b.) 68km

Thanks! :)

Sorry RazzMeTazz, I missed you!! >.<;
I'm going to have to draw this one out, but I don't have time right now, sorry. :\ If no one gets back to you before tomorrow afternoon, I'll have something for you.
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on March 02, 2015, 08:58:58 pm
thanks; I understand 
Title: Re: VCE Further Maths Question Thread!
Post by: Mintyfreshmints on March 04, 2015, 02:23:05 pm
I have a transition matrix diagram question:
In a transition matrix diagram do you have to label a loop around a point, with 100%, if there is no transition away from that point? E.g A proportion of 1 of the people at A will be at A after the next transition...
If you do not label the 100% loop on the diagram is it still technically correct or not? Because to me it seems redundant however I can also see why it should be there.
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on March 04, 2015, 07:19:37 pm
Thanks EulerFan101!

:)

Also, can anyone please explain the difference between a vertex and an apex? Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: TheAspiringDoc on March 04, 2015, 07:44:17 pm
Thanks EulerFan101!

:)

Also, can anyone please explain the difference between a vertex and an apex? Thanks!
to quote MathIsFun (very useful btw):
Quote
Apex=The point (vertex) furthest from the base of an object.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on March 04, 2015, 07:52:16 pm
Thanks EulerFan101!

:)

Also, can anyone please explain the difference between a vertex and an apex? Thanks!

I am so sorry RazzMeTazz - I wrote up a post earlier, but for whatever reason it's gone!! Thankfully, I kept the image, see attached. (edit: Apparently it's too large, grrrr. Explains why it didn't post last time, though... If you still want it, PM me an e-mail, I'll send it that way. Otherwise, see statement

Basically, I disagree with the way it's worded - it makes no sense, and following it their answers seem to make no sense (note: I did initially read it wrong and went straight north instead of west, but it basically means my triangle is rotated 90 degrees clockwise from what it should be - all values would be exactly the same)


I have a transition matrix diagram question:
In a transition matrix diagram do you have to label a loop around a point, with 100%, if there is no transition away from that point? E.g A proportion of 1 of the people at A will be at A after the next transition...
If you do not label the 100% loop on the diagram is it still technically correct or not? Because to me it seems redundant however I can also see why it should be there.

Yes, you should. If A doesn't point to itself, and doesn't point to anything else, then the interpretation is that we can't continue on from A. However, this makes no sense, since the idea of a transition matrix is that it can be applied an infinite amount of times. So, A should always continue on to something, even if this means you must point it to itself.

Alternatively, if you have no loop, someone else reading your information would just assume you've forgotten about it, and would have no idea where A actually goes, and might just make a guess which completely ruins your data.

(note: I don't know how strict VCAA are on this - I'm speaking strictly from a statistician's point of view)
Title: Re: VCE Further Maths Question Thread!
Post by: TheAspiringDoc on March 10, 2015, 06:22:49 pm
Um, how do you solve this?
If a+2 = 7, find the value of 3a-12 without solving for a.
I can solve it easy, I just don't get the 'without solving for a' part..
Thanks!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: LoadedWithPotatoes on March 10, 2015, 06:48:23 pm
a+2 = 7, multiply 3 by both sides
3a+6= 21, subtract 18 from both sides

Therefore, 3a-12=3
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on March 12, 2015, 04:49:00 pm
how many decimal points do we round answers to if it is not specified?
Title: Re: VCE Further Maths Question Thread!
Post by: kinslayer on March 14, 2015, 03:23:13 am
how many decimal points do we round answers to if it is not specified?

In a VCAA exam, if you are required to give an answer in decimal form, you will always be told how many decimal places to round to. In such a case, always try to carry as many significant digits as your calculator gives you and only round the final answer.
Title: Re: VCE Further Maths Question Thread!
Post by: Sardothienn on March 14, 2015, 07:56:29 am
In a further core sac are we suppose to draw residuals/ scatterplots and all those other charts accurately? It just seems too time consuming tbh
Title: Re: VCE Further Maths Question Thread!
Post by: korng on March 14, 2015, 03:52:50 pm
how's to prepare for further math first SACs ?  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 14, 2015, 11:46:29 pm
how's to prepare for further math first SACs ?  ;)

It depends on how you like to revise for Maths usually. Oh, and probably how you like making cheat sheets.

In a further core sac are we suppose to draw residuals/ scatterplots and all those other charts accurately? It just seems too time consuming tbh

Not necessarily. Further teachers are usually kinder and will usually put that sort of question either on the technology section (but still draw the whole graph to an approximate scale) or have less data (i.e. probably 15 points at most) to plot by hand with accuracy. It mostly depends on the person who's making your SAC though, so this could be wrong altogether. Just expect the worst and be prepared to draw any of them (but nothing too ridiculous, it still has to be doable). 
Title: Re: VCE Further Maths Question Thread!
Post by: TheAspiringDoc on March 16, 2015, 05:46:14 pm
I'm just not getting this 'without solving for the pronumeral, solve this equation' stuff..
This probably looks like child's play to you guys but could someone please show me how to do this (with full workings)
If 6a=2a+10, find the value of 13-2a without solving for a.
 :'( Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on March 16, 2015, 06:11:24 pm
I'm just not getting this 'without solving for the pronumeral, solve this equation' stuff..
This probably looks like child's play to you guys but could someone please show me how to do this (with full workings)
If 6a=2a+10, find the value of 13-2a without solving for a.
 :'( Thanks

If you can solve for a variable, you can do this stuff. However, instead of trying to make weird operations until you get to a single thing, you're doing weird operations to get to a complicated thing.

So, first thing we notice about the 13-2a? a is by itself, so let's work with that:



Next thing? There's a -2 in front of the a, not a 4, so we change that. How do we get from 4 to -2? Divide by -2:



Finally, what's left in what they told us? +13, so let's add in 13:



And we're done.
Title: Re: VCE Further Maths Question Thread!
Post by: TheAspiringDoc on March 16, 2015, 06:29:52 pm
Thanks for the speedy reply EulerFan101, but I'm warning you, if you continue to be this helpful, I'm going to have to change my username to EulerFanFan  :D
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on March 16, 2015, 07:43:43 pm
in my textbook it says
in a negatively skewed boxplot, the median occurs further towards the right end of the box & left tail is longer
and in a positively skewed boxplot, the median occurs further towards the left end of the box & right tail is longer
but
i saw a facebook post
https://www.facebook.com/photo.php?fbid=969678223063087&set=gm.431048803739825&type=1&theater

if you can't see it, the image is here: https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-xtf1/v/t1.0-9/11068300_969678223063087_3082187454809633619_n.jpg?oh=6683a0ed2ec77dced1089faf04e17683&oe=556FDC74&__gda__=1434052399_0a8b94eb1f21a4a3a4559be9324620dc
the comments are all saying it is positively skewed
but, the median is towards the right of the box, which is not a characteristic of positive skew (according to textbook)
so
is my textbook wrong
or is the boxplot not positively skewed & are all the comments wrong
lol
Title: Re: VCE Further Maths Question Thread!
Post by: bae on March 17, 2015, 01:17:12 pm
in my textbook it says
in a negatively skewed boxplot, the median occurs further towards the right end of the box & left tail is longer
and in a positively skewed boxplot, the median occurs further towards the left end of the box & right tail is longer
but
i saw a facebook post
https://www.facebook.com/photo.php?fbid=969678223063087&set=gm.431048803739825&type=1&theater

if you can't see it, the image is here: https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-xtf1/v/t1.0-9/11068300_969678223063087_3082187454809633619_n.jpg?oh=6683a0ed2ec77dced1089faf04e17683&oe=556FDC74&__gda__=1434052399_0a8b94eb1f21a4a3a4559be9324620dc
the comments are all saying it is positively skewed
but, the median is towards the right of the box, which is not a characteristic of positive skew (according to textbook)
so
is my textbook wrong
or is the boxplot not positively skewed & are all the comments wrong
lol

My textbook also says the same thing, negatively skewed = median further to right & left tail longer, positively skewed = median further to left & right tail longer. Your textbook says that it's negatively skewed, but I think because of the outlier on the right the boxplot is therefore positively skewed, like all the other comments.  :)

Title: Re: VCE Further Maths Question Thread!
Post by: stunfiskery on March 19, 2015, 08:43:07 pm
I've just received the results for my first Further Maths SAC. It was on Graphs and Relations (it was out of 40) and I just have a question on how my marks will be conveyed to VCAA. Hypothetically speaking, let's just say I got 97.5% and the SAC accounts for 20 VCAA marks. Of that how many VCAA marks would I get? 20? 19.5? Is it in the same ratio. For example is a 36/40 equivalent to 18/20 VCAA marks?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on March 19, 2015, 08:56:34 pm
I've just received the results for my first Further Maths SAC. It was on Graphs and Relations (it was out of 40) and I just have a question on how my marks will be conveyed to VCAA. Hypothetically speaking, let's just say I got 97.5% and the SAC accounts for 20 VCAA marks. Of that how many VCAA marks would I get? 20? 19.5? Is it in the same ratio. For example is a 36/40 equivalent to 18/20 VCAA marks?
It entirely depends on how your school has structured your SACs.
Title: Re: VCE Further Maths Question Thread!
Post by: chansena on March 22, 2015, 05:35:05 pm
Hi ALL!

What would i comment on this box plot. it is from chocolate sales in one month. I get confused with what to say. Other than the skewness my teacher has said to relate it back to the scenario in this case it is cholcate production but how do i relate it ???


Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on March 22, 2015, 06:22:07 pm
Hi ALL!

What would i comment on this box plot. it is from chocolate sales in one month. I get confused with what to say. Other than the skewness my teacher has said to relate it back to the scenario in this case it is cholcate production but how do i relate it ???

What's the range of sales? How about the median? What does the median suggest? Any points in there that we can't really consider? Why/why not? How spread out is the data? What does this suggest in the variation of chocolate sales each month?
Title: Re: VCE Further Maths Question Thread!
Post by: chansena on March 22, 2015, 06:55:56 pm
What's the range of sales? How about the median? What does the median suggest? Any points in there that we can't really consider? Why/why not? How spread out is the data? What does this suggest in the variation of chocolate sales each month?

The data is a  positive skew. The range of sales varied from 355  to 601 with one massive sale in chocolates with 906 in sales.

What does the median mean in a sales in a situation like this ? Would it mean most of the sales was at around the 461.5



Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 22, 2015, 08:03:22 pm
The data is a  positive skew. The range of sales varied from 355  to 601 with one massive sale in chocolates with 906 in sales.

What does the median mean in a sales in a situation like this ? Would it mean most of the sales was at around the 461.5

Well, consider this. What occurs to a mean when there's an outlier?
Spoiler
The mean is altered, drastically, as all the data is used to calculate an average.
Is the mean reliable in data where an outlier exists?
Spoiler
No, since the mean uses all the data.
What are the measures of centre that would be relevant to this data?
Spoiler
We know that there's the mean, median and mode. We've worked out that the mean would not be as accurate to find the centre in this data and the mode would probably be pointless, thus we're left with the median, which finds the middle number, without having to use all the data in its calculations.
Title: Re: VCE Further Maths Question Thread!
Post by: chansena on March 22, 2015, 10:18:12 pm
Cant decide which type of graph this would be for time series

Seasonal Pattern
Cyclical Pattern
Random
Downward / upwards trend


I'm tipping its a random but i just wanted more opinions on it

Thanks !
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on April 01, 2015, 09:03:38 pm
Can anyone explain how you get the answer in Question 5 of vcaa Exam 1-2005? Thankyou!
Title: Re: VCE Further Maths Question Thread!
Post by: Cosec on April 01, 2015, 09:40:50 pm
Can anyone explain how you get the answer in Question 5 of vcaa Exam 1-2005? Thankyou!

I cheated and looked at the answers but the way i got the correct answer is by putting the x variables, the number of mobile phones in list 1 on my cas, the y variables in list 2 whcih is the frequency, set it up and did a one variable analysis. Giving us a mean for the x variable of 1.1298701, which is (a) 1.13. As to why this is the case i have no clue, why you cant just find the mean of the x variables. If euler or alike can explain that it would be much appreciated! :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 01, 2015, 09:56:21 pm
Can anyone explain how you get the answer in Question 5 of vcaa Exam 1-2005? Thankyou!

Hey guys.
Reality is: you just have to take in the actual table properly.
One variable you need to omit. Try and have a guess as to which on it is!
Spoiler
Text messaging use is kind of useless in this one.
Then figure out the direction the no. of mobile phones are going:
Spoiler
Since they're the columns, check out the totals at the bottom of the table.
Then multiply the x value (no. of phones in a household) with the y value (the amount of households with that no. of phones.)
e.g. if there were 10 households with 1 phone, go 10 x 1 and so forth
Spoiler
so:
0 x 34
1 x 78
2 x 30
3 x 12
Then add them together:
Spoiler
0 + 78 + 60 + 36 = 174 phones
Note that this is the amount of phones all together...
so we have one last step: find the mean.
How do we usually do that?
Spoiler
mean = (sum of values)/ (no. of values there are)
So therefore we take our total and divide by the amount of households there are.
Spoiler
174 phones / 154 households = approx. 1.12987...
... and that's exactly how the answer arises. Thus the answer is A.

I hope that all made sense. Please tell me if that's not.
Title: Re: VCE Further Maths Question Thread!
Post by: Cosec on April 01, 2015, 10:03:28 pm
Hey guys.
Reality is: you just have to take in the actual table properly.
One variable you need to omit. Try and have a guess as to which on it is!
Spoiler
Text messaging use is kind of useless in this one.
Then figure out the direction the no. of mobile phones are going:
Spoiler
Since they're the columns, check out the totals at the bottom of the table.
Then multiply the x value (no. of phones in a household) with the y value (the amount of households with that no. of phones.)
e.g. if there were 10 households with 1 phone, go 10 x 1 and so forth
Spoiler
so:
0 x 34
1 x 78
2 x 30
3 x 12
Then add them together:
Spoiler
0 + 78 + 60 + 36 = 174 phones
Note that this is the amount of phones all together...
so we have one last step: find the mean.
How do we usually do that?
Spoiler
mean = (sum of values)/ (no. of values there are)
So therefore we take our total and divide by the amount of households there are.
Spoiler
174 phones / 154 households = approx. 1.12987...
... and that's exactly how the answer arises. Thus the answer is A.

I hope that all made sense. Please tell me if that's not.

Makes sense from a methods kids point of view, but never got taught it nor did i ever see it in the textbook (essentials)?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 01, 2015, 10:06:18 pm
Makes sense from a methods kids point of view, but never got taught it nor did i ever see it in the textbook (essentials)?

Actually, it's a Core thing. You should have learnt this if you have done the Core Module. If you haven't, I'd be glad to teach you this properly when I'm rested up.
Title: Re: VCE Further Maths Question Thread!
Post by: chansena on April 09, 2015, 03:32:32 pm
Hi,

Could someone please help me with this trig question. I keep getting the wrong answer to the text book.



Thanks !!  :)

Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on April 09, 2015, 03:44:14 pm
Hi,

Could someone please help me with this trig question. I keep getting the wrong answer to the text book.

Thanks !!  :)

Try drawing a diagram - the answer should be 8sin(angle). Sounds like a pretty silly flying fox, though...
Title: Re: VCE Further Maths Question Thread!
Post by: scarletmoon on April 12, 2015, 01:42:39 pm
How do you find IQR from a dot plot? In VCAA 2013 Exam 2 question 2b, I not sure how they got their IQR and Q1.

Why can't you solve this question by typing the values into the CAS (e.g "70" in column 1 and then "1" in column 2), finding the mean and standard deviation that way and going from there?

Also how do you find median in a dot plot? I'm stuck on VCAA 2012 exam 2 question 1a (LOL)
And I'm stuck on 1b as well
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 12, 2015, 03:46:08 pm
Quote from: scarletmoon
How do you find IQR from a dot plot? In VCAA 2013 Exam 2 question 2b, I not sure how they got their IQR and Q1.

Why can't you solve this question by typing the values into the CAS (e.g "70" in column 1 and then "1" in column 2), finding the mean and standard deviation that way and going from there?

Also how do you find median in a dot plot? I'm stuck on VCAA 2012 exam 2 question 1a (LOL)
And I'm stuck on 1b as well

Questions 1 and 2, in order:

Q1,a:
The question is asking for how many times the variable 'very high' appears in the set. Since it's in a pretty (and cheap to print) black and white bar chart, you can just eyeball it from the top of the bar to the frequency (in count, because it doesn't have a % sign) in the vertical axis.

Just in case what I'm trying to say isn't clear, I made a picture. <3
Spoiler
(http://i.imgur.com/U6pLYzT.png)
Here my lovely dotted line shows us that the 'number of countries that have a very high development index' is 31.

Q1,b: Here, they're asking for the percentage of the sum of 'low' and 'medium' development index values.
Spoiler

substituting the values in gives us:

Simplifying one step at a time gives us:


(rounded to four decimal places)

However, it is also stated in the question: 'Write your answer, correct to the nearest percentage' (which is poorly phrased imo because I'm pretty sure 61.44% is the nearest percentage since it's already... you know, a percentage. What they mean is the nearest integer (whole number) percentage, but I digress.)
So your answer is 61%.

Q2,a: Interpretting the dot plot, fun stuff.
Mode = 78 (It's the tallest tower, therefore the most occurring)
Range = 9 (max - min, 79-70)

Q2.b:
Spoiler
the question is asking you to prove that the number 70 is an outlier.
So we need to find the quartiles and the IQR.

It is shown on the plot that n = 28, so:

Either on your calculator or in your head:

All you need to do to find the median is to count 14.5 places from the left, because the points in a dot plot are already in order.
another picture in case that didn't make sense
(http://i.imgur.com/lVjnvCv.png)
Because you need the 14.5th position, you add the 14th and the 15th positions and divide them by two:



The median split the data into two equal halves. That means that there are 14 values on either side.

So now we need to find Q1 and Q3 to calculate the IQR and lower fence.



Therefore, Q1 = 75




therefore, Q3 = 78

So the IQR = 78 - 75
IQR = 3

Now we can work out the lower fence using the following:

Just sub in our values and you get:



Now we need to explain why the country with a development index of 70 is an outlier for this group of countries.
The appropriate calculation is the lower fence calculation above (more specifically the calculation is the once where you sub in the values), and the explanation can simply be:
"70 is an outlier because it is less than 70.5".
Hope this helped! :)
(Also I'm sorry if the format is iffy, I don't usually mess with latex)

Edit: in answer to your question
Quote
Why can't you solve this question by typing the values into the CAS (e.g "70" in column 1 and then "1" in column 2), finding the mean and standard deviation that way and going from there?

This is univariate data (the only variable is development index), so you should only ever need to put data into one column. Also, the mean and standard deviation must take very value in the column(s) into account to be calculated, so just entering 70 and the count (1) wouldn't give you the correct values for them. I think. I have a very flimsy knowledge of cool CAS tricks so there still might be a way to do it like that.

Edit 2: Also if you're not comfortable doing a question like 2b by hand, with a question like that the whole set is displayed so you could pretty easily put it into your CAS and do a one variable stat analysis.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on April 12, 2015, 05:51:05 pm
Holy crap, go MightyBeh! This place really needs a lot more love, you rock.

Also, the mean and standard deviation must take very value in the column(s) into account to be calculated, so just entering 70 and the count (1) wouldn't give you the correct values for them. I think. I have a very flimsy knowledge of cool CAS tricks so there still might be a way to do it like that.

In this case, if you just entered 70 as your only bit of data, then the CAS should say you have a mean of 70 and standard deviation of 0 (which is pretty bogus. :P). One data point is never enough to find a mean or sd.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 12, 2015, 06:52:35 pm
Quote from: EulerFan101
In this case, if you just entered 70 as your only bit of data, then the CAS should say you have a mean of 70 and standard deviation of 0 (which is pretty bogus. :P). One data point is never enough to find a mean or sd.
Thought so, time to edit my post with that exact information so I look smart.

Seriously though, I love the maths subs. It kinda sucks that everywhere but Methods and Spesh seem to be ghost towns. :(
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on April 12, 2015, 08:52:37 pm
Can you use the terms 'discrete' and 'continuous' to describe categorical data, or are these terms confined for use with 'numerical' data only?

Also what exactly does 'centre' and 'spread' of data mean?

:)
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 13, 2015, 05:45:44 am
I don't think so. Even if it were logical to describe categorical data numerically, using terms like discrete and continuous would probably be confusing. Generally with categorical data, you describe it in terms of the dominant category; conventionally with percentages.

Centre is what divides your data into two halves. We use the mean and median. Not sure about the other textbooks, but I thought Essentials had a really neat explanation for the difference between the two:
Quote
Whereas the median lies at the midpoint of a distribution, the mean is the balance point of the distribution. For approximately symmetric distributions, both the median and mean will be approximately equal in value.

Spread refers to... how spread out your data is? The spread puts a number on how tightly (or loosely) your data is grouped together. We use measurements like the range, standard deviation and IQR to calculate it.

If that makes sense. :)
Title: Re: VCE Further Maths Question Thread!
Post by: Garden on April 14, 2015, 06:45:40 pm
Hi all,

Regarding the following image, I'm inclined to classify the following box plot as slightly positively skewed on a SAC. Would it more closely resemble an approximately symmetric distribution? Is it appropriate to classify a box plot as slightly positively skewed?

(http://i57.tinypic.com/dgoxo2.png)

Similarly so with this one, although I'm more confident that this is positively skewed.

(http://i62.tinypic.com/346b814.png)

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: MagicGecko on April 14, 2015, 09:55:45 pm
Hi all,

Regarding the following image, I'm inclined to classify the following box plot as slightly positively skewed on a SAC. Would it more closely resemble an approximately symmetric distribution? Is it appropriate to classify a box plot as slightly positively skewed?

(http://i57.tinypic.com/dgoxo2.png)

Similarly so with this one, although I'm more confident that this is positively skewed.

(http://i62.tinypic.com/346b814.png)

Thanks!

I've never heard nor used the term 'slightly' positively skewed. From my knowledge, both box plots are positively skewed, mainly because the median line is more inclined to the left side. I get why you would think that the first one is approximately symmetric but the median line though.
Title: Re: VCE Further Maths Question Thread!
Post by: Garden on April 15, 2015, 07:22:52 am
Thanks for the clarification MagicGecko!
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on April 15, 2015, 11:48:37 am
Clarification:
You can quantify skew - there are formulas for you to figure out if something is symmetric and, if not symmetric, how skewed (say, +2, -3 or even +6) it is. This is definitely not in Further, you only need to identify if something is negatively skewed, symmetrical or positivity skewed.

Tl;dr, something can be slightly positively skewed, but you don't need to know this for Further.
Title: Re: VCE Further Maths Question Thread!
Post by: Garden on April 15, 2015, 07:18:28 pm
Thanks Euler!
Title: Re: VCE Further Maths Question Thread!
Post by: Vexna on April 17, 2015, 11:07:54 am
Can someone explain the whole process of finding seasonal indices, deseasonalising the data and adjusting it?

This is somewhat confusing and not my strong point when it comes to maths.
Title: Re: VCE Further Maths Question Thread!
Post by: scarletmoon on April 17, 2015, 06:20:24 pm
Ok so when I do practise exams for further,I do them with my CAS in radian mode (I always forget to change it to degrees bc I also do methods) and I get the right answers. Today I realised that I did my sac with my CAS in radian mode.

Would my IQR, regression equation, Pearson coefficient be different, should I go back next lesson and redo the calculations with my CAS in degree mode?

Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on April 17, 2015, 06:49:32 pm


Ok so when I do practise exams for further,I do them with my CAS in radian mode (I always forget to change it to degrees bc I also do methods) and I get the right answers. Today I realised that I did my sac with my CAS in radian mode.

Would my IQR, regression equation, Pearson coefficient be different, should I go back next lesson and redo the calculations with my CAS in degree mode?

No, they should all be the same. Degrees vs Radians is only an issue for trig stuff.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 17, 2015, 08:09:37 pm
Can someone explain the whole process of finding seasonal indices, deseasonalising the data and adjusting it?

I couldn't think of a good way to explain in-depth, so here's a general thing with a bunch of examples. Everything is to 4dp for convenience. If you were doing this in a SAC or exam, I would recommend you do all these calculations on your calculator (If you didn't know, there's a bunch of neat functions in the L&S application, if you've ever worked with Excel formulas they're pretty much the same).

Seasonal indices tell us how a particular season (Generally a day, month or quarter(3 months). Otherwise I believe it's defined as cyclical) compares to the average season.

The formula for a season index is:

It's worth noting that the sum of the seasonal indices equals the number of seasons. (For example, a has a SI of 0.75, b has 1.75, c has 1.0 and d has 0.50.

All that is really kind of abstract though, so it's easiest to explain (and hopefully understand) with an example.

So here's our data:
(http://i.imgur.com/w06vTyC.png)
Step 1 - Seasonal Average
So, first we work out the 'seasonal average'. This is done by adding up all of a seasons's values and dividing them by the number of seasons. In our data set, the seasons are quarters.
working out the seasonal average
The formula for the seasonal average is:

Here's that in context with our data.



Step 2 - Finding the Seasonal Index
So here, we have another table (With bigger gaps! What an advance in technology) :
(http://i.imgur.com/iIcjMjt.png)
There are kind of two parts to this step; first we have to find the seasonal index for each quarter per year (We'll call this section 2a, because everyone loves nested spoilers) and then we have the work out the "average" seasonal index for each quarter, overall (This is 2b. feel free to skip ahead).
2a.
This is a pretty easy step, it just takes some time and (possibly, depends on your preferences) fiddling with your CAS. What you need to do is divide each value by its corresponding seasonal (yearly) average, like so:

For for the first quarter in 2003:

(http://i.imgur.com/cUQqCqD.png)
We're rounding to 4dp for simplicity here, but I'd definitely recommend using exact values until you have to give a decimal or percentage answer because they're much more accurate and you're a lot less likely to make a rounding error... if you haven't done any rounding?
(http://i.imgur.com/U9VM9Fw.png)
Here's our table with our approximate values in it; now we're at 2b.

2b.

Here it is in terms of the first quarter:

Where from our original formula, Qn becomes Q1 and Nyears becomes 3 (years). I'm going to show Q2 as well, just to be sure:

Here's that on our table:
(http://i.imgur.com/jpWQdXo.png)
Step 3 - Deseasonalising
*If you're doing this with your calculator, I'd recommend you set your SI to a variable so you're less likely to make an input error. In a calculator page you can do this by entering the following:
**I'd also recommend doing this in a document as opposed to Scratchpad if you don't already because you're less likely to forget about it and mess up some other calculation for some other work. As a general rule I'd recommend making a new document for each class or (long) question dealing with data.
Code: [Select]
a:=0.7233, b:=1.2294, etc.To deseasonalise data, you use the following formula:

So if we were to do this for the first quarter of 2003, it would be:

if you're doing this on paper, it depends on the grouping on your graph, but usually rounding to 2dp or nearest whole number is the way to go.
Same thing for the second quarter of 2003:

Keep going until you end up with this:
(http://i.imgur.com/tiVf7yO.png)
(Rounded to the nearest whole number, again for convenience. You can keep it exact / 4dp if you're on your calculator)
Step 3a - Graphing the Deseasonalised Data
Same table as before, but here instead of using 20031,20032,20033... 20054 for our x axis (Always time with time series), we convert the years/quarters/seasons/etc. to an easier to read (and graph) value, like so:
(http://i.imgur.com/VEdc9JN.png)
I've put them into ordered pairs here so that it's clear how to graph them. I don't actually have a copy of the graph here but if it's really unclear (which it probably is, I'm not amazing at English), I can draw one for you. Just let me know :)
Step 4 - Predicting Using the Regression Line
Workout the regression line your preferred way with the data, it's not a huge deal. I generally find it's quickest and easiest to just get it when I plot it on the graph page, but that's up to you. Hopefully you should get something like this:

But it's also pretty common to have to write it in terms of the variables, so:
[text]Sales=5.6970+01364*QuarterNumber[/tex]

Now, you're nearly 100% guaranteed to be asked something along the lines of "Calculate the deseasonalised value for..." or "Make a prediction for the..." after that, so we're going to deal with both of those situations.

1) Using the equation of your regression line, calculate the deseasonalised value for the second quarter of 2006.
So after reading the question, (hopefully) you've noticed that the second quarter of 2006 doesn't actually exist. We'll first have to work out the Time(t) value (The "Quarter Number in our equation above"). To do that you could either:
a) Count the quarters until you're at the second quarter of 2006
b) Use some simple algebra to find it:

Where 3 is the number of full years preceding 2006, 4 is the number of quarter per year and "+2" is to calculate the second quarter.


So now that we know that t=14, we can substitute that into our equation and solve for the deseasonalised value.
It's fastest to use your calculator like so:
Code: [Select]
Solve(y=5.6970+(0.1364*14),yand you should get:

(round to the nearest whole number because we're talking about diiscrete data, specifically sales.)

2) "Use your deseasonalised value to find the correct seasonalised sale", or "predict the number of sales made in the second quarter in 2006".
With these, the second one especially, it's important to read the question (and highlight, if you so choose) that you're being asked for the seasonalised value, not the deseasonalised one. Lots of people forget to convert it.

We convert it by:

In English: Multiply the deseasonalised value by the appropriate seasonal index to find the sales value.

So, in terms of our question:




I think that's everything to do with working with seasonal indices, but I mostly copied this from my notes document and fixed some things so that they'd work on the forum. What makes sense to me might not make sense to you, so feel free to make me explain stuff if you need it. I'd also like to mention that I haven't proof read this so you can also yell at me for really terrible formatting mistakes. Don't worry, I'll only feel bad for not noticing them myself <3
sorry I'm using so many images, it's a lot neater than writing out every equation in LaTeX, and while I could use a BBCode table, these are screenshots from a summary sheet I made so it's a lot easier to share.
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on April 19, 2015, 04:45:13 pm
Would the terms 'bar graph' and 'column graph' be interchangeable, or if the question asked for  bar graph would you specifically have to draw bars that are going horizontally, and if it asked for column graphs would you have to draw vertical bars?

Because, looking through different textbooks and other resources, the two terms seem to be used synonymously?

:) Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on April 20, 2015, 10:23:17 pm
if this came up in the applications SAC (excel), how would I answer it?
using mean, range, iqr etc,describe your data in general terms

does this mean just stating the mean, range etc lol
what does 'in general terms' mean?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 21, 2015, 07:26:01 am
Would the terms 'bar graph' and 'column graph' be interchangeable, or if the question asked for  bar graph would you specifically have to draw bars that are going horizontally, and if it asked for column graphs would you have to draw vertical bars?
I'm not actually 100% on this one, but I'm pretty sure that they're used synonymously. I checked MathIsFun, and that seems to say they are the same; but sources based around MS Excel seem to be saying that bars are horizontal and columns are vertical (which is how Excel organises them so it's user friendly, I believe). If you're doing a question designed for an Excel based SAC, I'd differentiate between 'bar' and 'column'. Otherwise you should be safe just drawing it vertically (and I don't think I've seen a test question ask for anything other than that before - maybe a textbook though).

If you're really worried about it, judge it by the marks (say, 4 marks for drawing a bar chat showing all important features (pretty unlikely mark distribution, but you know)) or ask your teacher if they'll be marking on it.

Unless you're talking in terms of exams; I'd like to think they'd tell you if they wanted something specific. Then again, it's VCAA. They'll find a way to make it harder to understand.

if this came up in the applications SAC (excel), how would I answer it?
using mean, range, iqr etc,describe your data in general terms

does this mean just stating the mean, range etc lol
what does 'in general terms' mean?
Not sure on what 'general terms' means. It could mean not quoting the statistics in your comment, or rounding to integers or something like that. As a general rule, more information is better than less (as long as it's concise).

Since the question includes 'etc.' (I assume?) I'd say it's just asking you to write a report on it. What statistics you use kind of depends on the previous question(s); if you were asked to make a box plot I'd use the median(centre), IQR (spread), and comment on the shape and if there were any outliers. Most importantly all you need to do is cover all your bases - Shape, outliers, centre and spread (SOCS, if it helps you remember. It's always scribbled somewhere on my work).

I think it might just be an awkwardly phrased question though. As always, feel free to correct me if I'm wrong ;)

Title: Re: VCE Further Maths Question Thread!
Post by: Garden on April 21, 2015, 02:54:11 pm
Hi, I've got a few questions from broad to fairly specific, any help is greatly appreciated.

Is there an assumption that by using Pearson's correlation coefficient and r being lower than -0.24 or higher than 0.24, that the relationship is linear (assuming that the relationship is numeric and without outliers). Or can r be lower than -0.24 and higher than 0.24 and not be linear, even thought a weak/moderate/strong positive/negative relationship exists between the two variables.

For example, r in this case is 0.3515 (to 4 decimal places). From this, I've derived that a weak positive relationship exists between the two variables. Should I state this relationship is a weak linear positive relationship?

(http://i60.tinypic.com/vwwpvt.jpg)

I've also included the scatterplot if this' of any assistance.

(http://i60.tinypic.com/2nsp9co.png)

After further analysis using a residual plot, I've concluded that there is a clear pattern which confirms that the use of a linear equation to describe the relationship between the variables in non-suitable. Is this correct?

Can I jump from saying that a linear relationship exists between the variables when discussing r and then build a contradicting conclusion based on a residual analysis?

(http://i61.tinypic.com/e7fbpl.png)

Thanks again.  8)
Title: Re: VCE Further Maths Question Thread!
Post by: scarletmoon on April 21, 2015, 03:46:50 pm
Can deseasonalised values be larger than the actual value??
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on April 21, 2015, 05:21:22 pm
Can deseasonalised values be larger than the actual value??
Yes. They can be either bigger or smaller. Think about if you divide your actual value by the seasonal index (to get the deseasonalised figure obviously) and what happens when the seasonal index is <1.00 or great than >1.00. So the opposite applies for getting the actual value.
e.g deseasonalised figure is 3234 dogs, seasonal index is 1.4 in winter and 0.7 in summer.
calculating the actual value for winter dogs is given by 3234x1.4=4528 dogs. but if we want the summer dogs actual value then 3234x0.7=2264.
Make sense? I just said dogs because I couldn't think of anything
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 22, 2015, 05:28:33 am
For example, r in this case is 0.3515 (to 4 decimal places). From this, I've derived that a weak positive relationship exists between the two variables. Should I state this relationship is a weak linear positive relationship?

After further analysis using a residual plot, I've concluded that there is a clear pattern which confirms that the use of a linear equation to describe the relationship between the variables in non-suitable. Is this correct?

Can I jump from saying that a linear relationship exists between the variables when discussing r and then build a contradicting conclusion based on a residual analysis?

Thanks again.  8)

I'd say yes, call it linear if you're using r. When you use Pearson's, you're making the assumptions that: (Quoth Essentials, explanations are great. Love 'em)
You can always transform the data later on and state that it (Or, its r2 value) is the more appropriate because... or that it implies/shows that the natural data is not linear because... (so yes, you should be allowed to change your mind)

Seems pretty clear to me that your data is non-linear, but it probably still has quite a low Correlation/Determination.

*Although I haven't actually seen this one in practice. Maybe I just haven't run into a problem with outliers. I don't think it applies to your data anyway, so you should be fine.
Title: Re: VCE Further Maths Question Thread!
Post by: Garden on April 22, 2015, 06:13:32 am
I'd say yes, call it linear if you're using r. When you use Pearson's, you're making the assumptions that: (Quoth Essentials, explanations are great. Love 'em)
  • Variables are numeric
  • The relationship is linear
  • and that there are no outliers. The correlation coefficient can give a misleading indication of the strength of a linear relationship if there are outliers present*
You can always transform the data later on and state that it (Or, its r2 value) is the more appropriate because... or that it implies/shows that the natural data is not linear because... (so yes, you should be allowed to change your mind)

Seems pretty clear to me that your data is non-linear, but it probably still has quite a low Correlation/Determination.

*Although I haven't actually seen this one in practice. Maybe I just haven't run into a problem with outliers. I don't think it applies to your data anyway, so you should be fine.

Cheers Mighty!
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on April 24, 2015, 07:51:12 pm
Hi!
Just wondering if someone could help me with this question from the 2014 FM exam:

The seasonal index for heaters in winter is 1.25.
To correct for seasonality, the actual heater sales in winter should be

A. reduced by 20%
B. increased by 20%
C. reduced by 25%
D. increased by 25%
E. reduced by 75%


Have a SAC on Tuesday!  :-\
Thanks!!  :D
Title: Re: VCE Further Maths Question Thread!
Post by: random_person on April 24, 2015, 08:20:14 pm
Recall that:

x

x

=

= x

= x

This is a 20% reduction. A :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on April 24, 2015, 08:41:28 pm
Sorry to be annoying, but why is 0.8 x actual figure a 20% reduction? What am I missing?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on April 24, 2015, 08:47:59 pm
Sorry to be annoying, but why is 0.8 x actual figure a 20% reduction? What am I missing?

100% of something is the original amount (e.g. 1.0). 0.8 = 80% (100-80=20) of the existing amount.

Same situation where 200% of something is double the original (2x)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on April 24, 2015, 08:50:45 pm
OMG thanks! I felt so dumb...I realised the answer seconds after I posted the question. Must be my sleep signals messing with my brain. Thanks Aaron and random_person!  :D
Title: Re: VCE Further Maths Question Thread!
Post by: random_person on April 24, 2015, 08:53:40 pm
If you are unsure, you can plug in a value for the actual figure. It can be any value, but use 100 (Makes calculations much easier).

= x

We want to make the actual figure 100 (Any value to work out the percentage reduction).

= x =

Now, because the number has gone down from 100 to 80, it has decreased by 20. Right?

So, now we can work out the percentage that it has decreased.

% = x = % reduction.

This is a really long way, but if you are unsure, you can keep doing it this way! Make up any value for the actual value and it will work :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on April 24, 2015, 09:01:49 pm
Thanks so much! I get it now! You're a great teacher,  ;D.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 25, 2015, 04:26:22 pm
In regard to that question, n.a., it also appeared in 2011 Exam 1 somewhere if I recall correctly. Check that out too for extra practice!
Title: Re: VCE Further Maths Question Thread!
Post by: I am a unicorn on April 26, 2015, 07:02:33 pm
Hello :)

For part (d) of this textbook question I having some trouble... What is a residual plot?
The book doesn't explain it very well :'(

The table below shows the scores obtained by nine students on two tests. We want to be able to predict Test B scores from Test A scores.
Test A score (x) 18 15 9 12 11 19 11 14 16
Test B score (y) 15 17 11 10 13 17 11 15 19
Use your calculator to perform each of the following steps of a regression analysis.
a Construct a scatterplot. Name the variables test a and test b.
b Determine the equation of the least squares line along with the values of r and r 2.
c Display the regression line on the scatterplot.
d Obtain a residual plot.

Thankyou :) :) :)
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on April 26, 2015, 07:09:33 pm
Hello :)

For part (d) of this textbook question I having some trouble... What is a residual plot?
The book doesn't explain it very well :'(

The table below shows the scores obtained by nine students on two tests. We want to be able to predict Test B scores from Test A scores.
Test A score (x) 18 15 9 12 11 19 11 14 16
Test B score (y) 15 17 11 10 13 17 11 15 19
Use your calculator to perform each of the following steps of a regression analysis.
a Construct a scatterplot. Name the variables test a and test b.
b Determine the equation of the least squares line along with the values of r and r 2.
c Display the regression line on the scatterplot.
d Obtain a residual plot.

Thankyou :) :) :)

This can easily be done on your calculator :)

Once you have set up your scatterplot: click menu > analyse (4) > residuals (7) > residual plot (2)

Your residual plot will then appear!!
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on April 26, 2015, 07:20:23 pm
This can easily be done on your calculator :)

Once you have set up your scatterplot: click menu > analyse (4) > residuals (7) > residual plot (2)

Your residual plot will then appear!!
You can also get the residual plot by changing the variable on the y axis to 'stat.resid' (I think it's called that..) if you're using a ti-nspire
Title: Re: VCE Further Maths Question Thread!
Post by: random_person on April 26, 2015, 08:21:18 pm

 What is a residual plot?

The question asked what is a residual plot, but thanks for showing how to do it on a calculator :)

What is a residual plot?
A residual plot tells you how far each data value is away from your line of best fit. So, lets say your trend line passes through (4, 5) and your actual data value is at (4, 3) then the actual value is two units below the trend line, right? So on your residual plot, you would have a value at (0, -2). We then do this with all the actual values and plot them on the graph.

What is a residual plot used for?
A residual plot is used to determine whether a certain mathematical model is the best way of representing the data. For this, we look for patterns in the residual plot. If there is a pattern, then we need to apply a transformation to either the x or y axis. In further, you learn x^2, 1/x and log(x) transformations (and after you transform all your x/y values then find a new line of best fit and see if the residual plot shows a random pattern for the new model).

Hope this helps!
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on April 27, 2015, 12:52:07 pm
Hi,  I'm back!

Can someone have a look at the 2010 Exam 1? I'm wondering about the following questions:

1. Question 3. Can someone explain how to do that please?
2. Question 8. The correct answer is B, but I was pretty darn sure it was C. Isn't the y-intercept at 167? Am I reading it wrong?
3. Question 9. I got the answer right, but just generally, when doing a question like that, am I just supposed to sort of see a similar pattern between the actual data and the residual plots? Is that how it works? Coz that's what I've been doing....but is there a better way?

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on April 27, 2015, 01:06:39 pm
Is the distribution of this histogram bimodal? If not, what is it?
Title: Re: VCE Further Maths Question Thread!
Post by: random_person on April 27, 2015, 11:52:09 pm
Hi,  I'm back!

Can someone have a look at the 2010 Exam 1? I'm wondering about the following questions:

1. Question 3. Can someone explain how to do that please?
2. Question 8. The correct answer is B, but I was pretty darn sure it was C. Isn't the y-intercept at 167? Am I reading it wrong?
3. Question 9. I got the answer right, but just generally, when doing a question like that, am I just supposed to sort of see a similar pattern between the actual data and the residual plots? Is that how it works? Coz that's what I've been doing....but is there a better way?

Thanks!

Question 3

Question 3 Stimulus
(http://i.imgur.com/jQkg7NJ.jpg)
Question 3
(http://i.imgur.com/jZywnQz.jpg)

The 68% 95% 99.7% rule tells us that in a normally distributed data set:
68% of the data is within 1 standard deviation
95% of the data is within 2 standard deviations
99.7% of the data is within 3 standard deviations.

Because the question is asking you to use this rule, we say that the data is approximately normally distributed. Now using the boxplot, we can see that the median is 180 degrees. In a normally distributed data set, the mean=median. So the mean is 180 degrees. To find the standard deviation, we can find the interval which 68% of the data values lie. Approximately 38% of the data lie between 179 and 181 so 1 degree is incorrect. Keep doing this, and once we hit 68% at about 2 standard deviations making B the right answer.

Question 8

Question 8 Stimulus
(http://i.imgur.com/bWnnYDK.jpg)
Question 8
(http://i.imgur.com/yAH1NCU.jpg)

You are making a very common mistake! Look carefully at your x and y axis, and we can see that the origin is not located at (0, 0) and its located at (20, 160). This means that the y intercept will be a lot less than 167. The best way to do this is to find the gradient, and use the point (20, 167) to find the real y intercept. :P

Question 9

Question 9 Stimulus
(http://i.imgur.com/bWnnYDK.jpg)
Question 9
(http://i.imgur.com/RwCyPN1.jpg)

You can continue to do it that way, but the easiest way to do this question is to just rule out the incorrect answers by looking at different features of the graph. For example, we can see that there needs to be two values below the x axis, when x = 23.5. This rules out A and C. Next, we can see that four numbers have to be above the line y = 0 and four have to be below, because that is how it is with the original graph. This rules out D and E also :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on April 28, 2015, 07:30:57 pm
Thank you so much! That was very clear and easy to understand! Unfortunately, I ended up doing my SAC before I could see your reply! but thanks anyway! There weren't any similar questions, thank God!  ::)
Title: Re: VCE Further Maths Question Thread!
Post by: theBRENDAN97 on April 30, 2015, 05:06:27 pm
How do you confirm the skew of something, is it something to do with the proportion of mean to median?
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on May 01, 2015, 04:18:24 pm
When asked to list what types of transformations would be suitable for a table of data values, should I only base my answer on the 'circle of transformations' suggestion, or compare r-values for more accuracy? One of the transformations in the 'circle of transformations' gives a pretty low r value compared to the other transformations.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on May 01, 2015, 11:22:31 pm
How do you confirm the skew of something, is it something to do with the proportion of mean to median?
Thanks

You can, if you're just given these pieces of information.
A positively skewed graph will have the median on the left of the mean.
A symmetric one (similar to a bell curve/ normal distribution) will have the median and the mean at the same point/ value.
A negatively skewed graph will have the median on the right of the mean.

Alternatively, on a box plot, you will see this as:
positively skewed - the right 'whisker' will be longer than the left. (or the line from Q3 to the maximum)
symmetric - Q2 will be in the centre, both whiskers are equally long.
negatively skewed - the left 'whisker' will be long than the left.

Of course, you can work it out if you're given raw data as well.

(Source: some of this has been taken from my Further teacher's notes from last year.)

When asked to list what types of transformations would be suitable for a table of data values, should I only base my answer on the 'circle of transformations' suggestion, or compare r-values for more accuracy? One of the transformations in the 'circle of transformations' gives a pretty low r value compared to the other transformations.

I'm not really sure what you meant here (could you provide an example?), but how I interpreted this question, you're asking about questions which ask you what's the best transformation to apply for that set of data.

Well... the first thing is to see the overall look of the data. Is it curved? Which way is it curved?
How would an x2 or a 1/y transformation affect the data?
Would it have the highest possible r2 value? (Since the highest r2 value will provide you with the closest fitting transformation and 'neatest' line - i.e. "more accuracy" in your terms.) (I know I'm explaining this horribly, I'm sorry. I hope I explained it well enough. It's sort of difficult to word it.)
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on May 02, 2015, 01:26:53 am
When asked to list what types of transformations would be suitable for a table of data values.
I think the keyword here is list; definitely base it off the circle of transformations. As long as you're taking it from the right quadrant, it will be suitable. I'm 90% sure that they'll ask for 'most' suitable or appropriate if they want an r2. If it's a question written by a teacher you might want to double check though.

Generally, go by the marks. Not that it's always applicable, but if there's more marks for your question than transformations in your quadrant than I'd say it's also a good idea to list the r2 values and state which is most accurate.
(I know I'm explaining this horribly, I'm sorry. I hope I explained it well enough. It's sort of difficult to word it.)
^^^
This 100%. I would come around with answers way sooner if I knew how to put them into legible English.
Title: Re: VCE Further Maths Question Thread!
Post by: Wackky on May 04, 2015, 07:55:07 pm
Esssential Further Mathematics Question 21A 7b)

"Wendy and Frank buy and sell a block of land within the same financial year, making a profit of $62 000.
If Frank has other income of $32 000, and the profit is all his, how much capital gains tax must be paid on the land?"

The textbook answer says $21 480 but I keep getting $18 600 (Frank is in tax subdivision 3 so 62 000*0.30=18 600). Could I please have a second opinion from someone to clarify if I'm doing something wrong? Thanks. :)
Title: Re: VCE Further Maths Question Thread!
Post by: scarletmoon on May 06, 2015, 07:44:14 pm
When sketching inequalities do you shade the wanted or unwanted region. Does it matter as long as you have a key (stating what the shaded region represents) next to the graph?
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on May 06, 2015, 08:08:03 pm
When sketching inequalities do you shade the wanted or unwanted region. Does it matter as long as you have a key (stating what the shaded region represents) next to the graph?

You can shade either area as long as your key matches what you have shaded :)
Title: Re: VCE Further Maths Question Thread!
Post by: random_person on May 06, 2015, 11:17:16 pm
When sketching inequalities do you shade the wanted or unwanted region. Does it matter as long as you have a key (stating what the shaded region represents) next to the graph?

On exams they usually specify what region they want you to shade in. If you have a key you should be fine, but don't give the examiner a reason to deduct marks - easy thing is to just do what they have specified.
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on May 13, 2015, 05:57:18 pm
If you had to label the axis of a residual plot, what would you label them as?

Also, I had a conceptual question on a SAC.

You're given 200 data points (univariate data). You randomly select 20. You find the mid/min/max of your data.

If another person randomly selected 20 from the same 200 data points, do you expect the mid/min/max to be the same?
Title: Re: VCE Further Maths Question Thread!
Post by: Vexna on May 14, 2015, 09:53:48 am
Can someone explain to me what a triangular matrix is?

Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on May 14, 2015, 10:06:25 am
Can someone explain to me what a triangular matrix is?

Thanks.
It's when all the 0s of a matrix form a triangle on or just before the leading diagonal. They can be in the upper or lower corner, here's some examples:



Note that it doesn't matter what happens on the leading diagonal. The 0s in the last one could have a mixture of non-zeroes as well, I have just illustrated this way so that you can clearly see the "triangle".
Title: Re: VCE Further Maths Question Thread!
Post by: Vexna on May 14, 2015, 10:29:01 am
It's when all the 0s of a matrix form a triangle on or just before the leading diagonal. They can be in the upper or lower corner, here's some examples:



Note that it doesn't matter what happens on the leading diagonal. The 0s in the last one could have a mixture of non-zeroes as well, I have just illustrated this way so that you can clearly see the "triangle".

Thanks for such a clear explanation!
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on May 14, 2015, 07:24:49 pm
How many modes does there have to be before the data is considered to have "no modes"?

Example: 1, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9

The modes for this data are 1, 3, 5, 7, 9

Is having 5 modes too many?
It wouldn't matter. It wouldn't just randomly switch to "no modes", there is no set point for such a thing to happen haha!
Title: Re: VCE Further Maths Question Thread!
Post by: random_person on May 14, 2015, 10:00:17 pm
In a further core sac are we suppose to draw residuals/ scatterplots and all those other charts accurately? It just seems too time consuming tbh

Quite accurately in SACs depending on your teacher. My further teacher marked graphs quite harsh. Definitely label your axes and make your scale nice and even. On the exam, most questions will ask you to fill in a missing point, never seen an exam yet where you have to draw all the points.
Title: Re: VCE Further Maths Question Thread!
Post by: Losingmotivation on May 14, 2015, 11:30:26 pm
Hi everyone,
Had a question regarding residuals..
Say if I had a residual plot and it had a pattern (like the parabola kind of shape in the image attached), what transformation would you apply to make it linear?



Thanks! and goodluck for all your sacs everyone

Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on May 15, 2015, 05:07:16 am
in the image attached
I don't see an image :(
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on May 15, 2015, 09:30:03 pm
Hey everyone,

I have just dropped biology and am starting general maths 1/2. Do you think that it will impact my knowledge on the subject by starting a semester later?

Thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on May 15, 2015, 11:00:47 pm
Hey everyone,

I have just dropped biology and am starting general maths 1/2. Do you think that it will impact my knowledge on the subject by starting a semester later?

Thanks  :)

Wrong page, dude. But, to answer your question, if you're reasonably good at Maths and felt like you were on top of things in previous years (presumably Year 10 Maths), you should not be at too much of a disadvantage. The only problem you would have is catching up on the content that General Maths has already gone through.
Title: Re: VCE Further Maths Question Thread!
Post by: Losingmotivation on May 16, 2015, 05:54:20 pm
I don't see an image :(

idk it wont let me attach it for some reason. dammit. TT.TT
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on May 17, 2015, 05:22:30 am
idk it wont let me attach it for some reason. dammit. TT.TT

If you still haven't gotten it, you could upload it externally and insert it into your post like that. (Try Imgur, maybe?)
Title: Re: VCE Further Maths Question Thread!
Post by: I am a unicorn on May 17, 2015, 01:46:17 pm
Hi :)

Does anyone know why we use 'centering' when smoothing time series plots?
Like what does centering actually do to the data?

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on May 17, 2015, 02:23:32 pm
Hi :)

Does anyone know why we use 'centering' when smoothing time series plots?
Like what does centering actually do to the data?

Thanks :)

Centering is used when using even numbers (ie. 2 mean or 4 mean).

If we have an even number of data values, the value we find will fall between them, hence is not a time point from the original series; we don't want this to happen.

For example, 1 and 2 will become 1.5. However, if we centre the data we are finding the value that will form exactly on that point.

I'm not sure if this has clarified the concept enough for you? Let me know :)
Title: Re: VCE Further Maths Question Thread!
Post by: I am a unicorn on May 17, 2015, 02:56:14 pm
Centering is used when using even numbers (ie. 2 mean or 4 mean).

If we have an even number of data values, the value we find will fall between them, hence is not a time point from the original series; we don't want this to happen.

For example, 1 and 2 will become 1.5. However, if we centre the data we are finding the value that will form exactly on that point.

I'm not sure if this has clarified the concept enough for you? Let me know :)

Hi, thanks for answering my question :)
Really really good explanation  :) much better than the textbook  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Losingmotivation on May 17, 2015, 04:57:12 pm
If you still haven't gotten it, you could upload it externally and insert it into your post like that. (Try Imgur, maybe?)

its alright, all figured out now. asked my teacher. thanks anyways :)
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on May 18, 2015, 01:11:42 pm
Why might it be incorrect to assume that braking distance on cars is not normally distributed?
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on May 18, 2015, 01:26:41 pm
Why might it be incorrect to assume that braking distance on cars is not normally distributed?

Of course it would be. Remember that a normal distribution takes negative values - can a braking car break a negative distance?
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on May 18, 2015, 01:31:10 pm
Of course it would be. Remember that a normal distribution takes negative values - can a braking car break a negative distance?

Aha didn't think of it like that.

ty
Title: Re: VCE Further Maths Question Thread!
Post by: biy on May 18, 2015, 04:17:52 pm
do you think it's too late to get a statement for the further exams? I think i was deprived of a 50 since i was rank 1 all year and got A+ on all areas of study including BOTH exams, and the rank 3 got a 49.... I know 48 is a decent score, but I don't think i was fairly marked? Cheers :)
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on May 18, 2015, 04:44:00 pm
Did you get a exam slip of your score? Not just the grade, but your actual score?

I'd wager that the rank 3 just did better on the exam than you.
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on May 22, 2015, 04:59:54 pm
How would I do part h in the attachment without making guesses??
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on May 22, 2015, 06:08:55 pm
do you think it's too late to get a statement for the further exams? I think i was deprived of a 50 since i was rank 1 all year and got A+ on all areas of study including BOTH exams, and the rank 3 got a 49.... I know 48 is a decent score, but I don't think i was fairly marked? Cheers :)

I'm assuming you're talking about the Statement of Marks? According to the application form it closed on the 13th of February with the 12th of March being the absolute final chance. Unfortunately it is too late.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on May 23, 2015, 12:58:12 am
How would I do part h in the attachment without making guesses??

See Question 3e from Exam 2 in last year's paper. (Answers are out too.) This question is rather similar.
Title: Re: VCE Further Maths Question Thread!
Post by: I am a unicorn on May 24, 2015, 11:36:05 am
Hi :)

Just a quick question about units, do we need to give units for things like standard deviation?
For example, if we were given data on the 'number of children per school' and then asked to calculate the standard deviation, do we write the standard deviation is X children (or just X)

Thanks! :)
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on May 24, 2015, 11:56:30 am
Hi :)

Just a quick question about units, do we need to give units for things like standard deviation?
For example, if we were given data on the 'number of children per school' and then asked to calculate the standard deviation, do we write the standard deviation is X children (or just X)

Thanks! :)

You should just be writing X.
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on May 25, 2015, 08:13:48 pm
Would it be correct to say that the sum of the residuals from a regression line, would be close to 0?

:) Thankyou
Title: Re: VCE Further Maths Question Thread!
Post by: theBRENDAN97 on May 26, 2015, 05:44:16 pm
T= _                                  _   S= _     _
     |  0.66  0.04  0.04  0.08 |        |  25  |
     |  0.09  0.84  0.15  0.09 |        |  25  |
     |  0.13  0.08  0.77  0.07 |        |  25  |
     |  0.12  0.04  0.04  0.76 |        |  25  |
     -                                   -        -       -
     
Determine where the one hundred new cars will be in the long-term, how many weeks does it take to reach this steady state?
Is there a faster method to finding this?

I found the long-term= _            _
                                  | 12.4031 |  Adelaide
                                  | 42.5356 |  Canberra
                                  | 27.2318 |  Melbourne
                                  | 17.8295 |  Sydney
                                  -             -
Just wondering when you say the number of cars out of the matrix, even if it's above 0.5 do you round down seeing you can't have a fraction of a car? Or is it normal to round up?
Thankyou!!!
   
Title: Re: VCE Further Maths Question Thread!
Post by: more_vanilla on May 26, 2015, 06:25:15 pm
Hi!
Q: Given a table with average rainfall for 4 seasons, and the seasonal index for two of the seasons, how would i find the seasonal index for one of the missing seasons??
E.g. question 11 from core section of 2012 exam 1 (/attached pic) where we're asked to find the SI for spring
Answer was approx 1.13

Thank you :)
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on May 26, 2015, 08:10:51 pm
Hi!
Q: Given a table with average rainfall for 4 seasons, and the seasonal index for two of the seasons, how would i find the seasonal index for one of the missing seasons??
E.g. question 11 from core section of 2012 exam 1 (/attached pic) where we're asked to find the SI for spring
Answer was approx 1.13

Thank you :)


I'm not sure if this is right.... but this is how I worked it out.

4 - 1.01 - 0.96 = 2.03

2.03 is the sum of the winter and spring seasonal index

I then assumed that winter had a SI of 0.9 as its average rainfall was lower than that of summer, thus the seasonal index would be lower than 0.96.

Then, I did 2.03 - 0.9 which = 1.13 😊
Title: Re: VCE Further Maths Question Thread!
Post by: more_vanilla on May 26, 2015, 08:18:43 pm


I'm not sure if this is right.... but this is how I worked it out.

4 - 1.01 - 0.96 = 2.03

2.03 is the sum of the winter and spring seasonal index

I then assumed that winter had a SI of 0.9 as its average rainfall was lower than that of summer, thus the seasonal index would be lower than 0.96.

Then, I did 2.03 - 0.9 which = 1.13

Yeah I got the 2.03 but wasn't sure how to calculate the individual SI.
Your method makes sense... but i feel so insecure having to 'assume' the value of something :/
I guess I just want to be sure that something is right (especially for further T_T)

But thanks for helping me out ((:
Title: Re: VCE Further Maths Question Thread!
Post by: theBRENDAN97 on May 28, 2015, 06:49:52 pm
T= _                                  _   S= _     _
     |  0.66  0.04  0.04  0.08 |        |  25  |
     |  0.09  0.84  0.15  0.09 |        |  25  |
     |  0.13  0.08  0.77  0.07 |        |  25  |
     |  0.12  0.04  0.04  0.76 |        |  25  |
     -                                   -        -       -
     
Determine where the one hundred new cars will be in the long-term, how many weeks does it take to reach this steady state?
Is there a faster method to finding this?

I found the long-term= _            _
                                  | 12.4031 |  Adelaide
                                  | 42.5356 |  Canberra
                                  | 27.2318 |  Melbourne
                                  | 17.8295 |  Sydney
                                  -             -
[[Just wondering when you say the number of cars out of the matrix, even if it's above 0.5 do you round down seeing you can't have a fraction of a car? Or is it normal to round up? ]]
Thankyou!!!
   

Bump please I have a sac on this tomorrow.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on May 28, 2015, 07:38:01 pm
Your method makes sense... but i feel so insecure having to 'assume' the value of something :/
You could also find the seasonal index by doing the following:

Where SI is seasonal index, and SA is the seasonal average. The seasonal average is found by:


So, in context to your problem:
Spoiler

Then it's usually good practice with a question like this to check that your number is right by first substituting values you already have the answer to:

Which is true, so we're good to continue on with the others.

Then you could either use the addition/subtraction method to find Spring:

Or you could use the seasonal average again:

Just wondering when you say the number of cars out of the matrix, even if it's above 0.5 do you round down seeing you can't have a fraction of a car? Or is it normal to round up?     
Bump please I have a sac on this tomorrow.
It depends on the question. If it seems realistic to round down even if it's 0.5, do it. Further maths is primarily based around real world maths and if I were selling cars (or whatever the question is about, it's hard to tell) I wouldn't count profit on cars I couldn't technically sell. Might wanna ask your maths teacher if you're still not sure; they're the one marking your SAC, not me. :)
Title: Re: VCE Further Maths Question Thread!
Post by: chansena on June 01, 2015, 05:41:46 pm
Hi!


Could someone please help me with this question :)

Marcia is 1.5 m tall and casts a shadow 4 m long. Her shadow and the shadow cast by a tree
nearby are parallel on the ground. The end of Marcia’s shadow on the ground lines up with
the end of a shadow cast by the tree h m high. If the distance between the tree and Marcia
is 20 m, find h, the height of the tree.

 :-\
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on June 01, 2015, 05:56:19 pm
Hi!


Could someone please help me with this question :)

Marcia is 1.5 m tall and casts a shadow 4 m long. Her shadow and the shadow cast by a tree
nearby are parallel on the ground. The end of Marcia’s shadow on the ground lines up with
the end of a shadow cast by the tree h m high. If the distance between the tree and Marcia
is 20 m, find h, the height of the tree.

 :-\
similar triangles yeah
Title: Re: VCE Further Maths Question Thread!
Post by: chansena on June 01, 2015, 05:57:45 pm
similar triangles yeah

Yup but i keep getting the answer wrong I think im doing it correct
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on June 01, 2015, 07:40:05 pm
My textbook says: "Bivariate or (x,y,) data is data where both x and y could vary independently."

I thought in bivariate data there was always one independent and dependent variable?

:)
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on June 01, 2015, 08:41:14 pm
When would you say there is random variation in a time-series data?

Would it be whenever the trend is none of: cyclical or seasonal?

:)
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on June 02, 2015, 08:04:16 am
Marcia is 1.5 m tall and casts a shadow 4 m long. Her shadow and the shadow cast by a tree
nearby are parallel on the ground. The end of Marcia’s shadow on the ground lines up with
the end of a shadow cast by the tree h m high. If the distance between the tree and Marcia
is 20 m, find h, the height of the tree.

Not sure it's right, but I just had a quick look and got this:
Spoiler
My diagram, if you're interested
Don't judge me, I'm not an artist  8)

So what we have here is two triangles - Marcia and her shadow (triangle ABC); and the tree and its shadow (triangle ADE, don't fall for DCE. That'd be silly :) ).

Firstly, we have to find the scalar (let's call that x). We do that by taking the lengths of the same edge of the triangles.



Next, we apply that to the length that corresponds to h.




If you have time, you can also check that h is a reasonable number:
Value 'h' must be:
(true)
(true)
(true)
And finally, checking through the ratio between lines BC and AC, which should be the same and DE and AE.



So now we check that:

(true)

Therefore, the tree must be 9 metres tall.
You could also just do this problem by find the ratio I used before and doing some algebra by hand or on your CAS, like so:

My textbook says: "Bivariate or (x,y,) data is data where both x and y could vary independently."

I thought in bivariate data there was always one independent and dependent variable?

:)
Edit: Totally misread that. If both variables are independent, there's no relation between x and y. By extension, that means that Pearson's Correlation Coefficient and the Coefficient of Determination are either really low, or 0. I'm very close to 100% sure that you'll never get a question where both variables are dependent or independent as there's not much you can do with those in the way of SAC/exam questions. It's probably mentioned as a bit of background, so you're not totally blindsided if the VCAA or whoever brings it up in the future.

So you're pretty much guaranteed your normal dependent/independent combo, but there can be data that is fully independent or dependent.

When would you say there is random variation in a time-series data?

Would it be whenever the trend is none of: cyclical or seasonal?

:)

Unless your time series is a perfect line, there's always at least a little bit of random variation :)
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on June 05, 2015, 11:07:00 pm
kinda worried about mark allocations in further

i have a question where part a) (worth 2 marks) asks to find an interior angle of a (regular) pentagon
i just applied the rule that interior angle=180-360/n, where n= number of sides
=108 degrees

but in the solutions, the method used is dividing 360 by 5 (pentagon is made up of 5 triangles) to find the angles of each little triangle (=72 degrees) then doing 180-this (=108 degrees)
they allocated 1 mark for finding the angle after dividing (72) & 1 mark for the final answer (108)
however if i apply the formula, i skip the dividing step (well i still divide, but it is just part of the formula. the solutions name the inside angle etc, very specific)
would i not be awarded the mark? would a question this simple even be worth 2 marks?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on June 06, 2015, 10:19:08 am
would i not be awarded the mark? would a question this simple even be worth 2 marks?
I'd give you full marks for that; one mark for applying the formula and one mark for the correct answer. Well, as long as you wrote down your working out.

A question like this is probably only worth one mark on the exam though, so it's best to ask your teacher if you'd get the full marks on a SAC. :)
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on June 07, 2015, 07:34:56 pm
Thanks!
I have another question:
if a question asks you to find an answer and round to 1 decimal place (part a.), then asks you to do something else for part b that uses the answer to part a, should we uses the rounded number or the actual number?
eg
a) find radius to 1 d.p
b) calculate the perimeter of the circle

do you use the rounded radius or the actual value when calculating the perimeter?
I think that in methods you are supposed to use the actual number (unless specifically instructed not to), but in further questions & worked solutions, i noticed that they have always used the rounded number
Title: Re: VCE Further Maths Question Thread!
Post by: biy on June 07, 2015, 07:50:06 pm
Thanks!
I have another question:
if a question asks you to find an answer and round to 1 decimal place (part a.), then asks you to do something else for part b that uses the answer to part a, should we uses the rounded number or the actual number?
eg
a) find radius to 1 d.p
b) calculate the perimeter of the circle

do you use the rounded radius or the actual value when calculating the perimeter?
I think that in methods you are supposed to use the actual number (unless specifically instructed not to), but in further questions & worked solutions, i noticed that they have always used the rounded number

If it says to use the answer in Part a). then you must use the rounded answer, as that was the answer from part a). that you were instructed to use for part b).

:P :)
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on June 07, 2015, 08:17:21 pm
thanks biy
so if it does not tell you to use your rounded answer, you use the actual number?
or does it just always tell you to use the rounded answer

[e]
ive been doing a few years of further exams & noticed that the working in the assessor's reports always use the rounded numbers, whether or not it states to use them in the question

[e]
interestingly, i found one instance where both the rounded and unrounded answers were accepted
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/further2_assessrep_07.pdf
module 2, q 1c

[e]found a statement about it in the 2005 assessment report
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/furthermaths2nov05.pdf
"Exact numbers should be retained in the calculator and used in the second step unless the first step was the answer to a specific question. "
so it seems that if it is an answer to a previous question, it is assumed to be applied to other parts
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on June 09, 2015, 11:31:32 am
 Can someone please explain how to do parts d.) and e.) ? [in the image attached below]
I've also attached a photo with the answers :)

I keep getting the wrong answer :/ so I would appreciate any explanations!  :)

Thank you!

 
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on June 09, 2015, 02:48:52 pm
Can someone please explain how to do parts d.) and e.) ?
Ew, time series are annoying (imo).
2d
Quote from: 2d.
Use the least squares regression line and seasonal indices to estimate the sales for the business in the third quarter of 2004. Compare this with the actual figure for the third quarter of 2004 and find the percentage difference.
First off, there's two things the question is asking us for - a prediction of the cash made in the third quarter of 2004 and a calculation to show how accurate this is. I'm going to put these into two different spoilers because damn, I love spoilers.  ;)
First part
Right, so I've highlighted above the important parts of this question. First we need to use the regression line you worked out in part c - according to the answers, it was:

But first we need to put in the third quarter of 2004, which can be calculated like this:

Where 1 is the number of years that have passed, 4 is the number of seasons (well, quarters) in that year and the +3 is to represent the third quarter of the next year. So our quarter 7. This could also be found by counting it out on the table or graph, but... I like formulas, so nyuh.

So now we can substitute that into our regression equation to make a prediction like everything else in the core module:

(rounded to 2 decimal places)

But wait a second here, that prediction is wayyyy off. The actual value is 128. We're not finished yet, we need to multiply this by the appropriate seasonal index in order to get a deseasonalised value. I'm going to work out the seasonal index because a), I couldn't see it in the answers, and b) people often make a mistake here and that might be your issue :) .
(I am, however, skipping through the seasonal averages here because I'm too lazy to type that out. Unless you want it, in which case just let me know)


Ignore how that's messy, on a question like this I'd usually just throw that straight into my calculator. There's two values on top because we're working out a kind of average between the two appropriate seasonal indices so we can make a (slightly?) more accurate prediction. So our seasonal index is:


So like I said before, we just multiply this by our predicted value to deseasonalise it:

This is still not quite our answer, because the question states that all values are in thousands of dollars. All we need to do is multiply by 1000, so the sales in dollars for the third quarter of 2004 is (was? It's been ten years. :P) $128,174. My answer is 4 dollars off of the one you showed, because my rounding was a teensy bit inconsistent (hey, I blame the question for not stating how many decimal places!), but the method is the same.
second part
2e
Quote from: the question
Use the equation of the least squares regression line and the seasonal indices to forecast the sales for the business in the third quarter of 2005
Same stuff as before, but it's really important to note that's it's asking you for a totally unique value. So we first need to work out the value of the third quarter of 2005.

And then, like before, we put that in our regression equation:


This is not our final value! I seriously can't stress this enough - I tutor around my school casually (which means I work slave rates or for food  ::)) and this is seriously one of the most common mistakes people make (second only to not answering the question in context). We have to deseasonalise it first, by multiplying by the appropriate seasonal index. Luckily this is the third quarter like before so we can just grab that value instead of making me work out another one.


So that's our deseasonalised value. But we still haven't answered the question; remember that pesky context thing I mentioned like two sentences ago? That applies. Thankfully, you've highlighted the line in thousands of dollars so I'm pretty confident you already know ;)

Like the last one, I'm off by a teensy bit - that's a rounding issue. I think it's from the regression line, but it's not too much of a big deal here. Like I said before, my rounding was inconsistent. If the question doesn't sate how many decimal places to use, don't do what I did - pick a number and stick to it. Working with data, I'd recommend 4 decimal places (as that's easy to convert to percentage, and is more accurate than one or two).

I've also attached a photo with the answers :)
Legend. Saved me some time <3
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on June 16, 2015, 05:12:37 pm
I can't figure out how to do part b (see attachment). I've tried using the sine rule and made a mistake somewhere I think...any help would be awesome :)
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on June 16, 2015, 08:54:10 pm
I can't figure out how to do part b (see attachment). I've tried using the sine rule and made a mistake somewhere I think...any help would be awesome :)

i got 67.7m for part b. Is that correct? (if it is, i'll post the working out)
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on June 17, 2015, 04:32:01 pm
i got 67.7m for part b. Is that correct? (if it is, i'll post the working out)
Yeah that's it. That would be sooo good if you could, TIA!!!
Title: Re: VCE Further Maths Question Thread!
Post by: MorgnD on June 30, 2015, 01:37:06 pm
How do i complete this question from the core module? The answer booklet says the answer is e.

http://imgur.com/yvCKNrw

Thanks.

Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on June 30, 2015, 02:03:53 pm
The total sum of all indices must be 12. we are missing one of the twelve values. To find it use 12 minus the sum of the given values
Title: Re: VCE Further Maths Question Thread!
Post by: MorgnD on June 30, 2015, 02:18:58 pm
The total sum of all indices must be 12. we are missing one of the twelve values. To find it use 12 minus the sum of the given values

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: MorgnD on July 01, 2015, 11:43:48 am
How do i find r when i am given the equation of the least squares regression line and not a table of values?
Title: Re: VCE Further Maths Question Thread!
Post by: plato on July 02, 2015, 02:15:06 pm
How do i find r when i am given the equation of the least squares regression line and not a table of values?
A least squares regression equation can be found for any bivariate plot, regardless of the value of r.  Conversely, a known least squares regression line can fit an unlimited variation in the spread in a scatterplot.
Therefore, the equation alone cannot be used to find the value of r. You would need more information such as the standard deviation of both x and y and their mean values.
Title: Re: VCE Further Maths Question Thread!
Post by: dan97 on July 05, 2015, 08:12:49 pm
Hey i got a different answer to BoB regarding a networks question :/

The answer is apparently 5 but i found 6 trees

1- A-B-D-G
2- A-B-E-G
3- A-C-E-G
4- A-C-E-B-D-G
5- A-C-F-H-E-G
6- A-C-F-H-E-B-D-G

are one of these solutions wrong?
Title: Re: VCE Further Maths Question Thread!
Post by: dan97 on July 05, 2015, 09:02:01 pm
Another question from BoB... is the answer provided there wrong?

Question -  Draw a matrix of the graph.
The answer matrix says that A-C doesnt exist, however C-A does... is it wrong? Or am i missing something?
Title: Re: VCE Further Maths Question Thread!
Post by: plato on July 06, 2015, 11:18:54 pm
Hey i got a different answer to BoB regarding a networks question :/

The answer is apparently 5 but i found 6 trees

1- A-B-D-G
2- A-B-E-G
3- A-C-E-G
4- A-C-E-B-D-G
5- A-C-F-H-E-G
6- A-C-F-H-E-B-D-G

are one of these solutions wrong?
All of your six trees are valid.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on July 06, 2015, 11:20:50 pm
Another question from BoB... is the answer provided there wrong?

Question -  Draw a matrix of the graph.
The answer matrix says that A-C doesnt exist, however C-A does... is it wrong? Or am i missing something?

The graph does not show a connection from C to A. Hence the matrix should not.
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on July 07, 2015, 04:51:26 pm
Can't seem to get 83.6cm.
I got something like 85+ cm

cheers

I used similar triangles and got the ratio:

30/100 = x/12 (where x is the height of the smaller triangle.)
x = 3.6

The height of A above the ground is x + 80cm = 83.6cm

:)
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 03:31:09 pm
Hi couple of questions regarding backward scanning and critical paths

1) The question and graph in the attachment correspond to each other. The critical path by BoB is also shown there. That is wrong? Isn't it A-B-D-G?

2) How to go about the other question in the attachment? Help please. Thanks in advance :)
  ( i got this answer dont worry :) ) its 28%

Title: Re: VCE Further Maths Question Thread!
Post by: Berimbolo King on July 09, 2015, 03:51:21 pm
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

Module 3 question 2 c and d
Looking at the solutions, i kinda get it but not 100%. Could some please show me in detail how they get the answer. Seeing this question made me consider re-evaluating my aim for a 45+ study score.
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 04:12:50 pm
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

Module 3 question 2 c and d
Looking at the solutions, i kinda get it but not 100%. Could some please show me in detail how they get the answer. Seeing this question made me consider re-evaluating my aim for a 45+ study score.

Hi :)
 
Question 2C- you are looking for the breakeven point. Since the question is 'after how many hours' you can specify the exact breakeven point. They give u an equation d= -3x +16. Why dont we put this equation on the graph with michael :) this way we can see the breakeven point. The intercepts can be (0,16) and (5,1) Draw a line between these points and extending. The point where Michael and Katie meet is at 2 hours. This means that after 2 hours Katie passes Michael.

Question 2D-
3k apart can be from (Solve,Equation 1 (include time here)- Equation 2 = 3, time) on cas. This will give u a time of 13/8.

However the question asks u for how long they spoke to each other. You will have gotten this question right if u drew the graph. Because the line passes straight through at t=3... so 3 - 13/18 gives u the answer. Which is 1.38

Tips- Drawing the extra given equations with already an provided graph and equation is really important :)
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 09, 2015, 04:25:50 pm
Hey guys, i hope everyone is doing well in further.

This is not really a further maths question but i was wondering where everyone is up to in their further maths course? have you finished all SACS and finished the course? Or are you still completing the Further maths content and SACS? :P

Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 04:28:51 pm
Hey guys, i hope everyone is doing well in further.

This is not really a further maths question but i was wondering where everyone is up to in their further maths course? have you finished all SACS and finished the course? Or are you still completing the Further maths content and SACS? :P

I finished all the content in holidays before term 1.. (nerd lol).. I am now going back and doing 5-6 questions in every exercise.. there's a few things i forgot :(
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 09, 2015, 04:31:32 pm
I finished all the content in holidays before term 1.. (nerd lol).. I am now going back and doing 5-6 questions in every exercise.. there's a few things i forgot :(

Thats cool, dw i did something similar :P

Anyway have you finished al your SACS for the year?
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 04:34:51 pm
Thats cool, dw i did something similar :P

Anyway have you finished all your SACS for the year?

No i have 2 more to go.. Can't slack off during those.. need 100% for both. I had an allergic reaction during my matrices sac and got 74% :( fml and its my forte lol



Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 09, 2015, 04:36:53 pm
No i have 2 more to go.. Can't slack off during those.. need 100% for both. I had an allergic reaction during my matrices sac and got 74% :( fml and its my forte lol





Damn, thats really unfortunate  :-\ But im sure you can easily score a 100% in your final two! What SACS are they anyway?

I only have Graphs and Relations and Trig & Geo left
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 04:42:33 pm
Damn, thats really unfortunate  :-\ But im sure you can easily score a 100% in your final two! What SACS are they anyway?

I only have Graphs and Relations and Trig & Geo left

Graphs and Relations and Networks..

Is your textbook Maths Quest 12 Further Mathematics?

Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 09, 2015, 04:43:25 pm
Graphs and Relations and Networks..

Is your textbook Maths Quest 12 Further Mathematics?



Yup, How about you?
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 04:50:09 pm
Yup, How about you?

Same.. how good is 11D haha.. its a nice break from number punching on cas and further logic questions :D
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on July 09, 2015, 04:54:38 pm
Same.. how good is 11D haha.. its a nice break from number punching on cas and further logic questions :D

Hey, have you finished the coursework for networks yet? I've got a few questions to ask if you have.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 09, 2015, 04:56:43 pm
Same.. how good is 11D haha.. its a nice break from number punching on cas and further logic questions :D

I quite enjoy the Graphs and relations module :) I find it easy and fun. Not much content to learn either. Its cool.
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 04:58:20 pm
Hey, have you finished the coursework for networks yet? I've got a few questions to ask if you have.

I am currently as we speak starting a quota of questions from 15D.. any questions from 14A-15C i can help.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 09, 2015, 04:59:56 pm
I am currently as we speak starting a quote of questions from 15D.. any questions from 14A-15C i can help.

He might not be using maths quest :P, but you should be able to help him nevertheless  :)
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 05:01:24 pm
He might not be using maths quest :P, but you should be able to help him nevertheless  :)

You know what u made me think off... 'you should be able to help him'.. if only in further people get extra marks in the exam for doing other modules.. if they have extra time .. would be fun
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 09, 2015, 05:04:36 pm
You know what u made me think off... 'you should be able to help him'.. if only in further people get extra marks in the exam for doing other modules.. if they have extra time .. would be fun

Haha that would be cool, if u lost marks in some modules you can compensate with those extra modules :P

It would be a funny troll if you had extra time and you did those modules even though they arent going to be marked lol
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on July 09, 2015, 05:07:19 pm
I am currently as we speak starting a quote of questions from 15D.. any questions from 14A-15C i can help.

So, I see you are aiming for a high study score for further maths similar to what I want to achieve. Therefore, I'm assuming you know that every question is extremely important in the exam because losing ~6 marks can drop down your ss below 45. Hence, where i'm trying to go with this is whether or not it is 'dangerous' to do networks for the exam because of its ambiguity and the fact that it is based more on logical reasoning than maths; you generally do not know if your answer is absolutely correct. Therefore, are you planning to do another model for the exam to replace networks? That is what i'm most likely planning to do after I finished my networks sac. I want to see what you have to say, or anybody else, regarding this.
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 09, 2015, 05:17:58 pm
So, I see you are aiming for a high study score for further maths similar to what I want to achieve. Therefore, I'm assuming you know that every question is extremely important in the exam because losing ~6 marks can drop down your ss below 45. Hence, where i'm trying to go with this is whether or not it is 'dangerous' to do networks for the exam because of its ambiguity and the fact that it is based more on logical reasoning than maths; you generally do not know if your answer is absolutely correct. Therefore, are you planning to do another model for the exam to replace networks? That is what i'm most likely planning to do after I finished my networks sac. I want to see what you have to say, or anybody else, regarding this.

No i am gonna do networks for the exam. Mainly due to the fact i have a sac on networks. I personally don't want to study for something that wont be on the exam. Year 12 is a game.. u gotta find a way to get good marks in all subjects with your study time.. of course u have to compromise time (4 hours for one subjects.. 2 hours for another) by doing a different module on the exam.. u waste the time u spent practicing to get 100% on the networks sac.. and u have to teach yourself/ask questions/resources/teacher to ace this new module. You have to spend more time.. which means less time for other subjects.. or relaxing.. (which is important :P)..

For me personally i cant afford to learn new content.. i am aiming for a 48+ for Revolutions.. and in that case i spend 4 hours a day alone on that subject.. Thats my case.. you might be different. It really depends on your circumstances
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on July 10, 2015, 03:15:29 pm
Are step graphs simply just a hybrid function which is defined by constant functions?? Thankyou!
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on July 10, 2015, 04:26:54 pm
In response to the above questions, I've got a graphs and relations SAC next week and a Networks SAC towards the end of term.

Graphs and relations is extremely easy if you do methods, but sometimes the linear programming can get a bit tricky. I hate those goddamn discrete solutions when you have a continuous point, its a pain to work out.

Are step graphs simply just a hybrid function which is defined by constant functions?? Thankyou!

Yes.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on July 10, 2015, 07:29:38 pm
Hey Frank, did you do geometry and trigonometry module? How did you find the SAC?
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on July 10, 2015, 08:20:55 pm
Hey Frank, did you do geometry and trigonometry module? How did you find the SAC?
Nope, did matrices sorry.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on July 10, 2015, 08:23:15 pm
Hey Frank, did you do geometry and trigonometry module? How did you find the SAC?
I did Geometry and Trigonometry.

Just draw diagrams for everything! I lost some stupid marks on my SAC because I thought Cathy was looking towards the right of a watchtower with an angle of depression rather than towards the left. If I drew a diagram I would've realised that the particular situation was impossible.
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on July 11, 2015, 09:53:26 pm
What strategy do you guys use for those linear programming questions where the corner is continuous (eg. 10.2) but only integer solutions are accepted?
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 11, 2015, 10:00:08 pm
What strategy do you guys use for those linear programming questions where the corner is continuous (eg. 10.2) but only integer solutions are accepted?

integer numbers inside the area allowed- any numbers inside there. Time consuming but not many questions like these appears
Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on July 11, 2015, 11:14:53 pm
integer numbers inside the area allowed- any numbers inside there. Time consuming but not many questions like these appears

Yeah, going through past VCAA questions I couldn't find any.

But my teacher said I need to learn how to do this so I think it will be on the SAC coming up.
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 12, 2015, 12:01:40 am
Yeah, going through past VCAA questions I couldn't find any.

But my teacher said I need to learn how to do this so I think it will be on the SAC coming up.

Teacher said the same thing. I have done the textbook already and i am pretty positive its not on there. Yeah its worth looking at it if our teachers say its important.

In the unlikely event that it appears on the exam then you are in a great position :P
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on July 12, 2015, 10:52:18 am
How do you know when to use a point IN the feasible region and when to use a feasible region vertex?

Or should you never assume it is a corner?
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on July 12, 2015, 11:00:59 am
How do you know when to use a point IN the feasible region and when to use a feasible region vertex?

Or should you never assume it is a corner?

A corner is in the feasible region if the equations that make the feasible region are greater/less than or EQUAL to. That means you can use a corner. Its always the corner except for the content of the question. For example if the maximun profit made is in the corner (10.56,7.89) and the question is asking for how many tables to sell, you cant sell a 10.56 of a table. So then you have to look inside the feasible region for solid numbers to adjust yourself to the context of the question.
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on July 24, 2015, 03:55:31 pm
The answer to this is 1:9, however I had 1:27. The solutions said the scale factor had to be squared rather then cube because the length wasn't changing as the cross-sectional area did or something like that..I can't really follow what they mean...any help would be appreciated thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: plato on July 24, 2015, 06:58:38 pm
The answer to this is 1:9, however I had 1:27. The solutions said the scale factor had to be squared rather then cube because the length wasn't changing as the cross-sectional area did or something like that..I can't really follow what they mean...any help would be appreciated thanks!
Let's simplify the question by considering a cube with side length L. The volume is LxLxL =L3
If we triple the length of only one side, the volume is now LxLx3L=3L3 . This is only triple the original volume.
If we were to triple two of the sides of the original box, the volume is then Lx3Lx3L = 9L3 or 32L3
Only when we triple all three of the original sides will be get 3Lx3Lx3L = 27L3 which is 33 times the original volume

In summary - tripling only one dimension (ie L ot W or H) will multiply the original volume by 3 - ie only multiply by one scale factor
Tripling two dimensions only will multiply the original volume by 32 - ie square the scale factor
Tripling all three dimensions will multiply the original volume by 33 - ie cube the scale factor

Similarly if you were to multiply any two dimensions by 7, the volume will increase by a factor of 72 or 49

In your example, the ratio of the height of water:height of gauge = 1:3 or 1/3 as a fraction. This would also mean that the distance across the surface of the water to the sloping edge:similar distance across the top of the guage is also 1:3 or 1/3 as a fraction. But the width of the rain guage (between paralell triangular faces) has not changed. So only two dimensions are different and so we only square two ratios as in (1/3)2 = 1/9 or 1:9
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on July 26, 2015, 03:05:07 pm
Hey guys quick question, thanks in advance :)

The bearing of a ship,S from lighthouse,A, is 055 Degrees. A second lighthouse, B is due east of A. The bearing of S from B is 302 degrees. Find the magnitude of angle ASB.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on July 26, 2015, 05:36:11 pm
Hey guys quick question, thanks in advance :)

The bearing of a ship,S from lighthouse,A, is 055 Degrees. A second lighthouse, B is due east of A. The bearing of S from B is 302 degrees. Find the magnitude of angle ASB.

1. First step for a question like this is a diagram; my one's down below, but it's relatively simple as long you draw the compass markers along with each point.
(http://i.imgur.com/jV9t4N1.png)
obviously not to scale  ;)

2. Secondly, we need to find out the interior angles of our triangle so we can use the 180° rule to find the magnitude of ASB, or if you prefer the angle of S.

So to find the angle SAB, or the angle A, we us do this:


Where the 90 is used because the angle occupies solely the first quadrant. (if you need it, I can hook you up with a diagram for this, I'm a little ashamed it took me longer than it should to work that out  ::) )

We still don't have enough information to work out ASB, so let's work out SBA. It's not super obvious from my diagram, but the point S is in the fourth quadrant of B's compass so we do this to work out the magnitude:



So now we have the angles 35, 32 and x in our triangle. A quick bt of algebra or solve() should knock this right out:




And there (hopefully) is our answer: The magnitude of the angle ASB is 113°
Title: Re: VCE Further Maths Question Thread!
Post by: MorgnD on July 30, 2015, 09:15:43 pm
http://imgur.com/KmfyjLT
Can someone explain why E is the answer for this question?
Title: Re: VCE Further Maths Question Thread!
Post by: Floatzel98 on July 30, 2015, 09:22:49 pm
Key word here is vertical. Some of those answers are just straight line graphs. One is a hyperbola and one is a horizontal line.
Title: Re: VCE Further Maths Question Thread!
Post by: MorgnD on July 30, 2015, 09:24:34 pm
Key word here is vertical. Some of those answers are just straight line graphs. One is a hyperbola and one is a horizontal line.
Ahhh thank you
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on August 01, 2015, 04:27:28 pm
If a critical path goes through a dummy activity, do we include the dummy activity as part of the critical path?

For example, is the critical path B-G-J-M-N
                                                           or
                                             B-dummy-G-J-M-N
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on August 01, 2015, 08:50:43 pm
Quick question

The rectangular prism shown above has a square end with an area of 36 cm^2 (Just a regular rectangular prism...)

The length of the prism is twice the width of the prism. Point M is the midpoint of AB.
Angle CMD is closest to
A. 25.3°
B. 35.2°
C. 35.3°
D. 45.2°
E. 45.3°

I got C is this correct??
Thanks in advance
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on August 01, 2015, 09:05:48 pm
If a critical path goes through a dummy activity, do we include the dummy activity as part of the critical path?

For example, is the critical path B-G-J-M-N
                                                           or
                                             B-dummy-G-J-M-N

bump
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on August 01, 2015, 09:24:23 pm
Quick question

The rectangular prism shown above has a square end with an area of 36 cm^2 (Just a regular rectangular prism...)

The length of the prism is twice the width of the prism. Point M is the midpoint of AB.
Angle CMD is closest to
A. 25.3°
B. 35.2°
C. 35.3°
D. 45.2°
E. 45.3°

I got C is this correct??
Thanks in advance

Is there a picture that comes with the question? Because I don't know where point C, M and D are.
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on August 02, 2015, 11:13:42 am
If a critical path goes through a dummy activity, do we include the dummy activity as part of the critical path?

For example, is the critical path B-G-J-M-N
                                                           or
                                             B-dummy-G-J-M-N

The dummy of B would be classified as B'. Yes you include it as part of the critical path. Thus the critical path would be B-B'-G-M-N
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on August 05, 2015, 11:01:40 am
Is there a picture that comes with the question? Because I don't know where point C, M and D are.

Here's the question, coincidentally i have it lying around lol.

Title: Re: VCE Further Maths Question Thread!
Post by: Floatzel98 on August 05, 2015, 05:32:00 pm
Here's the question, coincidentally i have it lying around lol.
I got C as well. Should be correct :)
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on August 09, 2015, 12:46:02 pm
Ah thanks for that! Sorry I didn't have the picture with the question!
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on August 09, 2015, 03:20:34 pm
Could someone please explain how to do the question attached below?

(The answer is E)

Thankyou!
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 09, 2015, 03:41:10 pm
Could someone please explain how to do the question attached below?

(The answer is E)

Thankyou!
As printed, there is no correct answer to the question.
I suggest the difference equation is not meant to be
tn+1 = 2tn - 1
but
tn+1 = 2tn - 1 which would give E as the answer
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on August 09, 2015, 05:13:18 pm
As printed, there is no correct answer to the question.
I suggest the difference equation is not meant to be
tn+1 = 2tn - 1
but
tn+1 = 2tn - 1 which would give E as the answer

Thanks, that makes sense! :)
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on August 17, 2015, 11:14:30 am
Are we only expected to input integer values into objectives functions in vce?
Also with the 'sliding line' technique, why do we swap the coefficients of x and y at the start? thanksss
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 17, 2015, 08:39:33 pm
Are we only expected to input integer values into objectives functions in vce?
Also with the 'sliding line' technique, why do we swap the coefficients of x and y at the start? thanksss
I don't think you should restrict yourself to only thinking in integer terms.For example, non-integer values in objective functions could be examined if an answer is wanted correct to the nearest cent.
I am guessing at what you might mean by swapping the x and y coefficients "at the start"?
If the objective function is, say, P=12x-3y, then the sliding line method is easier if you could rewrite this function in the form y=mx+c
So P=12x-3y would become y=4x-P/3
Then slide a line, with a gradient of 4, up as far as you can go, and still touch the feasible region, to maximise P or down as far as you can go to minimise P.

Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on August 17, 2015, 08:54:56 pm
I don't think you should restrict yourself to only thinking in integer terms.For example, non-integer values in objective functions could be examined if an answer is wanted correct to the nearest cent.
I am guessing at what you might mean by swapping the x and y coefficients "at the start"?
If the objective function is, say, P=12x-3y, then the sliding line method is easier if you could rewrite this function in the form y=mx+c
So P=12x-3y would become y=4x-P/3
Then slide a line, with a gradient of 4, up as far as you can go, and still touch the feasible region, to maximise P or down as far as you can go to minimise P.
Well I looked online and the sliding method I learnt was that you get the coefficients of x and y in the objective function, so in this case 12 for the x and -3 for the y and you plot an x coordinate (-3,0) and y coordinate (0,12) and use a ruler to get a line between these two points, which gives the gradient of 4 that you got.
Do you know any links or have any info on what technique to use for finding the maximum of an objective function which doesn't at a corner point for some reason? Or is it always the corner point? Thankyou Plato!
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on September 04, 2015, 05:54:57 pm
Can you call a histogram a descriptive statistic? This question was actually on a psych exam and the solutions said it could be but it doesn't sound right..pls confirm
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on September 04, 2015, 06:13:05 pm
Can you call a histogram a descriptive statistic? This question was actually on a psych exam and the solutions said it could be but it doesn't sound right..pls confirm

Yes it is - from a histogram you can identify how data is distributed (e.g. positively skewed, negatively skewed, bell shaped). From a uni statistics perspective, it is a descriptive statistic.
Title: Re: VCE Further Maths Question Thread!
Post by: mondray on September 04, 2015, 09:00:46 pm
I did further last year and a friend asked me for help today. Unfortunately I completely forgot how to work things out. I would appreciate it if someone could help me out with this so I can forward it to my friend. Thanks in advance!
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on September 04, 2015, 09:11:05 pm
I did further last year and a friend asked me for help today. Unfortunately I completely forgot how to work things out. I would appreciate it if someone could help me out with this so I can forward it to my friend. Thanks in advance!
My dodgy attempt...
Volume ratio is Vy:3.375Vx    where Vy is the volume of y and Vx the volume of x
==> linear scale ratio is Ly:((3.375)^1/3)Lx   where Ly is the length of y as a ratio to the length of x
For area scale factor, square the linear scale factor ===> (1.5)^2=2.25
Therefore tsa of x is 13.95/2.25 = 6.2units^2
Title: Re: VCE Further Maths Question Thread!
Post by: Mikyt3 on September 08, 2015, 09:43:21 pm
Help please
Title: Re: VCE Further Maths Question Thread!
Post by: bills on September 08, 2015, 10:14:33 pm
Help please






Therefore, the answer is A. (I hope that was right, haven't did matrices for ages)
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on September 08, 2015, 10:24:47 pm






Therefore, the answer is A. (I hope that was right, haven't did matrices for ages)

Damn, beat me to it. It's right though :)

In general:

Where A, X and B are matrices.

As A-1A = I (identity matrix), you get:
Title: Re: VCE Further Maths Question Thread!
Post by: Adiamond on September 09, 2015, 05:29:05 pm
If we are asked to use a percentage value in a question (e.g. The organisation had 62% of the market share) and the question was asking us for the initial state matrix, would the matrix need to be in the decimal or integer form (e.g. 0.62 or 62)?
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on September 09, 2015, 05:37:03 pm
If we are asked to use a percentage value in a question (e.g. The organisation had 62% of the market share) and the question was asking us for the initial state matrix, would the matrix need to be in the decimal or integer form (e.g. 0.62 or 62)?

decimal form
Title: Re: VCE Further Maths Question Thread!
Post by: Adiamond on September 09, 2015, 05:38:07 pm
decimal form
Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on September 09, 2015, 08:33:07 pm
decimal form

Worth mentioning that sometimes they might refer to it as a 'proportion'. It came up in my SAC, and I think a few (company) practice exams.
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on September 12, 2015, 02:25:49 pm
Could someone tell me how to do q9 in 2010 VCAA exam 1?
Your help would be very appreciated :)

Oh... and does anyone have the solutions to the 2011 neap FM exam 1. I got this exam from Practice Exams - Where to get them for free? So please don't lock my post..
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on September 12, 2015, 02:46:42 pm
Could someone tell me how to do q9 in 2010 VCAA exam 1?
Your help would be very appreciated :)
Assuming that you mean the Core, here's how I did it:
(http://i.imgur.com/ykLd4pU.png)

Have a look at this for a second. There's a couple of notable patterns in relation to the points and the regression line:
1. Just left of 24cm, there are two dots that are vertically in line, below the regression line.
2. The second last point on the graph is significantly more distant from the regression line from the others, and is positive.
3. the first point is close to and above the regression line.

That should be more than enough information to eliminate to find our answer, like so:

(http://i.imgur.com/oz56pBq.png)
Edit: Whoops, made a mistake. D doesn't match criteria 2 or 3, it does match 1. Likewise, E does match criteria one and instead does not match criteria 3. The answer is still B though :)
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on September 12, 2015, 03:25:07 pm
Thanks so much!
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on September 12, 2015, 06:24:57 pm
Need help with Q8 Linear Relations FM 2013 exam 1. And also Q9 Linear Relations FM 2010 VCAA exam 1.
Your help would be very appreciated!
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on September 13, 2015, 09:53:07 am
Need help with Q8 Linear Relations FM 2013 exam 1. And also Q9 Linear Relations FM 2010 VCAA exam 1.
Your help would be very appreciated!

Too lazy to put a picture in, sorry! ;)

This one was actually kind of tough - I checked out the examiner's report and the itute solutions and neither of them really gave a clear, step by step explanation on how to do the question - although itute was a bit better than the VCAA.

Because Z is maximised at the points M and N, we can say that Z(m) and Z(n) are equal. For that to make much sense though, we need to know the coordinates of M and N. They're pretty clear on the graph as long as you work out the the interval is 5 (and maybe have a ruler to double check your points line up) but if you really wanted to you could set up some simultaneous equations to find them, too.

In any case, the coordinates of M and N are (20,50) and (45,25) respectively. We can set up two equations/functions for Z with this information:
(M)
(N)

Because we know Z has to be equal for both M and N to find a and b, we can quickly throw out some of the options that would give us something ridiculous - this means we don't have to worry about either of the options with negative values (A, E) and can probably get away without checking that D fits our rules because the numbers are pretty different to A, B and C. (Note: With multiple choice questions, you can usually eliminate two options after reading the question or minimal working out: in this case it was D and E)

So that leaves us with option B and option C to check, like so:
B.
B.
We can already see that these are equal (and therefore, B is the answer), but let's check C to be sure we haven't messed up somewhere:
C.
C.

So B is our answer - of course some of the constraints I set were maybe a little too general (option A could've probably been a reasonable choice) but in the end, there's only five equations to check so realistically you probably wouldn't need to set any at all. Hope that was helpful :)
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on September 19, 2015, 10:30:11 am
For a residual plot, does the x-axis scale remain the same and the y scale changes? thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 19, 2015, 10:46:53 am
For a residual plot, does the x-axis scale remain the same and the y scale changes? thanks

Yes :)

The x-axis remains the original x values but the y-axis becomes the residual values
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on September 20, 2015, 11:54:11 pm
for the exams, are we expected to know how to plot residuals on our CAS?
also, would we ever need to smooth a large number of results?
Title: Re: VCE Further Maths Question Thread!
Post by: Adiamond on September 21, 2015, 12:48:36 am
for the exams, are we expected to know how to plot residuals on our CAS?
also, would we ever need to smooth a large number of results?
I've seen some residual plots in the multiple choice, most can be done through elimination but if you have some extra time at the end it might be useful to plot the residual on your CAS, as for smoothing large numbers of results, you won't have to.
But it's definitely good to know how to do 4-moving median smoothing with centring and maybe even practice with 6-moving median/mean just to get a good feel for it.

-Someone please correct me if i'm wrong for the smoothing thing, i've not done too many exams.
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on September 21, 2015, 06:56:36 am
I've seen some residual plots in the multiple choice, most can be done through elimination but if you have some extra time at the end it might be useful to plot the residual on your CAS, as for smoothing large numbers of results, you won't have to.
But it's definitely good to know how to do 4-moving median smoothing with centring and maybe even practice with 6-moving median/mean just to get a good feel for it.

-Someone please correct me if i'm wrong for the smoothing thing, i've not done too many exams.

Yeah its usually from 2-6, the most common one i have seen is 5
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 21, 2015, 09:27:53 am
for the exams, are we expected to know how to plot residuals on our CAS?

It's not necessary, however I would recommend learning how to do it (it's pretty simple)! Usually on an exam 2 they would only require you to plot one (or two) residual points and they would give the rest to you - just because plotting a whole residual graph takes a lot of time.

Learning to do it on your CAS could come in handy for a multiple choice question or even to just double check your work :D
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on September 21, 2015, 09:43:32 am
thanks guys  ;D
also
do we need to label points with coordinates when we plot them?
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 21, 2015, 11:16:12 am
thanks guys  ;D
also
do we need to label points with coordinates when we plot them?

I'm not entirely sure what the rules are... but my teacher said to always label your coordinates so that the examiners are guaranteed to know where you are plotting :)
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 26, 2015, 11:40:08 am
Are we expected to know blending for graphs and relations?
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on September 26, 2015, 11:59:43 am
Are we expected to know blending for graphs and relations?

I have no clue what blending is and i have done every exam.. so probably not
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 26, 2015, 12:35:19 pm
Thanks!!

Also, for core, if a value is on the upper/lower fence is it considered an outlier? Or are outliers only points beyond the fences?
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on September 26, 2015, 12:48:44 pm
Thanks!!

Also, for core, if a value is on the upper/lower fence is it considered an outlier? Or are outliers only points beyond the fences?

fences? If they are a dot on the scale of a boxplot its an outlier. If you need to draw a boxplot and want to know which one is an outlier u can work it out with Q1-1.5xIQR and Q3+1.5xIQR. I dont get what u mean by fences.
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 26, 2015, 01:21:57 pm
fences? If they are a dot on the scale of a boxplot its an outlier. If you need to draw a boxplot and want to know which one is an outlier u can work it out with Q1-1.5xIQR and Q3+1.5xIQR. I dont get what u mean by fences.

At my school we call fences the exact point of (Q1 - 1.5IQR) and (Q3 + 1.5IQR).

So what I mean... those points mentioned above [(Q1 - 1.5IQR) and (Q3 + 1.5IQR)], if something was equal to that value would it be an outlier or not?

Example: If Q1 - 1.5IQR = 4 and I have a data value that was 4 - is this value an outlier? or not?
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on September 26, 2015, 01:54:38 pm
At my school we call fences the exact point of (Q1 - 1.5IQR) and (Q3 + 1.5IQR).

So what I mean... those points mentioned above [(Q1 - 1.5IQR) and (Q3 + 1.5IQR)], if something was equal to that value would it be an outlier or not?

Example: If Q1 - 1.5IQR = 4 and I have a data value that was 4 - is this value an outlier? or not?

An outlier must be below the lower fence or above the upper fence.

In response to your question, 4 is not an outlier because it is not less than the lower fence (4 cannot be below 4, can it?)
Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on September 26, 2015, 02:11:24 pm
At my school we call fences the exact point of (Q1 - 1.5IQR) and (Q3 + 1.5IQR).

So what I mean... those points mentioned above [(Q1 - 1.5IQR) and (Q3 + 1.5IQR)], if something was equal to that value would it be an outlier or not?

Example: If Q1 - 1.5IQR = 4 and I have a data value that was 4 - is this value an outlier? or not?

My book says it is an outlier - the equation is Q1-1.5xIQR (<=)x(>=)Q3+1.5xIQR, the (<=) means that it could be equal to, so it would be an outlier.

But other people are saying it isnt, so before i sue my book for trying to ruin my chance of a 50, i will wait for others to say stuff
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on September 26, 2015, 02:42:03 pm
My book says it is an outlier - the equation is Q1-1.5xIQR (<=)x(>=)Q3+1.5xIQR, the (<=) means that it could be equal to, so it would be an outlier.

But other people are saying it isnt, so before i sue my book for trying to ruin my chance of a 50, i will wait for others to say stuff

Well, according to maths quest, what i said above is correct because an outlier lies outside the interval of the attached picture.

What book are you using?
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 26, 2015, 03:27:53 pm
Well, according to maths quest, what i said above is correct because an outlier lies outside the interval of the attached picture.

What book are you using?

I use Essentials, and my book just says less than/greater than but not equal to? Ahhh!!

I have attached a photo.
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on September 26, 2015, 03:39:04 pm
I use Essentials, and my book just says less than/greater than but not equal to? Ahhh!!

I have attached a photo.

Yes, that's correct. What maths quest and essentials are saying is the same thing.

An outlier is a data point that is outside this interval
Q1 - 1.5 x IQR <= x <= Q3 + 1.5 x IQR

which is the same thing as an outlier that is within these intervals:
x < Q1 - 1.5 x IQR  and  x > Q3 + 1.5 x IQR
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 26, 2015, 03:58:22 pm
Yes, that's correct. What maths quest and essentials are saying is the same thing.

An outlier is a data point that is outside this interval
Q1 - 1.5 x IQR <= x <= Q3 + 1.5 x IQR

which is the same thing as an outlier that is within these intervals:
x < Q1 - 1.5 x IQR  and  x > Q3 + 1.5 x IQR

Isn't Maths Quest saying that an outlier can be, for instance, the value of Q1 - 1.5IQR, whereas Essentials is saying that would not be an outlier as it has to be less than (and not equal) to that value?

Sorry I'm really confused now :/
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on September 26, 2015, 04:03:44 pm
Isn't Maths Quest saying that an outlier can be, for instance, the value of Q1 - 1.5IQR, whereas Essentials is saying that would not be an outlier as it has to be less than (and not equal) to that value?

Sorry I'm really confused now :/

No, maths quest is not saying that. It is saying that an outlier must be less than (and not equal to) Q1 - 1.5IQR, which is what essentials is saying.

Basically, just understand this:
An outlier must be less than (but not equal to) Q1 - 1.5IQR or greater than (but not equal to) Q3 + 1.5IQR
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on September 26, 2015, 04:13:48 pm
No, maths quest is not saying that. It is saying that an outlier must be less than (and not equal to) Q1 - 1.5IQR, which is what essentials is saying.

Basically, just understand this:
An outlier must be less than (but not equal to) Q1 - 1.5IQR or greater than (but not equal to) Q3 + 1.5IQR

Oh right, sorry!

I totally misread the photo you attached and I assumed that x was the outlier (whereas it's the complete opposite haha).

Thanks for your help!! And sorry for all the confusion!
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on October 01, 2015, 08:08:28 pm
(http://i.imgur.com/XQVVfKN.png)
the answer is B
does that mean when considering average rate of change, we just look at the number (as if it had | | around it) and ignore the sign (positive/negative)
in this case it asked for maximum rate & the answer was when it was decreasing fastest
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on October 01, 2015, 08:15:09 pm
(http://i.imgur.com/XQVVfKN.png)
the answer is B
does that mean when considering average rate of change, we just look at the number (as if it had | | around it) and ignore the sign (positive/negative)
in this case it asked for maximum rate & the answer was when it was decreasing fastest

Yes, you just ignore the sign :)

The rate of change is basically just asking where the distance between one point and another is the greatest - this distance can be increasing or decreasing.

Hope this makes sense!!
Title: Re: VCE Further Maths Question Thread!
Post by: I am a unicorn on October 03, 2015, 01:04:22 am
Could someone please explain how to do this question?
(Graph is attached)

Using the 68–95–99.7% rule, the standard deviation for temperature is closest to
A. 1 °C
B. 2 °C
C. 3 °C
D. 4 °C
E. 6 °C

Spoiler
Answer is B

I thought we were meant to use the formula 'standard deviation=range/4' but it turns out that was wrong...

Thank you! :)

Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 03, 2015, 07:02:07 am
I thought we were meant to use the formula 'standard deviation=range/4' but it turns out that was wrong...

I thought the same when I did that question! My teacher told me to just do it graphically and mark the graph with the standard deviations given to you. Here:
Spoiler
(http://i.imgur.com/nrEG3xc.png)

I've only marked out a standard deviation of 2°C to save some time, but here you can see it fits the normal distribution's bell curve almost perfectly, whereas the others would be significantly over or under fitting (from memory).

Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 03, 2015, 04:15:11 pm
I thought we were meant to use the formula 'standard deviation=range/4' but it turns out that was wrong...
Thank you! :)
I thought the same when I did that question! My teacher told me to just do it graphically and mark the graph with the standard deviations given to you.

This was VCAA 2010 Exam 1 Core Q3 wasn't it?
Well, I'm just going to put this out there (and please don't hate me for saying this, I do this with good intention), but anything with standard deviation isn't always going to work out nicely - there's often exceptions. The curve you have here isn't exactly symmetrical, so you can't use that formula. (That formula only works in some cases. Be careful.)
 
It's possible to do this mathematically by inputting the data here into your CAS calculator's spreadsheet pages and getting the statistics (menu + 4 + 1 +1 on the colour CAS), but, it will take longer than the graphical version that MightyBeh has used. There are a number of other ways in which you could do this via calculator, some of which are not discussed in Further. With a sensible guess, you can eliminate many of the options, such as E (too big).

Changing the subject now, you guys should also note the following:
Title: Re: VCE Further Maths Question Thread!
Post by: I am a unicorn on October 03, 2015, 05:19:02 pm
I thought the same when I did that question! My teacher told me to just do it graphically and mark the graph with the standard deviations given to you. Here:
Spoiler
(http://i.imgur.com/nrEG3xc.png)

I've only marked out a standard deviation of 2°C to save some time, but here you can see it fits the normal distribution's bell curve almost perfectly, whereas the others would be significantly over or under fitting (from memory).
It's possible to do this mathematically by inputting the data here into your CAS calculator's spreadsheet pages and getting the statistics (menu + 4 + 1 +1 on the colour CAS), but, it will take longer than the graphical version that MightyBeh has used. There are a number of other ways in which you could do this via calculator, some of which are not discussed in Further. With a sensible guess, you can eliminate many of the options, such as E (too big).

Thanks MightyBeh and AngelWings! :)
Title: Re: VCE Further Maths Question Thread!
Post by: Berimbolo King on October 03, 2015, 05:57:55 pm
Could someone please explain how to do this question?
(Graph is attached)

Using the 68–95–99.7% rule, the standard deviation for temperature is closest to
A. 1 °C
B. 2 °C
C. 3 °C
D. 4 °C
E. 6 °C

Spoiler
Answer is B

I thought we were meant to use the formula 'standard deviation=range/4' but it turns out that was wrong...

Thank you! :)
My teacher told me when dealing with large data sets standard deviation= range/6.
Its not in the textbook and there was a similar question on my sac.
Title: Re: VCE Further Maths Question Thread!
Post by: belle123 on October 03, 2015, 07:27:52 pm
NUMBER PATTERNS

the sum of the first four terms of a geometric sequence has the value -30
the sum of the first and third terms is 30

the value of the common ratio for this sequence is:

a) -3
b) -2
c) -1
d) 0
e) 1


thanks in advance
Title: Re: VCE Further Maths Question Thread!
Post by: Berimbolo King on October 03, 2015, 07:42:20 pm
NUMBER PATTERNS

the sum of the first four terms of a geometric sequence has the value -30
the sum of the first and third terms is 30

the value of the common ratio for this sequence is:

a) -3
b) -2
c) -1
d) 0
e) 1


thanks in advance
I got b) -2
Equation 1 a(r^(4)-1)/(r-1)=-30
Equation 2 a+a(r)^(3-1)=30
Solve for a and r
a=6 and r=-2

Sorry i hope thats clear dunno how to use latex yet :/
Title: Re: VCE Further Maths Question Thread!
Post by: belle123 on October 03, 2015, 07:55:24 pm
I got b) -2
Equation 1 a(r^(4)-1)/(r-1)=-30
Equation 2 a+a(r)^(3-1)=30
Solve for a and r
a=6 and r=-2

Sorry i hope thats clear dunno how to use latex yet :/


yeah that does make sense!
thank you so much  :D
Title: Re: VCE Further Maths Question Thread!
Post by: Berimbolo King on October 03, 2015, 07:58:00 pm

yeah that does make sense!
thank you so much  :D
Youre welcome  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on October 04, 2015, 10:54:13 am
if a (1/y) transformation is done, and y=mx+c becomes 1/y=mx+c, is "1/y" now called the dependant variable? (instead of y)
something very similar to this came up heffernan 2015 prac exam 2 & the dependant variable was called 1/y
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on October 04, 2015, 11:14:21 am
if a (1/y) transformation is done, and y=mx+c becomes 1/y=mx+c, is "1/y" now called the dependant variable? (instead of y)
something very similar to this came up heffernan 2015 prac exam 2 & the dependant variable was called 1/y

I recently completed this exam however my school is marking it for us so I haven't got the solutions yet.

I wrote 1/y as my answer.

This was my reasoning: a dependent variable is defined as the variable that is measured. Since in this instant you were measuring 1/y not just y, it is considered the dependent variable. Does that make sense? :)
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on October 04, 2015, 11:16:54 am
I recently completed this exam however my school is marking it for us so I haven't got the solutions yet.

I wrote 1/y as my answer.

This was my reasoning: a dependent variable is defined as the variable that is measured. Since in this instant you were measuring 1/y not just y, it is considered the dependent variable. Does that make sense? :)
yep, thanks

another question
if something is 'one and a half times bigger than' something else, is it 1.5x the size or 2.5x the size
i think it is 2.5x but heffernan thinks 1.5x
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on October 04, 2015, 11:33:17 am
yep, thanks

another question
if something is 'one and a half times bigger than' something else, is it 1.5x the size or 2.5x the size
i think it is 2.5x but heffernan thinks 1.5x

I completely understand where you got your answer. I think the wording of the question is a bit funky (company papers are always like this hahaha)!

I'm not entirely sure... but I certainly don't see how you're wrong. Since the question said 1.5 times BIGGER (and not 'the size') I think you're right :)
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on October 07, 2015, 11:23:35 pm
Why is option D wrong?
in the solution, it says that you can only say 49% of the variation of the dependant variable is explained by variation in the independant variable but doesn't this work the other way around as well?
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on October 07, 2015, 11:42:22 pm
also,
how are we supposed to know these transformations? my textbook has a list of transformations & when to apply them but some of these are not in there...
is this likely to come up in an exam 1? (this is from MAV)
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 08, 2015, 06:04:29 am
Why is option D wrong?
in the solution, it says that you can only say 49% of the variation of the dependant variable is explained by variation in the independant variable but doesn't this work the other way around as well?
It doesn't work both ways, it's a bit like working out the gradient with 'run' over 'rise' instead the standard 'rise'/'run'.

also,
how are we supposed to know these transformations? my textbook has a list of transformations & when to apply them but some of these are not in there...
Looks like a pretty standard circle of transformations question to me? Does your textbook have all of these?
(http://i.imgur.com/a5V2ZjP.png)

is this likely to come up in an exam 1? (this is from MAV)

Probably not, but it's good to know anyway.  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 09, 2015, 11:36:59 pm
For Question 2.b) I was wondering, how do you know the two triangles given are similar triangles (Although the question doesnt really ask for this).

Also how would you solve question 2.d)

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 10, 2015, 01:06:15 am
The triangles in 2b. are similar because of the markings on the lines - I believe triangles indicate they're parallel, and short dashes indicate that they're the same length. Having two parallel lines means you 'know' that two angles are equal, and by extension you can find out the value of the third.

As for 2d., the second triangle has been rotated and flipped. After you notice, it's pretty simply:

Title: Re: VCE Further Maths Question Thread!
Post by: _fruitcake_ on October 10, 2015, 09:02:48 am
also,
how are we supposed to know these transformations? my textbook has a list of transformations & when to apply them but some of these are not in there...
is this likely to come up in an exam 1? (this is from MAV)

It comes up sometimes. Vcaa like putting these in the exam 2 as 5 markers often, but u never know it could be in the exam 1 this year. Grab off all the transformations, stick it in your book, its better safe than sorry.

I had useless crap in my summary book, such as when something is already inversed, to get it out of inverse u simply inverse it again. The 2015 mav prac exam had that :)
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 10, 2015, 08:19:17 pm
Thankyou for your help MightyBeh! :)

Could someone please help me on how to do the following attached question? Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 10, 2015, 08:49:06 pm
Thankyou for your help MightyBeh! :)

Could someone please help me on how to do the following attached question? Thanks!

Is the answer D? I'm pretty sure it can't be any of the answers with a 4 in it because that triangle isn't similar to any of the others (as far as I can tell, anyway).

Not confident on that though, I got a different (but pretty similar) answer when I did it myself.


Answer is A, if someone else doesn't I'll add working out later ;)
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 10, 2015, 09:05:44 pm
Thankyou for your help MightyBeh! :)

Could someone please help me on how to do the following attached question? Thanks!

Uhh is the answer A? If that's right i'll post the working out.
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on October 10, 2015, 09:06:54 pm
Yep thats what I thought too A...
Title: Re: VCE Further Maths Question Thread!
Post by: IntelxD on October 10, 2015, 09:38:41 pm
The answer is A. You need to recognise the similarity that exists between the two triangles which may not be apparent at first. Whilst there are a few ways to do this, the first thing I thought of was to reflect the lower triangle in the vertical axis to setup a diagram where you have angles between parallel lines. From here, it should be easy to recognise the equality that exists between the angles (alternate angles) in the triangles and thus the similarity between the two.
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 11, 2015, 09:24:41 am
Thanks for all the help everyone! Yes the answer is A :)

(Sorry I forgot to post the answer alongside the question! )
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 11, 2015, 09:47:01 am
I'm a bit unsure of how to do this question (Attached below) I don't really know which length you need to first find by using Pythagoras' theorm to figure out length BG?

Would it be from Point B to the middle of line DC?

Any help would be great!

The answer is 415cm :)

Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 11, 2015, 10:54:49 am
I'm a bit unsure of how to do this question (Attached below) I don't really know which length you need to first find by using Pythagoras' theorm to figure out length BG?

Would it be from Point B to the middle of line DC?

Any help would be great!

The answer is 415cm :)

You need to find GC, which is the same as .

If that doesn't help, here's the rest:
Spoiler
Measurements are in centimetres

(http://i.imgur.com/cUbt3NT.png)





(http://i.imgur.com/tN7lYF7.png)
Same thing with BG, but I'm too lazy to type it out (sorry! <3)
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on October 11, 2015, 03:58:59 pm
Hi, do you guys reckon it's worth doing ITUTE exams?
Cheers.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 12, 2015, 07:48:03 pm
Hi, do you guys reckon it's worth doing ITUTE exams?
Cheers.
Haven't tried them myself, but skimming through their 2014 batch makes me think that they might stray a bit from the course. Probably good to do if you have nothing else left, but otherwise I'd steer clear.

(Also, they don't write questions for all the modules?)
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 12, 2015, 10:56:24 pm
For the following contour map (image attached below) to find the horizontal distance between points A and B would I measure either the red line or the pink line with my ruler? (Before using the scale to convert this value to the distance in reality)

Any help would be great! :)
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 12, 2015, 11:33:06 pm
For the following contour map (image attached below) to find the horizontal distance between points A and B would I measure either the red line or the pink line with my ruler? (Before using the scale to convert this value to the distance in reality)

Any help would be great! :)

Red line.
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on October 13, 2015, 07:41:37 pm
Hi guys.
With Q 3 f(i) (VCAA 2012 Exam 2) in the examiners report, they say -"Alternatively, the ‘sliding line’ method could be used".
I got the question correct; but what is the 'sliding line' method?
Cheers.
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 13, 2015, 09:17:36 pm
Hi guys.
With Q 3 f(i) (VCAA 2012 Exam 2) in the examiners report, they say -"Alternatively, the ‘sliding line’ method could be used".
I got the question correct; but what is the 'sliding line' method?
Cheers.

what module is this?
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 14, 2015, 10:19:29 am
Can someone please explain how to do this question? (attached below)

The correct answer is D :)
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on October 14, 2015, 11:00:49 am
Graphs and relations
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 14, 2015, 05:53:44 pm
Can someone please explain how to do this question? (attached below)

The correct answer is D :)

There's probably a more accurate method, but I just drew a diagram.

That angle to the south is slightly less than the one to the north, so we know the line MP will end a little closer to that side when the sides OM and OP are the same length (note: I don't think they're the same in my diagram ::) ).
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on October 14, 2015, 07:22:45 pm
Also you can just sub in a random magnitude for each line. To make it simple just let both lines have a length of one. Then set up a diagram like mightybeh
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on October 14, 2015, 07:50:38 pm
Hi guys.
With Q 3 f(i) (VCAA 2012 Exam 2) in the examiners report, they say -"Alternatively, the ‘sliding line’ method could be used".
I got the question correct; but what is the 'sliding line' method?
Cheers.

Pretty much you rearrange the objective function until you have an equation in terms of y. Then using your ruler (this is why this technique is rarely use as it can be inaccurate), you slide your ruler across the feasible region (with it angled according to the equation you found), where the last point your ruler touches is the max/min value. For maximising, you begin sliding ruler from bottom left corner to top right, for minimising you start sliding ruler from top right to bottom left... does that make sense??
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 14, 2015, 09:47:46 pm
Thanks so much for the detailed explanation MightyBeh!

Thanks StupidProdigy! :)
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 15, 2015, 05:24:28 pm
Pretty much you rearrange the objective function until you have an equation in terms of y. Then using your ruler (this is why this technique is rarely use as it can be inaccurate), you slide your ruler across the feasible region (with it angled according to the equation you found), where the last point your ruler touches is the max/min value. For maximising, you begin sliding ruler from bottom left corner to top right, for minimising you start sliding ruler from top right to bottom left... does that make sense??

Wow lol, that method spells human error all over it,

Do you ever recommend using this method? Ever?
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on October 15, 2015, 06:25:29 pm
Wow lol, that method spells human error all over it,

Do you ever recommend using this method? Ever?

Yes. For (usually multiple choice) questions that don't give any values.

This type of question came up on one of the company papers I have done, and my teacher said the only way to solve it was to use the sliding line technique.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 15, 2015, 07:38:57 pm
Yes. For (usually multiple choice) questions that don't give any values.

This type of question came up on one of the company papers I have done, and my teacher said the only way to solve it was to use the sliding line technique.

Strange, i've never encountered a question where i was required to use this technique.
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on October 15, 2015, 08:31:07 pm
Strange, i've never encountered a question where i was required to use this technique.

It was mentioned in a VCAA examiners report....

So I would highly recommend learning how to do it. It is only unreliable when the data points are close together, otherwise it's a great way to proof-read your linear programming questions.
Title: Re: VCE Further Maths Question Thread!
Post by: Math_lord on October 16, 2015, 10:26:34 pm
PLEASE HELP!!

-A data set of 8 values has the following characteristics
Mode=41
Mean=32
Median=37.5
Range=32

One of the data set values is 36
Complete the data values in ascending order

17(already gven in the question),___,_____,_____,_____,_____,_____,_____
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 16, 2015, 10:33:15 pm
PLEASE HELP!!

-A data set of 8 values has the following characteristics
Mode=41
Mean=32
Median=37.5
Range=32

One of the data set values is 36
Complete the data values in ascending order

17(already gven in the question),___,_____,_____,_____,_____,_____,_____

17, 29, 36, 37, 38, 41, 41, 49

Is this correct? I'll provide an explanation if it is.
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on October 16, 2015, 10:43:24 pm
Nope... The mean is 32.
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on October 16, 2015, 11:13:49 pm
PLEASE HELP!!

-A data set of 8 values has the following characteristics
Mode=41
Mean=32
Median=37.5
Range=32

One of the data set values is 36
Complete the data values in ascending order

17(already gven in the question),___,_____,_____,_____,_____,_____,_____
I don't think the question works..maybe I'm missing something. I got to (17,a,b,36,39,41,41,49). Must be two 41's for it to be the mode, must have 39 to get a median of 37.5. Got the 49 from the range instruction. So that left me with a and b, which cannot give a sum and be numbers less than 17 and fit the instruction that the mean=32
edit: not the only one with this problem which is a relief, the question is wrong I'd say.
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 16, 2015, 11:55:39 pm
I don't think the question works..maybe I'm missing something. I got to (17,a,b,36,39,41,41,49). Must be two 41's for it to be the mode, must have 39 to get a median of 37.5. Got the 49 from the range instruction. So that left me with a and b, which cannot give a sum and be numbers less than 17 and fit the instruction that the mean=32
edit: not the only one with this problem which is a relief, the question is wrong I'd say.

When i did the question again, that is what i also got.
a + b = 33
This is impossible without one of them being lower than 17
Hence, i don't think there is a solution to this problem
Title: Re: VCE Further Maths Question Thread!
Post by: plato on October 17, 2015, 08:20:55 pm
It was mentioned in a VCAA examiners report....

So I would highly recommend learning how to do it. It is only unreliable when the data points are close together, otherwise it's a great way to proof-read your linear programming questions.
The sliding line method is best done by calculation rather than sliding a ruler. If you compare the calculated gradient of the objective function with the caculated gradients of the constraints, you can see which lines are steeper in comparison with others. It can then be easy to imagine sliding the objective function to its limit.
The sliding line method is not stipulated in the 2015 study design and so cannot be examined in 2015. However, it is written in the new study design starting in 2016 and so will be fair game from next year.
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 18, 2015, 07:02:21 pm
This question is for the Networks module.

When we have a loop in a network, does it count as a 1 or 2 in the adjacent matrix?
For example, for the network diagram below, which matrix is the correct one? (i don't know how to use the fancy tools to make an actual matrix)
      [0  1  1  1 0]                          [0  1  1  1  0]
      |1  0  1  2  0|                         |1  0  1  2   0|
A= |1  1  0  0  1|        OR       B= |1  1  0  0  1|
      |1  2  0  0  1|                         |1  2  0  0  1| 
      [0  1  1  1  1]                         [0  1  1  1  2]   

Maths quest says that A is correct,  but a neap exam says B is correct
Title: Re: VCE Further Maths Question Thread!
Post by: TheAspiringDoc on October 18, 2015, 07:08:29 pm
Must be two 41's for it to be the mode
Perhaps this is where everyone is going wrong? What if the were, say, three 41s?
Title: Re: VCE Further Maths Question Thread!
Post by: Math_lord on October 18, 2015, 07:17:26 pm
Hey guys,
Thanks so much for all helping out :)!
In the end, after so many possibilities, i have come to a final conclusion...THIS QUESTION IS WRONG

REASON: Because since the mean is 32 and there are 8 numbers(32*8=256) we should be getting a total of 256 when the numbers are added up, which clearly doesn't seem to occur.
Title: Re: VCE Further Maths Question Thread!
Post by: TheAspiringDoc on October 18, 2015, 07:19:31 pm
Hey guys,
Thanks so much for all helping out :)!
In the end, after so many possibilities, i have come to a final conclusion...THIS QUESTION IS WRONG

REASON: Because since the mean is 32 and there are 8 numbers(32*8=256) we should be getting a total of 256 when the numbers are added up, which clearly doesn't seem to occur.
Yes, but the whole question pretty much revolves around the "clearly doesn't seem to occur" bit, so that's not areally a valid reason?  ???
Title: Re: VCE Further Maths Question Thread!
Post by: Math_lord on October 18, 2015, 07:22:25 pm
Yes, but the whole question pretty much revolves around the "clearly doesn't seem to occur" bit, so that's not areally a valid reason?  ???

plezz.... The question is wrong because when preparing the task, iam pretty sure the teacher was meant to change the mean to something else ;)
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on October 22, 2015, 04:09:59 pm
Need help with Q9 MODULE 2 EXAM 1 2009.
Cheers.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 22, 2015, 05:35:29 pm
Need help with Q9 MODULE 2 EXAM 1 2009.
Cheers.
This one took a few steps, and there's probably a few ways to go about it. Here's how I did it though:

Firstly, the only part of the diagram we currently have enough to work with is the triangle at the bottom.
(http://i.imgur.com/luH1For.jpg)

We have the three side lengths, so we can only work out the area (Heron's rule) or any of the angles (cosine rule). Given that the question has nothing to do with finding the area, cosine rule is the obvious choice here. For simplicity, I'm finding the angle QMT. (Note that TQM is a right angle, I just forgot to add that to my diagram ::) )

For simplicity's sake, let the angle QMT = theta



Next we need to find the length TQ (the distance between the pole and the wall) because the pole will fall along this line and (conveniently? ;) ) create a triangle for us to work with.

(http://i.imgur.com/ynMqjJf.jpg)
(again note that the angle MQT is 90 degrees, I just didn't mark it (whoops))

Finally, it's just some pythagoras'
(http://i.imgur.com/3mZQkMC.jpg)

Hope that's clear, it was a kind of round-about question.
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 22, 2015, 07:35:06 pm
I managed to get the right answer for the attached question below. However, my working out was overly complicated and, although i got the right answer, i believe there is a much simpler way of working it out.

Can someone please attempt the question and post their working out?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 22, 2015, 07:47:29 pm
I managed to get the right answer for the attached question below. However, my working out was overly complicated and, although i got the right answer, i believe there is a much simpler way of working it out.

Can someone please attempt the question and post their working out?

What's the answer? I think I got it but my method feels too simple  ::)
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 22, 2015, 08:00:06 pm
What's the answer? I think I got it but my method feels too simple  ::)

Post your answer and i'll say if it's right or wrong. This has been the most challenging question i've seen in further maths so far, so it's good practice.
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on October 22, 2015, 08:02:55 pm
Post your answer and i'll say if it's right or wrong. This has been the most challenging question i've seen in further maths so far, so it's good practice.
1/sqrt(2pi)?
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 22, 2015, 08:06:21 pm
1/sqrt(2pi)?

Nope. But remember the question asked for three decimal places, so your answer would be 0.399, but it's still not right.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 22, 2015, 08:13:59 pm
Nope. But remember the question asked for three decimal places, so your answer would be 0.399, but it's still not right.

Wouldn't it just be finding the area of the triangle: using herons formula. Which comes to 0.43301

Then since area ratio is 1:2. Divide area of the triangle by two: 0.21650
To find area of circle


Then since pi*r^2 = area of the circle

Divide 0.21650 by pi = 0.06891 and then sqrt of 0.06891 = 0.263

Isn't that it?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 22, 2015, 08:16:43 pm
I got 0.214m, yay or nay?
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 22, 2015, 08:17:24 pm
Wouldn't it just be finding the area of the triangle: using herons formula. Which comes to 0.43301

Then since area ratio is 1:2. Divide area of the triangle by two: 0.21650
To find area of circle


Then since pi*r^2 = area of the circle

Divide 0.21650 by pi = 0.06891 and then sqrt of 0.06891 = 0.263

Isn't that it?

I see where you're coming from, and that's how i originally thought of it, but that's not it.

The scale factor is for the area of the SHADED region of the triangle to the area of the REFLECTIVE material. Not for the area of the WHOLE triangle to the area of the REFLECTIVE material.

You got mixed up here.
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 22, 2015, 08:19:42 pm
I got 0.214m, yay or nay?

Yay :)

Is this how you worked it out?

A(shaded region) = [0.5 x sin(60)] - [pi x r^2]
A(reflective material) = [0.25 x sin(60)] - [0.5 x pi x r^2]
pi x r^2 = [0.25 x sin(60)] - [0.5 x pi x r^2]
r = 0.214 m

This question was in fact a VCAA question. Only 4% got full marks.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 22, 2015, 08:22:56 pm
Yay :)

Is this how you worked it out?

A(shaded region) = [0.5 x sin(60)] - [pi x r^2]
A(reflective material) = [0.25 x sin(60)] - [0.5 x pi x r^2]
pi x r^2 = [0.25 x sin(60)] - [0.5 x pi x r^2]
r = 0.214 m

This question was in fact a VCAA question. Only 4% got full marks.


Oh right I see, I'm on my phone so I didn't really read the question properly lol. Anyways good question to post. What year is this from?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 22, 2015, 08:23:28 pm
Yay :)

Is this how you worked it out?

A(shaded region) = 0.5 x sin(60) - pi x r^2
A(reflective material) = 0.25 x sin(60) - 0.5 x pi x r^2
pi x r^2 = 0.25 x sin(60) - 0.5 x pi x r^2
r = 0.214 m

This question was in fact a VCAA question. Only 4% for full marks.

Nope! Working's attached :)

Edit: Although the method was very similar
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 22, 2015, 08:27:24 pm

Oh right I see, I'm on my phone so I didn't really read the question properly lol. Anyways good question to post. What year is this from?

2004 exam 2

Nope! Working's attached :)

Edit: Although the method was very similar

Oh, i see. So you just found the area of the triangle differently.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 22, 2015, 08:30:26 pm
2004 exam 2

Oh, i see. So you just found the area of the triangle differently.

I can see why only 4% got it full marks. I can see many people making the same mistake I did at first glance.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 22, 2015, 08:32:14 pm
2004 exam 2

Oh, i see. So you just found the area of the triangle differently.

Yep! I actually really liked this question, I should give those older exams a shot  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 22, 2015, 08:36:10 pm
Yep! I actually really liked this question, I should give those older exams a shot  ;)

Yeah this question was actually really cool. Geo  and trig is my favourite module so if there are more questions like these I should give those older exams a shot.
Title: Re: VCE Further Maths Question Thread!
Post by: coolbeans on October 23, 2015, 11:57:37 am
My teacher all year has been teaching us business maths, networks & decision maths and matrices. I got my sac back for business and I did terrible so my cousin has decided to last minute teach me trig/geometry for the exam IN ONE WEEK! Does anyone think this a reasonable/horrible idea, considering business was my weakest subject in further? I find trig and geometry a lot simpler and less complicated than business (because business has sooo many formulas to remember) but i'm just worried I'm going to crash and burn when the exam comes around!!
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on October 23, 2015, 12:01:43 pm
My teacher all year has been teaching us business maths, networks & decision maths and matrices. I got my sac back for business and I did terrible so my cousin has decided to last minute teach me trig/geometry for the exam IN ONE WEEK! Does anyone think this a reasonable/horrible idea, considering business was my weakest subject in further? I find trig and geometry a lot simpler and less complicated than business (because business has sooo many formulas to remember) but i'm just worried I'm going to crash and burn when the exam comes around!!

It is a risk (no doubt), but if you think you can understand that topic more than business maths... I say go for it. I contemplated doing this when I was in Year 12, and I honestly regret not doing it. I was the opposite, I hated geo/trig.

Just make sure you go over the past exams and ensure that you understand how to solve problems in geo/trig, because you really need to solve them at a fast pace (so to speak), as 90 minutes isn't a significant amount of time. This is what stumps alot of people in Further, careless mistakes.
Title: Re: VCE Further Maths Question Thread!
Post by: mattcorr_ on October 23, 2015, 01:42:32 pm
Matrices module, 2011, Exam 1, Question 8

The assessors report does not cover this module because it was completed 'reasonably well' which leaves illiterates like me, helpless

Can someone show a worked solution, my cas does not want to solve for x with these types of questions
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 23, 2015, 02:34:22 pm
Matrices module, 2011, Exam 1, Question 8

The assessors report does not cover this module because it was completed 'reasonably well' which leaves illiterates like me, helpless

Can someone show a worked solution, my cas does not want to solve for x with these types of questions

Key word is inverse.
According to the question, , or 'k' in matrix A is equal to the inverse in the same place.

To find the inverse manually, you need to work out the determinant (ad-bc). Working's attached if that doesn't clear it up for you :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 23, 2015, 02:39:58 pm
Matrices module, 2011, Exam 1, Question 8

The assessors report does not cover this module because it was completed 'reasonably well' which leaves illiterates like me, helpless

Can someone show a worked solution, my cas does not want to solve for x with these types of questions

So basically:

1: Using CAS, find the inverse of the matrix in the question.
2: This gives you a matrix with all inverse values in terms of k.
3: The one that we are concerned with is the one in the corresponding position to k in the original matrix; that is: (-9/4(4k-9)) -1/4.
4: W know that these two are equal because the question tells us that the matrix equals it's inverse.
5: So now, put these into the CAS and solve for k.
6: CAS will give you k=0 or k=2.
7: Try both of them in the matrix and find their inverses. Only k=2 will give you the exact same matrix as the inverse.
8: Therefore, answer is D.
Hope that helps!
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 24, 2015, 10:45:44 am
Hey Further Maths students,
Im having trouble with understanding this question and why they used the volume scale factor, since the radius for both shapes is the same, wouldn't the sides be out of proportions and therefore the use of k, k^2 or even k^3 become impossible?
-i have attached the question, but its the first time doing this so i may have done it wrong, so ill link the VCAA exam it is off. (http://)
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath2-w.pdf    Page 15, Q4B TRIG

-VCAA used the solution of: (20/50)^3=0.064, 1-0.064=93.6%        I just dont understand the first bit, and if anyone has a different way of solving this or explaining this, that would be great! I prefer longer methods, like actually finding the volume of both, although this did not work when i tried that....

Thanks in advance, good luck everyone.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 24, 2015, 11:13:13 am
Hey Further Maths students,
Im having trouble with understanding this question and why they used the volume scale factor, since the radius for both shapes is the same, wouldn't the sides be out of proportions and therefore the use of k, k^2 or even k^3 become impossible?
-i have attached the question, but its the first time doing this so i may have done it wrong, so ill link the VCAA exam it is off. ()
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath2-w.pdf    Page 15, Q4B TRIG

-VCAA used the solution of: (20/50)^3=0.064, 1-0.064=93.6%        I just dont understand the first bit, and if anyone has a different way of solving this or explaining this, that would be great! I prefer longer methods, like actually finding the volume of both, although this did not work when i tried that....

Thanks in advance, good luck everyone.

Same method as shown by the VCAA, but with diagrams because why not. In the assessor's report, it looks like people assumed that the radius would stay the same even though there's less oil; which is pretty reasonable until you draw a diagram. Attached my poorly drawn working out if it makes it any clearer :)
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on October 24, 2015, 11:20:19 am
Hey Further Maths students,
Im having trouble with understanding this question and why they used the volume scale factor, since the radius for both shapes is the same, wouldn't the sides be out of proportions and therefore the use of k, k^2 or even k^3 become impossible?
-i have attached the question, but its the first time doing this so i may have done it wrong, so ill link the VCAA exam it is off. ()
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath2-w.pdf    Page 15, Q4B TRIG

-VCAA used the solution of: (20/50)^3=0.064, 1-0.064=93.6%        I just dont understand the first bit, and if anyone has a different way of solving this or explaining this, that would be great! I prefer longer methods, like actually finding the volume of both, although this did not work when i tried that....

Thanks in advance, good luck everyone.
Alternative way (basically the same but with more working and a bit more intuitive)-Choose an arbitrary radius, say for example 2cm (initial radius when h=50). Then find the little radius at h=20 by scaling down using your arbitrary value. So 2/50=r/20 --->r=4/5. So Big volume=(pi*2^2*50)/3 and small volume=(pi*(4/5)^2*20)/3. Now just do 1-(small volume/big volume)
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 24, 2015, 11:26:51 am
Thank you so much!
Those diagrams will actually help me with future tricks that VCAA will use as i completely forgot the radius of a cone is not uniform (decreases as you reach the pointy end)
-I completely understand this now, once again thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 24, 2015, 11:28:42 am
Previous message was to the first response......

-This is to the second response i got.....
Oh that also makes sense, that shall be helpful if they use another type of shape to try and trick me in the exam, thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 24, 2015, 02:38:10 pm
Hi everyone
I was going over all the past exam papers I have done and I am stuck on question 13 from Core 2006 exam 1.
I'm just confused about how they got 0.86 in the formula on VCAA report
Title: Re: VCE Further Maths Question Thread!
Post by: Lawyer on October 24, 2015, 02:48:01 pm
Hi everyone
I was going over all the past exam papers I have done and I am stuck on question 13 from Core 2006 exam 1.
I'm just confused about how they got 0.86 in the formula on VCAA report

deseasonalised number of unemployed = 373.3 – 3.38 × month number
The month number is June which is 6
Thus 373.3-3.38x6 = 353.02.

But the question asks for actual number (actual number= deseasonalised figure x seasonal index)
Thus 353.02x0.86.
The 0.86 is the seasonal index of June which is shown in the box below Question 11- that explicitly says it refers to questions 11,12 and 13.

Thus the answer is 303.5 which is closest to A.
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 24, 2015, 02:52:51 pm
I didn't even realise there was a table there :-[  Should read the questions carefully
Thank You so much :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 25, 2015, 12:44:22 pm
Hi guys,

Can someone help me with VCAA 2007 Exam 1 Question 9 from Graphs and Relations?

Thanks! :)
Title: Re: VCE Further Maths Question Thread!
Post by: Lawyer on October 25, 2015, 01:01:21 pm
Hi guys,

Can someone help me with VCAA 2007 Exam 1 Question 9 from Graphs and Relations?

Thanks! :)

Okay so the question asks you for to maximise at y= 2x + ky. And it has to be at the point (100,0)

Immediately from this question i get the feeling that the lower k the better. Why? Because the point is asking at (100,0) So it does not matter what k is, because k times y= 0. However the greater the value K is then the greater all the other points are.

You have 5 choices: A) 1 B) 2 ect. If K=1, then it would maximise (100,0) because all the other points (50,0) (25,25) and (50,50) would maximise the objective function as k increase.

So to maximise the point (100,0) at 2x+ky then k would have to be the smallest, so that (100,0) = 200, would not be smaller than the other points.

Further explanation: Lets take k=1. Then 2x100+1x0=200. If we substitute 1 into the other points, the max value would still be 200, which is at (100,0)
However if we take 2. The 2x100+2x0= still equals 200, but it is not the only maximum value as now the points (50,50) is. So 2x50+2x50=200. So if it was 2 then the maximun value would exist at (100,0) and (50,50) but the question asks for only at (100,0) so it has to be lower than 2, which is 1, thus it is A
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 25, 2015, 01:03:29 pm
Hi guys,

Can someone help me with VCAA 2007 Exam 1 Question 9 from Graphs and Relations?

Thanks! :)

Probably not the fastest way to do it, but I'd first cross out 4 and 5 (because they're silly, try checking the function with those at (50,50)) then define a function so I could quickly test the rest:
Code: [Select]
Define Z(k,x,y)=2x+(k*y)
Then you can test each one using the following
Code: [Select]
z(k,x1,y1) ≥ z(k,x2,y2)
So testing k=1;
Code: [Select]
z(1,50,50) ≥ z(1,100,0)comes up with false, so we know that the point (100,0) is larger than (50,50) when k = 1.

Making sure that this is consistent, testing k = 2 comes up with 'true' (because they're equal at this point, Z=200).

Testing k = 3 in the same format also comes up true so that can't be our answer.

I picked (50,50) as the testing point because the others seemed kinda far out but in exam conditions I'd probably recommend checking them at least once. So the answer is A. 1

Edit: Damn, Lawyer beat me to it  ::)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 25, 2015, 01:24:04 pm
Thank you so much, Lawyer and MightyBeh! :)
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 25, 2015, 07:05:26 pm
Hi,
Can anyone please help me with question 9 from 2008 exam 1 (Graphs and Relations) Why isn't the answer E?
and also questions 8 2009 exam 1 (Graphs and Relations)
Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 25, 2015, 07:18:58 pm
Okay, I can help you with the 2009 Question 8:

-So we know that he has a fixed cost of $150 and he also needs to pay each worker $20 which is also part of his cost.
-There are 3 workers, so the actual cost is $60 per hour, if you take into account all the workers he needs to pay.
-Therefore, your cost equation is C=60x+150, where x is the number of hours worked, and C is cost.
-The question tells us that the job takes 4 hours, so now sub in x=4 into the cost equation and you get Cost= $390.
-Now for the revenue cost, we don't the amount he charges, but we do know that it takes 4 hours, and he charges by the hour.
-Therefore, your revenue equation is: R=4p, where R is revenue, and p is the price he charges.
-To break even, the cost should equal revenue so: 390=4p.
-Solve for p. 
-Ta-dah! Hope that helps! :)
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 25, 2015, 07:48:08 pm
Thank you so much n.a
You made it so much easier to understand the question :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 25, 2015, 08:19:18 pm
No worries, and I'm sorry I couldn't help with the other one, only I got that wrong too, so...can't help much. But I'm sure the amazing AN people will be on it soon! :)
Title: Re: VCE Further Maths Question Thread!
Post by: bae on October 25, 2015, 08:46:18 pm
Hi,

I'm really stuck on question 2c and onwards in matrices on last years exam 2, could anyone explain to me how I'm supposed to keep the state matrix constant?

Thanks  :D

PS, I got 36/40 on exam 1 and 47/60 on exam 2 (lower than usual) anyone know what kind of SS I'm in for??
Title: Re: VCE Further Maths Question Thread!
Post by: paper-back on October 25, 2015, 08:47:36 pm
Hi,
Can anyone please help me with question 9 from 2008 exam 1 (Graphs and Relations) Why isn't the answer E?
and also questions 8 2009 exam 1 (Graphs and Relations)
Thank you

For Question 9;
We know that Profit = Revenue - cost
We can determine the cost function through finding the equation of the straight line which is:
C = 2x + 50
Since the person has sold 150 cards, their cost will total to: $350 (2x150+50=350)
The person has sold 150 cards, so their revenue will be 150 x y (where y = selling price)
Since the profit is $175, we can plug all these information into the P= R -C equation so that;
175 = 150y+350

Solve for y, and you get the selling price as $3.50

EDIT: holi moli, ignore me. I thought you were asking for question 9 of 2009
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 25, 2015, 08:48:53 pm
Hi,
Can anyone please help me with question 9 from 2008 exam 1 (Graphs and Relations) Why isn't the answer E?

E is correct if you forget (like I did the first time I did the question ::) ) that only the corner points of the feasible region are to be included in your calculation (I'm looking at you, (0,100)  >:().

To (accurately) find the coordinates of point M we first need to know the equation of the lines and solve for the intersection. I'm too lazy to type it out so I'm going to assume you had no issues with this part and know that the coordinates of M are (20,50). (Let me know if you did have issues though and I'll show you <3 )

So our corner points are: (0,60), (20,50), (40,0) and (0,0). Obviously we don't need to include 0,0 though because none of the equations are going to be maximised there.

Then I just subbed in the three reasonable points to each equation (thankfully the answer is A.)

(0,60)
(M)
(40,0)

So the function Z = x + y is maximised at the point M. :)

But I'm sure the amazing AN people will be on it soon! :)

(http://i.imgur.com/lo5ILSl.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: paper-back on October 25, 2015, 08:56:39 pm
Hi,

I'm really stuck on question 2c and onwards in matrices on last years exam 2, could anyone explain to me how I'm supposed to keep the state matrix constant?

Thanks  :D

PS, I got 36/40 on exam 1 and 47/60 on exam 2 (lower than usual) anyone know what kind of SS I'm in for??

Are you referring to where it states that "the number of voters in the city is expected to remain constant until the election is held in June?"
Title: Re: VCE Further Maths Question Thread!
Post by: bae on October 25, 2015, 08:58:23 pm
Are you referring to where it states that "the number of voters in the city is expected to remain constant until the election is held in June?"

Yes exactly that, I don't get how to keep it constant
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 25, 2015, 09:02:49 pm
Hi,

I'm really stuck on question 2c and onwards in matrices on last years exam 2, could anyone explain to me how I'm supposed to keep the state matrix constant?

Thanks  :D

PS, I got 36/40 on exam 1 and 47/60 on exam 2 (lower than usual) anyone know what kind of SS I'm in for??

What's your SAC average?

Workings for 2c - 2d are attached, did you need help with question 3 as well?  :)

Edit: Do you mean in the part before 2b where it says 'the number of voters in the city is expected to remain constant'? 90% sure that just means the sum of all the values in any state matrix will add up to 12000.
Title: Re: VCE Further Maths Question Thread!
Post by: bae on October 25, 2015, 09:41:35 pm
What's your SAC average?

Workings for 2c - 2d are attached, did you need help with question 3 as well?  :)

Edit: Do you mean in the part before 2b where it says 'the number of voters in the city is expected to remain constant'? 90% sure that just means the sum of all the values in any state matrix will add up to 12000.

Thanks heaps! Yeah that's what I meant with the state matrix. My sac average is A+

See, for your working out you do S3=T^2 x S1, I enter the exact same thing in my calculator yet my answer will always exceed 12000, is it something to do with my settings??

EDIT [ Thanks for the help, I think it was something to do with my calculator because it's working now :) ]
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 25, 2015, 09:46:16 pm
EDIT: holi moli, ignore me. I thought you were asking for question 9 of 2009
haha its okay paper-back. Thank you anyway for helping :)
E is correct if you forget (like I did the first time I did the question ::) ) that only the corner points of the feasible region are to be included in your calculation (I'm looking at you, (0,100)  >:().

To (accurately) find the coordinates of point M we first need to know the equation of the lines and solve for the intersection. I'm too lazy to type it out so I'm going to assume you had no issues with this part and know that the coordinates of M are (20,50). (Let me know if you did have issues though and I'll show you <3 )

So our corner points are: (0,60), (20,50), (40,0) and (0,0). Obviously we don't need to include 0,0 though because none of the equations are going to be maximised there.

Then I just subbed in the three reasonable points to each equation (thankfully the answer is A.)

(0,60)
(M)
(40,0)

So the function Z = x + y is maximised at the point M. :)

(http://i.imgur.com/lo5ILSl.jpg)
I still don't understand MightyBeh :( Because I got the two  equations and the intersection (20,50) then I sub 20 and 50 into Z=x+4y and I got 220. Why isn't that right?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 25, 2015, 09:50:17 pm
Thanks heaps! Yeah that's what I meant with the state matrix. My sac average is A+
With your 2014 exam scores, around ~39+ raw I think.

I still don't understand MightyBeh :( Because I got the two  equations and the intersection (20,50) then I sub 20 and 50 into Z=x+4y and I got 220. Why isn't that right?


Because when you test other corner points of the feasible region, (0,60) and (40,0), you get 240 and 40, which means the function is maximised at (0,60) instead of M. :)
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 25, 2015, 09:56:37 pm
Thank you so much!!! :) MightyBeh
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 25, 2015, 09:58:38 pm
Thank you so much!!! :) MightyBeh
you're welcome! <3
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 25, 2015, 10:22:03 pm
How many marks can you lose in exam 2 for a 50 study score? Assuming full marks in SACs and exam 1
Title: Re: VCE Further Maths Question Thread!
Post by: paper-back on October 25, 2015, 10:31:11 pm
How many marks can you lose in exam 2 for a 50 study score? Assuming full marks in SACs and exam 1
Probably around 3 max
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 25, 2015, 10:53:47 pm
Hi, I have more questions 2009  exam 2 question 4 (graphs and relation)
When it says determine the maximum total profit what points do we use (corner points or points within the feasible region)
and question 3 part d 2007 exam 2 (graphs and relation)
Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 25, 2015, 10:54:42 pm
Hey guys, i got both these questions correct, however im not really sure i know the reasoning behind them so if anyone is able to clarify why that would be great.

So with Question 1 B here, they convert the sides lengths into the same unit of measurement (cm or m, both work) which i understand, and then they use k^2 which again i understand.

With Question 5 here,a block of land has an area of 4000m^2, and the map is 10cm^2. Following the last question, wouldnt we have to convert these into the same measurement? Can anyone explain clearly to me why they dont do this?

Cheers!
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 26, 2015, 10:16:07 pm
Hey guys, i got both these questions correct, however im not really sure i know the reasoning behind them so if anyone is able to clarify why that would be great.

So with Question 1 B here, they convert the sides lengths into the same unit of measurement (cm or m, both work) which i understand, and then they use k^2 which again i understand.

With Question 5 here,a block of land has an area of 4000m^2, and the map is 10cm^2. Following the last question, wouldnt we have to convert these into the same measurement? Can anyone explain clearly to me why they dont do this?

Cheers!

So, Question 1b ii:
-We know that a 3cm line represents 600 cm, so linear scale factor (k)= 1:200. Keep in mind that you have to convert both of them to the same unit, preferably cm.
-Next, to find the area scale factor, you need to square k. That gives you 1:40 000
-Now, you need to find x:600 000, because 60m^2 = 600 000 cm^2.
-Solve, and that gives you 15 cm^2.

Question 5:
-Area scale factor is 10:40 000 000 if you convert 4000 m^2 to cm^2.
-Simplifies to 1 cm:4 000 000 cm
-Square root to find linear scale factor. That gives you 1 cm:2000 cm
-Convert to metres.

Hope that helps!
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 26, 2015, 11:02:27 pm
Yes that works thank you, idk what i was doing. Probably just over worked and tired lol , as ive actually been doing really well on the practice exams and then i get stuck on something easy because of silly mistakes...

Cheers though!!
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 27, 2015, 10:46:01 am
Okay, so now I have a question about scales. When a question talks about the measurements of a map as being in mm, do we always convert it to cm? That is, do we always assume that scales are in cm:cm; like where it says 1:5000, would it always be assumed that it is referring to cm, seeing as they hardly ever specify the units?

Yeah, my wording's a bit off.
Everyone excited/nervous/bleh about the exam coming up? 
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 27, 2015, 11:29:33 am
Okay, so now I have a question about scales. When a question talks about the measurements of a map as being in mm, do we always convert it to cm? That is, do we always assume that scales are in cm:cm; like where it says 1:5000, would it always be assumed that it is referring to cm, seeing as they hardly ever specify the units?

Yeah, my wording's a bit off.
Everyone excited/nervous/bleh about the exam coming up?

I would assume 1 unit : x units? I reckon that if it seemed ambiguous at all in a VCAA question they'd specify units.

Pretty bleh about exam 1 personally, but think exam 2 will turn out okay  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 27, 2015, 12:22:09 pm
I would assume 1 unit : x units? I reckon that if it seemed ambiguous at all in a VCAA question they'd specify units.

Pretty bleh about exam 1 personally, but think exam 2 will turn out okay  ;)

Thanks, and you'll do great; you seem really smart! :)

I have another question:
For the Question attached and highlighted, I did it and got 200%, but the answer is 100%. Why is that?

Title: Re: VCE Further Maths Question Thread!
Post by: dankfrank420 on October 27, 2015, 12:44:14 pm
Thanks, and you'll do great; you seem really smart! :)

I have another question:
For the Question attached and highlighted, I did it and got 200%, but the answer is 100%. Why is that?

You may have calculated that 2011 is twice the original (hence 200%), but this is an INCREASE by only 100%, since the original of 2005 is already 100% of the 2005.

Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 27, 2015, 12:46:13 pm
You may have calculated that 2011 is twice the original (hence 200%), but this is an INCREASE by only 100%, since the original of 2005 is already 100% of the 2005.



Damn yeah I was about to ask for working out  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 27, 2015, 01:01:00 pm
You may have calculated that 2011 is twice the original (hence 200%), but this is an INCREASE by only 100%, since the original of 2005 is already 100% of the 2005.

Yeah, that's pretty much what I did. Thanks! :)
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 06:42:24 pm
Hey guys. 2013 VCAA Exam 1: Can you please help me with question 8 Trig and question 7 and 8 in graphs and relations. Thanks so much!
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 27, 2015, 06:53:47 pm
Hey guys. 2013 VCAA Exam 1: Can you please help me with question 8 Trig and question 7 and 8 in graphs and relations. Thanks so much!

For Question 8, Geo and Trig, basically you'd have to draw a diagram to get the answer, *was sort of lazy drawing it out right now, so here's the solution from itute. Basically you find the angle of the larger triangle as 51 degrees, and then since it lies on a 180 degree line you take away 51 from 180 to get the bearing of Black tower from white tower.


For Question 7 Graphs and Relations, all you really have to do is find the gradient of the straight line, as it represent the value for k in the rule. so the rule is H = k/d^2, to find k just find the gradient of the straight line which you could use any two points for. You should get the gradient as 58.4. Hence the rule is H=58.4/d^2.

Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 07:16:53 pm
For Question 8, Geo and Trig, basically you'd have to draw a diagram to get the answer, *was sort of lazy drawing it out right now, so here's the solution from itute. Basically you find the angle of the larger triangle as 51 degrees, and then since it lies on a 180 degree line you take away 51 from 180 to get the bearing of Black tower from white tower.


For Question 7 Graphs and Relations, all you really have to do is find the gradient of the straight line, as it represent the value for k in the rule. so the rule is H = k/d^2, to find k just find the gradient of the straight line which you could use any two points for. You should get the gradient as 58.4. Hence the rule is H=58.4/d^2.

Why can't I substitute in numbers for x and y to get k? 25.7 = k/(0.44^2). The answer I got was C; H = 4.98/d^2. I substituted in the x coordinate H = 4.98/(0.44^2) and the answer is 25.7, the y value in the question. What am I doing wrong? And can you help me with question 8? Thanks you so much!!
Title: Re: VCE Further Maths Question Thread!
Post by: Losingmotivation on October 27, 2015, 07:35:25 pm
Hey everyone, I'm aware that the SS you get is quite dependent upon both your sacs and your exam, but considering you have an A average in your sacs (most likely going to scale up from the level of difficulty??), what kind of percentage should you be aiming for in the exam to have a chance of obtaining a SS of over 40?

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 27, 2015, 07:47:04 pm
Why can't I substitute in numbers for x and y to get k? 25.7 = k/(0.44^2). The answer I got was C; H = 4.98/d^2. I substituted in the x coordinate H = 4.98/(0.44^2) and the answer is 25.7, the y value in the question. What am I doing wrong? And can you help me with question 8? Thanks you so much!!

I've explained this one before! I think Latex is being weird though so if the worded explanation isn't enough I'll re-do the working out. :)

Although I'd also like to add since doing that the first time I've run into this rule which I think was mentioned in the itute and VCAA solutions:
(x/a) + (y/b) = 1,
where a and b are the x and y intercepts, respectively. (pretty sure it's relevant ::) )

Hey everyone, I'm aware that the SS you get is quite dependent upon both your sacs and your exam, but considering you have an A average in your sacs (most likely going to scale up from the level of difficulty??), what kind of percentage should you be aiming for in the exam to have a chance of obtaining a SS of over 40?

Thanks!

Definitely above 90%. No more than a couple of marks each exam, it gets pretty competitive above 40

EDIT; Fixed the link ::)
Title: Re: VCE Further Maths Question Thread!
Post by: Losingmotivation on October 27, 2015, 07:57:04 pm
o.O okayyy.. will try!

thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 07:59:06 pm
I've explained this one before! I think Latex is being weird though so if the worded explanation isn't enough I'll re-do the working out. :)

Although I'd also like to add since doing that the first time I've run into this rule which I think was mentioned in the itute and VCAA solutions:
(x/a) + (y/b) = 1,
where a and b are the x and y intercepts, respectively. (pretty sure it's relevant ::) )



That link won't work. Can you copy the worked solution or tell me how to find it? And how would I use that formula? Both the x and y ints are 0, so 0/a + 0/b != 1.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 27, 2015, 08:10:56 pm

That link won't work. Can you copy the worked solution or tell me how to find it? And how would I use that formula? Both the x and y ints are 0, so 0/a + 0/b != 1.

Fixed the link, whoops. I don't understand how the x and y intercepts are 0, but I also didn't do the question using that rule. Just thought I'd put it out there ;)
Title: Re: VCE Further Maths Question Thread!
Post by: @#035;3 on October 27, 2015, 08:15:28 pm
What should I do over the next two days to prepare for the exam.
I've ran out of exam 1's..
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 27, 2015, 08:25:36 pm
What should I do over the next two days to prepare for the exam.
I've ran out of exam 1's..

Maybe redo VCAA exams you made some mistakes on or perfect your bound reference.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 27, 2015, 08:31:23 pm
Why can't I substitute in numbers for x and y to get k? 25.7 = k/(0.44^2). The answer I got was C; H = 4.98/d^2. I substituted in the x coordinate H = 4.98/(0.44^2) and the answer is 25.7, the y value in the question. What am I doing wrong? And can you help me with question 8? Thanks you so much!!

You can't substitute the coordinates to find k here, because it's plotted as H against 1/d^2, if you had the original graph, which would be H against D, you would be able to use it to find the coefficient. Since you have the transformed graph, you'll need to find the K using the gradient of the straight line.
Title: Re: VCE Further Maths Question Thread!
Post by: j0yce on October 27, 2015, 08:48:18 pm
Hi
Could someone please explain Q.3a (matrices module) from last years exam 2?
I've read the examiners report but still don't understand it!
I thought element 0.4 (row 2, column 3) in matrix T  would have some role in the answer??
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 27, 2015, 09:01:16 pm
Hi
Could someone please explain Q.3a (matrices module) from last years exam 2?
I've read the examiners report but still don't understand it!
I thought element 0.4 (row 2, column 3) in matrix T  would have some role in the answer??


I'll try explain this as best as i can, in the first transition matrix, you see that 10% of B changes to C before C withdraws, That's clear right? You can see from the matrix.

Next, in the second matrix, which depicts what would happen after Mr Choi withdraws, 10% would split equally, 5% will go to A (10% to 15%) and 5% to B (80% to 85%), you can see how the 10% would split equally between A and B, right? since 5% of a total 10% goes to B, 5/10 * 100 = 50%
Title: Re: VCE Further Maths Question Thread!
Post by: j0yce on October 27, 2015, 09:29:42 pm

I'll try explain this as best as i can, in the first transition matrix, you see that 10% of B changes to C before C withdraws, That's clear right? You can see from the matrix.

Next, in the second matrix, which depicts what would happen after Mr Choi withdraws, 10% would split equally, 5% will go to A (10% to 15%) and 5% to B (80% to 85%), you can see how the 10% would split equally between A and B, right? since 5% of a total 10% goes to B, 5/10 * 100 = 50%


Oh I get it! Thank you so much! I was struggling with this question for so long :)
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 27, 2015, 09:31:27 pm

Oh I get it! Thank you so much! I was struggling with this question for so long :)

You're very welcome :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 27, 2015, 10:11:10 pm
Question 3 from VCAA 2010 Exam 1, please! :)
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 10:14:49 pm
You can't substitute the coordinates to find k here, because it's plotted as H against 1/d^2, if you had the original graph, which would be H against D, you would be able to use it to find the coefficient. Since you have the transformed graph, you'll need to find the K using the gradient of the straight line.

Thanks dude! That helped me so much :D
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 27, 2015, 10:15:18 pm
Question 3 from VCAA 2010 Exam 1, please! :)

Covered this one too, link. :)
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 10:16:14 pm

Oh I get it! Thank you so much! I was struggling with this question for so long :)

When my teacher told me, I was surprised how easy it was too haha.
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 10:30:41 pm
I've explained this one before! I think Latex is being weird though so if the worded explanation isn't enough I'll re-do the working out. :)

Although I'd also like to add since doing that the first time I've run into this rule which I think was mentioned in the itute and VCAA solutions:
(x/a) + (y/b) = 1,
where a and b are the x and y intercepts, respectively. (pretty sure it's relevant ::) )

Definitely above 90%. No more than a couple of marks each exam, it gets pretty competitive above 40

EDIT; Fixed the link ::)

The images aren't loading for me :(
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 27, 2015, 10:36:22 pm
The images aren't loading for me :(

Here's copied but without the latex, hopefully that makes it readable :)

Spoiler
This one was actually kind of tough - I checked out the examiner's report and the itute solutions and neither of them really gave a clear, step by step explanation on how to do the question - although itute was a bit better than the VCAA.

Because Z is maximised at the points M and N, we can say that Z(m) and Z(n) are equal. For that to make much sense though, we need to know the coordinates of M and N. They're pretty clear on the graph as long as you work out the the interval is 5 (and maybe have a ruler to double check your points line up) but if you really wanted to you could set up some simultaneous equations to find them, too.

In any case, the coordinates of M and N are (20,50) and (45,25) respectively. We can set up two equations/functions for Z with this information:
Z = 20a + 50b (M)
Z = 45a + 25b (N)

Because we know Z has to be equal for both M and N to find a and b, we can quickly throw out some of the options that would give us something ridiculous - this means we don't have to worry about either of the options with negative values (A, E) and can probably get away without checking that D fits our rules because the numbers are pretty different to A, B and C. (Note: With multiple choice questions, you can usually eliminate two options after reading the question or minimal working out: in this case it was D and E)

So that leaves us with option B and option C to check, like so:
B. Z = 45*15 + 25*15 =1050
B. Z = 20*15 + 50*15=1050
We can already see that these are equal (and therefore, B is the answer), but let's check C to be sure we haven't messed up somewhere:
C. Z = 45*15 + 25*25 =1300
C.  Z = 20*15 + 50*25 =1550

So B is our answer - of course some of the constraints I set were maybe a little too general (option A could've probably been a reasonable choice) but in the end, there's only five equations to check so realistically you probably wouldn't need to set any at all.
Title: Re: VCE Further Maths Question Thread!
Post by: Zealous on October 27, 2015, 10:59:57 pm
Just want to say, awesome work to all of you who are actively helping out in this thread! Especially MightyBeh and TheMereCat - you seem to be on top of everything.  I'm sure your contributions are helping many more than just the people who ask the question. :)
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 11:09:17 pm
Here's copied but without the latex, hopefully that makes it readable :)

Spoiler
This one was actually kind of tough - I checked out the examiner's report and the itute solutions and neither of them really gave a clear, step by step explanation on how to do the question - although itute was a bit better than the VCAA.

Because Z is maximised at the points M and N, we can say that Z(m) and Z(n) are equal. For that to make much sense though, we need to know the coordinates of M and N. They're pretty clear on the graph as long as you work out the the interval is 5 (and maybe have a ruler to double check your points line up) but if you really wanted to you could set up some simultaneous equations to find them, too.

In any case, the coordinates of M and N are (20,50) and (45,25) respectively. We can set up two equations/functions for Z with this information:
Z = 20a + 50b (M)
Z = 45a + 25b (N)

Because we know Z has to be equal for both M and N to find a and b, we can quickly throw out some of the options that would give us something ridiculous - this means we don't have to worry about either of the options with negative values (A, E) and can probably get away without checking that D fits our rules because the numbers are pretty different to A, B and C. (Note: With multiple choice questions, you can usually eliminate two options after reading the question or minimal working out: in this case it was D and E)

So that leaves us with option B and option C to check, like so:
B. Z = 45*15 + 25*15 =1050
B. Z = 20*15 + 50*15=1050
We can already see that these are equal (and therefore, B is the answer), but let's check C to be sure we haven't messed up somewhere:
C. Z = 45*15 + 25*25 =1300
C.  Z = 20*15 + 50*25 =1550

So B is our answer - of course some of the constraints I set were maybe a little too general (option A could've probably been a reasonable choice) but in the end, there's only five equations to check so realistically you probably wouldn't need to set any at all.

That's very helpful. Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 27, 2015, 11:26:37 pm
Can you guys help me with question 7 Matrices from Further Exam 1 2013?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 28, 2015, 12:05:40 am
Can you guys help me with question 7 Matrices from Further Exam 1 2013?
First you need to consider how you would get the mean in a set of data. (Think back to Core Module.)
Spoiler
sum of data divided by number of data pieces
Then, you need to see how you would combine the matrices you are given to get the set of data. Since the matrices S and R are filled with 1s, you know that multiplication would just spit out the same number... and we know that with matrix multiplication you must add these together.

In terms of the choices:
Spoiler
Automatically ditch E. Option E would make no sense in terms of the matrix dimensions. 15 x 1, 3 x 15, 1 x 3 - you can't realistically multiply these together.
Same with C: 3 x 15, 1 x 3, 15 x 1

So you're left with A, B and D.
A wouldn't make sense because we want it per class, not per student. (Did you read "class" in the question?)
B wouldn't make sense because it would give a matrix with dimensions: 3 x 15, 15 x 3 = a 3 x 3 matrix. Going back to the question, we want the mean of each class, so we want the sum of the fifteen numbers per line ie. 1 number. Thus, this is incorrect also, as it receives 3 numbers, but we want 1.

Thus we receive the last option D.

Checking:
To find the mean, we know that there are 15 pieces of data per row and using the mean formula, you should receive the fact that we need to divide the sum by 15. Thus 1/15 should exist outside the matrix in our answer. (D has this, so it's a good sign. E, too, but...) Anyway, you can apply the mean formula on Class A on your calculator and you'd find that D will give you what you want rather than E.
EDIT: Please see the attached file. I realise screwed up the dimensions and did it correctly there.

If that doesn't quite make sense, please PM me and I'll try to explain again.
Title: Re: VCE Further Maths Question Thread!
Post by: epichedgehog on October 28, 2015, 11:15:08 am
Hi, could someone please explain VCAA 2013 Exam 2 Graphs and Relations question 4? specifically, 4ei and 4eii? I've read the examiner's report but I don't really understand it still.
Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 28, 2015, 11:37:53 am
Hi, could someone please explain VCAA 2013 Exam 2 Graphs and Relations question 4? specifically, 4ei and 4eii? I've read the examiner's report but I don't really understand it still.
Thanks!

For 4ei, you take your answers from the last part (4d/4c) and apply the rules they give you in the question. ($60 per powered, $30 per unpowered)
The cost function that comes out of that is:
cost = 60x + 30y

Then we just sub in our two minimums from 4d to find the lower cost;
(2,9) cost = 60(2) + 30(9) = $390
(3,8) cost = 60(3) + 30(8) = $420

So clearly (2,9) is the real minimum of the function, with the lowest cost being $390

For 4eii,
I'm not 100% sure on the logic, but here's itute's solutions which are a bit clearer than the VCAA's.
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 28, 2015, 11:42:15 am
Hi, could someone please explain VCAA 2013 Exam 2 Graphs and Relations question 4? specifically, 4ei and 4eii? I've read the examiner's report but I don't really understand it still.
Thanks!


For this question, you'd obviously have to refer to the solution region in the graph, you can see that there are some integer points that could be solutions in your graph right?

Since in this context we're talking about an integer number of things (power and unpowered camps) we really can't have the maximum at the corner vertex, since we're more than likely to get a decimal amount of camp sites, which is impossible.

By looking at the solution region, you can see the smallest integer number of powered and unpowered camp sites will occur at either 2,9 or 3,8. Anything beyond below that is a decimal or not in the solution region so it has to be one of those two points. using the objective function 60x+30y you find that the point 2,9 gives the minimum cost which is $390.

For question 4 eii you have to understand that since all girls have to use one campsite and all boys have to use one campsites,  it means that there are 24 boys at powered campsite and 24 girls and unpowered camp sites. powered campsites carry 6 people, 24/6 = 4, so X must equal to 4 powered campsites required is = 4. Unpowered campsites carry 4 people, 24/4 = 6.  unpowered campsites required would be 6.

So look at the solution region, you see that 4,6 isn't in that region and it has to match constraints y => 2x, to match this constraint y= 2* 4 and so y must = 8. so the points we have now are 4,8

Now just find the cost using the objective function 60x+30y, and you get 480$.



It's a bit long but i hope you understand..


EDIT: So MightyBeh beat me to it :P
Title: Re: VCE Further Maths Question Thread!
Post by: epichedgehog on October 28, 2015, 11:52:03 am
For 4ei, you take your answers from the last part (4d/4c) and apply the rules they give you in the question. ($60 per powered, $30 per unpowered)
The cost function that comes out of that is:
cost = 60x + 30y

Then we just sub in our two minimums from 4d to find the lower cost;
(2,9) cost = 60(2) + 30(9) = $390
(3,8) cost = 60(3) + 30(8) = $420

So clearly (2,9) is the real minimum of the function, with the lowest cost being $390

For 4eii,
I'm not 100% sure on the logic, but here's itute's solutions which are a bit clearer than the VCAA's.

Thank you very much, I understand now :).
Title: Re: VCE Further Maths Question Thread!
Post by: epichedgehog on October 28, 2015, 11:53:43 am

For this question, you'd obviously have to refer to the solution region in the graph, you can see that there are some integer points that could be solutions in your graph right?

Since in this context we're talking about an integer number of things (power and unpowered camps) we really can't have the maximum at the corner vertex, since we're more than likely to get a decimal amount of camp sites, which is impossible.

By looking at the solution region, you can see the smallest integer number of powered and unpowered camp sites will occur at either 2,9 or 3,8. Anything beyond below that is a decimal or not in the solution region so it has to be one of those two points. using the objective function 60x+30y you find that the point 2,9 gives the minimum cost which is $390.

For question 4 eii you have to understand that since all girls have to use one campsite and all boys have to use one campsites,  it means that there are 24 boys at powered campsite and 24 girls and unpowered camp sites. powered campsites carry 6 people, 24/6 = 4, so X must equal to 4 powered campsites required is = 4. Unpowered campsites carry 4 people, 24/4 = 6.  unpowered campsites required would be 6.

So look at the solution region, you see that 4,6 isn't in that region and it has to match constraints y => 2x, to match this constraint y= 2* 4 and so y must = 8. so the points we have now are 4,8

Now just find the cost using the objective function 60x+30y, and you get 480$.



It's a bit long but i hope you understand..


EDIT: So MightyBeh beat me to it :P

thanks! I was just a little confused about why x = 4 and y = 6, but now it's much clearer. :)
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 28, 2015, 03:43:47 pm
How do you tell the difference between cyclic and random variations in time series? I understand seasonal variation has to have regular intervals between the peaks and troughs, but is it possible for it to get confusing with cyclic sometimes as well?
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 28, 2015, 03:49:02 pm
How do you tell the difference between cyclic and random variations in time series? I understand seasonal variation has to have regular intervals between the peaks and troughs, but is it possible for it to get confusing with cyclic sometimes as well?

From everything ive seen, theres been no confusing ones,
However, these videos might help you as she explains it good, https://www.youtube.com/watch?v=ca0rDWo7IpI
At six minutes she explains what youre talking about.
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 28, 2015, 05:02:38 pm
Hello again guys,
Heres a matrices  question aswell as a core one..
For the core one i have no idea why the answer gave would best suit the stem and leaf plot, as i believe distance travelled would be a better answer...

For the matrices one, i have only seen this question once, and im confused on how to do it. If anyone has any idea on the theory behind it, or atleast the method of solving any question like that, i will be grateful.
Title: Re: VCE Further Maths Question Thread!
Post by: Law on October 28, 2015, 05:31:09 pm
Hello again guys,
Heres a matrices  question aswell as a core one..
For the core one i have no idea why the answer gave would best suit the stem and leaf plot, as i believe distance travelled would be a better answer...

For the matrices one, i have only seen this question once, and im confused on how to do it. If anyone has any idea on the theory behind it, or atleast the method of solving any question like that, i will be grateful.

Core question:
A back-to back stem plot measures bivariate data, involving a numerical variable and a categorical variable with 2 categories. Thus it would car's speed (numerical value) and the only categorical variable with 2 categories (drivers sex: male or female)

Matrices Question:
So T1 x S0= S1. To make S1 and S2 constant you need to add and subtract the number that changes from S1 to S2.

There is an illustration in the attachment.

Edit: Raw 50 paint job skills
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 28, 2015, 05:31:54 pm
Hello again guys,
Heres a matrices  question aswell as a core one..
For the core one i have no idea why the answer gave would best suit the stem and leaf plot, as i believe distance travelled would be a better answer...

For the matrices one, i have only seen this question once, and im confused on how to do it. If anyone has any idea on the theory behind it, or atleast the method of solving any question like that, i will be grateful.


For the Core question, the one that make the most sense is answer E, which is Driver's sex male or female. Since you're sort of comparing only two things side by side (Categorical variable) and average speed in km/hr (numerical variable) the best suited would be a back to back stemplot, given that there is 1) a categorical variable and a numerical variable. and 2) Since there is only two categories, Male and female. Distance travelled won't really work since it is a numerical variable as well. A back to back stemplot is designed for a categorical and numerical variable.


For the Matrices one, you want to know how many eggs, baby trout and adult trout, that could be added or removed at the pond of each year will allow the population to remain constant.

For this question you firstly have to find S1 and once you do that you takeaway S1 from S0. Basically S0-S1 Once you found that difference, you know that if you add that amount every year, the population will remain constant.


Not great at explaining that one, but if you need further explanation let me know.


EDIT: Law already answered :P
Title: Re: VCE Further Maths Question Thread!
Post by: ineedbiohelp on October 28, 2015, 06:03:35 pm
For the Matrices one, you want to know how many eggs, baby trout and adult trout, that could be added or removed at the pond of each year will allow the population to remain constant.

For this question you firstly have to find S1 and once you do that you takeaway S1 from S0. Basically S0-S1 Once you found that difference, you know that if you add that amount every year, the population will remain constant.


Not great at explaining that one, but if you need further explanation let me know.


EDIT: Law already answered :P


Okay i understand the core one, thanks to both of you,

But for the matrices one, what does it mean  for the population to remain constant? i assume it means like a steady state so the values wont change at all from one year to the next, but when i subsitute these new added values into the S0, the values change yet again? Im pretty sure i can just always use S0-S1 if the question comes up, but id like to understand what it means as ill understand it easier,

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Law on October 28, 2015, 06:12:05 pm

Okay i understand the core one, thanks to both of you,

But for the matrices one, what does it mean  for the population to remain constant? i assume it means like a steady state so the values wont change at all from one year to the next, but when i subsitute these new added values into the S0, the values change yet again? Im pretty sure i can just always use S0-S1 if the question comes up, but id like to understand what it means as ill understand it easier,

Thanks :)

Dont add them to S0 because thats the initial state, you cant change it. However the question asks at the end of each year. So you have to change S1. Remenber T1 x S0= S1.

For example= Lets take Eggs. At S0 Eggs=10,000. Then at the end of the year it equals 0. So to make it constant it each year, to make it equal 0 each year, you would need to add 10,000 at the end of each year. Thus S1=S2 which =S3.
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on October 28, 2015, 06:25:32 pm
How do you guys do those weird matrices questions? The ones with m and n and whatnot. I always find myself guessing them in the end. (Usually MCQs).

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 28, 2015, 11:14:32 pm
You can't substitute the coordinates to find k here, because it's plotted as H against 1/d^2, if you had the original graph, which would be H against D, you would be able to use it to find the coefficient. Since you have the transformed graph, you'll need to find the K using the gradient of the straight line.

Hey. I found a worked solution for an insight exam 1 for a transformed data (as you can see in the attached image) they just substituted in points instead of finding the gradient. So confused about this! Please help anyone.
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on October 28, 2015, 11:19:44 pm
How do you guys do those weird matrices questions? The ones with m and n and whatnot. I always find myself guessing them in the end. (Usually MCQs).

Thanks!

Having no idea what type of questions you're talking about, my suggestion is to sub in values for n and m and see if that helps you at all. (I might be able to give better advice if you show me a question, hahah.)
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 28, 2015, 11:21:23 pm
How do you guys do those weird matrices questions? The ones with m and n and whatnot. I always find myself guessing them in the end. (Usually MCQs).

Thanks!

What I do is I put the letters on my calculator and it usually works out.
Title: Re: VCE Further Maths Question Thread!
Post by: Law on October 29, 2015, 08:48:24 am
Hey. I found a worked solution for an insight exam 1 for a transformed data (as you can see in the attached image) they just substituted in points instead of finding the gradient. So confused about this! Please help anyone.

Always think about these type of questions as y=(any variable) multiplied by x. For the sake of this question. Lets make this variable (k)

In this question y is plotted against x^3.
The rule connecting y and x would thus be y=kx^3.

We got coordinates in the graph= (8,2)
We sub these points in= 2=k8.

Now when we sub x in= It is not 8^3 its simply 8 because its already cubed. And the rule is y=kx^3

So solve(y=k x 8,k) and k equals= 1/4.

Thus y=1/4 times x^3. We can simplify this to x^3/4.
Thus y=x^3/4.
That is C.

Title: Re: VCE Further Maths Question Thread!
Post by: Law on October 29, 2015, 09:34:53 am
How do you guys do those weird matrices questions? The ones with m and n and whatnot. I always find myself guessing them in the end. (Usually MCQs).

Thanks!

Here is variable matrices question from the past 3 years. Do you want me to post more?
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 29, 2015, 09:54:14 am
Always think about these type of questions as y=(any variable) multiplied by x. For the sake of this question. Lets make this variable (k)

In this question y is plotted against x^3.
The rule connecting y and x would thus be y=kx^3.

We got coordinates in the graph= (8,2)
We sub these points in= 2=k8.

Now when we sub x in= It is not 8^3 its simply 8 because its already cubed. And the rule is y=kx^3

So solve(y=k x 8,k) and k equals= 1/4.

Thus y=1/4 times x^3. We can simplify this to x^3/4.
Thus y=x^3/4.
That is C.

This is what TheMereCat said:
You can't substitute the coordinates to find k here, because it's plotted as H against 1/d^2, if you had the original graph, which would be H against D, you would be able to use it to find the coefficient. Since you have the transformed graph, you'll need to find the K using the gradient of the straight line.
Title: Re: VCE Further Maths Question Thread!
Post by: Law on October 29, 2015, 10:20:12 am
This is what TheMereCat said:

For the question you posted I subbed in the co-ordinates and got the right answer. So yeah you can use them.

I see from his answer that he is talking about d^2, so its a different question. I looked for a bit but i cant find it. I have always subbed in the co-ordinates and got all the answers right though, so it might be a different kind of question.
Title: Re: VCE Further Maths Question Thread!
Post by: cipskailok1 on October 29, 2015, 01:01:27 pm
need help with this question from paper 1 VCE 2013 : Module 1 Number Patterns, Question 8.

Question 8

The initial rate of pay for a job is $10 per hour.
A worker’s skill increases the longer she works on this job. As a result, the hourly rate of pay increases each
month.
The hourly rate of pay in the nth month of working on this job is given by the difference equation

Sn+1= 0.2×Sn + 15         S1= 10

The maximum hourly rate of pay that the worker can earn in this job is closest to
A.
  $3.00
B.
 $12.00
C.
 $12.50
D.
 $18.75
E.
 $75.00
Title: Re: VCE Further Maths Question Thread!
Post by: RazzMeTazz on October 29, 2015, 01:59:13 pm
Is the moving average smoothing technique affected by outliers ? For this reason would it be more advantageous to use median smoothing if outliers are present ? Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 29, 2015, 02:04:40 pm
Is the moving average smoothing technique affected by outliers ? For this reason would it be more advantageous to use median smoothing if outliers are present ? Thanks :)

Yep!
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on October 29, 2015, 02:08:07 pm
Here is variable matrices question from the past 3 years. Do you want me to post more?

OMG Mr/Ms. Law. That would be amazing if you could do that!

Thanks so much. I really need to do well, after yesterday's fiasco...
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 29, 2015, 02:55:24 pm
Would you ever need to find outliers of bivariate data? If so, how would you do it?
Title: Re: VCE Further Maths Question Thread!
Post by: epichedgehog on October 29, 2015, 03:27:17 pm
hi all,
here's a question from NEAP 2006 graphs + relations (Q10):
shouldn't b, c and e all be suitable options, according to the circle of transformations? i'm a little confused at NEAP's explanation, i don't remember learning anything like it in class.
thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 29, 2015, 03:36:05 pm
For Question 9, is the question incorrect?

Since residual = y-ypredicted.

Shouldn't you have to use the equation, then square root the value to find y, then do 2-2.5

to get something close to ~0.5?

apparently the answer is B, and they squared the y value- minus y2 predicted value....

Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 29, 2015, 03:43:30 pm
hi all,
here's a question from NEAP 2006 graphs + relations (Q10):
shouldn't b, c and e all be suitable options, according to the circle of transformations? i'm a little confused at NEAP's explanation, i don't remember learning anything like it in class.
thanks!

Yeah, they all should be suitable... so just ignore it

For Question 9, is the question incorrect?

Since residual = y-ypredicted.

Shouldn't you have to use the equation, then square root the value to find y, then do 2-2.5

to get something close to ~0.5?

apparently the answer is B, and they squared the y value- minus y2 predicted value....



Yes, this question is correct.

It's asking for the residual for the transformed data. Not the original data
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 29, 2015, 04:13:24 pm
1. Good luck for your Exam 1 tomorrow, people. I know you'll all do well. :)
2. I edited my previous post answering bedigursman's question about VCAA 2013 Exam 1 Matrices Q7 and it now has a detailed explanation on the attachment, just to let anyone who wants help with that question know.
3.
need help with this question from paper 1 VCE 2013 : Module 1 Number Patterns, Question 8.

Question 8

The initial rate of pay for a job is $10 per hour.
A worker’s skill increases the longer she works on this job. As a result, the hourly rate of pay increases each
month.
The hourly rate of pay in the nth month of working on this job is given by the difference equation

Sn+1= 0.2×Sn + 15         S1= 10

The maximum hourly rate of pay that the worker can earn in this job is closest to
A.
  $3.00
B.
 $12.00
C.
 $12.50
D.
 $18.75
E.
 $75.00
Put this sequence into the calculator and check when it starts to become constant.
Take the number at which it plateaus at.
You'll get 18.75.
Answer is D.

Would you ever need to find outliers of bivariate data? If so, how would you do it?
Yeah, but it's more likely to be an Exam 1 type question and unlikely to appear; chances are they'll ask for the residual from a given point with a given equation (see above two posts for an example).

Back to the point, they're generally very clear about it. For example, a scatterplot with a point that's completely away from everything else (hence the method is self explanatory) and they could possibly ask you something about the outlier.
e.g. Not just "Find coordinates of the outlier.", but "Which of the following methods would be affected by an outlier?" and so forth.
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 29, 2015, 04:54:30 pm
Thanks, AngelWings! Super nervous about tomorrow! :/

Another question:
VCAA 2012 Q6 from Geo&Trig:

I got it wrong and understand that it has to do with linear and volume scale factors. But the reason I got it wrong was because I did the following:

V=((pi) x (r^2)) x h
V2=((pi) x (3r^2)) x 3h
This gave me 9( (pi) x (h) x (r^2) ).
Then I just subbed in (pi) x (h) x (r^2)=V, and got 9V.

What did I do wrong?
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on October 29, 2015, 05:01:14 pm
Thanks, AngelWings! Super nervous about tomorrow! :/

Another question:
VCAA 2012 Q6 from Geo&Trig:

I got it wrong and understand that it has to do with linear and volume scale factors. But the reason I got it wrong was because I did the following:

V=((pi) x (r^2)) x h
V2=((pi) x (3r^2)) x 3h  (3r)^2 not 3(r^2) I think just having a quick look
This gave me 9( (pi) x (h) x (r^2) ).
Then I just subbed in (pi) x (h) x (r^2)=V, and got 9V.

What did I do wrong?
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 29, 2015, 05:01:55 pm
Thanks, AngelWings! Super nervous about tomorrow! :/

Another question:
VCAA 2012 Q6 from Geo&Trig:

I got it wrong and understand that it has to do with linear and volume scale factors. But the reason I got it wrong was because I did the following:

V=((pi) x (r^2)) x h
V2=((pi) x (3r^2)) x 3h
This gave me 9( (pi) x (h) x (r^2) ).
Then I just subbed in (pi) x (h) x (r^2)=V, and got 9V.

What did I do wrong?

V = pi x R^2 x H

Therefore, because the R is multiplied by 3 and H is multiplied by 3, the volume becomes:

V = pi x (3R)^2 x 3H
   = pi x 9R x 3H
   = 27 x pi x R x H

This is the same as:

27 x V

Hence, the answer is D

EDIT: StupidProdigy identified the mistake
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 29, 2015, 05:11:58 pm
Thanks, AngelWings! Super nervous about tomorrow! :/

You guys have worked hard (I assume), so you guys have nothing to worry about. Try your best, breathe, be prepared and smash it out of the park.

While you're on that paper, n.a, have a look at Q9 of the Geometry section.
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 29, 2015, 05:38:38 pm
Hi
Can anyone please help me with question 13 (core) question 9 (number patterns) and question 9 (matrices) from 2014 exam 1
Thank you  :)
Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on October 29, 2015, 05:48:34 pm
Hi
Can anyone please help me with question 13 (core) question 9 (number patterns) and question 9 (matrices) from 2014 exam 1
Thank you  :)
For question 13:
1. Divide the graph into three regions, were the regions have 5, 6, 5 data points respectively
2. Calculate the median value of the first region (3, 8 )
3. Calculate the median value of the third region (14, 8 )
4. Calculate the gradient using m = (y2 - y1) / (x2 - x1)
                                                      = (8 - 8 ) / (14 - 3)
                                                      = 0

For question 9 matrices:
You should know that multiplying a matrix with its inverse results in the identity matrix. That is: A x A^-1 = I
Hence, we know that B is the inverse of A (vise versa)

So, when a question ever asks if something is true, it's best to try them with actual values. Let's set up some matrices
A = [ 2   3]           and         A^-1 = B = [-1  0.5]
       [6    3]           and                           [3     -1]

Just plug these matrices in each answer and see which one yields the incorrect response
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 29, 2015, 05:58:07 pm
Thank you BakedDwarf  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on October 29, 2015, 07:48:01 pm
Can someone explain Q12 (CORE) from VCAA 2014?

Cheers!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 29, 2015, 07:53:32 pm
Can someone explain Q12 (CORE) from VCAA 2014?

Cheers!
I've actually done this one in detail before and asked anybody who didn't know how to do it to PM me, but I guess I'll put it on the forum for you all, 'cause I'm feeling nice.

Spoiler
The question is the following:
The seasonal index for heaters in winter is 1.25. To correct for seasonality, the actual heater sales in winter should be:
A. reduced by 20%.
B. increased by 20%.
C. reduced by 25%.
D. increased by 25%.
E. reduced by 75%.

So where to begin?
Let's use what we know and what we want. For this, we want to get 1 ("correcting for seasonality" goal) and we know seasonal index is 1.25. We know we want to make the number smaller (1.25 --> 1.00), so we divide: 1/1.25 = 0.80.
This (0.80) is lower than 1, so that's a decrease. It eliminates B and D instantly. We, then, just subtract: 1 - 0.80 = 0.20 to find out how much the decrease was (divided by 100, since it's still in decimal form).
Thus this gives you the result of A.

The same method may be applied to VCAA 2011 Exam 1 Q12, but you must consider the case. If it is obviously an increase, then subtract 1 from the larger result. Note that you still have to apply the 1/(seasonal index) rule, but the last step (the subtraction) is the part it differs. If not, apply as per above.
Title: Re: VCE Further Maths Question Thread!
Post by: n.a on October 29, 2015, 09:01:10 pm
You guys have worked hard (I assume), so you guys have nothing to worry about. Try your best, breathe, be prepared and smash it out of the park.

While you're on that paper, n.a, have a look at Q9 of the Geometry section.

Yup, surprisingly, I did it correctly! One of those questions that seem hard in the beginning and actually work out in the end, I guess! :)

And thank you StupidProdigy and BakedDwarf, I get it now. Damned brackets.
Title: Re: VCE Further Maths Question Thread!
Post by: girl1234 on October 30, 2015, 12:08:23 am
Hey guys, i get a bit confused with questions that give data and ask how it's best displayed? Can anyone help with what each method of displaying data (box plots/bar charts/histogram etc) are used for ??
Title: Re: VCE Further Maths Question Thread!
Post by: Lumierys on October 30, 2015, 12:09:20 am
For VCAA 2008 Further Exam 1. Core question 10. What's the difference between multiple choice's D and E?
Title: Re: VCE Further Maths Question Thread!
Post by: kavmeh on October 30, 2015, 12:14:30 am
Hi
Can anyone please help me with question 3d and 3e (Number patterns)
and question 1e (graphs and relations)
Sorry it's a bit late but the website wasn't working before  :)
Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: girl1234 on October 30, 2015, 12:36:13 am
For VCAA 2008 Further Exam 1. Core question 10. What's the difference between multiple choice's D and E?

D implies it's definitive/will happen whereas E suggests there's an association

hope that helped somewhat, can't really explain stuff too well and it's late :D
Title: Re: VCE Further Maths Question Thread!
Post by: lifeisnotascore on October 30, 2015, 01:09:57 am
In the five number summary, when stating the maximum, can it also be an outlier?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 30, 2015, 06:45:11 am
Hey guys, i get a bit confused with questions that give data and ask how it's best displayed? Can anyone help with what each method of displaying data (box plots/bar charts/histogram etc) are used for ??
My understanding:

dotplot/boxplot are for data that have a list of numerical values.
(tried to do an example with tables, but they're not working? ???)

stem and leaf/ back-to-back stem and leaf is similar, except it retains the numerical values. In a back-to-back stem plot, you have the same type of numerical data but not necessarily the same quality measured over two categories. (eg. Male/Female, test scores)

Barcharts are for measuring the frequency (count or percentage) of an occurrence. (eg. Votes, percentages per candidate)

Histograms are the same thing but with numerical data (eg. Average heat of ovens. Number of family members)

Scatter plots are for bivariate data (so when one variable is linked to another).

Is that all of them? idek at this point ;)

In the five number summary, when stating the maximum, can it also be an outlier?
Yep! (so can the minimum)

EDIT: Oh yeah and good luck for exam 1 and stuff. ::)
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on October 30, 2015, 09:41:48 am
I've actually done this one in detail before and asked anybody who didn't know how to do it to PM me, but I guess I'll put it on the forum for you all, 'cause I'm feeling nice.

Thanks so much! Thanks for feelin' nice!
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 30, 2015, 10:25:38 am
What's the consensus on mean vs. median? Doing a check on my bound reference and it's not there.

Is it just outliers/skew = median, symmetric/no outliers = mean?
Title: Re: VCE Further Maths Question Thread!
Post by: Darkknight26 on October 30, 2015, 10:36:02 am
Quick Question- When applying a log transformation to linearise the data, do we you natural log or log base 10?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 30, 2015, 10:37:59 am
Quick Question- When applying a log transformation to linearise the data, do we you natural log or log base 10?
base 10, it should be the default on the TI if you leave the field blank.  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Darkknight26 on October 30, 2015, 10:39:57 am
base 10, it should be the default on the TI if you leave the field blank.  :)

thanks, I have the classpad :)
Title: Re: VCE Further Maths Question Thread!
Post by: TheMereCat on October 30, 2015, 10:42:38 am
What's the consensus on mean vs. median? Doing a check on my bound reference and it's not there.

Is it just outliers/skew = median, symmetric/no outliers = mean?

Yeah no extreme values/outliers and skew means you should use mean

And for extreme values/outliers and skew you should use median.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 30, 2015, 10:46:08 am
Yeah no extreme values/outliers and skew means you should use mean

And for extreme values/outliers and skew you should use median.
Awesome, thanks <3
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on October 30, 2015, 11:04:34 am
I'm taking a protractor and ruler into the exam as a final resort (bearings questions). I struggled to do VCAA 2013 Geo & Trig Q8, and I got the right answer by double checking with a calculated sketch.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 30, 2015, 11:10:37 am
I'm taking a protractor and ruler into the exam as a final resort (bearings questions). I struggled to do VCAA 2013 Geo & Trig Q8, and I got the right answer by double checking with a calculated sketch.
We can bring in a protractor? I swear bearings will be the last thing I see  ::)
Title: Re: VCE Further Maths Question Thread!
Post by: bedigursimran on October 30, 2015, 11:13:24 am
We can bring in a protractor? I swear bearings will be the last thing I see  ::)

Crap. I don't have a protractor. I'll have to do with what I've got.
Title: Re: VCE Further Maths Question Thread!
Post by: Lumierys on October 30, 2015, 11:18:33 am
Crap. I don't have a protractor. I'll have to do with what I've got.

From the VCE exams navigator booklet:
"Basic stationery items do not include...or geometrical drawing instruments such as compasses, set squares, and protractors."
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 30, 2015, 11:19:39 am
From the VCE exams navigator booklet:
"Basic stationery items do not include...or geometrical drawing instruments such as compasses, set squares, and protractors."

Aww, damn. Thanks for that anyway  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: Lumierys on October 30, 2015, 11:20:46 am
What's the difference between a cyclic variation graph and a seasonal variation graph? I swear they look the same
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 30, 2015, 11:22:39 am
What's the difference between a cyclic variation graph and a seasonal variation graph? I swear they look the same

Cyclic is repetition over longer periods of time;

You'll see seasonal more than once a year (usually)

You'll see cyclic every year or couple of years
Title: Re: VCE Further Maths Question Thread!
Post by: epichedgehog on October 30, 2015, 11:25:52 am
What's the difference between a cyclic variation graph and a seasonal variation graph? I swear they look the same

this video explains it pretty well (I saw a link to it on another further maths thread):

https://www.youtube.com/watch?v=ca0rDWo7IpI
Title: Re: VCE Further Maths Question Thread!
Post by: Lumierys on October 30, 2015, 11:42:04 am
this video explains it pretty well (I saw a link to it on another further maths thread):

https://www.youtube.com/watch?v=ca0rDWo7IpI

Thank you soo much epichedgehog and MightyBeh :D
Title: Re: VCE Further Maths Question Thread!
Post by: mattcorr_ on October 30, 2015, 04:13:28 pm
Greetings

Who's game enough to discuss answers?
Title: Re: VCE Further Maths Question Thread!
Post by: StupidProdigy on October 30, 2015, 04:15:13 pm
Can someone tell me the answer for q9 of graphs and relations pwease.
this should probably be an exam discussion thread I'm guessing but oh well
Title: Re: VCE Further Maths Question Thread!
Post by: epichedgehog on October 30, 2015, 04:18:54 pm
Can someone tell me the answer for q9 of graphs and relations pwease.
this should probably be an exam discussion thread I'm guessing but oh well

I got C (point R)
Title: Re: VCE Further Maths Question Thread!
Post by: laurarm on October 30, 2015, 07:23:26 pm
I got C (point R)

So did I
Title: Re: VCE Further Maths Question Thread!
Post by: sawoshi on November 01, 2015, 07:53:16 pm
Hi, can anyone tell me how to solve question 3b. in the matrices module of the vcaa 2010 exam 2 paper?

Title: Re: VCE Further Maths Question Thread!
Post by: BakedDwarf on November 01, 2015, 08:00:40 pm
Hi, can anyone tell me how to solve question 3b. in the matrices module of the vcaa 2010 exam 2 paper?

Find the inverse of the 3x3 matrix from part A. The bottom left value is x.
Title: Re: VCE Further Maths Question Thread!
Post by: Orson on November 01, 2015, 09:57:34 pm
Anyone still got that 3-Median formula?

Anyways...Thanks everyone for all your help! I wish you all good luck, and I wish you all the best. I hope to meet you all one day, you're a great bunch of people!

-Orson
Title: Re: VCE Further Maths Question Thread!
Post by: keltingmeith on November 01, 2015, 10:03:54 pm
Anyone still got that 3-Median formula?

Anyways...Thanks everyone for all your help! I wish you all good luck, and I wish you all the best. I hope to meet you all one day, you're a great bunch of people!

-Orson

On the off-chance nobody sees this before the exam (because, hey, it's 10 on the night before...), I do remember seeing these two:

c=(1/3)(yL+yM+yH)-m(xL+xM+xH)

c=(1/3)(y1+y2+y3)-b(x1+x2+x3)
b=(y3-y1)/(x3-x1)

Not sure if relevant because I never managed to learn Further's time series stuff... :P (fun fact: this is actually the reason I stay away from core, because cbf learning time series LOL)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on December 13, 2015, 01:48:38 pm
I've just started the core for statistics. In regards to histograms, I'm unsure of what data I need to put into the set interval on the CAS. How do I know what my HStart and HStep should be?

Help would be muchly appreciated!
Title: Re: VCE Further Maths Question Thread!
Post by: Swagadaktal on December 13, 2015, 04:46:04 pm
I've just started the core for statistics. In regards to histograms, I'm unsure of what data I need to put into the set interval on the CAS. How do I know what my HStart and HStep should be?

Help would be muchly appreciated!
yo fam you dont need to worry about that, all you need to do is cntrl + menu --> graph fit --> fit to data (i think, its been a long time so i might of mixed it up) and you're set) unless the question is very specific, but i doubt it would be
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on January 22, 2016, 12:29:43 pm
Could someone please help me with the following problem on seasonal indices:

To correct for seasonality, the actual number of bathing suits sold in Autumn should be:

The seasonal index of Autumn is 0.4

The answer is an increase of 250% but if we must take 250% of the actual figure to get the deseasonalised values isn't this an increase of 150%?

Thanks in advance
Title: Re: VCE Further Maths Question Thread!
Post by: Darth_Pepe on January 22, 2016, 01:08:22 pm
Could someone please help me with the following problem on seasonal indices:

To correct for seasonality, the actual number of bathing suits sold in Autumn should be:

The seasonal index of Autumn is 0.4

The answer is an increase of 250% but if we must take 250% of the actual figure to get the deseasonalised values isn't this an increase of 150%?

Thanks in advance

I always do 100/seasonal index to show how much to increase or decrease.

So 100/0.4 = 250, which means we must increase by 250%
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on January 22, 2016, 01:12:43 pm
I always do 100/seasonal index to show how much to increase or decrease.

So 100/0.4 = 250, which means we must increase by 250%

But what happens to the original 100% which is already accounted for?
Title: Re: VCE Further Maths Question Thread!
Post by: Darth_Pepe on January 22, 2016, 01:40:28 pm
But what happens to the original 100% which is already accounted for?

I dont understand your question. You are correcting for seasonality. If its 0.4, it must go up to 1. Thus 1/0.4 = 250% increase
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on January 22, 2016, 01:46:13 pm
But what happens to the original 100% which is already accounted for?

Where is this question from? :)

I think the answer should be an increase  of 150% or 250% of the original seasonal index.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on January 22, 2016, 02:53:41 pm
Where is this question from? :)

I think the answer should be an increase  of 150% or 250% of the original seasonal index.

It is from chapter 6 review of Cambridge. I understand how it is an increase of 250% but if the 100% is already accounted for I can't see why it isn't an increase of 150%.
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on January 22, 2016, 03:01:10 pm
It is from chapter 6 review of Cambridge. I understand how it is an increase of 250% but if the 100% is already accounted for I can't see why it isn't an increase of 150%.

The answer is wrong.

As you suggested, the answer should be an increase of 150% :)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on January 22, 2016, 04:14:16 pm
The answer is wrong.

As you suggested, the answer should be an increase of 150% :)

Thanks Peanut Butter  :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on February 06, 2016, 04:50:41 pm
For this question attached.

how do you find q1 and q3.

Because the median is the average between the dots i have circled in red ?

so which dot do i use as the median then?( in order to allow me to find q1 and q3) ?
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on February 06, 2016, 06:13:28 pm
For this question attached.

how do you find q1 and q3.

Because the median is the average between the dots i have circled in red ?

so which dot do i use as the median then?( in order to allow me to find q1 and q3) ?


When two values are the median, you take the value that is halfway between both of them. Therefore, your median would be 2.

So instead of circling both the medians, put a line between them. Then, just count the dots and find your Q1 and Q3 as usual :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on February 06, 2016, 08:10:30 pm
When two values are the median, you take the value that is halfway between both of them. Therefore, your median would be 2.

So instead of circling both the medians, put a line between them. Then, just count the dots and find your Q1 and Q3 as usual :)

Thanks Peanut Butter  :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on February 06, 2016, 09:32:43 pm
For the distribution attached .

the answer says The outliers are at 5, 8, 36 and 40.

However when you check for the lower fence you get 6.

therefore 8 shouldn't be a outlier right?

so the outliers should be 5,36 and 40 
right?
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on February 06, 2016, 09:58:17 pm
For the distribution attached .

the answer says The outliers are at 5, 8, 36 and 40.

However when you check for the lower fence you get 6.

therefore 8 shouldn't be a outlier right?

so the outliers should be 5,36 and 40 
right?

Yes, the outliers should be at 5, 36 and 40.

The box plot is incorrect. You might also notice that the upper fence should be at 30, however the whisker seems to extend further than this. This question is completely wrong :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on February 06, 2016, 10:13:05 pm
Yes, the outliers should be at 5, 36 and 40.

The box plot is incorrect. You might also notice that the upper fence should be at 30, however the whisker seems to extend further than this. This question is completely wrong :)

Thanks for clarifying  Peanut Butter  :)

the further book literally has so many errors !!

also when we mention these outliers can we say their values directly?

or do we have to say that they are possible outliers and then state their values ?
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on February 06, 2016, 10:31:38 pm
Thanks for clarifying  Peanut Butter  :)

the further book literally has so many errors !!

also when we mention these outliers can we say their values directly?

or do we have to say that they are possible outliers and then state their values ?


You have used the formula to prove that the values are outliers.

You can just say something like: the data contains outliers at 5, 36 and 40

Does that answer your question? :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on February 07, 2016, 05:17:10 am
You have used the formula to prove that the values are outliers.

You can just say something like: the data contains outliers at 5, 36 and 40

Does that answer your question? :)

yep it does thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on February 07, 2016, 01:18:25 pm
How would you go about answering these types of questions as attached?

the answer says b) On average, brand A batteries have longer and less variable lifetimes.

Like how do they determine the above answer ?
Title: Re: VCE Further Maths Question Thread!
Post by: Darth_Pepe on February 07, 2016, 01:33:37 pm
How would you go about answering these types of questions as attached?

the answer says b) On average, brand A batteries have longer and less variable lifetimes.

Like how do they determine the above answer ?


Brand A has a higher median than Brand B. Which means on average they have longer lifetimes. ( I should be quoting medians here..this is why i didnt get a 50 in further lol)
Brand B has more variability than A. Roughly Brand B has variations from 18-52 hours compared to A's 22-50 hours. Thus on average Brand A batteries have longer and less variable lifetimes.

Always express the answer with numerical proof.. vcaa made a point about that sometime ago.
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on February 07, 2016, 06:14:12 pm

Brand A has a higher median than Brand B. Which means on average they have longer lifetimes. ( I should be quoting medians here..this is why i didnt get a 50 in further lol)
Brand B has more variability than A. Roughly Brand B has variations from 18-52 hours compared to A's 22-50 hours. Thus on average Brand A batteries have longer and less variable lifetimes.

Always express the answer with numerical proof.. vcaa made a point about that sometime ago.

Thanks Darth_Pepe  :) nice explanation !!
Title: Re: VCE Further Maths Question Thread!
Post by: snow257 on February 10, 2016, 06:30:02 pm
What is the question asking you to do if it says 'compare'? E.g. Compare the mean and standard deviation to the median and IQR for the sample. Btw, I haven't done further maths 1/2.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on February 10, 2016, 10:01:03 pm
What is the question asking you to do if it says 'compare'? E.g. Compare the mean and standard deviation to the median and IQR for the sample. Btw, I haven't done further maths 1/2.
Probably just a short comment on the differences - the mean/median are measures of centre and in a symmetrical distribution they should be about the same. A mean significantly different from the median usually implies a skew and/or outliers. Standard deviation with the IQR seems a bit odd though, since the numbers don't really line up (1sx is 34%, IQR is 50%). A comment on whether the mean or median is more appropriate for the data is mostly optional but a good idea most of the time.
Title: Re: VCE Further Maths Question Thread!
Post by: Darth_Pepe on February 10, 2016, 10:26:04 pm
What is the question asking you to do if it says 'compare'? E.g. Compare the mean and standard deviation to the median and IQR for the sample. Btw, I haven't done further maths 1/2.

Comparing mean and median allows you to know if they are negatively skewed or positively skewed. I cant remenber right now but i think these are how you know:
Mean = median: Data is symmetrical
Mean > median: Positive skewed
Mean < median: Negative skewed.

Comparing standard deviation and IQR allows you to know which has more deviation. This type of question is not common, but the mean and median is. Be sure to use numerical proof :) Such as The mean (21.3) is larger than the median (20.7) which means that the data is positive skewed.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on February 12, 2016, 07:26:41 am
Hi everyone,

My first SAC for further maths is in term 2, which is based off excel. We are given a long list of data and must plot a range of graphs and write an analysis.

If anyone has done a similar SAC and could provide me with some information regarding the particular types of graphs that must be plotted and any other skills required, it would be greatly appreciated since my knowledge of excel is very poor.

Thanks in advance  :)
Title: Re: VCE Further Maths Question Thread!
Post by: friedchromosome on February 29, 2016, 09:08:54 pm
Does anyone have any practice sacs they could send over on the first couple of chapters of core?? Or know where I can get any? thanks
Title: Re: VCE Further Maths Question Thread!
Post by: abbytennant on February 29, 2016, 09:51:31 pm
First sac tomorrow on recursion!!
If anyone could help me with this one last question I'm stuck on that'd be great!

Geoff invests $18000 in an investment account. After 2 years the investment account contains $19282.05. If the account pays r% interest per annum compounded quarterly, find the value of r to one decimal place.

Thanks xx
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on February 29, 2016, 09:57:46 pm
Does anyone have any practice sacs they could send over on the first couple of chapters of core?? Or know where I can get any? thanks

I'm the same! I would really appreciate some recent SACs if possible! Especially any tips about Excel in regards to the statistics SAC.
Title: Re: VCE Further Maths Question Thread!
Post by: friedchromosome on March 01, 2016, 07:23:26 pm
I'm the same! I would really appreciate some recent SACs if possible! Especially any tips about Excel in regards to the statistics SAC.
I find it extremely impossible that the whole state can't help a sister out  :o
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 04, 2016, 09:07:31 pm
I find it extremely impossible that the whole state can't help a sister out  :o

We would if we could. Check up the Legal section of the rules for AN forums and you'll actually find out that practise SACs are actually school property and copyrighted. To avoid copyright issues and what not, we cannot supply practise SACs. 

I can suggest that you check up old VCAA exams, such as 2002-2005's Exam 2 for Excel-based SACs.
For Core, I would advise any Core modules in practise exams from other places besides VCAA, such as TSFX, TSSM, Heffernan and so forth. I would also recommend Checkpoints, StudyOn and (AN's own) ExamPro books as good resources to test your knowledge, as well as other Further textbooks. An alternative would be to make your own.
Hopefully those resources will keep you going for a while.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on March 06, 2016, 10:19:32 am
We would if we could. Check up the Legal section of the rules for AN forums and you'll actually find out that practise SACs are actually school property and copyrighted. To avoid copyright issues and what not, we cannot supply practise SACs. 

I can suggest that you check up old VCAA exams, such as 2002-2005's Exam 2 for Excel-based SACs.
For Core, I would advise any Core modules in practise exams from other places besides VCAA, such as TSFX, TSSM, Heffernan and so forth. I would also recommend Checkpoints, StudyOn and (AN's own) ExamPro books as good resources to test your knowledge, as well as other Further textbooks. An alternative would be to make your own.
Hopefully those resources will keep you going for a while.

Thanks for the clarification, I was unaware of this until now.  :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 06, 2016, 02:21:14 pm
Thanks for the clarification, I was unaware of this until now.  :)

No problems. Feel free to ask about anything Further-related and we can see how far we can go, within the confines of AN's rules. .

In terms of Excel based SACs, it's basically on everything you've learnt: regression lines, all types of smoothing, all types of lines, measure of centre... the list goes on. Anything you can do on a graphic calculator is generally what's assessable - they generally would make you do it on there, because that's the one you'd be using in your exams, not Excel on computers.
Title: Re: VCE Further Maths Question Thread!
Post by: Sammyboi on March 09, 2016, 06:49:38 pm
What modules is everyone doing?

I'm doing:
1) Number Patterns
2) Graphs and Relations
3) Matrices

I think we are doing..

1) Martices
2) Networks
Title: Re: VCE Further Maths Question Thread!
Post by: matttz1994 on March 23, 2016, 09:26:21 pm
Hey guys,
I don't understand how I got this question wrong. Aren't 0, 1, 2, 3 and '4 or more' categories for the number of DVD players? How are they numerical variables if there are only 5 things (categories!) that we can choose from? What's the difference between these requirements and a list of ordinal categorical requirements?
Cheers :)

P.S: link to image, in case you can't see the attachment: http://i.imgur.com/BJg4Oqv.png
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on March 23, 2016, 09:59:22 pm
Hey guys,
I don't understand how I got this question wrong. Aren't 0, 1, 2, 3 and '4 or more' categories for the number of DVD players? How are they numerical variables if there are only 5 things (categories!) that we can choose from? What's the difference between these requirements and a list of ordinal categorical requirements?
Cheers :)

P.S: link to image, in case you can't see the attachment: http://i.imgur.com/BJg4Oqv.png

Hey,

Sorry if this does't make any sense.

For this question, it would be discrete numerical variables because the number of DVD players are able to be counted in whole numbers; hence the small number of options. If they were continuous they would be measurable, yet this is not the case.

Thus, the 'number' of DVD players cannot be ordinal categorical variables because they are not representing a particular characteristic , rather just a number.

Title: Re: VCE Further Maths Question Thread!
Post by: kingy123 on March 29, 2016, 03:25:01 pm
Hey guys

I was just hoping someone would explain to me what the difference between seasonal and cyclic time series data is.
Title: Re: VCE Further Maths Question Thread!
Post by: Señor on March 29, 2016, 04:14:20 pm
Hey guys

I was just hoping someone would explain to me what the difference between seasonal and cyclic time series data is.

The difference between seasonal and cyclic time series data is that with cyclic time series there is no regular periods between peeks.
Title: Re: VCE Further Maths Question Thread!
Post by: avince on April 01, 2016, 02:30:11 pm
Hi guys,
Any general tips and revision strategies for recursion and financial modelling?
I have a SAC for this core topic coming up in mid-may.
I haven't started this topic at school as of yet.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 01, 2016, 03:12:19 pm
I was just hoping someone would explain to me what the difference between seasonal and cyclic time series data is.
The difference between seasonal and cyclic time series data is that with cyclic time series there is no regular periods between peaks.
Actually, seasonal variation has roughly regular intervals that repeat within a year or less, whereas cyclic is a repeating pattern beyond a year (though the trend can be much more vague, as Senor said).

Hi guys,
Any general tips and revision strategies for recursion and financial modelling?
I have a SAC for this core topic coming up in mid-may.
I haven't started this topic at school as of yet.

Thanks
As for recursion and financial modelling, I can suggest that you try more related Checkpoints questions to keep up to speed. Check up some more questions online - I'm sure you could find a few with a quick search. Unfortunately, it's been a long time since I studied this, so I'm afraid I'm not the most helpful person on AN.
Title: Re: VCE Further Maths Question Thread!
Post by: minerva on April 01, 2016, 08:30:39 pm
Hi, could someone please explain "Correcting for seasonlity"? I don't understand how or why it's used.
Here's a question I'm stuck on:
The seasonal index of January is 1.2 and the actual sales figure is 9.6.
To correct the actual monthly sales figure for seasonality we need to:
A) decrease the actual sales figures by around 20%
B) increase the actual sales figures by around 20%
C) decrease the actual sales figures by around 17%
D) increase the actual sales figures by around 17%
E) increase the actual sales figures by around 80%

Thanks in advance :)
Title: Re: VCE Further Maths Question Thread!
Post by: Peanut Butter on April 01, 2016, 08:55:20 pm
Hi, could someone please explain "Correcting for seasonlity"? I don't understand how or why it's used.
Here's a question I'm stuck on:
The seasonal index of January is 1.2 and the actual sales figure is 9.6.
To correct the actual monthly sales figure for seasonality we need to:
A) decrease the actual sales figures by around 20%
B) increase the actual sales figures by around 20%
C) decrease the actual sales figures by around 17%
D) increase the actual sales figures by around 17%
E) increase the actual sales figures by around 80%

Thanks in advance :)

"To correct for seasonality" means to basically get a seasonal index of one. So you want to go from 1.2 to 1. Since the SI is getting lower, it must be decreasing (therefore the answer has to be either a or c).

To figure out the percentage:

(1.2-1)/1.2 * 100 = 17 %

That formula ^ is pretty much the difference in seasonal indices over the original seasonal index. Does that make sense? :)
Title: Re: VCE Further Maths Question Thread!
Post by: minerva on April 01, 2016, 09:14:23 pm
"To correct for seasonality" means to basically get a seasonal index of one. So you want to go from 1.2 to 1. Since the SI is getting lower, it must be decreasing (therefore the answer has to be either a or c).

To figure out the percentage:

(1.2-1)/1.2 * 100 = 17 %

That formula ^ is pretty much the difference in seasonal indices over the original seasonal index. Does that make sense? :)

Yes, thanks!!
Btw, I'm just fangirling over your 50 raw, haha. Congrats and thanks for that post on your Further experience and advice. Much appreciated.
Title: Re: VCE Further Maths Question Thread!
Post by: kingy123 on April 06, 2016, 02:33:18 pm
Hey could someone please tell me if by smoothing the time series, do we try to remove seasonality and random fluctuations in the time series, or just the random fluctuations????

Any help would be great
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on April 06, 2016, 03:04:54 pm
Hey could someone please tell me if by smoothing the time series, do we try to remove seasonality and random fluctuations in the time series, or just the random fluctuations????

Any help would be great

Hi Kingy,

Yes the aim is to diseasonalise the data to try and uncover some sort of trend. Therefore in doing this we are removing random fluctuations.

I hope this helps  :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on April 06, 2016, 07:17:52 pm
How does the lack of a clear pattern in a  residual plot support the assumption that the relationship between the RV AND EV is linear?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on April 06, 2016, 07:58:46 pm
How does the lack of a clear pattern in a  residual plot support the assumption that the relationship between the RV AND EV is linear?

Hey,

I can't give you a very technical answer, but if there was a clear pattern (such as a U-shaped curve) it would suggest that the points would be better suited to a non-linear model.

Check out this website, it explains it better than I can  :D : http://stattrek.com/statistics/dictionary.aspx?definition=Residual%20plot
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on April 06, 2016, 08:08:21 pm
Hi Everyone,

Could you please help me with the following questions relating to finance  :D

Thanks in advance
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on April 06, 2016, 10:49:13 pm
Hey,

I can't give you a very technical answer, but if there was a clear pattern (such as a U-shaped curve) it would suggest that the points would be better suited to a non-linear model.

Check out this website, it explains it better than I can  :D : http://stattrek.com/statistics/dictionary.aspx?definition=Residual%20plot

Thanks clarke54321   :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 07, 2016, 05:46:55 pm
How does the lack of a clear pattern in a  residual plot support the assumption that the relationship between the RV AND EV is linear?
I can't give you a very technical answer, but if there was a clear pattern (such as a U-shaped curve) it would suggest that the points would be better suited to a non-linear model.

Check out this website, it explains it better than I can  :D : http://stattrek.com/statistics/dictionary.aspx?definition=Residual%20plot
Just an addition to Clarke54321's post quoted above, 'randomness' is generally needed to cancel out positive and negative residuals, as such, a +5 residual would be cancelled out by a -5 residual and so forth.
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on April 07, 2016, 06:13:09 pm
Just an addition to Clarke54321's post quoted above, 'randomness' is generally needed to cancel out positive and negative residuals, as such, a +5 residual would be cancelled out by a -5 residual and so forth.

Thanks AngelWings  :)
Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on April 18, 2016, 10:14:00 pm
Hi, can someone please explain how to do this recursion question? I don't get how you can go from u(n+1) to u(n-1). Thank you :)
Title: Re: VCE Further Maths Question Thread!
Post by: plato on April 19, 2016, 04:12:43 pm
I think this is a misprint if the answer is meant to be E.
I think it should read un+1 = 2un - 1
Title: Re: VCE Further Maths Question Thread!
Post by: death to the vcaa on April 19, 2016, 06:38:22 pm
Hey guys, it would raeally be appreciated if you guys could tell me an estimated study score for these results:
Sacs: B+
Exam 1 A+
Exam 2: A+
So far, I am doing terribly for sacs but am doing really good for practice exams, but I have a weak cohort that will probably struggle in the exams but do alright on the sacs, meaning my ranking will be around 5-10 and my sacs will probably scale down. I would really just like to get an estimate on my study score. Hoping to get above 40. Btw, I am in year 10 so if I screw up further, do use think it would be worth me repeating it in year 11 along side methods 3/4?
Title: Re: VCE Further Maths Question Thread!
Post by: on April 19, 2016, 07:17:07 pm
Hey guys, it would raeally be appreciated if you guys could tell me an estimated study score for these results:
Sacs: B+
Exam 1 A+
Exam 2: A+
So far, I am doing terribly for sacs but am doing really good for practice exams, but I have a weak cohort that will probably struggle in the exams but do alright on the sacs, meaning my ranking will be around 5-10 and my sacs will probably scale down. I would really just like to get an estimate on my study score. Hoping to get above 40. Btw, I am in year 10 so if I screw up further, do use think it would be worth me repeating it in year 11 along side methods 3/4?

A % here would be better than "A+"

For example:

GA1: B+
GA2: 37/40 (A+)
GA3: 53/60 (A+)
This might scrape you a 40, probably 39-41

On the other hand
GA1: B+
GA2: 40/40 (A+)
GA3: 57/60 (A+)
This is most likely a 47-49

If you give us a mark out of 40 and 60 for the exams then it would be easier to estimate.

On the other question: Repeating further isnt much of a benefit. Its a highly competitive subject and chances are that the exam might be easier the next year and then even harder to get a better score.
Title: Re: VCE Further Maths Question Thread!
Post by: death to the vcaa on April 19, 2016, 07:42:59 pm
Thank you so much. That's reassuring. I appreciate it man  :) :) :) :) :) :)
Title: Re: VCE Further Maths Question Thread!
Post by: Cristiano on April 19, 2016, 08:01:06 pm
Hi, can someone please explain how to do this recursion question? I don't get how you can go from u(n+1) to u(n-1). Thank you :)

We know that so we must find the second term. Using the equation,    

= 2 × -3 -1


So, the answer is E, as it is the only choice with the second term being -7  :)
Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on April 20, 2016, 05:08:44 pm
Thanks plato and Cristiano for the replies!
Title: Re: VCE Further Maths Question Thread!
Post by: minerva on April 20, 2016, 11:04:40 pm
Hi, can someone please help me with "How does an outlier affect the r value (correlation coefficient)?"
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 21, 2016, 05:22:24 am
Hi, can someone please help me with "How does an outlier affect the r value (correlation coefficient)?"
Remember that r is for classifying the strength of a linear relationship, and it's calculated using every point of data that you have. On top of that, the mean and the standard deviation are both pretty heavily affected by outliers (mean will be much higher/lower, standard deviation will be really high when it shouldn't) so the correlation coefficient is pretty useless if you include outliers.


* you don't need to know this equation

Graphically, this means that the line won't actually be the closest fit to the data because it'll be 'pulled' toward the outlier.

This one's without outliers
(http://i.imgur.com/6BeK8Kj.png)

This one has an outlier
(http://i.imgur.com/k6zU5tz.png)
Title: Re: VCE Further Maths Question Thread!
Post by: YellowTongue on April 23, 2016, 07:32:25 am
How would you describe a time series trend using "general terms"?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on April 23, 2016, 08:21:31 am
How would you describe a time series trend using "general terms"?

Hey,

I would think that you would just say something along the lines of 'this time series shows an increasing or decreasing trend.'
Title: Re: VCE Further Maths Question Thread!
Post by: Señor on April 23, 2016, 09:14:54 am
How would you describe a time series trend using "general terms"?

Im not sure if this is what you are looking for...but if you mean about a general line going upward or downwards then it is a Secular upward/downward trend.
Title: Re: VCE Further Maths Question Thread!
Post by: minerva on April 25, 2016, 09:39:01 pm
Hey guys, how do you know if a scatterplot has an outlier? Are you meant to be able to tell simply by looking at the scatterplot or can the correlation coefficient indicate the presence of an outlier/s?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on April 25, 2016, 09:51:04 pm
Hey guys, how do you know if a scatterplot has an outlier? Are you meant to be able to tell simply by looking at the scatterplot or can the correlation coefficient indicate the presence of an outlier/s?

Hi,

As far as my knowledge goes, I think that you are only able to tell if there is an outlier by observation. I haven't actually learnt of any calculation which is able to detect an outlier in a scatterplot.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on April 26, 2016, 11:43:57 pm

Hey guys, how do you know if a scatterplot has an outlier? Are you meant to be able to tell simply by looking at the scatterplot or can the correlation coefficient indicate the presence of an outlier/s?
Hey Minerva,
Just to add on to Clarke, I believe it is a bit of both. What I usually do is doing 2 calculations to find the correlation coefficient; one with outlier and one without. If your coefficient shows an extreme change than you are 100% confident that it is an outlier. This method just gives you that extra oomph in knowing you're right :')
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on April 27, 2016, 07:14:37 am
Hey Minerva,
Just to add on to Clarke, I believe it is a bit of both. What I usually do is doing 2 calculations to find the correlation coefficient; one with outlier and one without. If your coefficient shows an extreme change than you are 100% confident that it is an outlier. This method just gives you that extra oomph in knowing you're right :')

That's really effective, I never though of that  :)
Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on May 01, 2016, 08:43:18 pm
Hi, can someone tell me how to do this question without listing out all the terms? Thank you :)
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on May 17, 2016, 06:46:10 pm
Hey guys, does anyone know how to use the TI-Nspire CAS functions for financial maths (amortisation table, etc)? If so, pls let me know as I have my sac on Friday and am totally lost.
Title: Re: VCE Further Maths Question Thread!
Post by: friedchromosome on May 19, 2016, 03:50:31 pm
Hey guys, seeing as financial maths is apart of statistics now, i could really use some pointers as to where i can gain the most practise from for these 2 chapters, if anyone has some worksheets please message me !!!!! thanks
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on May 21, 2016, 11:55:51 am
Hi all,

I have my recursion and finance SAC coming up this week and just have a question.

When finding the rate for compound interest loans and investments the model is 1+ r/100, whilst the model for reducing balance depreciation is 1-r/100. Could someone please explain the significance of the 1.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on May 21, 2016, 01:26:37 pm
Hi all,

I have my recursion and finance SAC coming up this week and just have a question.

When finding the rate for compound interest loans and investments the model is 1+ r/100, whilst the model for reducing balance depreciation is 1-r/100. Could someone please explain the significance of the 1.

Thanks

My interpretation of '1' is simply the 'original' amount (1 = 100% = the original or principal amount).

Take into consideration the brackets (1 + r)

If the interest rate is 5%, then its 1 + (5/100) which is 1.05, MEANING the original amount (100%) plus an additional 5% = 105% = 1.05. Then of course, 1.05 is multiplied by itself however many periods/years.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on May 21, 2016, 01:33:35 pm
My interpretation of '1' is simply the 'original' amount (1 = 100% = the original or principal amount).

Take into consideration the brackets (1 + r)

If the interest rate is 5%, then its 1 + (5/100) which is 1.05, MEANING the original amount (100%) plus an additional 5% = 105% = 1.05. Then of course, 1.05 is multiplied by itself however many periods/years.

Thanks Aaron  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on May 23, 2016, 11:43:13 am
Guys, how do I go about doing this one?

Quote
Ali invested $26,000 into an account earning compound interest at the rate of 4.5% per annum. After 5 compounding periods, the value of Ali's investment will be $26,614.86 correct to the nearest cent.
The annual interest rate is compounding

A) weekly
B) fortnightly
C) monthly
D) quarterly
E) annually

Definitely missing something simple here. The answer is A but I keep getting something completely different.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on May 23, 2016, 01:12:41 pm

Guys, how do I go about doing this one?

Definitely missing something simple here. The answer is A but I keep getting something completely different.

I think there's a typo in this question. I tried everything

My first method I used was [26000*(1+4.5/100*n)^5=26614.86] n=9.6
This has to be the right answer but bc you said its weekly the actual answer should be 52.

I then wanted to see if the question was actually correct. So I used 52 as my n

[26000*(1+4.5/100*52)^5] for this I got the answer 26112.69 which wasn't the amount mentioned in the question.

So I think the question is written wrong, or I made a mistake.
Guys, If I did anything wrong in my working out, pls let me know

Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on May 24, 2016, 09:21:45 pm
Guys what does 'equal bin width' mean on the CAS? And when would I need to utilise the function?
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on May 28, 2016, 05:29:42 pm
For this question attached i have a query.

i got the equation as Vn=(0.918)^n x Vo

now we know V10=13770 therefore Vo=32397.17399

the book says the initial cost is $32397.17

however i rounded up and said the initial cost is $32397.18

reason is because when you sub my initial cost value into the equation you have a value of at least $13770.
where as  when you sub in the books initial cost value into the equation you have a value of less than $13770.


Who would be right in this case and whats the best thing to do in these situations ?

Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on May 28, 2016, 10:15:39 pm
This rule for the effective interest  rate(attached) is for when n is  the number of times the interest compounds each year.

What if in a question something is depreciating instead of compounding  , whats the rule then?

Would it just be
 
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on May 29, 2016, 04:07:19 pm
For this question attached i have a query.

i got the equation as Vn=(0.918)^n x Vo

now we know V10=13770 therefore Vo=32397.17399

the book says the initial cost is $32397.17

however i rounded up and said the initial cost is $32397.18

reason is because when you sub my initial cost value into the equation you have a value of at least $13770.
where as  when you sub in the books initial cost value into the equation you have a value of less than $13770.


Who would be right in this case and whats the best thing to do in these situations ?

This rule for the effective interest  rate(attached) is for when n is  the number of times the interest compounds each year.

What if in a question something is depreciating instead of compounding  , whats the rule then?

Would it just be
 

Can anyone help with these ?  :)
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 31, 2016, 05:17:57 pm
Guys, how do I go about doing this one?

Definitely missing something simple here. The answer is A but I keep getting something completely different.
As a.t has said, there is an error here if we say there are 52 weeks in a year (which is what I expect VCAA would want you to assume; although 52 weeks is only 364 days.)
I used the calculator finance solver to find FV when interest is charged:
weekly = $26,112.69 as a.t. found
fortnightly = $26,225.78
monthly = $26,491.17
quarterly = $27,495.78
annually = $32,400.73
The closest answer on offer is A.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 31, 2016, 05:29:58 pm
For this question attached i have a query.
i got the equation as Vn=(0.918)^n x Vo
now we know V10=13770 therefore Vo=32397.17399
the book says the initial cost is $32397.17
however i rounded up and said the initial cost is $32397.18
reason is because when you sub my initial cost value into the equation you have a value of at least $13770.
where as  when you sub in the books initial cost value into the equation you have a value of less than $13770.

Who would be right in this case and whats the best thing to do in these situations ?
The book value after 10 years is likely to have been rounded to the nearest ten dollars. Therefore, it would make more sense for the question to ask for the initial cost of the machine rounded at least to the nearest dollar, if not the nearest ten dollars. You would expect greater clarity in a text book and I would think an exam question would avoid the issue. Given all this, I would round the answer here to the nearest cent.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 31, 2016, 05:39:53 pm
This rule for the effective interest  rate(attached) is for when n is  the number of times the interest compounds each year.
What if in a question something is depreciating instead of compounding  , whats the rule then?
Would it just be
 
The study design only links the topic of effective interest rates to investments or loans. Therefore, I don't think application to depreciation is an issue to worry about.
The format of the formula for effective interet rate is slighly different to what VCAA has published on the new formula sheet in their sample exam papers for 2016. Find this on the VCAA website on the same page as you would look to find past further maths exam papers.
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on May 31, 2016, 06:04:10 pm
The book value after 10 years is likely to have been rounded to the nearest ten dollars. Therefore, it would make more sense for the question to ask for the initial cost of the machine rounded at least to the nearest dollar, if not the nearest ten dollars. You would expect greater clarity in a text book and I would think an exam question would avoid the issue. Given all this, I would round the answer here to the nearest cent.

The study design only links the topic of effective interest rates to investments or loans. Therefore, I don't think application to depreciation is an issue to worry about.
The format of the formula for effective interet rate is slighly different to what VCAA has published on the new formula sheet in their sample exam papers for 2016. Find this on the VCAA website on the same page as you would look to find past further maths exam papers.


Thanks so much plato  :) :D
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on May 31, 2016, 07:02:09 pm
If you were to use the financial solver on the CAS how would you show working out , on the paper?

Say the question was worth like 3marks.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 31, 2016, 09:24:13 pm
Just show the labelled list of values for N, I, PV etc
Title: Re: VCE Further Maths Question Thread!
Post by: YellowTongue on June 09, 2016, 06:36:26 pm
How would I answer the attached financial maths question?

Thanks for your help  :)
Title: Re: VCE Further Maths Question Thread!
Post by: KKK on June 09, 2016, 07:13:57 pm
How would I answer the attached financial maths question?

Thanks for your help  :)

Answer would just be E, since it's reducing 10 minutes each time " each following day". Constantly reducing at a fixed rate of 10 minutes each time.  Correct me if i'm wrong :)
Title: Re: VCE Further Maths Question Thread!
Post by: Hzahra12 on June 13, 2016, 10:46:37 pm
Anyone willing to help me with this
Annuity 2.8% compounded fortnightly for first 11 years,the balance $ 100 000 , then value drawback to 2.3%p.a compounded fornightly to final 11 years
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on June 16, 2016, 03:33:31 pm
Can someone help me with the attached question? The answer is 144652 L but I got 142237.
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on June 16, 2016, 06:21:57 pm
Can someone help me with the attached question? The answer is 144652 L but I got 142237.
Your figure is after 6 days, the answer is 144652L.
Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on June 27, 2016, 12:10:21 am
Hi, can someone show me how to do this Geo & Trig question? Thanks

Calculate the shortest distance from Newcastle, Australia (latitude 33°S, longitude 153°E) to Mendoza, Argentina (latitude 33°S, longitude 72°W), correct to the nearest kilometre.

The answer is 15 080km.
Title: Re: VCE Further Maths Question Thread!
Post by: val265 on June 28, 2016, 05:27:08 pm
Hi can someone please help me with this question


How to work out the annual depreciation if they give the initial purchase price?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on June 28, 2016, 06:57:26 pm
Hi can someone please help me with this question


How to work out the annual depreciation if they give the initial purchase price?

Hi,

Can you please give some more details of the question. Usually for these types of questions, I use the generic formula and fill in the parts that are known to me (ie. how often it compounds) and then use my CAS to solve the unknown value.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on June 28, 2016, 10:18:09 pm
Hi, can someone show me how to do this Geo & Trig question? Thanks
Calculate the shortest distance from Newcastle, Australia (latitude 33°S, longitude 153°E) to Mendoza, Argentina (latitude 33°S, longitude 72°W), correct to the nearest kilometre.
The answer is 15 080km.
First find the radius of the "parallel" (the line of latitude) that passes through both cities.
If the radius of the Earth is 6400, then the radius of this parallel  is 6400 sin(57) =  5367.5 km
The minimum angle at the Earth's axis between the two cities is 152 - 72 = 81 degrees.
The distance along the line of latitude between Newcastle and Mendoza is then:
81/360 x the circumference of a circle that has a radius of 5367.5km.  I calculate this as 7588km

This is not really the shortest distance. The shortest distance between the two cities is "as the crow flies" and is called the geodesic distance . This calculates to be about 7373 km with a complicated formula well beyond Further.

Title: Re: VCE Further Maths Question Thread!
Post by: val265 on July 01, 2016, 04:44:44 pm
Hi can someone please help me to work out part D

Hugo is a professional bike rider. The value of his bike will be depreciated over time using a flat-rate depreciation method. The graph below shows his bike’s initial purchase price and its value after each year for a period of 3 years.
What was the initial purchase price of the bike?  8000
What is the value of the annual depreciation?   1500

 d. The bike can also be depreciated using a unit-cost depreciation method. The value of the bike is reduced by $0.25 for every kilometre it travels. After 2 years, the total depreciation will be the same as the flat-rate depreciation as described above.
How many kilometres did the bike travel in the 2-year period?


If anyone has the online cambridge textbook it is Chapter 10 review Question 1 part d in extended respone

I would really appreciate the help
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on July 05, 2016, 02:36:27 pm
Hi all,

Is there a correct number of cuts you can apportion to a network? What I mean is, can VCAA take marks off if you have done, say 6 cuts, when there were supposed to be 5 made?

Sorry, I hope this makes some sense.  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Complex on July 05, 2016, 02:38:13 pm
Hi all,

Is there a correct number of cuts you can apportion to a network? What I mean is, can VCAA take marks off if you have done, say 6 cuts, when there were supposed to be 5 made?

Sorry, I hope this makes some sense.  :)

Yeah there always is. They will take marks off if u get it wrong by one, they r stingy like that
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on July 05, 2016, 03:47:53 pm
Hi everyone,

Does anyone have advice on how to work out these types of questions with efficiency? Or networks in general?

Thank-you in advance  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Complex on July 05, 2016, 04:41:18 pm
Hi everyone,

Does anyone have advice on how to work out these types of questions with efficiency? Or networks in general?

Thank-you in advance  :)

Generally for these questions its best to not use cuts but just to find the maximum flow (minimum inflow). Cuts are innefective because they get messy and sometimes its easy to just simply miss the minimum cut.

Take this answer with some salt because i havent considered further since i left the exam room for it.

I think...

Source 1 > Sink 1 = 19km (The fastest way there is 13+6)
Source 2> Sink 2 = 14km (8+6)

Are those the right answers?

If you need Source 1 > sink 2 = 34km (15+12+9+1+6)
And Source 2 > Sink 1 = 35km (14+7+12+2)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on July 07, 2016, 04:12:20 pm
Hi Everyone,

Is it possible for there to be two critical paths?

For example, with the attached image, there could be a critical path of K-N-Q-T and K-R-T.

Thanks in advance  :)
Title: Re: VCE Further Maths Question Thread!
Post by: maylovesgelati on July 11, 2016, 07:09:43 pm
How do you do this question on a CAS calculator?

David enters into an arrangement to buy a car for $5000 deposit and monthly repayments of $1100 per month for two years. If the purchase price of the car is $24 990, then the flat rate of interest per annum this represents is closest to:
a) 2.8%
b) 5.6%
c) 12.8%
d) 16.0%
e) 32.0%
Title: Re: VCE Further Maths Question Thread!
Post by: death to the vcaa on July 14, 2016, 11:37:23 am
I stuffed up my recursion and financial SAC. I got 79% on it and also got 92% on my data SAC. I was wondering whether it was still possible to achieve a 40 ss in further?
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on July 15, 2016, 07:44:39 pm
I stuffed up my recursion and financial SAC. I got 79% on it and also got 92% on my data SAC. I was wondering whether it was still possible to achieve a 40 ss in further?
Yes

Like your username btw!  :P
Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on July 24, 2016, 04:42:17 pm
Hi guys, how do I find the area of this triangle using one of the 3 methods from Geo&Trig?
Thanks! :)
Title: Re: VCE Further Maths Question Thread!
Post by: RuiAce on July 24, 2016, 04:57:28 pm
Hi guys, how do I find the area of this triangle using one of the 3 methods from Geo&Trig?
Thanks! :)

Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on July 24, 2016, 05:03:05 pm
Cheers, just a question: how do you know that 5mm is perpendicular to b // it's a 90degree angle?
Title: Re: VCE Further Maths Question Thread!
Post by: RuiAce on July 24, 2016, 05:23:31 pm
Cheers, just a question: how do you know that 5mm is perpendicular to b // it's a 90degree angle?
Oh I assumed that. If that wasn't the case then we actually don't have enough information to find the area.
Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on July 24, 2016, 05:49:19 pm
Ok thanks for your help :)
Title: Re: VCE Further Maths Question Thread!
Post by: minerva on August 06, 2016, 10:59:40 pm
Can anyone please help me with this question?
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on August 06, 2016, 11:11:41 pm

Can anyone please help me with this question?
Unique solution means when you only get one answer. So for simultaneous equations that means when you only get one set of coordinates for when the lines intersect. Easiest way to do it is to put it in the CAS to solve the equations simultaneously.
Equation 1- is just the same line. The lines are both the same (one is just multiplied by 2), so if u graph it out, you will get infinite points of intersections
Equations 3 and 4 are exactly the same too

So that leaves you only with equations 2 and 5.
For equation 2 ur solution is (0,6). Meaning, your lines will intersect in the coordinate (0,6). And equation 5 is a horizontal and vertical line. So they have to meet at (8,2).
 
This means you only have 2 equations that give you 2 u unique solutions so your answer must be B.

Correct me if I made any mistakes and feel free to ask me again if you couldn't understand my explanation.

 
Title: Re: VCE Further Maths Question Thread!
Post by: eth-dog on August 08, 2016, 08:53:38 pm
Just wondering, how do you find the distance around a great circle that passes through two points? I have had plenty of questions which ask for the distance between two points but i haven't had one asking 'that passes through two points'. I have attached a picture of the question.

Any help is appreciated. Btw the answer is very similar to question b.

Answers:
a) 6182km
b) 3237km
c) 3234km
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on August 09, 2016, 06:18:54 pm
Hi Guys,

How is this graph planar? Even when rearranging the edges so that they don't intersect wouldn't they still cross due to their positioning?

Thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Vaike on August 20, 2016, 10:08:21 pm
Hi Guys,

How is this graph planar? Even when rearranging the edges so that they don't intersect wouldn't they still cross due to their positioning?

Thanks  :)

Sorry for the poorly drawn diagram, but here's how you can redraw it to be planar. Also, I think any graph with 4 or less vertices can be planar, someone please correct me if I am mistaken :)

Title: Re: VCE Further Maths Question Thread!
Post by: YellowTongue on August 24, 2016, 04:18:05 pm
When given the longitudes of two locations and asked to find the time difference, what do you do if the difference is not a multiple of 15? E.g. if one location has a longitude of 37 degrees east whilst another has a longitude of 6 degrees east, do you round according to standard numerical rounding (i.e. down in this case)?

Or if you had a 57 degress and 2 degree longitude, would you round up?
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on August 26, 2016, 10:22:27 am
Could someone please give an explanation/show the working out for the attached question? I'm pretty sure I understand it but I'd appreciate a second opinion. :)

Edit: Attached another question. I have a SAC tomorrow so if anyone could provide an explanation/working out ASAP it would be much appreciated!
Title: Re: VCE Further Maths Question Thread!
Post by: chenay0123 on August 28, 2016, 03:09:04 pm
Hey, can someone show me how to put this question in matrix form? thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: val265 on September 04, 2016, 01:33:47 pm
Hey guys,
Just wondering in Bearings if it says find A from B  do we start at B?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on September 04, 2016, 01:36:05 pm
Hey guys,
Just wondering in Bearings if it says find A from B  do we start at B?

Yes [as long as it says that, not the other way around]

If there's a specific question, please post it (so that members on here understand the full context of the question).
Title: Re: VCE Further Maths Question Thread!
Post by: Sine on September 04, 2016, 01:37:28 pm
this is one of those "tricks" that also comes up in spec which many people trip up on so make sure to check
Title: Re: VCE Further Maths Question Thread!
Post by: val265 on September 11, 2016, 03:32:41 pm
Hey guys what is the formula of a major segment for spherical geometry?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 11, 2016, 06:01:58 pm
Hey everyone,

Can someone please explain to me why the mean is greater than the median for positively skewed data and vice versa for negatively skewed data.

Thanks very much!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Jakeybaby on September 11, 2016, 06:32:28 pm
Hey everyone,

Can someone please explain to me why the mean is greater than the median for positively skewed data and vice versa for negatively skewed data.

Thanks very much!  :)
Let's consider two separate samples taken:

Sample 1: 1 3 7 3 2 3 6 3 2 4 3 5 7 3 1
Sample 2: 7 7 6 3 8 9 7 6 4 2 2 6 8 9 6

Organising the samples in ascending order we get:

Sample 1: 1 1 2 2 3 3 3 3 3 3 4 5 6 7 7
Sample 2: 2 3 4 6 6 6 6 7 7 7 8 9 9 9

We can see that for sample 1, there are more values towards the negative end of the distribution.
Hence, we see a distribution which looks similar to the following:
(http://www.ken-szulczyk.com/misc/statistics/asymmetric_distribution_01.png)

We can see from the ascending ordered sample that the median for Sample 1 is 3.
Through some simple calculations, the mean is 6.

And then from Sample 2, we see that there are more values at the higher end (towards the positive end). Hence:
(http://www.ken-szulczyk.com/misc/statistics/asymmetric_distribution_02.png)
The median for Sample 2 is 6.47 and the mean is 7.
 
If we think about it, it is more likely for a data value to occur at the lower end of the scale, due to the fact that more values occur at the lower end. The mean calculates the average of all the values, this also means that the mean is affected by outliers, whereas the median is uneffected by outliers, hence, the mean is always going to be larger in unimodial distributions.
Quote
The mean is pulled in the direction of the extreme scores or tail (same as the direction of the skew)

So, for the general rule of thumb, the mean always occurs at the same end of the skew.
Title: Re: VCE Further Maths Question Thread!
Post by: Manige123 on September 12, 2016, 05:40:45 pm
Urgently need help with this question, sac is tomorrow! (Liner programming)

A maker of blended whiskey buys its raw material from three supplies: McAllister, McBride and McCallum. THe maker wishes to purchase a total of 200 litres of whiskey from the three suppliers. The whiskey must contain a minimum of malt and barley. Each suppliers minimum amounts of malt and barley are shown:
McCallister: 7% Malt
McBride: 2% Malt
McCallum: 5% Malt
Minimum amount of ingredient allowed: 4%
x= amount of whiskey bought from McCallister, y= amount of whiskey bought from McBride and 200-x-y = amount of whiskey bought from McCallum.
Define the constraint inequation caused by the restriction on Malt.

answer is 2x-3y > or = to -200.

I know how to do these types of questions and for some reason once i reach 2x-3y, my equation is something like 2x-3y+100<4

PLEASE HELP MUCH APPRECIATED THANKS IN ADVANCE

Title: Re: VCE Further Maths Question Thread!
Post by: Drewballs on September 12, 2016, 06:12:46 pm
So this is the only way I can find that answer is if you multiply the 4 by 200 (4% for each litre of whisky purchased)

7x+2y+5(200-x-y) > or = to 4 x 200
7x+2y+1000-5x-5y> or = to 800
7x-5x+2y-5y+1000> or = to 800
2x-3y+1000> or = to 800
2x-3y> or = to  -200

Title: Re: VCE Further Maths Question Thread!
Post by: Hydroxyl on September 13, 2016, 02:31:04 pm
This is a question from the Sample exam.

Consider the following four statements. A permutation matrix is always:
I a square matrix
II a binary matrix
III a diagonal matrix
IV equal to the transpose of itself.
How many of the statements above are true?
A. 0
B. 1
C. 2
D. 3
E. 4


The answers say C, which is 2. But I've done some calculations and found that Statement IV (A permutation matrix is always equal to the transpose of itself) is true.

I'm confused about this..

Anyone that can help, it would be appreciated.

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on September 15, 2016, 05:57:55 pm
This is a question from the Sample exam.

Consider the following four statements. A permutation matrix is always:
I a square matrix
II a binary matrix
III a diagonal matrix
IV equal to the transpose of itself.
How many of the statements above are true?
A. 0
B. 1
C. 2
D. 3
E. 4


The answers say C, which is 2. But I've done some calculations and found that Statement IV (A permutation matrix is always equal to the transpose of itself) is true.

I'm confused about this..

Anyone that can help, it would be appreciated.

Thanks :)


I think Option 4 is only true for 3x3 permutation matrices. For example a 4x4 permutation matrix can have 1s in row 1 column 2, row 2 column 3, row 3 column 1 and row 4 column 4 and the transpose is obviously not the same.

Hey, can someone show me how to put this question in matrix form? thanks :)

You make C and R both the same variable, for example y, as they are both costs. And then you keep n as number of jeans and solve the simultaneous equations.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on September 17, 2016, 03:35:21 pm
Hey guys
If I need to make a boxplot and a I have outliers on either ends of the boxplot, what will my min and max value be? Do my tails go up to the value in the lower fence which is the minimum and the same for the upper fence?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 17, 2016, 03:38:45 pm
Hey guys
If I need to make a boxplot and a I have outliers on either ends of the boxplot, what will my min and max value be? Do my tails go up to the value in the lower fence which is the minimum and the same for the upper fence?

Hey,

If you have outliers, these will count as your min or max value. If you don't have outliers, the ends of the tails will be your max and min.

I hope that answered your question!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on September 17, 2016, 03:40:06 pm

Hey,

If you have outliers, these will count as your min or max value. If you don't have outliers, the ends of the tails will be your max and min.

I hope that answered your question!  :)
That helped!
What if I have outliers, where will my tails extend to?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 17, 2016, 03:47:48 pm
That helped!
What if I have outliers, where will my tails extend to?

If you have outliers, your outliers will be beyond your tails.

However, in some circumstances, you may be given a diagram of a box plot where you have single points beyond your tails. In this case, you cannot just assume that they are outliers. Here, you must apply the upper and lower fence formula (Upper Fence: Q3+1.5*IQR and Lower Fence Q1-1.5*IQR) to work out if they are outliers.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on September 17, 2016, 03:53:16 pm

If you have outliers, your outliers will be beyond your tails.

However, in some circumstances, you may be given a diagram of a box plot where you have single points beyond your tails. In this case, you cannot just assume that they are outliers. Here, you must apply the upper and lower fence formula (Upper Fence: Q3+1.5*IQR and Lower Fence Q1-1.5*IQR) to work out if they are outliers.
Thanks!
Also, how can the standard deviation be used when comparing data distributions in terms of centre and spread?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 17, 2016, 04:04:36 pm
Thanks!
Also, how can the standard deviation be used when comparing data distributions in terms of centre and spread?

If one data distribution has a higher standard deviation than the other, you could conclude that this distribution is more variable than the other. This is because it will be moving further and further away from the mean.

In terms of centre, mean would be a more appropriate measure as opposed to standard deviation.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on September 17, 2016, 04:10:16 pm

If one data distribution has a higher standard deviation than the other, you could conclude that this distribution is more variable than the other. This is because it will be moving further and further away from the mean.

In terms of centre, mean would be a more appropriate measure as opposed to standard deviation.
Thank you!!
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on September 17, 2016, 05:35:00 pm
Hi guys,
I have a question related to time plot graphs. My textbook doesn't seem to explain how to go about with identifying different trends, could someone please explain how to determine whether a graph is cyclic or seasonal. What are the differences and how do you know when either is present in a graph?

Cheers  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Maths Forever on September 17, 2016, 07:10:34 pm
Does anyone know if this question involves an inverse relationship? Itute solutions gave a negative answer in their solutions...... This is from the sample exam for the new Further Maths study design.


Question 5 (4 marks)
There is an association between the variables population density, in people per square kilometre,
and area, in square kilometres, of 38 inner suburbs of the same city.
For this association, r2 = 0.141

a. Write down the value of the correlation coefficient for this association between the variables
population density and area.
Round your answer to three decimal places.

Thanks!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Maths Forever on September 17, 2016, 07:12:46 pm
The solutions from Itute:

Q5a
population density = population / area,

inverse relationship between population density and area, .: r = − sqrt(0.141), approximately − 0.375
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on September 17, 2016, 10:38:36 pm
The solutions from Itute:

Does anyone know if this question involves an inverse relationship? Itute solutions gave a negative answer in their solutions...... This is from the sample exam for the new Further Maths study design.


Question 5 (4 marks)
There is an association between the variables population density, in people per square kilometre,
and area, in square kilometres, of 38 inner suburbs of the same city.
For this association, r2 = 0.141

a. Write down the value of the correlation coefficient for this association between the variables
population density and area.
Round your answer to three decimal places.

Thanks!  :)

Q5a
population density = population / area,

inverse relationship between population density and area, .: r = − sqrt(0.141), approximately − 0.375

Im assuming r2 refers to the correlation coefficient of determination. In this case the correlation coefficient will be the square root of the r2 value. It is only negative if the scatter plot has a negative skew. A negative skew would look like a linear function with a negative gradient. :)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 18, 2016, 07:35:40 am
Q5a
population density = population / area,

inverse relationship between population density and area, .: r = − sqrt(0.141), approximately − 0.375


Im assuming r2 refers to the correlation coefficient of determination. In this case the correlation coefficient will be the square root of the r2 value. It is only negative if the scatter plot has a negative skew. A negative skew would look like a linear function with a negative gradient. :)

Hey,

For this question, however, there is no indication as to whether the correlation is positive or negative.
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on September 18, 2016, 02:00:21 pm
A bit of a stupid question I guess but in relation to the attached question, my understanding is that the 6 wouldn't be counted because its heading from the sink to the source and hence would be: 8+4+11=23
But its multiple choice and the options are: 4, 11, 14, 21, and 29.

So, in all cases should I definitely be counting the 6 thereby getting 29?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 18, 2016, 02:40:38 pm
A bit of a stupid question I guess but in relation to the attached question, my understanding is that the 6 wouldn't be counted because its heading from the sink to the source and hence would be: 8+4+11=23
But its multiple choice and the options are: 4, 11, 14, 21, and 29.

So, in all cases should I definitely be counting the 6 thereby getting 29?

Hi Coffee,

Yes, you should be counting the 6 to obtain 29.

Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on September 18, 2016, 02:55:01 pm
Hi Coffee,

Yes, you should be counting the 6 to obtain 29.


Thanks, Clarke. I was a bit confused since in the textbook it said not to if it was moving upwards like in the above example. ???
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 18, 2016, 03:06:32 pm
Thanks, Clarke. I was a bit confused since in the textbook it said not to if it was moving upwards like in the above example. ???

Hi Coffee,

As seen in the attached image, the weight on the edge F to B (6) wouldn't be counted as you've already been trapped by the 20. That's the only way I can think of these cuts.  :)

I agree, that some textbooks can be confusing in their explanations.
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on September 18, 2016, 03:42:55 pm
Hope you guys don't mind me asking another question (this one is a bit lengthy). I'm mostly confused by the wording of the question and what its actually asking me to do.

1. The Houndsworth Town Sports Association is planning a sports carnival. Traffic through the town will be diverted around the sporting venues during the carnival. The network (attached below) shows the road that can be used during the carnival represented by the edges and intersection of those roads shown as vertices.
The number on the edges are the maximum number of cars that can travel on the road each hour. The roads will be restricted to allow one-way traffic only, as shown by the arrows.


a. How many cars per hour can enter the diversion roads?
I'm guessing this is just asking from A - B, thus 180? But correct me if I'm wrong.

One cut (Cut 1) is shown on the diagram above.
b. i. If the capacity of Cut 1 is 150, what is the value of m?


ii. Show that the smallest value of m that will ensure there will be no build-up of cars at intersection B is 50.

The capacity of the road between intersection B and intersection E is 50 (m = 50). The maximum flow through the network is currently 150 cars per hour.
c. Mark in the cut that determines the maximum flow on the network above.


I don't quite understand how m = 50? I thought it would just be 150-130=20.

The Sport Association have noticed that there could be a build-up of traffic at intersection E and F.
d. If the road between intersections F and H was improved, what is the maximum capacity is should take to the solve the potential traffic build-up at F?

In order to solve the potential build-up of traffic at intersection E, the Sports Association open another road from intersection E to intersection D.
e. i. What is the minimum capacity of this road that will avoid traffic build-up at intersection E?

ii. Explain why a road between intersection E and D cannot solve potential traffic build-up in the network.


Super sorry for the incredibly lengthy question, I'm just really confused about what the hell its asking me to do and how to go about getting there.
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on September 18, 2016, 07:25:34 pm
Hope you guys don't mind me asking another question (this one is a bit lengthy). I'm mostly confused by the wording of the question and what its actually asking me to do.

1. The Houndsworth Town Sports Association is planning a sports carnival. Traffic through the town will be diverted around the sporting venues during the carnival. The network (attached below) shows the road that can be used during the carnival represented by the edges and intersection of those roads shown as vertices.
The number on the edges are the maximum number of cars that can travel on the road each hour. The roads will be restricted to allow one-way traffic only, as shown by the arrows.


a. How many cars per hour can enter the diversion roads?
I'm guessing this is just asking from A - B, thus 180? But correct me if I'm wrong.

One cut (Cut 1) is shown on the diagram above.
b. i. If the capacity of Cut 1 is 150, what is the value of m?


ii. Show that the smallest value of m that will ensure there will be no build-up of cars at intersection B is 50.

The capacity of the road between intersection B and intersection E is 50 (m = 50). The maximum flow through the network is currently 150 cars per hour.
c. Mark in the cut that determines the maximum flow on the network above.


I don't quite understand how m = 50? I thought it would just be 150-130=20.

The Sport Association have noticed that there could be a build-up of traffic at intersection E and F.
d. If the road between intersections F and H was improved, what is the maximum capacity is should take to the solve the potential traffic build-up at F?

In order to solve the potential build-up of traffic at intersection E, the Sports Association open another road from intersection E to intersection D.
e. i. What is the minimum capacity of this road that will avoid traffic build-up at intersection E?

ii. Explain why a road between intersection E and D cannot solve potential traffic build-up in the network.


Super sorry for the incredibly lengthy question, I'm just really confused about what the hell its asking me to do and how to go about getting there.

1. a. I think you're right but not 100% sure.
b. i. You're right, the answer is 30
ii. The inflow to node B is 180 which comes from the source, which means to prevent congestion the outflow cannot exceed 180. We already have 90+40=130 so m has to be maximum of 50 so that the cut doesn't exceed 180.
c. The cut goes through 30, 40 and 80.
d. The inflow is 100 and the outflow is only 80 which is 20 less. So we should increase it to 100.
e. i. The inflow is 50 and the outflow is only 30 which is 20 less. So the new road from E to D should be at least 20.
ii. I think it's because there's still some congestion at other intersections in the network, for example the outflow of C is 100 which exceeds its inflow of 90. Not 100% sure.

Hope I helped.
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on September 18, 2016, 09:41:17 pm
1. a. I think you're right but not 100% sure.
b. i. You're right, the answer is 30
ii. The inflow to node B is 180 which comes from the source, which means to prevent congestion the outflow cannot exceed 180. We already have 90+40=130 so m has to be maximum of 50 so that the cut doesn't exceed 180.
c. The cut goes through 30, 40 and 80.
d. The inflow is 100 and the outflow is only 80 which is 20 less. So we should increase it to 100.
e. i. The inflow is 50 and the outflow is only 30 which is 20 less. So the new road from E to D should be at least 20.
ii. I think it's because there's still some congestion at other intersections in the network, for example the outflow of C is 100 which exceeds its inflow of 90. Not 100% sure.

Hope I helped.

You're brilliant, Kimahso. Thank you so much, that's incredibly helpful!
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 19, 2016, 10:53:32 am
Hi everyone,

I understand that postcode is a categorical variable, however, is it nominal or ordinal? Can you please explain why?

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on September 19, 2016, 02:40:59 pm
Hi everyone,

I understand that postcode is a categorical variable, however, is it nominal or ordinal? Can you please explain why?

Thanks!
I think postcodes are ordinal as you can put them in order e.g. 3000, 3001, 3002 etc

Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on September 20, 2016, 09:27:17 am
Hi guys,

How would I go about working out the following question?

1. The ovens and other equipment in Phillip's kitchen have been depreciated using a flat-rate depreciation method. A recurrence relation that models the value of the kitchen equipment after n years, Vn, is shown below.
Vo = 5800, Vn+1=Vn-350
a. What was the original purchase price of the kitchen equipment?


Thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: RuiAce on September 20, 2016, 09:32:51 am
Hi guys,

How would I go about working out the following question?

1. The ovens and other equipment in Phillip's kitchen have been depreciated using a flat-rate depreciation method. A recurrence relation that models the value of the kitchen equipment after n years, Vn, is shown below.
Vo = 5800, Vn+1=Vn-350
a. What was the original purchase price of the kitchen equipment?


Thanks  :)
Wouldn't that just be 5800
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on September 20, 2016, 09:52:36 am
Wouldn't that just be 5800

Haha, is that legit what its asking me?  ;D :P I'm so sorry, I overthink these things man.
Title: Re: VCE Further Maths Question Thread!
Post by: KDB on September 20, 2016, 01:02:12 pm
Haha, is that legit what its asking me?  ;D :P I'm so sorry, I overthink these things man.

Vo means the starting point/original purchase price
Title: Re: VCE Further Maths Question Thread!
Post by: val265 on September 20, 2016, 08:52:13 pm
Hey guys,
can anyone pls help me out in finding an area of a major segment?
Title: Re: VCE Further Maths Question Thread!
Post by: jayleno on September 26, 2016, 02:55:08 am
How many marks can you afford to lose in both further math exams in order to score an A or an A plus :p?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 26, 2016, 07:47:36 am
How many marks can you afford to lose in both further math exams in order to score an A or an A plus :p?

Hi Jayleno,

This varies from year to year depending on the difficulty of the exams and hence, how everyone performs.

However, to get an indication, you might want to take a look at the graded distribution for Further Maths. This is on the VCAA website.

Hope this helped!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: RuiAce on September 26, 2016, 08:42:22 am
Hey guys,
can anyone pls help me out in finding an area of a major segment?
Not sure if this was unintentionally unanswered but for a major segment, you're better off doing this.

Area of major segment
= Area of entire circle - Area of minor segment
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on September 26, 2016, 02:22:48 pm
Hi guys,
I was just wondering, when comparing parallel box plots, what would it imply if there was a statement saying "the test scores in Box plot A, on average were higher, than the Box plot B"
Title: Re: VCE Further Maths Question Thread!
Post by: AhNeon on September 26, 2016, 03:06:53 pm
Hi guys,
I was just wondering, when comparing parallel box plots, what would it imply if there was a statement saying "the test scores in Box plot A, on average were higher, than the Box plot B"

"the median of Box plot A is higher than the median of Box plot B"
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on September 26, 2016, 05:30:46 pm

"the median of Box plot A is higher than the median of Box plot B"

[/quote]
Alright, but is the median the only factor you could discuss. I understand it is the main one though.
Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: AhNeon on September 26, 2016, 05:45:38 pm
"the median of Box plot A is higher than the median of Box plot B"


Alright, but is the median the only factor you could discuss. I understand it is the main one though.
Thanks :)

In this question, yeh. If it just said to compare the box plot you could talk about IQR, range, outliers and so on. But when asked about one thing like the median, it's best to just talk about that thing so you don't start waffling.
Title: Re: VCE Further Maths Question Thread!
Post by: RuiAce on September 26, 2016, 05:46:04 pm
"the median of Box plot A is higher than the median of Box plot B"


Alright, but is the median the only factor you could discuss. I understand it is the main one though.
Thanks :)
A box plot gives you information on the min, lower quartile, median, upper quartile and max. You can infer range and IQR by extension.

It doesn't show anything about the mean or standard deviation explicitly.
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on September 28, 2016, 08:48:34 pm
Hi everyone,

I understand that postcode is a categorical variable, however, is it nominal or ordinal? Can you please explain why?

Thanks!

According to the 2016 VCAA Sample Exam it's nominal although according to the ABS website it's ordinal (which makes sense IMO).
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 28, 2016, 09:52:12 pm
According to the 2016 VCAA Sample Exam it's nominal although according to the ABS website it's ordinal (which makes sense IMO).

Hmm…. That's interesting. Well, if VCAA say it's nominal then I better go with nominal.

Although, it does make sense for it to be ordinal.
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on September 29, 2016, 05:40:42 pm
According to the 2016 VCAA Sample Exam it's nominal although according to the ABS website it's ordinal (which makes sense IMO).
My bad! I can see the arguments for both  :P
Title: Re: VCE Further Maths Question Thread!
Post by: AhNeon on September 29, 2016, 06:16:55 pm
How about age? Is it discrete or continuous cos ive seen questions with differing answers
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on September 29, 2016, 06:30:33 pm

My bad! I can see the arguments for both  :P

What's your argument for it being categorically nominal?
Title: Re: VCE Further Maths Question Thread!
Post by: RuiAce on September 29, 2016, 06:34:54 pm
How about age? Is it discrete or continuous cos ive seen questions with differing answers
If you're going to round to, say, the nearest year, then it is discrete.

Age is technically continuous as you can be, say, 40.28154353163 years old
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on September 30, 2016, 08:06:00 pm
What's your argument for it being categorically nominal?
I'm leaning to ordinal, someone who thinks it is nominal would probably argue better than me.

I guess you could argue that you can't really put locations in order, as that is what postcodes represent.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on September 30, 2016, 08:19:23 pm
I'm leaning to ordinal, someone who thinks it is nominal would probably argue better than me.

I guess you could argue that you can't really put locations in order, as that is what postcodes represent.

I agree. I wish VCAA would provide their justification as to why it is nominal.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on September 30, 2016, 09:54:22 pm
Total guess but could it be that postcodes act as 'labels' for certain areas? Particularly on a map or for postage (like 7000 -> Middle of nowhere, Tasmania). I think either Nominal or Ordinal are reasonably valid assertions. Unless it changed this year the distinction between types of categorical data isn't important anyway, yeah? :)
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 02, 2016, 05:50:50 pm
 :) This a question from the sample exam issued:

"There is an association between the variables population density, in people per square kilometre, and area, in square kilometres, of 38 inner suburbs of the same city.
For this association, r^2 = 0.141"

This is the solution:

population density = population/area , inverse relationship
between population density and area, .: r = − sqrt(0.141) ≈ − 0.375

So basically, what does it mean by inverse relationship. Our textbook never really explained that. Also how can you tell if the r value is negative or not since there is no scatter plot to determine it.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 02, 2016, 06:30:06 pm
:) This a question from the sample exam issued:

"There is an association between the variables population density, in people per square kilometre, and area, in square kilometres, of 38 inner suburbs of the same city.
For this association, r^2 = 0.141"

This is the solution:

population density = population/area , inverse relationship
between population density and area, .: r = − sqrt(0.141) ≈ − 0.375

So basically, what does it mean by inverse relationship. Our textbook never really explained that. Also how can you tell if the r value is negative or not since there is no scatter plot to determine it.

Hey,

I questioned this too!! It's so odd, I've never seen a question like this without the actual scatterplot or some further information.
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 02, 2016, 07:58:03 pm
Hey,

I questioned this too!! It's so odd, I've never seen a question like this without the actual scatterplot or some further information.

Same!
And I couldn't find anything in my textbook related to 'inverse relationships'.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 02, 2016, 08:36:28 pm
I believe inverse relationship is the same as reciprocal; it should be in your textbook in the transforming data part. It might not be explicitly mentioned, though. If you think of area as the IV and call it x, it might be a little more intuitive. The relation 1/x will be smaller for larger values of x (edit: Implying that if you were to model it with a line it would have a negative slope); 1/6 is less than 1/3, and so on. Correct me if I'm wrong though, it seems like a pretty odd question imo.
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 03, 2016, 08:09:37 pm
If you were calculating total interest paid, if there are 30.8 payments for example,
would you multiply 30.8 by the payment amount. Or would you round it up to 31 first?
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 03, 2016, 11:13:06 pm
Can someone pls explain this question to me? Correct answer is B
thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: RuiAce on October 03, 2016, 11:50:49 pm
Can someone pls explain this question to me? Correct answer is B
thanks!
This looks like some kind of question I'd get in microeconomics regarding production possibility curves...




Title: Re: VCE Further Maths Question Thread!
Post by: YellowTongue on October 04, 2016, 10:15:26 pm
I have a few questions regarding NEAP Exam One 2016. The question are attached below.

CORE

Question 18: The answer I got is C ($2440). I entered the following into my CAS.

N: 120
I: 5
PV: 23000
Pmt: BLANK
FV: 0
Ppy: 12
Cpy: 12

The solutions say that A is the correct response. Is this a mistake?

Question 24: The answer I got is A ($16.12). However the solutions gave B. I am not entirely certain about the correct way to work this one out, but I entered the following into my calculator.

N: 60 and then 1825
I: 5
PV: 25000
Pmt: 0
FV: BLANK
Ppy: 12 and then 365
Cpy: 12 and then 365

Have I made a mistake?

Geometry and Mensuration

Question 4: I'm not entirely certain how to go about answering/visualising this question. I got the correct answer (D), but I don't really understand the scenario where there are different longitudes and latitudes for each coordinate. How should I visualise this?

[img]https://s13.postimg.org/iy1e4m2ab/Question_18.jpg[/img]

[img]https://s13.postimg.org/tm553gc9f/Question_24.jpg[/img]

[img]https://s13.postimg.org/xfylcltlf/Question_4.jpg[/img]

Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 05, 2016, 12:06:57 am
I have a few questions regarding NEAP Exam One 2016. The question are attached below.

CORE

Question 18: The answer I got is C ($2440). I entered the following into my CAS.

N: 120
I: 5
PV: 23000
Pmt: BLANK
FV: 0
Ppy: 12
Cpy: 12

The solutions say that A is the correct response. Is this a mistake?

Question 24: The answer I got is A ($16.12). However the solutions gave B. I am not entirely certain about the correct way to work this one out, but I entered the following into my calculator.

N: 60 and then 1825
I: 5
PV: 25000
Pmt: 0
FV: BLANK
Ppy: 12 and then 365
Cpy: 12 and then 365

Have I made a mistake?

Geometry and Mensuration

Question 4: I'm not entirely certain how to go about answering/visualising this question. I got the correct answer (D), but I don't really understand the scenario where there are different longitudes and latitudes for each coordinate. How should I visualise this?

[img]https://s13.postimg.org/iy1e4m2ab/Question_18.jpg[/img]

[img]https://s13.postimg.org/tm553gc9f/Question_24.jpg[/img]

[img]https://s13.postimg.org/xfylcltlf/Question_4.jpg[/img]



For the core questions I had the same answer as you.
Im finding the finance stuff really annoying, especially the rounding in particular. Like when do you need to round payments and such.
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 09, 2016, 08:47:21 am
How would you do this question attached ?

Answer is E
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 09, 2016, 12:54:31 pm
How would you do this question attached ?

Answer is E

A is true because the humidity was increasing for 7 of the days out of the total 10.
C is true as the humidity was above 50% for 5.5 days out of the total 10.
D is true as in both days 2 and 3, the humidity increases by 20% (day 2 is represented by the second column, day 3 is represented by the third column)
E is not true because on day 7 it decreases by 15% and on day 9 it increases by about 15%.
I didn't even bother checking B but E is obviously not true therefore it's the answer.
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 10, 2016, 05:28:46 pm
A is true because the humidity was increasing for 7 of the days out of the total 10.
C is true as the humidity was above 50% for 5.5 days out of the total 10.
D is true as in both days 2 and 3, the humidity increases by 20% (day 2 is represented by the second column, day 3 is represented by the third column)
E is not true because on day 7 it decreases by 15% and on day 9 it increases by about 15%.
I didn't even bother checking B but E is obviously not true therefore it's the answer.

Thanks so much Kimahso   :)
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 10, 2016, 05:37:13 pm
For everyone doing graphs and relations:

Theres a question about a chick selling coffee. Now, it asks for the break even point, which i calculated to be 71.2.
However I was just wondering since you cant sell 0.2 of a coffee, would you round the breakeven point. In the answer it says 72,
I wanted to know in which cases you have to round the break even point. And also how would you know whether to round it up or down?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 10, 2016, 05:53:41 pm
For everyone doing graphs and relations:

Theres a question about a chick selling coffee. Now, it asks for the break even point, which i calculated to be 71.2.
However I was just wondering since you cant sell 0.2 of a coffee, would you round the breakeven point. In the answer it says 72,
I wanted to know in which cases you have to round the break even point. And also how would you know whether to round it up or down?

Round up for pretty much everything. 71.2 coffees is pretty inarguably more than 71.0 coffees, but like you said you can only sell whole coffees so you need to round up. It's pretty much a context check; you should generally be able to tell how you should round by thinking about the question. :)

As for whether to round up or down, it depends on what's the better outcome. In this case selling more coffee is the better outcome in terms of profit so you round up. It's a bit like those normal distribution questions about running or golf or whatever, where it's better to have lower numbers. Alternatively looking at it on a graph is a pretty easy way to tell what you should do.
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 10, 2016, 07:41:39 pm
Round up for pretty much everything. 71.2 coffees is pretty inarguably more than 71.0 coffees, but like you said you can only sell whole coffees so you need to round up. It's pretty much a context check; you should generally be able to tell how you should round by thinking about the question. :)

As for whether to round up or down, it depends on what's the better outcome. In this case selling more coffee is the better outcome in terms of profit so you round up. It's a bit like those normal distribution questions about running or golf or whatever, where it's better to have lower numbers. Alternatively looking at it on a graph is a pretty easy way to tell what you should do.

Thankss :)
Title: Re: VCE Further Maths Question Thread!
Post by: markkovacev on October 11, 2016, 11:52:27 am
If you don't get a 50 in further you have to be pretty dense
Title: Re: VCE Further Maths Question Thread!
Post by: Andy Falkiner on October 11, 2016, 11:54:55 am
If you don't get a 50 in further you have to be pretty dense

I got 45 last year and nearly killed myself
Title: Re: VCE Further Maths Question Thread!
Post by: MattJackman on October 11, 2016, 12:02:00 pm
So True andy i was really upset with my score too  :'( :'(
Title: Re: VCE Further Maths Question Thread!
Post by: brenden on October 11, 2016, 12:33:07 pm
I got 45 last year and nearly killed myself
If you don't get a 50 in further you have to be pretty dense
So True andy i was really upset with my score too  :'( :'(
Given that two of you registered like an hour ago and the three of you have been making stupid posts on this thread and in this thread, I can only assume you thought it'd be a hilarious time to troll ATAR Notes etc etc. Fair enough, each to their own, right? But I'll tell you one time: stop being stupid or I'll just call your school and ask them to tell you the same.

Cheers boys. Study hard!
Title: Re: VCE Further Maths Question Thread!
Post by: Escobar on October 13, 2016, 08:46:20 pm
does anyone know how to do this?
http://i.imgur.com/ADjS053.jpg
Title: Re: VCE Further Maths Question Thread!
Post by: Maths Forever on October 13, 2016, 09:11:31 pm
does anyone know how to do this?
http://i.imgur.com/ADjS053.jpg

I would say the answer is D: 11 206.

The question asks for the predicted minimum number of penguins over the quarters 16, 17, 18, 19 and 20 (since this is the next 5 quarters).

We first must work out the deseasonalised figures for these quarters using the trend line.

Quarter 16: [4.5 + 0.73 (16)] x 1000 = 16 180
Quarter 17: [4.5 + 0.73 (17)] x 1000 = 16 910
Quarter 18: [4.5 + 0.73 (18)] x 1000 = 17 640
Quarter 19: [4.5 + 0.73 (19)] x 1000 = 18 370
Quarter 20: [4.5 + 0.73 (19)] x 1000 = 19 100

Now, using the formula, Actual Figure = Deseasonalised Figure x Seasonal Index, we can compute the actual predicted values for these quarters.

Quarter 16: 16 180 x 1.30 = 21 034
Quarter 17: 16 910 x 1.20 = 20 292
Quarter 18: 17 640 x 0.89 = 15 699.6
Quarter 19: 18 370 x 0.61 = 11 205.7
Quarter 20: 19 100 x 1.30 = 24 830

We recognise that quarter 19 has the minimum predicted value, and if we round up we find that the predicted value is 11 206. Hence, the answer is D!









Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 13, 2016, 09:39:00 pm
Hi everyone,

If a question in the Financial and Recursion module asks how many months will it take to fully repay the loan and the answer is 18.25, for example, do I round this up to 19 months (even if it says round to the nearest whole number)?

It makes sense for this to be the case as a loan can't be fully paid in those 18 months.

Thanks!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: KDB on October 14, 2016, 05:07:05 pm
Hi everyone,

If a question in the Financial and Recursion module asks how many months will it take to fully repay the loan and the answer is 18.25, for example, do I round this up to 19 months (even if it says round to the nearest whole number)?

It makes sense for this to be the case as a loan can't be fully paid in those 18 months.

Thanks!  :)

Yes, you would round up to 19 months. Only in this case because you can't pay the full amount in 18 months, as there would still be a balance remaining.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 14, 2016, 05:32:29 pm
Hi Everyone,

How do you know if three mean smoothing is more appropriate than four mean smoothing from a table of data?

Also, is study score a continuous or discrete data value?
Title: Re: VCE Further Maths Question Thread!
Post by: KDB on October 14, 2016, 08:47:56 pm
Hi Everyone,

How do you know if three mean smoothing is more appropriate than four mean smoothing from a table of data?

Also, is study score a continuous or discrete data value?

Three mean smoothing is usually more appropriate because it gets rid of less of the data. So if there are not many data points then three mean smoothing should be more appropriate. I think if there is lots of data then four mean smoothing would be more effective.
But yeah, if theres less amount of data, you dont want to get rid of more.

I'd say a study score is a discrete value, but then again, taking scaling into account, it seems continuous because you can have scores of like 47.2 etc. But to be safe id say test results/scores are discrete values.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 20, 2016, 12:26:13 pm
Hey guys,

Can someone help me with this question? the answer is B
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 20, 2016, 01:46:41 pm
Hey guys,

Can someone help me with this question? the answer is B

Hi Moaning Myrtle,

Anyone please correct me if I'm wrong, but I believe this question relates to the old study design. Effective interest is still examinable in the current one, but it's applied differently from the previous Business Maths module.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 20, 2016, 04:53:59 pm
Hi Moaning Myrtle,

Anyone please correct me if I'm wrong, but I believe this question relates to the old study design. Effective interest is still examinable in the current one, but it's applied differently from the previous Business Maths module.
Yeah, I had a feeling it might've been. Thanks for the help.

Also, are annuities and perpetuities a 'type' of interest-only loan?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 20, 2016, 06:29:00 pm
Yeah, I had a feeling it might've been. Thanks for the help.

Also, are annuities and perpetuities a 'type' of interest-only loan?

Out of curiosity, where did the question come from?

Not exactly.

A perpetuity is where you invest a sum of money and receive a fixed sum of money periodically (ie. every month). The money that you receive is the interest that the investment is generating. In this way, a perpetuity is a type of annuity!

An interest only loan is where you periodically pay back the amount of interest the loan is generating. That is, you aren't paying off any of the principal, just the interest that the loan is accumulating.

In this way, the formula for perpetuities and interest only loans is exactly the same. The only difference is that with a perpetuity you are receiving the payment (which is the interest from your investment) and an interest-only loan you are paying the payment (which is the interest accumulating from your loan).

Just to be clear, an annuity is an investment that earns compound interest and from
which regular payments are made (ie. a perpetuity minus the regular payments).


Wow! A lot to take in. If this isn't clear, please ask me to rephrase it!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 22, 2016, 10:08:06 am
Hi,

Does anyone know the real difference between saying that a time series plot is irregular or has no trend at all? Also, what is a secular trend?

Another question I have is the attached finance one. Could someone please help. 

Thanks!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 22, 2016, 10:59:14 am
How would you go about this question?

Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 22, 2016, 11:43:48 am
How would you go about this question?

Hi,

I have written out some solutions. I'm not sure if it makes sense. But in any case the answer is 2 which is C.
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 22, 2016, 02:45:21 pm
Hi,

I have written out some solutions. I'm not sure if it makes sense. But in any case the answer is 2 which is C.


TYSM!! :)
Title: Re: VCE Further Maths Question Thread!
Post by: AhNeon on October 22, 2016, 03:04:01 pm
If you apply a transformation to a variable, let's say 1/y=3.73+3.1456x, and the question asks 'what is the dependent/response variable', would you say y, or 1/y
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 22, 2016, 03:15:28 pm
If you apply a transformation to a variable, let's say 1/y=3.73+3.1456x, and the question asks 'what is the dependent/response variable', would you say y, or 1/y

I havent read anything that confirms it directly, but I was doing a trial in which I was given an equation with a transformed variable.
The question was asking for the r^2 sentence, and the answer had the variable written in the transformed state eg. Log(death rate).
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 22, 2016, 04:15:56 pm
I havent read anything that confirms it directly, but I was doing a trial in which I was given an equation with a transformed variable.
The question was asking for the r^2 sentence, and the answer had the variable written in the transformed state eg. Log(death rate).

Yes, I would also agree that it needs to be given in its transformed state.
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 23, 2016, 09:47:54 am
Can someone kindly help me with this? :)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 23, 2016, 09:54:48 am
Can someone kindly help me with this? :)

Hey,

Would it just be 1.53/9= 170g?

Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 23, 2016, 10:11:04 am
Hey,

Would it just be 1.53/9= 170g?



OMG, im such an idiot. I read it as 'mean weight instead of total weight'.
Regardless, I love you clarke legit. Always answering my questions <3
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 23, 2016, 10:11:51 am
OMG, im such an idiot. I read it as 'mean weight instead of total weight'.
Regardless, I love you clarke legit. Always answering my questions <3

Haha that's fine. I always do the same thing when reading questions.

I must work on this before exams!  :P
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 23, 2016, 05:42:00 pm
?

Moderator warning: Please contribute more to your posts in the future.
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 23, 2016, 06:20:13 pm
?

Moderator warning: Please contribute more to your posts in the future.

Hey,

I'm 95% sure that this is from the old study design. Someone correct me if I am wrong, however.
Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 23, 2016, 06:50:42 pm
Hey everyone! Is it worth doing the NEAP Trial Exam for 2016? I started on Exam 1 and I'm finding it really hard. Not sure if I'm just getting dumber or NEAP is just generally hard, hahah
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 23, 2016, 06:50:46 pm

Hey,

I'm 95% sure that this is from the old study design. Someone correct me if I am wrong, however.
Hey anything with deposits involved is from the old study design yeah?
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on October 23, 2016, 07:30:14 pm
?

Moderator warning: Please contribute more to your posts in the future.
Others say this is on the old study design but I'll take a crack anyway. $3000 deposit means we have already paid $3000. Therefore we must pay $12000 off the loan.

36 monthly payments = 12 payments per year over 3 years

If we pay $400 monthly, that is $4800 per year. If we are paying off a $12000 loan over three years that can equate to paying $4000 off the principal each year.

Therefore, if we pay $4800 each year, but only paying off $4000 off the principle, we are paying $800 interest. 800/4000 = 0.2. Therefore, the annual interest rate is 20%.

E.

Not a great explanation, let me know if I am incorrect  :) Hope that helps!
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 24, 2016, 04:27:27 pm
Out of curiosity, where did the question come from?

It was from an MAV paper, I think it was 2015 but don't take my word for it

Hi,

Does anyone know the real difference between saying that a time series plot is irregular or has no trend at all? Also, what is a secular trend?

Another question I have is the attached finance one. Could someone please help. 

Thanks!  :)

Hmm, I think the plot can't not have a trend. If there is no visible trend it has to be irregular.
Someone pls confirm, I'm just hypothesising.

Also, Clarke54321, what's the answer for the finance question you attached?
Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 24, 2016, 05:18:15 pm
Do you guys think VCAA will make this year's exam hard?
Title: Re: VCE Further Maths Question Thread!
Post by: Drewballs on October 24, 2016, 05:19:45 pm
I reckon it will be easy, with the new study design they need to "test the waters" to see how students respond to questions
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 24, 2016, 06:37:08 pm
If you lose 3-4 marks in total over both exams, can you get a 45?
Title: Re: VCE Further Maths Question Thread!
Post by: Vaike on October 24, 2016, 06:46:16 pm
If you lose 3-4 marks in total over both exams, can you get a 45?

As long as your sac marks are up to scratch that sounds plausible.
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on October 24, 2016, 06:50:56 pm
If you lose 3-4 marks in total over both exams, can you get a 45?
Yeah, but go in with the mindset you won't lose any!  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 24, 2016, 09:00:43 pm

Also, Clarke54321, what's the answer for the finance question you attached?

Hey, the answer is A. However, my teacher put a question mark next to it.

I've got a strong feeling that this too is out of the study design.
Title: Re: VCE Further Maths Question Thread!
Post by: ccdes0001 on October 25, 2016, 04:05:09 pm
I was just wondering if its worth it to go through the number pattern module from the old exams
thanks
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 25, 2016, 04:11:05 pm
(http://uploads.tapatalk-cdn.com/20161024/9ec3e03145d2f9719993693568904170.jpg)
Hey guys, can someone pls explain part B. I did it but my answer is differing quite a bit from the solutions itute provided.
Spoiler
(http://uploads.tapatalk-cdn.com/20161024/845a8f9b135bb621f1dbc5584bcc549a.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 25, 2016, 04:25:28 pm
(http://uploads.tapatalk-cdn.com/20161024/9ec3e03145d2f9719993693568904170.jpg)
Hey guys, can someone pls explain part B. I did it but my answer is differing quite a bit from the solutions itute provided.
Spoiler
(http://uploads.tapatalk-cdn.com/20161024/845a8f9b135bb621f1dbc5584bcc549a.jpg)

Hey,

Itute are wrong!!! I had this same problem, but their solutions to this question are wrong except the first part. 
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 25, 2016, 04:32:04 pm

Hey,

Itute are wrong!!! I had this same problem, but their solutions to this question are wrong except the first part.

Omg, thank god!!! I was so worried bc my answers were completely off.

Was your answer for the part b i $802.48?
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 25, 2016, 10:11:27 pm
Omg, thank god!!! I was so worried bc my answers were completely off.

Was your answer for the part b i $802.48?

I think my answer was $802.47 instead of .48. I might have just rounded wrongly!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 25, 2016, 11:19:52 pm

I think my answer was $802.47 instead of .48. I might have just rounded wrongly!  :)
My teacher was telling us that bc it says minimum u would have to round up to .48?? Does that make sense?

Also, what was your answer for part c? I got 802.53
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 26, 2016, 06:51:57 pm

My teacher was telling us that bc it says minimum u would have to round up to .48?? Does that make sense?

Also, what was your answer for part c? I got 802.53

Bump!!
anyone else want to share their replies for part b and c? I need to confirm if what I did is right
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on October 27, 2016, 09:30:58 am
For Exam 2 (V3), Q4 in Section A I got y=7.72664+7.70152x but according to iTutes it's 7700+7700. Does anyone know where I might have gone wrong?
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 09:33:26 am

For Exam 2 (V3), Q4 in Section A I got y=7.72664+7.70152x but according to iTutes it's 7700+7700. Does anyone know where I might have gone wrong?
Is this from the sample exam? Can you attach your question so we can see what you're talking about?
Also apparently itute's solutions are wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: KDB on October 27, 2016, 09:34:29 am
For Exam 2 (V3), Q4 in Section A I got y=7.72664+7.70152x but according to iTutes it's 7700+7700. Does anyone know where I might have gone wrong?

Yes the equation should be y=7.7+7.7x, itute's answers are wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on October 27, 2016, 09:49:12 am
Is this from the sample exam? Can you attach your question so we can see what you're talking about?
Also apparently itute's solutions are wrong.
Attached below :)

Yes the equation should be y=7.7+7.7x, itute's answers are wrong.
Ok, I just asked my teacher and apparently I need to multiply it by 100?

Also, for the following question I get 7700+7700log(90)=22747.7 but according to iTutes it's 23000. Am I wrong?
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 10:02:53 am

Attached below :)
Ok, I just asked my teacher and apparently I need to multiply it by 100?

Also, for the following question I get 7700+7700log(90)=22747.7 but according to iTutes it's 23000. Am I wrong?
Your answer is right, I don't think you need to multiply it by 100. Itute's soloutions are wrong!!! I think this question was previously in the 2012 or 2014 paper, so if u go there u can see that 7.7 is the right answer
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on October 27, 2016, 10:11:46 am
Your answer is right, I don't think you need to multiply it by 100. Itute's soloutions are wrong!!! I think this question was previously in the 2012 or 2014 paper, so if u go there u can see that 7.7 is the right answer

Thank you :)
Title: Re: VCE Further Maths Question Thread!
Post by: YellowTongue on October 27, 2016, 11:00:06 am
Would the variable 'roadworthiness' (i.e. either roadworthy or unroadworthy) be classed as nominal or ordinal data?

Thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 11:19:12 am

Would the variable 'roadworthiness' (i.e. either roadworthy or unroadworthy) be classed as nominal or ordinal data?

Thanks  :)
Nominal, don't think it can be ordered
Title: Re: VCE Further Maths Question Thread!
Post by: powergab on October 27, 2016, 11:50:36 am
Hi!

With the financial solver do you always round? So if you get a future value that you have to put in the present value box do you use the whole number or the rounded number?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: KDB on October 27, 2016, 12:02:59 pm
Hi!

With the financial solver do you always round? So if you get a future value that you have to put in the present value box do you use the whole number or the rounded number?

Thanks


Use exact values, only round for the final answer - and to however many decimal places that it says.
Title: Re: VCE Further Maths Question Thread!
Post by: sinatra on October 27, 2016, 12:16:20 pm
Hello everybody!
If I am hoping for a 35 study score, roughly what mark out of the 40 should I be aiming for on the exam 1?
Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Chow12 on October 27, 2016, 12:22:02 pm
The seasonal index for heaters in winter is 1.25 to correct for seasonality, the actual heater sales in winter should be? A) reduced by 20% B)increased by 20% C) reduced by 25% D) increased by 25% E) reduced by 75%
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 12:25:34 pm

The seasonal index for heaters in winter is 1.25 to correct for seasonality, the actual heater sales in winter should be? A) reduced by 20% B)increased by 20% C) reduced by 25% D) increased by 25% E) reduced by 75%
Do 1/1.25= 0.8
Meaning it is reduced by 20% so A is the answer
Title: Re: VCE Further Maths Question Thread!
Post by: powergab on October 27, 2016, 12:53:56 pm

Use exact values, only round for the final answer - and to however many decimal places that it says.

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 27, 2016, 03:40:39 pm
Is it true we have to use pen on the exam 2?
Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 27, 2016, 03:41:51 pm
Is it true we have to use pen on the exam 2?

Yes, your answers will show up more clearly when your exam is scanned and marked
Title: Re: VCE Further Maths Question Thread!
Post by: clarke54321 on October 27, 2016, 03:44:33 pm
Is it true we have to use pen on the exam 2?

I know people who just used really dark pencil, which also worked.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 03:58:03 pm
Interest earned is just FV - PV yeah??
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 27, 2016, 04:02:18 pm
In regards to rounding again, im so confused on what to do?!?
Our teacher sent us this from VCAA: "In general, only unrounded answers should be used for subsequent calculations. However, rounded answers should be used in financial modelling if this answer represents a physically payable amount. Dollar values can only be ‘paid’ if they are at most 2 decimal places. If a financial solver returns, for example, a repayment amount of $156.7643256 then this must be rounded to $156.76 for any future calculations using the solver. This is different to calculations in other areas, for example, geometry where it is appropriate to use multiple decimal places for calculated quantities that are used in future calculations."
So do we round or not in financial calculator when taking fv to pv for another calculation?
Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 27, 2016, 04:06:26 pm
In regards to rounding again, im so confused on what to do?!?
Our teacher sent us this from VCAA: "In general, only unrounded answers should be used for subsequent calculations. However, rounded answers should be used in financial modelling if this answer represents a physically payable amount. Dollar values can only be ‘paid’ if they are at most 2 decimal places. If a financial solver returns, for example, a repayment amount of $156.7643256 then this must be rounded to $156.76 for any future calculations using the solver. This is different to calculations in other areas, for example, geometry where it is appropriate to use multiple decimal places for calculated quantities that are used in future calculations."
So do we round or not in financial calculator when taking fv to pv for another calculation?

I would say we round it first before doing any another calculation, but I'm not entirely sure
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on October 27, 2016, 05:19:21 pm
The seasonal index for heaters in winter is 1.25 to correct for seasonality, the actual heater sales in winter should be? A) reduced by 20% B)increased by 20% C) reduced by 25% D) increased by 25% E) reduced by 75%
The way I do it is, you need to reduce 1.25 to 1... So you need to decrease it by 0.25. 0.25/1.25 = 20%, therefore A, reduce by 20%.  :)

Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 05:20:58 pm

In regards to rounding again, im so confused on what to do?!?
Our teacher sent us this from VCAA: "In general, only unrounded answers should be used for subsequent calculations. However, rounded answers should be used in financial modelling if this answer represents a physically payable amount. Dollar values can only be ‘paid’ if they are at most 2 decimal places. If a financial solver returns, for example, a repayment amount of $156.7643256 then this must be rounded to $156.76 for any future calculations using the solver. This is different to calculations in other areas, for example, geometry where it is appropriate to use multiple decimal places for calculated quantities that are used in future calculations."
So do we round or not in financial calculator when taking fv to pv for another calculation?
Hey I kind of get what vcaa is saying. For eg if u had a payment of -43.26738 then ur fv would be 0. But to find the extra payment that u need to pay, u need to make ur Payment -43.27 to find the amt of money left. Bc it'll be a tiny number the decimal places make a huge difference.
Title: Re: VCE Further Maths Question Thread!
Post by: KDB on October 27, 2016, 06:07:54 pm

Can anybody please detail their explanation to this question!

Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 27, 2016, 06:16:57 pm
Can anybody please detail their explanation to this question!

Thanks.
Working's attached. Really you just need to repeat pythagoras' theorem a few times, but there might be a faster way that I neglected.
Title: Re: VCE Further Maths Question Thread!
Post by: KDB on October 27, 2016, 06:25:17 pm
Working's attached. Really you just need to repeat pythagoras' theorem a few times, but there might be a faster way that I neglected.

Thanks so much  :)
Title: Re: VCE Further Maths Question Thread!
Post by: blossum on October 27, 2016, 07:29:19 pm
Hiya! If anyone could give me guidance on this question regarding one and two step dominance matrices, I'll repay you with a giant watermelon :']
Click here for the question
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 27, 2016, 07:46:19 pm
Hiya! If anyone could give me guidance on this question regarding one and two step dominance matrices, I'll repay you with a giant watermelon :']
Click here for the question

Leanne has 1 two-step dominance, which implies that the person he dominates has 1 one-step dominance, which can only be Neil. Thus Leanne dominates Neil.

Ken has 2 one-step dominances and also 2 two-step dominances, which means that the two people he dominates each have 1 one-step dominance, which can only be Leanne and Neil. Thus Ken dominates Leanne and Neil.

Neil has 1 one-step dominance and 2 two-step dominances, which means he dominates either Ken or Maggy. We already established that Ken dominates Neil, thus Neil can only dominate Maggy.

Maggy has 2 one-step dominances and 3 two-step dominances, which means that one of the people he dominates has 1 one-step dominance and the other person that he dominates has 2 one-step dominances. We already established that Neil dominates Maggy so that means the only other person who has 1 one-step dominance that can be dominated is Leanne. And obviously the other person who has 2 one-step dominances is Ken. Thus, Maggy dominates Ken and Leanne.

Ok that sounds really confusing but it's much simpler when you actually think it through. Hope I helped.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 07:58:52 pm
Hiya! If anyone could give me guidance on this question regarding one and two step dominance matrices, I'll repay you with a giant watermelon :']
Click here for the question
(http://uploads.tapatalk-cdn.com/20161027/e5c18527c9bb730faae95524fdbd8bac.jpg)
Thanks for the above reply! I don't really understand it though
I tried doing it the trial and error way and it took approx 4 mins :/
Rip me tmr... :(
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 27, 2016, 09:35:51 pm
For this question attached i got the answer C, but answers say B who is correct ?
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 27, 2016, 09:37:58 pm
For this question attached i got the answer E, but answers say D who is correct ?
Title: Re: VCE Further Maths Question Thread!
Post by: Coffee on October 27, 2016, 09:38:30 pm
Could someone please help me out with the attached questions? I'm not sure what formulas I'm supposed to be using :-\

Thanks, guys!

Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 09:42:42 pm
For this question attached i got the answer C, but answers say B who is correct ?
Hmm for this don't you have to add your payment value to the 'extra value' and that will be ur final payment?
But if the question is asking for the 'extra payment' then I think C is correct

For this question attached i got the answer E, but answers say D who is correct ?
For this one, I think you are right. The Answers must be wrong

Could someone please help me out with the attached questions? I'm not sure what formulas I'm supposed to be using :-\

Thanks, guys!
The answer for 7d is to be done separately. So it says after 2years. First find out what the flat rate depreciation would be (you already did this in part a). Your answer is $6000. So, it's saying that the value MUST be the same, meaning that the value has to be 6000. So just plop this in ur cas solve(6000=8400-0.25n,n) n will equal 9600. Meaning when the bike has travelled 9600 km, it's value will be the same as flat rate depreciation after 2 years.
Title: Re: VCE Further Maths Question Thread!
Post by: AhNeon on October 27, 2016, 09:48:04 pm
How would you guys approach 2010 MC question 3
It basically asks for the standard deviation when it gives iqr and a boxplot
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 09:58:02 pm

How would you guys approach 2010 MC question 3
It basically asks for the standard deviation when it gives iqr and a boxplot
If you look at the histogram it looks like a bell curve meaning the normal distribution rule can be used. Your mean is 180, and 180 keeps increasing or decreasing by 2. Hence 2 is ur standard deviation.
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 27, 2016, 10:12:28 pm
Hmm for this don't you have to add your payment value to the 'extra value' and that will be ur final payment?
But if the question is asking for the 'extra payment' then I think C is correct
For this one, I think you are right. The Answers must be wrong


Thanks moaning myrtle  :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 27, 2016, 10:34:06 pm
For this question the answer should be C) 40km right ? not what the answers have (D)
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 27, 2016, 10:37:54 pm
For this question the answer should be C) 40km right ? not what the answers have (D)

Yeah it should be 40km, D! :)
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 10:38:08 pm

For this question the answer should be C) 40km right ? not what the answers have (D)
Yup the answer should be c. It must be a typo from the solutions
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 27, 2016, 10:39:19 pm
For this question attached i got the answer C, but answers say B who is correct ?

I got B.
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 27, 2016, 10:42:47 pm
Yeah it should be 40km, D! :)

Yup the answer should be c. It must be a typo from the solutions

Thanks for confirming  :) cant believe these exams have these many errors !!!( thank god for you guys  ;) :))

Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 10:44:33 pm
Thanks for confirming  :) cant believe these exams have these many errors !!!( thank god for you guys  ;) :))
AHahahh, most company exams have many mistakes

I got B.
Really? Can you pls post your explanation for B?
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 27, 2016, 10:49:18 pm
AHahahh, most company exams have many mistakes
Really? Can you pls post your explanation for B?

Using finance solver:

N: 35

I%: 3.85

PV: 42000

Pmt: -1260

FV: -760.18

PPY/CPY: 12/12

The person still needs to pay the bank $760.18
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 27, 2016, 10:55:22 pm

Using finance solver:

N: 35

I%: 3.85

PV: 42000

Pmt: -1260

FV: -760.18

PPY/CPY: 12/12

The person still needs to pay the bank $760.18
Omg I feel so stupid now. I think my fingers became a bit too excited bc I swear I remember putting the same values in :/
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 27, 2016, 11:01:50 pm
Omg I feel so stupid now. I think my fingers became a bit too excited bc I swear I remember putting the same values in :/

hahahahahaha
do you reckon the vcaa exam will be relatively easy. im kinda scared now, i cant afford to drop any marks
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 28, 2016, 12:25:24 am
Hey Again,

This question... how do you do it? Apparently the answer is E according to VCAA.  :(
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 28, 2016, 12:45:27 am
Hey Again,

This question... how do you do it? Apparently the answer is E according to VCAA.  :(
Because the order is 3 * 2, C is out. The i and j are 'coordinates' of the matrix, so we can eliminate another two be checking the first element of the matrix, where (i,j) -> (1,1). Adding the i and j components like given in the rule gives us '2', which means A and D are not the correct answer. Comparing the remaining B and E, the first element that differs is at (2,1), which means the value should be 3, Eliminating B. The only option left to choose is E. :)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 28, 2016, 02:44:09 am
For this question attached and solution.

shouldnt sum of frequencies = 2+4+6+3+11+5+3+3=37

=> (31/37) x 100=83.78 %

How did solutions get sum of frequency as 34?
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 28, 2016, 03:10:33 am
How do u do this whole question...it's on 2016 vcaa sample exam?
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 28, 2016, 05:55:28 am
For this question attached and solution.

shouldnt sum of frequencies = 2+4+6+3+11+5+3+3=37

=> (31/37) x 100=83.78 %

How did solutions get sum of frequency as 34?
You added in an extra 3 at the end

hahahahahaha
do you reckon the vcaa exam will be relatively easy. im kinda scared now, i cant afford to drop any marks
I think the exam will be easy bc it's the first year of a new SD, but I'm not sure. I'm just going to go with my gut feeling in the exam


How do u do this whole question...it's on 2016 vcaa sample exam?
Click this link, most of the answers are there
VCAA Sample Exam? http://atarnotes.com/forum/index.php?topic=166015
Title: Re: VCE Further Maths Question Thread!
Post by: YellowTongue on October 28, 2016, 07:31:42 am
How do you find the difference between two locations of different lattitude and longitude?
Title: Re: VCE Further Maths Question Thread!
Post by: TooLazy on October 28, 2016, 10:12:11 am
If i lose 1 mark on this exam, and 3-4 on the next one, what study score would i be expecting
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 28, 2016, 10:17:15 am
If i lose 1 mark on this exam, and 3-4 on the next one, what study score would i be expecting

A good one!  :D  You can never know for sure because there are so many variables that take a role, however you are in a pretty sweet spot if you only drop 5 overall.
Title: Re: VCE Further Maths Question Thread!
Post by: blossum on October 28, 2016, 10:21:37 am
Hihi
Financial question here, would like the steps involved ^^

NEAP 2016 Exam 1
Q24
A loan is taken where there are no repayments until the end of the 5-year period.
How much extra interest is charged when the compounding period is changed from monthly to daily on a loan of $25,000 at 5%pa?
(A is 96.88)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 28, 2016, 10:28:18 am
What marks did people get for the 2016 sample exam 1 and what did you think of the difficulty ?
Title: Re: VCE Further Maths Question Thread!
Post by: YellowTongue on October 28, 2016, 10:40:27 am
Hihi
Financial question here, would like the steps involved ^^

NEAP 2016 Exam 1
Q24
A loan is taken where there are no repayments until the end of the 5-year period.
How much extra interest is charged when the compounding period is changed from monthly to daily on a loan of $25,000 at 5%pa?
(A is 96.88)

The answer is supposed to be $16.12 (according to my teacher).

Hopefully that is what you are getting. Otherwise I can write up the solution for you  :).
Title: Re: VCE Further Maths Question Thread!
Post by: blossum on October 28, 2016, 10:46:09 am
The answer is supposed to be $16.12 (according to my teacher).

Hopefully that is what you are getting. Otherwise I can write up the solution for you  :).
Yeah got it! Thank you c:

'Nother question though:
What's the difference between confounding and coincidence correlation? An example would be nice too (http://i.imgur.com/V3d9HPx.gif)
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 28, 2016, 10:51:57 am
Yeah got it! Thank you c:

'Nother question though:
What's the difference between confounding and coincidence correlation? An example would be nice too (http://i.imgur.com/V3d9HPx.gif)
An example of confounding V
(http://uploads.tapatalk-cdn.com/20161027/6d9d16cddfe0ab3ccf4021c3b3dccbd3.jpg)
And coincidence is just coincidence. I remember there was an example in the book about people that like cheese usually gettin divorced. But does liking cheese cause getting divorced? Nope, it's purely coincidental!
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 28, 2016, 10:55:35 am
An example of confounding V
(http://uploads.tapatalk-cdn.com/20161027/6d9d16cddfe0ab3ccf4021c3b3dccbd3.jpg)
And coincidence is just coincidence. I remember there was an example in the book about people that like cheese usually gettin divorced. But does liking cheese cause getting divorced? Nope, it's purely coincidental!

Wait is that a part of the course? Haven't seen it in past VCAA exams. :S
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 28, 2016, 11:00:05 am
Wait is that a part of the course? Haven't seen it in past VCAA exams. :S

It's in the study design but isn't a strong measure for testing students so hasn't been used much in any exams. My assumption.
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 28, 2016, 04:37:37 pm
How do you do question 2 core? I got B .........
Title: Re: VCE Further Maths Question Thread!
Post by: jazzaa36 on October 28, 2016, 05:02:02 pm
Got B aswell   8)
Title: Re: VCE Further Maths Question Thread!
Post by: ringring on October 28, 2016, 05:03:13 pm
i got D it seems like an equal amount of people got either D or B..
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 28, 2016, 05:09:30 pm
i got D it seems like an equal amount of people got either D or B..
Yeh  I got D as well initially then looked in my cambridge essentials textbook and saw this    :o     

what do you peeps think?
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 28, 2016, 05:12:49 pm
like question 5d its pretty similar to question 2  on exam?
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 28, 2016, 05:13:46 pm

Yeh  I got D as well initially then looked in my cambridge essentials textbook and saw this    :o     

what do you peeps think?
Post this in the further exam discussion thread. It'll prove useful to a lot of people as this question stumped many
Title: Re: VCE Further Maths Question Thread!
Post by: Sheri54371 on October 28, 2016, 05:25:48 pm
Where can I find the further exam discussion thread?
Title: Re: VCE Further Maths Question Thread!
Post by: Sheri54371 on October 28, 2016, 05:26:30 pm
Where can I find the further exam discussion thread?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 28, 2016, 05:27:28 pm
Here. :)
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 28, 2016, 05:28:36 pm

Where can I find the further exam discussion thread?
Click on this link
Suggested Answers (and Discussion) of the Further Maths Exam! http://atarnotes.com/forum/index.php?topic=168376
Title: Re: VCE Further Maths Question Thread!
Post by: cimw6 on October 28, 2016, 05:53:41 pm
if I'm averaging 85-90% for further and make a total of 10 mistakes between exam 1 and 2, will I still be able to achieve a 40?
Title: Re: VCE Further Maths Question Thread!
Post by: minerva on October 28, 2016, 07:53:08 pm
I'm really disappointed .. I just found that I've made 4 wrong answers. I have an A average in SACs and assuming that I got an A on Exam 1, is it still possible for me to get a 40?
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on October 28, 2016, 08:26:17 pm
I'm really disappointed .. I just found that I've made 4 wrong answers. I have an A average in SACs and assuming that I got an A on Exam 1, is it still possible for me to get a 40?
Yes
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 29, 2016, 12:14:32 pm
(http://uploads.tapatalk-cdn.com/20161028/5d76f23d0e4397effc2a229195eaec87.jpg)
Guys is the inequation for part b x> (or equal to) 2y   ??
Title: Re: VCE Further Maths Question Thread!
Post by: samsung4545 on October 29, 2016, 12:23:30 pm
 :o whar study score should I expect to receive with the number 1 ranking for sacs (99/100) with exam 1 37-38/40?  Maybe a 59/60 for Exam 2
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 29, 2016, 12:33:21 pm
:o whar study score should I expect to receive with the number 1 ranking for sacs (99/100) with exam 1 37-38/40?  Maybe a 59/60 for Exam 2

Assuming http://studyscorecalc.com is correct, you sir, will be looking at about 47+
But there are loads of variables that can play a role in your result so don't be banking on anything, just do well and wait till December 12th (or whenever they're released ahah)
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 29, 2016, 12:34:50 pm
(http://uploads.tapatalk-cdn.com/20161028/5d76f23d0e4397effc2a229195eaec87.jpg)
Guys is the inequation for part b x> (or equal to) 2y   ??
Seems fine to me. :)
Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 29, 2016, 02:14:09 pm
How do you guys think we should study for exam 2? Just do more practice exams? Not really sure what else to do, I feel like I've done enough already  ::)
Title: Re: VCE Further Maths Question Thread!
Post by: staceyschh on October 29, 2016, 02:44:27 pm
How do you guys think we should study for exam 2? Just do more practice exams? Not really sure what else to do, I feel like I've done enough already  ::)

Best advice I can give you (Which my teacher said to me yesterday)

Do practise exams. But also, go through the study design. Check off the dot points that were addressed in Exam 1. Whatever wasn't in exam 1, is more than likely to be in exam 2.

these are my predictions (stats) for exam 2 based on yesterday:


DATA ANALYSIS

- Describing the shapes of graphs
- Interpereting box plots
- IQR/Range
- Outliers- fence equations i.e- Q3 x (1.5 x IQR)
- Comparing data sets
- Back to back stem plots
- Explanatory/Response Variables
- R and R^2 will definately be on it
- Least squares reg
- Time series
- Trend lines
- Interpolation/Extrapolation
- Causation/Correlation
- Smoothing data
- Calulating the mean
- Z scores ( was touched on but not greatly )
- Interpereting bivariate data
- Interpereting a least squares regression equation:

Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 29, 2016, 03:18:52 pm
Thank you so much staceyschh!

Can someone please help me with this from the study design:
-cause and effect; the difference between observation and experimentation when collecting data and the need for experimentation to definitively determine cause and effect
-non-causal explanations for an observed association including common response, confounding, and coincidence; discussion and communication of these explanations in a particular situation in a systematic and concise manner.

My textbook doesn't really explain this
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 29, 2016, 04:20:09 pm
I was wondering for the first question I attached, my teacher says you round to 19 but others say round to 18 payments as it is the 'nearest whole number', unlike 19. Please help!!!
Title: Re: VCE Further Maths Question Thread!
Post by: Aurora22 on October 29, 2016, 04:40:54 pm
I don't see why the Further kids have to miss out on their own question thread! Post anything you're stuck with here and we'll try our best to help you out.

It might be a good idea to sticky this thread, just like the Methods and Specialist ones.

I need help with crashing in NETWORKS, my teacher doesnt know it and i dont either.
Title: Re: VCE Further Maths Question Thread!
Post by: staceyschh on October 29, 2016, 05:37:08 pm
I was wondering for the first question I attached, my teacher says you round to 19 but others say round to 18 payments as it is the 'nearest whole number', unlike 19. Please help!!!

Put it in your finance solver, after 18 payments there still is x amount of dollars/cents remaining on the balance. You need to round up when it comes to looking for number of payments until the fv value is actually 0 on the dot.

You could have 10 payments of $100 and then the 11th payment only be $3.50 paying off whats left. Does that make sense?
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 29, 2016, 08:10:19 pm
I need help with crashing in NETWORKS, my teacher doesnt know it and i dont either.

Crashing is just reducing the duration of an activity. A question might be that that an activity is crashed by 2 hours and you have to find out what effect this has on the project completion time.
Title: Re: VCE Further Maths Question Thread!
Post by: masch on October 29, 2016, 08:16:21 pm
I was wondering for the first question I attached, my teacher says you round to 19 but others say round to 18 payments as it is the 'nearest whole number', unlike 19. Please help!!!


The question is flawed. The request to round down to the nearest whole number does not effectively answer the original question.
Title: Re: VCE Further Maths Question Thread!
Post by: Legemeton on October 29, 2016, 08:22:55 pm
quick question. On the VCE 2015 further written exam 2.
Can someone explain the question 3e on the networks module to me and how the answer is 33 minutes, 7 minutes increase?
I don't understand why you just won't just go to F and H again. and rather divert? It is because of the mention of least effect?

Cheers
Title: Re: VCE Further Maths Question Thread!
Post by: leetheastronaut on October 29, 2016, 08:32:42 pm
hey, can someone please help me with this question? I've attached a picture underneath

question: Find the shortest distance along the surface of the bowl between C and D where CD is the diameter of the water surface, to the nearest whole centimetre.
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 29, 2016, 09:02:29 pm
quick question. On the VCE 2015 further written exam 2.
Can someone explain the question 3e on the networks module to me and how the answer is 33 minutes, 7 minutes increase?
I don't understand why you just won't just go to F and H again. and rather divert? It is because of the mention of least effect?

Cheers

Write down the ESTs for each activity on your new network (with the dummy activity) and you'll find out that the completion time increases from 26 to 33. I was actually confused about that question too until I did that.
Title: Re: VCE Further Maths Question Thread!
Post by: Legemeton on October 29, 2016, 09:09:30 pm
Write down the ESTs for each activity on your new network (with the dummy activity) and you'll find out that the completion time increases from 26 to 33. I was actually confused about that question too until I did that.

Where would you place the dummy activity? my critical path remains to be 35
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 29, 2016, 09:28:26 pm
Does anyone have suggested solutions for the 2016 VCAA Sample Exam 2 (Short Answer) for further?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 29, 2016, 09:33:40 pm
hey, can someone please help me with this question? I've attached a picture underneath

question: Find the shortest distance along the surface of the bowl between C and D where CD is the diameter of the water surface, to the nearest whole centimetre.
Not 100% sure I'm correct, so let me know if it's wrong. ::)
Title: Re: VCE Further Maths Question Thread!
Post by: knightrider on October 29, 2016, 09:55:48 pm
For questions where we have to find recurrence relations.

if they dont tell you what to round to do we just write the exact value down when stating the rule ?( as in exact R value in rule Vn+1=RVn)

Thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 29, 2016, 09:55:58 pm
Hey, can someone please help me with this question from VCAA 2014 Exam 2 (Q3b from the business module): The cricket club had invested $45 550 in an account for four years. After four years of compounding interest, the value of the investment was $60 000.
Interest on the account had been calculated and paid quarterly.
b. What was the annual rate of interest for this investment?
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 29, 2016, 10:11:50 pm
Where would you place the dummy activity? my critical path remains to be 35

Oops I thought you were talking about a different question. So basically you want to finish B and D first because it takes a total of 12 minutes as opposed to A and C which takes a total of 13 minutes. Right after that you can do D (because we know C and D can't occur at the same time), then F and H and I as in the normal critical path. So you end up adding 3+9+8+6+3+4 which = 33. It's a difficult question and kind of hard to explain, sorry if I confuse you.

Hey, can someone please help me with this question from VCAA 2014 Exam 2 (Q3b from the business module): The cricket club had invested $45 550 in an account for four years. After four years of compounding interest, the value of the investment was $60 000.
Interest on the account had been calculated and paid quarterly.
b. What was the annual rate of interest for this investment?

Enter N=16, PV=45550, Pmt=0, FV=-60000, Ppy=Cpy=4 and you'll get annual interest rate to be 6.948, round to 6.9%.
Title: Re: VCE Further Maths Question Thread!
Post by: Legemeton on October 29, 2016, 10:21:41 pm
Oops I thought you were talking about a different question. So basically you want to finish B and D first because it takes a total of 12 minutes as opposed to A and C which takes a total of 13 minutes. Right after that you can do D (because we know C and D can't occur at the same time), then F and H and I as in the normal critical path. So you end up adding 3+9+8+6+3+4 which = 33. It's a difficult question and kind of hard to explain, sorry if I confuse you.

Enter N=16, PV=45550, Pmt=0, FV=-60000, Ppy=Cpy=4 and you'll get annual interest rate to be 6.948, round to 6.9%.

I understand it all but isn't it when finding the critical path you are looking for the longest path? then wouldn't you go A - C rather than B-D? when going B-D you would still have to do C. As it dose not specify with C or D must be done first
Title: Re: VCE Further Maths Question Thread!
Post by: QueenSmarty on October 29, 2016, 10:24:59 pm
Oops I thought you were talking about a different question. So basically you want to finish B and D first because it takes a total of 12 minutes as opposed to A and C which takes a total of 13 minutes. Right after that you can do D (because we know C and D can't occur at the same time), then F and H and I as in the normal critical path. So you end up adding 3+9+8+6+3+4 which = 33. It's a difficult question and kind of hard to explain, sorry if I confuse you.

Enter N=16, PV=45550, Pmt=0, FV=-60000, Ppy=Cpy=4 and you'll get annual interest rate to be 6.948, round to 6.9%.

Ah, can't believe it was that easy. Thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 29, 2016, 11:10:55 pm
Ah, can't believe it was that easy. Thank you!

No worries.

I understand it all but isn't it when finding the critical path you are looking for the longest path? then wouldn't you go A - C rather than B-D? when going B-D you would still have to do C. As it dose not specify with C or D must be done first

A critical path is usually the longest path because you can't complete the project without completing the longer duration activities first. But this isn't a typical critical path problem.

"when going B-D you would still have to do C" - that's why you do C right after completing B and D? If you do that you'll realise that all activities are able to be completed in 33 minutes hence it's the critical path (in this circumstance where C and D can't be completed at the same time).

It doesn't specify if you go with C or D first because you have to figure out which one will have the least impact on the minimum completion time. If you go with C first as you suggest, then the path would be A-C-D-F-H-I which is 5+8+9+6+3+4=35. Which is obviously more than 33.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 29, 2016, 11:16:24 pm
Can someone help me with this pls?
Title: Re: VCE Further Maths Question Thread!
Post by: Legemeton on October 29, 2016, 11:25:52 pm
No worries.

A critical path is usually the longest path because you can't complete the project without completing the longer duration activities first. But this isn't a typical critical path problem.

"when going B-D you would still have to do C" - that's why you do C right after completing B and D? If you do that you'll realise that all activities are able to be completed in 33 minutes hence it's the critical path (in this circumstance where C and D can't be completed at the same time).

It doesn't specify if you go with C or D first because you have to figure out which one will have the least impact on the minimum completion time. If you go with C first as you suggest, then the path would be A-C-D-F-H-I which is 5+8+9+6+3+4=35. Which is obviously more than 33.

cheers lad much thanks
Title: Re: VCE Further Maths Question Thread!
Post by: jazzaa36 on October 29, 2016, 11:52:15 pm
Alright I was at Tudor and my Tudor was talking about how someone forgot to shade in what module they were doing and they got zero that section . I JUST REALISED I TICKED THE BOX INSTEAD OF SHADING ( the area where it has 4 boxes and u choose your module) but I did write down what module it was in the box and it was ticked. Will I be penalised or am I just overreacting ???  :-X
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 30, 2016, 12:03:17 am
Can someone help me with this pls?

Not entirely sure if i'm on the ball but here goes:

Bank 1: $3585.04 per month for 20 years = $3585.04*240
= Total Payed = $860409.60
Total Payed - $500,000 = Interest Paid
Interest Paid = $360,409.60

Bank 2: $3585.04 per month for first 10 years = $3585.04*120
= total payed in 10 years = $430204.60 and keeping that in mind.

Using financial Solver:
N:120 (10 years)
I: 5%
PV: $500,000
PmT: $3585.04
FV: $266,811.57 Found because all other values are given to us. (Our new Present value after the 10 year mark)
PpY: 12
CpY: 12

Now with $266,811.57 left to pay for the remaining 10 years the financial solver is updated as follows:
N:120 (10 years)
I: 7%
PV: $266,811.57
PmT: $2409.34
FV: 0
PpY: 52
CpY: 52

Now as we already payed $430204.60 in the first 10 years, we now pay $2409.34 per month for the last 10 years, so:
$430204.60 + $2409.34 * 120 = Total Payed in 20 years
Total Payed in 20 years = $719.325.60
Total Payed - $500,000 = Interest Paid
Interest Paid = $219,325.60

Now using both banks' Interest Paid amounts:
Bank A (Interest paid): $360,409.60
Bank B (Interest paid): $219,325.60


Therefore, Bank B will incur the lower interest amount and is the recommended bank for Shannon  ;)

Also, if this question was just one mark, could we not just assume it is Bank B because shorter the compound, lesser the interest and duration of loan...

Either way correct me if I'm wrong guys. xx


Title: Re: VCE Further Maths Question Thread!
Post by: EdwinJS on October 30, 2016, 12:05:13 am
Alright I was at Tudor and my Tudor was talking about how someone forgot to shade in what module they were doing and they got zero that section . I JUST REALISED I TICKED THE BOX INSTEAD OF SHADING ( the area where it has 4 boxes and u choose your module) but I did write down what module it was in the box and it was ticked. Will I be penalised or am I just overreacting ???  :-X

Multiple Choice is all computerised so if it does not pickup that you shaded in the box it will give it an error and not sure what happens next - maybe goes into a pile with others that manually need to be checked with the written module and marked that way, I'm not too sure  ???.
Title: Re: VCE Further Maths Question Thread!
Post by: jazzaa36 on October 30, 2016, 12:11:01 am
Multiple Choice is all computerised so if it does not pickup that you shaded in the box it will give it an error and not sure what happens next - maybe goes into a pile with others that manually need to be checked with the written module and marked that way, I'm not too sure  ???.

Fkk shitting bricks now  :-\
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on October 30, 2016, 09:32:44 am
Fkk shitting bricks now  :-\
Speak to your VCE co-ordinator or equivalent at your school, the earlier the better. I'm sure you'll be fine.
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 30, 2016, 09:34:18 am
Can someone help me with this pls?

I got the same answer as EdwinJS (Bank B charges less interest) but I got a different amount for Bank B.

Got the same amount of interest of $360409.60 for Bank A.

For Bank B enter:
N:120 (10 years)
I: 5%
PV: -$500,000
PmT: $3585.04
FV: $266,811.57
PpY: 12
CpY: 12

I think EdwinJS is wrong in thinking that the loan payment changes or that it has to continue for another 10 years because it doesn't say that anywhere (in the brackets it says which loan will incur the least interest and time) Enter:

N: 78.47
I: 7%
PV: -$266,811.57
PmT: $3585.04
FV: 0
PpY: 52
CpY: 52

Add 78.47+120 to get total loan amount of 198.47 months. 198.47*3585.04 = $711537 total repayments for Bank B loan. 711537-500000 = $211537 interest incurred on Bank B loan.

So Bank A's loan incurs $360409.06 interest in 240 months. And Bank B's loan incurs $211537 interest in about 199 months.
Title: Re: VCE Further Maths Question Thread!
Post by: masch on October 30, 2016, 09:37:59 am
Alright I was at Tudor and my Tudor was talking about how someone forgot to shade in what module they were doing and they got zero that section . I JUST REALISED I TICKED THE BOX INSTEAD OF SHADING ( the area where it has 4 boxes and u choose your module) but I did write down what module it was in the box and it was ticked. Will I be penalised or am I just overreacting ???  :-X

My teacher told me that if the computer doesn't pick it up then it will be checked manually. The tick should be enough ...so just chill. It's all good  8)
Title: Re: VCE Further Maths Question Thread!
Post by: masch on October 30, 2016, 10:23:00 am
I got the same answer as EdwinJS (Bank B charges less interest) but I got a different amount for Bank B.

Got the same amount of interest of $360409.60 for Bank A.

For Bank B enter:
N:120 (10 years)
I: 5%
PV: -$500,000
PmT: $3585.04
FV: $266,811.57
PpY: 12
CpY: 12

I think EdwinJS is wrong in thinking that the loan payment changes or that it has to continue for another 10 years because it doesn't say that anywhere (in the brackets it says which loan will incur the least interest and time) Enter:

N: 78.47
I: 7%
PV: -$266,811.57
PmT: $3585.04
FV: 0
PpY: 52
CpY: 52

Add 78.47+120 to get total loan amount of 198.47 months. 198.47*3585.04 = $711537 total repayments for Bank B loan. 711537-500000 = $211537 interest incurred on Bank B loan.

So Bank A's loan incurs $360409.06 interest in 240 months. And Bank B's loan incurs $211537 interest in about 199 months.

I agree that you can't assume that the loan goes for another 10 years once the rate changes to 7% but I don't think you can assume that the payment will be 3585.04 per week. Is this guy loaded with money?...That's about $14000 payment per month. I'm not sure if this is realistic???
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 30, 2016, 11:10:28 am
I agree that you can't assume that the loan goes for another 10 years once the rate changes to 7% but I don't think you can assume that the payment will be 3585.04 per week. Is this guy loaded with money?...That's about $14000 payment per month. I'm not sure if this is realistic???

lol you're right. Instead of setting both the Ppy and Cpy to 52 just change Cpy to 52 and keep Ppy as 12 and you'll pay off the rest in 97.97 months. Then 97.97+120 = 217.974 months of repayments. Then 217.974*3585.04 = $781444 total repayments. Interest is 781444-500000 = $281444, which ends up taking less time and incurring less interest than Bank A's option.

Although I've never seen a question where you had to set the Cpy and Ppy to different values, I doubt they'll test this concept in the exam.
Title: Re: VCE Further Maths Question Thread!
Post by: ayesha2011t on October 30, 2016, 11:25:52 am

Can someone help me with this pls?
Thanks for the help guys!

The solutions provided -->(http://uploads.tapatalk-cdn.com/20161029/ce1ea6a256bddf5ab53d8ff75f008991.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 30, 2016, 11:55:53 am
Thanks for the help guys!

The solutions provided -->(http://uploads.tapatalk-cdn.com/20161029/ce1ea6a256bddf5ab53d8ff75f008991.jpg)

Wow such great solutions.  ::)

Just hope that this type of question doesn't appear in the exam.
Title: Re: VCE Further Maths Question Thread!
Post by: melissaromeo on October 30, 2016, 12:02:42 pm
Hi, can anyone link me to the answers of the sample exam 2 the short answer one thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: haxor4chan on October 30, 2016, 02:50:29 pm
Heyyy, was just wondering how to do the last question on this about final payment??? (forget about my working out i think its wrong)
Title: Re: VCE Further Maths Question Thread!
Post by: Rosella on October 30, 2016, 02:57:05 pm
Ive had a question in a MAV exam where its asking if the variable "age of graduates" (in years) is discrete or continuous. I thought it would be discrete as age in years can be counted, but the suggested answers say continuous. Whos right?
Title: Re: VCE Further Maths Question Thread!
Post by: ed33 on October 30, 2016, 03:44:49 pm
Hey, do we need to know average rate of inflation, GST and capital gain for tomorrow's exam or is it part of the old SD for financial? I have come across a few of these questions from past exams. Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Cornrow Kenny on October 30, 2016, 03:56:19 pm
Ive had a question in a MAV exam where its asking if the variable "age of graduates" (in years) is discrete or continuous. I thought it would be discrete as age in years can be counted, but the suggested answers say continuous. Whos right?
Age is continuous. Technically you are only say 18 years old for 1 second, after that you would be 18 and 1 second, 18 and 2 seconds etc, so your age is not "18" but 18.xyz etc

Hope that makes sense  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Jayz2398 on October 30, 2016, 04:06:02 pm
Not 100% sure I'm correct, so let me know if it's wrong. ::)

I tried working it out along the bottom of the 20cm radius bowl, and it ends up being a little bit shorter.

(http://uploads.tapatalk-cdn.com/20161029/f66dab4add111a643c52b8c75c8f831f.jpg)

EDIT: realised I didn't write 2cos-1(3/5) in my workings, but still calculated with it.
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on October 30, 2016, 04:07:03 pm
Ive had a question in a MAV exam where its asking if the variable "age of graduates" (in years) is discrete or continuous. I thought it would be discrete as age in years can be counted, but the suggested answers say continuous. Whos right?

I've just had a look at this question on the exam and I believe it to be continuous. It does not explicitly state "age in years". You cannot automatically make these assumptions unless it is explicitly stated in the question. Age could be any sort of value, such as 18 years old or 18 years and 6 months (which would be 18.5). Even though in most cases we as people really just round age down to the nearest whole number, we cannot ignore the fact these values actually exist.

Hey, do we need to know average rate of inflation, GST and capital gain for tomorrow's exam or is it part of the old SD for financial? I have come across a few of these questions from past exams. Thanks :)

I would say no, given these aren't mentioned in the revised study design for 2016. Here's the study design if you want to have a look further. Cover the points listed: http://www.vcaa.vic.edu.au/Documents/vce/mathematics/MathematicsSD-2016.pdf

I guess if you REALLY wanted to protect yourself, you could always include just the different formulas at the back of your bound notes.
Title: Re: VCE Further Maths Question Thread!
Post by: ed33 on October 30, 2016, 04:31:05 pm
I've just had a look at this question on the exam and I believe it to be continuous. It does not explicitly state "age in years". You cannot automatically make these assumptions unless it is explicitly stated in the question. Age could be any sort of value, such as 18 years old or 18 years and 6 months (which would be 18.5). Even though in most cases we as people really just round age down to the nearest whole number, we cannot ignore the fact these values actually exist.

I would say no, given these aren't mentioned in the revised study design for 2016. Here's the study design if you want to have a look further. Cover the points listed: http://www.vcaa.vic.edu.au/Documents/vce/mathematics/MathematicsSD-2016.pdf

I guess if you REALLY wanted to protect yourself, you could always include just the different formulas at the back of your bound notes.

Thanks for your help!
Title: Re: VCE Further Maths Question Thread!
Post by: blossum on October 30, 2016, 06:04:41 pm
Heyyy, was just wondering how to do the last question on this about final payment??? (forget about my working out i think its wrong)
Forgive me/correct me if I'm wrong! My brain's a little fried from today.
Working out
9.a) I think is 71 repayments as on finance solver:
N =? (70.81)
I = 5.4
PV = 230,000
Pmt = -3800
FV = 0
Ppy =12

b) After two years so n = 24, then FV becomes 160089.82
Interest = annual rate/ months/100 x this
Interest = 5.4/1200 x 160089.82 = 720.40

Therefore amount that reduces principal = payment - interest
= 3800 -720.40
= 3079.60

c) After two years (24 payments) we saw he still owed 160089.82
So use finance solver to find new repayments over 10 months
N = 10
I = 6
PV = 160089.82
Pmt = ?       -> 16,452.52 damn he rich
FV = 0
Ppy = 12

d) Find the balance on the second last repayment (9th month, to determine the payment on the tenth) so
N= 9
I = 6
PV = 160089.82
Pmt = -16452.52
FV = ?        -> $16370.69 owing
Ppy = 12

Tenth payment
Interest + 16452.52
Interest = 5.4/1200 x 16370.69 = 73.67
Tenth payment = $1652.52

THOUGH, I have no idea if I'm right LOL. Someone help x]
It feels like I looked into it too hard to only be marked 1 point per question..

//e: Oops, ty Kimahso!

For some reason I can't do this question, save me!

Invested $45,550 for four years. After four years of compounding interest, the investment was $60,000.
Interest had been calculated and paid quarterly.
What was the annual rate of interest for this investment?

Title: Re: VCE Further Maths Question Thread!
Post by: Kimahso on October 30, 2016, 06:22:35 pm
Forgive me/correct me if I'm wrong! My brain's a little fried from today.
Working out
9.a) I think is 71 repayments as on finance solver:
N =? (70.81)
I = 5.4
PV = 230,000
Pmt = -3800
FV = 0
Ppy =12

b) After two years so n = 24, then FV becomes 160089.82
Interest = annual rate/ months/100 x this
Interest = 5.4/1200 x 160089.82 = 720.40

Therefore amount that reduces principal = payment - interest
= 3800 -720.40
= 3079.60

c) After two years (24 payments) we saw he still owed 160089.82
So use finance solver to find new repayments over 10 months
N = 10
I = 5.4
PV = 160089.82
Pmt = ?       -> 16,407.87 damn he rich
FV = 0
Ppy = 12

d) Find the balance on the second last repayment (9th month, to determine the payment on the tenth) so
N= 9
I = 5.4
PV = 160089.82
Pmt = 16407.87
FV = ?        -> $16334.39 owing
Ppy = 12

Tenth payment
Interest + 16334.39
Interest = 5.4/1200 x 16334.39 = 73.50
Tenth payment = $16407.89

THOUGH, I have no idea if I'm right LOL. Someone help x]
It feels like I looked into it too hard to only be marked 1 point per question..

For some reason I can't do this question, save me!

Invested $45,550 for four years. After four years of compounding interest, the investment was $60,000.
Interest had been calculated and paid quarterly.
What was the annual rate of interest for this investment?


You didn't change the interest rate from 5.4 to 6 for parts c and d but other than that I think it's right.

For your question:
N=16
I=?
PV=-45550
Pmt=0
FV=60000
Ppy=Cpy=4

And you get 6.948% annual interest.
Title: Re: VCE Further Maths Question Thread!
Post by: SexGodDosia on October 30, 2016, 06:55:29 pm
Hey can anyone come up with 5 generic terms on how to describe the general pattern of some statistics/ describing the shape of the distribution

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: blossum on October 30, 2016, 09:24:05 pm
-snip-
Thanks!

Hey can anyone come up with 5 generic terms on how to describe the general pattern of some statistics/ describing the shape of the distribution

Thanks :)
Not sure if this is what you're looking for?
Negatively skewed, positively skewed, symmetric with outliers

Example for comparing two data sets:
Male and female results are, on average, approximately the same. Both have a  mean of around 14.5 However, the males' results are more widely spread. The standard deviation of the males is 2.8 compared to 1.6 for the females. Female results are symmetrically skewed, as shown by the stem plots.

Or for regression?
Positive/negative
Linear/non-linear
Strong/moderate/weak association
With outliers

Time series?
Seasonal, cyclic, structural change, random fluctuations, increasing/decreasing trend...

Example for time series:
The time series plot shows an increasing trend between the quarters March 2013 to June 2014. There is a structural change between June 2014 and September 2014 when the number of commuters jumps dramatically.
There is an increasing trend between September 2014 and December 2015.

_ _ _

Question regarding networks and flow capacity!
I hate these questions:

Click for pic
If all paths leading out of the arena are working at full capacity and the path leading from G to C is closed, what net effect, if any, will this have on the maximum flow into the station?
And one more on the picture
Title: Re: VCE Further Maths Question Thread!
Post by: SexGodDosia on October 30, 2016, 10:18:52 pm
Not sure if this is what you're looking for?
Negatively skewed, positively skewed, symmetric with outliers

Example for comparing two data sets:
Male and female results are, on average, approximately the same. Both have a  mean of around 14.5 However, the males' results are more widely spread. The standard deviation of the males is 2.8 compared to 1.6 for the females. Female results are symmetrically skewed, as shown by the stem plots.

Or for regression?
Positive/negative
Linear/non-linear
Strong/moderate/weak association
With outliers

Time series?
Seasonal, cyclic, structural change, random fluctuations, increasing/decreasing trend...

Example for time series:
The time series plot shows an increasing trend between the quarters March 2013 to June 2014. There is a structural change between June 2014 and September 2014 when the number of commuters jumps dramatically.
There is an increasing trend between September 2014 and December 2015.

Perfect thanks
Title: Re: VCE Further Maths Question Thread!
Post by: minerva on October 31, 2016, 08:35:47 pm
Hey, does anyone know where I can find 2016 Further exam 2?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 31, 2016, 08:40:08 pm
Hey, does anyone know where I can find 2016 Further exam 2?
Right here :)
Title: Re: VCE Further Maths Question Thread!
Post by: doitforthequestions on November 12, 2016, 06:50:00 pm
Anyone know how to solve the coordinates for B. Have been stuck on this for awhile.
Title: Re: VCE Further Maths Question Thread!
Post by: littledreamer on January 23, 2017, 09:40:50 pm
hey guys, i just picked up unit 3 further without a foundation in 1/2 and in the first chapter they asked: Comment on the shape of the histogram. What does this tell you about the distribution of this data set? We had to draw a histogram on CAS which seemed like it was all levelled. Anyway, I have no idea what kind of shapes histograms can be and what a distribution of a data set is (as well as potential answers), can someone please explain :) Do histograms make up a big part of core? thanks so much!
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on January 23, 2017, 09:48:38 pm
hey guys, i just picked up unit 3 further without a foundation in 1/2 and in the first chapter they asked: Comment on the shape of the histogram. What does this tell you about the distribution of this data set? We had to draw a histogram on CAS which seemed like it was all levelled. Anyway, I have no idea what kind of shapes histograms can be and what a distribution of a data set is (as well as potential answers), can someone please explain :) Do histograms make up a big part of core? thanks so much!

Histograms and the interpretation of visual data representations is an important part of the Core section (statistics, part 1 of 2) so you should spend the time understanding this. There are three key features of a histogram: shape/outliers, centre and spread. Your question is asking specifically regarding shape - therefore the key terms you would be focusing on are: positively skewed, negatively skewed and symmetrical (or bell-shaped).

In terms of commenting regarding the distribution, I would discuss centre and spread along with what it means for a histogram to be 'positively skewed' (as an example).

Every textbook should discuss this in detail as it's part of the core section - meaning every student doing Further has to complete it. Have a look around

Good luck :)
Title: Re: VCE Further Maths Question Thread!
Post by: littledreamer on January 24, 2017, 04:47:46 pm
Thanks Aaron!

Can anyone solve this question too: The pH scale measures acidity using a log (base 10) scale. For each decrease in pH of 1, the acidity of a substance increases by a factor of 10. If a liquid’s pH value decreases by 0.7, by how much has the acidity of the liquid increased? I somewhat understand using log base 10 but not when it comes to pH, is this also a big part of core? Thanks again :)
Title: Re: VCE Further Maths Question Thread!
Post by: Shadowxo on January 24, 2017, 05:20:30 pm
Thanks Aaron!

Can anyone solve this question too: The pH scale measures acidity using a log (base 10) scale. For each decrease in pH of 1, the acidity of a substance increases by a factor of 10. If a liquid’s pH value decreases by 0.7, by how much has the acidity of the liquid increased? I somewhat understand using log base 10 but not when it comes to pH, is this also a big part of core? Thanks again :)

Hi, I didn't actually do further but I've done chemistry :P
Can't answer about the course but here's the pH solution
It increases by 10^decrease in pH = 100.7 = 5.012

pH = -log10(acidity)
10-pH = acidity
pH decreases by 0.7. let pH represent the initial pH
new acidity = 10-(pH - 0.7) = 10-pH*100.7 = 10-pH*5.012
The new acidity is 5.012x more than the original acidity
Hope this helps a little :P
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on January 24, 2017, 06:22:40 pm
In addition to the above answer:

For the second part of your question, "is this also a big part of core":

- These types of problem based questions are common. It challenges you to think for yourself and apply what you've learnt. They are really valuable to understand, especially for the exams.

- In terms of a specific question regarding acidity and pH levels, I doubt you will need to know this *specifically*... but it's just one application question of many.

- The two main areas of the Core section are statistics/data analysis and finance/recursion. The topics within these two areas comprise the core section.
Title: Re: VCE Further Maths Question Thread!
Post by: NAT0003 on February 28, 2017, 09:35:03 am
What is the trickiest part of further
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on February 28, 2017, 07:35:23 pm
What is the trickiest part of further

This is going to vary for everyone. In Further 3/4, it's broken down into various modules and each school/ individual take different modules to their own liking, as long as they complete two + the core modules (recursion and finance modelling & data and statistics). Some don't like Core, others don't like the modules their school does.
Title: Re: VCE Further Maths Question Thread!
Post by: Joseph41 on March 07, 2017, 01:12:11 pm
Hey, 2017 VCEers! If you want to ask a VCE Further question, you've come to the right place!

IMPORTANT: In order to ask a question, you will have to click here and make an ATAR Notes account.

Once you've done that, you can simply hit "reply", as shown in the image below.

(http://i.imgur.com/c9r3C2B.png)

Ask away, and all the best with Further this year! ;D
Title: Re: VCE Further Maths Question Thread!
Post by: Finlayh on March 07, 2017, 08:18:23 pm
Hi, I got 93% on my first further maths SAC. Has that ruined my chance of getting a study score of 50?
Title: Re: VCE Further Maths Question Thread!
Post by: Hena_omarzaii on March 07, 2017, 08:28:34 pm
Hi, what types of percentages in ur sacs do u need for further to get 40+   :D
Title: Re: VCE Further Maths Question Thread!
Post by: Joseph41 on March 07, 2017, 09:32:19 pm
Hi, I got 93% on my first further maths SAC. Has that ruined my chance of getting a study score of 50?

Hey Finlayh! ;D Welcome to the forums.

To answer your question bluntly, no, not at all. Achieving a study score of 50 does not require 100% in every SAC. And like, one might argue that's even more the case for Further, where ~66% of the study score is based on the exams. :)

So no, your SAC result has definitely not ruined your chance of a 50. :)

Hi, what types of percentages in ur sacs do u need for further to get 40+   :D


Hey Hena_omarzaii, how's it going? :) Welcome to the forums! ;D

This is actually a really difficult question to answer, because study scores don't really depend on your raw results (due to scaling and technical stuff like that). Because SACs change from school to school, it wouldn't really make sense to judge students based on what percentages they achieved; as such, I wouldn't want to give you a definitive answer on this. :-\
Title: Re: VCE Further Maths Question Thread!
Post by: MattBro on March 10, 2017, 08:04:42 am
Good day,

Any of you got tips and tricks for Data Analysis. I find it to be a bs topic with some of the extended response answers to be annoying to answer.


Also on our first SAC on Data Analysis the teachers made it very challenging and I got 87.5%. Which surprised me because I thought I did poorly. If I get in the 90% on SAC's and smash out the exam will I possibly get 38 - 40 range?

Just the classic worried VCE student  :o ;D


Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on March 10, 2017, 11:55:25 am
Absolutely. Probably closer to the 38 end unless you completely dominate the exams.  :)

As for tips for data analysis; read everything really carefully. Not just the question, but the graphs and scales too. There's a lot that's easy to mess up with data analysis so make sure you're working with as many decimal places (if not exact values) as possible to avoid rounding mistakes. For filling in tables and things, make sure you're entering the right thing in the right place; back when I did further maths, I triple checked but that's probably excessive. Some people find that having 'copy-paste' responses for worded questions in their summary is helpful. If you use the TI calculator, there's a lot of good functions in there that teachers generally don't use/know about that can save you time. Just be careful, because sometimes they're not actually relevant or use different models to what's given in further maths. I'm not sure about the CASIO. It's faster to do a lot of things by hand but I recommend checking on the calculator anyway to make sure you haven't made any silly mistakes.
Title: Re: VCE Further Maths Question Thread!
Post by: NAT0003 on March 10, 2017, 12:21:04 pm
Does our school choose modules for 3/4 or can we choose them
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on March 10, 2017, 12:35:08 pm
Your school chooses the modules that you will have SACs on. However if you really, really hate them, there's nothing stopping you from learning different ones for the exam and choosing them. On exam 1, you fill in bubbles indicating which modules you are doing - no one can stop you from doing the ones you'd like. For exam 2, it's marked by real people so they'll go through and see which sections you've completed. If you do more modules than the core + 2 that's prescribed, they'll pick which ones get included in your exam score, although I'm not sure how they pick. Probably in booklet order.

I wouldn't recommend learning new modules, but there's no rules against it. :)
Title: Re: VCE Further Maths Question Thread!
Post by: NAT0003 on March 10, 2017, 04:26:02 pm
For a 50 in further can you lose any marks across both exams
Title: Re: VCE Further Maths Question Thread!
Post by: zuleika on March 12, 2017, 12:13:56 pm
Is there a quick and easy way to do seasonal adjustment on CAS (ti-nspire). I find it takes a lot of time solving by hand.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 12, 2017, 02:59:38 pm
Is there a quick and easy way to do seasonal adjustment on CAS (ti-nspire). I find it takes a lot of time solving by hand.

According to my 2014 Further cheat sheets for calculating seasonal indices:
"Step 1: Calculate monthly/ quarterly/ yearly/ etc. average of data [by using the 'mean' function or by fraction symbol.]
Step 2: Express each as a decimal for each figure e.g. Data/ average = decimal [press menu + 2 + 1* for decimal if fraction.]
Step 3: Average ratios from step 2, to get each season's index...
The seasonal indices in the table above should add to how many seasons/ cycles it has, due to its intervals."
Not exactly quick, but should be slightly faster than by hand. Hopefully that helps.

* According to the TI NSpire black and white screen (black calculator) that I had. Should still be similar on other models.
Title: Re: VCE Further Maths Question Thread!
Post by: npnp on March 15, 2017, 05:45:44 pm
Standard Deviation : 10
Mean: 40

What is the range of the top 97.5%?

[Note] I understand you must go 2 standard deviations down so the bottom of the range is 20 however I don't understand how many you go up. As 3 up there is still another 0.15% on the top, so do you go 4?

Moderator edit [Aaron]: Thread merged with VCE Further Question Thread.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 15, 2017, 06:24:08 pm
Standard Deviation : 10
Mean: 40

What is the range of the top 97.5%?

[Note] I understand you must go 2 standard deviations down so the bottom of the range is 20 however I don't understand how many you go up. As 3 up there is still another 0.15% on the top, so do you go 4?

Moderator edit [Aaron]: Thread merged with VCE Further Question Thread.

Yes, basically. You do need to include that 0.15% of data. For 97.5%, you're roughly going to get the data either above or below 2 standard deviations of the data, so that means all the data above -2 this image or below 2 on the same image.  If you subtract the 2 standard deviations you missed, you will have 100% (all data) - ( 0.15% + 2.35%) = 100% - 2.5% = 97.5%.

In your example:
SD (standard deviation) = 10, mean = 40
So that means for our values for SDs are:
working out
3 SDs below mean: 40 - 3 x 10 = 40 - 30 = 10
2 SDs below mean: 40 - 2 x 10 = 20
1 SD below mean... etc.
In order they are: 10 (-3 SDs), 20 (-2 SDs), 30 (-1 SD), 40 (mean), 50 (+1 SD), 60 (+2 SDs), 70 (+3 SDs)
So because we want the top 97.5%, we would have to take anything from -2 SDs, so >/= 20 *insert units here*.
Range here would therefore be 4 SDs - (-2 SDs) = 80 - 20 = 60 *insert units here* .
Title: Re: VCE Further Maths Question Thread!
Post by: smiley123 on March 19, 2017, 07:44:57 am
 For this question: Sketch a negatively skewed distribution with mean 50 and standard deviation 10, how do I know that it is 2 standard deviations from the mean and 95% of the data is within the range of 30 and 70?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 19, 2017, 02:40:05 pm
For this question: Sketch a negatively skewed distribution with mean 50 and standard deviation 10, how do I know that it is 2 standard deviations from the mean and 95% of the data is within the range of 30 and 70?

Even though it is negatively skewed, the only distribution you are taught in Further regarding standard deviations in detail is the balanced normal distribution. It doesn't give us much to work on. Beyond the scope of the course, however, the normal distribution's 68-95-99.7% rule is only an approximation. It actually has a little bit of leeway on either side. While it is close to accurate, if data is skewed either side, we just assume that the approximation kind of covers it. This can only be applied for those that cover large areas e.g. 68%/ 95%/ 99.7% of the data, because the finer you get the more errors you get away from the true data (in other words, it becomes inaccurate). 

We're also assuming that the skew isn't huge, the IQR has barely moved, but the median and mean are no longer equal/ close to equal to each other. (Basically the bulk of the data has shifted a little to the right for a negative skew, which you can see visually here.) Since we aren't given any more information than this, we apply these assumptions as if it's normal and just sketch it differently (as a negative/ positive skew).
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinaB19 on March 22, 2017, 12:29:28 pm
Help with question 2 please if possible
Title: Re: VCE Further Maths Question Thread!
Post by: Guest8373727727 on March 23, 2017, 05:48:18 pm
Need help with 4 b)

(http://i64.tinypic.com/dfdiip.jpg)
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on March 24, 2017, 02:37:17 pm
So...back to the postcodes issue. Nominal or ordinal? Give your reasoning. VCAA says nominal, other exam companies say ordinal. Some people say ordinal and some say nominal. Whats the safest bet if given this question on the exam? Take VCAA's side and say nominal?
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on March 24, 2017, 07:51:16 pm
I can see the logic behind calling them ordinal, since as numbers you could put them in order and get a somewhat sensical list of areas that are close to each other. One flaw in that is that for example there's a big jump between 0899 (in NT) and the next closest number, 1000 (in NSW). I'd personally argue for nominal because postcodes act as geographical labels, and the numbers translate to actual town names; 3458 is Suburb X, Y, Z and W while 3450 could be suburb R, and once you turn them into towns, how do you order them then? Alphabetically doesn't match the postcode numbers, and neither does population size or any other metric as far as I'm aware.

ofc I'm not a professor of postcodes or anything so my reasoning could be totally flawed, but you should go with the VCAA, they're the ones who mark it. Good luck. :)

Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 26, 2017, 03:25:18 pm
Need help with 4 b)

(http://i64.tinypic.com/dfdiip.jpg)

Hey Guest8373727727! I don't think what you're doing is actually Further Maths, but Methods, so you've accidentally posted to the wrong thread.
Perhaps next time you can try this thread instead?

Nonetheless, I can help you to some degree. (It's been a while since I did Methods.)
Explanation and Answering Question 4b
You're stating transformations, so you don't necessarily have to do this with the given equation. All you have to know is what changes f(x) to what the question wants you to end up. In this case, you want g(x), which is g(x) = f(x+2) + 4 .
Let's take a look at what you need to do in order to change f(x) to f(x+2) + 4. I'll give you a hint: you'll have two steps. Why? Because you have two big differences from f(x) --> f(x+2) + 4
Step 1
Let's start off by doing the stuff in the brackets, because they're usually harder to change later.
Note: there's a general rule of thumb out there that states that you should do dilations, reflections and transformations respectively. Caveat here -this doesn't work for everything and as long as you state the steps in an order that receives the same graph, it doesn't matter which order you do them in.
Since there are no coefficients, there are no dilations involved. There are no reflections either, because the f(x) would have had negative coefficients. This means we have two translations.
To move something in the brackets, in terms of translations, we usually need to think a little backwards. A positive term gives a left shift in the x-axis, whilst a negative term gives shift to the right. (You can graph x2 and (x+1)2 to prove this yourself.)
The "+ 2" in the brackets therefore moves f(x) left 2 units. State this as "translate 2 units to the left" or similar.
Step 2
Now that we have gone from f(x) to f(x+2), we need to add the 4. This is a shift in the y-axis and is more instinctive. Positive units means a shift up and negative does the opposite.
Therefore, to go from f(x+2) to f(x+2)+4, we need to "translate 4 units up".
That's it! You transformed f(x) --> f(x+2) --> f(x+2)+4 .

Title: Re: VCE Further Maths Question Thread!
Post by: SMOKIE on March 26, 2017, 07:17:12 pm
How do you find moving mean smoothing, median smoothing and seasonal indices on the cas?
 Also can someone explain how to graphically median smooth a time series?
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 27, 2017, 12:13:38 am
Help with question 2 please if possible

Based on a transformations table, I think the y2 transformation should be correct. Not entirely sure, but the higher r2 value and randomness upon transformation seems to correspond correctly with my answer.

How do you find moving mean smoothing, median smoothing and seasonal indices on the cas?
Also can someone explain how to graphically median smooth a time series?
Thanks
1.
Spoiler
Mean and median smoothing don't really involve the CAS at all (only to find the mean, really) and are more graphically drawn by hand. If it is a question involving them without drawing it graphically, it can usually be done by using only sections of that data.
Seasonal indices are primarily questions with tables to fully work them out and also don't use the CAS much either. Here's a post I wrote about calculating them this way:
According to my 2014 Further cheat sheets for calculating seasonal indices:
"Step 1: Calculate monthly/ quarterly/ yearly/ etc. average of data [by using the 'mean' function or by fraction symbol.]
Step 2: Express each as a decimal for each figure e.g. Data/ average = decimal [press menu + 2 + 1* for decimal if fraction.]
Step 3: Average ratios from step 2, to get each season's index...
The seasonal indices in the table above should add to how many seasons/ cycles it has, due to its intervals."
Not exactly quick, but should be slightly faster than by hand. Hopefully that helps.

* According to the TI NSpire black and white screen (black calculator) that I had. Should still be similar on other models.
Like smoothing, it will either be fill the blank or use sections of the data. If the question supplies very little information (typically a number or two), then it's likely a deseasonalising question, where the formula is deseasonalised value = actual value/ seasonal index .
tl;dr : All three don't really use the CAS much at all.

2.
Spoiler
- Have a graph of the time series with you.
- Take first few points (depends on which type of smoothing it is - either 3 or 4 points i.e. 3 for 3 median, 4 for 4 median)
- Find median of those
- Place x coordinate at centre of the 3/4 points and y coordinate at the median value you just found
- Repeat last three steps for the 2nd, 3rd and 4th points on the original time series if 3 median smoothing or 2nd, 3rd, 4th and 5th points if 4 median.
- Continue doing each set of 3/4 points until you reach the last 3/4 values. (Still find the median of the last 3/4 values though!)
- Connect all the new dots of your smoothed points with straight lines
Title: Re: VCE Further Maths Question Thread!
Post by: SMOKIE on March 27, 2017, 06:38:05 pm
Any tips and tricks on a  bound reference for sacs and end of year exam? 
Should i include all the important formulas at the front or go from chapter by chapter?
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 27, 2017, 07:05:18 pm
Any tips and tricks on a  bound reference for sacs and end of year exam? 
Should i include all the important formulas at the front or go from chapter by chapter?
Thanks

Depends on you. My preference is that I left cheat sheets at the beginning with a contents page, then individual notes in the back, chapter by chapter. Remember that you won't have much time to flip through looking for specific things, so it's smarter to leave important formulas together somewhere. 
Tips and Tricks - Bound Reference
I would recommend:
1. getting started on this ASAP, because you won't want a massive looming task at the end of the year.
2. making it fit the requirements listed by VCAA. (You must anyway if you plan on bringing one.)
3. using different books for theory and textbook questions to save time.
4. buying yourself some sticker tabs or a pack of highlighters to mark out chapters.
5. organising it how you can understand and easily read it. It's worse if you can't read your own notes when you're stressed.
Tips and Tricks - SAC cheat sheets
I would recommend:
1. make it short and sweet.
2. keep it colour coded and consistent.
3. write calculator tips and leave an example where you see fit, especially if you're iffy with a concept.
Those should be more than enough to help you for now. :) If you need a sample page, Engage Education has some great free samples or PM me and if I have the time, I'll send one over.
Title: Re: VCE Further Maths Question Thread!
Post by: zxcvbnm18 on March 27, 2017, 09:42:33 pm
Depends on you. My preference is that I left cheat sheets at the beginning with a contents page, then individual notes in the back, chapter by chapter. Remember that you won't have much time to flip through looking for specific things, so it's smarter to leave important formulas together somewhere. 
Tips and Tricks - Bound Reference
I would recommend:
1. getting started on this ASAP, because you won't want a massive looming task at the end of the year.
2. making it fit the requirements listed by VCAA. (You must anyway if you plan on bringing one.)
3. using different books for theory and textbook questions to save time.
4. buying yourself some sticker tabs or a pack of highlighters to mark out chapters.
5. organising it how you can understand and easily read it. It's worse if you can't read your own notes when you're stressed.
Tips and Tricks - SAC cheat sheets
I would recommend:
1. make it short and sweet.
2. keep it colour coded and consistent.
3. write calculator tips and leave an example where you see fit, especially if you're iffy with a concept.
Those should be more than enough to help you for now. :) If you need a sample page, Engage Education has some great free samples or PM me and if I have the time, I'll send one over.


Where can we find the free samples from engage? I cant seem to find them
Title: Re: VCE Further Maths Question Thread!
Post by: Joseph41 on March 29, 2017, 05:53:02 pm
Any tips and tricks on a  bound reference for sacs and end of year exam? 
Should i include all the important formulas at the front or go from chapter by chapter?
Thanks

Have you read this article? ;D

How to Make a Killer Bound Reference
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinaB19 on March 29, 2017, 06:06:21 pm
Hey! Does anyone have any old practice SACs (or just any practice questions in general) for data analysis that they could post?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 30, 2017, 06:01:06 pm
Where can we find the free samples from engage? I cant seem to find them
Looks like it's currently under renovation. So sorry about that. I didn't know. I think it'll be up and running again soon.
On the bright side, making your own is a good opportunity for you to revise, so maybe take a hint from AN's very own Stick and their post on bound references.

Hey! Does anyone have any old practice SACs (or just any practice questions in general) for data analysis that they could post?
We can't post old practise SACs as these are the legal property of the school or person. I can, however, direct you to Checkpoints and ExamPro, which will provide great practise questions.

Title: Re: VCE Further Maths Question Thread!
Post by: EdwinaB19 on March 30, 2017, 08:26:06 pm
We can't post old practise SACs as these are the legal property of the school or person. I can, however, direct you to Checkpoints and ExamPro, which will provide great practise questions.

Thank you for letting me know! I've done Checkpoints for data analysis but I'll give ExamPro a go
Title: Re: VCE Further Maths Question Thread!
Post by: zxcvbnm18 on April 04, 2017, 07:00:38 pm
What kind of things do we have to write about when describing a time series plot and a smoothed time series plot? What kind of things about the graph should we focus on?  Also do we have to write our descriptions in any specific way?
Title: Re: VCE Further Maths Question Thread!
Post by: apan on April 06, 2017, 10:02:57 pm
What kind of things do we have to write about when describing a time series plot and a smoothed time series plot? What kind of things about the graph should we focus on?  Also do we have to write our descriptions in any specific way?

Hey! When describing a time series plot you should talk about:
- Trends (positive/upward? negative/downwards? no trend?)
- Are there any irregular or random fluctuations?(short term fluctuations) or is the time series fairly predictable? I also used to point out the degree e.g "there is small amount of random fluctuations in this time series"
- Is there seasonal variation? These are usually easy to spot, look for peaks and lows (cyclical) occurring around the same time  (e.g a time series of a week and general peaks on thursdays but lows on fridays). But remember seasonal variation must be within one calendar year. For example you can say "peaks are generally during the month of January over the years" however you cannot say "Peaks during every second year e.g peaks in the year 1995, 1997, 1999" as this is more than one calendar year (hopefully this makes sense!)
- Is there any structural change? Probably the hardest to spot, but it is when something big happens and changes the pattern of the plot. E.g if there is a general upward trend, then suddenly there is a downward trend on the plot, you could say this is structural change. There is more than one trend visible on the plot! Don't confuse this with irregular fluctuations as this is LONG TERM whereas irregular fluctuations are SHORT TERM and are outliers.

The wording can be tricky but something nice, simple and straight to the point makes the examiners happy! Something like, "In this time series, we can see a steep upward trend with seasonal variation (as there are peaks every January and lows every March). There is some slight irregular fluctuations, and some outliers at the point (x, y, z).

Hope this helps! Good luck!
Title: Re: VCE Further Maths Question Thread!
Post by: zxcvbnm18 on April 07, 2017, 11:30:29 am
Thank you so much! This is really helpful! :) :) :) :) :) :) :)
Title: Re: VCE Further Maths Question Thread!
Post by: ooft on April 11, 2017, 08:10:53 pm
So I have a SAC coming up next term for Data Analysis, and whilst preparing for it, I've noticed that I am repeatedly getting answers ever so slightly wrong due to rounding. I think it is because I generally round during working out, and not only my for final answer. Does it really matter if you round during the working out? or are you meant to use the un-rounded values until you give your final answer?Or does it simply not matter?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on April 11, 2017, 08:18:19 pm
So I have a SAC coming up next term for Data Analysis, and whilst preparing for it, I've noticed that I am repeatedly getting answers ever so slightly wrong due to rounding. I think it is because I generally round during working out, and not only my for final answer. Does it really matter if you round during the working out? or are you meant to use the un-rounded values until you give your final answer?Or does it simply not matter?

It does matter - many assessment reports have indicated that rounding should only be done at the end of your working out (e.g. your final answer). This keeps your answer as accurate as possible. The more you use rounded values during your calculations, the further out your final answer will be from the actual one.

My tip would be to always show your full working out, indicate how you arrived at your answer and most of all, read the question and its requirements (some ask for answers to a specific number of decimal places)
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 11, 2017, 11:04:21 pm
Is 64 pages for my bound refrence to small?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on April 11, 2017, 11:14:38 pm
Is 64 pages for my bound refrence to small?

You should create a bound reference that is right for you. There is no guideline to the amount of pages your bound reference should be.

Ideally your bound reference acts as a support in your exams, so it should not be too detailed. A good starting point is completing a few VCAA exams using only your bound reference (the sections you have been taught at least) - this will indicate whether it needs some finetuning.

Keep in mind that each exam is only 90 minutes duration, so you won't have time to sit there and go through your bound reference in detail. It goes very fast.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 11, 2017, 11:39:59 pm
You should create a bound reference that is right for you. There is no guideline to the amount of pages your bound reference should be.

Ideally your bound reference acts as a support in your exams, so it should not be too detailed. A good starting point is completing a few VCAA exams using only your bound reference (the sections you have been taught at least) - this will indicate whether it needs some finetuning.

Keep in mind that each exam is only 90 minutes duration, so you won't have time to sit there and go through your bound reference in detail. It goes very fast.
Yeah but it dont know what is right for me and how many pages is right for me
Im really concerned i will run out of pages and have to dopy evreything to another textbook whch is extremely tedious
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 12, 2017, 06:13:37 pm
Yeah but it dont know what is right for me and how many pages is right for me
Im really concerned i will run out of pages and have to dopy evreything to another textbook whch is extremely tedious
If you are a detailed person who loves having notes with you/ started it with detailed notes and are carrying through with it, I'd say 64 pages is not enough. If you are less worried about detail/ haven't got many notes in it right now, then 64 pages will suffice. It will depend on you. 

I would attach extra pages in case. My bound reference from Further actually has about 15 blank pages at the end in case I was ever going to add more details. Although there is no precise number, it is better to have more than less for now. (Just make sure you know how much is blank.) There is no loss in binding more pages, because you can tear them out later (and recycle them). If you really want a numerical answer: whatever you end up with by the time you finish your content + another 5-10 pages for exam questions you did wrong during practise.
Title: Re: VCE Further Maths Question Thread!
Post by: BSmith on April 13, 2017, 12:01:31 pm
Hi, im doing some transformations stuff and am having trouble with getting an answer back out of the equation.

To put it simply, the transformation i did was 1/y vs x and it turned out to (-1.441e-5) + x(2.34e-5)
how do i get an answer out of this? it needs to be somewhere around 6 thousand to make sense in the data.

the original least squares regression line was 1151.58 - 411.8x.

any help is appreciated.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 13, 2017, 12:01:47 pm
If you are a detailed person who loves having notes with you/ started it with detailed notes and are carrying through with it, I'd say 64 pages is not enough. If you are less worried about detail/ haven't got many notes in it right now, then 64 pages will suffice. It will depend on you. 

I would attach extra pages in case. My bound reference from Further actually has about 15 blank pages at the end in case I was ever going to add more details. Although there is no precise number, it is better to have more than less for now. (Just make sure you know how much is blank.) There is no loss in binding more pages, because you can tear them out later (and recycle them). If you really want a numerical answer: whatever you end up with by the time you finish your content + another 5-10 pages for exam questions you did wrong during practise.
So how do i attach more pages to them
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 13, 2017, 12:04:11 pm
Hi, im doing some transformations stuff and am having trouble with getting an answer back out of the equation.

To put it simply, the transformation i did was 1/y vs x and it turned out to (-1.441e-5) + x(2.34e-5)
how do i get an answer out of this? it needs to be somewhere around 6 thousand to make sense in the data.

the original least squares regression line was 1151.58 - 411.8x.

any help is appreciated.
Hey, whatwas the original question?
Title: Re: VCE Further Maths Question Thread!
Post by: BSmith on April 13, 2017, 12:12:36 pm
i have attached both the data set, the equation  worked out from that through regression and the transformations i have done. 1/price was the strongest but i am unsure how to take the new equation and get the price data from it.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 13, 2017, 12:29:45 pm
Ok so when u fill in that data of the age of corola which should be on the x axis as it is the explanatory response and the prive should be the y as it is the response variable you should see. Non linear line that goes straight that curves to the right, therefore according to the forumlas you need you change your x axis by 1over x or your y axis by 1/yaxis or your x axis by kig x ir tour yaxis by log y.

Im going to change my x acis to 1/x and you will see that it is now linear. Remember to do this you go back to list and spread shits and add a new collum and call it xsq as it cant be x which would be the same name as the x column. and underneath it press = 1/xand select variable refrence and you should see a list of values

Then go back to your graph and change the x axis by clicking on it to 1/x and then press menu-analyze-regression-show linear and thats your equation, plug in 10 to the x in that equation and u have your answer for 5c.
(Yep so my equation was y=15399.3x + 2683.59
Title: Re: VCE Further Maths Question Thread!
Post by: BSmith on April 13, 2017, 12:36:26 pm
Don't you then have to transform that answer again to get the real answer. Also I am struggling to work out 1/y which is 1/price. As it gives me an answer has such small values. I get how to transform it but when I plug in 10 the answer comes out as 0.147... which isn't right.
Title: Re: VCE Further Maths Question Thread!
Post by: BSmith on April 13, 2017, 12:53:57 pm

Ok so when u fill in that data of the age of corola which should be on the x axis as it is the explanatory response and the prive should be the y as it is the response variable you should see. Non linear line that goes straight that curves to the right, therefore according to the forumlas you need you change your x axis by 1over x or your y axis by 1/yaxis or your x axis by kig x ir tour yaxis by log y.

Im going to change my x acis to 1/x and you will see that it is now linear. Remember to do this you go back to list and spread shits and add a new collum and call it xsq as it cant be x which would be the same name as the x column. and underneath it press = 1/xand select variable refrence and you should see a list of values

Then go back to your graph and change the x axis by clicking on it to 1/x and then press menu-analyze-regression-show linear and thats your equation, plug in 10 to the x in that equation and u have your answer for 5c.
(Yep so my equation was y=15399.3x + 2683.59

I got that also, I'm looking to work out 1/price. I got an answer but I don't know how to derive a solution from the equation.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 13, 2017, 12:56:08 pm
By transform what do u mean
Also if i did 1/y instead of 1/x i would not get an answer coming out as a big value. I have a small value
This is correct because in your first picture the equation of 1/y vs age is -.0000144x-.0000234x which is the equation i got and when u plug in 10 u shouldnt get a big value
But when i did 1/x it worked and seemed to fit i with the current trend of data. I dont think 1/y works. Correct me if im wrong
I reckon theres something wrong with the question im not sure sorry, as it said right there that the equation of the graph of 1/y vs price was thoose long lists of 0s and decimals points so u cant really get a big answer out of that
Title: Re: VCE Further Maths Question Thread!
Post by: BSmith on April 13, 2017, 01:17:33 pm
Yeh I thought it was about perculiar. 1/y gave the strongest r value but like you said, given how many .000 are in it, I don't know how to get a decent answer out of it. I'll just use the next strongest. Thanks you for your time.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 21, 2017, 02:27:06 pm
So how do i attach more pages to them
Taping pages in is fine, iirc. I would double check the guidelines on VCAA and with your teacher in case. Pretty sure I did this with my Methods one.

In my opinion though, I would recommend that you just add a small stack of blank printer paper to the end, tear off the cover of your bound reference notebook and get it properly bound at your local Officeworks or favoured binding place for a few dollars. (It's almost always under $10, even with the fancier backings and spines.) If it is one of those books where the pages are hard to tear because they were originally A3 pages (usually your average < $1 exercise book), such as this or these, then cut at the crease where the spine is so you actually have separate A4 pages before binding.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 21, 2017, 10:03:57 pm
Taping pages in is fine, iirc. I would double check the guidelines on VCAA and with your teacher in case. Pretty sure I did this with my Methods one.

In my opinion though, I would recommend that you just add a small stack of blank printer paper to the end, tear off the cover of your bound reference notebook and get it properly bound at your local Officeworks or favoured binding place for a few dollars. (It's almost always under $10, even with the fancier backings and spines.) If it is one of those books where the pages are hard to tear because they were originally A3 pages (usually your average < $1 exercise book), such as this or these, then cut at the crease where the spine is so you actually have separate A4 pages before binding.
How about cutting at the red line?
Title: Re: VCE Further Maths Question Thread!
Post by: drepwns on April 22, 2017, 10:15:02 am
Would it be appropriate to use that term in VCE Further math? I know that it's recognised as a term in Excel, but would using the term 'Q4' or 'Fourth quartile' be applicable? Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Hungry4Apples on April 22, 2017, 01:56:47 pm
I assume so, however I (2016 further maths-49) would probably say the top 25% or something to do with the percentages but 'fourth quartlie' should be g. I suggest reading through the exam reports and see how the suggested answers have written it in the past!
Title: Re: VCE Further Maths Question Thread!
Post by: agb99 on April 24, 2017, 09:53:40 am
hey
i am stuck on the attached questions, any help will be appreciated.....

thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Hungry4Apples on April 24, 2017, 04:31:05 pm
hey
i am stuck on the attached questions, any help will be appreciated.....

thanks!

So for question one, three median smothing and five median smoothing are very similar. It works by taking the data point we want to smooth and then using the points around it to find the 'middle value'. So for an example of three median smoothing, take data point 2, we compare data points 1,2 and 3 and take the 'middle' value and replace data point 2 with that value. FIve median moving works the same except we take two to the left and two to the right.
a) i - we have values 30 (point 3), 40 (point 4) and 22.5 (point 5), since 30 is the middle value it is the value of point 4 after 3 median smoothing

For the second question we use the formula Seasonal Index=Actual Figure/Desonalised Figure

so Deseasonalised Figure = Actual Figure/Seasonal Index

DF=AF/1.2 in this case

Since we are dividing by 1.2, we are basically multiplying AF by 1/1.2 or 0.83

1-0.83=.17, so we are reducing the AF by 17%

For the second q
Title: Re: VCE Further Maths Question Thread!
Post by: drepwns on April 24, 2017, 10:39:04 pm
Hey there,
if I write out the coefficient of determination (r^2) as both a decimal and a percentage, is that okay?
I did so in my SAC today, and I'm feeling very anxious as to whether I lost a mark for that or not.
Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: drepwns on April 24, 2017, 10:46:01 pm
Hello again,
so today in my SAC - I used both the correlation coefficient and the residual plot to suggest the superior predictive model.
I recognise that using the coefficient of determination is the right way, but yet again - the pressure under SAC conditions eats away at me.
Is using the correlation coefficient alright, or was I meant to use the coefficient of determination? Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on April 25, 2017, 12:19:52 am
How about cutting at the red line?
Should be just as fine. Might make it a little harder to read some of the notes beside the red line when bound, but whatever floats your boat. :)

hey
i am stuck on the attached questions, any help will be appreciated.....

thanks!
Looks like Hungry4Apples has you covered for this!
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 25, 2017, 10:25:03 am
Hey there,
if I write out the coefficient of determination (r^2) as both a decimal and a percentage, is that okay?
I did so in my SAC today, and I'm feeling very anxious as to whether I lost a mark for that or not.
Thanks!
Could you give an example? It sounds like it's fine though. If it's something along the lines of 'the coefficient of determination of 0.9284 (92.84%) indicates that ...', I can't imagine you'd lose marks. :)
Title: Re: VCE Further Maths Question Thread!
Post by: drepwns on April 25, 2017, 10:50:45 am
Could you give an example? It sounds like it's fine though. If it's something along the lines of 'the coefficient of determination of 0.9284 (92.84%) indicates that ...', I can't imagine you'd lose marks. :)

If I can remember clearly, the question asked to specify the coefficient of determination, and then interpret it. What I did was write out 'coefficient of determination = 0.642 or 64.2% and then in the next line, I interpreted it using 'the coefficient of determination of 64.2% indicates that...'
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on April 25, 2017, 12:45:14 pm
If I can remember clearly, the question asked to specify the coefficient of determination, and then interpret it. What I did was write out 'coefficient of determination = 0.642 or 64.2% and then in the next line, I interpreted it using 'the coefficient of determination of 64.2% indicates that...'
That's perfectly fine! You should get full marks for that. :)
Title: Re: VCE Further Maths Question Thread!
Post by: Hungry4Apples on April 25, 2017, 11:37:24 pm
Hello again,
so today in my SAC - I used both the correlation coefficient and the residual plot to suggest the superior predictive model.
I recognise that using the coefficient of determination is the right way, but yet again - the pressure under SAC conditions eats away at me.
Is using the correlation coefficient alright, or was I meant to use the coefficient of determination? Thanks.

From memory the coefficient of determination is used to determine how much of the variation in the dependant variable can be explained by the variation in the independent variable. I'm pretty sure that the correlation coefficient is used to determine how strong the linear relationship is so I think you should be safe.
Title: Re: VCE Further Maths Question Thread!
Post by: Mariamnourine on April 26, 2017, 09:20:36 am
Hey everyone!!!

I did my first SAC and got a 70/80 (88%) . I was rank 4 ans was quite surprised with my score (and rank!) as I had not done the last chapter in time for my SAC
However I was curious, can someone tell me their SAC marks and exam marks- ans what overall study score did you get?
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 26, 2017, 10:54:44 am
Hey everyone!!!

I did my first SAC and got a 70/80 (88%) . I was rank 4 ans was quite surprised with my score (and rank!) as I had not done the last chapter in time for my SAC
However I was curious, can someone tell me their SAC marks and exam marks- ans what overall study score did you get?
Its ultimately your exam scores that determind your study scores. I've heard alot of people getting good or bad study scored only to get completley different study scores to what they got in their ss
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on April 30, 2017, 08:56:52 pm
What do I say for 'Which prediction from part d and c is more reliable ?

is it related to intra/extrapolation.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on April 30, 2017, 09:01:03 pm
What do I say for 'Which prediction from part d and c is more reliable ?

is it related to intra/extrapolation.
No, its rekated to the r value which is the correlatin coeffection. A higher r value means its more accurate. The correlation coefficient is a measurement of the strength of a linear relationship which is the x and y axis.

Interpolation and expolation is used to determing weather a data would be considered accurate or not, as iterpolation is predicting values within a data set which means it would be reliable however if its predicts outside a dataset its not accurate and therefore is expolation
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on May 01, 2017, 06:14:59 pm
Can someone help me with this ASAP 
Really dont get it

"In 1990 18.4% of the population in Belarus were obese whereas in 2010 17.1% of the population were obese. Calculate and interpret the residual value when the least square regression line is used to predict the 2010 from 1990. Round to 1 decimal place.

- Have the 1990 and 2010 data sets on my calc

HOW WOULD I GO ABOUT ANSWERSING THIS I DONT GET WHAT IT MEANS???

'interpret the vertical intercept of least square regression line in terms of variables 1990 and 2010"
i have the data for 2010 on 1990 on my calc

Mod Edit [Aaron]: Posts merged. Double posting unjustified.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on May 01, 2017, 06:22:28 pm
Can someone help me with this ASAP 
Really dont get it

"In 1990 18.4% of the population in Belarus were obese whereas in 2010 17.1% of the population were obese. Calculate and interpret the residual value when the least square regression line is used to predict the 2010 from 1990. Round to 1 decimal place.

- Have the 1990 and 2010 data sets on my calc
residual value is the original value - predicted value
In this case the original value is 17.1 since its the orginal value as its stated that the rate is 17.1% in your question
The precdicted value is simply the value when u plug 18.4%'in your regression line
Then just put thoose two vales in the residual equation and you should get the answer

Ps a residual measures the distance between the regression line and the actual corodinates on the graph
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on May 01, 2017, 06:24:29 pm
Can someone help me with this ASAP 
Really dont get it

"In 1990 18.4% of the population in Belarus were obese whereas in 2010 17.1% of the population were obese. Calculate and interpret the residual value when the least square regression line is used to predict the 2010 from 1990. Round to 1 decimal place.

- Have the 1990 and 2010 data sets on my calc

HOW WOULD I GO ABOUT ANSWERSING THIS I DONT GET WHAT IT MEANS???

'interpret the vertical intercept of least square regression line in terms of variables 1990 and 2010"
i have the data for 2010 on 1990 on my calc

Mod Edit [Aaron]: Posts merged. Double posting unjustified.

I had this exact same question on my sac.
so you do
17.1%-(8.1+0.93*18.4%)
=-8.112x-8.1
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on May 01, 2017, 06:28:44 pm
I had this exact same question on my sac.
so you do
17.1%-(8.1+0.93*18.4%)
=-8.112x-8.1
Thank you so much legit lifesaver! dont know of this is too much of a ask but im so lost, what would you say for the interpt part of the question
? thanks again all good if you can't answer xxxx
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on May 01, 2017, 06:29:43 pm
Can someone help me with this ASAP 
Really dont get it

"In 1990 18.4% of the population in Belarus were obese whereas in 2010 17.1% of the population were obese. Calculate and interpret the residual value when the least square regression line is used to predict the 2010 from 1990. Round to 1 decimal place.

- Have the 1990 and 2010 data sets on my calc

HOW WOULD I GO ABOUT ANSWERSING THIS I DONT GET WHAT IT MEANS???

'interpret the vertical intercept of least square regression line in terms of variables 1990 and 2010"
i have the data for 2010 on 1990 on my calc

Mod Edit [Aaron]: Posts merged. Double posting unjustified.
The vertical intercept estimates the average vlaue of the response variable when the explanatory variable equals 0

since you wish to predict the obesity rate in 2010 this is your response rate
Since the obesity rate in 1990 is used to predit the rate of obesity in 2010 this is your explanatory variable

For eg, if rate of obesity in 2010= 7.8 x rate of obesity in 1990 +70
You would just say
The intercept estimates the rate of obesity in 2019 will be 70 when the rate of obesity in 1990 is 0
Just simply locate the 70 and say thats the predicted response variable when the explanatory variable is 0. Of course u have to say what the resonse and explanatory variable is
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on May 01, 2017, 06:30:22 pm
I had this exact same question on my sac.
so you do
17.1%-(8.1+0.93*18.4%)
=-8.112x-8.1
Also where  did you get the 8.1+0.93 bit?
my least sq regression line equation was y=6.24+0.993x
with y being twentyten and x being 1990
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on May 01, 2017, 06:33:04 pm
I had this exact same question on my sac.
so you do
17.1%-(8.1+0.93*18.4%)
=-8.112x-8.1
I had this exact same question on my sac.
so you do
17.1%-(8.1+0.93*18.4%)
=-8.112x-8.1
I dont know what the regression line is since i dont have the data but whatever it is you put the 1990 obesity rate in the x.
As the x means the explanatory variable
And the 1990 obesity rate is used to predict the 2010 obesity rate oddly
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on May 01, 2017, 06:33:43 pm
Also where  did you get the 8.1+0.93 bit?
my least sq regression line equation was y=6.24+0.993x
with y being twentyten and x being 1990

My least squares regression was 8.1+0.93*1990.
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on May 01, 2017, 06:37:14 pm
Thank you so much legit lifesaver! dont know of this is too much of a ask but im so lost, what would you say for the interpt part of the question
? thanks again all good if you can't answer xxxx

The way my teacher interepreted it was 2010 is expected to be 8.1% for a 0% in 1990
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on May 01, 2017, 07:30:16 pm
for working out the vertical intercept i did 17.1%(6.24+0.993x18.4%)
=-7.4
would this be correct?

Also for the residual question i did
original=17.1%
predicted=6.24+0.993(18.4)
=24.5
residual=actual-predicted
=17.1-24.5=-7.4

Got the same answer for both? feel like I've made a mistake somewhere?


---

"Comment on the improvement or otherwise of each of the transformed equations compared to the original equation (y=6.24+0.993x) . Use mathmatical reasoning to support your comments"

Ok so i found that the orginial equation y=6.24+0.993x had a higher r2 value than the others it was 0.800 and th other transformed questions y2=0.57
logx=0.53
and 1/x=0.26

so based on this the orginal is an imporvment but im not sure on the wording or how to explain this?  Anyone know how i would go about it?

Mod Edit [Aaron]: Merged double post again.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on May 02, 2017, 03:55:59 pm
for working out the vertical intercept i did 17.1%(6.24+0.993x18.4%)
=-7.4
would this be correct?

Also for the residual question i did
original=17.1%
predicted=6.24+0.993(18.4)
=24.5
residual=actual-predicted
=17.1-24.5=-7.4

Got the same answer for both? feel like I've made a mistake somewhere?


---

"Comment on the improvement or otherwise of each of the transformed equations compared to the original equation (y=6.24+0.993x) . Use mathmatical reasoning to support your comments"

Ok so i found that the orginial equation y=6.24+0.993x had a higher r2 value than the others it was 0.800 and th other transformed questions y2=0.57
logx=0.53
and 1/x=0.26

so based on this the orginal is an imporvment but im not sure on the wording or how to explain this?  Anyone know how i would go about it?

Mod Edit [Aaron]: Merged double post again.
Whats the original question
Title: Re: VCE Further Maths Question Thread!
Post by: Joseph41 on May 04, 2017, 01:54:36 pm
Welcome to the Further Maths Questions thread!

To post a question or response, you'll first need to make a free ATAR Notes account. It should take about four seconds! Then, simply scroll down to the bottom of this thread and type in the "Quick Reply" box, as shown below!

(http://i.imgur.com/pvuRqvX.png)

Alternatively, feel free to browse 120 pages of previous questions and answers! Navigate the thread with these page number buttons, found at the top and bottom of each page.

(http://i.imgur.com/qRNwZaO.png)

All the best! :)
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on May 07, 2017, 11:33:52 am
Hey guys,
I was wondering whether or not we need to include units when giving residual values?

AND

when we write linear equations do we have to write it in terms of the variables?
as in deseasonalised sales=39 + 23xtime period
or can we just do y=mx+c (if so would we have to first define the variables?)

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on May 07, 2017, 06:57:31 pm
Hey guys,
I was wondering whether or not we need to include units when giving residual values?

AND

when we write linear equations do we have to write it in terms of the variables?
as in deseasonalised sales=39 + 23xtime period
or can we just do y=mx+c (if so would we have to first define the variables?)

thanks

Q1. Depends on your scenario. I tend not to, unless it's a worded question, but you'd best check with your teacher as I'm about 3 years out of date.
Q2. I like to use the first one that you listed, but I believe either is fine as long as the variables are defined. Again, check with your teacher.
Title: Re: VCE Further Maths Question Thread!
Post by: nicnia on May 11, 2017, 05:50:46 pm
This is probably a very dumb question!! But finishing my further sac today and later discussing with my friends left me very worried about this lol

Say I obtain a value of 150.3 and need to round it to 3 significant figures. How would I go about that? I ended up rounding it to 151 but many of my friends rounded it to 150 (which is 2 SF's?), and I took my textbook in too which is what I based it off but some of them told me the textbook itself is wrong. Some rounded it to 150.0 but isn't that 4 SF's?... I ended up asking my physics teacher and he said it seemed odd to round it up to 151.

I'm probably overthinking it but would love a clear answer to this!!
Title: Re: VCE Further Maths Question Thread!
Post by: Frosty_Ryan on May 12, 2017, 10:09:23 pm
Hi,
Could someone help me out with question 11, b (recurrence relations):
Really just need someone to explain how its done... The question is attached below
Thanks a heap xD
Title: Re: VCE Further Maths Question Thread!
Post by: Hungry4Apples on May 13, 2017, 11:50:07 am
Hi,
Could someone help me out with question 11, b (recurrence relations):
Really just need someone to explain how its done... The question is attached below
Thanks a heap xD

So it asks for the first seven terms u0 being the first. You simply sub in the previous u value to find the next. I think where you are getting confused is to do with the n-1 part.
All you need to think about is finding the terms, so for u1, you need to sub in u0, since n=1 so n-1=1-1=0
so the first seven terms are, 6, -5 (-6+1), 6 (--5+1), -5, 6, -5, 6
The pattern repeats because it is -u(n+1), so the negative makes a negative a positive
Same technique applies to part 2
Title: Re: VCE Further Maths Question Thread!
Post by: Frosty_Ryan on May 13, 2017, 03:42:44 pm
So it asks for the first seven terms u0 being the first. You simply sub in the previous u value to find the next. I think where you are getting confused is to do with the n-1 part.
All you need to think about is finding the terms, so for u1, you need to sub in u0, since n=1 so n-1=1-1=0
so the first seven terms are, 6, -5 (-6+1), 6 (--5+1), -5, 6, -5, 6
The pattern repeats because it is -u(n+1), so the negative makes a negative a positive
Same technique applies to part 2

Hi,
 Would you be able to help me with Question 11.B, I understand 11.A completely.
However, no matter what i do it doesn't seem to work out.
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on May 20, 2017, 09:41:39 pm
This is probably a very dumb question!! But finishing my further sac today and later discussing with my friends left me very worried about this lol

Say I obtain a value of 150.3 and need to round it to 3 significant figures. How would I go about that? I ended up rounding it to 151 but many of my friends rounded it to 150 (which is 2 SF's?), and I took my textbook in too which is what I based it off but some of them told me the textbook itself is wrong. Some rounded it to 150.0 but isn't that 4 SF's?... I ended up asking my physics teacher and he said it seemed odd to round it up to 151.

I'm probably overthinking it but would love a clear answer to this!!
This is always the tricky part because the 'rules' of significant figures actually vary a little bit between people, let alone in VCE - and this is one that changes between people. I'd say that would normally be 2 significant figures, but some claim 3 for this. If you don't get the mark for it, it's something that can be argued with your teacher and possibly won. They usually do give a little leniency when it comes down to small things like that, with around 1.0 error either side where rounding errors would've occurred. It'll be best if you ask your teacher whether 150 is 3 significant figures or not. (If I were in the same position, I probably would have written 1.50 x 102 to avoid the issue altogether.)

Hi,
 Would you be able to help me with Question 11.B, I understand 11.A completely.
However, no matter what i do it doesn't seem to work out.
Thanks
Have you tried substituting n=2 and using your value for u1 into the equation? If not, give it a go. The rest may come after you go forwards and backwards with values you know or find out along the way.   

Where can we find the free samples from engage? I cant seem to find them
It's back up and running again, but this time they only have practise exams*. Sorry for that. You can check it out here. Good luck!
If you're keen on getting your hands on a copy of some sample reference pages, I can attach the contents page of mine on to a future post.

* Just realised I've been talking about the wrong company the whole time! It was Connect Education. Due to copyrights, I can't supply it and the website that used to have it has been taken down. I'm terribly sorry to have sent you on a wild goose chase!
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 22, 2017, 11:17:07 pm
This is probably a very dumb question!! But finishing my further sac today and later discussing with my friends left me very worried about this lol

Say I obtain a value of 150.3 and need to round it to 3 significant figures. How would I go about that? I ended up rounding it to 151 but many of my friends rounded it to 150 (which is 2 SF's?), and I took my textbook in too which is what I based it off but some of them told me the textbook itself is wrong. Some rounded it to 150.0 but isn't that 4 SF's?... I ended up asking my physics teacher and he said it seemed odd to round it up to 151.

I'm probably overthinking it but would love a clear answer to this!!
150.3 is rounded to three significant figures by writing 150. The zero in this example is the third significant figure.
It is only when you get to have to round 150.5, 150.6, etc will 3 significant figures give 151
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 22, 2017, 11:23:32 pm
Hi,
 Would you be able to help me with Question 11.B, I understand 11.A completely.
However, no matter what i do it doesn't seem to work out.
Thanks
The recurrence relation in Question 11 B. has got at least two problems as far as the study design is concerned.
First, and significantly, it is not a first-order recurrence relation and so is not within the scope of the Further curriculum.

U(n+1) is two terms beyond U(n-1) and I thinke there is only enough information given to find U(3), U(5), U(7)  etc. The even-numbered terms within the first seven could only be found if a second "initial" term was given given.

Second, and more trivial, the initial term should be written before the rule, not after it, and should usually be U(0) rather than U(1) but someone may have tried to avoid U(n-1) representing a term called U(-1) as a first term.
Title: Re: VCE Further Maths Question Thread!
Post by: mardi on June 03, 2017, 03:51:35 pm
in b), would i include the H0 in the number of iterations?
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 03, 2017, 05:56:31 pm
in b), would i include the H0 in the number of iterations?
Hey Mardi, no you would not
As h0 pretty much means its 0 times if that makes any sense.
Ps im from your school. <3
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on June 04, 2017, 12:43:49 pm
Hey,
I am confused about using rounded and unrounded answers in Further. In the exam, what are we expected to use?
For example, if part a asked for an answer to 2 dp
and then for part b you need to use part a's answer, do we use the rounded or unrounded answer??

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 04, 2017, 12:53:16 pm
Hey,
I am confused about using rounded and unrounded answers in Further. In the exam, what are we expected to use?
For example, if part a asked for an answer to 2 dp
and then for part b you need to use part a's answer, do we use the rounded or unrounded answer??

thanks
Best to use the unrouded to increase accuracy
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on June 04, 2017, 01:43:47 pm
Can anyone show me a example of how they've laid out there boud refernce for chap8/9?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on June 04, 2017, 02:09:52 pm
Hey,
I am confused about using rounded and unrounded answers in Further. In the exam, what are we expected to use?
For example, if part a asked for an answer to 2 dp
and then for part b you need to use part a's answer, do we use the rounded or unrounded answer??

thanks

Hey BlinkieBill, according to the examiner reports for previous years.

All your calculations should be unrounded until you arrive at the final answer.

Rule of thumb: Rounded answers should only be used for the final answer. At no stage should you be rounding during working out, unless it is specifically stated. Always follow what the question is asking.

So ideally, if a question relies on an answer from the previous one.. then you would be using the final answer (the rounded one).

In your specific example, Part A asks for an answer to 2 decimal places. This is a clue to say that this answer should be rounded in the end.

I have answered this question in an older thread. You can see my response here: https://atarnotes.com/forum/index.php?topic=167481.msg899816#msg899816
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 05, 2017, 04:01:35 pm
Hey guys what do i pit in my finace solver for all of question 8 and 9 as i got it wrong

And for the second picture where its chapter 8 review how do i do question 7c
Thank you

(Ps wtf i cant upload thoose 2 pictures cause they are to large apparently)
http://imgur.com/a/a4UsE
Title: Re: VCE Further Maths Question Thread!
Post by: Sirius on June 05, 2017, 09:09:03 pm
Hey guys what do i pit in my finace solver for all of question 8 and 9 as i got it wrong

For 9G, do you mean question 7?
Question 7:
a) N: 60
     I : 6.15
     PV: -25000
    Pmt: -120
    FV: need to be determined = 42378.588
    Ppy and cpy both are 12

b) All same except of Pmt which is now 120 not -120
Question 8: a) N: 120
                          I : 6
                          PV : 0
                          Pmt: -500
                          FV: 81939.67
                          Ppy and cpy 12
b) after ten years
N: 120
I: 6
PV : -81939.67 from previous question
Pmt 500
FV : 67141.10
Ppy and cpy 12

Hope that helps  ;D
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 05, 2017, 09:14:04 pm
For 9G, do you mean question 7?
Question 7:
a) N: 60
     I : 6.15
     PV: -25000
    Pmt: -120
    FV: need to be determined = 42378.588
    Ppy and cpy both are 12

b) All same except of Pmt which is now 120 not -120
Question 8: a) N: 120
                          I : 6
                          PV : 0
                          Pmt: -500
                          FV: 81939.67
                          Ppy and cpy 12
b) after ten years
N: 120
I: 6
PV : -81939.67 from previous question
Pmt 500
FV : 67141.10
Ppy and cpy 12

Hope that helps  ;D

Thank you Siruis black!
Nah i got question 7 right originally right sorry
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 05, 2017, 09:25:37 pm
Hey could u answer theese questions (my teacher isnt responding and i have my sac tomorow :(
http://imgur.com/a/NKJcG
For the first picture, how do i do 9 and 10
For the second pic, how do i do 2b
For the third pic, how do i do 3d ii
And for the last pic how do i gp question 3
Title: Re: VCE Further Maths Question Thread!
Post by: Sirius on June 05, 2017, 09:28:14 pm
And for the second picture where its chapter 8 review how do i do question 7c
Thank you

No worries.  :)
For chapter 8 review question:
c) You can convert the equation from part a to find the nth term of the sequence
Vn  = Rn * V0
Therefore V 12 = 1.0056712 * 30000
                                              =  $32104.80
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on June 05, 2017, 09:40:43 pm
Hey guys what do i pit in my finace solver for all of question 8 and 9 as i got it wrong

And for the second picture where its chapter 8 review how do i do question 7c
Thank you

(Ps wtf i cant upload thoose 2 pictures cause they are to large apparently)
http://imgur.com/a/a4UsE


Okay Hun,
Financial modelling can be daunting, but it's simple:
So for question 7c this is how you would do it:
You can either keep putting the recurrence relation into your calculator 12 times until you get the answer, however this would be time-consuming and opens the doors for error. An easier way to do this would be: using the nth term rule : Vn+1= (1+R/100)^n * Vo ( if you can't understand this formula, it is on page 286 on your textbook under COMPOUND INTEREST LOANS AND INVESTMENT)
Then, it's simple, you substitute the values : Vn + (1+ 6.8/12/100)^12* 30000
And you will end up with :$ 32104.80.  For this question I think you're a bit confused you don't use the finance solver, just use the nth term

If you are referring to the 7d, then you would use the finance solver for that one and this is how you would do it:

N: 18 (compounded for 18 months)
I(%): 6.8
PV: 30000 (initial amount that we loaned, remember it's positive because we borrowed it)
Pmt:0
FV: ? (this is what we want to find out)
Ppy/Cpy: 12

And when you press enter, voila!! you get your answer :$ 33211.94

Title: Re: VCE Further Maths Question Thread!
Post by: Sirius on June 05, 2017, 09:42:05 pm
Hey could u answer theese questions
For the first picture, how do i do 9 and 10

Question 9: Find equation in the nth term
so V0= unknown
R= (1+ (11.65/2)/100) = 1.05825 and V42= $2529.14
Therefore 2529.14 = 1.05842 * V0
By algebra V0 = $234.566
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 05, 2017, 09:43:00 pm

Okay Hun,
Financial modelling can be daunting, but it's simple:
So for question 7c this is how you would do it:
You can either keep putting the recurrence relation into your calculator 12 times until you get the answer, however this would be time-consuming and opens the doors for error. An easier way to do this would be: using the nth term rule : Vn+1= (1+R/100)^n * Vo ( if you can't understand this formula, it is on page 286 on your textbook under COMPOUND INTEREST LOANS AND INVESTMENT)
Then, it's simple, you substitute the values : Vn + (1+ 6.8/12/100)^12* 30000
And you will end up with :$ 32104.80.  For this question I think you're a bit confused you don't use the finance solver, just use the nth term

If you are referring to the 7d, then you would use the finance solver for that one and this is how you would do it:

N: 18 (compounded for 18 months)
I(%): 6.8
PV: 30000 (initial amount that we loaned, remember it's positive because we borrowed it)
Pmt:0
FV: ? (this is what we want to find out)
Yeah i got it
Thanks 'hun'!!
Its the hardest further topic so far
Ppy/Cpy: 12

And when you press enter, voila!! you get your answer :$ 33211.94


Yeah i got it. Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: Sirius on June 05, 2017, 09:57:04 pm
Hey could u answer theese questions (my teacher isnt responding and i have my sac tomorow :(
http://imgur.com/a/NKJcG
For the first picture, how do i do 9 and 10
Question 10

Solve (19282.65 = R8 * 18000)
You get R = 1.00864 and R = 1 + (r/4)/100
1+ ( r/4)/100 = 1.00864
And solve this and you get r = 3.456
Title: Re: VCE Further Maths Question Thread!
Post by: Sirius on June 05, 2017, 10:09:38 pm
For the second pic, how do i do 2b

I hope you understand  :)
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 06, 2017, 10:44:05 am
Question 10

Solve (19282.65 = R8 * 18000)
You get R = 1.00864 and R = 1 + (r/4)/100

And solve this and you get r = 3.456
Why do u do 1+(r/4)/100=1.00864

I hope you understand  :)
Thank you sirius black


Mod Edit: Double post merged.... again
Title: Re: VCE Further Maths Question Thread!
Post by: Sirius on June 06, 2017, 02:16:31 pm
Why do u do 1+(r/4)/100=1.00864

Sorry for the late reply but as R is equal to 1+ (interest rate/compounding periods)/100.
To find the interest rate I used the R  value (1.00864) and solved the equation.
Let me know if you don't catch on. Sorry if this caused any confusion. There may be more than one way you can solve this!.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on June 07, 2017, 06:16:50 pm
Hey,
I am confused about using rounded and unrounded answers in Further. In the exam, what are we expected to use?
For example, if part a asked for an answer to 2 dp
and then for part b you need to use part a's answer, do we use the rounded or unrounded answer??

thanks
At a meeting with assessors this year, we were told that the correct answer will be the same either way. But they suggest the previous answer, rounded as required in that question, is the better option to use.
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on June 11, 2017, 12:45:17 pm
Hey, for the Core Data Analysis section, I was wondering whether or not a distribution has to be perfectly symmetrical to describe it as symmetrical in the exam?
And if something is reasonably symmetrical, but not perfectly, could you say it was slightly positively/negatively skewed?
Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: TFAnime123 on June 11, 2017, 03:32:06 pm
Hey all,
Can someone help me with this question?

The seasonal indices for the number of bathing suits sold at a surf shop are given in the
table.
Quarter:            Summer  Autumn     Winter     Spring
Seasonal index: 1.8             0.4           0.3          1.5

12. To correct for seasonality, the actual number of bathing suits sold in Autumn
should be:
A) reduced by 60%
B) reduced by 40%
C) increased by 40%
D) increased by 60%
E) increased by 250%

I'm not too sure if the textbook has a typo, but I seem to get 'increased by 150%'
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on June 11, 2017, 04:09:45 pm
Hey, for the Core Data Analysis section, I was wondering whether or not a distribution has to be perfectly symmetrical to describe it as symmetrical in the exam?
And if something is reasonably symmetrical, but not perfectly, could you say it was slightly positively/negatively skewed?
Thanks.
I think I remember that it doesn't necessarily have to be perfectly symmetrical to say that it is, although it is best to err on the side of caution and say that it is slightly positively/ negatively skewed as the case may be. Generally past papers have been reasonably clear as to whether they're looking for slightly skewed or symmetrical.

Hey all,
Can someone help me with this question?

The seasonal indices for the number of bathing suits sold at a surf shop are given in the
table.
Quarter:            Summer  Autumn     Winter     Spring
Seasonal index: 1.8             0.4           0.3          1.5

12. To correct for seasonality, the actual number of bathing suits sold in Autumn
should be:
A) reduced by 60%
B) reduced by 40%
C) increased by 40%
D) increased by 60%
E) increased by 250%

I'm not too sure if the textbook has a typo, but I seem to get 'increased by 150%'
It looks like you're right in this case and that's just a typo. (Then again, I just glimpsed this for a second.)
I don't have the time to properly link you to my previous post way back when I did a similar exam question (VCAA Exam 1 2011 Core Q11), but search through my many posts to find it and it'll show you a similar method to check your answer.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 12, 2017, 01:10:57 pm
Hey guys, how do i do the lastt question
I dont know the concept
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on June 12, 2017, 05:25:56 pm
Hey guys, how do i do the lastt question
I dont know the concept

This requires you to know how the mean and standard deviation are calculated.
Do you remember how to...
...calculate a mean?
You can do so by taking the sum of all the data and then dividing by the number of data pieces (samples).
...calculate a standard deviation?
To calculate a standard deviation, you must take the variance of the data (so the data variation, or how far one single data point is away from the mean) and then take its square root. You can search the true formula, involving the sum of squares if you'd like the whole statistics story there or the entire formula if you want, but all you need to really know is that standard deviation is the spread of data and that's where the normal distribution comes from (it assumes your data is normal or close to it).

Working out + Answer
From this, you can tell that by changing the points directly, you'll definitely be influencing the mean - and, if you read the question correctly, say that the stakes are reduced by 5 cm - so you know that the mean will likely also go down 5 cm. This cuts out options B and E automatically.

Then we need to know if the standard deviation will change. The spread will not move if the points are directly changed. That's because it is according to the position of the mean, rather than the points themselves; all the points will change, so the mean changes, but how far each point from the mean is, will not. (PM me if this isn't an adequate explanation for you... I'll be back regularly in about a week - after my exams are over.)

Summary: mean - will change, standard deviation - will not change.
The correct option should be option C.
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on June 12, 2017, 09:28:07 pm
This requires you to know how the mean and standard deviation are calculated.
Do you remember how to...
...calculate a mean?
You can do so by taking the sum of all the data and then dividing by the number of data pieces (samples).
...calculate a standard deviation?
To calculate a standard deviation, you must take the variance of the data (so the data variation, or how far one single data point is away from the mean) and then take its square root. You can search the true formula, involving the sum of squares if you'd like the whole statistics story there or the entire formula if you want, but all you need to really know is that standard deviation is the spread of data and that's where the normal distribution comes from (it assumes your data is normal or close to it).

Working out + Answer
From this, you can tell that by changing the points directly, you'll definitely be influencing the mean - and, if you read the question correctly, say that the stakes are reduced by 5 cm - so you know that the mean will likely also go down 5 cm. This cuts out options B and E automatically.

Then we need to know if the standard deviation will change. The spread will not move if the points are directly changed. That's because it is according to the position of the mean, rather than the points themselves; all the points will change, so the mean changes, but how far each point from the mean is, will not. (PM me if this isn't an adequate explanation for you... I'll be back regularly in about a week - after my exams are over.)

Summary: mean - will change, standard deviation - will not change.
The correct option should be option C.
I dont get why standard deviation doesnt change, i just accept that it just doesnt.

The spread will not move if the points are directly changed. That's because it is according to the position of the mean,
Not to sure about that, is that because the ratio of the other points to the mean stay the same?

Not to sure what sd is :/
Thank you so much! :)
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on June 14, 2017, 06:44:32 pm
Math sac tomorrow and im kind of freaking out. I have done the chapters (8,9) and the practice sac and have made my notes for chap 9 but not 8 yet. Has anyone done the financial math sac yet and if so how was it? and tips
Title: Re: VCE Further Maths Question Thread!
Post by: Sirius on June 14, 2017, 09:19:44 pm
Math sac tomorrow and im kind of freaking out. I have done the chapters (8,9) and the practice sac and have made my notes for chap 9 but not 8 yet. Has anyone done the financial math sac yet and if so how was it? and tips

Hey Pmmenotes,
I completed my financial math Sac recently. I personally used my textbook rather than my notes as this is what I was confident with. But you can equally use your own notes. Whatever works best for you!  :)
Some Tips:
- Include a lot of example questions in your notes: As you are making your notes I would highly recommend chucking in questions you found difficult so that you can refer back to them if you are stuck. For my sac I came to a question that I was completely stuck on and did not know how to solve. In vain hope I was flipping through my textbook and to my utter surprise I found a very similar worked example question (coincidence? Maybe :P). Moral of the story: Include a fair amount of examples in your notes.
-Know your equations/formulas: In financial maths there are a heaps of different equations for different loans and investments and whatnot (depreciation, annuities, perpetuity etc.), therefore it is highly important to know which one of these the question is asking you to apply. Whether the question is asking for a reducing balance loan or a interest only loan know these equations and when to use them. It is really not that difficult, you will have these in your notes anyways. Just try not to confuse them as much as I do! ;)
-[During the SAC] Read the question twice and highlight important parts: Sometimes what I tend to do is answer the question partly (especially when it has two or more sections) or misread it and supply my answer to 3 decimal places when it clearly asked to 2 d.p. You can use other techniques to overcome this problem such as check all answers at the end of the SAC etc. This is just a general tip yet I always fall for it.  :'(

Last thing, walk into that room with confidence and please don't be scared. Being calm and collected would lead to less errors in the SAC. Therefore be confident in your abilities and give it your best shot tomorrow and you will do great :D .
Hope this has helped you a little. And good luck for your sac :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on June 15, 2017, 05:36:39 pm
I dont get why standard deviation doesnt change, i just accept that it just doesnt.

The spread will not move if the points are directly changed. That's because it is according to the position of the mean,
Not to sure about that, is that because the ratio of the other points to the mean stay the same?

Not to sure what sd is :/
Thank you so much! :)

It takes a lot more explaining than the time I have now, but I'd be happy to come back at the end of next week to discuss this if you wish. I currently am on exams (2 down, 3 more to go) and right now on a study break, so I'll come back to this soon. Pop me a PM to remind me if I forget, please. Sorry about the delay!
However, you can kind of say that the ratio remains the same. I guess that's one way you can think of it.

Math sac tomorrow and im kind of freaking out. I have done the chapters (8,9) and the practice sac and have made my notes for chap 9 but not 8 yet. Has anyone done the financial math sac yet and if so how was it? and tips
Sorry I didn't see this earlier; had a killer exam this morning! Sirius has a great answer, but I thought I'd add my two cents, despite not doing financial maths since Year 9 maths (it wasn't part of Core until last year).
Each school has a different SAC, although they should remain close to the exam, so ideally, you should've been doing practise questions from either VCAA or a company paper and writing your cheat sheet up in a way you understand it most.
For financial maths, I would highly recommend that you try some of the old Sequences & Series (old module 1) and see if you can do those. They are pretty similar in structure and format. At a glance, it also seems to be mostly a matter of deriving the correct equation, knowing the patterns and inputting the correct function into your calculator.
Hopefully that helps for your next SAC or the exams.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on June 17, 2017, 12:10:15 am
-Know your equations/formulas: In financial maths there are a heaps of different equations for different loans and investments and whatnot (depreciation, annuities, perpetuity etc.), therefore it is highly important to know which one of these the question is asking you to apply. Whether the question is asking for a reducing balance loan or a interest only loan know these equations and when to use them. It is really not that difficult, you will have these in your notes anyways. Just try not to confuse them as much as I do! ;)

I cannot agree that there are heaps of equations and formulas in the current Further financial curriculum. There is only the compound interest formula along with basic percentage calculations to solve simple loan, investment and depreciation problems. You do not need any other financial formula.
I think the main focus is on understanding the growth or decay of the balances of the types loan, investment and depreciation defined in the study design. Recurrence relations and amortisation tables can illustrate how and why these balances change. Once pure compound growth or decay is identified, the compound interest formula may then be used. You could also use a financial solver app on the calculator here as well.
A more complex problem can include a regular payment or withdrawal, as well as compounding growth. For such problems, the compound interest formula is not appropriate and the financial solver app should be used.
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on June 17, 2017, 12:35:10 pm
Hello everyone

I was just wondering, does any one have to answers to the NELSON further math Book (chapter on matrices?)

Please, it would really help me because I would like to know if I got them right
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on June 22, 2017, 10:24:27 pm
I dont get why standard deviation doesnt change, i just accept that it just doesnt.
The spread will not move if the points are directly changed. That's because it is according to the position of the mean,
Not to sure about that, is that because the ratio of the other points to the mean stay the same?
Not to sure what sd is :/
Thank you so much! :)
It takes a lot more explaining than the time I have now, but I'd be happy to come back at the end of next week to discuss this if you wish. I currently am on exams (2 down, 3 more to go) and right now on a study break, so I'll come back to this soon.
However, you can kind of say that the ratio remains the same. I guess that's one way you can think of it.
I'm back after a wild 36 hours the day before yesterday (had to deal with some Semester 2 stuff yesterday). I've attached a PDF document below for you guys to read. You'll need Adobe Reader to view it. If anyone has any troubles understanding it, feel free to PM me. 
Title: Re: VCE Further Maths Question Thread!
Post by: danfer073 on July 03, 2017, 09:24:32 pm
(http://uploads.tapatalk-cdn.com/20170703/057066504183d73932b6dba4f2e6dbb2.jpg)
Please can you help me work out part C

Mod edit: Merged with Further Maths Q&A
Title: Re: VCE Further Maths Question Thread!
Post by: Jackie Chan on July 03, 2017, 09:53:22 pm
(http://uploads.tapatalk-cdn.com/20170703/057066504183d73932b6dba4f2e6dbb2.jpg)
Please can you help me work out part C

Mod edit: Merged with Further Maths Q&A

Hi!
For part c, you need to use the rule for simple interest investments/loans:
Vn = V0 + n x r/100 x V0

So with this in mind, the question asks for the interest rate that company A needs to offer if after 5 years, both investments are worth $6722.75 (answer from part b, which is the amount Meghan will get if she invests her money with company B)

So:
solve (6722.75= 5000 + 5 x r/100 x 5000,r) on your CAS to get 6.891 = 6.9%
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on July 14, 2017, 07:46:46 pm
http://imgur.com/a/P0CCe
Hi, for question 321 B wht do i draw 2x on tthe graph
And how do i do ei and ii
Title: Re: VCE Further Maths Question Thread!
Post by: pmmenotes on July 23, 2017, 11:33:40 am
Hey guys my bound reference is two books sticky taped together do you thinks thats alright my teacher said he didnt know.
Title: Re: VCE Further Maths Question Thread!
Post by: brady_price on July 23, 2017, 11:50:53 am
Hey guys my bound reference is two books sticky taped together do you thinks thats alright my teacher said he didnt know.

Hey!

Depends what you mean by sticky taped. You are allowed to combine books for your bound reference, but they must adhere to the VCAA guidelines. See if your school (try the library perhaps?) has a heavy duty stapler, and get them to staple the spines of the books together (this can be done, trust me, my school did it for me), and then use some intense heavy duty tape to cover the spines. Basically, the books have to "become one", the guidelines specify that there has to be a "single spine", which basically means you can heavy duty tape along the spines and you're fine, so long as the books cannot come apart.

Here's the link to the guidelines (scroll down to "Mathematics examinations: use of bound references")
http://www.vcaa.vic.edu.au/Pages/vce/exams/authorisedmaterials.aspx#bound

Good luck!
Title: Re: VCE Further Maths Question Thread!
Post by: Shadowxo on July 23, 2017, 01:43:11 pm
http://imgur.com/a/P0CCe
Hi, for question 321 B wht do i draw 2x on tthe graph
And how do i do ei and ii

Hi, sorry this reply is so late. I don't do further but I'll see if I can help :)
So for 321.b), the number of dogs clipped is at least 2* number of dogs washed
So y ≥ 2*x
You'd have to draw the line y=2x and since it's a greater than or equal sign, it'd be the area above this line.

Profit = 40x + 30y
e)(i) I'm not sure if they expect you to work it out mathematically as it's only worth 1 mark per part. Profit from one dog washed is more than a clipped dog. This means one x is worth more than one y. Also, x and y have to be whole numbers. So, I believe you could either use the graph or guess-and-check. As washing a dog is both faster and gives more money, you want the largest x value. Using the graph (from VCAA answers) the largest x value within the bounds is 2, and for an x value of 2 the largest y value is 6.
Alternatively, you can start with the maximum number of dogs clipped which is 8, and decrease number of clips by one and increase number of washes by one (they take similar time to complete, so doing this just a few times is easy). 2 washes and 6 clips is the highest number of washes possible, and 6 clips is the highest number of clips with 2 washes. (clips ≥ 2*washes)
This question's more interpreting from the graph rather than solving it.
e)(ii) Just sub in these values.

Sorry my answer's not more concise (and a bit late) but hope this helps anyway :)
Title: Re: VCE Further Maths Question Thread!
Post by: Melody_Zhou66 on August 09, 2017, 09:45:23 pm
Hello! I'm new to this page:

My question is what are the recommended modules to complete for the end of year exam this year?

Any tips for summary books/bound references?

Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on August 09, 2017, 09:47:29 pm
Quote
My question is what are the recommended modules to complete for the end of year exam this year?
Complete the ones you have done as a cohort at your school. In my opinion it is not worth it to try and be adventurous and try a module you have not had extensive experience with.

Quote
Any tips for summary books/bound references?
Don't make it too lengthy, don't bring in a textbook. You have 90 minutes per exam.... and when you consider the amount of questions, it isn't much time per. You have to know *exactly* where to find certain points if you have to use your reference at any point.
Title: Re: VCE Further Maths Question Thread!
Post by: DanicaG17 on August 15, 2017, 06:09:47 pm
Hey... just a question that kinda need help on...
The rectangular prism shown has a volume of 12.8cm3. A second rectangular prism is made with half length, 4 times height and 2 times width. the volume of the second prism is???
Anyone able to help???
Title: Re: VCE Further Maths Question Thread!
Post by: Shadowxo on August 15, 2017, 06:17:26 pm
Hey... just a question that kinda need help on...
The rectangular prism shown has a volume of 12.8cm3. A second rectangular prism is made with half length, 4 times height and 2 times width. the volume of the second prism is???
Anyone able to help???
So we know the volume of a rectangular prism is L*W*H
Let Vi = volume of the initial prism, Li be the length of the initial prism etc. V2 is the volume of the second prism
Vi=Li*Wi*Hi
V2 = 1/2 *Li*2*Wi *4*Hi* = 4*Li*Wi*Hi = 4Vi
So it's just 4*12.8

If you want to do it quicker just divide by 2, multiply by 4 and multiply by 2 (earlier typo).
Title: Re: VCE Further Maths Question Thread!
Post by: DanicaG17 on August 15, 2017, 08:55:33 pm
So we know the volume of a rectangular prism is L*W*H
Let Vi = volume of the initial prism, Li be the length of the initial prism etc. V2 is the volume of the second prism
Vi=Li*Wi*Hi
V2 = 1/2 *Li*2*Wi *4*Hi* = 4*Li*Wi*Hi = 4Vi
So it's just 4*12.8

If you want to do it quicker just divide by 2, multiply by 4 and multiply by 4.
So we know the volume of a rectangular prism is L*W*H
Let Vi = volume of the initial prism, Li be the length of the initial prism etc. V2 is the volume of the second prism
Vi=Li*Wi*Hi
V2 = 1/2 *Li*2*Wi *4*Hi* = 4*Li*Wi*Hi = 4Vi
So it's just 4*12.8

If you want to do it quicker just divide by 2, multiply by 4 and multiply by 4.

Thanks heaps!!
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on August 23, 2017, 06:04:04 pm
Hey,

Would appreciate it if someone could help me answer Question 4 d) from the following attachment. I have attached the whole extended response question for context.

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: addictwithatextbook on August 26, 2017, 11:30:25 am
Hello, this is my first ever post on AtarNotes :) I don't know if this question has been asked yet, but in
Can somebody tell me how activity H has a float time of 2 days, as it says in the examination report? I can only see it having a float time of 1 day.

Thanks in advance.
Title: Re: VCE Further Maths Question Thread!
Post by: plato on August 26, 2017, 09:06:45 pm
The critical path is AEIJ and is 15 days long.
The path CGJM is 14 days and so each of these activities has a float time of one.
The path CHM is 13 days which means H must have a float of two because C and M are known to have a float of one from above.
Title: Re: VCE Further Maths Question Thread!
Post by: addictwithatextbook on August 29, 2017, 03:40:02 pm
The critical path is AEIJ and is 15 days long.
The path CGJM is 14 days and so each of these activities has a float time of one.
The path CHM is 13 days which means H must have a float of two because C and M are known to have a float of one from above.

Thanks heaps, plato!  :D
Title: Re: VCE Further Maths Question Thread!
Post by: merryn_hall on September 02, 2017, 05:23:58 pm
Can someone please explain a foolproof way to do Hungarian algorithm
 :) :) :) :) :) :)
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on September 17, 2017, 08:19:06 pm
Pls help, my sac is in 2 days
https://imgur.com/a/ysHVu
Not sure how to do q15
Title: Re: VCE Further Maths Question Thread!
Post by: Peter Griffin on September 20, 2017, 11:48:51 am
Pls help, my sac is in 2 days
https://imgur.com/a/ysHVu
Not sure how to do q15


I need the full image of the graph to help you with that question..
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on September 30, 2017, 11:48:18 am
hey guys,


I was just doing a question that required me to find 22.3% of 5170000. However when a get my answer it says 1.15291E6. What does the E mean????
Title: Re: VCE Further Maths Question Thread!
Post by: www on September 30, 2017, 12:16:12 pm
hey guys,


I was just doing a question that required me to find 22.3% of 5170000. However when a get my answer it says 1.15291E6. What does the E mean????

Think of the E as 10 to the power of X, where X is the number after it - so E6 would be 10^6.

1.15291E6 means to multiply 1.15291 and 10^6 (in other words, move the decimal point 6 times to the right), which gives you 1152910!
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on September 30, 2017, 09:05:09 pm
Think of the E as 10 to the power of X, where X is the number after it - so E6 would be 10^6.

1.15291E6 means to multiply 1.15291 and 10^6 (in other words, move the decimal point 6 times to the right), which gives you 1152910!

ohhhhh I get it. Thanks so much [that was the correct answer on the practice test I was doing btw]
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on October 05, 2017, 05:51:31 pm
https://imgur.com/a/oeEBU
Hey guys just some questions in that link, i wrote it on the paper except on c annd d, how do i do that
Title: Re: VCE Further Maths Question Thread!
Post by: EEEEEEP on October 05, 2017, 06:01:37 pm
https://imgur.com/a/oeEBU
Hey guys just some questions in that link, i wrote it on the paper except on c annd d, how do i do that
250, 000 x 1.005 = 251250 - Value before withdrawl
THUS
Interest = 250k - 250.1250K = 1250 =)

Title: Re: VCE Further Maths Question Thread!
Post by: Shadowxo on October 06, 2017, 10:11:34 am
https://imgur.com/a/oeEBU
Hey guys just some questions in that link, i wrote it on the paper except on c annd d, how do i do that
I'll answer a couple more questions for you :)
4. It looks like you need to go over sequences. a) If tn+1=3tn-4, then you know the value of a term is the 3*(previous term) -4. So t1=3*t0-4 = 3*2 -4=6-4 = 2 which is the same as t0. So every term in the sequence is the same, which is unusual because they often change (for 1 mark I imagine you'd only need to say it's unusual because every term is 2).
b) it's actually the Fibonacci sequence with some different starting terms (but you don't need to know that). You should be able to see from the rule that a term is equal to the previous term + the term before that, ie the sum of the past 2 terms. So the sequence goes 3, 4, 3+4=7, 7+4=11, 11+7=18 etc ie 3,4,7,11,18.

For 6d (depreciation)
Method 1: It starts off at 150000 and decreases by 15% of the original price per year. So decreases by 0.15*150000= 22500 per year
So the value is 150000-22500*n
Method 2: The value reduces by 20% per year. So initial value is 150000, value after a year is 0.8*150000, value after two years is 0.8*0.8*150000. You were on the right track.
Value is initial value * 0.8n = 0.8n * 150000
Title: Re: VCE Further Maths Question Thread!
Post by: TheCommando on October 06, 2017, 05:04:58 pm
250, 000 x 1.005 = 251250 - Value before withdrawl
THUS
Interest = 250k - 250.1250K = 1250 =)

Thank you! that make sense
its just that the solutions were literally just answers and didnt explain much
I'll answer a couple more questions for you :)
4. It looks like you need to go over sequences. a) If tn+1=3tn-4, then you know the value of a term is the 3*(previous term) -4. So t1=3*t0-4 = 3*2 -4=6-4 = 2 which is the same as t0. So every term in the sequence is the same, which is unusual because they often change (for 1 mark I imagine you'd only need to say it's unusual because every term is 2).
b) it's actually the Fibonacci sequence with some different starting terms (but you don't need to know that). You should be able to see from the rule that a term is equal to the previous term + the term before that, ie the sum of the past 2 terms. So the sequence goes 3, 4, 3+4=7, 7+4=11, 11+7=18 etc ie 3,4,7,11,18.

For 6d (depreciation)
Method 1: It starts off at 150000 and decreases by 15% of the original price per year. So decreases by 0.15*150000= 22500 per year
So the value is 150000-22500*n
Method 2: The value reduces by 20% per year. So initial value is 150000, value after a year is 0.8*150000, value after two years is 0.8*0.8*150000. You were on the right track.
Value is initial value * 0.8n = 0.8n * 150000
Thank you so much! Super helpful!!
Title: Re: VCE Further Maths Question Thread!
Post by: ImmaculateJeff on October 06, 2017, 05:28:41 pm
Pls help, my sac is in 2 days
https://imgur.com/a/ysHVu
Not sure how to do q15

It is C because none of the numbers can connect to themselves which D shows
Title: Re: VCE Further Maths Question Thread!
Post by: Angelx001 on October 07, 2017, 07:54:53 pm
On the CAS, is 'finance solver' ONLY for compound interest (i.e. not simple interest)?
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on October 07, 2017, 09:48:30 pm
Think of the E as 10 to the power of X, where X is the number after it - so E6 would be 10^6.

1.15291E6 means to multiply 1.15291 and 10^6 (in other words, move the decimal point 6 times to the right), which gives you 1152910!

Okay, I know what the annoying E' means on the calculator, but is there any way to get rid of it? Because my answers for the extended response are always wrong when I divide huge numbers [mainly because of that annoying E']
Title: Re: VCE Further Maths Question Thread!
Post by: zofromuxo on October 07, 2017, 09:53:58 pm
On the CAS, is 'finance solver' ONLY for compound interest (i.e. not simple interest)?

By CAS, I'm assuming Classpad II model.
You can use simple interest with finanical solver by clearing the going into Edit => Clear All => Ok
It will then take you to the main menu, where you should see Simple Interest as the first choice on the list.
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on October 07, 2017, 09:57:27 pm
How to I know if I should use the formula for simple interest or the finance solver?

because I was doing a past exam and I got the answer completely wrong cause I used the formula and not he finance solver
Title: Re: VCE Further Maths Question Thread!
Post by: zofromuxo on October 07, 2017, 10:05:51 pm
How to I know if I should use the formula for simple interest or the finance solver?

because I was doing a past exam and I got the answer completely wrong cause I used the formula and not he finance solver
The finance solver for the simple interest page is the same as the formula instead on the finanical solver your inputting what it is asking you.
That being said, if you find the formula easier to use then do that as opposed to the financial solver.

This was a common thread of discussion when this study design came out was whether to use Financial solver for simple interest questions or just use the formula. It all came down to what you personally feel comfortable with.

Also you shouldn't get the question right If you used the financial solver as opposed to the formula. They should both give you the correct answer.
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on October 07, 2017, 11:36:43 pm
The finance solver for the simple interest page is the same as the formula instead on the finanical solver your inputting what it is asking you.
That being said, if you find the formula easier to use then do that as opposed to the financial solver.

This was a common thread of discussion when this study design came out was whether to use Financial solver for simple interest questions or just use the formula. It all came down to what you personally feel comfortable with.

Also you shouldn't get the question right If you used the financial solver as opposed to the formula. They should both give you the correct answer.


Damn, I made  a typo, I meant to ask in relation to compound interest not simple interest. [so how do I know if I use the finance solver or the equation for COMPOUND INTEREST?]
Title: Re: VCE Further Maths Question Thread!
Post by: zofromuxo on October 08, 2017, 07:56:41 am

Damn, I made  a typo, I meant to ask in relation to compound interest not simple interest. [so how do I know if I use the finance solver or the equation for COMPOUND INTEREST?]
It would be the same thing as I mentioned for simple interest, do what is comfortable .
I had a Year 11 student, who refused to use financial solver because they didn't understand how to use it at all.

But I personally use Financial solver because it helps tell me what information the question gives me and therefore what information I require to get the solution the question is asking me for. 
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on October 11, 2017, 08:17:17 pm
Hey people,

Where the hell can I find the solutions to the FM 2017 exams for the northern hemisphere, I cant seem to find them ANYWHERE and I'm starting to get a BIT JUST A BIT annoyed.
Title: Re: VCE Further Maths Question Thread!
Post by: mtDNA on October 11, 2017, 08:22:55 pm
Hey people,

Where the hell can I find the solutions to the FM 2017 exams for the northern hemisphere, I cant seem to find them ANYWHERE and I'm starting to get a BIT JUST A BIT annoyed.

I’m not sure if there are any answers listed on the website, so perhaps just ask your teacher if they’d be happy to write up some solutions/mark your paper (I’m sure they’d be happy to do it).
Title: Re: VCE Further Maths Question Thread!
Post by: kimtran99 on October 12, 2017, 08:00:49 pm
hey guys,
i need help on graphs and relations , i cant seem to understand it whatsoever
is there any tips you guys could give me??
Title: Re: VCE Further Maths Question Thread!
Post by: MightyBeh on October 12, 2017, 09:26:18 pm
hey guys,
i need help on graphs and relations , i cant seem to understand it whatsoever
is there any tips you guys could give me??
If it really is everything that you get stuck on, I'd suggest you go back through that section of your textbook thoroughly. Khan Academy is also a good resource for learning the content, I'm pretty sure most of the stuff from graphs and relations fits into algebra 1 and algebra 2. You're probably better off using it in companion to your textbook and just searching for the relevant bits and pieces as you need it though, because there's a lot of irrelevant stuff in there.

I can't really give you advice based on the whole module but if you were to mention specific topics you were struggling with I'm sure I could come up with some stuff. :)
Title: Re: VCE Further Maths Question Thread!
Post by: plato on October 13, 2017, 02:42:49 pm
Hey people,

Where the hell can I find the solutions to the FM 2017 exams for the northern hemisphere, I cant seem to find them ANYWHERE and I'm starting to get a BIT JUST A BIT annoyed.
You can find the exams and reports at:
http://www.vcaa.vic.edu.au/Pages/vce/nht/resources.aspx
Title: Re: VCE Further Maths Question Thread!
Post by: Bob2468 on October 15, 2017, 04:37:51 pm
In the exam, do I have to show working out for one mark questions?

Thanks in adavance
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 15, 2017, 04:44:02 pm
In the exam, do I have to show working out for one mark questions?

Thanks in adavance
Not that I know of, however, it is probably in your best interest to write down one line of quick calculation to show where it came from in case people get picky or you accidentally get it wrong somehow.
Title: Re: VCE Further Maths Question Thread!
Post by: mtDNA on October 16, 2017, 11:26:47 pm
In the exam, do I have to show working out for one mark questions?

Thanks in adavance

They will still award full marks, but there is a higher chance of making a silly mistake by not putting pen to paper
Title: Re: VCE Further Maths Question Thread!
Post by: crackleking on October 18, 2017, 07:51:31 pm
Do you think you have to know population statistics and correlation and causality as it's in the study design and I haven't seen it on past vcaa exams before?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 18, 2017, 07:59:38 pm
Do you think you have to know population statistics and correlation and causality as it's in the study design and I haven't seen it on past vcaa exams before?
Population statistics? Maybe not, but definitely correlation and causality. Both of those have been indirectly or directly in exams before, so keep it in your mind! :)  (Ideally, I'd put all of this in your bound reference as a "just in case" situation.)
Title: Re: VCE Further Maths Question Thread!
Post by: Ashjames on October 21, 2017, 07:40:58 pm
out of curiosity, how many marks can you drop on both exams for FM to be guaranteed a 40+
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinaB19 on October 21, 2017, 09:13:33 pm
What's the most reliable way of distinguishing between a random fluctuation and seasonality when analysing a time series?
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on October 22, 2017, 07:04:27 pm
Hey guys, I can't seem to understand why that's the answer. Why is my answer unacceptable?
Title: Re: VCE Further Maths Question Thread!
Post by: Sine on October 22, 2017, 07:21:23 pm
Hey guys, I can't seem to understand why that's the answer. Why is my answer unacceptable?
I've never done further but i'll try to help :)

the first 60 tanks sell for 500
then tank 61,62,63...,150 sell for 700
The end point (60,30000) you have from the 60 tanks should be the start point for the second line (the line where each tank costs 700) You have incorrectly included it on the part (a) line
The answers have this part correct

Then from there the equation will not be 700n since it doesn't start at the origin it starts at the endpoint for the first 60 tanks which is the point (60, 30000) Thus you will have a different equation for the line.

Also I think your position for 60 tanks on the graph is a little off your points there seem to be directly between 50 and 75  (i.e. 62.5) so try to make it clear that it isn't directly between 50 and 75 placing it a little to the left.
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on October 22, 2017, 07:29:23 pm
I've never done further but i'll try to help :)

the first 60 tanks sell for 500
then tank 61,62,63...,150 sell for 700
The end point (60,30000) you have from the 60 tanks should be the start point for the second line (the line where each tank costs 700) You have incorrectly included it on the part (a) line
The answers have this part correct

Then from there the equation will not be 700n since it doesn't start at the origin it starts at the endpoint for the first 60 tanks which is the point (60, 30000) Thus you will have a different equation for the line.

Also I think your position for 60 tanks on the graph is a little off your points there seem to be directly between 50 and 75  (i.e. 62.5) so try to make it clear that it isn't directly between 50 and 75 placing it a little to the left.


Why must the new graph begin where the previous one left off? Can't this just be a type of step graph? Or can step graphs only ever be horizontal and angled graphs must always connect?
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on October 22, 2017, 07:35:20 pm
Also, for part d. How can the effective interest rate possibly be what Neap claim in their solutions? Shouldn't it be 12.97 ? Neither the book nor the formula sheet have the formula that Neap use. Should I mark this as correct or incorrect?
Title: Re: VCE Further Maths Question Thread!
Post by: Sine on October 22, 2017, 09:10:20 pm
Why must the new graph begin where the previous one left off? Can't this just be a type of step graph? Or can step graphs only ever be horizontal and angled graphs must always connect?
Think of it logically if the cost goes to X and then you continue selling the cost can't magically jump an extra 1000$ right? This is just one situation here were they sell 60 tanks for some cost and then continue selling tanks at a different cost.
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on October 23, 2017, 10:17:43 am
When doing the VCCA practice exams from their past study design, is it recommended to do number patterns as well?
Title: Re: VCE Further Maths Question Thread!
Post by: zofromuxo on October 23, 2017, 10:30:57 am
When doing the VCCA practice exams from their past study design, is it recommended to do number patterns as well?
Yes. Most of the questions should be relevant to the current study design as well.
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on October 23, 2017, 10:56:18 am
Thank you :)
Title: Re: VCE Further Maths Question Thread!
Post by: Mariamnourine on October 23, 2017, 12:10:05 pm
Hey guys,

Just got an email sent to me by one of my classmates and I thought it would be really useful for all you guys as well.

So if you hop on to this website: http://vicmathsnotes.weebly.com/year-12-further-maths.html, You will find all the relevant practice exam questions [for EVERY module] for a specific area you struggle in, for example, there is a subheading for 'Matrix multiplication', and when you click on it it provides you with ALL the relevant VCAA questions in this area!!

Pretty cool, yeah?

Let me know if you're having trouble finding them and I'll talk you through it step-by-step [shouldn't be a challenge though!]

Enjoy and happy studying!  ;)
Title: Re: VCE Further Maths Question Thread!
Post by: Mariamnourine on October 23, 2017, 12:14:18 pm
What's the most reliable way of distinguishing between a random fluctuation and seasonality when analysing a time series?


Well here it goes:

Random fluctuation- doesn't have a time period, so it can fluctuate at 6 months, then again at 8 months, then at 11 months [there is no pattern]

Seasonality- usually fluctuates over 4 quarters, so every 3 months it'll fluctuate. Try breaking up the plot into 3 month intervals, if all 4 intervals seem the same, its seasonality, if not, then they are random fluctuations.

feel free to ask for clarifications!
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on October 23, 2017, 02:10:50 pm
Think of it logically if the cost goes to X and then you continue selling the cost can't magically jump an extra 1000$ right? This is just one situation here were they sell 60 tanks for some cost and then continue selling tanks at a different cost.

Ahh I see. Thanks!
What about that effective interest rate thing? I just completed another Neap prac exam (2008, 1) and again I used the formula sheet/textbook's methods while Neap used their own method to get totally different answers. Who's correct here? Neap claims the effective interest rate is like twice the normal interest rate!
The question states: $500 item under a hire-purchase agreement. A 10% deposit is paid. Then $23/month is paid for 2 years. The effective interest rate is:... I calculated it to be r=11.33%-->reff=11.94% (which is not an option), but Neap say it's 21.8%. Who's right here?
Title: Re: VCE Further Maths Question Thread!
Post by: Creamysnow on October 23, 2017, 07:02:39 pm
Can someone help me with this question?

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: Nicko912 on October 23, 2017, 09:57:09 pm
Can anyone figure these financial ones out? I get a different answer on financial solver compared to when I use equations (not sure why).

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Mariamnourine on October 23, 2017, 10:01:12 pm
Can anyone figure these financial ones out? I get a different answer on financial solver compared to when I use equations (not sure why).

Thanks

I'll help you solve them out once I get the answers for these- to avoid intimidation because I'm also in year 12. In relation to getting a different answer, it's talking about repayments, so you need to use finance solver
Title: Re: VCE Further Maths Question Thread!
Post by: Mariamnourine on October 23, 2017, 10:21:16 pm
Can anyone figure these financial ones out? I get a different answer on financial solver compared to when I use equations (not sure why).

Thanks

This are the answers I got:

a) 19 months
b) $802.47
c)$802.50

tell me if there correct so I can explain, if not then we'll try and figure them out together.
Title: Re: VCE Further Maths Question Thread!
Post by: Nicko912 on October 23, 2017, 10:32:31 pm
This are the answers I got:

a) 19 months
b) $802.47
c)$802.50

tell me if there correct so I can explain, if not then we'll try and figure them out together.

Those are the answers I got too. But the answers from itute give different answers (They could be wrong, what's your opinion on how they worked it out?)

For Part b ii) Did you use the PMT of -802.47 that gives FV = -0.025... then add it on to the payment to get $802.50 as the final answer? That's how I got it.. Thanks for the help so far!
Title: Re: VCE Further Maths Question Thread!
Post by: Mariamnourine on October 23, 2017, 10:38:19 pm
Those are the answers I got too. But the answers from itute give different answers (They could be wrong, what's your opinion on how they worked it out?)

For Part b ii) Did you use the PMT of -802.47 that gives FV = -0.025... then add it on to the payment to get $802.50 as the final answer? That's how I got it.. Thanks for the help so far!

You used itute answers, no wonder why you got them wrong. My math teacher tells us NEVER to use itute answers, even when he was going through some questions, he released they were wrong because he had gotten a different answer.They are defeinitly right answers.

Yes, for part bi) I solved the future value for 5 years, which was $5501.99, then I put this value in the PV, and then I changed N to 7, and then I clicked on PMT and it gave me $802.47.

bii) I just clicked on future value and I got -0.025 [whih rounds up to -0.03] Then I added this to $802.47, which gave me $802.50
Title: Re: VCE Further Maths Question Thread!
Post by: isobelj on October 28, 2017, 08:25:23 pm
Please help!! I have a question about financial maths

"The price of the equipment, $8360, included 10% GST (Goods and Services Tax). Calculate the price of the equipment before the GST was added."

I know that the answer is 8360/1.1 = 7600, but I am struggling to understand why the answer isn't 8360*0.9 = 7524.

Thanks in advance!!
Title: Re: VCE Further Maths Question Thread!
Post by: atarno on October 28, 2017, 09:19:02 pm
Quote
Please help!! I have a question about financial maths

"The price of the equipment, $8360, included 10% GST (Goods and Services Tax). Calculate the price of the equipment before the GST was added."

I know that the answer is 8360/1.1 = 7600, but I am struggling to understand why the answer isn't 8360*0.9 = 7524.

Thanks in advance!!

8360 is 7600 plus 10% of 7600 added on.
7600 + (10/100)*7600 = 7600 + 760 = 8360

Doing 0.9*8360 is like subtracting 10% of 8360 which is not the same as adding 10% of 7600.
8360 - (10/100)*8360 = 8360 - 836 = 7524

10% of 8360 is greater than 10% of 7600. (836>760).

Think of dividing by 1.1 as a shortcut of going backwards algebraically.

Let's say 7360 = x.
100% + 10% of x = 8360
1.1x = 8360

Now, we divide by 1.1 on both sides to find x
1.1x/1.1 = 8360/1.1
x = 8360/1.1
x = 7600
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on October 29, 2017, 04:29:31 pm
Are questions relating to GST and hire purchase plan  still relevant to the study design?
Title: Re: VCE Further Maths Question Thread!
Post by: Jackie Chan on October 29, 2017, 04:32:58 pm
Are questions relating to GST and hire purchase plan  still relevant to the study design?

No they're not :)
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on October 29, 2017, 04:36:24 pm
Are questions relating to GST and hire purchase plan  still relevant to the study design?

Still relevant to General Year 11, but not for further.
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on October 29, 2017, 05:08:35 pm
Still relevant to General Year 11, but not for further.

Thank you
Title: Re: VCE Further Maths Question Thread!
Post by: MarkyBoy on October 29, 2017, 09:42:27 pm
Hi everyone,

For the further exam, is it acceptable to bring in a workbook (my notes throughout the year) and duct tape it to a further maths company notes book? I will make sure that I tape it together very firmly to ensure that the two books won't separate.

Thanks very much
Title: Re: VCE Further Maths Question Thread!
Post by: Nomi16 on October 29, 2017, 10:26:51 pm
Hi everyone,
Can anyone help me out with the last question in graph and relations module of the 2016 VCAA exam 2?
Thanks in advance!
Title: Re: VCE Further Maths Question Thread!
Post by: Jackie Chan on October 29, 2017, 10:33:47 pm
Hi everyone,

For the further exam, is it acceptable to bring in a workbook (my notes throughout the year) and duct tape it to a further maths company notes book? I will make sure that I tape it together very firmly to ensure that the two books won't separate.

Thanks very much

"The bound reference must be in book format of A4 size or smaller when closed.
The number of pages is not specified.
Pages must be permanently bound and securely attached to the spine.
There must be a single horizontal or vertical spine.
The bound reference may be:
- a textbook
- a securely bound lecture pad
- a permanently bound student-constructed set of notes without fold-outs
- an exercise book.
The form of binding is not specified but it must be secure, and pages must not be readily detachable or designed to be removed. Binding can include cloth, glue, staple, spiral or comb binding."
  ~ http://www.vcaa.vic.edu.au/Pages/vce/exams/authorisedmaterials.aspx#bound

^^ so long as it adheres to all these requirements you should be fine  :)
Just remember that if any pages fall out, the exam supervisor will remove it and it will be reported as a breach of rules.

Title: Re: VCE Further Maths Question Thread!
Post by: Peter Griffin on October 29, 2017, 11:14:04 pm
Need help for Graphs and the types of data which are used for each!
Using mainly the Australian Bureau of Statistics and the Cambridge textbook I have made this list of notes; however, when faced with multiple options in exam 1, I sometimes make a mistake as the data can possibly fall within more than one graph and its quite frustrating! So I am looking for someone with the perfect notes who can help me with this issue.

Two-Way Frequency table: categorical data

Bar Chart: Categorical data

Stacked or Segmented Bar Chart: Comparing two or more categorical variables
Frequency Table: Categorical or discrete numerical data

Dot Plots: Categorical and discrete numerical data

Stem and Leaf Plot: Discrete and continuous numerical data

Back to Back Stem and Leaf Plot: Categorical (i.e. Sex) Discrete and continuous numerical data

Histograms: Ungrouped Discrete and continuous numerical data

Box Plot: Categorical and discrete numerical data

Parallel Box Plot: Numerical data sets

Scatter Plot: Numerical data
Title: Re: VCE Further Maths Question Thread!
Post by: isobelj on October 30, 2017, 08:20:32 pm
8360 is 7600 plus 10% of 7600 added on.
7600 + (10/100)*7600 = 7600 + 760 = 8360

Doing 0.9*8360 is like subtracting 10% of 8360 which is not the same as adding 10% of 7600.
8360 - (10/100)*8360 = 8360 - 836 = 7524

10% of 8360 is greater than 10% of 7600. (836>760).

Think of dividing by 1.1 as a shortcut of going backwards algebraically.

Let's say 7360 = x.
100% + 10% of x = 8360
1.1x = 8360

Now, we divide by 1.1 on both sides to find x
1.1x/1.1 = 8360/1.1
x = 8360/1.1
x = 7600

Thank you so much!!
Title: Re: VCE Further Maths Question Thread!
Post by: rg_123 on October 30, 2017, 08:32:23 pm
Hi everyone,

If a question comes up in the finance section of the exam and asks for us to round to the nearest whole number (for payments) must we always round up? For example let's say you get 12.3 payments on the finance solver, do you have to go up to 13 if the question asks to the nearest whole number?
Thanks :D
Title: Re: VCE Further Maths Question Thread!
Post by: Jackie Chan on October 30, 2017, 08:37:51 pm
Hi everyone,

If a question comes up in the finance section of the exam and asks for us to round to the nearest whole number (for payments) must we always round up? For example let's say you get 12.3 payments on the finance solver, do you have to go up to 13 if the question asks to the nearest whole number?
Thanks :D

I would say yes because only 12 payments will not pay off the whole loan; you would still have a bit left to owe back (that 0.3).
:)
Title: Re: VCE Further Maths Question Thread!
Post by: zofromuxo on October 30, 2017, 08:39:51 pm
Hi everyone,

If a question comes up in the finance section of the exam and asks for us to round to the nearest whole number (for payments) must we always round up? For example let's say you get 12.3 payments on the finance solver, do you have to go up to 13 if the question asks to the nearest whole number?
Thanks :D
Always round up
Title: Re: VCE Further Maths Question Thread!
Post by: Peter Griffin on October 30, 2017, 08:42:46 pm
Need help for Graphs and the types of data which are used for each!
Using mainly the Australian Bureau of Statistics and the Cambridge textbook I have made this list of notes; however, when faced with multiple options in exam 1, I sometimes make a mistake as the data can possibly fall within more than one graph and its quite frustrating! So I am looking for someone with the perfect notes who can help me with this issue.

Two-Way Frequency table: categorical data

Bar Chart: Categorical data

Stacked or Segmented Bar Chart: Comparing two or more categorical variables
Frequency Table: Categorical or discrete numerical data

Dot Plots: Categorical and discrete numerical data

Stem and Leaf Plot: Discrete and continuous numerical data

Back to Back Stem and Leaf Plot: Categorical (i.e. Sex) Discrete and continuous numerical data

Histograms: Ungrouped Discrete and continuous numerical data

Box Plot: Categorical and discrete numerical data

Parallel Box Plot: Numerical data sets

Scatter Plot: Numerical data

Repost need help..
Title: Re: VCE Further Maths Question Thread!
Post by: Jackie Chan on October 30, 2017, 08:49:59 pm
Repost need help..

I relied on the Cambridge Textbook's notes on this topic for these types of questions and sometimes it just doesn't work out as more than one graph is appropriate according to their notes. I think when it comes to this, you just have to use common sense and actually picture whether a type of graph would suit the data.
Title: Re: VCE Further Maths Question Thread!
Post by: Peter Griffin on October 30, 2017, 10:11:45 pm
I relied on the Cambridge Textbook's notes on this topic for these types of questions and sometimes it just doesn't work out as more than one graph is appropriate according to their notes. I think when it comes to this, you just have to use common sense and actually picture whether a type of graph would suit the data.

Alright, cheers! Its the only type of question that annoys me because it isn't only one correct answer.. I hope the exam makes it easy in choosing which!
Title: Re: VCE Further Maths Question Thread!
Post by: zxcvbnm18 on November 01, 2017, 03:03:17 pm
Hi is there a quicker way to do multiple choice question 8 on the 2016 sample further maths exam 1 ?
Title: Re: VCE Further Maths Question Thread!
Post by: SMOKIE on November 01, 2017, 04:21:18 pm
hey boys can anyone help me with some questions
Q5 and Q8 for graphs and relations
Q4 for matrices
Q24 from finance

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017FM1-nht-w.pdf

Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 01, 2017, 06:59:08 pm
Hey y'all,
just wanted to ask what are some of the more difficult concepts vcaa tests us on that I should revise?
Im doing networks and matrices, but it would be nice if someone could also tell me what some of the harder concepts in the financial module are?
thanksssssssss.
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 01, 2017, 07:29:00 pm
also, just wanna confirm that we dont need to know the sum of terms equation that was preivously required in number patterns?

and ... how can i use normCdf to check my normal distribution answers on my CAS??
Title: Re: VCE Further Maths Question Thread!
Post by: Opengangs on November 01, 2017, 10:55:51 pm
hey boys can anyone help me with some questions
Q5 and Q8 for graphs and relations
Q4 for matrices
Q24 from finance

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017FM1-nht-w.pdf
Q5: Clearly the  inequalities compose of: x <= 7, 2 <= y <= 6.
To find the equations of the lines, we find the slope by using the rise over run formula.
One of the lines has a gradient of 3, meaning the equation of the line is: y = 3(x - 3), and so y = 3x - 9
Now, we know that the inequality of that line is: y <= 3x - 9, since the shaded area is always sitting below the line.

Rearranging, we get: 3x - y => 9 (D)

Q8: We define the rate of change to be the slope at any given point, so we first find the rate for the first 15 minutes; this tells us about the rate at which BOTH hoses are leaving: 400/15 = 80/3 (this rate of change is const).
Now, we need to find the time it takes to fill 600L of water, and since we have the rate, we just need to find the time it takes.

80/3 = 600/t
t = 1800/80 = 45/2 = 22.5
We are given that it takes 9 minutes less to fill the full 600L than a, so let 22.5 = a - 9
a = 31.5

Now, we just need to find the slope between 15 and 31.5 minutes.
Thus, rate of change = (600 - 400)/(31.5 - 15) = 200/16.5 = 12.121212... which is approximately 12 minutes (A)

MODULE 1 - MATRICES
Q4: (A) clearly works: m1 1 = 2(1) + 1 = 3
(B): By considering i as 1, we need to verify that each element follows the rule.
m1 1 = 3 works
m1 2 = 2(1) + 2 = 4 works
m1 3 = 2(1) + 3 = 5 works
Thus, (B) also works.

It follows that (C) and (E) satisfies the rule, meaning that the matrix (D) doesn't.

SECTION A - RECURSION AND FINANCIAL MODELLING
Q24:
What we want to find is the principal amount - that is, P0.
Consider the compound interest formula: P(1 + r/100)^n, being compounded annually.
To reduce it down to monthly installments, we need to convert the rate and the value of n so that we are compounding them over monthly installments.
P(1 + r/1200)^(n/12)
After six months, we get: P(1 + r/1200)^6 = 4418.80 (equation 1)
After two years, we get: P(1 + r/1200)^24 = 4862.80 (equation 2)

Substitute equation 1 into equation 2: 4418.80(1 + r/1200)^18 = 4862.80
~1.1 = (1 + r/1200)^18
Solving for r should give you 6.400089204... rounded to 6.4.

Now, substitute that into either equation 1 or equation 2.
P(1 + r/1200)^6 = 4418.80
Solving for P should give you $4, 279.9998904... ~~ $4, 280 (C)
Title: Re: VCE Further Maths Question Thread!
Post by: jemma.clayton on November 02, 2017, 10:27:32 am
Need some help with a matrices question from th 2011 VCAA exam 1.

Matrix A is a 3x3 matrix. Seven of the elements in matrix A are zero. Matrix B contains six elements, none of which are zero. Assuming the matrix product AB is defined, the minimum number of zero elements in the product matrix AB is:
A. 0
B. 1
C. 2
D. 4
E. 6
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on November 02, 2017, 10:45:01 am
I need some help with this question. It is from the 2011 exam.
Title: Re: VCE Further Maths Question Thread!
Post by: mtDNA on November 02, 2017, 01:36:29 pm
I need some help with this question. It is from the 2011 exam.

Do x/seasonal index, so here do x/0.8. This will give you 1.25x. So to correct you increase by 25%
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 02, 2017, 01:49:20 pm
Do you suggest i put my practice sacs / exmas i have done for maths in my bound reference book?
Title: Re: VCE Further Maths Question Thread!
Post by: zofromuxo on November 02, 2017, 01:56:45 pm
Do you suggest i put my practice sacs / exmas i have done for maths in my bound reference book?
I would put only the questions you struggle with in your bound reference and not all the practice sacs/exams in it.
Title: Re: VCE Further Maths Question Thread!
Post by: atarno on November 02, 2017, 04:08:18 pm
Hey guys!

I've attached a question below which has me absolutely stumped. It's a question from 2016 Insight and I've never come across a trend line where deseasonalised sales are predicted from sales; it doesn't make sense to me.

I've also attached the answer if needed.

Any help would be greatly appreciated!
Title: Re: VCE Further Maths Question Thread!
Post by: SMOKIE on November 02, 2017, 04:30:37 pm
can someone explain to me about inequalities
i.e " Xavier must work at least twice as many hours as Younnis"  and let x be Xavier and y be Younnis. I dont understand why its y<=x/2?

thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Asznee on November 02, 2017, 04:37:45 pm
Hey guys!

I've attached a question below which has me absolutely stumped. It's a question from 2016 Insight and I've never come across a trend line where deseasonalised sales are predicted from sales; it doesn't make sense to me.

I've also attached the answer if needed.

Deseasonalised data is aiming to find an underlying trend in seasonal data,
When we're predicting data outside of the samples taken (forecasting for instance), we must use the deseasonilised regression line to find the deseasonalised value and the times it by that months sI, which will get it back to an actual prediction.

Summary, in forecasting, use deseasonalised regression line and then multiply that deseasonalised prediction by its si to convert it back to actual sales.


Any help would be greatly appreciated!

Hey guys!

I've attached a question below which has me absolutely stumped. It's a question from 2016 Insight and I've never come across a trend line where deseasonalised sales are predicted from sales; it doesn't make sense to me.

I've also attached the answer if needed.

Any help would be greatly appreciated!

Title: Re: VCE Further Maths Question Thread!
Post by: MattBro on November 02, 2017, 04:51:31 pm
Can someone please help me with this financial math multiple choice question, it has got me. The answers B but even following their suggested method to work it out (attached also) I still can seem to get even close to their answer.
Title: Re: VCE Further Maths Question Thread!
Post by: Maya24 on November 02, 2017, 04:54:22 pm
can someone explain to me about inequalities
i.e " Xavier must work at least twice as many hours as Younnis"  and let x be Xavier and y be Younnis. I dont understand why its y<=x/2?

thanks!

So its saying that xavier has too work at least twice as many hours as yunnis meaning that he can work more. Therefore xavier has to work greater than or equal to yunnis, so when you substitute 2 into x,y becomes one thus the inequality is correct. If you substitute any number as x, y will always be  twices as less.
Title: Re: VCE Further Maths Question Thread!
Post by: mtDNA on November 02, 2017, 05:01:59 pm
Can someone please help me with this financial math multiple choice question, it has got me. The answers B but even following their suggested method to work it out (attached also) I still can seem to get even close to their answer.

My friends and I were doing this question and we all got A, so we came to the conclusion that the solutions proposed an error (unless someone else can explain why it is B...)
Title: Re: VCE Further Maths Question Thread!
Post by: KidClutch on November 02, 2017, 05:19:23 pm
Hey guys, can someone explain how the answer is C?
I'm pretty sure it's B but maybe I could be wrong
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 02, 2017, 05:31:54 pm
Hey all!
I'm free to talk for the next half day or so. If you have any last minute questions regarding Further, I'll try my best to help you all out. :)
Since I studied Further back in 2014, which had us study 3 modules + Data and Stats (Core, until 2016), I'm mostly familiar with:
- Data and Stats
- Graphs and Relations
- Geometry and Measurement
- the old Sequences and Series modules (which carries into some of the Financial Recursions section in the Core module).
I've personally also tried Matrices, but it's a bit of a hit and miss right now, but I'll try to help anyone with any last minute questions in general!
If not, one of the other trusty ANers will help you out! 


To all Class of 2017 Further students:

Finish that last practise exam, make the final touches to your bound reference and correct that final silly mistake. 
Take a deep breath, breathe in, breathe out and get a good night's rest.
You guys CAN and WILL conquer this. Keep your minds sharp and your game sharper.
You're almost there.
Good luck!   


Spoiler
Hey guys, can someone explain how the answer is C?
I'm pretty sure it's B but maybe I could be wrong
I think you might be right. At least, B is what I get from my rusty knowledge.
I think they didn't factor in that it was profit and accidentally calculated net earnings.
Title: Re: VCE Further Maths Question Thread!
Post by: rosiemac on November 02, 2017, 05:51:00 pm
Hi guys if someone could help with this question that would be great!
i have no idea what to do with it
thanks heaps!!!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 02, 2017, 06:20:01 pm
Hi guys if someone could help with this question that would be great!
i have no idea what to do with it
thanks heaps!!!
Alright, so I have never done this before, so please take this with caution. I - probably, maybe, likely - will get this wrong.
Spoiler
From this site, I took their formulas and input the following numbers in:
I = (12 months x 2 years) x $25 = $600
P = $500 - $50 = $450
t = 2 years
T = I - P = $600 - $450 = $150
Spoiler
Thus you substitute the numbers into the rf formula to get:
rf = (100 x 150) / (450 x 2) = 16.7% approximately. (Please excuse lack of LaTeX.)
My assumption then is that B is right.

EDIT: I failed on my first try. Good going, AngelWings.  :-\
Title: Re: VCE Further Maths Question Thread!
Post by: mtDNA on November 02, 2017, 06:20:23 pm
Hi guys if someone could help with this question that would be great!
i have no idea what to do with it
thanks heaps!!!

http://www.itute.com/wp-content/uploads/2009-vcaa-further-mathematics-exam-1-solutions.pdf
Title: Re: VCE Further Maths Question Thread!
Post by: mtDNA on November 02, 2017, 06:22:59 pm
Alright, so I have never done this before, so please take this with caution. I - probably, maybe, likely - will get this wrong.
Spoiler
From this site, I took their formulas and input the following numbers in:
I = (12 months x 2 years) x $25 = $600
P = $500 - $50 = $450
t = 2 years
Spoiler
Thus you substitute the numbers into the rf formula to get:
rf = (100 x 600) / (450 x 2) = 66.7% approximately. (Please excuse lack of LaTeX.)
My assumption then is that E is right.

I initially thought E as well, but when I checked I saw it was B.

That being said, I’m 99% sure that hire-purchase isn’t in the course anymore (this was from 2009 VCAA)
Title: Re: VCE Further Maths Question Thread!
Post by: rosiemac on November 02, 2017, 07:55:12 pm
I initially thought E as well, but when I checked I saw it was B.

That being said, I’m 99% sure that hire-purchase isn’t in the course anymore (this was from 2009 VCAA)

thank you!!!
Title: Re: VCE Further Maths Question Thread!
Post by: rosiemac on November 02, 2017, 08:02:06 pm
thank you!!!!
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 02, 2017, 08:36:06 pm
hey need help with Q7 of matrices in 2017 NHT
how do you interpret two-step dominances??
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 02, 2017, 08:59:20 pm
hey need help with Q7 of matrices in 2017 NHT
how do you interpret two-step dominances??
While I don't entirely understand this and don't think I've ever encountered this either, I do have a resource for you right here from Engage Education.
Sorry I couldn't be of more help!
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on November 02, 2017, 09:12:58 pm
I circled the one that I think is the answer and pointed to the one which MAV thinks is correct. Who's right?
Title: Re: VCE Further Maths Question Thread!
Post by: emmaline on November 02, 2017, 09:42:50 pm
Hi, would really appreciate if someone could help with this question. I don't understand why it's C and not B. Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: anicawajswelner on November 02, 2017, 09:44:24 pm
CAN SOMEONE PLZ EXPLAIN THE SLIDING LINE TO ME?!!?!?!?!?!
Title: Re: VCE Further Maths Question Thread!
Post by: emmaline on November 02, 2017, 09:45:28 pm
Oh the question didn't attach
Title: Re: VCE Further Maths Question Thread!
Post by: Eric11267 on November 02, 2017, 09:55:14 pm
Oh the question didn't attach
Sorry, I don't do further maths so take what I say with a grain of salt.
Both B and C will have that general shape and pass through the point (4,1/10). The only thing I would say is maybe look at the graphs scale. At x=1 the y value is quite clearly under 1. Subbing in x=1 would give you 8/5 for B and 2/5 for C so I guess it would be C for this reason. Anyone feel free to correct me because I'm clueless about further maths
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 02, 2017, 09:56:26 pm
I circled the one that I think is the answer and pointed to the one which MAV thinks is correct. Who's right?
first Q: MAV is correct since the two variables are not completely random
2nd Q: r=.68 is moderate, not weak
and the word 'tends' indicates that it is not an exact causal relationship,  so you shud try to find answers with the word 'tends'
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on November 02, 2017, 10:05:55 pm
CAN SOMEONE PLZ EXPLAIN THE SLIDING LINE TO ME?!!?!?!?!?!

The objective function has a gradient. Place your ruler on the graph parallel to that gradient. Now slide your ruler up and down the graph while maintaining that gradient. The last vertex to touch your ruler while you're sliding up/down is the maximum/minimum point. If your ruler touches an edge (parallel to your ruler), then all points along that edge are valid maximum/minimum values of the objective function.

Oh the question didn't attach

Both are correct if you don't have a CAS or if the graph isn't perfectly to scale. But n=1 (i.e. C) is more accurate if you graph both n=1 and n=2 on your CAS.

first Q: MAV is correct since the two variables are not completely random
2nd Q: r=.68 is moderate, not weak
and the word 'tends' indicates that it is not an exact causal relationship,  so you shud try to find answers with the word 'tends'

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 02, 2017, 10:18:11 pm
I circled the one that I think is the answer and pointed to the one which MAV thinks is correct. Who's right?
Question 11 shows that there is a trend there that appears to have a moderate correlation. There is likely some sort of explanation, making C more correct.
Question 6 is B. Sorry man. An r value (correlation coefficient) of 0.68 is positive and of moderate strength, not weak. This is one of those where you have to watch the wording to get right.
A little explanation...
Options A and D are incorrect because it's not a coefficient of determination. C is wrong because it's not "causal", it's an association/ correlation. Math doesn't work quite the way E says it to be.

Hi, would really appreciate if someone could help with this question. I don't understand why it's C and not B. Thanks!
Spoiler
There's a bit of a trick to this question because it's not actually clear, but the difference is in the slope. Yeah, that's the tricky part. If you go back and graph the two graphs into the calculator, you'd realise there's a solid gap between x = 0 and x = 0.3 for Option B, which doesn't appear in this graph. Measuring this graph, you can see that the gap is really small, like smaller than 0.3. Luckily, VCAA are usually clearer than this. 

I just realised I was beaten to the punch. Oh well, hopefully these help somebody.
Title: Re: VCE Further Maths Question Thread!
Post by: Creamysnow on November 02, 2017, 10:20:19 pm
CAN SOMEONE PLEASE EXPLAIN THIS QUESTION!!!
Title: Re: VCE Further Maths Question Thread!
Post by: Mariamnourine on November 02, 2017, 10:37:25 pm
Hi, would really appreciate if someone could help with this question. I don't understand why it's C and not B. Thanks!

So they gave you the point. y=4 and x=1/10

Literally substitute x into the equation and see if you get y=4. when I tried for B, The answer was 160, when I tried for C, the answer was 4, which is correct.
Title: Re: VCE Further Maths Question Thread!
Post by: Opengangs on November 02, 2017, 10:41:32 pm
CAN SOMEONE PLEASE EXPLAIN THIS QUESTION!!!
Use the fact that triangle ABD and triangle ABC are similar (they are equiangular).
This implies that the ratios of sides are in proportion.
Thus, the area of triangle ABC is (40/24)^2*100 ~~ 278cm^2
Title: Re: VCE Further Maths Question Thread!
Post by: Angelx001 on November 02, 2017, 11:03:05 pm
Can someone explain 2008 exam 1 question 9??? (core!!)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 02, 2017, 11:10:08 pm
Can someone explain  2008 exam 1 question 9??? (core!!)
I assumed VCAA E1 2008 Core Q9.
Spoiler
You should be looking at the y axis (weight) and finding the median of the 12 points from there, so look at the 6th and 7th points and get their average. You must count from bottom to top of the y axis in order of their y coordinates.
The points give y values of 430g and 450g, so their average is 440g.
The answer is C.
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 02, 2017, 11:13:41 pm
HOW do i do correction for seasonality?
QUESTION was - the seasonal index for sales in winter is 0.75
To correct seasonality, the actual sales in winter should be
a)increased by 25%
b) reduced by 25%
c)reduced by 33%
d)increased by 33%

I have no idea how to do it and thought it was c, but the answer is D
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 02, 2017, 11:19:29 pm
HOW do i do correction for seasonality?
QUESTION was - the seasonal index for sales in winter is 0.75
To correct seasonality, the actual sales in winter should be
a)increased by 25%
b) reduced by 25%
c)reduced by 33%
d)increased by 33%

I have no idea how to do it and thought it was c, but the answer is D

This type of question always comes up once in a while. It came up in 2014. I remember sitting this exam with this one in my reference book. I've previously done a 2011 one which was awfully similar too. (If that gap is accurate, it's due for a come back but before that it hadn't been around for years, so... who knows?) Here's how to do it:
Spoiler
What you want is a seasonal index of 1.
The seasonal index for winter given is 0.75.
Grab 1/ 0.75 = 1.33 (approx.)
This is 133%, so find the difference between that and 100%. Note that 133% is higher than 100% (thus an increase).
This gives an increase of 33%.
Hope that helps!
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 02, 2017, 11:20:46 pm
RECURSION/FINANCIAL -  Can someone please explain why the answer is C.
I knew it was either C or D but had no idea how i can tell between unit cost and flat rate with such little information!
THANKS
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 02, 2017, 11:30:34 pm
RECURSION/FINANCIAL -  Can someone please explain why the answer is C.
I knew it was either C or D but had no idea how i can tell between unit cost and flat rate with such little information!
THANKS
Not too sure, but upon my 5 seconds of research, I found the difference to be the definition of each, so maybe that's something to check with your notes or textbook. C just seemed to suit the situation more. Also, maybe the use of V0 over V1? But I wouldn't have any idea about that. Haven't looked into financial recursions much.
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 02, 2017, 11:34:58 pm
Not too sure, but upon my 5 seconds of research, I found the difference to be the definition of each, so maybe that's something to check with your notes or textbook. C just seemed to suit the situation more. Also, maybe the use of V0 over V1? But I wouldn't have any idea about that. Haven't looked into financial recursions much.

Thank you soo much for answering both my questons! Correcting seasonal index explanation made perfect sense (feeling much confident)!
Yeah i believed C was correct, their is no difference in the recurrence relation of unit-cost and flat-rate so proably a poor question! Thank alot anyways!
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 03, 2017, 12:50:50 am
RECURSION / FINANCE  -Can someone please explain to me how to get the answer?
The solutions said that the monthly interest rate would be 7.2% / 1200....why 1200??
Title: Re: VCE Further Maths Question Thread!
Post by: darcypeaceee on November 03, 2017, 01:01:31 am
RECURSION / FINANCE  -Can someone please explain to me how to get the answer?
The solutions said that the monthly interest rate would be 7.2% / 1200....why 1200??

I'm not 100% sure if I'm correct, but I believe they've combined 12 (compounding monthly) with 100 to get the monthly interest rate.
Title: Re: VCE Further Maths Question Thread!
Post by: Opengangs on November 03, 2017, 06:53:22 am
7.2% is the interest rate compounded annually, so to find the interest rate compounded monthly, we need to divide by 12.

So we get (7.2/100)/12 = 7.2/1200
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 03, 2017, 07:52:04 am
HEY, can someone explain how to get question 8! I got 7 which was E but have no idea how to get question 8
NETWORKS
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 03, 2017, 08:36:50 am
Recursion - Also how o i solve for this, it said to use finance solver which i did but received the incorrect value :-(
Q. Loan is taken out where there are no repayments until end of year 5
How much extra interest is charged when the compounding period is changed from monthly to daily on a loan of $25000 at 5% per annum?
a) $16.21
b)$96.88
c)$112.75
Title: Re: VCE Further Maths Question Thread!
Post by: darcypeaceee on November 03, 2017, 09:46:31 am
Recursion - Also how o i solve for this, it said to use finance solver which i did but received the incorrect value :-(
Q. Loan is taken out where there are no repayments until end of year 5
How much extra interest is charged when the compounding period is changed from monthly to daily on a loan of $25000 at 5% per annum?
a) $16.21
b)$96.88
c)$112.75

If you look on page 129 people were talking about how they might've got the answer wrong. So if you got A I'm pretty sure you're correct! :)
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 03, 2017, 10:07:59 am
HEY, can someone explain how to get question 8! I got 7 which was E but have no idea how to get question 8
NETWORKS
hey you just need to rewrite all the possible paths with e and f and change it up according to the new change. so i think you add 6 hours the F's EST or something. check, im not 100% sure
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 03, 2017, 10:15:24 am
If you look on page 129 people were talking about how they might've got the answer wrong. So if you got A I'm pretty sure you're correct! :)
Thank You! Yeah i am not getting A either = :-( , my answer is like in the thousands...
Title: Re: VCE Further Maths Question Thread!
Post by: Gretel99 on November 03, 2017, 10:19:10 am
Can someone please help with this question from the 2017 Insight paper: (geometry and measurement)
A teacher, located at Torquay (38 S, 144E) releases the results of her exam to all students at the same time.
What time will student Georgia who is in Terang (38 S, 142 E) receive her results if the teacher releases them at 9:30 a.m in Torquay?
a). 9.22 am
b). 9.30 am
c) 9:38 am
d) 10.00 am
e) 10:38 am

To me the answer should be A as Torquay is further east than Terang and would therefore be ahead in time, but the answer is C?
Am i reading this wrong?

Thankyou!
Title: Re: VCE Further Maths Question Thread!
Post by: mammes on November 03, 2017, 10:22:51 am
HEY, can someone explain how to get question 8! I got 7 which was E but have no idea how to get question 8
NETWORKS

Spoiler
Redraw the network with E going straight up with D.

What should happen is the critical path which was ACDFH = 27 becomes ACEFG = 29

The answer should be delayed by 2 hrs.
Title: Re: VCE Further Maths Question Thread!
Post by: mammes on November 03, 2017, 10:33:48 am
Recursion - Also how o i solve for this, it said to use finance solver which i did but received the incorrect value :-(
Q. Loan is taken out where there are no repayments until end of year 5
How much extra interest is charged when the compounding period is changed from monthly to daily on a loan of $25000 at 5% per annum?
a) $16.21
b)$96.88
c)$112.75

Spoiler
Use FS

n=12*5
pv=250000
pmt = 0
i = 5%
py/cy = 12

solve for fv = 32083.97

n=365*5
pv=250000
pmt = 0
i = 5%
py/cy = 365

solve for fv = 32100.09

32083.97-32100.09 = $16.21
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 03, 2017, 11:42:14 am
Can someone please help with this question from the 2017 Insight paper: (geometry and measurement)
A teacher, located at Torquay (38 S, 144E) releases the results of her exam to all students at the same time.
What time will student Georgia who is in Terang (38 S, 142 E) receive her results if the teacher releases them at 9:30 a.m in Torquay?
a). 9.22 am
b). 9.30 am
c) 9:38 am
d) 10.00 am
e) 10:38 am

To me the answer should be A as Torquay is further east than Terang and would therefore be ahead in time, but the answer is C?
Am i reading this wrong?

Thankyou!
I forgot they updated the Geometry and Measurement module. This is one of the newer things. I think you might be right though. -2 degrees in longitude should yield 8 minutes earlier. I may be wrong though because, like I said, this isn’t something I have done.
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on November 03, 2017, 04:32:57 pm
So....where they both ordinal? Someone please say yes. You can order them by sweetness from lowest sweetness to most sweet (light->scented->sugar).. i changed my answer from ordinal&nominal to ordinal&ordinal in literally the last 7 seconds before handing in the paper. I decided to bite the bullet just incase VCAA decide to be annoying with this question.
Title: Re: VCE Further Maths Question Thread!
Post by: loukoa on November 03, 2017, 04:40:54 pm
Pretty sure it was ordinal & nominal!

So....where they both ordinal? Someone please say yes. You can order them by sweetness from lowest sweetness to most sweet (light->scented->sugar).. i changed my answer from ordinal&nominal to ordinal&ordinal in literally the last 7 seconds before handing in the paper. I decided to bite the bullet just incase VCAA decide to be annoying with this question.
Title: Re: VCE Further Maths Question Thread!
Post by: Marionn on November 03, 2017, 04:56:50 pm
Pretty sure it was ordinal & nominal!


But you can order them and isn't that the same justification that vcaa had for last year with under and over 50?
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on November 03, 2017, 05:01:02 pm
But you can order them and isn't that the same justification that vcaa had for last year with under and over 50?

Last years is very very clearly ordinal. But this years....not as sure
Title: Re: VCE Further Maths Question Thread!
Post by: Landa on November 03, 2017, 05:09:14 pm
But you can order them and isn't that the same justification that vcaa had for last year with under and over 50?

It’s nominal most likely (in my opinion) as saying that light, scented and sugar is ordered is almost the same as saying red, orange and yellow are ordered.

There is no interval between the values: ‘light, scented and sugar’ like all ordinal data do (e.g. level of satisfaction, shoe size) to confirm this. I think if instead the level of sweetness was worded differently e.g. high sweetness, medium sweetness etc. it would have been more clear as ordinal.
Title: Re: VCE Further Maths Question Thread!
Post by: Mattjbr2 on November 03, 2017, 05:25:59 pm
It’s nominal most likely (in my opinion) as saying that light, scented and sugar is ordered is almost the same as saying red, orange and yellow are ordered.

There is no interval between the values: ‘light, scented and sugar’ like all ordinal data do (e.g. level of satisfaction, shoe size) to confirm this. I think if instead the level of sweetness was worded differently e.g. high sweetness, medium sweetness etc. it would have been more clear as ordinal.

But....red orange and yellow can be ordered by wavelength  ;D
Title: Re: VCE Further Maths Question Thread!
Post by: Landa on November 03, 2017, 05:36:32 pm
But....red orange and yellow can be ordered by wavelength  ;D

If that’s the case then types of animals can be ordered by evolution/genetics😄(I don’t do bio so don’t mind my wording😂)
Title: Re: VCE Further Maths Question Thread!
Post by: total_nerd on November 03, 2017, 10:48:31 pm
I found question 8 of geometry tricky. Did anyone understand it
Title: Re: VCE Further Maths Question Thread!
Post by: elle6299 on November 04, 2017, 05:42:56 pm
Hey, I was just wondering if when working out bearings, is it always in a clockwise direction and never anticlockwise?
Thanks in advance!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 04, 2017, 07:07:49 pm
I found question 8 of geometry tricky. Did anyone understand it
Using the copy of the exam, I can tell you that Geometry Question 8 can be calculated by forming an equilateral triangle using the radii of the three circles and subtracting out the area of the three sectors you've formed inside the triangle. If that doesn't make sense, PM me and I'll draw it out for you after I've completed my own uni exams (I have one left).

To all Further Class of 2017 students,

Please do not be bogged down by Exam 1 any more. There's no use crying over spilt milk.
Learn from your mistakes, keep going and don't give up! These ~48 hrs can be used productively to revise for Exam 2, if you so choose.
There is currently a list of Exam 2 potential questions for viewing.
Keep your heads up, think forward and do your best. Don't look back.
You guys can do it! Good luck.
Title: Re: VCE Further Maths Question Thread!
Post by: MattBro on November 04, 2017, 07:40:45 pm
Hey guys,
For Exam Two, it say that for financial math all answers should be rounded to the nearest cent unless otherwise instructed.
Does that mean for a value of say $1865.292, do i round to $1865.29 or $1865.30?

Thanks and good luck to all on Monday
Title: Re: VCE Further Maths Question Thread!
Post by: Nicko912 on November 04, 2017, 10:48:55 pm
For the Median smoothing questions where they usually ask "Complete the three-median smoothing by marking each remaining smoothed point with a
cross (×) on the time series plot below." -- Do you have to join the line at the end between the crosses after they have been plotted or not? I've been seeing some inconsistencies.. so I'm unsure.. Cheers
Title: Re: VCE Further Maths Question Thread!
Post by: darcypeaceee on November 04, 2017, 11:13:07 pm
Hey guys,
For Exam Two, it say that for financial math all answers should be rounded to the nearest cent unless otherwise instructed.
Does that mean for a value of say $1865.292, do i round to $1865.29 or $1865.30?

Thanks and good luck to all on Monday

In that scenario you'd round to $1865.29, however if it was $1865.295, then you'd round to $1865.30.
Title: Re: VCE Further Maths Question Thread!
Post by: dec.hargreaves on November 05, 2017, 11:09:10 am
Can someone please help with this question from the 2017 Insight paper: (geometry and measurement)
A teacher, located at Torquay (38 S, 144E) releases the results of her exam to all students at the same time.
What time will student Georgia who is in Terang (38 S, 142 E) receive her results if the teacher releases them at 9:30 a.m in Torquay?
a). 9.22 am
b). 9.30 am
c) 9:38 am
d) 10.00 am
e) 10:38 am

To me the answer should be A as Torquay is further east than Terang and would therefore be ahead in time, but the answer is C?
Am i reading this wrong?

Thankyou!
I've never done this module so I could be completely wrong. But if the teacher releases them at 9:30, then there is no way that someone could get the answers earlier than that
Title: Re: VCE Further Maths Question Thread!
Post by: mtDNA on November 05, 2017, 12:57:35 pm
Could someone please explain how to do question 9 bii (finance) from the 2016 Sample exam? I’ve seen solutions with different answers, so I just wanted to check if my working is correct  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Maggies on November 05, 2017, 01:24:50 pm
Can someone please explain Permutation/transpose matrices to me?
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 05, 2017, 02:41:09 pm
Hey,
if we are to write down a matrix and the elements represent prices, do we have to write it to 2dp??
i got a 2x1 column matrix where one element is an integer and the other is an exact decimal
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 05, 2017, 02:58:39 pm
How do you answer - interpret the standard score?
from further 2016 sample exam Q5bii
Title: Re: VCE Further Maths Question Thread!
Post by: blood on November 05, 2017, 03:11:38 pm
Can anyone help me to work out this question and show how they worked it out please.

' Kuong invests $8500 at 6% interest per annum, compounding quaterly. The amount of interest he earns during the fourth year of investment is?

P.S the answer is $623.63 but not sure how it is worked out.

Thanks

Mod edit: Post restored. Please do not delete a question after it has been answered.
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 05, 2017, 03:19:50 pm
Can anyone help me to work out this question and show how they worked it out please.
' Kuong invests $8500 at 6% interest per annum, compounding quaterly. The amount of interest he earns during the fourth year of investment is?
P.S the answer is $623.63 but not sure how it is worked out.
Thanks

Hey i plugged all this into my financial solver.
For N=12 (after 3 years) I got FV= 10162.75
N=16 (after four years) I got FV= 10786.38
Then i subtracted and got 623.23 - you can subtract since there are no additions or payments

Mod edit: Post restored.
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on November 05, 2017, 03:20:40 pm
Can anyone help me to work out this question and show how they worked it out please.

' Kuong invests $8500 at 6% interest per annum, compounding quaterly. The amount of interest he earns during the fourth year of investment is?

P.S the answer is $623.63 but not sure how it is worked out.

Thanks

This is how i'd work it out.. obviously there may be an easier way. You want to find out how much interest is earned over the 4th year of the investment.

4 years, compounding quarterly: 8500(1+(0.06/4))^16 = $10786.377 (future value after the 4th year, rounded)
3 years, compounding quarterly: 8500(1+(0.06/4))^12 = $10162.754 (future value after the 3rd year, rounded)

difference: 10786.377 - 10162.754 = approx 623.623

Edit: same as BlinkieBill's... i'll keep mine since it shows the formula if you were to do by hand
Title: Re: VCE Further Maths Question Thread!
Post by: blood on November 05, 2017, 03:57:07 pm
This is how i'd work it out.. obviously there may be an easier way. You want to find out how much interest is earned over the 4th year of the investment.

4 years, compounding quarterly: 8500(1+(0.06/4))^16 = $10786.377 (future value after the 4th year, rounded)
3 years, compounding quarterly: 8500(1+(0.06/4))^12 = $10162.754 (future value after the 3rd year, rounded)

difference: 10786.377 - 10162.754 = approx 623.623

Edit: same as BlinkieBill's... i'll keep mine since it shows the formula if you were to do by hand

Hey i plugged all this into my financial solver.
For N=12 (after 3 years) I got FV= 10162.75
N=16 (after four years) I got FV= 10786.38
Then i subtracted and got 623.23 - you can subtract since there are no additions or payments

Mod edit: Post restored.


Thanks both
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 05, 2017, 03:58:45 pm
Hey
how important are units in further?
do we get marks taken off for not writing them??
Title: Re: VCE Further Maths Question Thread!
Post by: blood on November 05, 2017, 04:06:35 pm
Can any help with this questions, please

The value of of the car could also be depreciated using reducing balance depreciation.
Using the this method, the value Vn, in dollars, of the car after n years would be modelled by the recurrence relation
Vo = 28000 Vn+1= 0.29Vn
After how many years would the car first have a value less than $10,000?

I can do it on the casio classpad in sequence but what working out would you do?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Steve252 on November 05, 2017, 04:19:16 pm
Hey
how important are units in further?
do we get marks taken off for not writing them??


I think just like Methods and Specialist, missing units will only cost you 1 mark irrespective of how many times you forget them
And they definitely matter, as such small details split the top students.
Title: Re: VCE Further Maths Question Thread!
Post by: dec.hargreaves on November 05, 2017, 05:03:56 pm
Can any help with this questions, please

The value of of the car could also be depreciated using reducing balance depreciation.
Using the this method, the value Vn, in dollars, of the car after n years would be modelled by the recurrence relation
Vo = 28000 Vn+1= 0.29Vn
After how many years would the car first have a value less than $10,000?

I can do it on the casio classpad in sequence but what working out would you do?

Thanks
I would usually say "after x amount of years the value of the car is y"
could be different
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 05, 2017, 05:16:56 pm
Matrices Help
Can someone please explain Permutation/transpose matrices to me?
I don't remember much of this, but I definitely remember it was also covered in Methods. Would recommend you look for some Methods resources or check out this Khan Academy link for transpose matrices and this Wolfram Alpha link for permutation matrices. Sorry that I'm not super helpful here.

if we are to write down a matrix and the elements represent prices, do we have to write it to 2dp??
i got a 2x1 column matrix where one element is an integer and the other is an exact decimal
If it represents prices, just enough zeroes to give 2dp. It's easier to see a price in 2dp because we work with cents and they'll probably ask you to round to it anyway. Same goes with integer dollars, unless otherwise stated.
How do you answer - interpret the standard score?
from further 2016 sample exam Q5bii
Sample Exam 2016 E2 Core Question 5bii
The question is as follows:
Quote
Interpret the z-score of this suburb’s population density with reference to the mean population
density.
I would write a sentence like "This suburb's population density was relatively [higher/ lower] than the mean population density, with a [positive/negative] z score of [insert z score here]. This indicates that [more/ less] people live in this suburb per square kilometre."
Remember: positive z score = this suburb > mean, negative z score = this suburb < mean, (z = 0) = this suburb = mean.

Financial and Recursions Help
I can do it on the casio classpad in sequence but what working out would you do?
I would usually say "after x amount of years the value of the car is y"
could be different
What I used to do was write up a line of the equation I used and the numbers I originally substituted with.
Then, I'd add a small table with two columns with what a few of the n (n= 1, 2, draw a few dots, [insert number before answer and answer]) and Vn values were.
Then, I'd write down one last line with the actual answer underneath that.
This was mostly for the Number Patterns module, which existed before the change in 2016, but should be similar in Financial Maths and Recursions.
Dec.Hargreaves might be right since my knowledge is outdated.
Title: Re: VCE Further Maths Question Thread!
Post by: elle6299 on November 05, 2017, 05:45:21 pm
Hey, I was just wondering if someone could help me on how I would go about this question (geometry and measurement)!

'Two similar cones of radius 4 cm and r cm (smaller than the first) are shown below.
The volume of the larger cone is three times the volume of the smaller cone.
The value of r is closest to...'
Options are 0.8 (A), 1.9 (B), 2.1 (C), 2.5 (D), and 2.8 (E).

Thankyou in advance!!
Title: Re: VCE Further Maths Question Thread!
Post by: Shaqattack on November 05, 2017, 05:58:16 pm
when drawing a regression line, what do vcca look for.?
Is it enough to get 2 points on the graph accurate from the equation present or does the line need to go through specific points?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 05, 2017, 06:07:30 pm
Hey, I was just wondering if someone could help me on how I would go about this question (geometry and measurement)!

'Two similar cones of radius 4 cm and r cm (smaller than the first) are shown below.
The volume of the larger cone is three times the volume of the smaller cone.
The value of r is closest to...'
Options are 0.8 (A), 1.9 (B), 2.1 (C), 2.5 (D), and 2.8 (E).

Thankyou in advance!!
Spoiler
Knowing that the cones are similar, the volumes of the cones will be = 43 : r3.
We also know that the volume of the larger cone will be 3x the volume of the smaller one, so 3b: b, where b is the volume of the smaller cone, which is r3. Thus we actually have:
Spoiler
r3 = b
The question states that the larger cone's volume is 3 times that of the smaller cone's.
If I call the smaller cone's volume 'b', then 3b is the larger cone's volume.
We found that smaller cone's volume (b) is also r3 when scaled from length.
Substitute b = r3 into 3b and you get: 3b = 3r3.
3b = 3r3 = 43 = 64
This can help you find r, which would be:
Spoiler
3r3 = 64
r3 = 64/3
r = cube root of 64/3 = 2.77 cm approx.
which rounds to 2.8.

This gives Option E.
Hope that helps.

when drawing a regression line, what do vcca look for.?
Is it enough to get 2 points on the graph accurate from the equation present or does the line need to go through specific points?
They will intend for you to use some reference points that are not too close to each other and draw the line over the entire graph provided.
Do not draw by eye and take the least squares regression equation into account.
The line usually must go through two important points and have the same general slope as indicated in the equation.
Please see VCAA 2014 E2 Core Question 2b in the Examination Report as a reference.
Title: Re: VCE Further Maths Question Thread!
Post by: elle6299 on November 05, 2017, 06:13:31 pm
Spoiler
Knowing that the cones are similar, the volumes of the cones will be = 43 : r3.
We also know that the volume of the larger cone will be 3x the volume of the smaller one, so 3b: b, where b is the volume of the smaller cone, which is r3. Thus we actually have:
Spoiler
r3 = b
3b = 3r3 = 43 = 64
This can help you find r, which would be:
Spoiler
3r3 = 64
r3 = 64/3
r = cube root of 64/3 = 2.77 cm approx.
which rounds to 2.8.

This gives Option E.
Hope that helps.

Thankyou! May I ask, where did you get the 3b = 3r^3
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 05, 2017, 06:20:45 pm
Thankyou! May I ask, where did you get the 3b = 3r^3
Oh, sorry! Should've said that b is just an arbitrary number that I used to make the volume of the smaller cone, so it wasn't going to be the same pronumeral (and less confusing).

The question states that the larger cone's volume is 3 times that of the smaller cone's.
If I call the smaller cone's volume 'b', then 3b is the larger cone's volume.
We found that smaller cone's volume (b) is also r3 when scaled from length.
Substitute b = r3 into 3b and you get: 3b = 3r3.

That should make a bit more sense now.
Title: Re: VCE Further Maths Question Thread!
Post by: elle6299 on November 05, 2017, 06:22:28 pm
Oh, sorry! Should've said that b is just an arbitrary number that I used to make the volume of the smaller cone, so it wasn't going to be the same pronumeral (and less confusing).

The question states that the larger cone's volume is 3 times that of the smaller cone's.
If I call the smaller cone's volume 'b', then 3b is the larger cone's volume.
We found that smaller cone's volume (b) is also r3 when scaled from length.
Substitute b = r3 into 3b and you get: 3b = 3r3.

That should make a bit more sense now.

YES!! Thankyou, I've been trying to work out this question since last night!
Thankyou so much x
Title: Re: VCE Further Maths Question Thread!
Post by: masonjar on November 05, 2017, 06:31:02 pm
heylo,

I just had a quick question about financial stuff.

If they don't give you much information in the question for amortisation tables, what are various ways to find out the different columns in the table? Like the interest, payment, principal reduction ,etc,etc

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: isobelj on November 05, 2017, 07:07:37 pm
(http://uploads.tapatalk-cdn.com/20171105/4ee8b5e450759d542807194c4aa19d98.jpg)

How do I find the value of the last payment? I thought you had to take the last balance of the loan before it hit negatives and then take interest on that. But apparently you take the payment and add that on to the final balance, but that doesn’t really make sense.. why would you pay more than what the balance is worth? Picture attached is the specific question I’m having trouble with (d).
Title: Re: VCE Further Maths Question Thread!
Post by: pippinpie on November 05, 2017, 07:18:02 pm
For part d you have to add the amount that remains on the loan after 12 months to the $950 payment as the loan is to be paid within 12 months. Hence, the final payment is 950 + 149.67 = $109967
Title: Re: VCE Further Maths Question Thread!
Post by: emmaline on November 05, 2017, 07:37:18 pm
When we are using an objective function and are trying to find the maximum or minimum, is it a given that the maximum or minimum point will always be a corner point of the feasible region?
Title: Re: VCE Further Maths Question Thread!
Post by: BlinkieBill on November 05, 2017, 07:39:22 pm
Hi
For financial questions - does writing down the financial solver inputs actually count as working out??
I want to put some working down for them multi-steps to at least get 1/2 marks ya know
Title: Re: VCE Further Maths Question Thread!
Post by: pippinpie on November 05, 2017, 08:05:33 pm
Hi
For financial questions - does writing down the financial solver inputs actually count as working out??
I want to put some working down for them multi-steps to at least get 1/2 marks ya know
Yeah, VCAA confirmed this in Examiners Reports for previous years :)
Title: Re: VCE Further Maths Question Thread!
Post by: pippinpie on November 05, 2017, 08:07:28 pm
So, I was wondering for Geometry whether VCAA can use angles in degrees, minutes and seconds and if so how would you convert on the CAS...

Because it was on a TSSM practice exam I did and I had never come across it before

Mod edit: Posts merged. Please edit your existing post rather than double posting.
Title: Re: VCE Further Maths Question Thread!
Post by: janepage on November 05, 2017, 08:12:56 pm
Has anyone done 2015 exam 2, networks question 3???
Title: Re: VCE Further Maths Question Thread!
Post by: emmaline on November 05, 2017, 08:24:55 pm
Is 'year' numerical or categorical?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on November 05, 2017, 08:46:03 pm
Is 'year' numerical or categorical?

Depends on the context in which 'year' is used. For example, year of birth imo would be categorical. Years old (e.g. 15, 20) would be numerical.

Year could literally mean anything
Title: Re: VCE Further Maths Question Thread!
Post by: Angelx001 on November 05, 2017, 09:02:24 pm
Can someone please help me with 2009 exam 2 VCAA question 4.c
Reducing balance method by $11 046.83 . answer is $11 046.83 as the 'greater depreciation amount' but i don't get what it means by this & how they worked it out??
Thanks heaps1!! !
Title: Re: VCE Further Maths Question Thread!
Post by: MattBro on November 05, 2017, 09:07:37 pm
VCE Further Mathematics 2 (NHT) 2017

I have a question about drawing the graph in module 4
Question 1c ii.

I also attached the answer for the value of value of k from the previous question

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: hmdeadas on November 05, 2017, 09:35:02 pm
Hey, so when a questions asks " use RECURIONS to show value after x years" - do i use the recurance realtion or the rule for the nth term formula?
Title: Re: VCE Further Maths Question Thread!
Post by: Landa on November 05, 2017, 09:38:30 pm
Pen or pencil for the exam?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 05, 2017, 09:41:41 pm
Core: Financial Recursions
I just had a quick question about financial stuff.
If they don't give you much information in the question for amortisation tables, what are various ways to find out the different columns in the table? Like the interest, payment, principal reduction ,etc,etc
I can't help so much here, but I have a couple of links that might help (try the given Further formula sheet and this amortisation table site). Hope that helps.
Calculator Help
So, I was wondering for Geometry whether VCAA can use angles in degrees, minutes and seconds and if so how would you convert on the CAS...
Because it was on a TSSM practice exam I did and I had never come across it before
Mod edit: Posts merged. Please edit your existing post rather than double posting.
This video should help. Hopefully you have the same calculator. If you have the ClassPad, try this site instead.
Graphs and Relations (??)
When we are using an objective function and are trying to find the maximum or minimum, is it a given that the maximum or minimum point will always be a corner point of the feasible region?
Not sure what you mean here.
If you're talking about the Graphs and Relations module and you have a bunch of linear inequalities while looking for maxima or minima, they don't necessarily have to be in corners of the feasible region. VCAA tries to find equations that make the maxima/ maxima near them though, if they aren't, due to the fact that they'll likely make the questions about the same difficulty as the other modules.
NHT 2017 E2 Graphs and Relations Question 1cii
VCE Further Mathematics 2 (NHT) 2017

I have a question about drawing the graph in module 4
Question 1c ii.

I also attached the answer for the value of value of k from the previous question
Not sure what your question was, but my understanding of the question is that they want you to graph it when under the 1/x transformation, so you're essentially going 60 / (1/x) = 60x. Thus the answer.
Technical Questions
Pen or pencil for the exam?
Either is fine as long as you don't write lightly in pencil and don't use anything lighter than HB. Pen is generally preferred due to its legibility.
Title: Re: VCE Further Maths Question Thread!
Post by: Landa on November 05, 2017, 09:48:32 pm
Hey, so when a questions asks " use RECURIONS to show value after x years" - do i use the recurance realtion or the rule for the nth term formula?


In the case of "using recurrsions", use the recurrence relation to work out the answer (nth term formula should give the same answer though), they're asking you to "show", so show your calculations for the years leading up to the xth year.

Only when a question asks you to "write down a recurrence relation" or "rule" it will matter which formula you write/use.
Title: Re: VCE Further Maths Question Thread!
Post by: Landa on November 05, 2017, 09:59:31 pm
Can you lose marks for not including units for residuals? (this was a two mark question) - attached is 2017 nht exam solutions
Title: Re: VCE Further Maths Question Thread!
Post by: Angelx001 on November 05, 2017, 10:01:43 pm
Can someone please help me with 2009 exam 2 VCAA question 4.c
Reducing balance method by $11 046.83 . answer is $11 046.83 as the 'greater depreciation amount' but i don't get what it means by this & how they worked it out??
Thanks heaps1!! !
someone please?!?! :(

Title: Re: VCE Further Maths Question Thread!
Post by: Joseph41 on November 06, 2017, 11:14:53 am
Congratulations, everybody. :)

For all exam discussion, please head over to this thread.
Title: Re: VCE Further Maths Question Thread!
Post by: Kendog on November 06, 2017, 11:35:29 am
Where can i get the answers for exam 1
Title: Re: VCE Further Maths Question Thread!
Post by: Joseph41 on November 06, 2017, 12:49:28 pm
Where can i get the answers for exam 1

Right here. :)

P.S. Welcome to ATAR Notes!
Title: Re: VCE Further Maths Question Thread!
Post by: Etee on November 06, 2017, 03:11:47 pm
If I got a mid A in sacs, mid b on exam one but a low c on exam two what study score would I be looking at
Title: Re: VCE Further Maths Question Thread!
Post by: winged dragon 151 on November 06, 2017, 09:47:45 pm
Does any one have answers for linear graphs and relations exam 2 2017? I think I might have dropped 3 marks tops in that exam (rest I did terribly)
Title: Re: VCE Further Maths Question Thread!
Post by: idontknow__ on November 07, 2017, 02:54:45 pm
I don't see why the Further kids have to miss out on their own question thread! Post anything you're stuck with here and we'll try our best to help you out.

It might be a good idea to sticky this thread, just like the Methods and Specialist ones.

Can you estimate my SS ? 37/40 exam 1 and 54 or 53/60 for exam 2
Title: Re: VCE Further Maths Question Thread!
Post by: BaileyG14 on November 08, 2017, 08:52:08 pm
Does anyone happen to have the worked solutions to 2017 exam 2? Cant find them anywhere.
Title: Re: VCE Further Maths Question Thread!
Post by: winged dragon 151 on November 09, 2017, 09:40:31 am
SS Enquiry (Further)

Mid B+ (maybe scaled to low A????) in a weak cohort
Mid B-low B+ Exam 1
High A+- Exam 2

35 scaled possible?
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on December 22, 2017, 06:38:11 pm
Are further exams before 2016 similar to the current study design?
Title: Re: VCE Further Maths Question Thread!
Post by: EdwinaB19 on December 22, 2017, 06:53:04 pm
They are reasonably similar. You’ll find pre-2016 finance questions don’t quite extensively test the current study design, but there are still plenty of finance related questions in the business-related mathematics and recursion modules of the pre-2016 exams. I found that everything else was still super relevant to the current study design.
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on December 22, 2017, 07:30:39 pm
They are reasonably similar. You’ll find pre-2016 finance questions don’t quite extensively test the current study design, but there are still plenty of finance related questions in the business-related mathematics and recursion modules of the pre-2016 exams. I found that everything else was still super relevant to the current study design.
Thanks 8)
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on December 29, 2017, 12:33:20 pm
For the core data analysis part of further, are the core data analysis section of past exams a good way to revise for sacs  after attempting all the past sacs from my school?
Is the core data analysis section from further exam before 2016 similar to the current study design?
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on December 29, 2017, 01:16:21 pm
For the core data analysis part of further, are the core data analysis section of past exams a good way to revise for sacs  after attempting all the past sacs from my school?
Is the core data analysis section from further exam before 2016 similar to the current study design?
Thanks
Yes to both your questions. You'll need to find some newer stuff or check out the number patterns and business maths modules for help in the financial recursion modules though, as that's a newer addition in recent years.
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on December 29, 2017, 03:00:03 pm
Yes to both your questions. You'll need to find some newer stuff or check out the number patterns and business maths modules for help in the financial recursion modules though, as that's a newer addition in recent years.
Thanks AngelWings
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on January 05, 2018, 04:50:05 pm
The ages of people surveyed was normally distributed with a mean of 19.5 years and a standard deviation of 2.9 years
Estimate the percentage of people between 19.5 and 25.3
Estimate the percentage of people below 16.6

Does anybody know what formula is needed and how these questions are worked out?
Title: Re: VCE Further Maths Question Thread!
Post by: VanillaRice on January 05, 2018, 04:57:16 pm
The ages of people surveyed was normally distributed with a mean of 19.5 years and a standard deviation of 2.9 years
Estimate the percentage of people between 19.5 and 25.3
Estimate the percentage of people below 16.6

Does anybody know what formula is needed and how these questions are worked out?
I didn't do Further, but I suspect this is an application of the 68-95-99.7% rule for normal distributions. That is, 68% of values will lie 1 SD from the mean, 95% will lie 2 SD from the mean, and 99.7% will lie 3 SD from the mean. The best way to answer this type of question (from my knowledge) is to draw a normal distribution curve, shade the area which you want, and work it out from there :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on January 05, 2018, 05:15:04 pm
The ages of people surveyed was normally distributed with a mean of 19.5 years and a standard deviation of 2.9 years
Estimate the percentage of people between 19.5 and 25.3
Estimate the percentage of people below 16.6

Does anybody know what formula is needed and how these questions are worked out?
I didn't do Further, but I suspect this is an application of the 68-95-99.7% rule for normal distributions. That is, 68% of values will lie 1 SD from the mean, 95% will lie 2 SD from the mean, and 99.7% will lie 3 SD from the mean. The best way to answer this type of question (from my knowledge) is to draw a normal distribution curve, shade the area which you want, and work it out from there :)
VanillaRice has already answered your question, but I'd like to recommend that you copy the image of the normal distribution with the standard deviations and associated percentages straight into your bound reference. This type of question is one that reappears frequently in exams.
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on January 05, 2018, 08:42:39 pm
Could someone explain standard deviation?

Somehow I made it through general without knowing how to work it out. 😂 I’ve seen a formula but there’s a symbol I don’t know, (it sort of looks like £ but less money-like I think?) I asked but they looked at me funny and said I should know it because we had already done our SAC on it.

Like, what even is standard deviation? Is it something about how different the data is?
Title: Re: VCE Further Maths Question Thread!
Post by: VanillaRice on January 05, 2018, 08:46:03 pm
Could someone explain standard deviation?

Somehow I made it through general without knowing how to work it out. 😂 I’ve seen a formula but there’s a symbol I don’t know, (it sort of looks like £ but less money-like I think?) I asked but they looked at me funny and said I should know it because we had already done our SAC on it.

Like, what even is standard deviation? Is it something about how different the data is?
Standard deviation is essentially how spread out a set of data is. By spread out, I mean that on average, how far away are the values from the mean? I guess you could see it as how 'different' each of the values in your data set is different from the mean.

The big 'E' you see in the formula is capital Greek sigma, and basically means you add up something. In this case, you find the differences between every single value in your dataset and the mean, square this difference, and then add them all up.

Hope this helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: Dr. Nick on January 06, 2018, 07:46:39 am
So I was doing this question, which asks you to convert a two-way-frequency table into a percentage two way frequency table but I noticed that the explanatory variables were in the rows instead of the columns where they usually are placed. So I rearranged the table to place the explanatory variables in the columns and use their totals to get percentages... but then I checked my answer and they didnt do that. I thought that you always use the explanatory totals to get percentages?

The question also then asked to create a percentage segmented bar graph, and they has placed the response variable on the horizontal axis and the explanatory variable on the vertical axis.

Can someone please explain why im wrong? - Ive attched the answers


Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on January 06, 2018, 10:21:57 am
Thanks guys for the help :)
Does anyone know if it's possible to work out deseasonalized figures for a group of data on the CAS?
Title: Re: VCE Further Maths Question Thread!
Post by: MissSmiley on January 06, 2018, 11:32:59 am
Can someone please explain why im wrong? - Ive attched the answers
Hi there,
You're right!
The simple trick to remember where to put the response and explantory variable is just picture a graph. So the response on the y-axis and the explanatory on the x.
So in that case, like you said, the response variable (number of blood donors) should go in the rows, and the explanatory (age group) in the colums.
I don't know why your textbook gives that answer as the two way percentage frequency table...
And the percentage segmented bar chart has faults as well. You're right, the age groups should have separate bar charts, and the colour coding should be "whether or not they were blood donors or not," and obviously their percentages would be on the "percentage frequency" (y-axis)
I've attached two pictures that correctly represent what you should do with the two-way frequency table and percentage segemented.
I think your task would be to double check with your teacher straight away when school starts. But at the moment, you're right!
Does your textbook do this for every single problem?
Feel free to ask me if you want any explanation about the photos (i.e. which variable is 'x' and which one is 'y')
Hope this helps ! :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on January 06, 2018, 12:54:22 pm
Thanks guys for the help :)
Does anyone know if it's possible to work out deseasonalized figures for a group of data on the CAS?
There is, but the way you’d do it would be similar to how you do it on Excel. In all honesty, there won’t be a time you’d be have to do the entire thing in an exam (perhaps one value in the entire table is possible), but there is a chance it’ll be an application SAC (usually this is broken down to parts, so there is some guidance). If anything, it might be faster to do it as a table on paper and use the CAS for its basic calculator functions.
Title: Re: VCE Further Maths Question Thread!
Post by: Dr. Nick on January 06, 2018, 03:04:52 pm
Hi, thank you so much for the response! This question was from the online work sheets that comes with the textbook, and it's not an actual textbook question which is why it's probably inaccurate but I'll make sure to double check with my teacher once school starts, thanks again for the help  :)
Title: Re: VCE Further Maths Question Thread!
Post by: Dr. Nick on January 06, 2018, 07:09:32 pm
What's the best way to determine the type of association depicted in a scatter plot through inspection/without calculating the correlation coefficient? These questions are usually multiple choice, and I always get them wrong because I keep overthinking it... is there any mathematical method or do you have to just know on your own?


Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on January 06, 2018, 08:07:04 pm
I have merged your threads with our stickied VCE Further Maths Question thread @Dr. Nick. Please post content-related queries here instead rather than creating a separate thread for each question. Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: MissSmiley on January 06, 2018, 08:28:48 pm
What's the best way to determine the type of association depicted in a scatter plot through inspection/without calculating the correlation coefficient? These questions are usually multiple choice, and I always get them wrong because I keep overthinking it... is there any mathematical method or do you have to just know on your own?
Here's a diagram for all the scatterplot associations (linear), strong, moderate, weak and positive and negative. And obviously non-linear would be curved somewhere in the scatterplot.
Whilst this is a useful visual aid, please don't fall into VCAA's trap of merely looking at any scatterplot without calculating the 'r' value and jumping to conclusions about its associations. Because you never know, for e.g. 'strong' and 'moderate' relationships can look very very similar!
Instead, judge by the correlation coefficient value! (And it's really easily found on the CAS, so no need to stress about that, if you've got all your x and y values sorted out!)
To judge from the 'r' value, I'm sure you have some sort of table or diagram that has the range of values of 'r' and then what relationship that would mean (e.g. strong positive relationship, weak negative relationship)
Hope this helps! :)
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on January 06, 2018, 08:52:18 pm
Here's a diagram for all the scatterplot associations (linear), strong, moderate, weak and positive and negative. And obviously non-linear would be curved somewhere in the scatterplot.
Whilst this is a useful visual aid, please don't fall into VCAA's trap of merely looking at any scatterplot without calculating the 'r' value and jumping to conclusions about its associations. Because you never know, for e.g. 'strong' and 'moderate' relationships can look very very similar!
Instead, judge by the correlation coefficient value! (And it's really easily found on the CAS, so no need to stress about that, if you've got all your x and y values sorted out!)
To judge from the 'r' value, I'm sure you have some sort of table or diagram that has the range of values of 'r' and then what relationship that would mean (e.g. strong positive relationship, weak negative relationship)
Hope this helps! :)
If r is a positive association, then would r^2 also be a positive association?
Title: Re: VCE Further Maths Question Thread!
Post by: jazzycab on January 06, 2018, 09:25:09 pm
If r is a positive association, then would r^2 also be a positive association?

This tells us the proportion of variability in the response variable that can be explained by the variability in the explanatory variable (other variability can be attributed to other factors).
Although values closer to 1 would indicate stronger associations, the coefficient of determination on its own doesn't tell us anything about the direction. This is a property that can only be attributed to the r value
Title: Re: VCE Further Maths Question Thread!
Post by: Dr. Nick on January 07, 2018, 09:24:42 am
Here's a diagram for all the scatterplot associations (linear), strong, moderate, weak and positive and negative. And obviously non-linear would be curved somewhere in the scatterplot.
Whilst this is a useful visual aid, please don't fall into VCAA's trap of merely looking at any scatterplot without calculating the 'r' value and jumping to conclusions about its associations. Because you never know, for e.g. 'strong' and 'moderate' relationships can look very very similar!
Instead, judge by the correlation coefficient value! (And it's really easily found on the CAS, so no need to stress about that, if you've got all your x and y values sorted out!)
To judge from the 'r' value, I'm sure you have some sort of table or diagram that has the range of values of 'r' and then what relationship that would mean (e.g. strong positive relationship, weak negative relationship)
Hope this helps! :)


Thanks! I prefer the method of calculating r, but some questions say to do it through inspection but from now on i'll just calculate r just to be sure.
Title: Re: VCE Further Maths Question Thread!
Post by: Dr. Nick on January 07, 2018, 02:11:25 pm
Hi again
why does 12.47 round to 13 (if you want it to be to two significant figures?)

wouldn't you just look at the next number after 2 which in the case of this example is 4 and according to the rule numbers 0-4 you dont round up? My answer was 12 but my textbook says its 13.

I understand why 12.57 would round to 13 (for two sig fig) but why would 12.47?

Title: Re: VCE Further Maths Question Thread!
Post by: Vaike on January 07, 2018, 02:29:33 pm
My answer was 12 but my textbook says its 13.

Hiya. I'd be inclined to assume it's an error in the textbook's answers;  there a often small mistakes like this in the answer section and from what I can I tell your answer of 12 should indeed be correct.
Title: Re: VCE Further Maths Question Thread!
Post by: Dr. Nick on January 07, 2018, 05:29:04 pm
Hiya. I'd be inclined to assume it's an error in the textbook's answers;  there a often small mistakes like this in the answer section and from what I can I tell your answer of 12 should indeed be correct.

Thanks for the help!! ill double check with my teacher once school starts.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on January 07, 2018, 07:12:39 pm
Hi again
why does 12.47 round to 13 (if you want it to be to two significant figures?)

wouldn't you just look at the next number after 2 which in the case of this example is 4 and according to the rule numbers 0-4 you dont round up? My answer was 12 but my textbook says its 13.

I understand why 12.57 would round to 13 (for two sig fig) but why would 12.47?
Aside from the small leeway given to some questions (e.g. to compensate for preemptive rounding), it could also be the scenario it is in. If the question is a worded question about the minimum number of trees that will line the side of a freeway (just a random example) and the answer becomes 12.47, then it'll have to be rounded up to 13, not 12. This is due to the feasibility of the scenario, as 12 wouldn't quite reach the minimum. (If that makes sense. If it doesn't, I'll find an example to explain what I mean.)

As you stated, normal rules state that to round to 2 sig. fig.s, you'd round 12.47 to 12. Depending on the nature of the question, however, it might be one of these exceptions.
Title: Re: VCE Further Maths Question Thread!
Post by: ellimurphy on January 25, 2018, 09:54:36 pm
Can someone please explain correcting for seasonality to me?
I've been trying to work it out for a solid hour!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on January 25, 2018, 11:35:56 pm
Can someone please explain correcting for seasonality to me?
I've been trying to work it out for a solid hour!
Correcting for seasonality is a bit of a long one to explain. In the shortest explanation of this, the main equation you'll need is: actual value = deseasonalised value x seasonal index. Basically what you want to do is to correct it to 1 or 100 (whatever the case may be) to get it back to 'normal', so that 1 or 100 is the actual value and apply the above equation. 
Some classic questions regarding correcting for seasonality are found: here, here, How to calculate seasonal indices, VCAA Exam 1 2014 Core Q12 and VCAA Exam 1 2011 Core Q12*.

* I explained this question on this thread ages back, so I don't remember where it's gone, but here's a quick explanation.
VCAA E1 2011 Core Q12
The 'actual value' you want is 1. The seasonal index you have been given is 0.80.
Apply to formula: actual value = deseasonalised value x seasonal index
1 = deseasonalised value x 0.80
deseasonalised value = 1 / 0.80 = 1.25   <--- I switched the subject around
1.25 - 1.00 = 0.25                                     <--- I took away 1 to see its relative position against the actual value. Multiply by 100 to get percentage.
This provides a 25% increase. (Note: It was + 0.25.)

Yeah, sorry that doesn't quite explain correcting for seasonality, but I've run out of time to throw up a document. I'm sure someone will give a much better explanation than my two minute one above.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on January 26, 2018, 09:39:11 am
Does anyone have a cas guide on doing seasonal adjustments quickly on the spreadsheet?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on January 26, 2018, 11:40:32 am
Does anyone have a cas guide on doing seasonal adjustments quickly on the spreadsheet?
See “how to calculate seasonal indices” link in previous post.
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on February 01, 2018, 04:28:46 pm
Does anyone know how to make a good further maths summary book, and what should be in it, and would the same thing apply to math methods?
Title: Re: VCE Further Maths Question Thread!
Post by: Calebark on February 01, 2018, 04:36:19 pm
Does anyone know how to make a good further maths summary book, and what should be in it, and would the same thing apply to math methods?

We have an article on that which may help you.
Title: Re: VCE Further Maths Question Thread!
Post by: 011116 on February 01, 2018, 10:50:05 pm
how does one study for further like for that specific chapter, for example i finished a chapter and like did all the review questions and questions in the book but i want to test myself and my knowledge on the topic
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on February 02, 2018, 11:17:07 am
how does one study for further like for that specific chapter, for example i finished a chapter and like did all the review questions and questions in the book but i want to test myself and my knowledge on the topic
Generally the best way to do so is Checkpoints, books like ExamPro and practise exams. The chapters will be based loosely around the various modules in Further.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on February 04, 2018, 06:46:41 pm
I just wanted to get some opinions on how early practice exams should be started. I have almost finished the chapter questions for core and my modules but plan to finish chapter reviews and then A+ questions before starting exams.
Would it be too early to start exams in ~April?
Title: Re: VCE Further Maths Question Thread!
Post by: Vaike on February 04, 2018, 08:27:05 pm
Would it be too early to start exams in ~April?

To be honest, I think its way too early. You'll quickly run out of practice exams I'd think. The earliest I'd probably think about it is the beginning of August. It's really important that you don't burn out, as its important you're in the best spot possible come exam time, and that you're not simply sick of Further exams. Instead, I'd suggest practice SACs, other textbooks questions, revising over/constructing a bound reference, or just spending more time on your other subjects!
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on February 04, 2018, 08:36:37 pm
Fair enough. Thanks for the advice!
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on February 05, 2018, 06:26:34 pm
A few questions
1.How would you determine the location of the upper fence and the lower fence when you're shown a boxplot with outliers
2.If you're shown a boxplot with outliers and you're asked to estimate the percentage of values that are less than a certain number, do you include the outliers when determining the percentage?
3. the distribution of heights of 19-year old woman is approximately normal, with a mean of 170cm and a standard deviation of 5cm
What percentage of these women have heights: between 160 and 175 cm
like 160 is 2 standard deviations below the mean, and 175 is 1 standard deviation above the mean, so how would you work it out in this case since there are different standard deviations (2 and 1)
4. if you're given two variables, number in theatre and time (minutes), and given values for both variables and asked to draw a scatterplot, how do you determine the response and explanatory variables if they aren't given to you?

5. what's the difference between a positive and a negative association and how do you determine if 2 variables have a positive or negative association
for example
1. population density and distance from city centre
2. time using social media and time spent studying
Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: addictwithatextbook on February 05, 2018, 07:01:32 pm
A few questions
1.How would you determine the location of the upper fence and the lower fence when you're shown a boxplot with outliers.
2.If you're shown a boxplot with outliers and you're asked to estimate the percentage of values that are less than a certain number, do you include the outliers when determining the percentage?
3. the distribution of heights of 19-year old woman is approximately normal, with a mean of 170cm and a standard deviation of 5cm
What percentage of these women have heights: between 160 and 175 cm
like 160 is 2 standard deviations below the mean, and 175 is 1 standard deviation above the mean, so how would you work it out in this case since there are different standard deviations (2 and 1)
4. if you're given two variables, number in theatre and time (minutes), and given values for both variables and asked to draw a scatterplot, how do you determine the response and explanatory variables if they aren't given to you?

Thanks :)

Hey!
1. You would find them as normal - the ends of the box.

2. Yes.
When interpreting a box plot, outliers only affect your interpretation of the maximum and the minimum - if there is an outlier on any end, it is a maximum or a minimum, and not the ends of the whisker. All other interpretations - such as finding the IQR, median, upper fence, lower fence, and percentage of values from a data value that meets with a line on the box - are done as with no outliers. Rarely, or never, will they ask the percentage or number of values that are not outliers.

3. Use the normal distribution and 68-95-99.7% diagram (you should have one of these) - as you have identified with the number of s.d's below and above the mean, it will be 13.5% + 34% + 34%, or 64% + 13.5%.

4. Think of the variables - which one depends on what? Does time depend on the number of people in the theatre, or does the number of people in the theatre depend on the time? Which one makes sense? The response variable is the one that is dependent on/is affected by the explanatory variable. In this example, the time that goes on affects the number of people in the theatre. (As a side note, time will always be an explanatory variable, as time is time. It cannot be clearly affected by anything else).

5. A positive association occurs when the values of the response variable tends to increase as the explanatory variable increases (positive r value, regression line goes upwards), whereas a negative association occurs when the values of the response variable tends to decrease as the explanatory variable increase (negative r value, regression line goes downwards). The example requires more thinking than determining which variable is the response or explanatory. Think of real life.
For (1), does population density (RV) increase when distance from city centre (EV) increases, i.e. more towards the country? It doesn't, population density decreases, so there is a negative association between these variables. For (2), is it true that time studying is less when time using social media increases? (The RV and EV between these two can be interchangeable.)

I hope this was clear to you. :)
Title: Re: VCE Further Maths Question Thread!
Post by: behlanarobinson on February 13, 2018, 09:22:01 am
I just wanted to get some opinions on how early practice exams should be started. I have almost finished the chapter questions for core and my modules but plan to finish chapter reviews and then A+ questions before starting exams.
Would it be too early to start exams in ~April?
I did the questions our teacher gave us from old exams to prepare for Sacs however I didn't actually start doing practice exams until we finished all the content (mid term 3). I still managed to get through all the practice exams I could get my hands on (37 to be exact) and if I had've started earlier I would have had less to focus on prior to the exam and I would have forgotten what I learnt from doing the exam.
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on February 20, 2018, 07:58:49 am
Not exactly related to further but for my summary book for further maths  i just glued all the worked examples from my textbook into a notebook and now my notebook won't really close properly. Is there any way to fix this?
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on February 20, 2018, 08:10:12 am
Could you attach a picture of what you mean. I can't quote visualise it
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on February 20, 2018, 06:56:54 pm
Could you attach a picture of what you mean. I can't quote visualise it
My book closes but not fully, as in the pages don't really touch each other when closing
Title: Re: VCE Further Maths Question Thread!
Post by: Poet on March 03, 2018, 12:30:43 pm
Hey all,

I'm sort of confused about how to use logs and their functions in the CAS Classpad II. Can anyone help me with this, maybe give me an example question/tutorial to work through?
Also are they related to least squares regression? My class is going too fast for me and everything has been blurring together...

Thank you! x3
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 04, 2018, 02:52:23 pm
My book closes but not fully, as in the pages don't really touch each other when closing
Pretty sure that's fine, as long as the book is A4 or smaller in total.

Hey all,

I'm sort of confused about how to use logs and their functions in the CAS Classpad II. Can anyone help me with this, maybe give me an example question/tutorial to work through?
Also are they related to least squares regression? My class is going too fast for me and everything has been blurring together...

Thank you! x3
Logs are found on the second line after clicking the keyboard button, according to the first 5 seconds of this video. Ln is log with base e. Log by default is log to the base 10, but can be altered to have any base as necessary. Logs are used to (a) counteract exponential (kind of the same way division is the opposite of multiply) (b) used to find unknowns when they're the power e.g. 10x=100 can be undone by doing log10(100)=x. Further information can be found on here.

And least squares? If it's a log transformation, then yes. Otherwise, not really.

Hope that helps.
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on March 04, 2018, 02:59:03 pm
Hi angelwings,
Do you know if it's a breach of vcaa rules if my bound reference for further maths is bigger than A4 size?
Also, do you think it's good if my bound reference for further is just notes from my textbook and also worked examples from my textbook?
Thanks ;D
Title: Re: VCE Further Maths Question Thread!
Post by: VinnyD on March 04, 2018, 03:41:00 pm
Hi angelwings,
Do you know if it's a breach of vcaa rules if my bound reference for further maths is bigger than A4 size?
Also, do you think it's good if my bound reference for further is just notes from my textbook and also worked examples from my textbook?
Thanks ;D
Someone could correct me if i'm wrong but your pages, including your fold out pieces, have to be A4 size max.
Also i don't think anyone can really tell you what is and what is not a good idea for you bound ref because it is personal :) Just make sure that you are comfortable using it and it covers everything that you need for the exam. In my case, I'm using a notebook which will include hard questions and things that i tend to forget. 
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on March 04, 2018, 04:04:38 pm
Someone could correct me if i'm wrong but your pages, including your fold out pieces, have to be A4 size max.
Also i don't think anyone can really tell you what is and what is not a good idea for you bound ref because it is personal :) Just make sure that you are comfortable using it and it covers everything that you need for the exam. In my case, I'm using a notebook which will include hard questions and things that i tend to forget.
Thanks  ;D
Wouldn't it be a better idea to just take in the textbook for the exam, and the bound reference for sacs?
Title: Re: VCE Further Maths Question Thread!
Post by: VinnyD on March 04, 2018, 05:03:10 pm
Thanks  ;D
Wouldn't it be a better idea to just take in the textbook for the exam, and the bound reference for sacs?
Personally i think the textbook is a bit too easy in terms of it's questions, or they are worded incorrectly and so i tend to steer away from it. For me, it's much more reassuring making notes from scratch because:
1) the textbook is a bit big and so it'll take a bit of time to get to specific pages
2) There are some missing concepts in the book such as choosing the best transformation and explaining why
3) You can find the gaps in your knowledge and focus on them in your notes
4) You can put past VCAA questions in it

I'd also recommend using the bound ref you are going to take into the exam, in your sacs because you will become familiar with it.

Just my two cents but hope it helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on March 04, 2018, 05:04:55 pm
Highly recommend not taking in the textbook. You don't get much time in each of your exams and having to flick through pages and pages to find the specific content point that you're after takes time. Doing notes yourself will ensure that you know where things are for ready access, and not to mention the fact that you will understand what you've put in because ideally you've written it yourself. :)
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on March 04, 2018, 05:19:35 pm
Highly recommend not taking in the textbook. You don't get much time in each of your exams and having to flick through pages and pages to find the specific content point that you're after takes time. Doing notes yourself will ensure that you know where things are for ready access, and not to mention the fact that you will understand what you've put in because ideally you've written it yourself. :)
Is it true that writing things generally makes us remember them better as opposed to typing them?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 04, 2018, 05:33:24 pm
Do you know if it's a breach of vcaa rules if my bound reference for further maths is bigger than A4 size?
Also, do you think it's good if my bound reference for further is just notes from my textbook and also worked examples from my textbook?
Is it a breach if it's larger than A4? Yes it is. That include any tabs that sticks out of it.
Just notes and worked examples from a textbook? I find this to be a bit wasteful, but that's my opinion only. I usually annotate my notes and so forth to make them useful to me. My best advice in this situation is to actually cut down the pages you've stuck in there, so that it closes where possible. If that's not possible, then it's alright - just check this by your maths teacher to see if it's permitted.
Someone could correct me if i'm wrong but your pages, including your fold out pieces, have to be A4 size max.
Pretty much. See here for the rules.
Wouldn't it be a better idea to just take in the textbook for the exam, and the bound reference for sacs?
I would recommend that if you intend to take the textbook that it fits the VCAA rules and that you're familiar with where everything is. If you're intending to mark it with permanent tabs, don't forget that the entire book + tabs must be within A4 size. I actually think it's better to make your bound reference reference for exams, because you'll be way more familiar with that and you can reorganise everything to your standards (most students like to put in formulas, cheat sheets, questions they got wrong and concepts for each module they learnt). This is harder with a textbook.

Is it true that writing things generally makes us remember them better as opposed to typing them?
Yes, but I can't recall the stats properly, however I think it was marginally better.
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on March 05, 2018, 08:30:18 am
Does anyone know how a residual plot is drawn?
Title: Re: VCE Further Maths Question Thread!
Post by: MAGGOT on March 05, 2018, 10:00:44 am
Does anyone know how a residual plot is drawn?
I'm pretty sure the residual plot is the regression line turned so it's a straight horizontal line
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on March 08, 2018, 07:54:21 pm
How can we conclude if a residual plot suggests that the use of a linear model to fit data would not work?
Title: Re: VCE Further Maths Question Thread!
Post by: Bell9565 on March 08, 2018, 08:20:36 pm
How can we conclude if a residual plot suggests that the use of a linear model to fit data would not work?
If there is no pattern in the residual plot it suggests the data is linear. If there is a clear pattern (eg parabolic) then a linear model most likely would not fit - however after a transformation it may.
Title: Re: VCE Further Maths Question Thread!
Post by: Poet on March 08, 2018, 08:22:42 pm
How can we conclude if a residual plot suggests that the use of a linear model to fit data would not work?

If the residual plot shows a clear pattern, it is a non-linear association. You can assume it's linear if there is no clear pattern and the values are seen as randomly scattered. For example:
(http://www.statisticshowto.com/wp-content/uploads/2015/06/image014.gif)
This image is a residual plot with a pattern. This shows an obvious non-linear association between the points. However, in this plot:
(http://oregonstate.edu/instruct/st352/kollath/handouts/simplereg/residuals_files/image006.gif)
We cannot see any pattern, therefore verifying the values as linear.
Title: Re: VCE Further Maths Question Thread!
Post by: snowisawesome on March 12, 2018, 11:06:03 am
Y = -0.01+4.1x^2
But the question said to write the slope and intercept correct to one decimal
The answer said y = 4x^2
Does anyone know how to round -0.01 correct to one decimal place
Thanks ;D
Title: Re: VCE Further Maths Question Thread!
Post by: Yertle the Turtle on March 12, 2018, 01:40:00 pm
Y = -0.01+4.1x^2
But the question said to write the slope and intercept correct to one decimal
The answer said y = 4x^2
Does anyone know how to round -0.01 correct to one decimal place
Thanks ;D
0. That is really the only way to round it.
Title: Re: VCE Further Maths Question Thread!
Post by: tm11 on March 21, 2018, 07:33:35 pm
HELP HELP HELP!!!!

If we have the z score (-1.4) , the mean (0.471) and the standard deviation (0.128), how does this justify that the data is a normal distribution?? PLS HELP :)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 21, 2018, 08:27:10 pm
HELP HELP HELP!!!!

If we have the z score (-1.4) , the mean (0.471) and the standard deviation (0.128), how does this justify that the data is a normal distribution?? PLS HELP :)
If my stats skills don't serve me wrong, in order to get these statistics, mostly z score and often st. dev.., this is an assumption we make of the data set.
Title: Re: VCE Further Maths Question Thread!
Post by: Homer on April 11, 2018, 04:48:43 pm
How would you do C?  :o
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on April 21, 2018, 08:01:07 am
When we are drawing a graph (e.g a bar chart) Do we need to draw horizontal lines across? Like if our Y axis counts in 2’s do we need to do a dotted line for the numbers that aren’t listed or is that just something they do in textbooks to help us read it?
Title: Re: VCE Further Maths Question Thread!
Post by: jazzycab on April 21, 2018, 02:27:43 pm
When we are drawing a graph (e.g a bar chart) Do we need to draw horizontal lines across? Like if our Y axis counts in 2’s do we need to do a dotted line for the numbers that aren’t listed or is that just something they do in textbooks to help us read it?
In any VCE maths exam, you only need to draw on a graph whatever the question instructs you to draw, so, no, these lines are not necessary
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on April 25, 2018, 11:11:35 pm
Just need help with b i) and ii)
Title: Re: VCE Further Maths Question Thread!
Post by: MAGGOT on April 25, 2018, 11:42:41 pm
Just need help with b i) and ii)

7bi)
Rate * Previous balance of loan = Interest paid
Where interest paid = $100
           previous balance of loan = $4000
           rate = x
*Note you can use any numbers from the table as long as you use the interest paid of that row and the balance of loan from the row above of it
x * 4000 = 100
x = 0.025 * 100 = 2.5%
Therefore the quarterly interest rate is 2.5%
7bii)
The annual interest rate is x4 the amount of the quarterly interest rate
Rate = 2.5% * 4
         = 10.0%
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on May 05, 2018, 10:32:49 pm
need help with Q4, Q7 in 2013 further exam 1 -- business.


Title: Re: VCE Further Maths Question Thread!
Post by: jazzycab on May 06, 2018, 11:29:51 am
need help with Q4, Q7 in 2013 further exam 1 -- business.

For Question 4:
The total amount paid is the amount of each payment multiplied by the number of payments, plus the deposit: \(A=36\times400+3000=17400\).
The total amount of interest paid is the amount in excess of the purchase price: \(I=A-PP=17400-15500=2400\).
The interest rate can be then calculated using the simple interest equation (note that 36 months = 3 years and that interest can only be paid on the loan amount which is the amount remaining after the deposit has been paid \(P=15000-3000=12000\)):

So the answer is D.

For Question 7:
The graph is linear, which indicates simple interest. At 0 years, the investment value is $1000 (i.e. the principal investment amount). After 1 year, the investment amount is $1050. Thus, \(1050-1000=50\) is the amount of interest earned in 1 year. From this information, we can find the interest rate:

The second investment has $600 of interest earned in 8 years, at the same interest rate (5% p.a. simple interest):

So the answer is C.
Title: Re: VCE Further Maths Question Thread!
Post by: michaeljacksonftw on May 20, 2018, 07:28:58 pm
How do you work out the quarterly interest rate from an amortization table? (#financial maths sucks)
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on May 20, 2018, 11:49:39 pm
How do you work out the quarterly interest rate from an amortization table? (#financial maths sucks)


Interest paid/ Previous Balancex100 for what ever compounding interest rate.

For annual, do interest/previous balance x 100 x compounding periods (for example 4 for quarters)
Title: Re: VCE Further Maths Question Thread!
Post by: michaeljacksonftw on May 21, 2018, 01:40:05 pm
Our school split the core data analysis sac into 2 parts. In part A I got 38/40 but I stuffed up part B getting 32/40. So my overall score is 35/40. Can I still get a study score of 45 raw in further? A few people got 100% in both part A and part B, but we aren't told our rankings. Most of my marks I lost are careless. I'm in a strong cohort, last year there were about 40 40+ scores and a few 50s.
Title: Re: VCE Further Maths Question Thread!
Post by: CainBFG on May 24, 2018, 07:20:15 pm
PLEASE someone help with Financial Maths!!!! Notes or worksheets, ANYTHING!!!
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on May 31, 2018, 04:52:18 pm
Hi!
Can someone please explain what they are saying in the study design when they say
"cause and effect; the difference between observation and experimentation when collecting data and the need for experimentation to definitively determine cause and effect" and "non-causal explanations for an observed association including common response, confounding, and coincidence;discussion  and  communication  of  these  explanations  in  a  particular  situation  in  a  systematic  and  concise  manner." ?
I am not sure whether our teachers have explained this differently or whether we have missed learning it. Please explain?  :-\
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on May 31, 2018, 05:02:24 pm
Hi!
Can someone please explain what they are saying in the study design when they say
"cause and effect; the difference between observation and experimentation when collecting data and the need for experimentation to definitively determine cause and effect" and "non-causal explanations for an observed association including common response, confounding, and coincidence;discussion  and  communication  of  these  explanations  in  a  particular  situation  in  a  systematic  and  concise  manner." ?
I am not sure whether our teachers have explained this differently or whether we have missed learning it. Please explain?  :-\
This is basically just the whole 'correlation does not equal causation' thing. It's saying that just because something appears to be related does not mean that one thing causes the other. Experimentation allows other variables to be controlled whereas if only observation is used to determine the relationship there could be many, many other factors influencing it. (15 weird things that appear to be related)

The non-casual explanations are basically just explanations other than them being related.
Common response: Both of the variables measured are due to a 3rd unmeasured variable
Confounding: There are other uncontrolled variables affecting the results
Coincidence: They just happen to appear related.

The communication thing is just being able to say whether they are related and what other possible explanations for the apparent relationship could be (i.e. the things listed above).
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on May 31, 2018, 05:07:58 pm
This is basically just the whole 'correlation does not equal causation' thing. It's saying that just because something appears to be related does not mean that one thing causes the other. Experimentation allows other variables to be controlled whereas if only observation is used to determine the relationship there could be many, many other factors influencing it. (15 weird things that appear to be related)

The non-casual explanations are basically just explanations other than them being related.
Common response: Both of the variables measured are due to a 3rd unmeasured variable
Confounding: There are other uncontrolled variables affecting the results
Coincidence: They just happen to appear related.

The communication thing is just being able to say whether they are related and what other possible explanations for the apparent relationship could be (i.e. the things listed above).

Awesome thanks so much!!! ;)
Title: Re: VCE Further Maths Question Thread!
Post by: nicholas9027 on June 15, 2018, 11:03:25 am
Hey guys can you give me tips to help tackle these question pls
Chris borrows $100000 at 8% compounding monthly, to be paid over 10 years with repayments of $1213.28 each month. After 5 years, the interest rate is reduced to 7.5%pa. (i dont know what to do for the After 5 years interest rate change)
a)Find the new repayment required for Chris to pay off loan in the same amount of time.
b)How much money does Chris save due to the interest rate cut?
the answers
a) $1199
b)$856.80
Title: Re: VCE Further Maths Question Thread!
Post by: nicholas9027 on June 16, 2018, 02:30:41 pm
pls help^ im stuck :(
Title: Re: VCE Further Maths Question Thread!
Post by: MAGGOT on June 17, 2018, 01:36:07 pm
Hey guys can you give me tips to help tackle these question pls
Chris borrows $100000 at 8% compounding monthly, to be paid over 10 years with repayments of $1213.28 each month. After 5 years, the interest rate is reduced to 7.5%pa. (i dont know what to do for the After 5 years interest rate change)
a)Find the new repayment required for Chris to pay off loan in the same amount of time.
b)How much money does Chris save due to the interest rate cut?
the answers
a) $1199
b)$856.80

a)
1] First you need to find the future value after 5 years
n=5*12, 1=8, pv= 100,000, pmt= -1213.28, ppy=12
Solve for Fv
Fv= -59836.57

2] Then solve the new payments if the loan is payed off
n=60, i=7.5, pv= -fv <- previous fv but positive, fv=0, ppy=12
Solve for pmt
pmt= $1199.00

b)
1] You need to find the total amount paid for both types of options using:
           Number of payments x Payment amount
Using 8%
60 x 1199 = 72796.80
using 7.5%
60 x  1213.28 = 71940

2] Find the difference between the 2 numbers
72796.80 - 71940 = $856.80
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on June 27, 2018, 05:20:39 pm
How relevant are some of the extremely old exams from 2006-2015 to the new 16-18 study design? Should these earlier practice exams be done in timed conditions despite having a slightly different lay out of topics? Or would it be better to simply focus on the last two year's exams and other company trial exams that have been released following the study design change.
Title: Re: VCE Further Maths Question Thread!
Post by: cdiamond on June 27, 2018, 05:33:01 pm
How relevant are some of the extremely old exams from 2006-2015 to the new 16-18 study design? Should these earlier practice exams be done in timed conditions despite having a slightly different lay out of topics? Or would it be better to simply focus on the last two year's exams and other company trial exams that have been released following the study design change.
Hi Lear. First of all, the extremely old exams can still be used because all the main topics are still there - the core will be data analysis, and the other two modules will still be relevant, regarding financial, it is still tested as 'Business Related Mathematics' in these paper, and therefore you can still use them under timed conditions. However, do note that there will be slightly fewer questions if you are practicing using the older papers, therefore you should finish with lots of time to spare. I do recommend going through the older practice exams if you need practice, preferably the much later ones e.g. 2013-2015, but do remember that practicing the 2016 and 2017 exam papers are priority because you do need to get used to the questions asked in terms of Financial and Recursion Modelling [there will be more working out for this compared to Business Related Mathematics]. Company Trial Exams that have been released following the study design change is also a good way to practice. In summary, you can still use the older exam papers to practice and practicing is important so try to do as many papers and get as much practice in as possible. Good luck :)
Title: Re: VCE Further Maths Question Thread!
Post by: secretweapon on June 27, 2018, 07:40:11 pm
Is it worth doing checkpoints at this stage of the year as they spoil vcaa exams?
Title: Re: VCE Further Maths Question Thread!
Post by: Bri MT on June 28, 2018, 08:02:12 am
Is it worth doing checkpoints at this stage of the year as they spoil vcaa exams?
Is it worth doing checkpoints at this stage of the year as they spoil vcaa exams?

Imo getting the practice in early is significantly more valuable than any negatives of spoiling, with the exception of leaving the most recent VCAA exam until the end of the year, especially for maths
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on July 19, 2018, 04:36:15 pm
Hi.
Just wondering...does anybody know whether it is critical to know the process of Dijkstra's algorithm? Is there likely to be a question on the exams that ask for us to go through the process of finding an answer using the algorithm and we will lose marks if we dont?
If not, I won't waste time trying to get a thorough understanding of it, but if it is...well...I'm probably gonna have to try ::)
Title: Re: VCE Further Maths Question Thread!
Post by: lemonlemonlemon on July 20, 2018, 02:34:35 pm
Hi.
Just wondering...does anybody know whether it is critical to know the process of Dijkstra's algorithm? Is there likely to be a question on the exams that ask for us to go through the process of finding an answer using the algorithm and we will lose marks if we dont?
If not, I won't waste time trying to get a thorough understanding of it, but if it is...well...I'm probably gonna have to try ::)
It is included in the study design so I'll learn it just to be safe, it doesn't take much time.
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on July 20, 2018, 02:40:41 pm
If it's in the study design, it is examinable so it is worth looking at it and including it in your bound reference just to be sure.

Then again, if it is in the latest study design, your teacher should have gone over it. If it has been missed, i'd be raising it with your teacher.
Title: Re: VCE Further Maths Question Thread!
Post by: msminzy on July 22, 2018, 06:01:02 pm
can anyone help me with cuts in networks? It's really confusing me as I'm not sure how to find the maximum amount of cuts when calulcating flow and stuff (basically how do I know I'm not missing important cuts???)
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on August 08, 2018, 08:40:39 pm
How many marks can one afford to drop across both Exam 1 and 2 combined for a 50?
Assuming 100% SACs of course.
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on August 08, 2018, 10:27:52 pm
How many marks can one afford to drop across both Exam 1 and 2 combined for a 50?
Assuming 100% SACs of course.

Would like to know this too! Would someone who is rank 2-3 be able to get a 50? given that rank 1,2,3 only differ by a a few marks.
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on August 09, 2018, 02:02:30 pm
Would like to know this too! Would someone who is rank 2-3 be able to get a 50? given that rank 1,2,3 only differ by a a few marks.
It's possible. For example if rank 1 score 100% in exams, then rank 2 lost 1-2 mark on Exam 2.
Generally both will get 50.

BUT, if the 2nd highest exam score was for example 90%, then the 2nd ranked, even if achieving 100% in his/her exams may end up with 49 or lower (Since if you're 2nd ranked, you'll use the 2nd highest exam score to moderate your sac score, this is also why being first is beneficial)
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on August 09, 2018, 02:08:09 pm
How many marks can one afford to drop across both Exam 1 and 2 combined for a 50?
Assuming 100% SACs of course.
A safe bet is
Exam 1: 40/40

Exam 2: 58-59/60

Just don't lose a mark in the 1st exam, cause it will hurt more than losing a mark in the 2nd exam. Though it's not uncommon to get 50 if you lost 1 mark on Exam 1 and score full marks on the 2nd.
Title: Re: VCE Further Maths Question Thread!
Post by: Bell9565 on August 16, 2018, 09:26:55 am
How many marks can one afford to drop across both Exam 1 and 2 combined for a 50?
Assuming 100% SACs of course.

I dropped 1 mark on SACs, none on exam 1 and 1 on exam 2 as far as I'm aware :)
Title: Re: VCE Further Maths Question Thread!
Post by: Bell9565 on August 16, 2018, 09:28:57 am
can anyone help me with cuts in networks? It's really confusing me as I'm not sure how to find the maximum amount of cuts when calulcating flow and stuff (basically how do I know I'm not missing important cuts???)

Hey, I'd look into the exhaustion method for working it out (there's a few vids on youtube that explain it well). I would even do it for the ones where it said 'draw the cut' just to ensure I had the right one.
Title: Re: VCE Further Maths Question Thread!
Post by: Vaike on August 16, 2018, 05:10:12 pm
Hey, I'd look into the exhaustion method for working it out (there's a few vids on youtube that explain it well). I would even do it for the ones where it said 'draw the cut' just to ensure I had the right one.

Also would recommend looking into this. In my experience, I haven't ,met a single student who had learned this method in class, yet it makes finding the maximum flow so much easier.
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on August 18, 2018, 12:50:20 pm
Hey, I'd look into the exhaustion method for working it out (there's a few vids on youtube that explain it well). I would even do it for the ones where it said 'draw the cut' just to ensure I had the right one.

I found this much more time consuming, I prefer doing it all in my head (everyone's different i guess).

But this method is definitely useful if you have enough time when double checking your answers.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on August 18, 2018, 01:08:32 pm
Anyone got some good tips and tricks for graphs and relations module?
Particularly Linear Programming.
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on August 18, 2018, 05:05:48 pm
Anyone got some good tips and tricks for graphs and relations module?
Particularly Linear Programming.

The sliding rule method is generally glossed over in textbooks, but it is the conceptual basis for the corner point method, and it is often assessed in multiple choice questions. Do not neglect it.
Title: Re: VCE Further Maths Question Thread!
Post by: pip1704 on August 19, 2018, 08:31:15 am
Anyone got some good tips and tricks for graphs and relations module?
Particularly Linear Programming.

Just type it in your calculator
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on August 20, 2018, 02:52:09 pm
Can someone please explain how crashing projects work?

Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on August 24, 2018, 01:34:41 pm
Hey can anyone help me with the 2016 Exam 1 question 16? How do you find the seasonal index for something when theres two missing seasonal indices? I'm so confused lol
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on August 24, 2018, 07:19:34 pm
Hey can anyone help me with the 2016 Exam 1 question 16? How do you find the seasonal index for something when theres two missing seasonal indices? I'm so confused lol

What I would do for this (and there may be another, easier way), is to find the 'quarterly average' by adding all of the 'long term average' values together, and dividing it by the number of days of the week (7) (89+93+110+132+145+190+160/7=131.285714286). After this, divide the value for Saturday by the quarterly average (190/131.285714286=1.44722524483, which can be rounded to 1.45). Therefore, the answer is D.

Sorry, hope that wasn't too confusing!!! ;)
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on August 24, 2018, 07:45:41 pm
What I would do for this (and there may be another, easier way), is to find the 'quarterly average' by adding all of the 'long term average' values together, and dividing it by the number of days of the week (7) (89+93+110+132+145+190+160/7=131.285714286). After this, divide the value for Saturday by the quarterly average (190/131.285714286=1.44722524483, which can be rounded to 1.45). Therefore, the answer is D.

Sorry, hope that wasn't too confusing!!! ;)

Or, calculate the seasonal average using one of the day's long-term average and seasonal indices. For instance, using Monday's values we get that the seasonal average is 89/0.68 = 131. So Saturday's seasonal index is 190/131 = 1.45.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on September 10, 2018, 07:11:40 pm
Can someone explain question 9 and 10 on data analysis 2017 further exam 1?

Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on September 10, 2018, 09:21:26 pm
Has anyone got the answers to Neap VCE Further Mathematics Units 3&4 Trial Examination 2016?
Sorry, but it's against forum rules to provide this as it's copyrighted material.

Can someone explain question 9 and 10 on data analysis 2017 further exam 1?

Thanks.
I'm assuming this is for VCAA 2017 Exam 1? I won't provide the answers, but the thinking process very briefly.
VCAA 2017 E1 Data Analysis Q9 and Q10
Q9. Start by finding the point they're indicating and note whether the point is above or below the line. Below indicates negative and above is positive. Then use your ruler to define the difference between point and line.
Q10. Another word for standardised value is z score. Sound familiar? This should give you the formula you need (also found here). Plug in the numbers for the point given, the mean and the St Dev into your calculator and that should give you the right answer.

Does that help?
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on September 25, 2018, 04:17:02 pm
Is this still on the study design? (Q3 2006 exam 2)

If it is how would I go about doing it? This is also on exam 1 I think (or maybe it was 2007 exam 1). I know how to do 3 median smoothing but I've never had to get an equation from it. The provided solutions say to use 3 points but I don't know how I'm supposed to figure out which points to use?
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on September 25, 2018, 04:59:34 pm
Is this still on the study design? (Q3 2006 exam 2)

If it is how would I go about doing it? This is also on exam 1 I think (or maybe it was 2007 exam 1). I know how to do 3 median smoothing but I've never had to get an equation from it. The provided solutions say to use 3 points but I don't know how I'm supposed to figure out which points to use?

Three median line is not on the study design, you can skip those questions.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on September 26, 2018, 12:55:46 pm
Hi,
Just wondering whether we need to know about capital gains tax for the current study design? It came up in one of the questions for the 2012 Heffernan exam 2, so thought I should clarify.
If yes, can someone please explain how to work this out?
Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on September 26, 2018, 01:36:24 pm
The only way VCAA can ask a question about that is if they explain what it is in the question and it can be solved using basic further maths techniques.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on September 26, 2018, 07:19:02 pm
The only way VCAA can ask a question about that is if they explain what it is in the question and it can be solved using basic further maths techniques.
awesome, thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on September 30, 2018, 05:48:44 pm
Is there a way to calculate standard deviation using 68-95-99.7% rule apart from case for this data?

Answer is 10.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on September 30, 2018, 06:34:59 pm
Considering most of the data (certainly at least 99.7% of it) lies between 30 and 90, you can probably assume that there needs to be 6 standard deviations between 10 and 90. This stems from our knowledge that 99.7% of the data lies between -3sd and +3sd.
So we do 90-30=60
and then 60/6 = 10
Hope it helps :D

ETA: I guess the above does work on an assumption but similar can be done when considering 68% of the data. Very conveniently 67.5% of the data lies between 50 and 70 so there must be 2 standard deviations in between. (70-50)/2 = 10.  Tbh this is an excellent question that really tests understanding.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on September 30, 2018, 09:49:16 pm
How would you compare percentages for this data (that relates to dolphin activity)?

Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 01, 2018, 10:26:38 am
Just need some help with this question.
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 01, 2018, 10:52:35 am
How would you compare percentages for this data (that relates to dolphin activity)?

First you need to determine what the explanatory and response variables are, because dolphin activity was the variable being measured in this observational study, (and time is usually explanatory as it does not depend on any other variable), 'activity' is the response variable. Therefore in order to make a comparison between the variables, we will need to compare two different times of day, on the basis of one type of activity.

I think you're confused on how to add up the percentages, and for this one you would need to add up the columns (as this is where the explanatory variables are) conveniently, the sum of each column already adds up to 100, so you will not have to do a calculation.

My answer for this question would be:
The two-way table, suggests that there is an association between the time of day, and observed dolphin activity. For example, the percentage of dolphins who spent time travelling, differed based on whether it was morning, or noon, increasing from 8% to 40%


im pretty sure this is how to answer it... (according to past VCAA questions that are simillar)
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 01, 2018, 11:02:29 am
Just need some help with this question.
Answer is E
A: Is definitely false, as the interest paid will vary depending on the present value ( reducing balance loans do not have a fixed interest amount)
B:Not true, because although she missed the payment, interest will still be added to the loan. (think of how this would look like on a graph)
C: This is not true, because not only did she miss a payment, but interest will be added on the loan.
(for questions B and C, u can confirm on the TVM if you are not quite sure)
D:Not true, because she missed the third payment, interest was added to the loan, meaning she would have to pay that off, in adition to her initial plan of repaying the loan with 6*800 (4800) payments
E:True, for the reason I stated in D ^
Title: Re: VCE Further Maths Question Thread!
Post by: marauder52 on October 01, 2018, 04:54:11 pm
I was hoping someone could help me out with 2016 VCAA Exam 2 Graphs and Relations module Question 3D.
Even by looking at the examiners report below I do not understand.
(https://i.imgur.com/c6OG1BL.png)

How can they assume that since the gradient = -1 , m=n
There is a link there that I am not understanding.
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on October 01, 2018, 05:33:06 pm
I was hoping someone could help me out with 2016 VCAA Exam 2 Graphs and Relations module Question 3D.
Even by looking at the examiners report below I do not understand.
(https://i.imgur.com/c6OG1BL.png)

How can they assume that since the gradient = -1 , m=n
There is a link there that I am not understanding.
If you rearrange \(Q=mx+ny\) in terms of \(y\) you get, \(y=\frac{-m}{n}x+\frac{Q}{n}\). \(\frac{-m}{n}\) corresponds to the gradient of the profit equation so \(\frac{-m}{n}=-1\) therefore \(m=n\)
Hopefully this helps!
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 02, 2018, 12:47:00 pm
Any tips for calculating interest questions?

Having trouble with Q5. c) ii)

Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 02, 2018, 01:10:17 pm
Any tips for calculating interest questions?

Having trouble with Q5. c) ii)

Interest is equal to:

total amount paid - the amount paid off the loan
which is equal to
number of payments*monthly payment amount - initial value of the loan - amount that needs to be paid off (FV)
which for a reducing balance loan that has this relation : V0=x , Vn+1= (1+r/n*100)*Vn -- D
it would be
(D*n) - (V0-Vn)
and for a loan that has been fully paid off it would be
D*n - V0

In your case, the terms of the loan change, which must be accounted for while calculating interest.
 it would equal to:
11000*total number of payments - 480,000

lol I would give you the answer, but idk where my CAS is at the moment 
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 02, 2018, 01:13:35 pm
Any tips for calculating interest questions?

Having trouble with Q5. c) ii)


So to do that you'd first work out how much they payed over the first 3 years.
So it would be $11 000 X 12 (3 years X 4 quarters)
So $132 000

Then you'd work out how much they payed after the interest rate change
So using your answer from 5ci. of 73 quarters you would then do 73 X 11000
So $803 000

So in total they payed $132 000 + $803 000
=$935 000

So they borrowed $480 000 and payed $935 000
So interest = $935 000 - $480 000
Interest = $455 000

Edit: Beaten to it, but I do have my CAS so this has the actual values.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 02, 2018, 01:19:48 pm
Interest is equal to:

total amount paid - the amount paid off the loan
which is equal to
number of payments*monthly payment amount - initial value of the loan - amount that needs to be paid off (FV)
which for a reducing balance loan that has this relation : V0=x , Vn+1= (1+r/n*100)*Vn -- D
it would be
(D*n) - (V0-Vn)
and for a loan that has been fully paid off it would be
D*n - V0

In your case, the terms of the loan change, which must be accounted for while calculating interest.
 it would equal to:
11000*total number of payments - 480,000

lol I would give you the answer, but idk where my CAS is at the moment

I'm just confused with why interest equals total amount of payments - Pv.
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 02, 2018, 01:39:17 pm
I'm just confused with why interest equals total amount of payments - Pv.
The interest is the difference between the amount you borrowed (Pv) and the amount you payed back (total payments). So to work out the difference you subtract the amount you borrowed from the amount you payed back and you're left with the interest that you payed.
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 02, 2018, 01:47:48 pm
I'm just confused with why interest equals total amount of payments - Pv.

Also, just to add to what PhoenixxFire said, when you think about it, what is a reducing balance loan? Its comprised of three components
-the amount owed to the bank
-the payment value made every period
-and the interest rate

Each compounding period (month or quater or whatever) the  loan will increase by a certain amount, as interest would have been added to it. However, we reduce the balance of the loan by making our periodic payment, that decreases the amount we owe to the bank. However when we make this payment not only are we paying off the loan that we owe to the bank, but we are also paying off the interest that is added to it. In this way, our payments are not only paying off the loan, but also the interest that is calculated on the loan... as how else could the bank make a prophet? We can figure out how much interest we paid the bank in total, by calculating how much money we gave them to pay off the loan in total. (which is number of payments * payment) or (N * pmt). This is all the money we gave the bank to pay off our loan...but for some reason this amount is always higher than the initial amount of money we put in the bank (V0/ PV), because this money was also used to pay off interest, therefore we can calculate exactly how much of the amount that we paid went to paying interest by simply finding the difference between the amount we paid, and the initial value of the loan.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 02, 2018, 02:26:18 pm
Thanks for all your help phoenix + studyinggg.

Also, I put A for this question. Why would the answer be E?
Title: Re: VCE Further Maths Question Thread!
Post by: S200 on October 02, 2018, 03:11:04 pm
J is to L as K is to M?
Title: Re: VCE Further Maths Question Thread!
Post by: passbleh24 on October 03, 2018, 02:13:14 pm
Hey I have a question regarding the study design.
I just completed the 2012 Further Exam 1, and came across this question. I've attached it below.
It involves infinite geometric sequences and is quite strange. Is this type of question still a part of the study design? Would I need to learn how to do them?

Thank you for any input.
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 03, 2018, 02:41:06 pm
Hey I have a question regarding the study design.
I just completed the 2012 Further Exam 1, and came across this question. I've attached it below.
It involves infinite geometric sequences and is quite strange. Is this type of question still a part of the study design? Would I need to learn how to do them?

Thank you for any input.

If you are referring to financial maths, then no you don't need to know these type of sequences, as the only geometric and arithmetic sequences we need to know are first order relationships.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 03, 2018, 03:13:17 pm

Hey I have a question regarding the study design.
I just completed the 2012 Further Exam 1, and came across this question. I've attached it below.
It involves infinite geometric sequences and is quite strange. Is this type of question still a part of the study design? Would I need to learn how to do them?

Thank you for any input.

No, you do not need to know infinite sums anymore. Just a heads up, most of the number patterns module is no longer really relevant. The only thing vaguely useful is recurrence relations which VCAA predominantly just relates directly to financial math.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 04, 2018, 02:24:58 pm
A loan of $15,000 is taken out compounding monthly with an interest rate of 4.5% Per annum. Payments are also made monthly and the loan will be paid off in 7 years.
a) What is the monthly payment
b) How much interest is paid in the first two years.

For part b I seem to be getting different answers depending on if I make a reducing balance table and sum up the interest for each payment compared to using Financial solver.
Which method is correct?
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 04, 2018, 02:35:39 pm
A loan of $15,000 is taken out compounding monthly with an interest rate of 4.5% Per annum. Payments are also made monthly and the loan will be paid off in 7 years.
a) What is the monthly payment
b) How much interest is paid in the first two years.

For part b I seem to be getting different answers depending on if I make a reducing balance table and sum up the interest for each payment compared to using Financial solver.
Which method is correct?

I got $1187.94 using the TVM, I think its correct... I feel like the other method is more time consuming because you have to fill in the table up to 24 payments.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 04, 2018, 02:39:28 pm
I got $1187.94 using the TVM, I think its correct... I feel like the other method is more time consuming because you have to fill in the table up to 24 payments.
You're right. But a counter argument is that it is 'more correct' as TVM incurs rounding errors whereas the table doesn't. I get 1187.9986 using table.
Title: Re: VCE Further Maths Question Thread!
Post by: passbleh24 on October 04, 2018, 03:43:25 pm
Hey I have a question about the study design again.

For this question in 2013, it asks for the effective rate of interest. I know the difference between nominal and effective annual interest when its referring to compound interest but i don't understand what they're doing here at all.
What formula are the using? Is this something that isn't in the study design.

Thank you for any input.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 04, 2018, 03:46:39 pm
Hey I have a question about the study design again.

For this question in 2013, it asks for the effective rate of interest. I know the difference between nominal and effective annual interest when its referring to compound interest but i don't understand what they're doing here at all.
What formula are the using? Is this something that isn't in the study design.

Thank you for any input.
Hey,
I'm pretty sure this is from the old study design. I know our school taught us this way last year (Units 1/2), but said not to use it this year as effective rate of interest means something different. I would disregard these questions if they are from the old study design, as we no longer use this effective rate of interest.
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 04, 2018, 04:05:18 pm
I have a question about significant figures, this question required the value of 109.894 to be rounded to 3 significant figures, so how is 110 correct? I thought trailing zeros in non-decimal numbers are not significant? If this is the case... how would we round this number to 3 sigfig?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 04, 2018, 05:01:25 pm
I have a question about significant figures, this question required the value of 109.894 to be rounded to 3 significant figures, so how is 110 correct? I thought trailing zeros in non-decimal numbers are not significant? If this is the case... how would we round this number to 3 sigfig?
The guidelines for significant figures is as follows:
- All digits greater than zero are significant
- All zero's between significant digits are significant
- All zero's before non-zero digits are not significant
Regarding zero's after the decimal place
- If they fall before a decimal place, they are not significant
- if they fall after a decimal place, they are significant.

For the number 109.894, as the first digit, 1, is greater than zero, this is the first significant figure, and there are significant decimal numbers, the three numbers before the decimal place would be significant. As the following number, 8 is greater than 4, we round up the last digit from 9 to 10. Even though normally 110 would be 2 significant figures as the last value, zero, is before the decimal place, if we take in normal rounding laws, this is the only way that this can correctly be founded to 3 sig fig

Just as an idea, if 109.894 was asked to be rounded to different sig fig values...
1 sig fig:100
2 sig fig: 110
3 sig fig: 110
4 sig fig: 109.9
5 sig fig: 109.89
6 sig fig: 109.894


Sorry...reading that back to myself seemed a little confusing. Give me a yell if it makes no sense  :o ;)
Title: Re: VCE Further Maths Question Thread!
Post by: Further Maths 101 on October 04, 2018, 05:51:36 pm
Is it worth doing the NSW (HSC) bostes exam?
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 04, 2018, 05:54:56 pm

Is it worth doing the NSW (HSC) bostes exam?

There are enough further exams available. I would not bother.
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on October 04, 2018, 05:58:32 pm
Stick to VIC exams - if you do HSC ones, you have to sift through them and make sure the questions relate to the study design.. something you don't really have time to do, at this time of year.
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on October 04, 2018, 06:58:10 pm
You're right. But a counter argument is that it is 'more correct' as TVM incurs rounding errors whereas the table doesn't. I get 1187.9986 using table.

I got the same value (1187.99865079, on float12) using TVM solver.

First, I found the monthly payment to be 208.5024... This value is stored as –tvm.pmt.
Second, I found the balance of the loan after 24 payments to be 11183.9405... (I used the exact value of the monthly payment for this). This value is stored as -tvm.fv
Then I calculated the interest paid in the first two years by calculating 24*-tvm.pmt – (15000 – -tvm.fv). (ie. total paid in two years minus the principal reduction).

I believe there will be no rounding errors using this method.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 04, 2018, 07:41:39 pm
I got the same value (1187.99865079, on float12) using TVM solver.

First, I found the monthly payment to be 208.5024... This value is stored as –tvm.pmt.
Second, I found the balance of the loan after 24 payments to be 11183.9405... (I used the exact value of the monthly payment for this). This value is stored as -tvm.fv
Then I calculated the interest paid in the first two years by calculating 24*-tvm.pmt – (15000 – -tvm.fv). (ie. total paid in two years minus the principal reduction).

I believe there will be no rounding errors using this method.

Yep I have attached an image of my method where I summed the Interest earnt column over the 24 months.
(https://i.imgur.com/TpYkJYc.png)

The answers claim it to be $1187.94 which then should be incorrect by roughly $0.06 when rounding to 2 d.p....right?
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on October 04, 2018, 07:44:28 pm
<snip>

The answers claim it to be $1187.94 which then should be incorrect by roughly $0.06 when rounding to 2 d.p....right?

Where is the question / answer from? Past VCAA exam?

I think your method gives a correct answer when rounded to 2 d.p.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 04, 2018, 07:50:03 pm
Insight 2018 Exam I believe

I think the problem here is finding the monthly payment was a different sub question to the 2 year interest sub question. Insight used the rounded monthly payment from a) in order to find the interest incurred in part b)
Should we be using rounded for the next subquestion or exact?
(https://i.imgur.com/4XuDpeL.png)
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on October 04, 2018, 07:55:04 pm
Insight 2018 Exam I believe

<snip>

Is there any "hence" instruction, or any indication that the rounded answer from part a. is to be considered the actual monthly payment? (This is touching on issues in the other thread).

Otherwise, I'm inclined to think that Insight's answer is wrong, until I see evidence from VCAA that this kind of rounding is acceptable.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 04, 2018, 07:56:38 pm
Is there any "hence" instruction, or any indication that the rounded answer from part a. is to be considered the actual monthly payment? (This is touching on issues in the other thread).

Otherwise, I'm inclined to think that Insight's answer is wrong, until I see evidence from VCAA that this kind of rounding is acceptable.

(https://i.imgur.com/GhA7120.png)

Appears they have used rounded in c) as it is a following sub question to b)
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 05, 2018, 12:18:12 pm
Any advice for this question.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 05, 2018, 12:19:32 pm
Any advice for this question?

Got A, but answer is D.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 05, 2018, 12:48:41 pm

Any advice for this question.
Here’s a hint :
Amount of principal paid off is Payment - Interest charged for each month.
As it’s reducing balance you’d expect the interest to decrease over time while the payments remains the same.
Title: VCE Further Maths Question Thread!
Post by: Lear on October 05, 2018, 12:54:06 pm
Any advice for this question?

Got A, but answer is D.

In my opinion answer should be C.
4200-600=3600

Interest for the year = 0.06*3600=216
Total to paid that year = 3600+216= 3816
3816/12=318

NOTE: Hire Purchase is No longer on the study design for 3/4 I think
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 05, 2018, 12:56:30 pm
In my opinion answer should be C.
4200-600=3600

Interest for the year = 0.06*3600=216
Total to paid that year = 3600+216= 3816
3816/12=318

Yes it was C actually.

Also are these explanations ok.

Why interest decreases over time?
- for a reducing balance loan, payments are used to pay of the principal
- interest is calculated based on the outstanding principal value
- thus, as outstanding principal decreases, interest decreases
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 05, 2018, 12:59:41 pm
NOTE: Hire Purchase is No longer on the study design for 3/4 I think

Is hire purchase not just another term for simple interest? we got told that at school, so it will still be in the study design.
Title: VCE Further Maths Question Thread!
Post by: Lear on October 05, 2018, 01:03:47 pm
Is hire purchase not just another term for simple interest? we got told that at school, so it will still be in the study design.

Technically yes but there’s this weird question about effective interest rate on hire purchases that I’ve seen pop up often. Given that those don’t appear anymore I would expect hire purchases to also not be assessed.

Also hire purchase is specifically mentioned for units 1/2 but not 3/4
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 08, 2018, 06:06:07 pm
Just have a few questions. See attachments.

How do we answer question 3 vcaa exam 1 2010 (attached).

Why is the r value close to 0.78 in question 7 vcaa exam 1 2010? Doesn't this mean the association is strong, which the graph doesn't seem to be.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 08, 2018, 06:22:13 pm
are the vcaa 2010 answers wrong for question 4 a) ii). See attached.

Title: Re: VCE Further Maths Question Thread!
Post by: YggdrasilMamel on October 08, 2018, 06:48:57 pm
For the correlation problem, it's more of process of elimination. D and E are obviously incorrect because they have a negative value. C is unlikely as 0.2.. is not that strong of a correlation, and we at least see some of that on the graph. Looking at the graph, we can easily tell that it's not a perfect correlation, so we can assume it's not A so it must be B. It's a little wishy-washy, but all the other answers are too farfetched.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 08, 2018, 06:50:52 pm
How do we answer question 3 vcaa exam 1 2010 (attached).
It's been done recently.
are the vcaa 2010 answers wrong for question 4 a) ii). See attached.
I'm assuming this is from the financial maths module. Back in my day (which makes me sound old), financial recursions wasn't a part of the core modules, so I haven't done financial maths in ages. I'll leave this to someone else. Sorry!
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 08, 2018, 06:56:43 pm
are the vcaa 2010 answers wrong for question 4 a) ii). See attached.
Yes, looks like they have included a decimal in the wrong spot... the working out included beneath gives what would be the correct answer, you just need to round it to the nearest whole number.

Therefore, the final solution would be $188557
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 10, 2018, 06:38:39 am
Hi.
Is somebody able to explain how to work out this answer? Its from the 2015 Exam 1 VCAA exam.
I would have thought that you work out the amount of interest that is earned (5885.72-5870.5=15.22) and then divide this by the lowest monthly balance (15.22/4870.5=0.00312493), and then multiply it by 100, but this does not give any of the answers.

The correct answer is D.
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 10, 2018, 07:29:40 am
Hi.
Is somebody able to explain how to work out this answer? Its from the 2015 Exam 1 VCAA exam.
I would have thought that you work out the amount of interest that is earned (5885.72-5870.5=15.22) and then divide this by the lowest monthly balance (15.22/4870.5=0.00312493), and then multiply it by 100, but this does not give any of the answers.

The correct answer is D.
That’ll give you the monthly interest rate. You then have to times it by 12 as the question asks for the annual interest rate.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 10, 2018, 07:47:10 am
That’ll give you the monthly interest rate. You then have to times it by 12 as the question asks for the annual interest rate.
Haha yep that would make sense! I knew I was on the right track!  ::)
Thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 10, 2018, 07:49:17 pm
How to answer question 2 b) from 2009 further exam 2?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 10, 2018, 07:55:15 pm
How to answer question 2 b) from 2009 further exam 2?
2b from which section of the exam?
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 10, 2018, 09:31:00 pm
2b from which section of the exam?

business sorry!
Title: Re: VCE Further Maths Question Thread!
Post by: passbleh24 on October 10, 2018, 09:37:06 pm
Hey so for this question I was asked explain association.

As you can see, although the box plots have scales of 5 i wasn't accurate in my estimation of the medians of the three years. I estimated 51, 62 and 69. Would this still be considered right or would I need 52, 63 and 69 to be right.

Thanks!

Title: Re: VCE Further Maths Question Thread!
Post by: S200 on October 10, 2018, 09:51:08 pm
How to answer question 2 b) from 2009 further exam 2?
$250, $6 interest
Assume 12 months payment.

\(6\times 12=72\)

\(\frac {72}{250}=0.288\)

Therefore,
28.8%
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 11, 2018, 08:33:45 am
Hey so for this question I was asked explain association.

As you can see, although the box plots have scales of 5 i wasn't accurate in my estimation of the medians of the three years. I estimated 51, 62 and 69. Would this still be considered right or would I need 52, 63 and 69 to be right.

Thanks!

I would assume on these sort of questions that they would have some extent of leniency as to what is considered to be correct and incorrect, as there really isn't a clear number that each median corrosponds with.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 11, 2018, 05:58:49 pm
need help with

2013 Further exam 1, business related maths, question 4 and 7

2018 NHT further exam, matrices, question 8

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 11, 2018, 06:14:57 pm
need help with

2013 Further exam 1, business related maths, question 4 and 7

2018 NHT further exam, matrices, question 8

Thanks

2013 Exam 1
 Question 4 - Price after deposit = 15000-3000=12000
Total amount paid = 36*400 = 14400
Total interest paid = 14400-12000= 2400
Total interest paid per year = 2400/3 = 800
Interest rate per year = (800/1200) * 100 = 6.6667 therefore D

Question 7
As you can see from the graph the annual interest earnt is $50
This is (50/1000) * 100 = 5% per year

Now let the new amount of money invested = x
Amount of money earnt every year = 0.05x.
Therefore Amount of interest earned = x*0.05*8
Solve this for 600 gives us x=1500

I have not done the 2018 NHT exam and want to leave it till last so I will let someone else answer that question
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on October 11, 2018, 06:18:38 pm
You could at least include the questions so we don't have to go looking for them ourselves...

PSA to all:
If you're somebody who answers questions in this thread, please encourage them to have a go at it themselves and provide their current working out/understanding as well, as it identifies their misconceptions and gaps in understanding. Doing the q for them may help with that particular question but isn't the best way to addressing the skill.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 11, 2018, 06:23:31 pm
and an attempt/your current understanding
You'd hate to see the methods question thread :')
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on October 11, 2018, 06:24:35 pm
You'd hate to see the methods question thread :')

mate, I am well aware :P It was and continues to be one of my key frustrations both as a former natmod on AN and a teacher.

Spoonfeeding them the answer may help with getting the answer to that particular question, but if they just repeat the same flaw over and over in future questions have they really learnt? Could argue they will learn based on your worked solution which may be true, but in most cases it'll just get repeated later on.

Pleeeasseeee people, if you ask a question.... give us something more than just the actual question!! It will benefit you in the long run.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 11, 2018, 06:32:17 pm
mate, I am well aware :P It was and continues to be one of my key frustrations both as a former natmod on AN and a teacher.

Spoonfeeding them the answer may help with getting the answer to that particular question, but if they just repeat the same flaw over and over in future questions have they really learnt? Could argue they will learn based on your worked solution which may be true, but in most cases it'll just get repeated later on.

As someone who throughout the year has consistently contributed to that thread it has become a turn off for me very recently too. Perhaps some rule changes may be necessary such as showing some sort of working out or attempt at the question.
Title: Re: VCE Further Maths Question Thread!
Post by: kaylahsalvini on October 16, 2018, 06:24:50 pm
need help with

2013 Further exam 1, business related maths, question 4 and 7

2018 NHT further exam, matrices, question 8

Thanks

2018 NHT Exam 1 question 8
1) put the objective function 5x+2y=1 on a graph page, which gave me the co-ordinates (0,5) and (2,0)
2) then plot these on each graph and drew a line between them
3) on each graph, slide the line up to each point P, if that Point P is the first and only point you hit, then that is the minimum value

In the end i got E, which is correct

Hope this helps!
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 20, 2018, 03:46:45 pm
Hi, so the question below is from the 2017 NEAP trial exam.
I answered, B, but according to the answers, D is correct. Why is B incorrect, as (450000-20000)/100000 = 4.3?
Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: KiNSKi01 on October 20, 2018, 08:19:38 pm
Well that's kinda stupid  :P

I'm guessing the reason they have chosen D as answer over B is that you can only have a whole number of X-rays. Seems kinda ridiculous to me since B and D are mathematically equivalent
Title: Re: VCE Further Maths Question Thread!
Post by: faysalabdi on October 23, 2018, 02:29:51 pm
hi i would like to ask if i get 38/40 exam 1 and 55/60 exam 2 what would my study score be?
i am rank one in a weak cohort
Title: Re: VCE Further Maths Question Thread!
Post by: rainbowsparkles15 on October 24, 2018, 11:23:37 am
Hey guys,
Can a dummy be counted as a predecessor? (Networks)
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 24, 2018, 11:45:38 am
Hey guys,
Can a dummy be counted as a predecessor? (Networks)
Nope. It isn’t actually an activity. It would whatever the dummy is linking from that are the predecessors
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 24, 2018, 08:48:45 pm
Extremely odd question but does anyone know if we are allowed to write ON our bound references during the exam?
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on October 24, 2018, 08:52:17 pm
Extremely odd question but does anyone know if we are allowed to write ON our bound references during the exam?

The exam- navigator doesn't really say anything but: "If any page or part of a page is detached from the rest of the
bound reference, the page will be removed by the supervisor for the duration of the examination and the incident will be reported as
a potential breach of rules"

If your using it to work things out, maybe try writing at the back of the formula sheet which i think is given seperate to the exam
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 24, 2018, 08:56:35 pm
Thanks!
Don’t plan to use it for working out but rather have a premade checklist with common mistakes  at the back to tick off when I’ve finished my exam.
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 24, 2018, 11:47:32 pm
Thanks!
Don’t plan to use it for working out but rather have a premade checklist with common mistakes  at the back to tick off when I’ve finished my exam.
If you're worried about it just ask when you walk in, they'll tell you.

If they don’t want you writing in it then number the checklist and then write the numbers on your sheet and tick them off on there instead. I really doubt that it’d be an issue though.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 25, 2018, 06:06:45 am
Hi.
So firstly, is this question from the 2014 Exam 2 still relevant to the study design, and if so, is there any shortcut to adding up the total amount other than just calculating each year and adding each value together separately?
Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 25, 2018, 07:14:40 am
Technically it’s simply a recurrence relation that requires you to make a spread sheet and observe when the area exceeds 4. But VCAA does not (or has not rather) ask questions like those in the new study design. They primarily connect recursion to financial modelling. I found the number patterns module to be a waste of time in older exams.
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on October 25, 2018, 05:17:10 pm
hey everyone,
i've been doing exams lately and for the first page on exam 2 with the typical mode, range, median, do you include the units provided in the question? sometimes vcaa doesn't put units on their answers and sometimes they do so someone please help!!
also do residuals include units because i'm currently marking a NHT exam 2017 exam, and vcaa has written the answer to be "-18.9%" (the unit of the variable is %). i understood residual values to be just the difference between the actual value and predicted value.
thank you in advance!!  :)
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on October 25, 2018, 05:39:45 pm
NHT EXAM 2, Q2F
Can someone please explain to me why the answer is 84. The answer I got was 82.

To my understanding, it would be the transition matrix multiplied by K2, and then you get the answer from the matrix. You wouldn't add the B matrix because those people don't get the option of choosing their seats as stated by the question. So why does VCAA add the B matrix  :( ???
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 25, 2018, 07:32:43 pm
Would one lose marks for adding a unit where a statistic is calculated?
For example in the 2017 Exam 2, would 72 eggs rather than simply 72 for Question 1ai be marked as wrong?
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 25, 2018, 08:05:53 pm
Would one lose marks for adding a unit where a statistic is calculated?
For example in the 2017 Exam 2, would 72 eggs rather than simply 72 for Question 1ai be marked as wrong?
No. So long as it’s the correct unit of measurement you won’t lose marks

NHT EXAM 2, Q2F
Can someone please explain to me why the answer is 84. The answer I got was 82.

To my understanding, it would be the transition matrix multiplied by K2, and then you get the answer from the matrix. You wouldn't add the B matrix because those people don't get the option of choosing their seats as stated by the question. So why does VCAA add the B matrix  :( ???
Matrix B allocates the new members seats - they don’t choose their seats, so it’s still added. You multiply the T matrix by the state matrix, ending up with the people’s choice of seats, then you add B into their allocated seats.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 26, 2018, 02:16:14 pm
Do we need to know about hire purchase agreements for exam?
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 26, 2018, 02:58:56 pm
Hi,

I need help with  question 9 from the networks section (attached below).




Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on October 26, 2018, 03:11:22 pm
Do we need to know about hire purchase agreements for exam?
No
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 26, 2018, 04:04:10 pm
Hi,

I need help with  question 9 from the networks section (attached below).

Which exam is this from?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 26, 2018, 04:32:29 pm
Hi,
just wondering, will we loose marks if we write an answer without units? for example, if a question asks for the range of the temperature in a graph, can you just write, say, 20, or do we have to write 20 degrees celcius?
Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on October 26, 2018, 04:40:12 pm
Hi,
just wondering, will we loose marks if we write an answer without units? for example, if a question asks for the range of the temperature in a graph, can you just write, say, 20, or do we have to write 20 degrees celcius?
Thanks!

Yes. If you don't include units, you could mean anything. For e.g. if you write 20, then does this mean 20 degrees celsius or fahrenheit? Don't assume the examiner will put the pieces of the puzzle together themselves, cover all bases. This is a foundation skill which should be well and truly understood by Year 12.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 26, 2018, 06:16:45 pm
I believe this sort of a grey area. Some believe that since things such as range/median/IQR are *calculations* it is inappropriate to include units. For example, if we were to calculate the median amount of humans in 10 groups and we got a decimal value it would not make sense to put units as we cannot effectively have for example 6.5 humans. I’m not sure about further but I have lost marks in methods for providing a unit when calculating the expected value of a probability distribution table that involved some sort of tangible object/thing.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 26, 2018, 06:26:24 pm
Which exam is this from?

Hefernan or however u spell it.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 26, 2018, 06:36:05 pm
I believe this sort of a grey area. Some believe that since things such as range/median/IQR are *calculations* it is inappropriate to include units. For example, if we were to calculate the median amount of humans in 10 groups and we got a decimal value it would not make sense to put units as we cannot effectively have for example 6.5 humans. I’m not sure about further but I have lost marks in methods for providing a unit when calculating the expected value of a probability distribution table that involved some sort of tangible object/thing.

So is it best to include the units just to be safe?
Title: VCE Further Maths Question Thread!
Post by: Lear on October 26, 2018, 07:00:04 pm
I honestly don’t know. Like I’ve said I’ve lost marks for putting units in calculations before so ¯\_(ツ)_/¯

Also see last year’s exam 2 very first question. Asks for a calculation and answer scheme didn’t include units.
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on October 26, 2018, 08:17:23 pm
So is it best to include the units just to be safe?
Include units when asked. However you can include units even when not asked but make sure it is the correct unit as adopting an inaccurate unit will lead to a wrong answer. This is the same principle when people answer the question in a worded format (but if the worded format mislead from the question/answer, the answer will be wrong) when simply the numerical answer is what vcaa is looking for.

Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 27, 2018, 09:21:56 am
In the matrices module, if a question asks to calculate a S1 (for example), do we have to write out each of the matrices used in the calculation, or is it okay to just use the letter that they have been assigned (e.g. TxS0=S1 - S1 would obviously be written as the actual matrix)?

Sorry, that probably makes no sense haha.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 27, 2018, 09:34:08 pm
nht further exam 2, question 6 recurrence relations (attached below).

So if it said 1.5% per annum, then would $200.25 be the correct answer?

So does that mean the interest rate per annum is actually 18% (1.5x12)?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on October 27, 2018, 10:19:36 pm
nht further exam 2, question 6 recurrence relations (attached below).

So if it said 1.5% per annum, then would $200.25 be the correct answer?

So does that mean the interest rate per annum is actually 18% (1.5x12)?

Thanks
This is a little bit different than your usual financial core. There isn't an exact interest per annum but rather it charges its customers by 1.5% of interest if bills are not paid after the due date (in months). Therefore there will be no interest charged if they paid their bills on time. So the correct answer should be $203 (since Marcus paid his bills one month after due month, 1.015x200=203)
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 27, 2018, 10:54:47 pm
This is a little bit different than your usual financial core. There isn't an exact interest per annum but rather it charges its customers by 1.5% of interest if bills are not paid after the due date (in months). Therefore there will be no interest charged if they paid their bills on time. So the correct answer should be $203 (since Marcus paid his bills one month after due month, 1.015x200=203)

But it says interest on this amount will compound monthly?
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on October 28, 2018, 12:04:29 am
But it says interest on this amount will compound monthly?
Interest will compound for x amount of months that the customer doesn't pay its bill after due month, don't be confused with the your usual compound interest question. This one has a slightly different rule.
Title: Re: VCE Further Maths Question Thread!
Post by: vox nihili on October 28, 2018, 10:09:07 am
What does "decay arithmetically" mean? Have looked online for an answer but nothing really seems to explain this well.
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 28, 2018, 10:12:55 am
What does "decay arithmetically" mean? Have looked online for an answer but nothing really seems to explain this well.
I would assume it’s just referring to an arithmetic sequence with a negative difference. E.g 10, 8, 6, 4, etc
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on October 28, 2018, 10:15:21 am
What does "decay arithmetically" mean? Have looked online for an answer but nothing really seems to explain this well.

An arithmetic sequence is given by a recurrence relation of the form V(n+1) = Vn + D. If D < 0, the sequence decays arithmetically.

Edit: see PhoenixxFire for a nice example.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 28, 2018, 10:29:07 pm
Nht 2017 further maths exam 2, data analysis, question 2 b) iii).

Isn't the answer -19.0 and not -18.9?

Also, do we need units for residual values?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 28, 2018, 10:48:02 pm
Nht 2017 further maths exam 2, data analysis, question 2 b) iii).

Isn't the answer -19.0 and not -18.9?

Also, do we need units for residual values?

First Question
The answer is -18.9%. When you substitute 11.2oC into the equation, it'll spit out an answer. Take that answer away from 68% and you should get a residual of -18.9% when rounded. (It's actually -18.944%, which rounds down.)

P.S. I added units in mostly because the answer has it. I actually don't know if you're supposed to have units in residuals.

I'm usually one who does add units, just in case, but I'd take this with a grain of salt and ask your Further teacher for full confirmation. 
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 28, 2018, 10:48:43 pm
Wait...are residuals a percentage?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on October 28, 2018, 10:52:53 pm
Wait...are residuals a percentage?
No, just the units in this one is. The question itself had percentages, so... I think I added the units in unnecessarily in all honesty.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 29, 2018, 07:59:15 pm
Do you include lump sum payments in total interest paid during lets say, a reducing balance loan?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 29, 2018, 08:01:31 pm
Do you include lump sum payments in total interest paid during lets say, a reducing balance loan?
Are you talking about the lump sum of like an initial deposit that is payed, then reducing balance for the remaining value?
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 29, 2018, 08:05:15 pm
Do you include lump sum payments in total interest paid during lets say, a reducing balance loan?

I would not think so as we don't pay interest on lump sums.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on October 29, 2018, 08:17:44 pm
Are you talking about the lump sum of like an initial deposit that is payed, then reducing balance for the remaining value?

Yep. I now realise you wouldn't include interest on it, but would u include it in total amount paid for lets say a car.
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on October 29, 2018, 08:22:13 pm
Yep. I now realise you wouldn't include interest on it, but would u include it in total amount paid for lets say a car.
Yeah you would, it's still a payment.
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on October 30, 2018, 11:16:21 am
Yep. I now realise you wouldn't include interest on it, but would u include it in total amount paid for lets say a car.

Do you mind telling me which trial you did this question on? We had a simillar question on my SAC, butI haven't come across any yet in trials, I just wanna make sure I haven't forgotten how to do it haha :)
Title: Re: VCE Further Maths Question Thread!
Post by: theomccoy on October 30, 2018, 12:55:57 pm
Hi! Could someone please explain why 30% is the answer?
I don't the question or how to work it out at all... and it's the only one in the practice exam I couldn't get..  :P
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on October 30, 2018, 01:58:12 pm
Hi! Could someone please explain why 30% is the answer?
I don't the question or how to work it out at all... and it's the only one in the practice exam I couldn't get..  :P
I'm not sure if this is the right way of doing the question but you could say there are 120 rooms (as winter has 100% occupancy) and in Summer only 85 rooms are used. To have 100% occupancy in summer, you would need to close 35 of the 120 rooms which is equivalent to 29.2%.
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on October 31, 2018, 06:26:33 pm
Hey can someone help me with the 2017 NHT exam 1 question 7 from core? (Am I allowed to copy and paste the question on here?)
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 31, 2018, 06:27:21 pm
Yep you are!
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on October 31, 2018, 06:30:58 pm
Alright, so why is the option C?? Thanks in advance!

Question 7
A least squares line fitted to a scatterplot will always
A. maximise the number of data points lying on the line.
B. equalise the number of data points on either side of the line.
C. minimise the sum of the squares of the vertical distance from each data point to the line.
D. minimise the sum of the squares of the shortest distance from each data point to the line.
E. minimise the sum of the squares of the horizontal distance from each data point to the line.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 31, 2018, 06:37:48 pm
Ah yup, that really just comes down to knowing the definition of what that line is. It’s not really something you can ‘work out’ during the exam. It’s just a fact you are supposed to know.


Questions like these scare me the most as I don’t plan to take my textbook in and this sort of random things I dismissed when making my personal bound reference. Plz don’t do this VCAA :(
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on October 31, 2018, 06:52:04 pm
Ah yup, that really just comes down to knowing the definition of what that line is. It’s not really something you can ‘work out’ during the exam. It’s just a fact you are supposed to know.


Questions like these scare me the most as I don’t plan to take my textbook in and this sort of random things I dismissed when making my personal bound reference. Plz don’t do this VCAA :(

Are you serious... it’s like they make us focus on application questions so much that we ignore the “content” and then surprise us with a... definition??? This shit better not pop up on Friday
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on October 31, 2018, 06:55:22 pm
Are you serious... it’s like they make us focus on application questions so much that we ignore the “content” and then surprise us with a... definition??? This shit better not pop up on Friday
Its not really about definition, its about understanding. We should all know by now that adding all residual equals to 0 and that residual is vertical distance between the line and the actual dot, so by using the previous example. Its pretty obvious...
Title: Re: VCE Further Maths Question Thread!
Post by: tinkerbell101 on October 31, 2018, 06:57:07 pm
hey everyone, sorry if this question has already been answered but just in regards to time series plots, are irregular fluctuatiosn ALWAYS a feature? according to question 11 on the NH 2018 exam 1 examiner's report, they are but im not quite sure if this is right. thanks!!
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on October 31, 2018, 07:07:00 pm
hey everyone, sorry if this question has already been answered but just in regards to time series plots, are irregular fluctuatiosn ALWAYS a feature? according to question 11 on the NH 2018 exam 1 examiner's report, they are but im not quite sure if this is right. thanks!!
Yes
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 31, 2018, 07:30:20 pm
Its not really about definition, its about understanding. We should all know by now that adding all residual equals to 0 and that residual is vertical distance between the line and the actual dot, so by using the previous example. Its pretty obvious...

I think it’s reasonable for a person to not make the connection between ‘least squares’ and residual values. Often even the term 'least squares' is not taught and rather students are simply told to press certain buttons on their calculator to get ‘the line’ of the graph.
What may be obvious to you is not obvious to all students :)
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on October 31, 2018, 07:35:13 pm
I think it’s reasonable for a person to not make the connection between ‘least squares’ and residual values. Often even the term 'least squares' is not taught and rather students are simply told to press certain buttons on their calculator to get ‘the line’ of the graph.
What may be obvious to you is not obvious to all students :)
Completely true. I made the exact same mistake, and a few other people I know (including one student who is probably rank 1 in our cohort) made the exact same mistake. It's a very easy thing to not connect these two ideas.
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on October 31, 2018, 07:43:24 pm
Its not really about definition, its about understanding. We should all know by now that adding all residual equals to 0 and that residual is vertical distance between the line and the actual dot, so by using the previous example. Its pretty obvious...
Well I honestly didn’t know that... but thanks for the enlightenment lol
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on October 31, 2018, 07:47:49 pm
I think it’s reasonable for a person to not make the connection between ‘least squares’ and residual values. Often even the term 'least squares' is not taught and rather students are simply told to press certain buttons on their calculator to get ‘the line’ of the graph.
What may be obvious to you is not obvious to all students :)
This is spot on. I didn’t even know what the least square line did until I literally just google searched “least squares meaning”, which pretty much gives the answer to question 7. We weren’t really taught what it is or what it does, just how to find it and use it. (Gotta love atarnotes tho, thanks guys!)
Title: Re: VCE Further Maths Question Thread!
Post by: theomccoy on October 31, 2018, 09:54:00 pm
Have never had a great understanding of inverses so can't wrap my head around this question...

Anyone able to explain why the answer is A?
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on October 31, 2018, 10:13:31 pm
Have never had a great understanding of inverses so can't wrap my head around this question...

Anyone able to explain why the answer is A?

By definition of inverses, Q^–1 * Q gives the identity matrix.

Since Q = wP, we require that Q^–1 * wP is the identity matrix. Hence Q^–1 = (1/w) * P^–1, since P * P^–1 is the identity matrix, and w * (1/w) = 1.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on October 31, 2018, 10:16:05 pm

Have never had a great understanding of inverses so can't wrap my head around this question...

Anyone able to explain why the answer is A?

For questions like these I just like to define each term/variable and do the process. Following this I equate it with each answer to check which one is correct.
Title: Re: VCE Further Maths Question Thread!
Post by: theomccoy on October 31, 2018, 10:43:50 pm
By definition of inverses, Q^–1 * Q gives the identity matrix.

Since Q = wP, we require that Q^–1 * wP is the identity matrix. Hence Q^–1 = (1/w) * P^–1, since P * P^–1 is the identity matrix, and w * (1/w) = 1.

Ahhh very helpful! Thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: anne198 on November 01, 2018, 08:35:43 am
Hey Guys,

When drawing a least square regression line in exam 2 are you supposed to extend the line past the max and min x values of the data points given? I was thinking you don't extend the line because that would show extrapolation but the 2017 answers had a question that extended the line to reach the y axis etc.

Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 01, 2018, 08:38:01 am
Hey Guys,

When drawing a least square regression line in exam 2 are you supposed to extend the line past the max and min x values of the data points given? I was thinking you don't extend the line because that would show extrapolation but the 2017 answers had a question that extended the line to reach the y axis etc.
I would always just do it to the ends of the graph that it gives you. That way you can show the x intercept. Also, generally the line wont have a boundary or anything, so just go to the edges, even if it is extrapolation.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 01, 2018, 08:44:41 am

Hey Guys,

When drawing a least square regression line in exam 2 are you supposed to extend the line past the max and min x values of the data points given? I was thinking you don't extend the line because that would show extrapolation but the 2017 answers had a question that extended the line to reach the y axis etc.

Related to this, are we supposed to label the end points? I don’t recall any of the normal VCAA exams requiring labelling for the least square regression line but did 2018 NHT EXAM 2 last night and they had the end points labelled?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 01, 2018, 08:47:58 am
Related to this, are we supposed to label the end points? I don’t recall any of the normal VCAA exams requiring labelling for the least square regression line but did 2018 NHT EXAM 2 last night and they had the end points labelled?
Not sure whether it is required, but I always label a couple of points just in case my line is slightly off. Definitely label the y intercept, because this is generally easy enough to find from the line, and may be something in the middle and at the end.
If you are rushed for time, I would just leave it and come back and do it at the end.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 01, 2018, 08:58:25 am
The issue is if we haven’t been given an instruction to label we don’t know exactly how many decimal places we should label to. And VCAA often mentions how kids lose marks for putting extra yet incorrect information (haven’t said anything specifically on lines though)
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on November 01, 2018, 09:34:49 am
The issue is if we haven’t been given an instruction to label we don’t know exactly how many decimal places we should label to. And VCAA often mentions how kids lose marks for putting extra yet incorrect information (haven’t said anything specifically on lines though)
That's overkill, there is no need to label, just make sure your end points are accurate. Label or not, Vcaa still needs to check whether the line is correct.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 01, 2018, 10:11:24 am
That's overkill, there is no need to label, just make sure your end points are accurate. Label or not, Vcaa still needs to check whether the line is correct.

That's what I thought too until I saw the VCAA 2018 NHT Exam 2 report having them labelled. Now I am not too sure.
Interesting...
(https://i.imgur.com/29kzm50.png)
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on November 01, 2018, 10:31:17 am
That's what I thought too until I saw the VCAA 2018 NHT Exam 2 report having them labelled. Now I am not too sure.
Interesting...
(https://i.imgur.com/29kzm50.png)
I checked others and they weren't labelled. So I wouldn't worry about this, VCAA would of mentioned to include coords for end points if they were needed
Title: Re: VCE Further Maths Question Thread!
Post by: gracemccomb on November 01, 2018, 11:32:56 am
Can anyone help me with this question? I don't know how to find the residual without the actual value. Its from NHT Exam 1

Thank you!!
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 01, 2018, 11:55:20 am

Can anyone help me with this question? I don't know how to find the residual without the actual value. Its from NHT Exam 1

Thank you!!

The actual value is given in the table in previous parts
Title: Re: VCE Further Maths Question Thread!
Post by: xdmemeguy on November 01, 2018, 04:19:20 pm
In regards to Matrices, does VCAA by default put the win on the comlumns or the rows on dominance matrices.

Like this
  loses to
[  x   x   x ]
[  x   x   x ] wins
[  x   x   x ]

or

  wins
[  x   x   x ]
[  x   x   x ] loses to
[  x   x   x ]
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on November 01, 2018, 05:52:01 pm
Hey Guys,

When drawing a least square regression line in exam 2 are you supposed to extend the line past the max and min x values of the data points given? I was thinking you don't extend the line because that would show extrapolation but the 2017 answers had a question that extended the line to reach the y axis etc.

Draw the line for the entire length of the scale.

Yes, some points on your line may involve extrapolation, which would make the predictions less reliable. But the graph of the least-squares line is still correct when the line extends beyond the range of the data.
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on November 01, 2018, 05:57:16 pm
In regards to Matrices, does VCAA by default put the win on the comlumns or the rows on dominance matrices.

Like this
  loses to
[  x   x   x ]
[  x   x   x ] wins
[  x   x   x ]

or

  wins
[  x   x   x ]
[  x   x   x ] loses to
[  x   x   x ]

They would let you know from the question.
Title: Re: VCE Further Maths Question Thread!
Post by: Omarrr_2163 on November 01, 2018, 06:58:10 pm
What would be the inverse of the 2x2 matrix:
[2k  3k]
[4k  7k]

Thats one matrix btw^
Title: Re: VCE Further Maths Question Thread!
Post by: studyingg on November 01, 2018, 07:07:55 pm
What would be the inverse of the 2x2 matrix:
[2k  3k]
[4k  7k]

Thats one matrix btw^

1/2k^2 * \begin{pmatrix}7k&-3k\\ 4k&2k\end{pmatrix} or \begin{pmatrix}\frac{7}{2k}&-\frac{3}{2k}\\ \frac{2}{k}&\frac{1}{k}\end{pmatrix}
Title: Re: VCE Further Maths Question Thread!
Post by: nicholas9027 on November 01, 2018, 08:42:36 pm
Hey Guys,
I need help with this tricky NHT 2017 exam 1 question. the answers say something about 600/400 X 15
but i dont get it can someone pls explain
the answer is A by the way

Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: spursy on November 01, 2018, 08:49:42 pm
can someone tell me an easy method to crash in networks
i think there is a method where you list all the paths but i'm not sure
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 01, 2018, 08:55:56 pm
Hey Guys,
I need help with this tricky NHT 2017 exam 1 question. the answers say something about 600/400 X 15
but i dont get it can someone pls explain
the answer is A by the way

Thanks :)

If ALL points along AB are a solution, the Objective function must have the same gradient as the line AB.
Try it out and if you need more help let us know :)
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on November 01, 2018, 09:04:30 pm
Hey Guys,
I need help with this tricky NHT 2017 exam 1 question. the answers say something about 600/400 X 15
but i dont get it can someone pls explain
the answer is A by the way

Thanks :)
I think you've attached the wrong screenshot as the correct answer to the question in the screenshot is B
Title: Re: VCE Further Maths Question Thread!
Post by: Maliat on November 03, 2018, 01:10:42 pm
Hi guys!
I'm in yr 10 and just had my first 3&4 exam yesterday, further maths.
So far I've got A+ for all SACS and a sitting at rank 1
I was just wondering about what study score I can expect, I dropped a mark in exam 1  :'(
I've heard that SS depends also on how the state does and your school cohort.
Title: Re: VCE Further Maths Question Thread!
Post by: Sine on November 03, 2018, 01:12:21 pm
Hi guys!
I'm in yr 10 and just had my first 3&4 exam yesterday, further maths.
So far I've got A+ for all SACS and a sitting at rank 1
I was just wondering about what study score I can expect, I dropped a mark in exam 1  :'(
I've heard that SS depends also on how the state does and your school cohort.

You are rank 1 so your cohort won't impact you too much if you get the highest score (or close to the highest score) in your cohort. If you continue doing this well in exam 2 you are looking at a study score in the high 40's.
Title: Re: VCE Further Maths Question Thread!
Post by: Bell9565 on November 03, 2018, 02:37:24 pm
Hi guys!
I'm in yr 10 and just had my first 3&4 exam yesterday, further maths.
So far I've got A+ for all SACS and a sitting at rank 1
I was just wondering about what study score I can expect, I dropped a mark in exam 1  :'(
I've heard that SS depends also on how the state does and your school cohort.
It really depends on how you go on the exam on Monday - I know a kid who got a 50 as rank one who dropped 1 mark on exam 1 then full marked exam 2 ... then I know others who got low 40's because they bombed the 2nd exam with a similar 1st exam mark. It really really depends on how you do in exam 2 - either way you should be comfortably above 40!
A very (very) simplified way of how VCAA work out study scores is they rank every person in the state who did the subject then put it on a bell curve and deal out study scores based on where you sit on that bellcurve (you actually learn the maths behind it in methods 3/4 which if you're doing further in year 10 I'd assume you would do eventually). So if the rest of the state does worse than you, you'll be up the top and you'll get a 50 but if its an easy exam and lots of people do really well, you'll get a lower study score with the same exam mark. So your study score is how you do in relation to the state so yeah, the state does affect your study score to a degree.
If you're rank one and you do the best on both exams, you're cohort won't affect you... it only really starts making a difference if you're lower down and even then, its not ~that~ much. Once again, its all to do with the bellcurve and they pretty much just do it to moderate the SACs from different schools on that bellcurve i mentioned earlier however ultimately, you want everyone from your school to do well on the exams because then VCAA thinks you had harder SACs so you technically do better in them.
I hope that helps with your questions (just elaborating on what Sine said a little :) )
Title: Re: VCE Further Maths Question Thread!
Post by: Maliat on November 03, 2018, 02:56:55 pm
It really depends on how you go on the exam on Monday - I know a kid who got a 50 as rank one who dropped 1 mark on exam 1 then full marked exam 2 ... then I know others who got low 40's because they bombed the 2nd exam with a similar 1st exam mark. It really really depends on how you do in exam 2 - either way you should be comfortably above 40!

Thanks so much! Guess I'll be studying hard for Monday
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 03, 2018, 05:07:25 pm
Just want to clarify - one exam that I did (I think it was a VCAA?) said that irregular variation is a feature of every time series graph. Is this right?
I am correcting the 2018 Heffernan exam (2) and it does not mention this in the solution when it asks for the pattern in a time series plot that is shown above.
Title: Re: VCE Further Maths Question Thread!
Post by: spursy on November 03, 2018, 05:26:57 pm
Just want to clarify - one exam that I did (I think it was a VCAA?) said that irregular variation is a feature of every time series graph. Is this right?
I am correcting the 2018 Heffernan exam (2) and it does not mention this in the solution when it asks for the pattern in a time series plot that is shown above.

every time series has irregular fluctautions/variations
Title: Re: VCE Further Maths Question Thread!
Post by: dimenc on November 03, 2018, 07:16:27 pm
Hi Everyone, i was wondering if someone could explain how to do graphs and relations questions regarding when the objective function has the same gradient as a line on the graph. I know how to do that (yay it was on exam 1!), but i was just wondering how i would be to go about finding actual integers on the line, as in like a max or min?
Thanks :)
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on November 03, 2018, 07:32:21 pm
Hi Everyone, i was wondering if someone could explain how to do graphs and relations questions regarding when the objective function has the same gradient as a line on the graph. I know how to do that (yay it was on exam 1!), but i was just wondering how i would be to go about finding actual integers on the line, as in like a max or min?
Thanks :)

In general, finding integer points on a line is beyond the scope of the Further course (it's part of a branch of maths called "Diophantine equations"). For the purposes of Further, you'll generally only have to find integer points on a line that are between two corner points that have only a small handful of integer coordinates between them.

Because of this, one straightforward (albeit slightly tedious) technique is to (i) first identify the equation of the relevant boundary of the feasible region (ii) identify all possible integer values of the x-coordinates of the points on the line, between the corner points, (iii) then, for each of these possible integer x-coordinates, solve for the y-coordinate. Some of these y-coordinates may not be integers, but some of them could be. To find the max / min, just check the objective function at each point with integer values for the x- and y-coordinates.

For an example of this sort of question / method, try the very last question from NHT Exam 2, 2017.
Title: VCE Further Maths Question Thread!
Post by: Lear on November 03, 2018, 08:39:23 pm
You can graph the function and then open up table on the ti nspire cas to visually see which x values have a corresponding integer y value :)


NOTE: For this, you cannot use inequalities. Instead you’ll have to solve the given inequality for y and then graph it as a >function<
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on November 03, 2018, 08:56:39 pm
Quote

NOTE: For this, you cannot use inequalities. Instead you’ll have to solve the given inequality for y and then graph it as a >function<

if you update your cas, you can actually get an option on the graphs mode where you don't have to solve for y (Relations) not sure if you can put inequalities tho  8)


nevermind, tested this out rn and it doesn't work even with the relations on the cas.
Title: Re: VCE Further Maths Question Thread!
Post by: jol122333 on November 03, 2018, 09:02:56 pm
Can anyone tell me if we are meant to use pen in exam 2? I saw something about it in the 2017 examiner's report but I'd definitely prefer to use my mechanical pencil if we're allowed to!
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 03, 2018, 09:03:08 pm
I wanted to add - This technique is very useful for 2018 MAV EXAM 2 last question of graphs module.
Title: Re: VCE Further Maths Question Thread!
Post by: finnystew on November 03, 2018, 10:12:38 pm
Could someone help me with question 13.
As far as I was concerned if you don't have all the individual data you need this formula  r=(Σ(x-¯x)(y-¯y))/((n-1) s_x s_y )
so you generate (x,y) values with the least squares regression line but the question does not provide a n value?
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on November 03, 2018, 10:16:49 pm
Could someone help me with question 13.
As far as I was concerned if you don't have all the individual data you need this formula  r=(Σ(x-¯x)(y-¯y))/((n-1) s_x s_y )
so you generate (x,y) values with the least squares regression line but the question does not provide a n value?
You just had to use b=r X Sy/Sx and then just put that into the solve function on your CAS
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on November 03, 2018, 10:38:31 pm
Can anyone tell me if we are meant to use pen in exam 2? I saw something about it in the 2017 examiner's report but I'd definitely prefer to use my mechanical pencil if we're allowed to!

you have to use pens. the papers are scanned .
Title: Re: VCE Further Maths Question Thread!
Post by: Mustafasarwari28 on November 03, 2018, 11:09:08 pm
Hey Guys, can someone please help me with financial, i have no idea what type of formula to use of any question, Can someone help me understand it a bit more? Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 03, 2018, 11:10:37 pm

you have to use pens. the papers are scanned .

Are you sure?
I know quite a few people who did further in pencil last year and got study scores. Perhaps one must use a dark pencil?
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 03, 2018, 11:12:10 pm

Hey Guys, can someone please help me with financial, i have no idea what type of formula to use of any question, Can someone help me understand it a bit more? Thanks

It’s not easy to explain such an open question over forums. I would highly recommend looking at your textbook/study design and writing a list of what type of loans/investments there are and under these headings writing what formula you need to use.

If you have a specific question feel free to let us know.
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on November 03, 2018, 11:19:02 pm
Are you sure?
I know quite a few people who did further in pencil last year and got study scores. Perhaps one must use a dark pencil?

According to the frontpage instructions, it is a requirement for students to write in blue or black pen. Therefore realistically you should be following that advice. Perhaps pencil for initial working out/solutions but then going over it with pen?

Also from Exam 2 2017's examiner report:
Quote
Scanned images are used for assessing and students should ensure their answers can be clearly read. Students were asked to write in blue or black pen. Students are urged to take greater care with the presentation of their responses
Title: Re: VCE Further Maths Question Thread!
Post by: Mustafasarwari28 on November 03, 2018, 11:19:28 pm
Does anyone know the solution to Question 4b on the 2017 exam as i am not sure how to get the answer. Is there also any goof practice papers that can be similar to the exam on Monday
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on November 03, 2018, 11:26:04 pm
Does anyone know the solution to Question 4b on the 2017 exam as i am not sure how to get the answer. Is there also any goof practice papers that can be similar to the exam on Monday
Thanks

Answers for VCAA exams are via examiner reports, available here: https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/exams.aspx

In future, can you please post the actual question you're having trouble with (either text or screenshot will be fine).. rather than giving a brief reference meaning volunteers have to go searching for your exam and question. It's really the least you can do since you're receiving quality assistance 1 day out from your exam. :) Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 03, 2018, 11:30:55 pm

Does anyone know the solution to Question 4b on the 2017 exam as i am not sure how to get the answer. Is there also any goof practice papers that can be similar to the exam on Monday
Thanks

Please post the question here so we do not have to go looking for it. No one can even tell what module you are referring to.

Practice paper recommendations
- VCAA 2016 Exam 2
- VCAA 2017 NHT Exam 2
- VCAA 2017 Exam 2
- VCAA 2018 NHT Exam 2
- MAV 2018 Exam 2
- Heffernan 2018 Exam 2
Title: Re: VCE Further Maths Question Thread!
Post by: Mustafasarwari28 on November 03, 2018, 11:33:49 pm
 There you go, sorry about that.
Is there a high chance that the 2017 exam 2 questions will be similar to the upcoming one?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on November 03, 2018, 11:38:04 pm
Mustafa i'd be looking at the Exam Assessor Report for last year's Exam 2 and noting down the questions that alot of students got incorrect. They would be the first questions i'd predict would be on this year's one.

Here's the link for you: https://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/fm2_examrep17.pdf
Title: VCE Further Maths Question Thread!
Post by: Lear on November 04, 2018, 12:00:34 am
Mustafa i'd be looking at the Exam Assessor Report for last year's Exam 2 and noting down the questions that alot of students got incorrect. They would be the first questions i'd predict would be on this year's one.

Here's the link for you: https://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/fm2_examrep17.pdf

This.

I sat down on Friday morning before exam 1 and just did every question answered correct by less than 40% of the state since 2006.
I was shocked how many of those questions reoccurred in the exam 3 hours later (same concepts). At least 7-8 questions were pretty much the same.

Further is a super competitive subject and exam writers have to separate people one way or the other. The scope of what they can examine is only so wide so reusing old, under performed concepts is one way they can do that.

Make use of past examiner reports people!
Title: Re: VCE Further Maths Question Thread!
Post by: pm123 on November 04, 2018, 12:24:56 am
Hi,
For exam 2, in the exam guidelines it asks us to use pen. Are they adamant about that, or can we use pencil instead? I know that the exams are photocopied, so just wanted to be sure.
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 04, 2018, 12:26:34 am
Hi,
For exam 2, in the exam guidelines it asks us to use pen. Are they adamant about that, or can we use pencil instead? I know that the exams are photocopied, so just wanted to be sure.
Look at the top of this page. Already been answered.
Title: Re: VCE Further Maths Question Thread!
Post by: English101 on November 04, 2018, 10:10:44 am
Please post the question here so we do not have to go looking for it. No one can even tell what module you are referring to.

Practice paper recommendations
- VCAA 2016 Exam 2
- VCAA 2017 NHT Exam 2
- VCAA 2017 Exam 2
- VCAA 2018 NHT Exam 2
- MAV 2018 Exam 2
- Heffernan 2018 Exam 2

I would advised not doing NHT (only if you want a confiedence booster).
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 10:13:35 am
I would advised not doing NHT (only if you want a confiedence booster).
While the 2018 NHT was probably a lower standard, I felt like the 2017 one was still quite decent (although it was a while ago that I did it). It is still VCAA questions and so it is likely going to be better preparation than company exams. Thats just my opinion though.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 04, 2018, 10:15:36 am

I would advised not doing NHT (only if you want a confiedence booster).

I would argue a confidence booster before the exam would be a great thing! :D
Title: Re: VCE Further Maths Question Thread!
Post by: Richard Feynman 101 on November 04, 2018, 10:20:42 am
It will. However, lead you in blind as well as giving someone false hopes. I would do the VCAA 2017 exam as this are the only real exams.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 10:22:17 am
It will. However, lead you in blind as well as giving someone false hopes. I would do the VCAA 2017 exam as this are the only real exams.
VCAA 2016 as well as this is still the current study design.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 04, 2018, 10:34:34 am

It will. However, lead you in blind as well as giving someone false hopes. I would do the VCAA 2017 exam as this are the only real exams.

Oddly enough while I couldn’t 100% on either of 2017 NHT or 2018 NHT exam 2, managed to get it on 2017 VCAA.
Just goes to show that it can vary on person.
I found NHT exams to be of similar difficulty, especially 2017 NHT. :)
Title: Re: VCE Further Maths Question Thread!
Post by: anne198 on November 04, 2018, 11:12:08 am
it is possible to have a non linear relationship between two variables but still have the relationship be strong?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 11:16:19 am
it is possible to have a non linear relationship between two variables but still have the relationship be strong?
It would be possible, but I assume we wouldn't need to know this for further, as we are studying linear relationships. The only time that non-linear associations are involved in the course is when r is less than 25 (or greater than -25), when we are working with residual plots to determine whether the relationship is linear or non-linear based on residual placement, and for transformations.
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on November 04, 2018, 11:20:57 am
It would be possible, but I assume we wouldn't need to know this for further, as we are studying linear relationships. The only time that non-linear associations are involved in the course is when r is less than 25 (or greater than -25), when we are working with residual plots to determine whether the relationship is linear or non-linear based on residual placement, and for transformations.

I believe you are expected know how to judge the strength of the linearised form of a non-linear relationship – eg. determine the correlation coefficient of bivariate data after a log / reciprocal / squared transformation has been applied.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 11:23:12 am
I believe you are expected know how to judge the strength of the linearised form of a non-linear relationship – eg. determine the correlation coefficient of bivariate data after a log / reciprocal / squared transformation has been applied.

Yes, but that is after the data has been linearised with the transformation, so I wouldn't say it is judging the strength of non-linear data, as it is not the original data that is being judged.
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on November 04, 2018, 11:28:24 am
Yes, but that is after the data has been linearised with the transformation, so I wouldn't say it is judging the strength of non-linear data, as it is not the original data that is being judged.

Yes, I agree. Just trying to clarify the issue.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 11:40:10 am
Yes, I agree. Just trying to clarify the issue.
lol sorry!
Title: Re: VCE Further Maths Question Thread!
Post by: Omarrr_2163 on November 04, 2018, 02:17:11 pm
How would you do this?  :o
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on November 04, 2018, 02:26:40 pm
Genuinely trial and error for me!
Title: Re: VCE Further Maths Question Thread!
Post by: spursy on November 04, 2018, 02:40:58 pm
which one would be right?
Title: Re: VCE Further Maths Question Thread!
Post by: Omarrr_2163 on November 04, 2018, 02:44:50 pm
I'd say C
Title: Re: VCE Further Maths Question Thread!
Post by: jol122333 on November 04, 2018, 03:43:26 pm
Maybe a silly question but are you allowed to write outside the lines on exam 2?
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on November 04, 2018, 03:46:56 pm
Maybe a silly question but are you allowed to write outside the lines on exam 2?

Outside the lines as in page margins or the lines given underneath the question?

If margins, try not to as you risk it not being included in the scan for assessors to mark. If you have to, use additional space provided / on the page within the page margins.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 03:47:07 pm
Maybe a silly question but are you allowed to write outside the lines on exam 2?
Do you mean outside the border of the page? Like the yellow area on the image attached?

If so, I would say no. I have heard a few people talking about it over the forums, and while some suggest that you might be able to get away with it, it's probably better to be safe. My teacher mentioned that you can write on one of the blank pages if you very clearly label the question that it is from at the actual question and at the blank page, but try to fit it on the main page if you can
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on November 04, 2018, 03:50:28 pm
Do you mean outside the border of the page? Like the yellow area on the image attached?
pretty sure you don't, cause if its only the black border...you really can't even write it therefore making the text meaningless.
Title: Re: VCE Further Maths Question Thread!
Post by: xdmemeguy on November 04, 2018, 03:52:56 pm
Hey guys I need help with this VCAA question form 2015 exam 2.

The answer says the modal inerval is 70-75, but shouldnt it be 70-74 becaues its a histogram, and like 75+ are part of the following intervals?

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: spursy on November 04, 2018, 03:53:24 pm
what would you do for this
Title: Re: VCE Further Maths Question Thread!
Post by: xdmemeguy on November 04, 2018, 03:57:52 pm
what would you do for this

Look at the residual plot and if points are not randomly scattered above and below the x-axis the association is not linear, that association does not look linear as it tends to dip under the x-axis a lot towards the middle. To find the transformation compare the plot to the transformation circle. Maybe because a residual plot is given, draw a diagonal line accross all quadrants in the middle of the data. Then kind of pretend that line is the x-axis for your residual plot and compare the "make-do residual plot" with the actual one and chose the transformation depending on the one that is the most similar.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 04:10:44 pm
Hey guys I need help with this VCAA question form 2015 exam 2.
The answer says the modal inerval is 70-75, but shouldnt it be 70-74 becaues its a histogram, and like 75+ are part of the following intervals?
Thanks
You would say 70-75, because if this interval was 70-74 and the next was 75-80, then all of the values between 74 and 75 (e.g. 74.5) would be excluded. It would really be 74.9999999999999999999 going on forever but you would just say 75.

what would you do for this

If a question asks for whether a residual plot is linear or non-linear, you have to look at whether the data is randomly skattered or not.
(https://stattrek.com/img/sp16.gif) (https://stattrek.com/img/sp17.gif) (https://stattrek.com/img/sp18.gif)
(Images are from here)
I would say that this plot would say that the residuals would be non-linear, as it doesn't appear to be randomly scattered, and there is a patch around the centre that has no data (or little) above the x axis, but a lot below the axis.
To linearise this, you need to apply a transformation to the data. To do this, you need to go back to the original graph and look at the shape of the data. Your teacher might have given you a diagram about what transformation to use when the graph looks a certain way. If not, you could try looking it up.
This question is 2 marks, so I would say that it would be non-linear, and therefore requiring a transformation as the question asks.
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on November 04, 2018, 05:22:41 pm
what would you do for this

Search up "circle of transformations" online and include in your bound reference.

Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on November 04, 2018, 05:42:01 pm
Why is the mean affected by outliers and skewness?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 04, 2018, 05:49:04 pm
Why is the mean affected by outliers and skewness?
The mean takes into account all data points, including outliers and ones that would influence the skew of the data. Think back to how you calculate the mean and you'll notice that outliers will pull them in the direction they're in e.g. an outlier higher than the rest of the data will make the mean much higher than if the outlier's data was excluded.

Hope that makes sense.

Side note: Please modify posts instead of double posting unnecessarily. You can do so via the "modify" button on the top right of your posts.
Title: Re: VCE Further Maths Question Thread!
Post by: finnystew on November 04, 2018, 06:31:54 pm
Question 4 from VCAA sample exam attached
Requires you to create an equation for some log(x) transformed data. However the y is population (000's)
Looked at itute solutions and they come up with the equations population=7700+7700(log area)       ...2sf.
This is done if you x1000 the population data before graphing.

However if you don't do this you get the equation population=7.7+7.7(log area). Which also works but in the following question you just have to multiply your prediction by 1000 to get the answer.

Thoughts? Do you think they'd give marks for either equation?
Title: Re: VCE Further Maths Question Thread!
Post by: PopcornTime on November 04, 2018, 06:43:37 pm
Hi,
I was confused with one of the questions on NHT 2018  exam 2 (probably something simple that I am overseeing).
With Q7d) - how did they get an annual interest rate of 9.5%?
With the starting amount being ($5000) compounding monthly (assuming), how is the annual interest rate 9.5%?
I keep on getting 9.2% using both the eqn – (6000=(1+x/12/100)^24x5000) and finance solver (N=24, PV = -5000, PMT = 0, FV = 6000, CYPY = 12, giving I% as 9.2).
Thank you!

Its not compounding monthly though. Your thinking is correct, but get rid of the 12 (cause not compounding monthly and change 24 months to 2 years).

So it should be:

(1+x/100)^2 x 5000 = 6000, x

Hope that helps and good luck tomorrow!
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on November 04, 2018, 06:46:24 pm
Question 4 from VCAA sample exam attached
Requires you to create an equation for some log(x) transformed data. However the y is population (000's)
Looked at itute solutions and they come up with the equations population=7700+7700(log area)       ...2sf.
This is done if you x1000 the population data before graphing.

However if you don't do this you get the equation population=7.7+7.7(log area). Which also works but in the following question you just have to multiply your prediction by 1000 to get the answer.

Thoughts? Do you think they'd give marks for either equation?
considering the response variable isn't listed as population (in thousands) but rather population, then 7700 should be the correct answer
Title: Re: VCE Further Maths Question Thread!
Post by: pm123 on November 04, 2018, 06:47:24 pm
Its not compounding monthly though. Your thinking is correct, but get rid of the 12 (cause not compounding monthly and change 24 months to 2 years).

So it should be:

(1+x/100)^2 x 5000 = 6000, x

Hope that helps and good luck tomorrow!

Ok... that explains a lot.

Thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: spicyunicorn on November 04, 2018, 06:52:54 pm
Can someone please help me with Question 7 of the Graphs from the MC exam? I'm shocking at objective functions  :-\
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 06:56:42 pm
I don't know if anybody has noticed this yet, but the VCAA sample exam is basically just questions from a couple of past exams mixed together.
Most of the Data section is from the 2014 VCAA exam 2, the finance and matrices sections makes reference to a question that came up in the 2013 exam 2, and I am not sure about the others. Just thought I'd mention it as some of the questions overlap and if there aren't answers for the sample exam questions (there might be - I have no clue), you could probably use these for some answers.

Question 4 from VCAA sample exam attached
Requires you to create an equation for some log(x) transformed data. However the y is population (000's)
Looked at itute solutions and they come up with the equations population=7700+7700(log area)       ...2sf.
This is done if you x1000 the population data before graphing.

However if you don't do this you get the equation population=7.7+7.7(log area). Which also works but in the following question you just have to multiply your prediction by 1000 to get the answer.

Thoughts? Do you think they'd give marks for either equation?
I highly doubt that they would accept both answers. Even if something is written like population (thousands) you need to leave the data in it's original form to find the linear regression line, otherwise inputing data into the line would result in extremely incorrect results.

Edit: According to the 2014 examiners report (this exam has the same question in it), your answer would be required as 7.7, rather than 7700.
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on November 04, 2018, 06:59:09 pm
I don't know if anybody has noticed this yet, but the VCAA sample exam is basically just questions from a couple of past exams mixed together.
Most of the Data section is from the 2014 VCAA exam 2, the finance and matrices sections makes reference to a question that came up in the 2013 exam 2, and I am not sure about the others. Just thought I'd mention it as some of the questions overlap and if there aren't answers for the sample exam questions (there might be - I have no clue), you could probably use these for some answers.
I highly doubt that they would accept both answers. Even if something is written like population (thousands) you need to leave the data in it's original form to find the linear regression line, otherwise inputing data into the line would result in extremely incorrect results.
So which one do you mean original? 7700 or 7.7?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 07:00:39 pm
So which one do you mean original? 7700 or 7.7?
oh sorry the 2014 examiners report has 7.7 so this would be what they would accept. I'll edit to make clearer.

considering the response variable isn't listed as population (in thousands) but rather population, then 7700 should be the correct answer
The original data in the table along the side has it listed as population (thousands), so the thousands is the unit. If it were to say length (mm), the equation generally would not use the variable as length (mm), but just state length. It is the same for this, as thousands is simply the unit.
Title: Re: VCE Further Maths Question Thread!
Post by: VeryJuicyLemon on November 04, 2018, 07:07:09 pm
oh sorry the 2014 examiners report has 7.7 so this would be what they would accept. I'll edit to make clearer.
The original data in the table along the side has it listed as population (thousands), so the thousands is the unit. If it were to say length (mm), the equation generally would not use the variable as length (mm), but just state length. It is the same for this, as thousands is simply the unit.
that cleared some misunderstandings, neap (or some other companies, can't remember) did the full "7700" for regression, got me confused

always listen to vcaa  :)
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 07:10:58 pm
that cleared some misunderstandings, neap (or some other companies, can't remember) did the full "7700" for regression, got me confused
Ah I hate it when the companies give you answers that VCAA would consider wrong! Super confusing  :-\


always listen to vcaa  :)
100%. Examiner reports are the greatest thing they could have given us (apart from the answers to this years exam, of course  ;))
Title: Re: VCE Further Maths Question Thread!
Post by: melaniethephan on November 04, 2018, 07:35:27 pm
Can anyone please explain the answer to part c of this question? VCAA said the answer is 8 trucks. It's from VCAA 2017 NHT Further Exam Networks Module Q3. Thank you (:
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 07:41:37 pm
Can anyone explain the answer to part c of this question? VCAA said the answer is 8 trucks. It's from VCAA 2017 NHT Further Exam Networks Module Q3. Thank you (:
Basically for this, you just need to find the path from the entrance to the exit that will allow for the maximum number of trucks to pass through. They all have to follow each other, so if must be one path. Its similar to a max flow question, just with one path only.
Looking at the graph, the path that would allow for the largest number of trucks to pass through would be the path highlighted yellow in the attached document. Although some streets allow more than 8 trucks (e.g. two allow 9), there is one that allows only 8, and therefore this is the maximum number that will be able to pass through each day.
Title: Re: VCE Further Maths Question Thread!
Post by: spursy on November 04, 2018, 07:42:40 pm
if the question says-

Describe the trend, if any, over time

do we have to include irregular fluctuations and all that other stuff or do we only just say if it's increasing or decreasing?
Title: Re: VCE Further Maths Question Thread!
Post by: melaniethephan on November 04, 2018, 07:43:56 pm
Basically for this, you just need to find the path from the entrance to the exit that will allow for the maximum number of trucks to pass through. They all have to follow each other, so if must be one path. Its similar to a max flow question, just with one path only.
Looking at the graph, the path that would allow for the largest number of trucks to pass through would be the path highlighted yellow in the attached document. Although some streets allow more than 8 trucks (e.g. two allow 9), there is one that allows only 8, and therefore this is the maximum number that will be able to pass through each day.

THANK YOU SO MUCH YOU ARE A LIFE SAVER!!!! Thank you for replying so fast..
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 04, 2018, 08:13:54 pm
if the question says-

Describe the trend, if any, over time

do we have to include irregular fluctuations and all that other stuff or do we only just say if it's increasing or decreasing?
After looking through past exam 2's up to 2013, I haven't been able to find any questions asking this. However, in the 2017 NHT Exam 2, question 3 a of the data analysis section. According to the answers, all you need to say is increasing trend, as you suggested.
If it asks for the pattern of a time series plot, I would say this is when you use the irregular fluctuations/cyclic variation/seasonality etc. terminology.
Title: Re: VCE Further Maths Question Thread!
Post by: anne198 on November 04, 2018, 09:21:40 pm
When asked for shape of distribution do you include if there is outliers or not?
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on November 04, 2018, 09:37:57 pm
Hey can anyone help me with this 2007 exam 2 question. I cant seem to get 7.3...

b. Another store offers the same $7000 office furniture for $500 deposit and 36 monthly instalments of
$220.
 ii. Calculate the annual flat rate of interest charged by this store.
 Write your answer as a percentage correct to one decimal place
Title: Re: VCE Further Maths Question Thread!
Post by: userrrname on November 04, 2018, 09:40:05 pm
When asked for shape of distribution do you include if there is outliers or not?
Yes you do and I think you even have to mention the number of outliers for things like boxplots e.g "with two outliers"
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on November 04, 2018, 09:49:27 pm
Hey can anyone help me with this 2007 exam 2 question. I cant seem to get 7.3...

b. Another store offers the same $7000 office furniture for $500 deposit and 36 monthly instalments of
$220.
 ii. Calculate the annual flat rate of interest charged by this store.
 Write your answer as a percentage correct to one decimal place
7000-500 = 6500

220 X 36 = 7920

7920 - 6500 = 1420

1420/3 = 473.333333

473.333333.../6500 X 100 = 7.28%

Explanation:
7000-500 = 6500 (you need to subtract the deposit because you don't pay interest on it)

220 X 36 = 7920 (this is the total amount you actually pay)

7920 - 6500 = 1420 (this is the interest paid)

1420/3 = 473.333333 (this is the interest for 1 year. 36months = 3 years)

473.333333.../6500 X 100 = 7.28%
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on November 04, 2018, 09:59:06 pm
using reading time for solving questions or actually reading  :'( not sure what to do considering last time, i ran out of time to check all modules for exam 1  :-\
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on November 04, 2018, 10:09:32 pm
using reading time for solving questions or actually reading  :'( not sure what to do considering last time, i ran out of time to check all modules for exam 1  :-\
I use it to make note of all the details that normally trip me up - so noting whether an interest rate is monthly or annual or whatever. Just making note of easily avoidable errors so that I don't actually make them.
Title: Re: VCE Further Maths Question Thread!
Post by: vceme on November 04, 2018, 10:22:07 pm
I use it to make note of all the details that normally trip me up - so noting whether an interest rate is monthly or annual or whatever. Just making note of easily avoidable errors so that I don't actually make them.
yeah thats what i tried to do for exam 1 but i think my paranoia that i was making a silly mistake made me lose so much time....

Also:
Everyone please make sure your CAS is set to just FLOAT (it's caused people to lose marks because their cas setting aren't right)
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on November 05, 2018, 06:34:37 am
using reading time for solving questions or actually reading  :'( not sure what to do considering last time, i ran out of time to check all modules for exam 1  :-\
Yeah like PhoenixxFire said, definitely use reading time to try and comprehend questions and pinpoint anything you think you are going to have trouble with. Get an idea of what you have to come so you can plan out your time basically (e.g. if you notice that the financial area has quite a few questions that you took a long time with in practice exams, try to allocate a little longer to this and move through faster with other sections that you could do easily.)
Don't bother trying to solve it yet, because you will just have to try and remember it. Only do this at the end if you have read through it all at least once and comprehended it all, and then just do it for the basic questions, like median and stuff, because you don't have your calculator.

Edit: this is just what I try to do - if you really want to start solving to potentially save a minute or two, then go for it!

Also:
Everyone please make sure your CAS is set to just FLOAT (it's caused people to lose marks because their cas setting aren't right)
OMG yes the most incredible advice. I will never do this wrong again after it lost me a mark in one SAC - that I would otherwise have gotten 100% on  :'( .

Good luck today everyone!
Title: Re: VCE Further Maths Question Thread!
Post by: Vri123 on November 05, 2018, 01:46:45 pm
Could someone predict my study score?
Sacs: 87% (defs not rank one)
Exam one: 40/40
Exam two:58/60
Title: Re: VCE Further Maths Question Thread!
Post by: vox nihili on November 05, 2018, 04:14:54 pm
Could someone predict my study score?
Sacs: 87% (defs not rank one)
Exam one: 40/40
Exam two:58/60

Please post study score predictions in the study score question thread—this is for questions about Further content :)
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on November 24, 2018, 08:42:14 pm
A principal value of $10 000 is invested in an account earning compound interest at the rate of 9% per annum. The rule for the value of the investment after n years is shown as Vn = 1.09n * 10 000

Find the amount of interest earned in the fourth year, correct to the nearest cent
Title: Re: VCE Further Maths Question Thread!
Post by: S200 on November 24, 2018, 08:48:52 pm
could you just sub in 3 and 4 as \(n\) and then minus the \(V_3\) from the \(V_4\)?

the difference should be the interest?
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on November 24, 2018, 09:34:57 pm
could you just sub in 3 and 4 as \(n\) and then minus the \(V_3\) from the \(V_4\)?

the difference should be the interest?
Thanks, but why is V3 involved?
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on November 24, 2018, 09:38:12 pm
Thanks, but why is V3 involved?
The question only wants the interest in the fourth year not the total interest so you have to subtract the total interest earned in the first 3 years (v3) from the total interest earned in the first four years (v4) to get just the interest in the fourth year.
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on November 28, 2018, 07:15:33 pm
Q: The Central Australia tour visits Kakadu National Park where the students are shown a flock of the endangered lesser yellow-breasted scrub thrushes.  The Park Ranger leading the tour explains that there are only 2 500 birds remaining.  The Ranger tells the students that out of each 100 adult birds, only 5 chicks are raised each year.  However, on average, 500 birds die each year.

I wrote that the recurrence relation is V0 = 2500 , Vn+1 = Vn  - 500 , however I don't know how to add in the 100 adult birds and 5 chicks raised (or if it is even necessary to add it in)
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on November 28, 2018, 07:19:13 pm
Q: The Central Australia tour visits Kakadu National Park where the students are shown a flock of the endangered lesser yellow-breasted scrub thrushes.  The Park Ranger leading the tour explains that there are only 2 500 birds remaining.  The Ranger tells the students that out of each 100 adult birds, only 5 chicks are raised each year.  However, on average, 500 birds die each year.

I wrote that the recurrence relation is V0 = 2500 , Vn+1 = Vn  - 500 , however I don't know how to add in the 100 adult birds and 5 chicks raised (or if it is even necessary to add it in)
Yep it's necessary to add it in. 5 chicks per 100 birds is 5% so the recurrence relation would be Vn+1 = 1.05Vn - 500

It could potentially be a bit different depending on if the 5 chicks are added before or after the 500 die but I'm pretty sure it would be this way around.
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on November 29, 2018, 11:16:31 pm
Yep it's necessary to add it in. 5 chicks per 100 birds is 5% so the recurrence relation would be Vn+1 = 1.05Vn - 500

It could potentially be a bit different depending on if the 5 chicks are added before or after the 500 die but I'm pretty sure it would be this way around.

oh so it's like compound interest right ? :P
I can see what you've done, but I can't connected the dots. Can u please clarify what the 'compound factor' means for 'R' (in Vn=R^n * V0) ?
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on November 30, 2018, 09:06:53 am
oh so it's like compound interest right ? :P
I can see what you've done, but I can't connected the dots. Can u please clarify what the 'compound factor' means for 'R' (in Vn=R^n * V0) ?
Yeah sort of, you can't change this equation into Vn=R^n * V0 format because of the -500. You just have to leave it as Vn+1 = 1.05Vn - 500.

If you didn't have the -500 part of it then it would be Vn=1.05^n * 2500

But you can't do that because you have to -500 each equation.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 03, 2018, 01:42:11 pm
Hi Guys,

Can someone please explain how to do part (c). Question is in the attachment.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on December 03, 2018, 01:48:09 pm
Hi Guys,

Can someone please explain how to do part (c). Question is in the attachment.

Thanks

What is your current understanding of the question? Provide us with something to work with. Giving you the answer will not assist with your understanding. Why not have a go at it yourself and post how you think it can be done here. That way, we can not only give you the answer, but can address your misconceptions so that when you are given a different question like this in the future, you can be aware of the mistakes and rectify them.

In a situation like this, your incorrect working out / answer is actually a good thing because it will address the issues directly.

Once you've had a go, open spoiler
A "recurrence relation model" is essentially the same as what you see in the original question. Except instead of the 2500, -400 etc, you will use 1800 as the V0 value (as V0 represents the initial price/cost) and Vn+1 = Vn (original/prev. value) - 350 (depreciates 350 per year, which is why we use negative 350 instead of positive 350).

So the model:
V0 = 1800, Vn+1 = Vn - 350

Cheers.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 03, 2018, 05:44:33 pm
Thanks Aaron. I get it how to do it now.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 04, 2018, 11:36:06 am
Hi Guys,

Need help to do this question. It is about compound interest. Specifically, Modelling compound interest with recurrence relations. Thanks

I don't know how they got an R value of 1.005. The R value I obtained was 1.00375. Has it got to do with a rounding error. When are we meant to round our answers? In the final answer, when we convert the yearly rate to a monthly rate or when we find the R value.

The question and the answer in the book are in the attachments

All help will be appreciated. Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on December 04, 2018, 11:43:31 am
Hi Guys,

Need help to do this question. It is about compound interest. Specifically, Modelling compound interest with recurrence relations. Thanks

I don't know how they got an R value of 1.005. The R value I obtained was 1.00375. Has it got to do with a rounding error. When are we meant to round our answers? In the final answer, when we convert the yearly rate to a monthly rate or when we find the R value.

The question and the answer in the book are in the attachments

All help will be appreciated. Thanks
As the interest is compounding monthly, you need to divide 6(the monthly interest rate)/12(the number of months in 1 year)=0.5 %. Then you need to divide the 0.5 by 100 to have it as a decimal form of the percentage, and add this to 1, resulting in 1.005.
In other words, 1+(6/(100*12)=1.005.

Hope this makes some sense. How did you work it out?
Title: Re: VCE Further Maths Question Thread!
Post by: lacitam on December 04, 2018, 11:43:53 am
You divide the percentage interest by 12 because it's monthly, not annually.
Can you tell me your steps on how you got 1.00375? Not following where this came from. I'll explain where you stuffed up on.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 04, 2018, 11:55:16 am
Thanks Galaxy. For some reason, when I did the question, I was looking at the example as well and accidently took the values given from the example instead of the question in the attachment LOL ;D. Anyway, thanks for the help. Without you, I wouldn't have realised the silly mistake I made.
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on December 04, 2018, 11:56:31 am
Thanks Galaxy. For some reason, when I did the question, I was looking at the example as well and accidently took the values given from the example instead of the question in the attachment LOL ;D. Anyway, thanks for the help. Without you, I wouldn't have realised the silly mistake I made.
Haha I do that all of the time...looks like you were on the right track anyway, so thats amazing!
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 04, 2018, 11:58:44 am
Yeah Thanks

Is the annual depreciation rate always in terms of per annum? Or does it depend on what Vn is defined for. For instance, if Vn was defined for the value of a loan after n months, would the annual depreciation rate be in terms of per month then?


Mod Edit: Post merge. Try not to post multiple times in a row - It clutters the feed and makes it harder for people to help you :) you can edit your previous message with 'Modify' :)
Title: Re: VCE Further Maths Question Thread!
Post by: lacitam on December 04, 2018, 12:29:26 pm
It should be annually - you just have to convert the months to years. Although the question should specify it.
Take this with a grain of salt, I've not done general maths since last year, might need to get this double checked.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 05, 2018, 08:35:45 am
Hi Guys,

Can someone please tell me whether the solution in the book is correct because when I did it, I got a different answer. My answer was $3366.47. The answer given in the book is $14187.30. Question is in the attachment. It is in regards to Using a recurrence relation to analyse a reducing balance loan. 

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on December 05, 2018, 08:43:49 am
Yeah that answer is wrong - the balance definitely shouldn’t be going up in a reducing balance loan.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 05, 2018, 08:46:32 am
Yeah that answer is wrong - the balance definitely shouldn’t be going up in a reducing balance loan.

So is my answer correct?
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on December 05, 2018, 08:52:18 am
So is my answer correct?
Yep
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 05, 2018, 08:55:41 am
Yep

Okay. Thanks for your response and help.  :)
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 06, 2018, 04:39:51 pm
Hi Guys,

Need help with the questions in the attachment. Would really appreciate it if someone can help me to solve it. The quesiton is inregards to reducing balance loans with changing conditions.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on December 06, 2018, 04:46:04 pm
Hi Guys,

Need help with the questions in the attachment. Would really appreciate it if someone can help me to solve it. The quesiton is inregards to reducing balance loans with changing conditions.

Thanks
What specifically are you stuck on? How are you trying to approach the question at the moment? You’ll learn more from it if you do as much of it as you can and then post your workings and thought process behind it up here rather than us explaining the whole thing.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 06, 2018, 05:07:37 pm
What specifically are you stuck on? How are you trying to approach the question at the moment? You’ll learn more from it if you do as much of it as you can and then post your workings and thought process behind it up here rather than us explaining the whole thing.

For instance, how to do part (b). When you do it, what is the answer you get for it?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on December 06, 2018, 05:09:55 pm
For instance, how to do part (b). When you do it, what is the answer you get for it?
to work out the interest payed over the term of the loan, you need to calculate the amount that is payed in total (payments x years x compounding periods per year + downpayment --> 1384 x 30 x 12=498240) and then subtract the initial value ($179994.242...) of the loan from this (498240-179994.24=318245.75). So $318,245.75 in interest was payed.
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on December 06, 2018, 05:12:43 pm
What specifically are you stuck on? How are you trying to approach the question at the moment? You’ll learn more from it if you do as much of it as you can and then post your workings and thought process behind it up here rather than us explaining the whole thing.

I have already stated this to this particular user.

dream chaser, I am not trying to be rude here but this seems (from my perspective) like you're just wanting us to do your work for you. It is very important that you have a go at it yourself and show us what you have done so we can genuinely help you. If we just give you answers, you may be able to answer that question, but what about a different question on the same topic?

It will be much more beneficial to you if you take the time to attempt it first, as Further is a subject where mistakes are very common and hence what spreads students out on the distribution.

I am posting this as you have been posting quite a bit on here (and this is OK, we are more than willing to help you).. it's just that you need to show some effort too.

This is a PSA directed at all users who post questions in the Further board.. please actually try the question yourself or demonstrate you have at least had a think about it so we can target the misconceptions as well as provide you with the answer to move forward.

Again, I will repeat this because I don't want this post interpreted in the wrong way, it is fantastic that you all are posting questions... however please show some respect to the users who are voluntarily taking time out of their day to assist you by demonstrating effort in some way.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 06, 2018, 05:16:16 pm
I have already stated this to this particular user.

dream chaser, I am not trying to be rude here but this seems (from my perspective) like you're just wanting us to do your work for you. It is very important that you have a go at it yourself and show us what you have done so we can genuinely help you. If we just give you answers, you may be able to answer that question, but what about a different question on the same topic?

It will be much more beneficial to you if you take the time to attempt it first, as Further is a subject where mistakes are very common and hence what spreads students out on the distribution.

I am posting this as you have been posting quite a bit on here (and this is OK, we are more than willing to help you).. it's just that you need to show some effort too.

This is a PSA directed at all users who post questions in the Further board.. please actually try the question yourself or demonstrate you have at least had a think about it so we can target the misconceptions as well as provide you with the answer to move forward.

Aaron, I have tried to attempt the question my self as well before I posted for help on Atar Notes. The answer I got was the same as Galaxies. However, in the book, they give a different answer so I am completely confused what is right and what is wrong.
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on December 06, 2018, 05:18:28 pm
Aaron, I have tried to attempt the question my self as well before I posted for help on Atar Notes. The answer I got was the same as Galaxies. However, in the book, they give a different answer so I am completely confused what is right and what is wrong.

That's all cool, so show us your working out and how you got your answer so we can address it and tell you whether the book is right/wrong. :)

This is what I mean by 'showing effort' - if you believe the book is wrong or you're confused.. show us what you have and we can tell you whether you're right or not. It's a bit difficult without any working out from your end!

And.. if the book ends up being correct, showing working out means that we can tell you the exact point where you may have miscalculated or done something slightly wrong. It's a win-win!

Your working out doesn't have to be in LaTeX either - so if that's what you're worried about.. don't stress. You can attach a screenshot/photo of your working out (or upload via imgur.com and provide link) or even type it out. We should be able to interpret what you're trying to do, as long as it's step-by-step.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 06, 2018, 05:22:48 pm
That's all cool, so show us your working out and how you got your answer so we can address it and tell you whether the book is right/wrong. :)

If you really want me to show you how I did it, I'll show you.

First, you find the selling price of the house. I did this by using the financial solver on the CAS and substituting all the values I knew to find the unknown, which in this case on my CAS was PV(the present value). I got an answer of $229994.24. Then to find interest, you multiply 12 x 30 x 1384 - the selling price of the house - 50000. I wasn't sure if 50000 should be reduced or not. However, now i know. Thank you Galaxy for the help

The hard copy of the book says the answer for part (b) is $318245.76 whilst the answer of the online version of the book is $268245.76.

MOD EDIT: MERGED DOUBLE POST
Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on December 06, 2018, 05:26:30 pm
If you really want me to show you how I did it, I'll show you.

First, you find the selling price of the house. I did this by using the financial solver on the CAS and substituting all the values I knew to find the unknown, which in this case on my CAS was PV(the present value). I got an answer of $229994.24. Then to find interest, you multiply 12 x 30 x 1384 - the selling price of the house - 50000. I wasn't sure if 50000 should be reduced or not. However, now i know. Thank you Galaxy for the help

If your question had've included this working out and the question "I wasn't sure if 50000 should be reduced or not", we could've told you straight away without other users trying to decrypt what you're actually asking. :) So your understanding was OK up to that point.. so your actual question was relating to the 50000. Something to keep in mind for future questions! Straight to the point works wonders  8)

Asking the right question is often just as (if not more) important as asking a general 'help me with q5' type of question. You build on your conceptual understanding rather than simply remembering how to rote learn the formula/procedure which imo has minimal learning gain.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 24, 2018, 08:05:25 pm
Hi,

Would someone be able to explain to me how annuity works. I know that there is a formula used for it: Vn+1=RVn - D and that it is used to describe how much money is left in an investment. But I don't get the context of it or how it is used. For instance, I don't understand why the D value(payment received) minuses the value of the annuity. If someone is receiving money from the bank or insurance company, wouldn't there be more money in the investment?

Would appreciate all help given

Thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: redpanda83 on December 24, 2018, 08:23:56 pm
Hi,

Would someone be able to explain to me how annuity works. I know that there is a formula used for it: Vn+1=RVn - D and that it is used to describe how much money is left in an investment. But I don't get the context of it or how it is used. For instance, I don't understand why the D value(payment received) minuses the value of the annuity. If someone is receiving money from the bank or insurance company, wouldn't there be more money in the investment?

Would appreciate all help given

Thanks  :)
Think from the bank prespective.
You have x amount of money with you which someone gave to you(investment)
Now every n days/weeks/years you are giving D payment to the investor. Thus -D, if the investor adds payment to the investment it would be +D.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 24, 2018, 08:30:07 pm
Think from the bank prespective.
You have x amount of money with you which someone gave to you(investment)
Now every n days/weeks/years you are giving D payment to the investor. Thus -D, if the investor adds payment to the investment it would be +D.

Oh okay, so for annuities, think of it in terms of a bank perspective, not the person investing perspective?
Title: Re: VCE Further Maths Question Thread!
Post by: redpanda83 on December 24, 2018, 08:35:46 pm
Hi,

Would someone be able to explain to me how annuity works. I know that there is a formula used for it: Vn+1=RVn - D and that it is used to describe how much money is left in an investment. But I don't get the context of it or how it is used. For instance, I don't understand why the D value(payment received) minuses the value of the annuity. If someone is receiving money from the bank or insurance company, wouldn't there be more money in the investment?

Would appreciate all help given

Thanks  :)
Take this scenario,
you invested $1000 in a bank. Lets ignore interest rate just for now.
if bank said every months they will give you payment of $10.
you will gradually lose money from the $1000, on a realistic interest rate xD.
So, in this scenario Vn<V0. as some money is always given to you per n period.
and the difference between the money you gained and the initial amount = interest earned.
Scenario 2,
this time you will be putting D payment in the bank instead of recieving payment. so D is added onto V0.
...
on the cas, think from your perspective. The way i have done and taught others for sign is;
+ if the money is coming into your pocket
- if the money is going out of your pocket.
Always make sure FV and PV have different signs.
And think realistically, think what does negative sign what really means. like there is no such thing as negative money, but what it means is either you are loosing money/ owe money. Right! just look for the meaning and you will be fine

Oh okay, so for annuities, think of it in terms of a bank perspective, not the person investing perspective?

Well, it makes more sense that way to me.
OR i think i am the money xD and what does effect does D has on me.
There are multiple ways!

Mod Edit: Merged posts. Please refrain from double posting as stated in our forum guidelines
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 24, 2018, 08:46:00 pm
Take this scenario,
you invested $1000 in a bank. Lets ignore interest rate just for now.
if bank said every months they will give you payment of $10.
you will gradually lose money from the $1000, on a realistic interest rate xD.
So, in this scenario Vn<V0. as some money is always given to you per n period.
and the difference between the money you gained and the initial amount = interest earned.
Scenario 2,
this time you will be putting D payment in the bank instead of recieving payment. so D is added onto V0.
...
on the cas, think from your perspective. The way i have done and taught others for sign is;
+ if the money is coming into your pocket
- if the money is going out of your pocket.
Always make sure FV and PV have different signs.
And think realistically, think what does negative sign what really means. like there is no such thing as negative money, but what it means is either you are loosing money/ owe money. Right! just look for the meaning and you will be fine

Okay. However, I still don't understand why it is -D. If the bank is giving the investor money, wouldn't the value of the investment go up in value and hence, be +D?
Title: Re: VCE Further Maths Question Thread!
Post by: redpanda83 on December 24, 2018, 08:50:21 pm
Okay. However, I still don't understand why it is -D. If the money is giving the investor money, wouldn't the value of the investment go up in value?
no.
well its sign conventions. i will keep them consistent.
so you invested $1000 in bank. Thus out of your pocket and it will have - sign. -1000
Now you recieved payment of D, -1000 +D, lets say D = 10 from previous example.
So v0 = -1000
V1 = -1000+10 = -990.
The fomula is based on from the bank prespective
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 24, 2018, 08:51:42 pm
no.
well its sign conventions. i will keep them consistent.
so you invested $1000 in bank. Thus out of your pocket and it will have - sign. -1000
Now you recieved payment of D, -1000 +D, lets say D = 10 from previous example.
So v0 = -1000
V1 = -1000+10 = -990.
The fomula is based on from the bank prespective

Okay. Would the perpetuity formula be based from the bank perspective as well? Also, thanks for the help. Much appreciated  :D
Title: Re: VCE Further Maths Question Thread!
Post by: redpanda83 on December 24, 2018, 08:53:40 pm
Okay. However, I still don't understand why it is -D. If the bank is giving the investor money, wouldn't the value of the investment go up in value and hence, be +D?
Remember bank is giving the money back to you which in this should be greater than interest earned.
So think a friend gave you some money and asked you to give him some back on weekly basis.
So when you give him the money back, did you end up with more money or less money when you started?

Okay. Would the perpetuity formula be based from the bank perspective as well? Also, thanks for the help. Much appreciated  :D

Perpetuity is simple dont think much about it. But yeah it is.
D= interest. So no matter after how many period V0 stays the same.
Think a friend gave you the money, and he earns interest of $r. and what you do is basically give him $r xD.

In perpetuity, interest earned by bank = payment you received
this keeps the V0 consistent.
perpetuity is usually used by organisation who provides scholarships.

Also try to graphically represent a annuity and perpetuity over n period. See the pattern yourself how the money changes over time!

Mod Edit: Merged posts. Please refrain from chain posting. If you need to add more to your response, click on the 'modify' button in the top right corner.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 25, 2018, 07:07:35 pm
Also try to graphically represent a annuity and perpetuity over n period. See the pattern yourself how the money changes over time!

Okay. Thank you for your help
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 25, 2018, 07:15:50 pm
Hi Guys,

I need help with this question. This is the question:

Jarrod saves $500 per month in an account that pays interest at a rate of 6% per annum, compounding monthly.

(a) If he makes monthly deposits of $500 to the account, how much will he have in the account at the end of 10 years?

My understanding of question: I know for this question, I can use the financial solver to complete it. I know that it involves Annuity, however it also involves increasing the value of the investment as well. Therefore, an annuity investment. As a result of that, on the financial solver(CAS-the TI-nspire notation):

N=120
I(%)=6
PV=?
Pmt=-500
FV=?
PpY=12
CpY=12
PmtAt=END

Btw, PV=Present value of Annuity. In this case, how much is invested. FV=Future value of Annuity.

I know for the question, I need to find FV. That means, PV should be given but I don't think it is. Hence, why I can't complete the question. Could someone please help me  :D

All help will be appreciated

Thanks :)


Title: Re: VCE Further Maths Question Thread!
Post by: vceme on December 25, 2018, 08:12:26 pm
Hi Guys,

I need help with this question. This is the question:

Jarrod saves $500 per month in an account that pays interest at a rate of 6% per annum, compounding monthly.

(a) If he makes monthly deposits of $500 to the account, how much will he have in the account at the end of 10 years?

My understanding of question: I know for this question, I can use the financial solver to complete it. I know that it involves Annuity, however it also involves increasing the value of the investment as well. Therefore, an annuity investment. As a result of that, on the financial solver(CAS-the TI-nspire notation):

N=120
I(%)=6
PV=?
Pmt=-500
FV=?
PpY=12
CpY=12
PmtAt=END

Btw, PV=Present value of Annuity. In this case, how much is invested. FV=Future value of Annuity.

I know for the question, I need to find FV. That means, PV should be given but I don't think it is. Hence, why I can't complete the question. Could someone please help me  :D

All help will be appreciated

Thanks :)

I haven't done this in a looooong time but reading the question, you're right- they don't give you the PV value. It might be right to assume that the PV value  just starts with 0. What's the answer? This might be wrong so someone please check!!!
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 25, 2018, 08:34:50 pm
I haven't done this in a looooong time but reading the question, you're right- they don't give you the PV value. It might be right to assume that the PV value  just starts with 0. What's the answer? This might be wrong so someone please check!!!

I don't think that PV will be zero as the investment will not simply increase by not giving anything to the bank/insurace company in the first place. The answer is $81939.67.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 26, 2018, 12:47:02 pm
Hi Guys,

Need help with this question

Question: Roslyn earns an annual salary of $54200,which is paid monthly. She did not join the superannuation fund until her 37th birthday and she now pays 7% of her gross salary to the superannuation fund. Her employer contributes a further 14%.

(a) What amount of money is placed each month into her superannuation fund?
This question I am able to do. I did:
21/100 x $54200 = $11382. Then $11382/12 = $948.50 per month.

Now this is where I got stuck...

(b) The superannuation fund pays 4.2% per annum compound interest, compounded monthly. Assuming that Roslyn's annual salary remains constant, what is the amount of superannuation she will have available at her 60th birthday?

This is the way I did it, bare in mind this method is completely wrong as I got the wrong answer in the end.

Vn=R^n x V0, where R=1+r/100
Vn=R^n x 948.50
R=1+r/100
r=4.2/1=0.35% monthly rate
R=1+0.35/100  1.0035

Vn =(1.0035)^n x 948.50

V276=(1.0035)^276 x 948.50
V276 = $2487.90

Therefore my answer is $2487.90. However the actual answer to this question is $439829.26. Can someone please show me how to get this answer.

(c) Suppose that when Roslyn retires at 60 years of age, she places her superannuation in a perpetuity that will provide a monthly income without using any of the principal. If the perpetuity pays 4.25% per annum compounding monthly, what monthly payment will Roslyn receive?

My answer is completely wrong as I used the answer I obtained in part (b) for this.
D=r/100 x V0
r=4.25%/12
r=0.354167% monthly rate.
D=0.354167/100 x $2487.90
D=$8.81.

Therefore my answer is $8.81. The answer obtained in the book is $1557.73. How do I get that answer?

So basically I need help with part (b) and (c) with this question. Also, if anyone reads this, could you please read a couple of my previous posts on the Further Maths Questions Thread to see whether I am able to complete a previous question of mine. It was in regards to PV and FV and the topic was on annuity investments(I posted it yesterday).

All the help will be much appreciated. Thanks. By the way, Merry Christmas to Everyone for yesterday.  :) :D

Title: Re: VCE Further Maths Question Thread!
Post by: Aaron on December 26, 2018, 01:32:38 pm
Thank you very much dream chaser for helping us to assist you, by providing working out and your explanations. :) It is much appreciated that you've taken the time to read my post and acknowledge it.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 26, 2018, 01:41:43 pm
Thank you very much dream chaser for helping us to assist you, by providing working out and your explanations. :) It is much appreciated that you've taken the time to read my post and acknowledge it.

No problem Aaron  :) :D.
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on December 26, 2018, 02:04:55 pm
I don't think that PV will be zero as the investment will not simply increase by not giving anything to the bank/insurace company in the first place. The answer is $81939.67.
The PV will be zero because they're asking how much he will have in total after 10 years of saving. Unless otherwise stated, this means you can assume that he starts with 0 savings. Putting 0 as the PV will give you an answer of $81939.67

Hi Guys,

Need help with this question

Question: Roslyn earns an annual salary of $54200,which is paid monthly. She did not join the superannuation fund until her 37th birthday and she now pays 7% of her gross salary to the superannuation fund. Her employer contributes a further 14%.

(a) What amount of money is placed each month into her superannuation fund?
This question I am able to do. I did:
21/100 x $54200 = $11382. Then $11382/12 = $948.50 per month.

Now this is where I got stuck...

(b) The superannuation fund pays 4.2% per annum compound interest, compounded monthly. Assuming that Roslyn's annual salary remains constant, what is the amount of superannuation she will have available at her 60th birthday?

This is the way I did it, bare in mind this method is completely wrong as I got the wrong answer in the end.

Vn=R^n x V0, where R=1+r/100
Vn=R^n x 948.50
R=1+r/100
r=4.2/1=0.35% monthly rate
R=1+0.35/100  1.0035

Vn =(1.0035)^n x 948.50

V276=(1.0035)^276 x 948.50
V276 = $2487.90

Therefore my answer is $2487.90. However the actual answer to this question is $439829.26. Can someone please show me how to get this answer.
I would just put this into the finance solver on your CAS
N=276
I(%)=4.2
PV=0
Pmt=-948.50
FV=?
PpY=12
CpY=12
PmtAt=END

Which gives the answer that FV=439829.26

It probably is possible to work out without CAS, but you shouldn't need to.

(c) Suppose that when Roslyn retires at 60 years of age, she places her superannuation in a perpetuity that will provide a monthly income without using any of the principal. If the perpetuity pays 4.25% per annum compounding monthly, what monthly payment will Roslyn receive?

My answer is completely wrong as I used the answer I obtained in part (b) for this.
D=r/100 x V0
r=4.25%/12
r=0.354167% monthly rate.
D=0.354167/100 x $2487.90
D=$8.81.

Therefore my answer is $8.81. The answer obtained in the book is $1557.73. How do I get that answer?

So basically I need help with part (b) and (c) with this question. Also, if anyone reads this, could you please read a couple of my previous posts on the Further Maths Questions Thread to see whether I am able to complete a previous question of mine. It was in regards to PV and FV and the topic was on annuity investments(I posted it yesterday).

All the help will be much appreciated. Thanks. By the way, Merry Christmas to Everyone for yesterday.  :) :D

Your solution for this is fine, you just used the wrong value. Replace $2487.90 with $439829.26 and it'll give you the correct answer.
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on December 26, 2018, 02:10:15 pm
Hey Dream Chaser!
Echoing Aaron's comments above, thank you for showing your approach. Trust me when I say you will learn much better by recognising where you went wrong instead of simply being told what to do.
(b) The superannuation fund pays 4.2% per annum compound interest, compounded monthly. Assuming that Roslyn's annual salary remains constant, what is the amount of superannuation she will have available at her 60th birthday?

This is the way I did it, bare in mind this method is completely wrong as I got the wrong answer in the end.

Vn=R^n x V0, where R=1+r/100
Vn=R^n x 948.50
R=1+r/100
r=4.2/1=0.35% monthly rate
R=1+0.35/100  1.0035

Vn =(1.0035)^n x 948.50

V276=(1.0035)^276 x 948.50
V276 = $2487.90

Therefore my answer is $2487.90. However the actual answer to this question is $439829.26. Can someone please show me how to get this answer.

So for a superannuation, essentially the person starts of with a sum of money, and each month the employer adds an amount of money to the fund which compounds over time. Where you went wrong is that you treated the 948.50 as the initial value when it is not. The initial value is actually simply 0 while 948.50 is the amount of money added each month.
Because of the monthly addition you cannot raise the R value to a power n as each the month the V value is changing.
Here's the recurrence formula for this superannuation.
Vn+1=R*Vn + 948.50.
Now due to the additional 948.50 added every month, doing this formula 250+ times will take a while...
Luckily, you have your CAS!
Here's the inputs I used
N: 276 (12 months multiplied by (60-37) years)
I: 4.5 (This is always in percentage per annum and it is 4.5 from the question)
PV: 0 (There's no information on the initial value of the fund so we assume 0)
PMT: -948.50 (948.50 is being invested into the fund by the employer hence we use the negative)
FV: ?
CPY/CPY: 12

The future value is found to be $439829.26


Quote
(c) Suppose that when Roslyn retires at 60 years of age, she places her superannuation in a perpetuity that will provide a monthly income without using any of the principal. If the perpetuity pays 4.25% per annum compounding monthly, what monthly payment will Roslyn receive?

My answer is completely wrong as I used the answer I obtained in part (b) for this.
D=r/100 x V0
r=4.25%/12
r=0.354167% monthly rate.
D=0.354167/100 x $2487.90
D=$8.81.

Therefore my answer is $8.81. The answer obtained in the book is $1557.73. How do I get that answer?

Your working out is almost perfect. You just forgot to divide the 4.25 by 100 as you stated in the first line. The r should instead be 0.003542
Now we just need to multiply by the value from C which is 439829.26
This gives us 1557.73 as required.

You could also do this on financial solver
N: 1 (we just want to see the value of one payment)
I: 4.25%
PV: -439829.256 (from c and it is negative because it's an investment)
PMT: ? (we don't know)
FV: 439829.256 (Perpetuity value stays the same and hence FV is just positive value of PV)
PPY/CPY: 12

PMT = 1557.73

***Beaten by PF but i'll leave this as some of the financial solver explanations may be useful for understanding.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 27, 2018, 04:16:49 pm
Thank you both PhoenixxFire and Lear for the help. My apologies for not thanking you both earlier. Just a quick question. I don't understand why PV wouldn't equal -948.50. Isn't 948.50 how much the person initially invests which gets bigger over time. Also, this is an Annuity Investment right?
Title: VCE Further Maths Question Thread!
Post by: Lear on December 27, 2018, 04:31:34 pm
948.5 is not how much the initial investment is. It’s how much is being added by the employer every month.


Your super annual Annuation is there to support you once you retire.  Think of it as a retirement piggy bank. You start earning it when you start working. Your employer contributes to the piggy bank every month and it slowly piles up over time. Initially, of course, there was nothing in this piggy bank. However it starts adding up every time your employer adds another 948.50 to it. Once you retire you’re going to break open that piggy bank and it’ll support you :)
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 28, 2018, 05:16:04 pm
948.5 is not how much the initial investment is. It’s how much is being added by the employer every month.


Your super annual Annuation is there to support you once you retire.  Think of it as a retirement piggy bank. You start earning it when you start working. Your employer contributes to the piggy bank every month and it slowly piles up over time. Initially, of course, there was nothing in this piggy bank. However it starts adding up every time your employer adds another 948.50 to it. Once you retire you’re going to break open that piggy bank and it’ll support you :)

Okay. How come in my question it says that Roslyn pays 7% of her gross salary to the superannuation. Does this mean she alongside her employer is adding money into her superannuation fund or still only the employer each month. Also, does your last post informing me how a superannuation work apply for all superannuation's?

Is this how it works? So at the start, Roslyn starts with $0.00. Then after one month, she has $948.50. As 4.2%p.a /12 =0.35% monthly rate and 0.35/100 x $948.50 = $3.32. Then this gets added on to the $948.50 which makes $951.83. Therefore, she will have $951.83 in her superannuation account after one month. And this process continues every month right?

MOD EDIT: merged two consecutive posts. Try not to double post :)
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on December 28, 2018, 06:29:32 pm
Okay. How come in my question it says that Roslyn pays 7% of her gross salary to the superannuation. Does this mean she alongside her employer is adding money into her superannuation fund or still only the employer each month.
Yes, in this example both Roslyn and the employer contribute to Roslyn's super.
Is this how it works? So at the start, Roslyn starts with $0.00. Then after one month, she has $948.50. As 4.2%p.a /12 =0.35% monthly rate and 0.35/100 x $948.50 = $3.32. Then this gets added on to the $948.50 which makes $951.83. Therefore, she will have $951.83 in her superannuation account after one month. And this process continues every month right?
Almost, after one month she will have $948.50. After two months she will have 948.50*2=$1897 plus the interest on the first month amount (=$3.32) which is equal to $1900.32. This process continues each month.
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on December 28, 2018, 06:58:07 pm
Yes, in this example both Roslyn and the employer contribute to Roslyn's super.Almost, after one month she will have $948.50. After two months she will have 948.50*2=$1897 plus the interest on the first month amount (=$3.32) which is equal to $1900.32. This process continues each month.

Why wouldn't the first month be $951.82?

If V0 didn't equal zero, then there would be interest in the first month right?
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on December 28, 2018, 07:46:10 pm
Why wouldn't the first month be $951.82?

If V0 didn't equal zero, then there would be interest in the first month right?
I think you answered your own question. The first month isn't $951.82 as there wasn't any money in the super to gain interest over that time (as V0=0). You're correct in saying if V0 didn't equal zero, then there would be interest in the first month.
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on January 12, 2019, 08:10:23 pm
Hey can anyone please tell me if I've done these two questions correctly?

https://imgur.com/a/vmHFYo8
(took me way too long to try and attach this picture lol)

Sorry, for the second question, I change my answer to 84 months
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on January 12, 2019, 09:16:03 pm
Hey can anyone please tell me if I've done these two questions correctly?

https://imgur.com/a/vmHFYo8
(took me way too long to try and attach this picture lol)

Sorry, for the second question, I change my answer to 84 months
The first part looks right but why did you change your answer to 84 months in the second part?
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on January 13, 2019, 07:22:28 pm
The first part looks right but why did you change your answer to 84 months in the second part?
Thank you :)
Yeah my bad lol. What I did originally was round the year down first, then convert to months :P
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on January 13, 2019, 07:37:38 pm
Need help with question c please!
https://imgur.com/a/VJvY0V2
I'm not sure whether the answer is 1407 or 1408 players. Here is my thinking: if you plug in the numbers into the equation, you get 1407.37488.

As soon as 1 year elapsed, there will be 1407.37488 players. So if you round it down to 1407 players, this means that 1 year has not passed yet. However if you round it up to 1408 players, 1 year has already elapsed.
My working out is a bit messy to comprehend, but hopefully you understand :P
Title: Re: VCE Further Maths Question Thread!
Post by: MAGGOT on January 16, 2019, 09:00:57 am
Need help with question c please!
https://imgur.com/a/VJvY0V2
I'm not sure whether the answer is 1407 or 1408 players. Here is my thinking: if you plug in the numbers into the equation, you get 1407.37488.

As soon as 1 year elapsed, there will be 1407.37488 players. So if you round it down to 1407 players, this means that 1 year has not passed yet. However if you round it up to 1408 players, 1 year has already elapsed.
My working out is a bit messy to comprehend, but hopefully you understand :P

Your thinking process is right and after 1407 players, 1 year hasn't elapsed so when you round up, 1408 players is the answer.
Title: Re: VCE Further Maths Question Thread!
Post by: jnylle on January 21, 2019, 03:11:28 pm
just came up with a helpful idea for my summary book, but was wondering what kind of excerise books we're alowed to bring into the year 12 exam... :(
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on January 21, 2019, 03:19:29 pm
just came up with a helpful idea for my summary book, but was wondering what kind of excerise books we're alowed to bring into the year 12 exam... :(
It can be basically anything as long as it is A4 and securely bound. You also can't have notebooks with perforated edges.

Quote from: VCAA
The bound reference must be in book format of A4 size or smaller when closed.
The number of pages is not specified.
Pages must be permanently bound and securely attached to the spine.
There must be a single horizontal or vertical spine.
The bound reference may be:
a textbook
a securely bound lecture pad
a permanently bound student-constructed set of notes without fold-outs
an exercise book.
The form of binding is not specified but it must be secure, and pages must not be readily detachable or designed to be removed. Binding can include cloth, glue, staple, spiral or comb binding.
(From https://www.vcaa.vic.edu.au/Pages/vce/exams/authorisedmaterials.aspx#bound)
Title: Re: VCE Further Maths Question Thread!
Post by: andreag on January 21, 2019, 05:47:00 pm
Would it be helpful to do every past exam on the VCAA website like all the way to 2002, for exam/sac revision even though most of them are not part of the study design? 
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on January 21, 2019, 06:56:07 pm
Would it be helpful to do every past exam on the VCAA website like all the way to 2002, for exam/sac revision even though most of them are not part of the study design? 
Probably better to do the parts that remain relevant. I know since 2014 (when I did Further), there have been a lot of changes. Typically I'd advise doing VCAA exams closer to exams, as these are the closest you're going to get to the real deal.
Title: Re: VCE Further Maths Question Thread!
Post by: andreag on January 21, 2019, 07:13:32 pm
Probably better to do the parts that remain relevant. I know since 2014 (when I did Further), there have been a lot of changes. Typically I'd advise doing VCAA exams closer to exams, as these are the closest you're going to get to the real deal.

So how would you go about studying for sacs? Just using the relevant VCAA past exams? Are there other resources that will help like study guides or topic tests (from atar notes, checkpoints etc)?
Title: Re: VCE Further Maths Question Thread!
Post by: galaxy21 on January 21, 2019, 07:27:48 pm
So how would you go about studying for sacs? Just using the relevant VCAA past exams? Are there other resources that will help like study guides or topic tests (from atar notes, checkpoints etc)?
There are so many extra questions out there to help study for SAC's. Your school might give you SAC's from previous years which are definitely good to use. I used NEAP questions before most of my exams, as well as A+ questions. I only got a copy of the ATAR Notes topic tests later in the year, but these also seemed like they would have been really good prep for SAC's. There are so many resources for SAC prep questions out there, and it's up to you whether or not you use VCAA past questions. If you are going to use the past exam questions, though, it could be a good idea to get a checkpoints book as it easily splits up the relevant questions from the past few years, but remember you will still need questions for when you are preparing for the actual exams.

Edit: also, I would leave the past exams from this current study design for exam prep as they are going to be the most accurate representation of the exam!
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on January 30, 2019, 12:46:58 pm
Hi Guys,

Need help with this question regarding interest only loans.

Question: Jackson takes out an interest-only loan of $30 000 from the bank to buy a painting, which he hopes to resell at a profit in 12 months’ time. The interest on the loan is 9.25% per annum, compounding monthly, and he makes monthly payments on the loan. How much will he need to sell the painting for in order not to lose money?

My reasoning:
Monthly payment = 9.25/(12x100) x 30000 = $231.25

Total Payment for the Year = $231.25 x 12 = $2775

Sell Painting = $2775 + $30000 = $32775

My question is shouldn't the price of selling of the painting be more because ultimately, the person would have to give back that 30000 + interest or is it because it is an interest only loan that the answer I got is correct which gives the selling price of the painting.

Also, could someone please explain to me how annuities work.

All help will be much appreciated.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on January 30, 2019, 01:21:04 pm
My question is shouldn't the price of selling of the painting be more because ultimately, the person would have to give back that 30000 + interest or is it because it is an interest only loan that the answer I got is correct which gives the selling price of the painting.
Sometimes questions are framed in a way to make sense of the situation which can lead to confusion about what they're really asking for. In this case, you are just finding the amount that needs to be paid back on the loan. Although, I'm not sure if you're answer is right because it looks like you've calculated it assuming its simple interest rather than compound interest.

Quote
Also, could someone please explain to me how annuities work.
Is there any particular part of annuities you are having trouble with or just annuities in general?
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on February 03, 2019, 08:21:47 am
Hi Guys,

Can someone please explain to me why the answer to this question is A. I understand that the answer would be A,B or C because it is compound interest due to the graph being geometric. What is the difference between compounding and credited and are they always the same time period(for eg. If it is compounding monthly, this means that it is credited monthly as well).

Also, not related to this question but can we get questions related to savings accounts and its amortisation table. Is it part of the study design? Because in the Further Maths Cambridge book, they only have ammortisation tables for reducing balance loans and annuities individually. Not both together.

The question is in one of the attachments of this post. An example of a savings account is also given in the other attachment if you are unclear what it is.

All help will be much appreciated.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on February 03, 2019, 09:19:19 am
Hi Guys,

Can someone please explain to me why the answer to this question is A. I understand that the answer would be A,B or C because it is compound interest due to the graph being geometric. What is the difference between compounding and credited and are they always the same time period(for eg. If it is compounding monthly, this means that it is credited monthly as well).
Compounding is about how often the interest is calculated. e.g. if the interest is calculated monthly you'll get interest on previous months interest - so you'll end up with more money, whereas if it's calculated annually you'll only get interest on the base amount.
Credited refers to how often it gets paid into the account - this is normally the same as the compounding period but doesn't have to be.

The graph shows that money is only added to the account once a year. This means that it must be credited annually - the only option where this occurs is A.

Also, not related to this question but can we get questions related to savings accounts and its amortisation table. Is it part of the study design? Because in the Further Maths Cambridge book, they only have ammortisation tables for reducing balance loans and annuities individually. Not both together.

The question is in one of the attachments of this post. An example of a savings account is also given in the other attachment if you are unclear what it is.

All help will be much appreciated.

Thanks
The study design says that you need to know about amortisation of a reducing balance loan or annuity and that you need to be able to interpret amortisation tables, so I'm pretty sure that question would still be in the study design (it would come under being able to interpret it).
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on February 03, 2019, 09:24:01 am
Compounding is about how often the interest is calculated. e.g. if the interest is calculated monthly you'll get interest on previous months interest - so you'll end up with more money, whereas if it's calculated annually you'll only get interest on the base amount.
Credited refers to how often it gets paid into the account - this is normally the same as the compounding period but doesn't have to be.

The graph shows that money is only added to the account once a year. This means that it must be credited annually - the only option where this occurs is A.
The study design says that you need to know about amortisation of a reducing balance loan or annuity and that you need to be able to interpret amortisation tables, so I'm pretty sure that question would still be in the study design (it would come under being able to interpret it).

Thank you PhoenixxFire. Really appreciate it.
Title: Re: VCE Further Maths Question Thread!
Post by: marangutan on February 05, 2019, 06:58:30 pm
Anyone know if I'm doing this right? Thanks
https://imgur.com/a/rlr8Aer
Title: Re: VCE Further Maths Question Thread!
Post by: f0od on February 05, 2019, 09:49:54 pm
Hi! I've just started further maths this year, and I was wondering what does 'count' mean? For example, when I plot a histogram, I am asked to say what the 'count' is. Does it mean the values along the x axis that are part of a given interval?
Thanks so much!
Title: Re: VCE Further Maths Question Thread!
Post by: ashwani1972 on February 06, 2019, 10:24:29 pm
Hi

Could you please advise good practice books for Further Maths which is chapter wise and has answers.
Similarly is there any books available for previous year solved question papers.

Thnx
Title: Re: VCE Further Maths Question Thread!
Post by: CA15 on February 06, 2019, 11:44:40 pm
https://imgur.com/a/MU3vB2W

Hi,
I am having trouble with the correct method for this question.

I know how to calculate the time difference for it, which it is 32 minutes.

However from then my method of thinking is then subtracting 32 minutes from 6:03am and therefore getting the answer A however the correct answer is E.

My question is why do I have to add 32 minutes to 6:03am to get the answer E rather than subtracting 32 minutes?
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on February 07, 2019, 04:01:33 pm
https://imgur.com/a/MU3vB2W
My question is why do I have to add 32 minutes to 6:03am to get the answer E rather than subtracting 32 minutes?
Mallacoota is east of Portland so the sun will rise in Mallacoota earlier than in Portland

Anyone know if I'm doing this right? Thanks
https://imgur.com/a/rlr8Aer
You've got the recurrence part right but for part b, you've set n=3/2 when it should be 18 as the interest is being compounded monthly, so each month interest is being received.

Hi! I've just started further maths this year, and I was wondering what does 'count' mean? For example, when I plot a histogram, I am asked to say what the 'count' is. Does it mean the values along the x axis that are part of a given interval?
Thanks so much!
I think you're right, it's just the number of items belonging to a given x
Title: Re: VCE Further Maths Question Thread!
Post by: BAH0003 on February 13, 2019, 10:10:07 pm
Hi,

I was having trouble with this question, was wondering if anyone can explain.

Question is:

A single back-to-back stem plot would be an appropriate graphical tool to investigate the association between a car's speed, in kilometres per hour, and the:

A) Driver's age, in years.
B) Car's colour (white, red, grey, other).
C) Car's fuel consumption, in kilometres per litre.
D) Average distance travelled, in kilometres.
E) Driver's sex (female, male)

Answer is E not sure how.

Thanks  :)
Title: Re: VCE Further Maths Question Thread!
Post by: sweetiepi on February 13, 2019, 10:27:41 pm
Hi,

I was having trouble with this question, was wondering if anyone can explain.

Question is:

A single back-to-back stem plot would be an appropriate graphical tool to investigate the association between a car's speed, in kilometres per hour, and the:

A) Driver's age, in years.
B) Car's colour (white, red, grey, other).
C) Car's fuel consumption, in kilometres per litre.
D) Average distance travelled, in kilometres.
E) Driver's sex (female, male)

Answer is E not sure how.

Thanks  :)
I haven't done stem plots in ages, however:
E is correct as it is the only option that has two categories (the options stated are male and female) that can be compared side to side (i.e. number of males that drive at 40km/h in comparison to females that drive at 40km/h etc).
From how I see it, the other options require multiple stem plots as there's more than two comparable categories in each answer.

Hopefully that helps a little! :)

(Disclaimer: I'm not the best at explaining this, so if someone more mathematically-minded would like to butt in, pls do <3)
Title: Re: VCE Further Maths Question Thread!
Post by: jollyboat on February 19, 2019, 10:48:53 am
Hey, does anyone know for 5 number summaries whether you use outliers for minimum or maximum values, or whether you leave them out and use the highest/lowest non-outlier value?
Title: Re: VCE Further Maths Question Thread!
Post by: Lear on February 19, 2019, 11:20:04 am
You include them afaik
Title: Re: VCE Further Maths Question Thread!
Post by: KiNSKi01 on February 19, 2019, 06:53:49 pm
Yup always include them as min/max values  ;D
Title: Re: VCE Further Maths Question Thread!
Post by: lst1103 on February 20, 2019, 07:22:06 pm
Which KK point are people up to?
Title: Re: VCE Further Maths Question Thread!
Post by: Hala119 on February 21, 2019, 07:19:43 pm
Hi!

Does anyone know where I can find practise SACs?

Thanks in advance!
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on February 21, 2019, 07:28:21 pm
Hi!

Does anyone know where I can find practise SACs?

Thanks in advance!
We can't supply a school's or company's that you'd usually pay for due to copyright reasons. You can try writing your own questions, hope someone who wrote their own questions is willing to share or try questions from Checkpoints, ATAR Notes and previous VCAA questions though!
Title: Re: VCE Further Maths Question Thread!
Post by: dream chaser on February 27, 2019, 09:03:17 pm
Hi Guys,

Need help with part (c) with this question. Not sure how to tackle it. Would really appreciate the help thanks. Also, for part (a), I got $272.06 and part (b) $24735.17. I think they are correct. Could someone notify me on that as well.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: jnylle on March 14, 2019, 10:33:56 pm
how should i comment on the distribution of a boxplot in terms of its shape, centre and spread?
should i just list them out or would i have to write a few sentences???

- thank you in advanced! :)
Title: Re: VCE Further Maths Question Thread!
Post by: lst1103 on March 16, 2019, 02:09:17 pm
When a questions asks for the spread of data, do we give the range or the IQR??
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on March 16, 2019, 05:18:11 pm
Hi Guys,

Need help with part (c) with this question. Not sure how to tackle it. Would really appreciate the help thanks. Also, for part (a), I got $272.06 and part (b) $24735.17. I think they are correct. Could someone notify me on that as well.

Thanks
Bumping for you. Been a long time since I did financial maths (and it wasn't part of Core when I did Further). I'll let someone else help you to avoid inaccuracies. :)

how should i comment on the distribution of a boxplot in terms of its shape, centre and spread?
should i just list them out or would i have to write a few sentences???

- thank you in advanced! :)
According to my bound reference, sentences.

When a questions asks for the spread of data, do we give the range or the IQR??
The three valid stats you could provide as measures of spread are IQR, range and standard deviation. From memory, IQR is most reliable of the three, because the other two can be swayed quite easily by outliers. Not entirely sure here, but in the instance it's not specified, I'd be leaning towards putting all three if asked for numbers (depends on marks though) and, if commenting, probably just discuss the IQR.

As my information might be outdated or wrong, I'm happy to be corrected (and I apologise in advance if I am wrong). I'm using my own old notes from when I did Further *cough* 5 years ago *cough*.
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on March 24, 2019, 11:09:13 am
Hey everyone, was looking at my textbook trying to catch up because I have missed a lot of school but when an activity "crashes" does that mean that the time for that activity is now shorte.

So if activity G is 15 days long and crashes by 2 days. Does that mean the time now for activity G is 13.
I know its a simple question was just a bit confused as my teacher never explained crashing and just dove into the questions.

Thanks everyone!!
Crashing is just speeding up (or reducing) the completion time of a particular activity so your understanding is correct
Title: Re: VCE Further Maths Question Thread!
Post by: Zappi on March 25, 2019, 11:55:42 am
Is it a good idea to buy the ExamPro Further Maths book? Seems like it's for the old study design  :-[
(ISBN 978-0-9875376-0-7)
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on March 25, 2019, 03:45:27 pm
Is it a good idea to buy the ExamPro Further Maths book? Seems like it's for the old study design  :-[
(ISBN 978-0-9875376-0-7)
I can't remember how much the study design changed but I'd be a bit wary of getting it. It may be useful for just doing practice questions but I wouldn't count on it as being a substitute for past VCAA exams (as I'm not sure if the format is different in the exampro book). I'd probably only get it second hand, I don't think it's worth buying new as there are probably better options out there. 
Title: Re: VCE Further Maths Question Thread!
Post by: f0od on March 28, 2019, 09:41:30 pm
Why is using deseasonalisation on a graph not as accurate as using the moving mean average? Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: dani01 on March 30, 2019, 04:15:13 pm
Look at the attachment to know what I'm talking about.
How would you make this into a network?

Would you have an edge linking e.g Mr.J to Mr.W to Mrs Martinez  and all these teachers that are in a horizontal line. OR would you jst have an edge connecting Mr Smith and Mr W and then have 4 edges from Mr Ryan linking to all the teachers in that one line.

I don;t know if any of that makes sense. But thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: Little Miss Cocopops on March 30, 2019, 06:04:21 pm
Hey fam,
Silly question, but can a time series have a linear trend?
Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: rani_b on April 02, 2019, 01:04:59 pm
Hey guys!
We were asked to calculate percentage frequencies in a table, rounding it to one decimal place, and then creating a percentage segmented bar chart. Because of rounding, the percentage became 100.1% as the total for one of the categories - so when graphing, do I go up to 100.1?

This is for tomorrow, so i would be grateful for any help :)))))) Thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: MEH0010 on April 04, 2019, 06:05:48 pm
Are we still required to do a 3/5 median line? This includes marking points and drawing a 3/5 median line.
A key example of this is VCAA 2011 Exam 2 Question 3b. ;)

Title: Re: VCE Further Maths Question Thread!
Post by: celinaaa on April 16, 2019, 04:42:28 pm
Are we still required to do a 3/5 median line? This includes marking points and drawing a 3/5 median line.
A key example of this is VCAA 2011 Exam 2 Question 3b. ;)

Heyo,
3/5 median line is no longer part of the study design, so feel free to skip those questions! :)
Keep in mind though, the 3/5 median smoothing is still relevant to the current study design.

Good luck!
Title: Re: VCE Further Maths Question Thread!
Post by: ebampton1 on April 30, 2019, 05:51:51 pm
Hi everyone,
I just had a question on Data analysis. I was just wondering what the advantage of converting a two-way table into percentages would be, and if there is specific terminology I would have to use in answering the question. 
Thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: celinaaa on May 01, 2019, 07:26:17 pm
Hi everyone,
I just had a question on Data analysis. I was just wondering what the advantage of converting a two-way table into percentages would be, and if there is specific terminology I would have to use in answering the question. 
Thank you!

The advantage is that it's more useful to compare frequencies where the amount of data differs. So, if the amount of data was larger for one category than another (e.g. 30 total opinions from high school students and 12 from uni students), using percentages makes it easier to compare the relative frequencies.
I don't believe there is any specific terminology required to answer the question.

There's a good example for this on:
https://www.khanacademy.org/math/statistics-probability/analyzing-categorical-data/two-way-tables-for-categorical-data/a/two-way-tables-review

Hope this helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: f0od on May 04, 2019, 02:39:11 pm
Hey all, I'm not sure how to do this question and was wondering if anyone would be able to help me out

Geoff has a compound interest investment that earns interest compounding monthly. The balance of Geoff's compound interest investment was $4418.80 after 6 months. The balance of Geoff's compound interest investment was $4862.80 after 2 years. The amount of money that Geoff initially invested is closest to:
A. $4000
B. $4015
C. $4280
D. $4370
E. $4715

Thank you!

Title: Re: VCE Further Maths Question Thread!
Post by: NomotivationF on May 04, 2019, 04:14:42 pm
Hey all, I'm not sure how to do these questions and was wondering if anyone would be able to help me out

1. Geoff has a compound interest investment that earns interest compounding monthly. The balance of Geoff's compound interest investment was $4418.80 after 6 months. The balance of Geoff's compound interest investment was $4862.80 after 2 years. The amount of money that Geoff initially invested is closest to:
A. $4000
B. $4015
C. $4280
D. $4370
E. $4715

2. A printer was purchased for $680. After 4 years, the printer has a value of $125. On average, 1920 pages were printed every year during those 4 years. The value of the printer was depreciated using a unit cost method of depreciation. The depreciation in the value of the printer, per page printed, is closest to:
A. 3 cents
B. 4 cents
C. 5 cents
D. 6 cents
E. 7 cents

Thank you!

Hey, I don't have my calculator on me, but to solve question one you would use your financial calculator on the CAS.

Q1. Assuming that Geoff isn't adding money to this account, first you would want to calculate the annual interest rate. To do this enter the following in the financial solver.

N - 18 (24 months - 6 months)
I - (leave blank/0)
PV - -4418.80
Pmt - 0
FV - 4862.80
ppy - 12
cpy - 12
pmt at End.

Once you've found the annual interest rate, you can enter the following in your CAS,

N - 6 (Time taken to reach the first value mentioned)
PV - (0/leave blank)
I - (Enter value previously found)
Pmt - 0
FV - 4418.80
ppy - 12
cpy - 12
pmt at End.

This should give you your answer, (my guess is that it would be somewhere around $4280)

Q2. The Unit cost depreciation rule (from what I remember) is as follows
Vn = V0 - nD
V0 being the initial price of the asset
Vn being the value of the asset after n units of use
n being amount of 'uses'
D being cost of one 'use'

In this case, you are trying to find D. V0 = $680, 1920 x 4 = n (amount of uses) and Vn = $125.

In your cas you can simply type in Menu -> algebra -> solve (125 = 680 - (1920 x 4)x,x

This should give you your answer. Hope this helps :)

Title: Re: VCE Further Maths Question Thread!
Post by: Little Miss Cocopops on May 04, 2019, 06:40:26 pm
Where can you get free practice further data sacs.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: f0od on May 05, 2019, 11:21:21 am
Hey, I don't have my calculator on me, but to solve question one you would use your financial calculator on the CAS.

Q1. Assuming that Geoff isn't adding money to this account, first you would want to calculate the annual interest rate. To do this enter the following in the financial solver.

N - 18 (24 months - 6 months)
I - (leave blank/0)
PV - -4418.80
Pmt - 0
FV - 4862.80
ppy - 12
cpy - 12
pmt at End.

Once you've found the annual interest rate, you can enter the following in your CAS,

N - 6 (Time taken to reach the first value mentioned)
PV - (0/leave blank)
I - (Enter value previously found)
Pmt - 0
FV - 4418.80
ppy - 12
cpy - 12
pmt at End.

This should give you your answer, (my guess is that it would be somewhere around $4280)

Q2. The Unit cost depreciation rule (from what I remember) is as follows
Vn = V0 - nD
V0 being the initial price of the asset
Vn being the value of the asset after n units of use
n being amount of 'uses'
D being cost of one 'use'

In this case, you are trying to find D. V0 = $680, 1920 x 4 = n (amount of uses) and Vn = $125.

In your cas you can simply type in Menu -> algebra -> solve (125 = 680 - (1920 x 4)x,x

This should give you your answer. Hope this helps :)
Thanks so much!! I should've done it like this haha I initially did trial and error bleugh

Also, congrats on your accounting & further scores! am definitely aiming for a score like that in further! :D
Title: Re: VCE Further Maths Question Thread!
Post by: NomotivationF on May 05, 2019, 11:41:14 am

Also, congrats on your accounting & further scores! am definitely aiming for a score like that in further! :D

Thanks :). I’m sure you’ll be able to score high as well, just make sure to grind those practice exams towards the end of the year
Title: Re: VCE Further Maths Question Thread!
Post by: TAN0054 on May 16, 2019, 08:56:22 pm
Hi guys
Just got a 68% on my first further sac data and analysis
pretty bummed as i had high expectations
Does that mean that i would need a 90%+ for all other sacs and exam to even consider a 40ss or is that completely out of reach now
Also what are some study techniques and methods to maximize marks on sacs? Lost quite a few marks on the open ended questions, how are ways to minimize mistakes?
Also anyone got practice sacs for recursion analysis?
Thanks guys
Title: Re: VCE Further Maths Question Thread!
Post by: f0od on May 17, 2019, 10:46:31 pm
Hey,

I was wondering about the N value for finance solver

If an investment/whatever is compounding monthly (or other units), you times the yearly value by 12 right? This is what we were taught at school & what some of the examples in the cambridge further 3/4 textbook show

however, I've encountered a few questions where the answers in the textbook were the 'year' value, not the actual 'month' value (they did not times the 'year' value by 12). I've shown them below:

(9G q7&8 )
7) Bree has $25 000 in an account that pays interest at a rate of 6.15% per annum compounding monthly.
a) If she makes monthly deposits of $120 to the account, how much will she have in the account at the end of 5 years?
b) If she makes monthly withdrawals of $120 from the account, how much will she have in the account at the end of 5 years?

8 ) Jarrod saves $500 per month in an account that pays interest at a rate of 6% per annum, compounding monthly.
a) If he makes monthly deposits of $500 to the account, how much will he have in the account at the end of 10 years?
b) Suppose that, after 10 years of making deposits, Jarrod starts withdrawing $500 each month from the account. How much will he have in the account at the end of another 10 years?

Would the answers be the textbook's wrong and be a fluke or have I been learning incorrect content? :s

Thanks!
Title: Re: VCE Further Maths Question Thread!
Post by: turtlebanana on May 18, 2019, 11:50:26 am
Hey guys!
I've been trying to figure out how to do this question for 20 mins now lol.
Calculate the number of interest-bearing periods, n, required, and hence the time in more meaningful
terms when:
Vn = $2100, Vo = $1200, r = 3% per half-year


Using the formula Vn = Vo x Rn then i get
2100 = 1200 x (1 + (3/2)/100)n
Apparently, this is wrong and i'd appreciate if anyone can tell me why.

Also, can this problem be done using the Finance Solver?
Thanks

Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on May 18, 2019, 12:02:34 pm
Hey,

I was wondering about the N value for finance solver

N is the total number of payments from the first exchange of money (ie. borrowing or investment of a principal) to the final exchange of money (ie. the transfer of the outstanding balance to whomever it is owed). Assuming that the number of compounding periods per year = number of payments per year, then N also gives the total number of compounding periods.

Quote
If an investment/whatever is compounding monthly (or other units), you times the yearly value by 12 right? This is what we were taught at school & what some of the examples in the cambridge further 3/4 textbook show

Yes, to find the balance of an asset after y years, with monthly payments, then N will be y * 12.

Quote
however, I've encountered a few questions where the answers in the textbook were the 'year' value, not the actual 'month' value (they did not times the 'year' value by 12). I've shown them below:

(9G q7&8 )
7) Bree has $25 000 in an account that pays interest at a rate of 6.15% per annum compounding monthly.
a) If she makes monthly deposits of $120 to the account, how much will she have in the account at the end of 5 years?
b) If she makes monthly withdrawals of $120 from the account, how much will she have in the account at the end of 5 years?


For 7(a) I get the same answer as the textbook. Here are my tvm solver entries:
N = 5*12
I = 6.15
PV = –25000
Pmt = –120
FV = ?
PPY/CPY = 12

For (b), make Pmt = 120 and everything else the same, and I get the same answer as the textbook.

Quote
8 ) Jarrod saves $500 per month in an account that pays interest at a rate of 6% per annum, compounding monthly.
a) If he makes monthly deposits of $500 to the account, how much will he have in the account at the end of 10 years?
b) Suppose that, after 10 years of making deposits, Jarrod starts withdrawing $500 each month from the account. How much will he have in the account at the end of another 10 years?

Again, I got the same answers as the textbook. For (a), my tvm solver entries were:
N = 10*12
I = 6
PV = 0
Pmt = –500
FV = ?
PPY/CPY = 12

For (b), my tvm solver entries were:

PV = answer from (a)
Pmt = 500

Everything else the same as (a).


Quote
Would the answers be the textbook's wrong and be a fluke or have I been learning incorrect content? :s

Thanks!

I don't think you have misunderstood the content. Perhaps you have misunderstood these particular questions, or you have used incorrect tvm entries.
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on May 18, 2019, 12:07:09 pm
Hey guys!
I've been trying to figure out how to do this question for 20 mins now lol.
Calculate the number of interest-bearing periods, n, required, and hence the time in more meaningful
terms when:
Vn = $2100, Vo = $1200, r = 3% per half-year


Using the formula Vn = Vo x Rn then i get
2100 = 1200 x (1 + (3/2)/100)n
Apparently, this is wrong and i'd appreciate if anyone can tell me why.

It's not wrong. What is your reason for thinking it is wrong?

Quote
Also, can this problem be done using the Finance Solver?

Yes:
N = ?
I = 3
PV = 1200
Pmt = 0
FV = –2100
PPY/CPY = 2

(or you can do PV = –1200, FV = 2100).
Title: Re: VCE Further Maths Question Thread!
Post by: turtlebanana on May 18, 2019, 12:17:50 pm
It's not wrong. What is your reason for thinking it is wrong?

Yes:
N = ?
I = 3
PV = 1200
Pmt = 0
FV = –2100
PPY/CPY = 2

(or you can do PV = –1200, FV = 2100).

If i do it as above, i get n = 34.31 --> 34.31 half-year interest bearing periods = 17.16 years
However, according to the solutions, it says that there are 19 periods = 9.5 years

In order to see if the the textbook gave incorrect answers by mistake, i attempted several other questions that were exactly similar to this one. But i just ended up completely different answers to the textbook solutions just like how i did above.
(MathQuest Further Maths 6th Edition: Chapter 6.5 Q13a)
Title: Re: VCE Further Maths Question Thread!
Post by: f0od on May 18, 2019, 12:29:12 pm
N is the total number of payments from the first exchange of money (ie. borrowing or investment of a principal) to the final exchange of money (ie. the transfer of the outstanding balance to whomever it is owed). Assuming that the number of compounding periods per year = number of payments per year, then N also gives the total number of compounding periods.

Yes, to find the balance of an asset after y years, with monthly payments, then N will be y * 12.

For 7(a) I get the same answer as the textbook. Here are my tvm solver entries:
N = 5*12
I = 6.15
PV = –25000
Pmt = –120
FV = ?
PPY/CPY = 12

For (b), make Pmt = 120 and everything else the same, and I get the same answer as the textbook.

Again, I got the same answers as the textbook. For (a), my tvm solver entries were:
N = 10*12
I = 6
PV = 0
Pmt = –500
FV = ?
PPY/CPY = 12

For (b), my tvm solver entries were:

PV = answer from (a)
Pmt = 500

Everything else the same as (a).


I don't think you have misunderstood the content. Perhaps you have misunderstood these particular questions, or you have used incorrect tvm entries.
Yeah I entered those values into my finance solver as well, but got 42378.59 for the first question :L (the right answer came up when i changed the N value to 5 just to see what would happen)
I'm not sure whats up with my finance solver then awks

(And for 7b, I did the exact same values with +120 as the PMT and got 25569.07 for the FV :/)
Title: Re: VCE Further Maths Question Thread!
Post by: S_R_K on May 18, 2019, 07:39:33 pm
If i do it as above, i get n = 34.31 --> 34.31 half-year interest bearing periods = 17.16 years
However, according to the solutions, it says that there are 19 periods = 9.5 years

In order to see if the the textbook gave incorrect answers by mistake, i attempted several other questions that were exactly similar to this one. But i just ended up completely different answers to the textbook solutions just like how i did above.
(MathQuest Further Maths 6th Edition: Chapter 6.5 Q13a)

I get 19 periods if I solve 2100 = 1200*(1.03)^n for n. It seems that the authors of the solutions did not adjust the annual interest rate for the number of compounding periods per year. Check these questions with your teacher, but I would suggest the solutions are wrong.

Yeah I entered those values into my finance solver as well, but got 42378.59 for the first question :L (the right answer came up when i changed the N value to 5 just to see what would happen)
I'm not sure whats up with my finance solver then awks

(And for 7b, I did the exact same values with +120 as the PMT and got 25569.07 for the FV :/)

Yes, I got 42378.59 for 7(a) and 25569.07 for 7(b), and those are the answers given in my textbook. Are you using the revised edition of the textbook? The first edition of the book for the new study design was notorious for errors...
Title: Re: VCE Further Maths Question Thread!
Post by: f0od on May 19, 2019, 11:58:24 am
Yes, I got 42378.59 for 7(a) and 25569.07 for 7(b), and those are the answers given in my textbook. Are you using the revised edition of the textbook? The first edition of the book for the new study design was notorious for errors...
Ah I'm using the pdf copy of the textbook, which must be the older edition. That sucks :(
Thank you so much for your help though, and sorry for troubling you since the answers were right in the first place! :S
Title: Re: VCE Further Maths Question Thread!
Post by: plato on May 26, 2019, 04:10:33 pm
If i do it as above, i get n = 34.31 --> 34.31 half-year interest bearing periods = 17.16 years
However, according to the solutions, it says that there are 19 periods = 9.5 years

In order to see if the the textbook gave incorrect answers by mistake, i attempted several other questions that were exactly similar to this one. But i just ended up completely different answers to the textbook solutions just like how i did above.
(MathQuest Further Maths 6th Edition: Chapter 6.5 Q13a)

What you tried was:

N = ?
I = 3
PV = 1200
Pmt = 0
FV = –2100
PPY/CPY = 2

But the 3% is given as the interest rate per half-year. That means the value of I must be 6% for the full year.
That will give the desired answer of 18.93.. = 19 periods.
Title: Re: VCE Further Maths Question Thread!
Post by: almostdonewithschooling on June 16, 2019, 10:20:25 pm
hey with these?
ive done question 11a btw.
with 11b, is the ans wrong? it says 1680
Title: Re: VCE Further Maths Question Thread!
Post by: S200 on June 16, 2019, 10:58:12 pm
The whole thing of similar triangles is just ratios.

A:a, B:b, C:c.

How have you already tried working these out?
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on June 17, 2019, 09:13:55 am
hey with these?
ive done question 11a btw.
with 11b, is the ans wrong? it says 1680
The answer is 1680. The height of the pyramid isn't the same as the height of each triangle, you can use Pythagoras' theorem to find the height of the triangles. 
Title: Re: VCE Further Maths Question Thread!
Post by: Winter3 on June 17, 2019, 04:04:35 pm
Hi guys
Just got a 68% on my first further sac data and analysis
pretty bummed as i had high expectations
Does that mean that i would need a 90%+ for all other sacs and exam to even consider a 40ss or is that completely out of reach now
Also what are some study techniques and methods to maximize marks on sacs? Lost quite a few marks on the open ended questions, how are ways to minimize mistakes?
Also anyone got practice sacs for recursion analysis?
Thanks guys

You should be alright, I did further in year 11 last year. My data analysis SAC was similar to yours (72%) and I was really down about it, but I did manage to get 93% on financial maths, 96% on geometry and then 98% for matrices. This improved my ranking to some extent and I ended up with rank 7/60~. On the exam I did really well, my teacher thought that I full marked my exam to end up with 43 raw. From my experience doing further, i'd say that SAC rankings aren't too important unless you are aiming for 47+ like I was (then it can bump your score down a lot due to the competitiveness in the high band). As long as you get a respectable SAC ranking, look over past exams, then nail the actual exam, you will almost certainly end up with a 40 raw (basically its all about the exam and dropping the least marks you possibly can on it).

In terms of wether you need 90% on your remaining SACs. The only thing that the VCAA will see from your schools SACs are the rankings, no scores. Ask your classmates about their scores and get an idea of where you fit in the rankings, so yeah just make sure that you're doing better than your classmates.

And about tips for your upcoming SACs, the good news is that open ended questions don't appear again all year. The best method of study is to just tackle some textbook chapter review questions (multi choice, short answer, but focus on extended response) and get a deep understanding of the topic, because the questions are a lot less vague than the questions on data analysis.

Wishing you the best of luck mate!
Title: Re: VCE Further Maths Question Thread!
Post by: CA15 on June 26, 2019, 01:21:15 pm
https://imgur.com/a/sUMicMO

Hi,
I am having trouble doing 7 C), I understand how to do both A and B but I don’t understand the concept or how to do C.
Title: Re: VCE Further Maths Question Thread!
Post by: pugs on August 30, 2019, 09:03:31 pm
hey! i'm not entirely sure if these questions are in the further maths course – i've checked the study design but it's a bit vague on latitudes/longitudes so i was wondering if someone would be able to help me double check  :D

if they are, would someone be able to help me out please as i'm not sure on how to do them :L (the fact that both the latitudes and longitudes are different is messing with my head :()

thanks very much!

Find the distance around the parallel of latitude for the following locations:
a) X: latitude: 32ºS, longitude 50ºE ; Y: latitude 32ºN, longitude 80ºE
b) X: latitude: 12ºS, longitude 30ºE ; Y: latitude 12ºN, longitude 80ºE

note* my textbook is possibly the one with many typos because i've found some errors previously, so if someone has an updated textbook and would be able to check (19B q19b and c), that'd be awesome! tysmm
Title: Re: VCE Further Maths Question Thread!
Post by: plato on September 16, 2019, 11:17:49 pm
You cannot find the distance around the “parallel of latitude” between any two points that are not on the same parallel of latitude.
These two questions are beyond the scope of this course which covers only distances along a parallel (ie between two locations with the same latitude) or along a meridian (ie between two locations with the same longitude).
Title: Re: VCE Further Maths Question Thread!
Post by: blyatman on September 17, 2019, 10:17:30 am
hey! i'm not entirely sure if these questions are in the further maths course – i've checked the study design but it's a bit vague on latitudes/longitudes so i was wondering if someone would be able to help me double check  :D

if they are, would someone be able to help me out please as i'm not sure on how to do them :L (the fact that both the latitudes and longitudes are different is messing with my head :()

thanks very much!

Find the distance around the parallel of latitude for the following locations:
a) X: latitude: 32ºS, longitude 50ºE ; Y: latitude 32ºN, longitude 80ºE
b) X: latitude: 12ºS, longitude 30ºE ; Y: latitude 12ºN, longitude 80ºE

note* my textbook is possibly the one with many typos because i've found some errors previously, so if someone has an updated textbook and would be able to check (19B q19b and c), that'd be awesome! tysmm
If you're interested, the distance between any 2 lat,long locations is given by the Haversine formula: https://en.wikipedia.org/wiki/Haversine_formula

I've used this quite a bit at work.
Title: Re: VCE Further Maths Question Thread!
Post by: YussifK on September 19, 2019, 06:47:38 pm
hello, beautiful people, I hope everything is going as planned.. im in year 10 stressing about VCE, many people do great and many do not as great. which scares the crap out of me. so I have a question which has not been answered.

1. what marks and ranking do i need to get a study score of 30 in english.(ive been averaging 60's and i get 5/6/7/8 ranking in my class which has approx of 20 students )

2. How can i ace sacs, have any useful tips

3. is a 60-70 atar hard to achieve with C B's and A (with a average ranking)

4. Laslty, how to score 30+ study scores (average ranking

here are my year 11 and 12 subjects

year 11: Lab skills       year 12 (any tips to ace these subjects in terms of SACS and EXAMS) and is it hard to achieve a 60-70 atar with these subjects>    Thank you in Advance
           
  HHd                           HHD
             
 Pe                              Pe
           
  Methods                    further maths
             
 English                      English
             
 Biology                      biology
Title: Re: VCE Further Maths Question Thread!
Post by: rani_b on September 22, 2019, 07:40:10 pm

Hey guys!

So this is the answer to a question from an Insight exam from Matrices:
 
23% of members choosing C will change to W = 0.23 * 51=11.73 =12 people
9% of members choosing A will change to W = 0.09 *73 =6.57 = 7 people
65% of members choosing W will continue with W = 0.65 *101 = 65.65 =66 people
66+7+12 = 85
In total, 85 members will choose the weights class in the second week.

So I did this all in one step rather than than rounding after every step (basically 0.23 * 51 + 0.09 *73 +0.65 *101) and got 83.95, which i rounded to 84.

My question is, is this wrong? Has anyone seen this type of question on a VCAA exam and seen which method to use? 
Title: Re: VCE Further Maths Question Thread!
Post by: NomotivationF on September 23, 2019, 03:43:49 pm
Hey guys!

So this is the answer to a question from an Insight exam from Matrices:
 
23% of members choosing C will change to W = 0.23 * 51=11.73 =12 people
9% of members choosing A will change to W = 0.09 *73 =6.57 = 7 people
65% of members choosing W will continue with W = 0.65 *101 = 65.65 =66 people
66+7+12 = 85
In total, 85 members will choose the weights class in the second week.

So I did this all in one step rather than than rounding after every step (basically 0.23 * 51 + 0.09 *73 +0.65 *101) and got 83.95, which i rounded to 84.

My question is, is this wrong? Has anyone seen this type of question on a VCAA exam and seen which method to use?

Hey Rani, when I was studying further** last year the general consensus was to use unrounded answers for all your working out and then round at the end. With most vcaa questions, the final rounded answer will be the same regardless whether you rounded while working or not. However, if you need to round an answer in a previous question and use the same value for a new one, use the rounded value. Basically, use unrounded unless it says so.
Title: Re: VCE Further Maths Question Thread!
Post by: rani_b on September 23, 2019, 06:37:13 pm
Hey Rani, when I was studying methods last year the general consensus was to use unrounded answers for all your working out and then round at the end. With most vcaa questions, the final rounded answer will be the same regardless whether you rounded while working or not. However, if you need to round an answer in a previous question and use the same value for a new one, use the rounded value. Basically, use unrounded unless it says so.

Okay, thanks so much!
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on September 27, 2019, 10:50:14 pm
Hey AN

If someone helps me with a question from the NHT exam 2017, I'd greatly appreciate it. I have attached the photos below. I am having trouble with question 1C)ii. The original question is also attached.

Thanks
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on September 28, 2019, 12:31:03 am
Hey AN

If someone helps me with a question from the NHT exam 2017, I'd greatly appreciate it. I have attached the photos below. I am having trouble with question 1C)ii. The original question is also attached.

Thanks
Try substituting values into into the new transformed equation and see where it leads you. Also consider what an inverse transformation on the x axis does to your original graph.

Let me know if that didn’t quite help and you need some clues. :)
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on September 28, 2019, 01:55:13 pm
Try substituting values into into the new transformed equation and see where it leads you. Also consider what an inverse transformation on the x axis does to your original graph.

Let me know if that didn’t quite help and you need some clues. :)

Sorry but I don't quite understand
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on September 28, 2019, 04:33:27 pm
Sorry but I don't quite understand
Ok, I’ll try to break this down.
1. Remember the original equation. Then have a look at the original graph. How does the question Q1c)ii. differ to the original graph? (What transformation is used?)
2. We now want the transformed equation. It’ll make it easier to visualise and graph, as, if you work it out correctly, you’ll be able to substitute values and work out what type of graph you’ll be drawing. How can we do this given we know which transformation we are applying? Can we substitute something somewhere in the original equation to achieve this? If so, substitute as you see fit.
3. What sort of equation do you now have? Graph it. (Remember to substitute the value of k you would’ve worked out for the previous part of the question when you do this!)
4. Make sure you hit at least two points with their correct coordinates to gain the mark. (Assessors usually look for that in questions like this.)

Does what I’ve done and why I’m doing it make sense now?

Note
Note: You may have realised I did a few unnecessary steps e.g. find the transformed equation. This is because this is the way that I understand the most and thus can explain the best. (Plus, getting an equation means you can double check that you’ve got the right graph almost instantly.)  There’s more than one way to reason this question out and still get the same correct graph.
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on September 28, 2019, 04:48:01 pm
Ok, I’ll try to break this down.
1. Remember the original equation. Then have a look at the original graph. How does the question Q1c)ii. differ to the original graph? (What transformation is used?)
2. We now want the transformed equation. It’ll make it easier to visualise and graph, as, if you work it out correctly, you’ll be able to substitute values and work out what type of graph you’ll be drawing. How can we do this given we know which transformation we are applying? Can we substitute something somewhere in the original equation to achieve this? If so, substitute as you see fit.
3. What sort of equation do you now have? Graph it. (Remember to substitute the value of k you would’ve worked out for the previous part of the question when you do this!)
4. Make sure you hit at least two points with their correct coordinates to gain the mark. (Assessors usually look for that in questions like this.)

Does what I’ve done and why I’m doing it make sense now?

Note
Note: You may have realised I did a few unnecessary steps e.g. find the transformed equation. This is because this is the way that I understand the most and thus can explain the best. (Plus, getting an equation means you can double check that you’ve got the right graph almost instantly.)  There’s more than one way to reason this question out and still get the same correct graph.


So for the Q1c)i) I have gotten k=60 by doing the following: 30=k/2 (chose the point 2,30 and solved for k)
However, for part ii, the equation is avg speed= 1/time hence its no longer 60/time?
Title: Re: VCE Further Maths Question Thread!
Post by: DrDusk on September 28, 2019, 04:49:23 pm
Hey AN

If someone helps me with a question from the NHT exam 2017, I'd greatly appreciate it. I have attached the photos below. I am having trouble with question 1C)ii. The original question is also attached.

Thanks

Now I don't know how the VCE curriculum works, but if your up to this kind of topic, you would've done something like graphing earlier. If you have then I'm sure you would've looked at Hyperbolas and what not. That's exactly what this equation is, it's of the form y = 1/x, except the '1' is a k which only changes steepness and not the shape.
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on September 28, 2019, 04:51:03 pm
Now I don't know how the VCE curriculum works, but if your up to this kind of topic, you would've done something like graphing earlier. If you have then I'm sure you would've looked at Hyperbolas and what not. That's exactly what this equation is, it's of the form y = 1/x, except the '1' is a k which only changes steepness and not the shape.

I agree, but the answer is a linear graph...
Title: Re: VCE Further Maths Question Thread!
Post by: DrDusk on September 28, 2019, 04:52:14 pm
I agree, but the answer is a linear graph...

Oh I didn't read the question, I thought the graph in the second image was the answer to the first.
Title: Re: VCE Further Maths Question Thread!
Post by: DrDusk on September 28, 2019, 04:58:20 pm
I agree, but the answer is a linear graph...
It should be linear because your graphing y vs 1/x. Think of it this way. A linear graph at it's most basic form has an equation y = m(x). Graphing y vs x means as x increases, y increases in a constant proportion to it. Now consider the equation y = k/x. If we graph y vs x, as x increases y decreases giving a hyperbola. Now if we graph y vs 1/x, isn't this equation the same as graphing y vs x for y = mx. Think about it, y = k/x is of the form y = k(1/x), meaning that 'm' the gradient is k and the 'x' is replaced by 1/x. You could have anything in the brackets for example y = k(e^x). In that case graphing y vs e^x will be a linear graph, as y changes by a constant proportion when comparing it to e^x.

So in the end basically in the equation y = mx, you can 'replace' x with anything, but you must graph y vs whatever that is in the brackets.
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on September 28, 2019, 05:29:14 pm
It should be linear because your graphing y vs 1/x. Think of it this way. A linear graph at it's most basic form has an equation y = m(x). Graphing y vs x means as x increases, y increases in a constant proportion to it. Now consider the equation y = k/x. If we graph y vs x, as x increases y decreases giving a hyperbola. Now if we graph y vs 1/x, isn't this equation the same as graphing y vs x for y = mx. Think about it, y = k/x is of the form y = k(1/x), meaning that 'm' the gradient is k and the 'x' is replaced by 1/x. You could have anything in the brackets for example y = k(e^x). In that case graphing y vs e^x will be a linear graph, as y changes by a constant proportion when comparing it to e^x.

So in the end basically in the equation y = mx, you can 'replace' x with anything, but you must graph y vs whatever that is in the brackets.


oh I think I understand now. So would it be y=60(1/time) right? but when I do it I get: 60(1/1) =60 but when I do time=2 I get 60(1/2)=30 which is incorrect

sorry I'm bothering you people
Title: Re: VCE Further Maths Question Thread!
Post by: DrDusk on September 28, 2019, 05:42:48 pm

oh I think I understand now. So would it be y=60(1/time) right? but when I do it I get: 60(1/1) =60 but when I do time=2 I get 60(1/2)=30 which is incorrect

sorry I'm bothering you people
The data is not incorrect. Remember in essence your graphing y vs 1/x. So your points generated by those data values that you said will be (1/1, 60),(1/2, 30). If you take time = 3, you end up with the point (1/3, 20). Now just to check it's correct we can do m = (y2-y1)/(x2-x1), which gives us:



Well look at that, the gradient is just the value of 'k' which makes sense because the equation is y = k(1/time) and were graphing y vs 1/time which is a linear graph of gradient k.

sorry I'm bothering you people
Not at all, were here to help! =)
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on September 28, 2019, 05:44:09 pm

So for the Q1c)i) I have gotten k=60 by doing the following: 30=k/2 (chose the point 2,30 and solved for k)
However, for part ii, the equation is avg speed= 1/time hence its no longer 60/time?
Yup. Transformations tend to change the graph, equation and coordinates quite drastically, so you’re on the money there.

oh I think I understand now. So would it be y=60(1/time) right? but when I do it I get: 60(1/1) =60 but when I do time=2 I get 60(1/2)=30 which is incorrect

sorry I'm bothering you people
Really close! You’re missing a divided sign somewhere...

If you’re truly stuck...
Try to substitute the transformation applied on time (see Q1c)ii.) where (time) is in the original equation (the one with k). Then simplify this.


P.S. We’re more than happy to help; you’re not bothering us at all. We’d much rather see you understand the question than leave with you still quizzical.

Note: got beaten. Leaving this here anyway.
Title: Re: VCE Further Maths Question Thread!
Post by: yourfriendlyneighbourhoodghost on September 29, 2019, 03:51:54 pm
Hi,

The only subject I am worried about is math. I have done so many practice exams and have a really detailed summary book. It's weird because I answer all the textbook questions confidently and correct, but then on most of the vcaa practices I get them wrong or I don't understand in what what's to apply my knowledge. This is only for the data and finicancial math part.

Does any one have any notes or tips on how to get better?
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on September 29, 2019, 08:45:15 pm
Hi,

The only subject I am worried about is math. I have done so many practice exams and have a really detailed summary book. It's weird because I answer all the textbook questions confidently and correct, but then on most of the vcaa practices I get them wrong or I don't understand in what what's to apply my knowledge. This is only for the data and finicancial math part.

Does any one have any notes or tips on how to get better?
What’s the reason you’re getting the VCAA questions wrong? Is it the wording, identifying what type of question it is, dumb mistakes or something else entirely? Perhaps if you could look into this, you’d know how to fix this issue.

If it’s the wording throwing you off, take your time reading the question properly to ensure you know what the question is actually asking. If it’s identification, perhaps have a look at how questions are worded in your textbooks and connect them to those that are in the VCAA exams. There should be some similarities in key words, as the textbook will be aligned to the study design/ exam. If it’s dumb mistakes, reflect on what sort of mistakes you’re making and make a log of them to avoid doing the same mistakes again.

Hopefully that helps. :)
Title: Re: VCE Further Maths Question Thread!
Post by: DrDusk on September 29, 2019, 09:13:31 pm
Hi,

The only subject I am worried about is math. I have done so many practice exams and have a really detailed summary book. It's weird because I answer all the textbook questions confidently and correct, but then on most of the vcaa practices I get them wrong or I don't understand in what what's to apply my knowledge. This is only for the data and finicancial math part.

Does any one have any notes or tips on how to get better?
That's normal. Doing just textbook questions wont help for the final exam. What you need to be doing is past papers as this is what will build your ability to problem solve. Most textbooks only have very niche questions so you can learn the content, whereas the exam questions require you to apply this knowledge in many different formats that just aren't usually in textbooks. Most of the time textbook questions are easier compared to the actual final. So far I only know of one textbook here in nsw that has questions as hard as the actual paper.

You should only need to do a few textbook ones, then go straight to doing past papers.

All the best with your studies =)
Title: Re: VCE Further Maths Question Thread!
Post by: Sherlock.Holmes on October 12, 2019, 10:53:39 pm
Hey y'all
I have finished all further maths SACs this year and am now rank 1. Yes lots of pressure.
I have started doing practice exams but im not really doing extremely well. I'm making a lot of silly mistakes and not having enough time to properly finish the exams. I think my main weakness is the financial module, i make too mistakes in that, not just silly mistakes but actually not understanding what to do. Im not sure what i should do now, i was aiming for a 45+ study score but i feel like i wont get it anymore... :/
Title: Re: VCE Further Maths Question Thread!
Post by: yourfriendlyneighbourhoodghost on October 15, 2019, 08:22:37 am
Hi,
Thank you for taking time out to help students, I love ATAR notes so so much.

Anyway, how does this work? I don't understand how they got the answer with this explanation. The question was, what is the maximum flow from source to sink? and it didnt have any cuts on the original graph

Thank you (:
Title: Re: VCE Further Maths Question Thread!
Post by: Hedlosa on October 15, 2019, 12:44:25 pm
Hi,
Thank you for taking time out to help students, I love ATAR notes so so much.

Anyway, how does this work? I don't understand how they got the answer with this explanation.

Thank you (:
sorry but are you able to state what question this is for what exam? Just so I can get some context into what the question is asking.
Title: Re: VCE Further Maths Question Thread!
Post by: yourfriendlyneighbourhoodghost on October 16, 2019, 08:06:47 am
sorry but are you able to state what question this is for what exam? Just so I can get some context into what the question is asking.
it was what is the maximum flow from the source to the sink? :)
Title: Re: VCE Further Maths Question Thread!
Post by: AISHAB on October 17, 2019, 02:14:40 pm
Hi,

How do you find the equation of a line, from a graph?

Hefferman 2011 Q8

The graph does not begin at 0
Title: Re: VCE Further Maths Question Thread!
Post by: MEH0010 on October 21, 2019, 12:30:04 pm
Hi,

How do you find the equation of a line, from a graph?

Hefferman 2011 Q8

The graph does not begin at 0

Hey,
For these type of questions, i would choose two points from the regression line, in this case (75,68) and (85,60) and then put these points on your CAS or find the equation by hand, finding the gradient, then substituting two points into the equation to find the y-intercept.
Therefore, the answer is E
Another approach is by inspection, as the horizontal axis does not start at 0.
Hope this helps :)
Title: Re: VCE Further Maths Question Thread!
Post by: AISHAB on October 22, 2019, 12:55:57 pm
Hey,
For these type of questions, i would choose two points from the regression line, in this case (75,68) and (85,60) and then put these points on your CAS or find the equation by hand, finding the gradient, then substituting two points into the equation to find the y-intercept.
Therefore, the answer is E
Another approach is by inspection, as the horizontal axis does not start at 0.
Hope this helps :)

Thanks!

What about when you are given a scatterplot with its points and an equation (2017 FURTHER EXAM 2 - QUESTION 3B)
Egg density = 191 + 31.3 x number of female moths

How do you draw the graph of this least squares regression line?
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on October 22, 2019, 07:09:05 pm
Hi,

How do you find the equation of a line, from a graph?

Hefferman 2011 Q8

The graph does not begin at 0

Hey!

If you look carefully, the point where the line crosses the y axis is not really the y intercept because the corresponding x value isn't zero. Instead it is (75, 68) and if you choose another point, i.e: (85,60), then if you find the gradient by doing (y2-y1) / (x2-x1), which would give -0.8. So at the moment our equation is Y=-0.8x+c      Now let's substitute one of our points that we had chosen before to find c --> 68= -0.8 *75 + c --> c= 128       hence our equation is Y=-0.8x + 128 --> Closest is OPTION E!

Another way to do this question faster (only works on exam 1 due to giving us the options):
substitute a pair of points that are clear into all options and see which gives the correct option
i.e: (subbing point (75, 68))
Option A) 68 = 49- 1.09 * 75 --> 68 is not equal to -32.75
Option B) 68= 68+1.09 *75 --> 68 is not equal to 49.75
Option C) 68=68-0.76*75 --> 68 is not equal to11
Option D) 68= 68+0.76 *75 --> 68 is not equal to 125
Option E) 68= 125 - 0.76 *75 --> 68 is equal to 68 (CORRECT)
Title: Re: VCE Further Maths Question Thread!
Post by: Sherlock.Holmes on October 26, 2019, 01:05:26 pm
Hey y'all
Im having trouble with this specific question from the VCAA 2016 Exam, question 3 Graphs and Relations module

I have read the examiners report (below), but i do not understand how m=n
Only 7% of the state got it fully right!!
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on October 26, 2019, 01:51:50 pm
Hey y'all
Im having trouble with this specific question from the VCAA 2017 Exam, question 3 Graphs and Relations module

I have read the examiners report (below), but i do not understand how m=n
Only 7% of the state got it fully right!!
If you rearrange \(Q=mx+ny\) in terms of \(y\) you get, \(y=\frac{-m}{n}x+\frac{Q}{n}\). \(\frac{-m}{n}\) corresponds to the gradient of the profit equation so \(\frac{-m}{n}=-1\) therefore \(m=n\)
Hopefully this helps!
Title: Re: VCE Further Maths Question Thread!
Post by: Sherlock.Holmes on October 26, 2019, 03:56:13 pm
If you rearrange \(Q=mx+ny\) in terms of \(y\) you get, \(y=\frac{-m}{n}x+\frac{Q}{n}\). \(\frac{-m}{n}\) corresponds to the gradient of the profit equation so \(\frac{-m}{n}=-1\) therefore \(m=n\)
Hopefully this helps!

Oh okay, I understand it
Thank you so much
Title: Re: VCE Further Maths Question Thread!
Post by: Sherlock.Holmes on October 27, 2019, 06:11:34 pm
Hi again.

I was having a bit of confusion with q8 Graphs and Relations module 2018 exam 1.

My two equations were 16.75=2.25+8x+10y and 30.35=2.25+20x+18y
Solving this simultaneously I got x=0.36 and y=1.16 (rounded to two decimal places)

The examiners report tho showed 8x+10y=14.20  and 20x+18y=27.80 which is the same as mine but they got rid of the $2.55
However, these two equations gave them x=0.4 and y=1.1

And the question was asking the exact cost of a ride, not the closest.
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on October 27, 2019, 08:17:12 pm
Hi again.

I was having a bit of confusion with q8 Graphs and Relations module 2018 exam 1.

My two equations were 16.75=2.25+8x+10y and 30.35=2.25+20x+18y
Solving this simultaneously I got x=0.36 and y=1.16 (rounded to two decimal places)

The examiners report tho showed 8x+10y=14.20  and 20x+18y=27.80 which is the same as mine but they got rid of the $2.55
However, these two equations gave them x=0.4 and y=1.1

And the question was asking the exact cost of a ride, not the closest.
These equations should be 16.75=2.55+8x+10y and 30.35=2.55+20x+18y
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on October 27, 2019, 08:25:49 pm
These equations should be 16.75=2.55+8x+10y and 30.35=2.55+20x+18y


equations:
1) 16.75= 8t +10d +2.55
2) 30.35= 20t + 18d +2.55
t= time d= distance
t= 0.4
d=1.1

Roys ride: 0.4* 10 + 1.1 *15= 20.5 (excluding the fixed fee of 2.55)
hence we must add 2.55
= $23.05 (option D)
Title: Re: VCE Further Maths Question Thread!
Post by: Sherlock.Holmes on October 27, 2019, 08:48:31 pm
Ah yes, Thank you!
Title: Re: VCE Further Maths Question Thread!
Post by: rani_b on October 28, 2019, 08:49:49 pm
Hey guys!

With those descriptive questions, I wanted to clarify what exactly is needed for 2 marks.

For example, 2019 NHT Core Q5biii (attached), the examiners report says the following:

A statement that clearly indicated the contention is supported with a change or difference in one
category of likelihood of attack considered and a statement similar to one of the following using
column percentages was required. Approximate percentages were acceptable.
• The percentage of animals with low likelihood of attack decreases with increased exposure to
attack during sleep – low exposure 91%, medium exposure 89%, high exposure 11%
• The percentage of animals with medium likelihood of attack changes with increased exposure
to attack during sleep – low exposure 6%, medium exposure 0%, high exposure 11%
• The percentage of animals with high likelihood of attack increases with increased exposure to
attack during sleep – low exposure 3%, medium exposure 11%, high exposure 79%

Basically, what does the first statement have to be? Because the examples they've given are in addition to another statement, but I thought the ones they provided already indicate a change/difference?
Title: Re: VCE Further Maths Question Thread!
Post by: ashmi on October 29, 2019, 09:01:02 pm
Hey guys!

With those descriptive questions, I wanted to clarify what exactly is needed for 2 marks.

For example, 2019 NHT Core Q5biii (attached), the examiners report says the following:

A statement that clearly indicated the contention is supported with a change or difference in one
category of likelihood of attack considered and a statement similar to one of the following using
column percentages was required. Approximate percentages were acceptable.
• The percentage of animals with low likelihood of attack decreases with increased exposure to
attack during sleep – low exposure 91%, medium exposure 89%, high exposure 11%
• The percentage of animals with medium likelihood of attack changes with increased exposure
to attack during sleep – low exposure 6%, medium exposure 0%, high exposure 11%
• The percentage of animals with high likelihood of attack increases with increased exposure to
attack during sleep – low exposure 3%, medium exposure 11%, high exposure 79%

Basically, what does the first statement have to be? Because the examples they've given are in addition to another statement, but I thought the ones they provided already indicate a change/difference?

For the descriptive statement, you first need to say whether you agree or disagree and show if there is a relationship. In this case saying, "Yes, there is an association between the likelihood of attack and the exposure to attack during sleep" and then saying your statistics (In this case your percentages), however, you need to make sure that your writing shows that there is a clear connection between the two variables. (Make sure you have a general statement talking about the change). You could also write as the exposure increases, the chance of attack tends to increase, just anything that represents change.

If you think about it, just saying the percentages alone doesn't really answer the question by itself, so make sure your answer actually fulfils the questions. In this case, the question was, 'is there an association?'. (You know the answer is yes and the percentages are there to back up your answer!) ;D
Title: Re: VCE Further Maths Question Thread!
Post by: KiNSKi01 on October 30, 2019, 08:21:58 pm
Hey for q8 networks exam 1 2018 is there an easy way to spot this answer - I could only get it through trial and error

Seems like there should be an easier way
Title: Re: VCE Further Maths Question Thread!
Post by: cats for the cup 2019 on October 31, 2019, 01:04:11 pm
Just wondering what would be the rough percentage required for further maths exam to get 40+?
i have done well with sacs and stuff - high A's and A+....
Title: Re: VCE Further Maths Question Thread!
Post by: MB_ on October 31, 2019, 03:16:07 pm
Just wondering what would be the rough percentage required for further maths exam to get 40+?
i have done well with sacs and stuff - high A's and A+....
90% via https://twmpublications.com/statistics
Title: Re: VCE Further Maths Question Thread!
Post by: Abdulfaiz on October 31, 2019, 09:25:22 pm
 How do I attach a question ? Photo
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on October 31, 2019, 10:15:39 pm
How do I attach a question ? Photo
Hey!
If you click reply and scroll down to just below the box there's a tab that says "attachments and other options" if you click there then you'll be able to add an image.
Alternatively, you can upload it to an image sharing site like imgur and use the BBCode link to post it here.
Title: Re: VCE Further Maths Question Thread!
Post by: jannatsd_1998 on November 01, 2019, 08:52:55 pm
are you sure it’s ok if I forgot to shade it I’m stressing out so muxh and if they don’t mark it I would be really upset
Title: Re: VCE Further Maths Question Thread!
Post by: AngelWings on November 01, 2019, 09:18:44 pm
I forgot to shade what modules I did
I’m so worried
Do you think they won’t mark it??? :'( :'(
See here for a similar thread and my answer.
Title: Re: VCE Further Maths Question Thread!
Post by: jaceyjace on November 01, 2019, 09:50:58 pm
I forgot to shade what modules I did
I’m so worried
Do you think they won’t mark it??? :'( :'(
So did i in 2017 and my school got a phone call and i just had to confirm over the phone which 2 modules i completed!!
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 01, 2019, 11:38:56 pm
are you sure it’s ok if I forgot to shade it I’m stressing out so muxh and if they don’t mark it I would be really upset
VCAA will try to contact you by phone. If they cannot get onto you, they will contact your school. You not only will have to tell them which modules you answered, but also in which order you answered them.
Title: Re: VCE Further Maths Question Thread!
Post by: jannatsd_1998 on November 02, 2019, 01:47:28 am
So you mean which one I did in the first set of modules and which one I did for the second set?
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 02, 2019, 08:32:22 am
So you mean which one I did in the first set of modules and which one I did for the second set?
You did two modules. Let's say they were matrices and Networks. They will need to know which module you answered in the first box.
Title: Re: VCE Further Maths Question Thread!
Post by: Jim_Bob on November 02, 2019, 08:37:20 am
Hey guys, I'm sort of freaking out rn...
I'm ranked highly in a strong cohort, but scored a mere 37/40... so many dumb mistakes
What score do you think I need on exam 2 to achieve a 45+?
Thanks for the help
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on November 02, 2019, 09:31:36 am
Hey guys, I'm sort of freaking out rn...
I'm ranked highly in a strong cohort, but scored a mere 37/40... so many dumb mistakes
What score do you think I need on exam 2 to achieve a 45+?
Thanks for the help
Close to 100%
Title: Re: VCE Further Maths Question Thread!
Post by: tho0058 on November 02, 2019, 10:49:17 am
Hey guys, I'm sort of freaking out rn...
I'm ranked highly in a strong cohort, but scored a mere 37/40... so many dumb mistakes
What score do you think I need on exam 2 to achieve a 45+?
Thanks for the help

Where did you find the answers to the exam?
Title: Re: VCE Further Maths Question Thread!
Post by: Samvir_Singh on November 02, 2019, 07:16:40 pm
Hey everyone, is it still possible for me to get 40+ after 34/40 on the first exam (so many dumb errors)? My SAC avg was 92% for both units and I'm pretty highly ranked.

Cheers  :)
Title: Re: VCE Further Maths Question Thread!
Post by: KiNSKi01 on November 03, 2019, 12:27:18 am
Why is the LST of D 3? -thought it was 4
Title: Re: VCE Further Maths Question Thread!
Post by: beastquest1212 on November 03, 2019, 10:15:43 am
I'm just wondering what the conventions are for answering questions in terms of units.

For example, for 1 marks questions is it fine to write 15,000 instead of $15,000; 20 instead of 20 goals or 2 instead of 2mm. Etc

Cheers
Title: Re: VCE Further Maths Question Thread!
Post by: plato on November 03, 2019, 11:44:10 am
I'm just wondering what the conventions are for answering questions in terms of units.

For example, for 1 marks questions is it fine to write 15,000 instead of $15,000; 20 instead of 20 goals or 2 instead of 2mm. Etc

Cheers
Units are generally stated in the question. Your answer does not need to include the units.
Title: Re: VCE Further Maths Question Thread!
Post by: keightleennd on November 03, 2019, 05:36:36 pm
Why is the LST of D 3? -thought it was 4

I got 4 as well. The only way I can think of it being 3 is if they went the wrong way against the dummy line when they were backwards scanning. So they have gone from activity E down the dummy line to activity D. But this shouldn't work?
Title: Re: VCE Further Maths Question Thread!
Post by: Sherlock.Holmes on November 03, 2019, 07:15:44 pm
Can someone please explain Q3 from matrices module NHT exam 2019?
Title: Re: VCE Further Maths Question Thread!
Post by: KiNSKi01 on November 03, 2019, 07:43:16 pm
I got 4 as well. The only way I can think of it being 3 is if they went the wrong way against the dummy line when they were backwards scanning. So they have gone from activity E down the dummy line to activity D. But this shouldn't work?

Yeah thats what I thought as well- just checking

Would be shitting myself if i got something like that wrong in the exam tomoz
Title: Re: VCE Further Maths Question Thread!
Post by: ashmi on November 03, 2019, 08:06:19 pm
Can someone please explain Q3 from matrices module NHT exam 2019?

I'm going to assume you are talking about Exam 2 Matrices?
For this question, it tells you that there will always be 600 Gillen residents watching C3 whereas the remaining 1400 will not be watching C3. They give you a 2 by 2 matrix with row 2, column one already filled which is 0.35 (C3 to Not C3).

The first thing you can do off the bat is find V by doing 1 - 0.35 = 0.65 because we know that in a transition matrix, all the columns must equal 1.
The next thing to do is that now you know that 0.35 (the number given) times by 600 (your original Gillen residents watching C3), you get 210 which means the amount of not watching C3 (That moved from C3).

With this, all that is left to do is 210/1400 (Original not watching C3) and you get the proportion 0.15 for w. To find x just do 1 - 0.15 = 0.85.  ;D
Title: Re: VCE Further Maths Question Thread!
Post by: Sherlock.Holmes on November 03, 2019, 08:38:03 pm
Thank you so much
Makes sense 👍🏼
Title: Re: VCE Further Maths Question Thread!
Post by: Em.C11 on December 11, 2019, 02:50:57 pm
How do I find the centre/median for a skewed histogram? A symmetric one is fine but I am unsure for a skewed, if someone could explain it to me it would be well appreciated. Thanks.
Title: Re: VCE Further Maths Question Thread!
Post by: NomotivationF on December 11, 2019, 03:06:38 pm
How do I find the centre/median for a skewed histogram? A symmetric one is fine but I am unsure for a skewed, if someone could explain it to me it would be well appreciated. Thanks.

You would do the same as you would for any normal histogram. Just count from each side until you reach the middle number
Title: Re: VCE Further Maths Question Thread!
Post by: Em.C11 on December 11, 2019, 03:16:10 pm
You would do the same as you would for any normal histogram. Just count from each side until you reach the middle number
Even if their are higher frequency values on one side compared to the other? If you count to the middle number it's not necessarily even on both sides?
Title: Re: VCE Further Maths Question Thread!
Post by: NomotivationF on December 11, 2019, 03:55:18 pm
Even if their are higher frequency values on one side compared to the other? If you count to the middle number it's not necessarily even on both sides?

Is there any chance you can upload a picture of the question? I like to think of the histogram as a dot plot when finding medians. If you look at q3 from NHT 2018 Exam two for example, you would count the frequency of each bird weight if you wanted to find the median. Since there are 143 birds, and the weight of 0-1000 has a frequency of over 100, the median would be 0-1000 if you understand what I mean?
Title: Re: VCE Further Maths Question Thread!
Post by: Em.C11 on December 11, 2019, 04:09:47 pm
Is there any chance you can upload a picture of the question? I like to think of the histogram as a dot plot when finding medians. If you look at q3 from NHT 2018 Exam two for example, you would count the frequency of each bird weight if you wanted to find the median. Since there are 143 birds, and the weight of 0-1000 has a frequency of over 100, the median would be 0-1000 if you understand what I mean?
This is a question from the further textbook, it is asking to find the "approximate location of the centre"
Title: Re: VCE Further Maths Question Thread!
Post by: Sine on December 11, 2019, 04:57:31 pm
This is a question from the further textbook, it is asking to find the "approximate location of the centre"
I think you should manually count the total number of whatever is on this histogram and then go from either the left or right-hand side of the graph to find the certain point that there is 50% of the data above and 50% of the data below that point. This will find the median.
Title: Re: VCE Further Maths Question Thread!
Post by: Bri MT on December 11, 2019, 05:06:56 pm
This is a question from the further textbook, it is asking to find the "approximate location of the centre"

We can read this and see that the frequencies are:
13,15,12,11,8,6,5,4,4,2,1 (I'm doing this visually but for an assessment I'd use a ruler)
1+2+4+4+5+6+8+11 = 41   (summing from right to left)
13+15+12= 40                    (summing from left to right)

Thus the median value will be contained in the column with a frequency of 11 (the fourth column from the left)
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on December 11, 2019, 07:39:55 pm
This is a question from the further textbook, it is asking to find the "approximate location of the centre"

I remember having trouble with that earlier this year. In that specific question, the textbook is seemingly asking for an approximate median, hence I'd just see the "middle-ish" value as the median. However, for an exact median calculation, I'd do choose the (n+1)/2th value as the median (remember to add the frequencies in ascending order) :)
Title: Re: VCE Further Maths Question Thread!
Post by: Ionic Doc on December 13, 2019, 12:10:15 pm
Hey, everyone, I've been searching google but I can't seem to find anything

Could someone explain to me what this means

50 –< 55 seconds

thanks
Title: Re: VCE Further Maths Question Thread!
Post by: MEH0010 on December 13, 2019, 12:29:29 pm
Hey, everyone, I've been searching google but I can't seem to find anything

Could someone explain to me what this means

50 –< 55 seconds

thanks

Hello,
This means 50 seconds to less than 55 seconds
This includes 50 seconds but not 55 seconds
For example, 53 is a number between 50 –< 55 seconds.
Hope this helps
Title: Re: VCE Further Maths Question Thread!
Post by: morlin01 on December 29, 2019, 06:28:10 pm
For financial math-

Can someone distinguish for me when a question asks you to find the value of an investment or the interest earned "in" 2 years or "after" 2 years?

One question is that what is the total interest earned with an investment at $6000 with a simple interest rate of 3.5%p.a
a. in the first four years
b. after four years

Thank you - I hope this makes sense
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on December 29, 2019, 06:34:05 pm
For financial math-

Can someone distinguish for me when a question asks you to find the value of an investment or the interest earned "in" 2 years or "after" 2 years?

One question is that what is the total interest earned with an investment at $6000 with a simple interest rate of 3.5%p.a
a. in the first four years
b. after four years

Thank you - I hope this makes sense


From memory, I assumed the word "first" as the end of the 3rd year, and saw the word "after" as the end of the 4th year
Title: Re: VCE Further Maths Question Thread!
Post by: morlin01 on December 29, 2019, 06:47:16 pm
Is it correct to say that:
V0 = first year
V1 = second year
V2 = third year
V3 = fourth year
V4 = fifth year
V5 = sixth year
thankyou
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on December 29, 2019, 06:54:11 pm
Is it correct to say that:
V0 = first year
V1 = second year
V2 = third year
V3 = fourth year
V4 = fifth year
V5 = sixth year
thankyou

Yes that would be correct if and only the question mentions V0=start of the loan/investment. Sometimes questions consider the start of the loan/investment as V1.
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on December 29, 2019, 07:44:41 pm
Not at all haha :)

Part C) since it's simple interest, we use the following formula:    Interest (I) = [(Principle (P) * Rate (R) * Time (T)] / 100
Hence, (4000 * 5 * 6) /100 = 120000

Part D) it's asking for the value of her investment after 7 years, so you add the interest on top of the amount she initially invested.

 Interest earned in 7 years + initial investment ($4000)= 140000 + 4000= 144000 --> value of investment in 7 years.

Title: Re: VCE Further Maths Question Thread!
Post by: zoharreznik on January 10, 2020, 06:30:17 pm
Anyone who did Methods 3/4 in yr 11 and chose Further/Spesh 3/4 in yr 12 reply with how you found it- interested to know what experiences people had with it
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on January 10, 2020, 08:40:13 pm
Anyone who did Methods 3/4 in yr 11 and chose Further/Spesh 3/4 in yr 12 reply with how you found it- interested to know what experiences people had with it



I did something somewhat similar. I did further in year 11 and doing methods 3/4 in year 12 as well as spesh 3/4(without 1/2). I hated further, it was too boring as we begun revision within a few months due to its considerably easy to understand and short syllabus. However, despite methods being a 1/2 subject, I enjoyed it far more as it required me to think deeply. I am having the same thoughts about spesh (begun the content over the holidays); it's so mind-blowing when you understand a concept, making it interesting. In addition, spesh scales up crazily, so some motivation there. If anything, further will add on more stress imo since slipping up a few marks in the exam can cost you your study score, and on top of that, it will go down due to scaling :)
Title: Re: VCE Further Maths Question Thread!
Post by: David... on February 12, 2020, 05:40:57 pm
What is a hurdle
Title: Re: VCE Further Maths Question Thread!
Post by: PhoenixxFire on February 12, 2020, 06:11:03 pm
What is a hurdle
Is this in reference to a test of some sort? If so it normally means that you're required to pass it to pass the subject.
Title: Re: VCE Further Maths Question Thread!
Post by: ATAR_SLAYER on February 16, 2020, 12:59:53 pm
Hey everyone, just wanting to double check the answers to the following questions:

1) Fiona borrowed $740 000 to purchase a property at 5.2% p.a.. The loan is to be repaid in monthly repayments over the course of 30 years.

a) Calculate the monthly repayment value

b) Evaluate the value of the interest Fiona would pay over the course of the mortgage.

Thanks in advance!
Title: Re: VCE Further Maths Question Thread!
Post by: TheEagle on February 16, 2020, 01:09:49 pm
Hey everyone, just wanting to double check the answers to the following questions:

1) Fiona borrowed $740 000 to purchase a property at 5.2% p.a.. The loan is to be repaid in monthly repayments over the course of 30 years.

a) Calculate the monthly repayment value

b) Evaluate the value of the interest Fiona would pay over the course of the mortgage.

Thanks in advance!

a) 4063.42 (~2 d.p)

b) 722831.39 (~2 d.p)
Title: Re: VCE Further Maths Question Thread!
Post by: ATAR_SLAYER on February 16, 2020, 01:13:04 pm
a) 4063.42 (~2 d.p)

b) 722831.39 (~2 d.p)

Thank you! I got the same answers but wasn't entirely certain as to whether Finance Solver could be used (since it is never explicitly mentioned that it is compounding).
Title: Re: VCE Further Maths Question Thread!
Post by: ashmi on February 16, 2020, 01:38:23 pm
Thank you! I got the same answers but wasn't entirely certain as to whether Finance Solver could be used (since it is never explicitly mentioned that it is compounding).

You can use Finance solver since it's asking for "monthly repayments" which in this case would mean it is compounding! ;D (Compounding monthly really). Whenever you see repayments, just think Finance Solver as it makes the process so much easier. It would take quite a long time if you didn't use FS.

The stuff you would put in would be:
N = 360
I = 5.2
PV = 740,000
Pmt = (-4063.42) Answer.
FV = 0
Ppy/Cpy = 12

Hope that helps!

Edit: Do not use FS if it strictly says it's simple interest!
Title: Re: VCE Further Maths Question Thread!
Post by: ATAR_SLAYER on February 16, 2020, 01:46:24 pm
You can use Finance solver since it's asking for "monthly repayments" which in this case would mean it is compounding! ;D (Compounding monthly really). Whenever you see repayments, just think Finance Solver as it makes the process so much easier. It would take quite a long time if you didn't use FS.

The stuff you would put in would be:
N = 360
I = 5.2
PV = 740,000
Pmt = (-4063.42) Answer.
FV = 0
Ppy/Cpy = 12

Hope that helps!

That helped a lot! Thank you!

Also, just another question. How would you go about solving the following:

1) Robert wants to borrow $50 000. He is offered two options by two different financial institutions
- Option 1 = 7.32% p.a. simple interest
- Option 2 = 7.32% p.a. compounded fortnightly
Both options have a 10 years loan term
Calculate the monthly repayment under both options.
Title: Re: VCE Further Maths Question Thread!
Post by: ashmi on February 16, 2020, 02:42:35 pm
That helped a lot! Thank you!

Also, just another question. How would you go about solving the following:

1) Robert wants to borrow $50 000. He is offered two options by two different financial institutions
- Option 1 = 7.32% p.a. simple interest
- Option 2 = 7.32% p.a. compounded fortnightly
Both options have a 10 years loan term
Calculate the monthly repayment under both options.

So for Option 2, we can use Finance Solver:
N = 120 (12 monthly payments over the course of 10 years?)
I = 7.32
PV = 50,000 (Positive because Robert is borrowing)
Pmt = (-589.13) Answer
FV = 0
Ppy =12 (Because you want monthly repayments only)
Cpy = 26 (Fortnightly compounding periods)

(Note: Btw, I've never seen an exam question where the Ppy and Cpy is different. My answer above might be wrong so if someone wants to double-check please do!)

For Option 1 I would just do your simple interest formula, find how much over the course of the total 10 years and then separate them into monthly payments.
(I've never seen FS actually work for simple interest even with different repayment periods. You usually can only use FS when it's compounding (you can choose to use the compounding formulas or FS but not simple interest/FS)).
Title: Re: VCE General & Further Maths Question Thread!
Post by: David... on March 05, 2020, 06:31:45 am
does a hurdle effect the study score?
Title: Re: VCE General & Further Maths Question Thread!
Post by: colline on March 05, 2020, 12:47:37 pm
does a hurdle effect the study score?
Is this regarding a SAC your school has? I wasn't aware of schools making SACs with hurdle requirements. But if yes, then it would depend on your school's policy so best to ask them.
Title: Re: VCE General & Further Maths Question Thread!
Post by: David... on March 11, 2020, 06:59:20 pm
I am unsure on how to answer this question

Luisa and Jay have a farm. The weight (kg) of their sheep is approximately normally distributed with a mean of 73 kg and a standard deviation of 14 kg.

Luisa and Jay have 120 sheep. The expected number of sheep that weigh at least 59 kg is closest to:

A.  19
B.  41
C.  100
D.  101   

I know that it is asking for 84% of 120 which is 100.8 sheep. But do I round up or down?

My teacher said to keep the value of 100.

But the textbook would say to round.
Title: Re: VCE General & Further Maths Question Thread!
Post by: TheEagle on March 11, 2020, 09:10:10 pm
Follow the textbook when doing the questions, but for your sac, do as you teacher says. In the exam, you wouldn't need to round, they're usually whole numbers
Title: Re: VCE General & Further Maths Question Thread!
Post by: J_Rho on April 21, 2020, 12:57:27 pm
When you make a prediction from time-series data is it best to use the smoothed data or the original data? why why not??
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on April 21, 2020, 02:49:00 pm
When you make a prediction from time-series data is it best to use the smoothed data or the original data? why why not??

Smoothed data is best, provided that there is a consistent trend (ie always increasing, or always decreasing). Smoothing removes the effects of outliers / random noise.
Title: Re: VCE General & Further Maths Question Thread!
Post by: LachlanBarr8 on April 29, 2020, 08:16:34 pm
Hi Guys,

How would you comment on the blue (original data) and black (3 median smoothing) lines. I'm particularly not sure about the trends as they're borderline, also could you include random fluctuations in the comment?

Id say the blue is seasonal with a slighting increasing trend and the black reveals that there is no seasonality and with the trend perhaps being slightly increasing (or relatively constant not too sure!).

Much appreciated
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on April 29, 2020, 08:46:49 pm
Id say the blue is seasonal with a slighting increasing trend and the black reveals that there is no seasonality and with the trend perhaps being slightly increasing (or relatively constant not too sure!).

I would definitely agree with you. However, I would also say that the blue has some irregular fluctuations (almost all data has) and the blue is slightly increasing!
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on April 30, 2020, 03:10:05 pm
Hello!
I was wondering if someone could explain 5d to me? I got $993.41 but the answer was $319.41. Thanks!
Title: Re: VCE General & Further Maths Question Thread!
Post by: TheEagle on April 30, 2020, 03:16:09 pm
Hello!
I was wondering if someone could explain 5d to me? I got $993.41 but the answer was $319.41. Thanks!


In part d, they're asking for the depreciation IN the third year, meaning by how much did it reduce by in the third year (not throughout the three years)
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on April 30, 2020, 03:42:06 pm
In part d, they're asking for the depreciation IN the third year, meaning by how much did it reduce by in the third year (not throughout the three years)

Thankyou that makes so much sense!
Title: Re: VCE General & Further Maths Question Thread!
Post by: LachlanBarr8 on May 01, 2020, 06:43:29 pm
Hey Guys,

What type of distribution do you think the attached boxplot is?

Much appreciated
Title: Re: VCE General & Further Maths Question Thread!
Post by: TheEagle on May 01, 2020, 08:18:23 pm
Hey Guys,

What type of distribution do you think the attached boxplot is?

Much appreciated

Positively skewed. You should keep a diagram of each in your bound reference. Google 'Boxplot distributions' for diagrams
Title: Re: VCE General & Further Maths Question Thread!
Post by: LachlanBarr8 on May 01, 2020, 08:43:44 pm
Positively skewed. You should keep a diagram of each in your bound reference. Google 'Boxplot distributions' for diagrams

You wouldnt think it could be approximately symmetric?
Title: Re: VCE General & Further Maths Question Thread!
Post by: TheEagle on May 01, 2020, 09:46:19 pm
You wouldnt think it could be approximately symmetric?

From the zoom of the picture, it seems positive but idk
Title: Re: VCE General & Further Maths Question Thread!
Post by: hey1324mariya on May 05, 2020, 06:55:39 pm
Hi, I was wondering what the best software is to type up your bound reference. Need help please!!!!!
Title: Re: VCE General & Further Maths Question Thread!
Post by: ashmi on May 05, 2020, 07:24:35 pm
Hi, I was wondering what the best software is to type up your bound reference. Need help please!!!!!

Word was my saviour for Further last year 8).
Further is quite a wordy maths subject and I found that using Word with multiple tables seems to work well for me as it made it super easy to find something if I were to panic. You can insert equations into word or write using LaTeX too if that's your type of thing. (I currently have my Methods Bound reference on Word too and it's super handy as maths equations are easy to write into it. Plus you can convert it to a PDF when you are done for printing)

Some pictures of my old B.R are in the spoiler below if you want any ideas of how to go about constructing your own:
Spoiler
(https://i.imgur.com/8Rn8HTy.jpg)
(https://i.imgur.com/pAONNmA.jpg)
Hope that helps! :D
Title: Re: VCE General & Further Maths Question Thread!
Post by: J_Rho on May 05, 2020, 07:42:07 pm
Word was my saviour for Further last year 8).
Further is quite a wordy maths subject and I found that using Word with multiple tables seems to work well for me as it made it super easy to find something if I were to panic. You can insert equations into word or write using LaTeX too if that's your type of thing. (I currently have my Methods Bound reference on Word too and it's super handy as maths equations are easy to write into it. Plus you can convert it to a PDF when you are done for printing)

Some pictures of my old B.R are in the spoiler below if you want any ideas of how to go about constructing your own:
Spoiler
(https://i.imgur.com/8Rn8HTy.jpg)
(https://i.imgur.com/pAONNmA.jpg)
Hope that helps! :D
Your BR looks amazing!! Would you mind sharing it with us if you still have it on your computer??
Title: Re: VCE General & Further Maths Question Thread!
Post by: ashmi on May 05, 2020, 07:45:15 pm
Your BR looks amazing!! Would you mind sharing it with us if you still have it on your computer??

Hey hey J_Rho! ;D

If you go to this link here, look at the very bottom of the first post and there is a digital copy!
☆Further Maths | Guide☆
*Do note: The BR is based on the matrices and geometry modules ;D*
Hope that helps!
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on May 18, 2020, 07:28:13 pm
Hello all!

I was wondering if there was any particular way to find out the amount of the last payment (like in part dii of the attached question)?
Is there some way on the finance solver or do you have to use recursion rules or any other ways?

Thanks!
Eloise
Title: Re: VCE General & Further Maths Question Thread!
Post by: s110820 on May 18, 2020, 08:27:52 pm
Hi, eloisegrace,

I do QCE General Maths so I'm pretty sure our syllabi are extremely similar in terms of its content. However, as I have never done a recurrence relation in finding the "last payment" before, I'm going to give you my best advice: work backwards and trial and error. For example, if you have already constructed a recurrence relation for the question, I would recommend that you use your recurrence relation and substitute the multiplication/addition sign in the equation for either a division or subtraction sign. Trial and error using both methods and note what works and what doesn't work. Then, I would recommend marking your answer with the answers provided in the textbook. If your answer does not match the textbook answer, then I would recommend either referring to the worked examples in each chapter (most textbooks provide worked examples) or ask your teacher for help! They're here to help you every step along the way so please don't hesitate to ask them any questions that you may have.

Hopefully, this helps :)

Have a great week and kind regards,

Darcy Dillon.
Title: Re: VCE General & Further Maths Question Thread!
Post by: makram on May 20, 2020, 02:09:56 pm
Hey,

Does anyone know how the exam this year will look like considering we only need to complete one module? As in, will the time to complete the exam be reduced, or will there be more questions per module?

Thanks :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on May 20, 2020, 03:43:06 pm
Does anyone know how the exam this year will look like considering we only need to complete one module? As in, will the time to complete the exam be reduced, or will there be more questions per module?

I'm not sure if anyone knows exactly yet (not even VCAA hahaha) but due to the SAC weighting I am assuming that the exam will be 50% data analysis, 25% recursion and financial modelling, and 25% the chosen module. Maybe instead of the 16/8/8/8 split in past VCAA exams for exam 1, it will be 20/10/10? And exam 2 will most likely be similarly designed? Again I don't know but this is just a guess. I would try and not worry about the things that you can't control (exam style, time) and try and focus on the things you CAN control (practice questions, consistent revision, a bound reference that suits you).
 :) :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: morlin01 on September 10, 2020, 08:50:18 pm
does anyone know whether further examiners would accept this as a 'show that' answer?

thanks XD
Title: Re: VCE General & Further Maths Question Thread!
Post by: keltingmeith on September 10, 2020, 09:22:00 pm
does anyone know whether further examiners would accept this as a 'show that' answer?

thanks XD

It's only a 1 mark question, so that should be fine. If you REALLY want to cover your arse, you could list the equation in terms of pronumerals beforehand (V_n = V_(n-1) - D ==> V_n = V_(n-8) - 8D), but what you've written should be fine (and if my talking about equations just confused you, feel free to ignore it).
Title: Re: VCE General & Further Maths Question Thread!
Post by: Em.C11 on September 15, 2020, 11:07:11 am
How would I solve this if I'm not given the initial state matrix?

Title: Re: VCE General & Further Maths Question Thread!
Post by: keltingmeith on September 15, 2020, 11:58:57 am
How would I solve this if I'm not given the initial state matrix?



Good question! Do you know what happens if you raise a transition matrix to a stupidly high power (and in this case, even just to the power of 10 is enough, though you should typically do 50 for good measure)?
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on September 15, 2020, 01:45:29 pm
Hello all!

I was wondering if there was any particular way to find out the amount of the last payment (like in part dii of the attached question)?
Is there some way on the finance solver or do you have to use recursion rules or any other ways?

Thanks!
Eloise

I realise you asked this question a long time ago, but I thought I'd respond because I think the previous answer is not a recommended method, and it might be useful for exam revision. The best way to find the final payment of a reducing balance loan is the following.

1. Use finance solver to find the number of payments to reach future value = 0. It's likely that this will not exactly be a whole number, so round up to the next whole number to get a whole number of payments. Call this number N.
2. Find the future value after N number of payments, call this FV. This will not be zero, because you are slightly overpaying the debt by rounding up the exact number of payments required to the whole number.
3. The final payment is the regular payment amount – that future value.

Example.

Find the final payment amount for a reducing balance loan of $500000 at 5% interest p.a., compounding monthly, with monthly payments of $3200.

Step 1: The number of payments required to reach a future value of 0 is 253.1.... Round this up to 254.
Step 2: The future value after 254 payments is 2563.109.... This means 254 payments of $3200 will overpay the debt by $2563.11.
Step 3: Final payment is $3200 – 2563.11 = 636.89.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Em.C11 on September 16, 2020, 10:06:47 am
Good question! Do you know what happens if you raise a transition matrix to a stupidly high power (and in this case, even just to the power of 10 is enough, though you should typically do 50 for good measure)?
Yes, but to do that don't you need multiply T^n times So? How do I find the So values when it's only given for the rose?
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on September 16, 2020, 11:23:03 am
Yes, but to do that don't you need multiply T^n times So? How do I find the So values when it's only given for the rose?

You don't need to know the initial state matrix.

Suppose that \(T^{\infty} \times S_0\) is the steady state matrix. Then, for each row of \(T^{\infty}\), every column will have the same element. For row \(i\), call this number \(k_i\). Then, the number of members choosing champagne in the long term, will be \(k_1 \times \textrm{Total Number of Members}\) and similarly for the number of members choosing pinot gris, choosing rose, and choosing shiraz.

So given that you know the number of members choosing rose in the long term, you can work backwards to finding the total number of members (which is 1780, for your reference), and from there find the number of members choosing champagne in the long term.
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on September 17, 2020, 01:21:40 pm
does anyone know whether further examiners would accept this as a 'show that' answer?

No. That would not be acceptable. You would have to show the transposed calculation as (38000-16000)/8. This is explained in several past examiners reports.
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on September 22, 2020, 11:45:30 am
Hello everyone!

I was completing the 2015 Further Exam 1 and I got a bit stumped on Networks Question 8, l found some worked solutions (not from VCAA as they were not on the examiners report) and saw that they were using something called a dominance matrix. I have not learnt this for the networks module and by a quick look of the study design, it is not in the Networks section either. Is this part of the 2020 study design I have missed or was it only part of the old study design (2006-2015)?

Thank you!
Title: Re: VCE General & Further Maths Question Thread!
Post by: keltingmeith on September 22, 2020, 12:26:39 pm
Hello everyone!

I was completing the 2015 Further Exam 1 and I got a bit stumped on Networks Question 8, l found some worked solutions (not from VCAA as they were not on the examiners report) and saw that they were using something called a dominance matrix. I have not learnt this for the networks module and by a quick look of the study design, it is not in the Networks section either. Is this part of the 2020 study design I have missed or was it only part of the old study design (2006-2015)?

Thank you!

Yeah, so - I'm gonna be honest, I help out on these threads because I know the maths to do most of what's taught in Further (emphasis on most - I have a statistics degree and still have no clue how to teach core, what a joke lmao) and notice that not much help seems to float here otherwise, but I never followed VCAA myself. So, I had to do some research for this - and couldn't find the 2015 study design for comparison. I found the one for up to 2012, and to memory the 2012 maths study design was extended to 2015, so I think we can trust it.

According to the 2012 study design, dominance matrices WERE indeed included in networks. Based on the current study design, they're only in the matrices module, so it seems to me that you can safely ignore that question.
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on September 22, 2020, 02:11:27 pm
Matrix representations of networks and their application IS part of the current study design. So you could be asked something about a "dominance matrix", since that could be understood as an application of a matrix representation of a directed network.

What you are NOT required to know as part of the networks module is that if A is the one-step adjacency matrix (ie. where each entry gives the number of edges between the respective vertices), then A^n is the n-step adjacency matrix (where each entry gives the number of paths of n edges between the respective vertices).

Title: Re: VCE General & Further Maths Question Thread!
Post by: keltingmeith on September 22, 2020, 02:41:09 pm
Matrix representations of networks and their application IS part of the current study design. So you could be asked something about a "dominance matrix", since that could be understood as an application of a matrix representation of a directed network.

What you are NOT required to know as part of the networks module is that if A is the one-step adjacency matrix (ie. where each entry gives the number of edges between the respective vertices), then A^n is the n-step adjacency matrix (where each entry gives the number of paths of n edges between the respective vertices).



Out of curiosity, have we seen dominance matrices asked about before in the current study design? Seems odd they'd mention it explicitly in the old design, but not this one, if they were still going to ask about them
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on September 22, 2020, 03:36:13 pm
Out of curiosity, have we seen dominance matrices asked about before in the current study design? Seems odd they'd mention it explicitly in the old design, but not this one, if they were still going to ask about them

Not that I recall. My advice would be that, even if it's unlikely to be asked, it still appears to be within the scope of the course.
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on September 25, 2020, 07:38:33 pm
Not that I recall. My advice would be that, even if it's unlikely to be asked, it still appears to be within the scope of the course.
VCAA moved dominance matrices into the Matrices module starting 2016. Therefore no longer relevant in the Networks module.
Title: Re: VCE General & Further Maths Question Thread!
Post by: David... on September 30, 2020, 10:14:16 am
Hello,

I am slightly confused with rounding. My teacher said that the rounding depends on the context of the situation; saying you would always round down in certain contexts. For example, let's say that you got an answer of 277.8 cars and the question did not specify rounding, my teacher would have rounded down to 277 cars.
 
However, according to the trial exams I am doing, they would have rounded normally - (in this case, rounding up 278 cars).

Can someone please tell me how VCAA expects our answers to be rounded?

And is rounding to the "nearest" whole number/car/month (etc.) the same as rounding to the "correct" whole number/car/month (etc.)?

It would be greatly appreciated if anyone could answer my questions with VCAA examples, feel free to ignore these questions.

Thank you
Title: Re: VCE General & Further Maths Question Thread!
Post by: colline on September 30, 2020, 10:49:14 am
Hello,

I am slightly confused with rounding. My teacher said that the rounding depends on the context of the situation; saying you would always round down in certain contexts. For example, let's say that you got an answer of 277.8 cars and the question did not specify rounding, my teacher would have rounded down to 277 cars.
 
However, according to the trial exams I am doing, they would have rounded normally - (in this case, rounding up 278 cars).

Can someone please tell me how VCAA expects our answers to be rounded?

And is rounding to the "nearest" whole number/car/month (etc.) the same as rounding to the "correct" whole number/car/month (etc.)?

It would be greatly appreciated if anyone could answer my questions with VCAA examples, feel free to ignore these questions.

Thank you

Depends on the context of the question.

Say if the original question was something along the lines of, how many cars can I buy with X amount of money, and you get 277.8, you'd round down because even if the answer is closer to 278, you don't technically have enough to buy that amount.

Just round according to what makes logical sense.
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on October 13, 2020, 03:27:17 pm
Hello,

I am slightly confused with rounding. My teacher said that the rounding depends on the context of the situation; saying you would always round down in certain contexts. For example, let's say that you got an answer of 277.8 cars and the question did not specify rounding, my teacher would have rounded down to 277 cars.
 
However, according to the trial exams I am doing, they would have rounded normally - (in this case, rounding up 278 cars).

Can someone please tell me how VCAA expects our answers to be rounded?

And is rounding to the "nearest" whole number/car/month (etc.) the same as rounding to the "correct" whole number/car/month (etc.)?

It would be greatly appreciated if anyone could answer my questions with VCAA examples, feel free to ignore these questions.

Thank you
As has been pointed out, it does depend on the context of the question, but also on the wording.
I will use your answer of 277.8 cars
If the question had asked for the "maximum number of cars", then you would round DOWN to 277, because 278 is more than the decimal number calculated.
If the question had asked for the "minimum number of cars", then you would round UP to 278, because 277 is less than the decimal number calculated.
Incidentally, if the question had asked for the average, or mean, number of cars, and there was no rounding instruction, you would leave the answer as 277.8 because a mean value can be a decimal. 
Your other question was about the wording of the rounding instruction. Recent exam questions generally have such rounding instruction as a separate sentence. For example, "Round your answer to the nearest whole number."; in which case you would round a number such as 12.501 to 13
If instructed to "Round your answer to the nearest hundred cars.", you would then round a number such as 277.8 to 300
Title: Re: VCE General & Further Maths Question Thread!
Post by: czzn3 on October 31, 2020, 04:44:49 pm
When we're asked to draw a reg line, do we alw start from 0 or where the first data on x value is given?
Do ALL time series plot have irregular fluctuations?
When the data provides both year and numbers, which do we use for IV? (eg 1 for 2000, 2 for 2001)

Thanks in advance!


Title: Re: VCE General & Further Maths Question Thread!
Post by: jasonn_ly on October 31, 2020, 06:55:31 pm
Hi guys,

For further i am ranked 3-5, with the top end being extremely strong and was wondering would a 50 study score be possible if i were to get full marks or lose 1 mark in total across both exams? Or if i achieve such on the exam will my score still be dependent on hoping that those ranked higher than me full mark or get close to full marking the exam?

Thanks in advance

Definitely can get 50, just aim for 100% and you can't go wrong either way
Title: Re: VCE General & Further Maths Question Thread!
Post by: jasonn_ly on October 31, 2020, 07:00:19 pm
When we're asked to draw a reg line, do we alw start from 0 or where the first data on x value is given?
Do ALL time series plot have irregular fluctuations?
When the data provides both year and numbers, which do we use for IV? (eg 1 for 2000, 2 for 2001)

Thanks in advance!
- When sketching the regression line onto a graph, assuming its a scatterplot, identify where the y intercept is (it's not always at x=0!) and sub that x value into the equation to find the y intercept.
- You can tell if a time series plots has irregular fluctuations if values are not consistent, if the values for each season are dead consistent for every season that passes then it would be seasonal and have no irregular fluctuations, but usually thats not the case and irregular fluctuations are present.
- Usually they will specificy what the IV variable is, that being the 1 or 2000, keep in mind usually they provide the 1,2,3 etc there purposefully so you don't have to make an equation out of 2000, 2001 etc.
Title: Re: VCE General & Further Maths Question Thread!
Post by: LachlanBarr8 on November 11, 2020, 03:03:00 pm
Hey guys,

Could someone tell me what the LST for activity D is? I believe its 6, but the answers and my friend (rank 1) say its 12. I can understand why it would be 12; however, wouldn't it affect the overall completion time?

Much appreciated
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on November 11, 2020, 03:19:17 pm
Hey guys,

Could someone tell me what the LST for activity D is? I believe its 6, but the answers and my friend (rank 1) say its 12. I can understand why it would be 12; however, wouldn't it affect the overall completion time?

Much appreciated
The answer is 12.

For this network, the critical path is C-F-I-J with a length of 28. The path that activity D is on (A-D-G-J) has a length of 19. If you backwards scan from Activity J, you can see that the latest time to complete activity G is after 18 units. Therefore the latest time to complete activity D is after 12 units.

Additionally, the difference between the lengths of the 2 paths is 9 therefore the 3 non-critical paths on this network have a float time of 9. 3+9=12

Hope this helps :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: MaryK on November 14, 2020, 09:34:43 am
Has anyone posted the actual 2020 VCAA Further Maths Exam 1?
Title: Re: VCE General & Further Maths Question Thread!
Post by: thatdumbstudent on November 15, 2020, 03:52:11 pm
hi guys, this question is from the 2019 nht exam 2 and I can't seem to figure out how to find h? If anyone could explain to me how to get the answer that'd be much appreciated! (I've looked at the examiner's report but don't get it :-\)

d is 10m btw
Title: Re: VCE General & Further Maths Question Thread!
Post by: Cha0132 on November 18, 2020, 02:17:29 am
Hi Stick, i got a sac average of 98% in a strong cohort/high ranked, I think I dropped 2 marks on exam 1 and 3 marks on exam 2, can I still get 45+ in Further maths 2020
Title: Re: VCE General & Further Maths Question Thread!
Post by: cmati on November 22, 2020, 09:16:08 pm
Hi Stick, i got a sac average of 98% in a strong cohort/high ranked, I think I dropped 2 marks on exam 1 and 3 marks on exam 2, can I still get 45+ in Further maths 2020

Hey there Cha0132,
Congratulations on your amazing results!! I think you are in a great place to get a 45 study score or higher, do you know your exact ranking and how many students are in the cohort?
Title: Re: VCE General & Further Maths Question Thread!
Post by: AlannahBottino on November 29, 2020, 07:27:18 am
Hi, this year I accelerated in 3/4 methods and just completed the subject. I have picked up further as my fifth subject. How difficult will it be to pick up 3/4 further without having done units 1 and 2?

Thanks!  ;D
Title: Re: VCE General & Further Maths Question Thread!
Post by: fish58 on November 29, 2020, 09:58:16 am
Hello 😀

I am a Mathematics teacher and actually teach 11 General Maths and the year 12 equivalent which is Further Mathematics. Year 11 General is actually easier than standard year 10 Mathematics and you will have no difficulty at all doing Further Mathematics without having completed General Mathematics.

I hope your Methods examinations went well and you get the score you hope for 👍👍
Title: Re: VCE General & Further Maths Question Thread!
Post by: waterangel82 on November 29, 2020, 11:16:16 am
Hello 😀

I am a Mathematics teacher and actually teach 11 General Maths and the year 12 equivalent which is Further Mathematics. Year 11 General is actually easier than standard year 10 Mathematics and you will have no difficulty at all doing Further Mathematics without having completed General Mathematics.

I hope your Methods examinations went well and you get the score you hope for 👍👍

I definitely wouldn't say Year 11 General Maths is easier than Year 10 Standard maths, because you do learn new content in General Maths like Networks (if your school chooses to), and the difficulty of the assessments that your school sets. I personally found Year 11 General Maths (back when I did it) much more challenging than Further Maths simply because of the sheer amount of content we had to learn (our school decided to teach us every topic) and the assessments that were set by my school were very difficult (no one got above 84% in the Year 11 General maths final exam, and this was a select entry cohort).

Hi, this year I accelerated in 3/4 methods and just completed the subject. I have picked up further as my fifth subject. How difficult will it be to pick up 3/4 further without having done units 1 and 2?

Thanks!  ;D

It is definitely possible to pick up Further Maths without doing 1/2 General Maths, but there is some content in General Maths that is basically repeated in Further Maths, so there would be some students (who did General Maths) who would be relatively comfortable with the content already when they enter Further Maths. So I'd highly recommend you to study the Further Maths content over the break to familiarise yourself.
Title: Re: VCE General & Further Maths Question Thread!
Post by: AlannahBottino on November 30, 2020, 08:01:40 am
Thank you everyone for your advice :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: homeworkisapotato on January 09, 2021, 06:32:51 pm
Hi! I was wondering what exactly I need to know in this study design dot point:
population and sample, random numbers and their use to draw simple random samples from a population or
randomly allocate subjects to groups, the difference between population parameters (e.g., µ and σ), sample
statistics (e.g., mean and standard deviation of sample)

Do I need to know how to calculate the standard deviation of a population? I don't really understand what to know and how that is applied into math questions
Also, do you recommend any external resources to buy for additional practice questions?
Thank you so much in advance!
Title: Re: VCE General & Further Maths Question Thread!
Post by: eloisegrace on January 09, 2021, 09:24:08 pm
Hi! I was wondering what exactly I need to know in this study design dot point:
population and sample, random numbers and their use to draw simple random samples from a population or
randomly allocate subjects to groups, the difference between population parameters (e.g., µ and σ), sample
statistics (e.g., mean and standard deviation of sample)

Do I need to know how to calculate the standard deviation of a population? I don't really understand what to know and how that is applied into math questions
Also, do you recommend any external resources to buy for additional practice questions?
Thank you so much in advance!
Hi homeworkisapotato!

For this study design dot point, all I really knew how to do was collect a random sample (done on CAS, I only used it in my SAC tho), the difference between population parameters (sample is always used in further) and to calculate the mean and standard deviation you will always use your CAS!

Hope this helps :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on January 13, 2021, 10:04:23 pm
Some schools ask for the extended calculation process for standard deviation in their SAC, but you only use CAS for it in the exams. Forget about population parameters for this subject. It only uses sample means and sample standard deviations. The exams have never asked for the use of random numbers to select a sample.
Title: Re: VCE General & Further Maths Question Thread!
Post by: amanaazim on January 21, 2021, 10:59:25 am
hey guys so basically im struggling in the question where its like how to find the median from the histogram like its not always that the middle of the histogram is the median and im having a hard time to figure it out  by looking at the graph.

also for box plots how do i know how much of the data is there eg: if they give a boxplot of a sample of 48 children earning pocket money . how do i know in percentage how many children earned like more than $20 because there is no numbers on the boxplot to indicate that.

Title: Re: VCE General & Further Maths Question Thread!
Post by: Jinju-san on February 03, 2021, 06:23:21 pm
hey guys so basically im struggling in the question where its like how to find the median from the histogram like its not always that the middle of the histogram is the median and im having a hard time to figure it out  by looking at the graph.

also for box plots how do i know how much of the data is there eg: if they give a boxplot of a sample of 48 children earning pocket money . how do i know in percentage how many children earned like more than $20 because there is no numbers on the boxplot to indicate that.

Hi amanaazim!

So for the question where you are trying to determine the median of a histogram, you normally add up all of the frequencies for each bar to find the total number of data values. You then need to calculate which value would be the median value. For instance, if you have 100 data values, your median would be the average of the 50th and 51st values (add them and divide by 2). If you had 99 values, add 1 to this number (now 100) and divide by 2 (so your median is the 50th value). From here, you would look at the histogram and find the interval that contains the median (’n'th) value.

For the second question, I think the number of data values your boxplot would be showing is 48 (since you’ve mentioned that the sample number of children was 48). There should be a scale below the boxplot that allows you to determine where the median, 1st quartile and 3rd quartile are. If you can identify the value of the 3rd quartile (eg: $30), than you can conclude that 25% of the 48 children (12 children) would earn 30 or more dollars in pocket money…

Do you have a photo of the questions by any chance?
Title: confused
Post by: bigye on February 14, 2021, 02:40:15 pm
does anyone have any advice on how to answer questions confidently? like i know the content and most of the formulas but when it comes to getting a question with a scenario and coming up with ways to get an answer, i just cant. also i need help with this question. the answer is B but idk why.
Title: Re: VCE General & Further Maths Question Thread!
Post by: fish58 on February 16, 2021, 03:20:11 pm
Hi
It can’t be D or E because the amount paid off the loan at the beginning of the loan must be zero
It can’t be A because that graph indicates a flat rate of the original loan payment or the same dollar amount per year
B and C are the opposite of each other. It must be B because the amount paid off the principal actually increases from one year to the next which is indicated by the increasing vertical distance from one year to the next in each of the five years

Hopefully that helps 👍
Title: Re: VCE General & Further Maths Question Thread!
Post by: fish58 on February 16, 2021, 03:56:41 pm
Hi again,

With a reducing balance loan which is also a principal and interest loan there are two components which are the amount of interest you have to pay and the amount you are actually reducing the loan by. The interest rate remains the same in most questions. The interest amount is based on the total amount owing. As you make payments and the balance of the loan reduces, the interest component of your payment reduces and the amount that you are reducing the loan by increases.

Title: Re: VCE General & Further Maths Question Thread!
Post by: somethingeevee on March 14, 2021, 09:15:25 pm
are postcodes considered to be nominal or ordinal data?
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on April 08, 2021, 10:47:54 am

Ordinal, they all have a specific order such as 3000,3001,3002 and so on.

No. Postcodes are nominal, not ordinal. The area with postcode 3025 may be nowhere near postcode 3024 and certainly does not rank higher or lower than postcode 3024. The postcode is short method of naming a region. For example 3047 is an abbreviated way of describing Broadmeadows, and maybe some surrounding area.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on June 06, 2021, 10:05:21 pm
how do you work this out that this is 82%
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on June 06, 2021, 11:41:01 pm
What have you tried? I'm not overly sure what knowledge you have or the tools you have available to solve this question, so can you please provide more context?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on June 08, 2021, 09:37:20 pm
i did parts a and b which was just the probability that a healthy person will have a CBF reading below 94.4 which was the result given in the excel command and the probability that a person will have a CBF reading above 94.4 which was just 1- the result.
i just don't get part c why its 91%-9%
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on June 08, 2021, 10:09:22 pm
Note that for a density function such as this, \(P(x_1 \leq X \leq x_2) = P(X \leq x_2) - P(X \leq x_1)\). You've already calculated \(P(X \leq 94.4)\). Since this is normally distributed, you can conclude that \(P(X \leq 53.6) = P(X \geq 94.4) = 1 - P(X \leq 94.4)\) (how? - that's a question for you to ponder; this will definitely improve your understanding). We then apply the property I mentioned in my first sentence which yields the result given.

If you're still stuck let us know :) 
Title: Re: VCE General & Further Maths Question Thread!
Post by: ErnieTheBirdi on June 09, 2021, 12:04:23 pm
Someone please let me know, I recently royally screwed up my financial SAC ( I don't even know if I'll pass tbh). I scored a 91 % on the first DATA SAC. So my question is, if I do mess up my financial SAC but get 90+ on all the upcoming network and matrices SAC and then do relatively well in the exam. Does that still mean I am able to reach 45+ or at least in the mid 40 range for further? Or is that it for my goals and dreams in further?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Stormbreaker-X on June 09, 2021, 01:11:44 pm
Someone please let me know, I recently royally screwed up my financial SAC ( I don't even know if I'll pass tbh). I scored a 91 % on the first DATA SAC. So my question is, if I do mess up my financial SAC but get 90+ on all the upcoming network and matrices SAC and then do relatively well in the exam. Does that still mean I am able to reach 45+ or at least in the mid 40 range for further? Or is that it for my goals and dreams in further?
You can still score very highly as long as you ace your future SACs and the exam, which I know you will since you seem so committed. All the best :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on August 15, 2021, 09:23:40 pm
What’s the difference between bias and confounding in statistics
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on August 16, 2021, 09:58:54 am
What’s the difference between bias and confounding in statistics

Confounding is not really a statistical concept, but a causal one. In the context of experimental design, confounding variables are those which affect both the DV and IV, and hence "confound" any perceived association between the DV and IV.

When people talk about "bias" they could mean a few different things. Statisticians use it in a very precise way: bias is the difference between the expected value of an estimate of a population parameter (eg. sample mean or variance) and the true value of that population parameter (the population mean or variance). But more generally, people might talk about bias, in relation to data / statistics, by talking about features / flaws in the experimental design which tilted the conclusions in one direction.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on August 18, 2021, 08:38:28 pm
How do you do this question

A 95% confidence interval for the population mean based on a sample 109 observations is 48.26 to 52.39. Which of the following is most likely the 99% confidence interval?
A 48. 60 to 52.05
B 52.39 to 56.85
C 47.59 to 53.06

How do you work this out it’s 47.59 to 53.06
Title: Re: VCE General & Further Maths Question Thread!
Post by: Billuminati on August 18, 2021, 09:24:15 pm
How do you do this question

A 95% confidence interval for the population mean based on a sample 109 observations is 48.26 to 52.39. Which of the following is most likely the 99% confidence interval?
A 48. 60 to 52.05
B 52.39 to 56.85
C 47.59 to 53.06

How do you work this out it’s 47.59 to 53.06

50.325 is the mean, given that the degrees of freedom is quite high (108 as n= 109), you can assume a normal distribution.

52.39 - 50.325= 2.065 which represents 1.96 standard deviations (since this is the 95% CI).

Hence 1 standard deviation= 1.05357...

From the normal distribution, 99% CI is 2.58 standard deviations above or below the mean.

Hence upper fence of 99% CI= 50.325 + (2.58 x 1.05357...)= 53.04

And lower fence of 99% CI= 50.325 - (2.58 x 1.05357...)= 47.61

Which is the closest to option C. Note that I used the stats table provided in my uni physical + analytical chem unit so there's some minor rounding differences depending on which version of the table you use.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on August 19, 2021, 11:18:53 am
Thanks

If x is from a normal distribution with mean 5 and standard deviation 2 find
 p( -2.3< x < 8.5) to 4 decimal places . Use r commander to answer this question.

How would you do this question . The answer is 0.9598
Title: Re: VCE General & Further Maths Question Thread!
Post by: Billuminati on August 19, 2021, 12:47:28 pm
Thanks

If x is from a normal distribution with mean 5 and standard deviation 2 find
 p( -2.3< x < 8.5) to 4 decimal places . Use r commander to answer this question.

How would you do this question . The answer is 0.9598

You know the normal distribution has this formula:
https://www.thoughtco.com/thmb/8teul80x5qdrwyFNdvv_ATs_mJY=/1250x0/filters:no_upscale():max_bytes(150000):strip_icc()/bellformula-56b749555f9b5829f8380dc8.jpg

Plug in your values for standard deviation and mean, then use a definite integral with terminals of 8.5 on top and -2.3 on bottom to find the area under the normal distribution function
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on August 31, 2021, 12:04:23 pm
You know the normal distribution has this formula:
https://www.thoughtco.com/thmb/8teul80x5qdrwyFNdvv_ATs_mJY=/1250x0/filters:no_upscale():max_bytes(150000):strip_icc()/bellformula-56b749555f9b5829f8380dc8.jpg

Plug in your values for standard deviation and mean, then use a definite integral with terminals of 8.5 on top and -2.3 on bottom to find the area under the normal distribution function
**** This discussion about Confidence intervals and formula for a normal curve does not belong in this thread !
The only statistics, re Normal distributions ,that Further/General Mathematics students should be cocerned about are the difference between population and sample stats, the sample mean (denoted by x-bar), sample standard deviation (denoted by s),  the standardised score calculation  (denoted by z) and the 68%-95%-99.5% rule.
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on September 20, 2021, 01:59:47 pm
Hi, is time considered a discrete or continuous variable?
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on September 22, 2021, 03:22:16 pm
Can someone help me with what a "three-median line" is and how this is different to median smoothing? There was a question about 3-median line in the vcaa 2011 exam but I'm not sure if it's still relevant to the current study design. Thanks
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on September 22, 2021, 04:45:46 pm
Hi, is time considered a discrete or continuous variable?

It depends upon how the data is recorded. If the values are recorded with infinitesimal precision (ie. with infinitely long decimals like 1.4142135...) then it is a continuous variable. If the values are recorded in discrete chunks (ie. to the nearest hour or to the nearest day), then it is a discrete variable. On VCAA exams, the way in which the data is recorded is included in the question.

Can someone help me with what a "three-median line" is and how this is different to median smoothing? There was a question about 3-median line in the vcaa 2011 exam but I'm not sure if it's still relevant to the current study design. Thanks

It's a linear regression method (ie. trying to achieve a similar sort of thing to the least-squares regression method that you'll be more familiar with) using the median of three equal chunks of data. It is not a technique used to smooth each data point. It is no longer part of the study design.
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on September 22, 2021, 07:31:44 pm
Thank you!!!! :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on September 24, 2021, 11:18:50 pm
Hi, is time considered a discrete or continuous variable?
Continuous, as is evident in the sweeping second hand on an analog clock.
Title: Re: VCE General & Further Maths Question Thread!
Post by: plato on September 24, 2021, 11:20:50 pm
Can someone help me with what a "three-median line" is and how this is different to median smoothing? There was a question about 3-median line in the vcaa 2011 exam but I'm not sure if it's still relevant to the current study design. Thanks
The three median line is not in the current study design that commenced in 2016. You can ignore it. It is not the same as tmedian smoothing.
Title: Re: VCE General & Further Maths Question Thread!
Post by: simsgrove on October 02, 2021, 11:16:42 am
Looking for sols or answers for Further Maths NHT 2021   Anyone?
Title: Re: VCE General & Further Maths Question Thread!
Post by: simsgrove on October 02, 2021, 11:17:19 am
Looking for sols or answers for Further Maths NHT 2021   Anyone?
Title: Re: VCE General & Further Maths Question Thread!
Post by: somethingeevee on October 02, 2021, 01:15:29 pm
Looking for sols or answers for Further Maths NHT 2021   Anyone?

Found some solutions on youtube for exam 1 (check the description box to see any changes/updates):
Core solutions: https://www.youtube.com/watch?v=N0o7657hWNo&ab_channel=MaffsGuru
Module solutions: https://www.youtube.com/watch?v=bhpyXmx-4RM&ab_channel=MaffsGuru
Title: Re: VCE General & Further Maths Question Thread!
Post by: ThatKid690 on October 02, 2021, 02:19:48 pm
Looking for sols or answers for Further Maths NHT 2021   Anyone?

I did the exam, so I can help you with any questions if you want
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 09, 2021, 10:09:33 pm
how do you do this question   
It is claimed that 3 times as many students pass a unit than fail. If 200 student outcomes are observed, what is the expected number of passes if the claim is correct.
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on October 10, 2021, 12:39:27 pm
If the claim is correct, then for every four students, three pass.

Then, since we have 200 students, we would have three-quarters passing. How many is that?

Might also help to point out exactly what part you're stuck on in future.
Title: Re: VCE General & Further Maths Question Thread!
Post by: M-D on October 11, 2021, 07:14:07 am
Hi all,
I need some assistance with Further Math VCAA 2007 Exam 1 Module 3: Graphs and relations Question 9.
I have used the gradient formula to calculate the value of k=2. The correct answers is k=1. How is that possible?
Thanks
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on October 11, 2021, 11:37:14 am
If the function is \(Z = 2x +2y\), then the maximum value occurs everywhere on the boundary \(x + y \leq 100, x \in [50, 100]\). You are told that \(Z\) takes a maximum only at \((100, 0)\).

Hope this helps
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 13, 2021, 05:42:38 pm
Hello,

My question relates to some of the earlier questions asked.

This relate to graph and relation. How does the sliding method work. I have asked my teacher but still it does not make sense.

Thank you 
Title: Re: VCE General & Further Maths Question Thread!
Post by: Tjsdn on October 13, 2021, 09:04:51 pm
Our school only though us cores and modules 1(matrices) and 2(network).
However, I found module 3(geometry and measurement) easier than module 2(network).
Am I allow to complete modules 1 and 3 instead of module 2?
I asked my school teacher and they say that I should stick with the modules that I learned because it will stuff everyone's score. I don't get why that will stuff everyone's score.
Can somebody tell me the reasons and why I should stick with modules I learned at school? (I'm 100% sure I will do better if I do module 3 because I always get 100% on the practice exam if I pick modules 1 and 3.)
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 16, 2021, 02:01:12 pm
Our school only though us cores and modules 1(matrices) and 2(network).
However, I found module 3(geometry and measurement) easier than module 2(network).
Am I allow to complete modules 1 and 3 instead of module 2?
I asked my school teacher and they say that I should stick with the modules that I learned because it will stuff everyone's score. I don't get why that will stuff everyone's score.
Can somebody tell me the reasons and why I should stick with modules I learned at school? (I'm 100% sure I will do better if I do module 3 because I always get 100% on the practice exam if I pick modules 1 and 3.)

Hey! I don't think choosing another module will impact others' scores (that's not how it works). The reason people recommend sticking with the modules you learned at school is because generally that's what students feel most confident in (obviously because you know the content and have been formerly assessed on those areas already in your sacs). But if you feel more confident in module 3 than module 2 then I would say go for it - you want to maximise the marks you'll get on the exam. Hope this helps!
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 16, 2021, 02:05:57 pm
Can someone tell me why distance is a continuous variable? In 2016 vcaa sample exam 1 (question 4), the distance was recorded to the nearest tenth (?) of a kilometre e.g. 4.2, 0.8, 3.9 however this did not count as a discrete variable and I don't understand why? I thought that the type of variable depends on HOW it's recorded and not the nature of the variable itself. Any help would be appreciated, thanks
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 16, 2021, 02:10:06 pm
Looking for sols or answers for Further Maths NHT 2021   Anyone?

Hey, not sure if you're already aware of this but they recently uploaded the examiner's reports
https://www.vcaa.vic.edu.au/assessment/vce-assessment/past-examinations/NHT-past-exams/Pages/NHT-past-exams.aspx
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 16, 2021, 02:41:54 pm
also can someone help me with this question? the answer is D but (5, 3) lies on the line y = 8 - x. If the max occurs at this point wouldn't all the other integer points on this line also be a solution?
Title: Re: VCE General & Further Maths Question Thread!
Post by: lm21074 on October 16, 2021, 03:02:51 pm
The solution is the last point on the boundary of the feasible region (given by the points in the first sentence below the graph) to touch the sliding line or where you substitute the points into the formula and get the largest value of Z.

working through the options- using corner point principle here for efficiency
A. (1,5) - using corner point principle - Z = 17
B. (3,4) - Z = 18
C. (4,4) - Z = 20
D. (5, 3) - Z = 19
E. (6, 2) - Z = 18

However, (4,4) lies outside the feasible region. Moving to the second highest point, (5, 3) lies on the feasible region, therefore the answer is D.

Edit: didn't see this question

Can someone tell me why distance is a continuous variable? In 2016 vcaa sample exam 1 (question 4), the distance was recorded to the nearest tenth (?) of a kilometre e.g. 4.2, 0.8, 3.9 however this did not count as a discrete variable and I don't understand why? I thought that the type of variable depends on HOW it's recorded and not the nature of the variable itself. Any help would be appreciated, thanks
Discrete = can be counted (e.g. number of steps walked)
Continuous = can be measured

With the unit of kilometers, it can be measured (as a bit of a silly example, you can get a really long ruler and measure the distance).

Hope this helps.
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 17, 2021, 12:48:37 pm
Hi what study score am i likely to get with these scores
93/100 sac prob around rank 5-10
40/40 exam 1
58/60 exam 2
Title: Re: VCE General & Further Maths Question Thread!
Post by: VCEStudent2034 on October 17, 2021, 12:58:50 pm
Hi what study score am i likely to get with these scores
93/100 sac prob around rank 5-10
40/40 exam 1
58/60 exam 2
Hi tannicholas!

Just wondering, what were your SAC averages for Unit 3 and 4 separately?
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 17, 2021, 01:50:15 pm
Edit: didn't see this question
Discrete = can be counted (e.g. number of steps walked)
Continuous = can be measured

With the unit of kilometers, it can be measured (as a bit of a silly example, you can get a really long ruler and measure the distance).

Hope this helps.

Thanks! But what about height to the nearest cm? or weight to the nearest kg? you're technically still "measuring" these values but it's discrete...(a bit silly that I'm struggling with this haha but I wanna make sure I understand it properly)
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 17, 2021, 02:08:28 pm
Thanks! But what about height to the nearest cm? or weight to the nearest kg? you're technically still "measuring" these values but it's discrete...(a bit silly that I'm struggling with this haha but I wanna make sure I understand it properly)

Hi,

I can be wrong but it does not matter if it says "nearest Kg" or "nearest cm" it would still be continuous. As the person earlier said Discrete is counting. In this case you are measuring someone weight thus it has to still be continuous does not matter if it is full number or in decimal.
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 17, 2021, 02:41:52 pm
Hi,

I can be wrong but it does not matter if it says "nearest Kg" or "nearest cm" it would still be continuous. As the person earlier said Discrete is counting. In this case you are measuring someone weight thus it has to still be continuous does not matter if it is full number or in decimal.

Yeah ig that makes sense aHH but my teachers said it'd be discrete ://
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 17, 2021, 02:53:07 pm
Hi tannicholas!

Just wondering, what were your SAC averages for Unit 3 and 4 separately?
It was 93 for both units.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 17, 2021, 03:24:40 pm
Yeah ig that makes sense aHH but my teachers said it'd be discrete ://

Hi,

I do not think it would be discrete, you should ask your teacher why they feel it would be discrete.  As discrete is counting. I do not think we count weight or height. Just ask them the reason for it. Or ask other people in your class about it.
Title: Re: VCE General & Further Maths Question Thread!
Post by: S_R_K on October 17, 2021, 04:23:26 pm
Hi,

I can be wrong but it does not matter if it says "nearest Kg" or "nearest cm" it would still be continuous. As the person earlier said Discrete is counting. In this case you are measuring someone weight thus it has to still be continuous does not matter if it is full number or in decimal.

As I posted above earlier, classifications of data is relative to how the data is recorded. Statements like "weight and height are always continuous because you measure it" are misleading. The same quantity / variable can be any of the four types, depending on how it is measured / or how the data is recorded. I suppose the only thing that could be said is that weight / height / distance are continuous if no information about how they are recorded is given, then perhaps it might be implied that they are being recorded in the most precise way possible.

For instance, take distance.
(1) If measured in cm with infinite precision - ie, if conceivably you could record a value of 3.1415926... - then it is continuous.
(2) If measured in cm but rounded to the nearest whole number - ie. only numbers like 2, 6, 11, 13 etc are recorded in your data - then it is discrete.
(3) If recorded as "really short", "short", "long", "really long" then it is categorical ordinal.
(4) Silly example, but if recorded as "exhausting" "fun" "satisfying", then it is categorical nominal.

VCAA exam questions will always specify how the data is recorded.

A good example of this is 2017 Exam 1, Question 7, where students had to classify the variable number of moths, which is being recorded as "less than 250", "250-500", or "more than 500". 36% of students incorrectly classified this as numerical when in fact it is ordinal (the possible data values "less than 250", "250-500", or "more than 500" are not numerical values, they are categories with an implied ranking).
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 17, 2021, 04:36:55 pm
Yeah ig that makes sense aHH but my teachers said it'd be discrete ://
I've had a similar question about petrol prices
The question went like this, "is petrol prices discrete or continuous?"

I knew that petrol prices were rounded to 2 d.p because the previous bit of that question said so.  The petrol price is rounded to a terminating decimal and therefore discrete is the correct.

Continuous also doesn't exclusively mean can be measured. It just means that the value of something can change continuously as the word suggests and that the decimal doesn't terminate. 
Title: Re: VCE General & Further Maths Question Thread!
Post by: VCEStudent2034 on October 17, 2021, 04:40:01 pm
Hi what study score am i likely to get with these scores
93/100 sac prob around rank 5-10
40/40 exam 1
58/60 exam 2
Amazing scores! You’re looking at around a 48 raw (and scaled), but, as I always say, it really depends on your rank and overall strength of the cohort. All the best for the exams!
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 17, 2021, 04:42:35 pm
As I posted above earlier, classifications of data is relative to how the data is recorded. Statements like "weight and height are always continuous because you measure it" are misleading. The same quantity / variable can be any of the four types, depending on how it is measured / or how the data is recorded. I suppose the only thing that could be said is that weight / height / distance are continuous if no information about how they are recorded is given, then perhaps it might be implied that they are being recorded in the most precise way possible.

For instance, take distance.
(1) If measured in cm with infinite precision - ie, if conceivably you could record a value of 3.1415926... - then it is continuous.
(2) If measured in cm but rounded to the nearest whole number - ie. only numbers like 2, 6, 11, 13 etc are recorded in your data - then it is discrete.
(3) If recorded as "really short", "short", "long", "really long" then it is categorical ordinal.
(4) Silly example, but if recorded as "exhausting" "fun" "satisfying", then it is categorical nominal.

VCAA exam questions will always specify how the data is recorded.

A good example of this is 2017 Exam 1, Question 7, where students had to classify the variable number of moths, which is being recorded as "less than 250", "250-500", or "more than 500". 36% of students incorrectly classified this as numerical when in fact it is ordinal (the possible data values "less than 250", "250-500", or "more than 500" are not numerical values, they are categories with an implied ranking).

Yeah I agree. It is also related to the question. As true in some cases age could be "age 4 and before, 4 to 8 and 8 or above". Yeah. I mean when it is for sure numerical one.  Like how if it says height or weight.
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 17, 2021, 09:36:56 pm
I've had a similar question about petrol prices
The question went like this, "is petrol prices discrete or continuous?"

I knew that petrol prices were rounded to 2 d.p because the previous bit of that question said so.  The petrol price is rounded to a terminating decimal and therefore discrete is the correct.

Continuous also doesn't exclusively mean can be measured. It just means that the value of something can change continuously as the word suggests and that the decimal doesn't terminate.

Yes, hence my confusion. My question in the first place was about distance that was recorded to ONE decimal place e.g. 4.9km, 0.8km, 3.5km etc. (i.e. the distances weren't recorded with "infinite precision" [which is said to be continuous] nor to the nearest km [which would be discrete]). But, from what I've read in this thread, this would make it a DISCRETE variable, regardless of whether the distance was rounded to the nearest tenth of a kilometre OR if it was EXACTLY 4.9km, 0.8km and so forth (whether it was exact or rounded was not specified in the premise). However, in the solutions this was classified as a CONTINUOUS variable instead ... is there something fundamental that I'm missing or??? Are the answers wrong lmao
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 17, 2021, 10:12:53 pm
Yes, hence my confusion. My question in the first place was about distance that was recorded to ONE decimal place e.g. 4.9km, 0.8km, 3.5km etc. (i.e. the distances weren't recorded with "infinite precision" [which is said to be continuous] nor to the nearest km [which would be discrete]). But, from what I've read in this thread, this would make it a DISCRETE variable, regardless of whether the distance was rounded to the nearest tenth of a kilometre OR if it was EXACTLY 4.9km, 0.8km and so forth (whether it was exact or rounded was not specified in the premise). However, in the solutions this was classified as a CONTINUOUS variable instead ... is there something fundamental that I'm missing or??? Are the answers wrong lmao

It would be continuous. Because the distance is something which can be measured whereas discrete is something which you count. Doing the whole decimal thing is just to make it easier. In this case it is for sure not discrete as you are able to measure the distance. You cant count the distance hence it would be continuous.
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 17, 2021, 10:50:49 pm
Yes, hence my confusion. My question in the first place was about distance that was recorded to ONE decimal place e.g. 4.9km, 0.8km, 3.5km etc. (i.e. the distances weren't recorded with "infinite precision" [which is said to be continuous] nor to the nearest km [which would be discrete]). But, from what I've read in this thread, this would make it a DISCRETE variable, regardless of whether the distance was rounded to the nearest tenth of a kilometre OR if it was EXACTLY 4.9km, 0.8km and so forth (whether it was exact or rounded was not specified in the premise). However, in the solutions this was classified as a CONTINUOUS variable instead ... is there something fundamental that I'm missing or??? Are the answers wrong lmao

Could you please send or give the details of the question? Usually there's subtle differences in question wording which change a lot about what they're looking for.
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 17, 2021, 11:02:58 pm
Could you please send or give the details of the question? Usually there's subtle differences in question wording which change a lot about what they're looking for.

Yeah sure - also thank you to everyone for the help, I really appreciate it!!!!!!!!!!!! :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 17, 2021, 11:20:14 pm
The answer would be B 1. This is as Number of Children is the only one which can be counted, Thus it would be the only discrete numerical variable.
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 18, 2021, 09:28:53 am
Yeah sure - also thank you to everyone for the help, I really appreciate it!!!!!!!!!!!! :)
In this question, it didn't specifically say that distance is rounded to 1 dp so it's assumed that this variable is continuous. Please correct me if I'm wrong this is just my reasoning based on my teacher feedback.
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 18, 2021, 08:06:15 pm
In this question, it didn't specifically say that distance is rounded to 1 dp so it's assumed that this variable is continuous. Please correct me if I'm wrong this is just my reasoning based on my teacher feedback.

Okay yep that sounds right, thank you!
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 19, 2021, 05:33:17 pm
is it just me or are the exams for further maths getting harder since 2019?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 19, 2021, 06:25:53 pm
is it just me or are the exams for further maths getting harder since 2019?

You mean actual exam or trial exam?

As I have not done 2020 exam yet but could see it being bit tough.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 21, 2021, 09:38:19 pm
If someone could help with this question
Hypertension is commonly defined as a systolic blood pressure above 140mmHg. If a physician is given a report stating that a sample of 4women has an average systolic blood pressure below 140mmHg, can the physician conclude that none of the women has hypertension? Justify your answer
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on October 21, 2021, 10:47:29 pm
What do you think? Why do you think this?

If you think yes, prove however you choose that no matter what, no women have hypertension. Alternatively, if you think no, give a particular counterexample that proves that at least one of the women has hypertension.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 22, 2021, 06:12:04 pm
C) write down the null and alternate hypothesis for this test
H0 :p1 =0.52, q1 =0.48 HA : p1≠ 0.52 or Q1≠0.48

i don't understand why this is the null and alternate hypothesis can someone explain
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 23, 2021, 05:04:10 pm
If someone could help with this question
Hypertension is commonly defined as a systolic blood pressure above 140mmHg. If a physician is given a report stating that a sample of 4women has an average systolic blood pressure below 140mmHg, can the physician conclude that none of the women has hypertension? Justify your answer
No because a sample doesn't represent an entire population of women so your conclusion would be inaccurate. Also, is this actually a further maths question?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 23, 2021, 07:19:17 pm
Thanks
No it’s not a further maths question
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on October 23, 2021, 07:45:38 pm
No because a sample doesn't represent an entire population of women so your conclusion would be inaccurate. Also, is this actually a further maths question?

This doesn't answer the question. The question implies that we should be checking if the doctor can conclude that none of the women they've tested has hypertension, not some purported entire population. There is no mention of a population. Good attempt though

I purposefully left my response open-ended because we'd like to see more working out appended to any question.

Since an answer has now been posted up, I may as well: the answer is no, you cannot conclude that none of the women has hypertension. A simple counterexample can be found by letting the blood pressure of three of the women be 139mmHg and the other be 141mmHg. The average is clearly below 140mmHg, yet one is above 140mmHg (implying that said woman has hypertension).

Hope this helps
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 24, 2021, 01:31:51 pm
This doesn't answer the question. The question implies that we should be checking if the doctor can conclude that none of the women they've tested has hypertension, not some purported entire population. There is no mention of a population. Good attempt though

I purposefully left my response open-ended because we'd like to see more working out appended to any question.

Since an answer has now been posted up, I may as well: the answer is no, you cannot conclude that none of the women has hypertension. A simple counterexample can be found by letting the blood pressure of three of the women be 139mmHg and the other be 141mmHg. The average is clearly below 140mmHg, yet one is above 140mmHg (implying that said woman has hypertension).

Hope this helps
right makes sense i thought this was a science prac question instead of a medical question.
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 24, 2021, 08:01:28 pm
hi if someone could help me with this q that'd be great

I thought the constraint would be 5x + 3y ≤ 15 but the solutions said 5x + 3y 15; why is the number of seats greater than or equal to 15? shouldn't it be less than or equal to 15 because the students cannot share a helicopter with anyone else?

Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 24, 2021, 10:46:51 pm
Hi,

This is a good question. I could be wrong bit it could be including piolet as well which could make sense of why it being more than 15. The other reason could be that they are also including seats in the helicopter where no one is sitting. Which would mean more than 15 seats.

I hope this helps
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 25, 2021, 12:10:35 pm
Yeah ig the implication is that all 15 students are going on the helicopter so there's a minimum of 15 seats required ... a bit ambiguous though, anyways thanks!
Title: Re: VCE General & Further Maths Question Thread!
Post by: lm21074 on October 25, 2021, 12:24:22 pm
Yeah ig the implication is that all 15 students are going on the helicopter so there's a minimum of 15 seats required ... a bit ambiguous though, anyways thanks!
Yep, I don't think VCAA would be this ambiguous.
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 26, 2021, 09:54:10 am
Does anyone know strategies about how to guarantee full marks on exam 2 without making careless mistakes?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 26, 2021, 07:46:09 pm
for this question i don't get why this is the answer isn't it just 0.42 x 0.17. for independent events you x them and disjoint you add them
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 26, 2021, 07:49:21 pm
for this question int it just 0.69+ 0.4
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on October 26, 2021, 08:25:01 pm
for this question i don't get why this is the answer isn't it just 0.42 x 0.17. for independent events you x them and disjoint you add them

I'm not sure what you mean by the last part. This probably hints at a much larger gap in your understanding that we're missing. The solution is correct because when you want to find the probability of either event happening, you add the probability of each individual event, then subtract one instance of them both happening to account for double counting. Note that the last step doesn't exist for disjoint events since that is always 0 in that case.

As for why isn't it just 0.42 x 0.17; that's just because it's not intersection. Union implies an OR relationship, intersection implies an AND. Be careful when interpreting the question.

for this question int it just 0.69+ 0.4

How can it be 0.69+0.4? The probability of anything cannot exceed 1. This should already be ringing alarm bells in your head and telling you that you cannot possibly be correct. Again, reread the solutions which are correct; try to deduce how they step through it at the very least (it will help a little bit). Similar idea to the first question again here.
Title: Re: VCE General & Further Maths Question Thread!
Post by: lm21074 on October 26, 2021, 09:08:49 pm
Does anyone know strategies about how to guarantee full marks on exam 2 without making careless mistakes?
Unfortunately, there isn't really a way to guarantee full marks on exam 2 but I'd suggest checking your answers as you go and after you do them. By this, I mean check that you've entered numbers correctly into your CAS, the signs are correct on financial solver, you've put enough zeros in a calculation (I lost a mark on a SAC for writing 200 instead of 2000 - the epitome of careless mistakes :( ). If time permits, go through questions you found difficult first and then the rest of the questions.

Hope this helps :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 26, 2021, 09:50:04 pm
for this question ii
i don't understand why its 8.606 i thought it had to be less than 7.5358
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on October 26, 2021, 09:56:51 pm
i dont understand the answer for this question can someone explain and where did the 0.48 come from
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 26, 2021, 11:44:54 pm
Unfortunately, there isn't really a way to guarantee full marks on exam 2 but I'd suggest checking your answers as you go and after you do them. By this, I mean check that you've entered numbers correctly into your CAS, the signs are correct on financial solver, you've put enough zeros in a calculation (I lost a mark on a SAC for writing 200 instead of 2000 - the epitome of careless mistakes :( ). If time permits, go through questions you found difficult first and then the rest of the questions.

Hope this helps :)
thank you good news is that I haven't done some of these yet so there's still hope
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on October 27, 2021, 12:28:49 am
for this question ii
i don't understand why its 8.606 i thought it had to be less than 7.5358

You've got it the wrong way around; the lower bound for a smaller confidence interval will be higher than the lower bound of a larger confidence interval. Intuitively, this is because more or less the larger confidence interval needs to encompass more numbers, so to speak.

i dont understand the answer for this question can someone explain and where did the 0.48 come from

I feel like there's missing context here. Not sure what p and q mean in this context.

Hope this helps
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 28, 2021, 11:37:47 am
Can someone please solve this question and tell me what they got?
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 28, 2021, 11:41:35 am
Also can someone please tell me what you got for this question?
Title: Re: VCE General & Further Maths Question Thread!
Post by: GreenNinja on October 28, 2021, 11:58:57 am
Can someone please solve this question and tell me what they got?

Isn't this just counting??

..... Though i feel like I may be missing comething.
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on October 28, 2021, 12:04:39 pm
Can someone please solve this question and tell me what they got?

I'd be inclined to say that it is 36% (because I usually assume between is exclusive, as inclusivity is usually stated); but it should be made clear by the question. If in doubt, ask.

Also can someone please tell me what you got for this question?

This is really blurry and hard to read - if you have another picture I'd be happy to take a look at it later.
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 28, 2021, 12:12:18 pm
I'd be inclined to say that it is 36% (because I usually assume between is exclusive, as inclusivity is usually stated); but it should be made clear by the question. If in doubt, ask.

This is really blurry and hard to read - if you have another picture I'd be happy to take a look at it later.
Yeah that's what the solution said but "between" isn't really explicit because if we're talking about between 1 standard deviation and 2 standard deviation, we're including both the value at the 1 standard dev and the value at standard dev.

Also here's the question that was blurry   
Title: Re: VCE General & Further Maths Question Thread!
Post by: sleepeatrepeat on October 28, 2021, 12:55:49 pm
There are 9 numbers between 3 and 7 (4, 4, 4, 4, 5, 5, 5, 6, 6)
9 / 25 x 100 = 36%

deseasonalised temp = 23.71 + 0.457 x month
= 23.71 + 0.457 x 13
= 29.651

predicted temp = 29.651 x 1.13
= 33.5 degrees
= 34 degrees

Hope that helps... ;D
Title: Re: VCE General & Further Maths Question Thread!
Post by: lm21074 on October 28, 2021, 07:37:52 pm
There are 9 numbers between 3 and 7 (4, 4, 4, 4, 5, 5, 5, 6, 6)
9 / 25 x 100 = 36%

deseasonalised temp = 23.71 + 0.457 x month
= 23.71 + 0.457 x 13
= 29.651

predicted temp = 29.651 x 1.13
= 33.5 degrees
= 34 degrees

Hope that helps... ;D
Hey,
I'm just wondering how you got the seasonal index of 1.13?

Thanks :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: sleepeatrepeat on October 28, 2021, 09:11:15 pm
The 1.13 comes from Oct 2017 coz if oct 2017 is taken from the table and oct 2018 is added...they all need to have an average of 1 which means that the next month (Oct 2018) will have the same as the first month (Oct 2017)...

Sorry don't know how much of that makes sense... ??? :o
Title: Re: VCE General & Further Maths Question Thread!
Post by: M-D on October 29, 2021, 01:00:14 pm
Hi,

Does anyone have access to the VCAA 2005 and older VCAA exams?

On the VCAA page there are exams only up to 2006.

Thank you.
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 29, 2021, 05:34:52 pm
Hi can someone please tell me what you would've got for these questions and tell me what your solution was?

Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 29, 2021, 05:35:50 pm
someone has posted the answers
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 29, 2021, 05:43:48 pm
someone has posted the answers
where?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 29, 2021, 05:46:06 pm
Fruther math exam 1 solution it is in 2021 vce exam page
Title: Re: VCE General & Further Maths Question Thread!
Post by: Encly on October 29, 2021, 09:15:15 pm
Hey, does anyone have any tips on how to use reading time in Exam 2? What’s the most effective way to use it?
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on October 29, 2021, 09:46:15 pm
Hey, does anyone have any tips on how to use reading time in Exam 2? What’s the most effective way to use it?
hey! tbh I don't really think there's anything like the "most effective" way to use reading time. I would take 30secs-1min to just flick through the entire exam once and get a gist of how long it is. Then I personally prefer to read it in chronological order; if you know you take more time to do a particular section of the exam or you struggle with a module more than other sections then I'd probably suggest spending the majority of your reading time on those questions so you have a better idea of how to approach them when writing time starts. It's really just about doing what you feel comfortable with.

Hope this helps!
Title: Re: VCE General & Further Maths Question Thread!
Post by: tannicholas on October 30, 2021, 09:38:51 am
what study score am i likely to get with rank 10 in strong cohort

exam 1: 38/40
exam 2: 55/60
Title: Re: VCE General & Further Maths Question Thread!
Post by: MaryK on October 30, 2021, 12:09:10 pm
Where do I find a copy of the Further Exam 1 2021? Does Atar Notes publish it anywhere on their site?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on October 31, 2021, 08:28:02 pm


    Best of luck everyone for tomorrow's Further Exam. After tomorrow no   more further

     Hope You All Do great in it
Title: Re: VCE General & Further Maths Question Thread!
Post by: Chocolatepistachio on November 01, 2021, 03:41:11 pm
for independent for the upside down u you just times them right so its just 0.42x 0.17/0.17
i have no idea why they put p(c)/1
Title: Re: VCE General & Further Maths Question Thread!
Post by: fun_jirachi on November 01, 2021, 04:00:56 pm
If \(C, D\) are independent events then by definition \(P(C \cap D) = P(C)P(D)\).

This means that \(\frac{P(C \cap D)}{P(D)} = \frac{P(C)P(D)}{P(D)} = P(C)\). Note that what you've written there 0.42 x 0.17/0.17 is the same as the answer they've given.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Rtim7777 on November 10, 2021, 05:47:27 pm
Does anyone know if I need to pass the unit 2 General Maths exam? For reference I am not doing Further Maths next year and I failed 1 of the 3 SACs this semester. My exam is tomorrow
Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on November 10, 2021, 06:37:28 pm
Does anyone know if I need to pass the unit 2 General Maths exam? For reference I am not doing Further Maths next year and I failed 1 of the 3 SACs this semester. My exam is tomorrow

Hi,

First of all hope you exams goes well.

Now about your question. You need to be able to pass unit 1 and 2 for all your year 11 subject. It does not matte by how much but it is essential for you to pass unit 1 and 2.

Hope it helps. And again best of luck for your exam
Title: Re: VCE General & Further Maths Question Thread!
Post by: a weaponized ikea chair on November 29, 2021, 07:53:21 pm
Hello,

I am looking for confirmation of my working or correction of errors.

For A, I got 0.75%

For B, I got t(0) = 55000, t(n+1) = 1.0075 x t(n)

For C, I got t(n) = ((1.0075)^n) x 55000

For D, the one I am stuck on, I got $86,112.46. I understand the question as that the rule in part C is for n months, not n years, so t(60) would give the value after 5 years.

Thanks


Title: Re: VCE General & Further Maths Question Thread!
Post by: Commercekid2050 on November 29, 2021, 08:38:11 pm
Hello,

I am looking for confirmation of my working or correction of errors.

For A, I got 0.75%

For B, I got t(0) = 55000, t(n+1) = 1.0075 x t(n)

For C, I got t(n) = ((1.0075)^n) x 55000

For D, the one I am stuck on, I got $86,112.46. I understand the question as that the rule in part C is for n months, not n years, so t(60) would give the value after 5 years.

Thanks

Hi,

Just looked over all your answer I think they all are correct. The only think I would say would be for C. My teacher had told me that rule should always be written as Vn = V0*R. Though this is just a small part you should just confim with your teacher.

Also for last you would multiply 5 by 12 to get how many months it would be for 5 years.

Hope this s somewhat helpful
Title: Re: VCE General & Further Maths Question Thread!
Post by: 010000studyhard on January 28, 2022, 09:41:07 pm
Hey there,

Does any one have practice SACS for further maths.
If So DM me Immediately on ATAR NOTES.


THANKS
Title: Re: VCE General & Further Maths Question Thread!
Post by: Billuminati on January 28, 2022, 09:43:16 pm
Hey there,

Does any one have practice SACS for further maths.
If So DM me Immediately on ATAR NOTES.


THANKS

For everyone's benefit, I'll just post on the forums as well: https://drive.google.com/drive/folders/109a0ULOIpLr-Rwlj98rTdDBl8mmhr7id?usp=sharing
Title: Re: VCE General & Further Maths Question Thread!
Post by: a weaponized ikea chair on February 03, 2022, 08:28:37 pm
What is the difference, if any, between a question asking for "the first five recursions" and "the first five terms"?
Title: Re: VCE General & Further Maths Question Thread!
Post by: Golgi Apparatus on February 03, 2022, 09:50:36 pm
What is the difference, if any, between a question asking for "the first five recursions" and "the first five terms"?

I’m not sure if this is correct, so someone might want to confirm.

I would assume ‘the first 5 recursions’ means to apply the recursion rule 5 times (e.g. given V0, find V1, V2, V3, V4 and V5), while ‘the first 5 terms’ means the first 5 values in the sequence (e.g. V0, V1, V2, V3 and V4).
Title: Re: VCE General & Further Maths Question Thread!
Post by: Golgi Apparatus on February 09, 2022, 10:18:35 pm
I would start by converting the ratio to fractions, to work out what fraction of the cost each person contributed. You can add up each number in the ratio to get the denominator of the fractions, then use each number in the ratio as the numerators.

Spoiler
The sum of the numbers in the ratio is 10, so Mark contributed 3/10, Henry 1/10, Dale 4/10 (2/5) and Ben 2/10 (1/5).

Then multiply each fraction by the total cost to work out how much each person paid.
Title: Re: VCE General & Further Maths Question Thread!
Post by: Jimmonash1991 on February 20, 2022, 12:40:15 pm
G'day,

I am a tutor in Further Mathematics, but have a question for fellow experts and students.

The picture attached is of a question my student attempted. The content is on chapter 3 of cambridge, so is on least squares regression. A few issues:

- The original data has a massive outlier, so shouldn't even be subject to least squares regression per the assumptions

- The picture is of the residual plot, which to me has no real observable pattern given the outlier, however perhaps the definition of "pattern" is not so clear cut? I imagine the pattern being non-linear or curved or some such, so how do we distinguish between pattern and non pattern?

Thanks for the help. Hopefully someone more zen than I can help me understand why we'd approach this question despite the outlier being present!

Cheers
Title: Re: VCE General & Further Maths Question Thread!
Post by: Amydev8 on July 05, 2022, 01:20:10 pm
Graphs and relations question:
In the exam does it matter if you don't use the formula (y-y1)=m(x-x1)?
As I would prefer to work with y=mx+c but don't want to be losing marks if the other is necessary for the exam working out.
Thanks  :)
Title: Re: VCE General & Further Maths Question Thread!
Post by: Billuminati on July 05, 2022, 02:20:41 pm
Graphs and relations question:
In the exam does it matter if you don't use the formula (y-y1)=m(x-x1)?
As I would prefer to work with y=mx+c but don't want to be losing marks if the other is necessary for the exam working out.
Thanks  :)

I never had to use the first form. FM exams always ask questions in the gradient intercept form ie the y = mx + c one since they want you to interpret m and c in the context of the question
Title: Re: VCE General & Further Maths Question Thread!
Post by: valjaybj on July 05, 2022, 09:44:28 pm
G'day,

I am a tutor in Further Mathematics, but have a question for fellow experts and students.

The picture attached is of a question my student attempted. The content is on chapter 3 of cambridge, so is on least squares regression. A few issues:

- The original data has a massive outlier, so shouldn't even be subject to least squares regression per the assumptions

- The picture is of the residual plot, which to me has no real observable pattern given the outlier, however perhaps the definition of "pattern" is not so clear cut? I imagine the pattern being non-linear or curved or some such, so how do we distinguish between pattern and non pattern?

Thanks for the help. Hopefully someone more zen than I can help me understand why we'd approach this question despite the outlier being present!

Cheers

hi! this is quite a late reply haha but i think that's what they're actually asking for in terms of why a regression analysis is not appropriate for the data. like you said there's a very clear outlier, and also there seems to be a decreasing pattern and somewhat linearity in the rest of the residual plot. ofc a pattern in the residual plot indicates the data is non-linear and hence further supports why linear regression is not suitable for the data. i feel like you just have to go with the information they've provided and then use your observations to answer part g