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Author Topic: VCE General & Further Maths Question Thread!  (Read 750294 times)  Share 

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AngelWings

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Re: VCE Further Maths Question Thread!
« Reply #1725 on: March 12, 2017, 02:59:38 pm »
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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.
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npnp

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Re: VCE Further Maths Question Thread!
« Reply #1726 on: March 15, 2017, 05:45:44 pm »
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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.
« Last Edit: March 15, 2017, 05:48:26 pm by Aaron »

AngelWings

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Re: VCE Further Maths Question Thread!
« Reply #1727 on: March 15, 2017, 06:24:08 pm »
+1
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* .
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smiley123

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Re: VCE Further Maths Question Thread!
« Reply #1728 on: March 19, 2017, 07:44:57 am »
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 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?

AngelWings

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Re: VCE Further Maths Question Thread!
« Reply #1729 on: March 19, 2017, 02:40:05 pm »
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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).
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EdwinaB19

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Re: VCE Further Maths Question Thread!
« Reply #1730 on: March 22, 2017, 12:29:28 pm »
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Help with question 2 please if possible
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Guest8373727727

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Re: VCE Further Maths Question Thread!
« Reply #1731 on: March 23, 2017, 05:48:18 pm »
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Need help with 4 b)


Mattjbr2

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Re: VCE Further Maths Question Thread!
« Reply #1732 on: March 24, 2017, 02:37:17 pm »
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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?
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MightyBeh

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Re: VCE Further Maths Question Thread!
« Reply #1733 on: March 24, 2017, 07:51:16 pm »
+1
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. :)

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AngelWings

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Re: VCE Further Maths Question Thread!
« Reply #1734 on: March 26, 2017, 03:25:18 pm »
+1
Need help with 4 b)

(Image removed from quote.)

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 .

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SMOKIE

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Re: VCE Further Maths Question Thread!
« Reply #1735 on: March 26, 2017, 07:17:12 pm »
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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
« Last Edit: March 26, 2017, 07:21:03 pm by SMOKIE »

AngelWings

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Re: VCE Further Maths Question Thread!
« Reply #1736 on: March 27, 2017, 12:13:38 am »
+2
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
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SMOKIE

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Re: VCE Further Maths Question Thread!
« Reply #1737 on: March 27, 2017, 06:38:05 pm »
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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

AngelWings

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Re: VCE Further Maths Question Thread!
« Reply #1738 on: March 27, 2017, 07:05:18 pm »
+1
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.
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zxcvbnm18

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Re: VCE Further Maths Question Thread!
« Reply #1739 on: March 27, 2017, 09:42:33 pm »
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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