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March 29, 2024, 06:23:41 am

Author Topic: VCE Methods Question Thread!  (Read 4802677 times)  Share 

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keltingmeith

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Re: VCE Methods Question Thread!
« Reply #18900 on: October 25, 2020, 05:45:59 pm »
+8
Well whoops :p
At least there weren't any holes in my process.
Most of my incorrect answers seem to come from simple mistakes like this still unfortunately. Is this a common experience for you guys?

So, I don't know your personal circumstances. I don't know how you approach answering questions, checking your answers, etc. So sorry if I make an assumption that's wrong

But have you ever tried to proof-read one of your own essays? Ever notice how you proof-read it, and you maybe catch 1 or 2 errors, but most of it looks fine - then you get it back covered in red pen? It's because we suck at finding our own errors. This is common practice, extremely normal for everyone.

I also notice you posting a lot asking questions - which is fine, that's why the thread is here - but quite a few times, they're not "I don't understand this concept" questions, they're "I'm not getting the answer right and I don't know why" questions. And when it's the second type, they're usually examples of you making a silly little mistake that I'm sure you could've caught yourself, because you seem like a very bright kid.

So, how do you stop making these silly little mistakes? Get better at spotting your own mistakes. How do you get better at something nobody is good at to begin with? Practice. Before coming here to ask why you got a question wrong, scour the question. I don't mean just look at it, I don't mean give it a couple of looks over. I mean annotate each line. Make sure each number you put there is correct. Quadruple check all your formula, one pronumeral at a time. It will suck, and it will be long at first, but you will slowly get better at finding your mistakes. And once you've found all your mistakes, by yourself, you'll slowly start to stop making them, because you will have hard-wired those mistakes out of your brain. Just like riding a bicycle. But, if you don't learn to spot your own mistakes, and just keep asking us for help, you won't get any better at it.

Like, it's still fine to ask us questions, go ahead - we're here to help. But it might be worth your time to lean on us a little less, so that you get better at spotting your own mistakes, because that will lead you to stop making them.

james.358

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Re: VCE Methods Question Thread!
« Reply #18901 on: October 25, 2020, 06:23:57 pm »
+7
Hey Corey!

Just adding to the fantastic advice by Keltingmeith, you should try to follow "The 15 Minute Rule". Basically when you're stuck on something, you should work on it for about 15 minutes before seeking help. During that time you should try to get unstuck on your own, and note down everything you try. This will hopefully train your mind to become more independent and get better at spotting your own mistakes.

And like Keltingmeith said, there really is no shortcut to avoiding careless errors. Just keep practising, and ensure that you don't make the same mistake twice. For example when doing a particular type of question, you should almost subconsciously think about what you have done wrong on the question type before, and doing your best to avoid it this time.

Hope this helps!
James
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svnflower

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Re: VCE Methods Question Thread!
« Reply #18902 on: October 25, 2020, 06:52:08 pm »
0
Hello again ,

I'm stuck on this question. Do I need to use the Sn formula?

keltingmeith

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Re: VCE Methods Question Thread!
« Reply #18903 on: October 25, 2020, 07:09:28 pm »
+2
Hello again ,

I'm stuck on this question. Do I need to use the Sn formula?

Hey, so you might have the wrong thread - this thread is for VCE maths methods help, but this isn't actually in the VCE methods curriculum, so unfortunately nobody here is likely to be able to help you. Perchance you meant to go to the HSC boards?

EDIT: Okay, this question got to me, I couldn't just leave it alone. VCE kids, don't worry, you don't need to know how to do this. Anyway, first thing's first - let's figure out what kind of series it is. It doesn't look like it's an arithmetic series - if it were, then we'd see a lot of pluses and not a lot of square roots. Okay, so it's probably geometric - so we need to figure out the common ratio. First, we'll need to remove the sqrt(5), so let's do that:



Hang on a second - this is an arithmetic sequence! How sneaky. Watch what happens when divide by that sqrt(5):



It was in disguise the whole time, this is the sum of odd numbers! Okay, so now we have an equation for the sum of an arithmetic series, and that's:



Except, we don't know how long the sequence is, and a_n is what we're trying to find... Okay, but we have another formula we can use:



Now this, we can work with! So, sub in everything we know, and solve for n:



Rejecting the negative answer because, of course, a series must have a positive number of terms. So, we can now sub this into the equation from before to get the answer:



In which the last step is turning the number into the same form presented, but you could stop at the step before that (and I would encourage you to do this).

Also, a different formula you could've finished with is:



Pick your poison with this one

a weaponized ikea chair

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Re: VCE Methods Question Thread!
« Reply #18904 on: October 27, 2020, 07:38:02 pm »
0
i understand how to find the total number of combinations.

Can someone please explain how to find the number of combinations that contain ham? I know that it is 2^7 but I do not understand why or how.

fun_jirachi

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Re: VCE Methods Question Thread!
« Reply #18905 on: October 27, 2020, 07:46:50 pm »
+5
Hey there!

They mention you can have any combination of a list of ingredients ie. they can either be in the sandwich or not in the sandwich - notice how these are two options. If you're given that the sandwich has ham, then that 'blocks' it off as a choice (ie. you no longer have to make that choice any more) and thus have to choose from the seven other ingredients. You pick one of two choices for seven ingredients, ie 27

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a weaponized ikea chair

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Re: VCE Methods Question Thread!
« Reply #18906 on: October 27, 2020, 09:13:40 pm »
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Thanks for the reply, it helped.

Also, I found every other topic to be easy but when my class started combinations and their applications i just sought of hit a roadblock. Is it more difficult than the other topics or is my internal hatred for probability taking its toll?

fun_jirachi

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Re: VCE Methods Question Thread!
« Reply #18907 on: October 27, 2020, 09:24:27 pm »
+5
I'd say a bit of both. The internal hatred part makes you less inclined to study it or make sense of it, even if you don't notice this happening (in theory, anyway). Also, it is a hard topic; both because it's notoriously easy to get questions wrong while actually understanding the theory properly. Setting up an answer properly and understanding the wording of the question properly is mostly what screws people over in questions like these.

Hope that makes sense :)
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keltingmeith

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Re: VCE Methods Question Thread!
« Reply #18908 on: October 27, 2020, 09:27:27 pm »
+4
It's worth noting that combinatorics is not a part of 3/4 methods

a weaponized ikea chair

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Re: VCE Methods Question Thread!
« Reply #18909 on: October 27, 2020, 09:36:57 pm »
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It's worth noting that combinatorics is not a part of 3/4 methods
was it once a part of it, or was it never a part of it? I swear i read somewhere that had something similar to it in 3/4...

Sine

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Re: VCE Methods Question Thread!
« Reply #18910 on: October 27, 2020, 09:43:24 pm »
+4
was it once a part of it, or was it never a part of it? I swear i read somewhere that had something similar to it in 3/4...
permutations/combinatorics is heavily entrenched into the 1/2 course. For 3/4 combinatorics I am not sure if it is explicitly stated in the study design but it does help when you are considering some areas of probability so it can be worthwhile learning.

Rose34

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Re: VCE Methods Question Thread!
« Reply #18911 on: October 29, 2020, 07:38:24 pm »
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Hello everyone,

English is not my first language thus I struggle greatly with worded problems. My teacher keep on telling me the key to solve these problems is understanding but I have really tried that, I just do not seem to understand it. What do you suggest I do?

Thanks in advance.

james.358

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Re: VCE Methods Question Thread!
« Reply #18912 on: October 29, 2020, 08:39:32 pm »
+6
Hey Rose,

English is also my second language, and I used to struggle with worded problems as well. But I've managed to improve at it over the past few year, and here are some tips that will hopefully help you.

 - Immerse yourself in the situation and enjoy it! Especially if the task is creative, you should try to imagine yourself being the architect, epidemiologist, whatever your role is, rather than a mere student. Hopefully this helps you to stay more engaged with the task and be aware of issues such as domain (e.g. realise that values for lengths can't be negative, etc)

 - If you're likely to miss important information in the question, I suggest you develop a system to answer these questions. For example when reading the questions, I circle everything the question asks for (mark allocations) and underline important information you might forget (e.g. k>0, label coordinates, etc). These shouldn't take too long but will be very useful later on when checking. If you struggle to understand the question I suggest re-reading the information multiple times to make sure you have extracted all the necessary information.

 - Practice extended response questions! Improving at Maths is all about practice, and I'm sure you can find lots of worded problems in chapter reviews and past exams. As soon as you become familiar with these types of problems you will find that it becomes far less intimidating.

Hope this helps! If you have any other questions please don't hesitate to reply to the thread

Oh and FYI there is no need to double post across multiple threads, you will get a response just be a bit more patient :D

James
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Corey King

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Re: VCE Methods Question Thread!
« Reply #18913 on: October 31, 2020, 02:51:48 pm »
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So, I don't know your personal circumstances. I don't know how you approach answering questions, checking your answers, etc. So sorry if I make an assumption that's wrong

But have you ever tried to proof-read one of your own essays? Ever notice how you proof-read it, and you maybe catch 1 or 2 errors, but most of it looks fine - then you get it back covered in red pen? It's because we suck at finding our own errors. This is common practice, extremely normal for everyone.

I also notice you posting a lot asking questions - which is fine, that's why the thread is here - but quite a few times, they're not "I don't understand this concept" questions, they're "I'm not getting the answer right and I don't know why" questions. And when it's the second type, they're usually examples of you making a silly little mistake that I'm sure you could've caught yourself, because you seem like a very bright kid.

So, how do you stop making these silly little mistakes? Get better at spotting your own mistakes. How do you get better at something nobody is good at to begin with? Practice. Before coming here to ask why you got a question wrong, scour the question. I don't mean just look at it, I don't mean give it a couple of looks over. I mean annotate each line. Make sure each number you put there is correct. Quadruple check all your formula, one pronumeral at a time. It will suck, and it will be long at first, but you will slowly get better at finding your mistakes. And once you've found all your mistakes, by yourself, you'll slowly start to stop making them, because you will have hard-wired those mistakes out of your brain. Just like riding a bicycle. But, if you don't learn to spot your own mistakes, and just keep asking us for help, you won't get any better at it.

Like, it's still fine to ask us questions, go ahead - we're here to help. But it might be worth your time to lean on us a little less, so that you get better at spotting your own mistakes, because that will lead you to stop making them.

Thanks Kelting (and James). Being able to notice that when I'm asking that second kind of question it's probably due to human error and not a lack of conceptual knowledge has led me to asking no questions this last week! :P

I find that if I just leave it and come back the next study session, often the answer will just come to me. Even if I just mixed a sign up, I'll notice it where I didn't before. Curious!

This time I have an "I don't understand a concept" question.


So right now I'm doing quadratics, more specifically graphing circles.

I got a question where they asked me to find the center and radius of the circle from an equation (attached).

I decided to see if I could find any x intercepts first, so I used the old method for finding x-intercepts we learned in the section on parabolas.
I make y=0, then solved for x using the null factor theorum (as can be seen).
I got two x values, deduced the center point and radius, and thought I had it worked out.

Looking at the worked solution (attached) I can see they completed the square for y to put the equation in (circle form? :P)


My question is: Why does my method not work? It seems to follow the rules I've been taught previously, but it produces a different result than the complete the square method.

Much appreciated,
Corey

p0kem0n21

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Re: VCE Methods Question Thread!
« Reply #18914 on: October 31, 2020, 04:19:35 pm »
+5
This time I have an "I don't understand a concept" question.


So right now I'm doing quadratics, more specifically graphing circles.

I got a question where they asked me to find the center and radius of the circle from an equation (attached).

I decided to see if I could find any x intercepts first, so I used the old method for finding x-intercepts we learned in the section on parabolas.
I make y=0, then solved for x using the null factor theorum (as can be seen).
I got two x values, deduced the center point and radius, and thought I had it worked out.

Looking at the worked solution (attached) I can see they completed the square for y to put the equation in (circle form? :P)


My question is: Why does my method not work? It seems to follow the rules I've been taught previously, but it produces a different result than the complete the square method.

Much appreciated,
Corey

Not sure if this is a misconception of yours or not, but I would first like to address this regardless: a circle is not a quadratic. Although there is a degree two x variable, there's also a degree two y variable in the general equation which prevents us from classifying a circle as a quadratic. You may then ask: what type of equation is a circle? Well, for the purposes of the syllabus, a circle is just a circle. That's all there is to it  :) (If you're interested, you could search up "conics" which can give you more insight into a circle, but that's beyond the Methods curriculum, so don't stress if you don't understand it all). Also apologies if you already know that a circle is not a quadratic.

What you did was find the midpoint of the two x-intercepts, (4,0) and (-4,0), of the circle, getting (0,0) and assuming that this is the center of the circle. The issue with doing this is that, using your x-intercepts, you can only deduce the x-coordinate of the center, which is 0, in this case. However, we cannot assume that the center has the same y-coordinate as these x-intercepts (i.e. we cannot assume the y-coordinate is zero). Using your method, we would actually have to find the midpoint of the y-intercepts, which are (0,8) and (0,-2), and take the y-coordinate (3) of the midpoint (which is (0,3) ) to get the y-coordinate of the circle's center. We would then put these pieces of information together to get the center of (0,3).

From this, you can see that the method is a bit lengthy and requires a bunch of substitution and quadratic solving. Not to mention that calculating the radius could also be a disaster (not here, but in cases where neither the x-coordinate nor the y-coordinate of the center are 0). What's worse is that this method cannot be used with all circles, particularly those which have less than 2 x-intercepts and/or less than 2 y-intercepts. For example, try your method with a circle of this equation:

x2-4x+y2-4y+7=0

If you tried substituting x=0 or y=0 into the equation, you'll just end up getting a quadratic which cannot be solved. That's why the "complete the square" method is used with circles; you can complete the square with any quadratic you have, and deduce information from there. Ok, I just said that circles are not quadratics. However, you can treat the degree 2 x and y variables as quadratics. The thing is, you complete the square separately for your x and y variables. This process may be a bit confusing at times. In the above equation, you could write -4(x+y). Don't do that, that's keeping the x and y variables in the same brackets and will just lead to a load of confusion.