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Author Topic: VCE Methods Question Thread!  (Read 4803491 times)  Share 

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MB_

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Re: VCE Methods Question Thread!
« Reply #17460 on: December 18, 2018, 10:11:02 pm »
+4
b + 2 = f - 22
b + 2 + f - 22 = 40
The equation for the boy's age and father's age equaling 40 should be b + 2 + f + 2 = 40 where b can be substituted for f - 24
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Sine

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Re: VCE Methods Question Thread!
« Reply #17461 on: December 18, 2018, 10:12:50 pm »
+4
Also:
A boy is 24 years younger than his father. In two years time the sum of their ages will be 40. Find the present ages of father and son.
1)   b = f - 24
2)   (b+2) + (f+2) = 40

Sub 1 into 2
 (f - 24 +2) + (f+2) = 40
f - 22 + f + 2 = 40
2f - 20 = 40
2f = 60
f = 30
Sub f = 30 into 1)
b = 30 - 24 = 6


aspiringantelope

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Re: VCE Methods Question Thread!
« Reply #17462 on: December 18, 2018, 10:16:52 pm »
+1
Ok wow!!!
Thanks everyone for the swift replies!!! :D

AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17463 on: December 18, 2018, 10:27:54 pm »
+3
...
btw this is unrelated to the q but how do you put all the fractions on the same line using LaTeX instead of them being on different lines?
...

There are two types of equations, inline equations (which is what you are after) and display equations.

Use
Code: [Select]
\( \) for inline equations and use
Code: [Select]
\[ \] for display equations (or the tex tag).

For example,
Code: [Select]
\(\frac{a}{b}\) will yield:  \(\frac{a}{b}\).
Code: [Select]
\[\frac{a}{b}\] will yield:  \[\frac{a}{b}.\]
The inline equation uses a smaller fraction to squish it inline, but if you wish to override that, use \(\texttt{\dfrac}\) instead of \(\texttt{\frac}\).

For more on how to use \(\TeX\), check out Rui's amazing guide.
« Last Edit: December 18, 2018, 10:29:49 pm by dantraicos »
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Scribe

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Re: VCE Methods Question Thread!
« Reply #17464 on: December 19, 2018, 10:01:56 am »
0
Hi,

I was thinking of purchasing some resources for Maths Methods (and Specialist Maths). Does anyone here recommend the ATARNotes topic tests, NEAP smartstudy question guides, Derrick Ha's books, or anything else?

Thanks  :)

A Farm of Llamas

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Re: VCE Methods Question Thread!
« Reply #17465 on: December 19, 2018, 02:28:26 pm »
+1
Hi,

I was thinking of purchasing some resources for Maths Methods (and Specialist Maths). Does anyone here recommend the ATARNotes topic tests, NEAP smartstudy question guides, Derrick Ha's books, or anything else?

Thanks  :)

Those resources you've mentioned are great and I've used them before with success. Currently, my past students find Exam Pro Guides very useful. In terms of getting more practice, Cambridge Checkpoints are great for upcoming SACs and exams: Spesh and Methods.
Try this Maths Methods Practice Exam 1:
<Link>

AR1472

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Re: VCE Methods Question Thread!
« Reply #17466 on: December 20, 2018, 06:30:30 am »
0
Hey, I was just wondering, what are all the types of graphs that need to be memorised for 3/4? Like being able to draw them without the use of a CAS. I’ve only completed 1/2 (hence I only know a few of the more basic ones). I was doing some 3/4 preparatory questions (simple stuff like the implied domain when looking at a function) and I realised that some of the graphs I had to plot on the CAS because I had no idea what they looked like, unlike others which I could tell in my head.

Is there a list of graphs anywhere or something?? I’d like to learn how to graph all of them over the break because I always find myself falling behind in class when my teacher introduces a new graph.

Thanks to whoever answers!!

Unsplash

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Re: VCE Methods Question Thread!
« Reply #17467 on: December 20, 2018, 11:12:12 am »
+5
You should know all basic trig graphs (sin, cos, tan), quadratics, cubics (relatively simple ones), x^n, logarithmic graphs (I believe only base e and 10 are listed - may want to check this), exponential graphs, piecewise functions (just a combination of the previous list) and also how the addition of the various types of graphs works (search addition of ordinates for more information).

For all these graphs you should also understand how to graph transformations of them as well.

Page 71 in the Mathematics Study Design document is where this is listed.

lzxnl

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Re: VCE Methods Question Thread!
« Reply #17468 on: December 20, 2018, 07:23:38 pm »
+3
You should know all basic trig graphs (sin, cos, tan), quadratics, cubics (relatively simple ones), x^n, logarithmic graphs (I believe only base e and 10 are listed - may want to check this), exponential graphs, piecewise functions (just a combination of the previous list) and also how the addition of the various types of graphs works (search addition of ordinates for more information).

For all these graphs you should also understand how to graph transformations of them as well.

Page 71 in the Mathematics Study Design document is where this is listed.

However, addition of ordinates is more of a luxury to learn as it's not tested much. Everything else mentioned by FelixHarvey is essential.

I must note that the graph of any exponential graph involving an exponential of any base is just a series of transformations away from the graph of y = ex, and similarly, any log graph is also just a series of transformations away from the graph of y = log(x).

Hey, I was just wondering, what are all the types of graphs that need to be memorised for 3/4? Like being able to draw them without the use of a CAS. I’ve only completed 1/2 (hence I only know a few of the more basic ones). I was doing some 3/4 preparatory questions (simple stuff like the implied domain when looking at a function) and I realised that some of the graphs I had to plot on the CAS because I had no idea what they looked like, unlike others which I could tell in my head.

Is there a list of graphs anywhere or something?? I’d like to learn how to graph all of them over the break because I always find myself falling behind in class when my teacher introduces a new graph.

Thanks to whoever answers!!
For implied domains, you should generally be able to tell by looking at the function and asking yourself, what requirement needs to be satisfied for this thing to make sense? Let us consider a toy example.


It looks complicated. However, the trick is to note that there is a square root, and that you can't square root anything you want; the thing you're trying to square root can't be negative. Thus, you have the inequality

The issue is, you'd like to multiply top and bottom by x+1, but you don't know if it's positive or negative, so the inequality sign could flip. So, let's just assume x+1>0 and multiply. Now that it's positive, the inequality sign does not flip, and we find x >= 1. We assumed x + 1 > 0 too, so our solution is x >= 1 and x > -1, or just x >= 1.

What if x + 1 < 0? Now, the inequality sign flips, and we find x <= 1. We assumed x + 1 < 0, so x <= 1 and x < -1, which requires x < -1. So our total implied domain is

Be careful of the inequality signs; one doesn't include -1, one includes 1.

You can play a similar trick with fractions. Fractions are ok whenever the numerator is defined and the denominator is defined but nonzero. Most functions, like rational functions, tangents, logs, square roots will all have some restriction on what goes into them. You need to take those into account.
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peachxmh

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Re: VCE Methods Question Thread!
« Reply #17469 on: December 21, 2018, 01:08:33 pm »
0
If sin x = 0.3, cos α = 0.6 and tan θ = 0.7, find the value of tan(\(\frac{π}{2}\) - θ).
Is there anyway to do this question with only U1/2 knowledge? (bc I went and looked at the worked solutions and they use cotan(θ) which we haven't learnt about yet)
Otherwise, how would you approach it using U3/4 knowledge?
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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17470 on: December 21, 2018, 01:55:13 pm »
+7
If sin x = 0.3, cos α = 0.6 and tan θ = 0.7, find the value of tan(\(\frac{π}{2}\) - θ).
Is there anyway to do this question with only U1/2 knowledge? (bc I went and looked at the worked solutions and they use cotan(θ) which we haven't learnt about yet)
Otherwise, how would you approach it using U3/4 knowledge?

This is actually possible with just units 1&2 knowledge. Indeed, \[\tan\left(\frac{\pi}{2}-\theta\right)=\cot(\theta),\] but reciprocal circular functions aren't in the Methods course, so let's not use them. For your own interest, \(\cot(\theta)=\dfrac{1}{\tan(\theta)}\).

Anyway, here's one way you could go about this question: \begin{align*}\tan\left(\frac{\pi}{2}-\theta\right)&=\frac{\sin\left(\frac{\pi}{2}-\theta\right)}{\cos\left(\frac{\pi}{2}-\theta\right)}\\
&=\frac{\cos(\theta)}{\sin(\theta)}\quad\quad (\text{complement angle identities})\\
&=\frac{1}{\tan(\theta)}\\
&=\frac{1}{7/10}\\
&=\frac{10}{7}.\end{align*}
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Re: VCE Methods Question Thread!
« Reply #17471 on: December 22, 2018, 02:32:34 am »
0
Thanks to everyone who replied to my previous question! That really helped ^^

AR1472

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Re: VCE Methods Question Thread!
« Reply #17472 on: December 22, 2018, 05:20:59 am »
0
Does the ‘sum and product of functions’ come up often in methods? Like graphing (f+g)(x) and (fg)(x). I assume it’s important because it’s in the textbook... but my teachers have told us to skip the topic so I’m unsure whether it’s actually worth going over.

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Re: VCE Methods Question Thread!
« Reply #17473 on: December 22, 2018, 07:59:51 am »
+1
Does the ‘sum and product of functions’ come up often in methods? Like graphing (f+g)(x) and (fg)(x). I assume it’s important because it’s in the textbook... but my teachers have told us to skip the topic so I’m unsure whether it’s actually worth going over.
It doesn't tend to come up much,  but it's a pretty easy concept and in the study design so I'd cover it anyway (maybe graph a couple of each type)

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Re: VCE Methods Question Thread!
« Reply #17474 on: December 22, 2018, 10:05:37 am »
0

Does the ‘sum and product of functions’ come up often in methods? Like graphing (f+g)(x) and (fg)(x). I assume it’s important because it’s in the textbook... but my teachers have told us to skip the topic so I’m unsure whether it’s actually worth going over.
As it is in the study design it is entirely possible that VCAA may one day chuck it in Exam 1 to throw off people who may have just ‘skipped’ over a part of the study design.
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