Author Topic: Specialist Maths (Exam 1): Discussion, Questions & Potential Solutions (Read 23605 times)

Joseph41 · « **on:** October 09, 2018, 03:25:32 pm »

This thread is for all exam-related discussion. Was it easy? Was it hard? What did you get for each question? Feel free to post any and all of your thoughts below.

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Dais_Deorum · « **Reply #1 on:** November 07, 2018, 06:03:35 pm »

Can confirm last question is a vector calc. question. Heard it here first

Onyx · « **Reply #2 on:** November 07, 2018, 06:05:52 pm »

Quote from: Dais_Deorum on November 07, 2018, 06:03:35 pm

Can confirm last question is a vector calc. question. Heard it here first

Can confirm a mechanics q maybe an inclined plane or something
Also expect to see the yearly 3/4 marker implicit differentiation q

crouchie · « **Reply #3 on:** November 09, 2018, 07:52:38 am »

Solutions to the 2018 Specialist Maths Exam 1 are attached.

AlphaZero · « **Reply #4 on:** November 09, 2018, 09:10:51 am »

VCAA 2018 Specialist Exam 1 Provisional Solutions
Solutions by Daniel Traicos at TWM Publications

I thought it was a pretty good exam. Q10 was awesome I thought

Lear · « **Reply #5 on:** November 09, 2018, 09:13:55 am »

Does the VCAA wait a specific period of time before releasing exams to teachers? I'm surprised they get handed out while the exam is going on. But then again, the students are already sitting there. Pretty much no way to cheat.

I really wonder how VCAA manages to keep so many exams secure throughout the few weeks leading up to the exam and especially the morning before. I was thinking remote controlled padlocks on the bags containing the exams or something. Must be quite secure considering there hasn't been any leaks in past few years.

crouchie · « **Reply #6 on:** November 09, 2018, 09:31:50 am »

Quote from: Lear on November 09, 2018, 09:13:55 am

Does the VCAA wait a specific period of time before releasing exams to teachers? I'm surprised they get handed out while the exam is going on. But then again, the students are already sitting there. Pretty much no way to cheat.

A great question Lear. We are given the exam exactly 30 minutes after writing time commences. I believe this is due to the fact that students are allowed to be late to the exam by up to 30 minutes (https://www.vcaa.vic.edu.au/Pages/vce/exams/examsrules.aspx#arriveslate). Once 30 minutes is passed, there is no way anyone is entering the exam room, which is why teachers get access to it then. Surprisingly, you should see teachers when the exam gets given to them. Like kids in a candy store.

Quote from: Lear on November 09, 2018, 09:13:55 am

I really wonder how VCAA manages to keep so many exams secure throughout the few weeks leading up to the exam and especially the morning before. I was thinking remote controlled padlocks on the bags containing the exams or something. Must be quite secure considering there hasn't been any leaks in past few years.

I'm not privy to this information unfortunately, but I'm fairly certain the assessors, as they're external, are given access to a room of the school, which them, and only them, can access. This is where all exams are stored. Nobody, not even the principal, is allowed access to this room. Quite a secure setup really.

Quote from: dantraicos on November 09, 2018, 09:10:51 am

Haha, I don't get a copy until 10:15 am

Oh no, how do you get your copy? Does a teacher give you one after it's over? Or is it scanned and sent to you?

AlphaZero · « **Reply #7 on:** November 09, 2018, 09:51:02 am »

Quote from: crouchie on November 09, 2018, 09:31:50 am

Oh no, how do you get your copy? Does a teacher give you one after it's over? Or is it scanned and sent to you?

One of my students sends me a copy after the exam. (They actually do the subject, so I can't really ask them to send it any earlier lol).

HamConspiracy · « **Reply #8 on:** November 09, 2018, 10:50:00 am »

It wasn’t too bad, apparently the last question had a bit of a quirk with plus/minus that I ignored, so

. The rest of it was fine, and how about that partial fractions graph? o.o

DinWell · « **Reply #9 on:** November 09, 2018, 10:50:49 am »

Quote from: HamConspiracy on November 09, 2018, 10:50:00 am

It wasn’t too bad, apparently the last question had a bit of a quirk with plus/minus that I ignored, so . The rest of it was fine, and how about that partial fractions graph? o.o

Yeah lol. I think a lot of people will just take away the absolute and leave x^2-2. Did you think the graph question was difficult?

jazzycab · « **Reply #10 on:** November 09, 2018, 10:57:54 am »

My provisional answers - very rushed so I may have made some errors.

Question 1a

Question 1b

$\frac{g}{13}\text{ up the plane}$

Question 2a

$\begin{align*}\left|1+i\right|&=\sqrt{2}&\text{Arg}\left(1+i\right)&=\tan^{-1}{\left(1\right)}\\\text{Arg}\left(1+i\right)&=\frac{\pi}{4}&\therefore 1+i&=\sqrt{2}\text{cis}\left(\frac{\pi}{4}\right)\end{align*}$

Question 2b

$-8-8\sqrt{3}i$

Question 3

$\frac{-18}{\pi\sqrt{3}+6}$

Question 4

$\begin{align*}a&=2&b&=3\end{align*}$

Question 5

Question 6

$2\left(-i+j+\pi k\right)$

Question 7

$\frac{1}{2}$

Question 8a

$\begin{align*}\frac{dQ_{in}}{dt}&=0\times 5&V\left(t\right)&=16+\left(5-3\right)\\\frac{dQ_{out}}{dt}&=3\times \frac{Q}{V\left(t\right)}&&=\frac{Q}{16+2t}\\\frac{dQ}{dt}&=\frac{dQ_{in}}{dt}-\frac{dQ_{out}}{dt}&&=0-\frac{3Q}{16+2t}\\\therefore\frac{dQ}{dt}&=-\frac{3Q}{16+2t}\end{align*}$

Question 8b

$Q=\frac{32}{\left(16+2t\right)^\frac{3}{2}}$

Question 9a

$\begin{align*}1+\tan^{2}{\left(t\right)}&=\sec^{2}{\left(t\right)}&x&=\sec{\left(t\right)}\\y&=\frac{\sqrt{2}}{2}\tan{\left(t\right)}&\sec^{2}{\left(t\right)}&=x^2\\\tan^{2}{\left(t\right)}&=2y^2&\therefore 1+x^2&=2y^2\\\therefore 1&=x^2-2y^2\end{align*}$

Question 9b

$x=1,3$

Question 9c

$\frac{2\pi}{3}$

Question 10

$\begin{align*}a&=-1&b&=0\\c&=2\end{align*}$

Nason · « **Reply #11 on:** November 09, 2018, 10:58:11 am »

Quote from: DinWell on November 09, 2018, 10:50:49 am

Yeah lol. I think a lot of people will just take away the absolute and leave x^2-2. Did you think the graph question was difficult?

Why do you take the negative? Seems like I overlooked something

DinWell · « **Reply #12 on:** November 09, 2018, 10:59:50 am »

Quote from: Nason on November 09, 2018, 10:58:11 am

Why do you take the negative? Seems like I overlooked something

sqrt((x^2-2)^2) = abs(x^2-2).
since 0 <= x <= 1, x^2-2 is negative so we need to take the negative of x^2-2 to ensure that it's positive.
Since abs(a) = -a if a<0

DinWell · « **Reply #13 on:** November 09, 2018, 11:00:25 am »

Quote from: jazzycab on November 09, 2018, 10:57:54 am

My provisional answers - very rushed so I may have made some errors.
Question 1a
Question 1b
$\frac{g}{13}\text{ up the plane}$
Question 2a
$\begin{align*}\left|1+i\right|&=\sqrt{2}&\text{Arg}\left(1+i\right)&=\tan^{-1}{\left(1\right)}\\\text{Arg}\left(1+i\right)&=\frac{\pi}{4}&\therefore 1+i&=\sqrt{2}\text{cis}\left(\frac{\pi}{4}\right)\end{align*}$
Question 2b
$-8-8\sqrt{3}i$
Question 3
$\frac{-18}{\pi\sqrt{3}+6}$
Question 4
$\begin{align*}a&=2&b&=3\end{align*}$
Question 5
Question 6
$2\left(-i+j+\pi k\right)$
Question 7
$\frac{1}{2}$
Question 8a
$\begin{align*}\frac{dQ_{in}}{dt}&=0\times 5&V\left(t\right)&=16+\left(5-3\right)\\\frac{dQ_{out}}{dt}&=3\times \frac{Q}{V\left(t\right)}&&=\frac{Q}{16+2t}\\\frac{dQ}{dt}&=\frac{dQ_{in}}{dt}-\frac{dQ_{out}}{dt}&&=0-\frac{3Q}{16+2t}\\\therefore\frac{dQ}{dt}&=-\frac{3Q}{16+2t}\end{align*}$
Question 8b
$Q=\frac{2}{\left(16+2t\right)^\frac{1}{2}}$
Question 9a
$\begin{align*}1+\tan^{2}{\left(t\right)}&=\sec^{2}{\left(t\right)}&x&=\sec{\left(t\right)}\\y&=\frac{\sqrt{2}}{2}\tan{\left(t\right)}&\sec^{2}{\left(t\right)}&=x^2\\\tan^{2}{\left(t\right)}&=2y^2&\therefore 1+x^2&=2y^2\\\therefore 1&=x^2-2y^2\end{align*}$
Question 9b
$x=1,3$
Question 9c
$\frac{2\pi}{3}$
Question 10
$\begin{align*}a&=-1&b&=0\\c&=2\end{align*}$

Thanks jazzycab!

jazzycab · « **Reply #14 on:** November 09, 2018, 11:00:38 am »

Quote from: Nason on November 09, 2018, 10:58:11 am

Why do you take the negative? Seems like I overlooked something

I haven't had a good look at why properly yet, but if you don't take the negative, you'll end up with a negative distance (i.e. evaluate the integral and test)

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Author Topic: Specialist Maths (Exam 1): Discussion, Questions & Potential Solutions (Read 23605 times)

Joseph41

Specialist Maths (Exam 1): Discussion, Questions & Potential Solutions

Dais_Deorum

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Onyx

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crouchie

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AlphaZero

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Lear

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crouchie

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AlphaZero

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HamConspiracy

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DinWell

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jazzycab

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Nason

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DinWell

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DinWell

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