Student Written Methods Exam

[MathMethdz99-R]

Hey guys I got bored and decided to write up my own methods exam 1 lol.. If anyone's up for doing it, I'd be glad to hear feedback on it  thank you!

[MathMethdz99-R]

Also completed some solutions for the exam if there are any errors, please let me know but hopefully it should be all good!

https://drive.google.com/open?id=0B6TZTAdW49DzSE9hVktIQzBSa1U

[Sine]

I read through the exam and solutions and its a well written exam perhaps a little harder than vcaa standard.

Imo the only thing it lacks is that one type of vcaa question which is deceptively tricky even companies aren't able to replicate this so i wouldnt worry

[MathMethdz99-R]

thank you kindly

[uhoh]

Thanks for this exam! So tough

For 5b), how do you know p>0?

Can you explain the whole of Q8? I had a look at the ans but I don't understand what's going on

Same goes with Q10a)

[MathMethdz99-R]

Thanks for this exam! So tough

For 5b), how do you know p>0?

Can you explain the whole of Q8? I had a look at the ans but I don't understand what's going on

Same goes with Q10a)

thanks for the feedback! well basically for 5b) there's not enough information to actually solve for p since it just ends up cancelling but the reason i state it's a positive real constant is because it's probability so pr(a) has to be 0 or greater, but if p=0 things start to break down because for pr(b|a) pr(a) would be 0 and you can't divide by 0 so that's why. 
for 8a) you basically work with the integral so integral of sin is -cos and sub in the bounds. then pull the -1 out the front cuz it's just a constant multiple and then multiplying by 1/h is the same as dividing by h so it ends up being first principles in disguise. so remember f'(x) = limit h->0 (f(x+h) - f(x)) / h so like                  f'(pi/4) = lim h->0 (f(pi/4+h) - f(pi/4)) / h where f(x) is cos(x) so you derive cos(x) and sub in pi/4 to get -(-sin(pi/4)) which is sqrt(2)/2
for 8b) you derive cos(x) and sub in x=pi/4 to get a gradient of -sqrt(2)/2. so you just sub in pi/4 into cos(x) so it becomes cos(pi/4) = sqrt(2)/2 then use the tangent line formula
for 8c) basically since it's a left endpoint estimate, you just take y(0), y(1/2) and y(1) since that will cover your interval with rectangles of 1/2 units. so then you have to add up the rectangles (the width is always 1/2 at the bottom and the length is the value of the function) so 1/2 * y(0) + 1/2 * y(1/2) + 1/2 * y(1). and then use your exact values to calculate it.
for 8d) good thing you mentioned it it's actually a mistake haha... it should just be the integral from 0 to 3/2 of y=sin(pi/3 x) and yeah because the function is increasing, the left endpoint estimate will always under estimate the area as it leaves out parts.
hope i made some sense and was able to help

[MathMethdz99-R]

oh yeah and for 10 i just made it up because when you solve for m you get two values so i just decided to have it be the one where m>0 for simplicity.

[Max Kawasakii]

I had a flick through the exam, it is well written so my praises to you. I just doubled checked the Mathematical Methods study design and Combinations and permutations are no longer being examined; they do however remain as prerequisite knowledge for Specialist. By hand anyway students are no longer required to evaluate (17 3) relating to question 4.b; it's expected however you know how to do this on the CAS.

Could be baseless rambling on my behalf, but something to look into nonetheless.

[Sine]

from what i know there is nothing saying combinatorics/permutations can't come up on exam 1 

which part of the study design says otherwise, I couldnt find it 

[VanillaRice]

from what i know there is nothing saying combinatorics/permutations can't come up on exam 1 

which part of the study design says otherwise, I couldnt find it 

Not sure about VCAA, but a calculation of combinations appeared on my trial (non-VCAA) exam last year.

[Sine]

Not sure about VCAA, but a calculation of combinations appeared on my trial (non-VCAA) exam last year.

permutations won't come up but i think combinatorics can still come up in the form of the binomial distrbution but they would probably max it out at something like combinations include 6 so it's not too taxing.

or leave answer in the form of something like " a(b/c)^d(e/f)^g "

[Max Kawasakii]

permutations won't come up but i think combinatorics can still come up in the form of the binomial distrbution but they would probably max it out at something like combinations include 6 so it's not too taxing.

or leave answer in the form of something like " a(b/c)^d(e/f)^g "

Very valid point indeed, I scanned the study design properly this time sourced from;

http://www.vcaa.vic.edu.au/Documents/vce/mathematics/MathematicsSD-2016.pdf

Combinations are listed Under Unit 2 Methods; AOS 4 Probability and Statistics pg.38; Where they state combinations are included within the topic. However they do not reappear again key knowledge or key skills. This is the contrary for Specialist where they appear on pg45 AOS 2 Arithmetic and Numbers and again on pg 48, where they are included in key knowledge and skills.

I too have found that companies such as MAV and TSM and Hefferman have used them in their past 2016 exams.

Obviously knowing how to apply them can't hurt, and they're something I am fine with. What are your thoughts though? For it is for my class I am worried for as my teachers are under the pretense that VCAA won't be assessing them this year.

[someone000]

For Q8b I think you've mixed your signs the wrong way around. The gradient of y = cos(x) at x = π/4 is -√2/2.

[MathMethdz99-R]

For Q8b I think you've mixed your signs the wrong way around. The gradient of y = cos(x) at x = π/4 is -√2/2.

Oops lol I'll fix it now thanks for that!

[someone000]

All good. Great work, it was quite a challenging exam!