Cambridge HSC MX1 Textbook Marathon/Q&A (1 Viewer)

davidgoes4wce · Feb 21, 2016

Seeing that we have a thread open for Year 11 3 Unit Cambridge, I have decided to open up a thread for Year 12 3 Unit Cambridge for all discussion on questions that students are working on.

I'll kick the ball rolling

EXERCISE 2A
Q5j

Been spending only 3 minutes on this but i got my final answer in radians, not exact value, as required in the question.

$\frac{{2 \ cos^{2} (\frac{2\pi}{5})-1}}{1-2sin^{2} \frac{\pi}{10}}$

$$ My final answer came down to $ \frac{cos({\frac{4 \pi}{5}})}{ cos({\frac{\pi}{5}})}$

davidgoes4wce · Feb 21, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

$I tried to split the $ \frac{4 \pi}{5} $ into 2 parts e.g $ : (\frac{2 \pi}{5}, \frac{2 \pi}{5}), (\frac{3 \pi}{5} , \frac{\pi}{5} ) ,$ when looking at the numerator term to see if terms could cancel somehow$

davidgoes4wce · Feb 21, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

$Dealing with angles $ \frac{2 \pi}{5} $ and $ \frac{4 \pi}{5} $ makes the exact values process a bit harder. Unless there is a shortcut method I am missing.$

Drongoski · Feb 21, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

$\frac {cos(\frac {4\pi}{5})}{cos (\frac {\pi}{5})}= \frac {-cos(\pi - \frac{4\pi}{5})}{cos(\frac {\pi}{5})} = \frac {- cos (\frac {\pi}{5})}{cos(\frac {\pi}{5})}= -1$

eyeseeyou · Mar 11, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Wow, literally no one has commented on this thread

Speaking of year 12 maths topics (for extension 1) which would be the hardest maths topic and why? (e.g. in extension 2, Harder 3U is the hardest maths topic. Not sure why because I have never studied it)

InteGrand · Mar 11, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

eyeseeyou said:
Wow, literally no one has commented on this thread

Speaking of year 12 maths topics (for extension 1) which would be the hardest maths topic and why? (e.g. in extension 2, Harder 3U is the hardest maths topic. Not sure why because I have never studied it)

Probably Perms and Combs, judging by popular consensus.

Shuuya · Mar 11, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

InteGrand said:
Probably Perms and Combs, judging by popular consensus.

We did Perms and Combs around this time in year 11 :'(

ml125 · Mar 11, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

eyeseeyou said:
Wow, literally no one has commented on this thread

Speaking of year 12 maths topics (for extension 1) which would be the hardest maths topic and why? (e.g. in extension 2, Harder 3U is the hardest maths topic. Not sure why because I have never studied it)

Rather than Perms and Combs which many seem to find the hardest, I would probably say either Motion or Binomial - both of which have pretty easy concepts to grasp but the wording of questions can kinda get a bit confusing.

InteGrand · Mar 11, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Shuuya said:
We did Perms and Combs around this time in year 11 :'(

Nice! Yeah, most people seem to find combinatorics or binomials questions the hardest.

eyeseeyou · Mar 12, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Shuuya said:
We did Perms and Combs around this time in year 11 :'(

What the hell, why so early? Probs b/c you go to a top school

Paradoxica · Mar 12, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Will post here anyway since I don't want to open a new thread for just one question.

$\noindent The acceleration of a particle is denoted by $\ddot{x} = -2x^3$. The particle starts out at rest at $x=n^2. \\ $a) What is the initial direction of the particle?$ \\ $b) Find the algebraic equation between $\dot{x}$ and $x. \\ $c) Does the particle change direction?$ \\ $d) Describe the motion of the particle.$

How can you justify the particle changes direction without describing the motion beforehand?

Also, my teacher says you cannot use the phrase "simple harmonic motion".

Would it then be acceptable to instead describe the motion as "oscillatory"?

Shuuya · Apr 13, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Not sure how to do (b)

Thanks!

leehuan · Apr 13, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

cos(2θ)=7/25
2θ=cos^-1(7/25)
But θ = sin^-1(3/5)
So 2sin^-1(3/5) = cos^-1(7/25)

lol

Part a was harder

Shuuya · Apr 13, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

leehuan said:
cos(2θ)=7/25
2θ=cos^-1(7/25)
But θ = sin^-1(3/5)
So 2sin^-1(3/5) = cos^-1(7/25)

lol

.-.

Thanks xD

davidgoes4wce · Apr 13, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Always good to draw a diagram

leehuan · Apr 13, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

davidgoes4wce said:
Always good to draw a diagram

I think it (tfw still don't know Shuuya's gender) got part a) out. But tbh if you just used 1-sin^2(x)=cos(2x) that would've saved the need to draw out the triangle

hedgehog_7 · Apr 13, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Need help with q22 ex 3e motion cambridge yr 12

a particle moves on a line and the table below shows some observations of its positions at certain times

t 0 .....................7.................. 9 ................ 11.... 18
x 0 .......... (not given) ..........(not given) ...... 2 ......... 0

complete the table if the particle is moving with constant acceleration
complete the table if the particle is moving in a simple harmonic motion iwth centre the origin and period 12 seconds.

im confused on how to use this table to find velocity and acceleration? any thoughts thanks

leehuan · Apr 13, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

It was worded too horribly for me to figure it out when I looked at it being as tired as I am.

Here's the question to anyone else free to help formatted better

Screen Shot 2016-04-13 at 11.58.28 PM.png

davidgoes4wce · Apr 14, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

EX 4D
Q18 c

Can get the remainder of 8, just not sure about my working out for the A(x). Q(x) part

$P(x)=Q(x)(x^2-5)+x+4$

$P(-x)=Q(-x)(x^2-5)-x+4$

$Is it right to say$

$P(x)+P(-x)=Q(x)(x^2-5)+x+4 + Q(-x)(x^2-5)-x+4 ?$

$=Q(x) (x^2-5)+Q(-x)(x^2-5)+8$

davidgoes4wce · Apr 14, 2016

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

Paradoxica said:
Will post here anyway since I don't want to open a new thread for just one question.

$\noindent The acceleration of a particle is denoted by $\ddot{x} = -2x^3$. The particle starts out at rest at $x=n^2. \\ $a) What is the initial direction of the particle?$ \\ $b) Find the algebraic equation between $\dot{x}$ and $x. \\ $c) Does the particle change direction?$ \\ $d) Describe the motion of the particle.$

How can you justify the particle changes direction without describing the motion beforehand?

Also, my teacher says you cannot use the phrase "simple harmonic motion".

Would it then be acceptable to instead describe the motion as "oscillatory"?

Do you mind me asking where you got that question from? Also would you happen to have the answer? Just want to compare my answers.

Cambridge HSC MX1 Textbook Marathon/Q&A (1 Viewer)

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