# Thread: Cambridge HSC MX1 Textbook Marathon/Q&A

1. ## Cambridge HSC MX1 Textbook Marathon/Q&A

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.

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

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

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

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

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

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

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

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

5. ## 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)

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

Originally Posted by eyeseeyou
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.

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

Originally Posted by InteGrand
Probably Perms and Combs, judging by popular consensus.
We did Perms and Combs around this time in year 11 :'(

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

Originally Posted by eyeseeyou
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.

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

Originally Posted by Shuuya
We did Perms and Combs around this time in year 11 :'(
Nice! Yeah, most people seem to find combinatorics or binomials questions the hardest.

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

Originally Posted by Shuuya
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

11. ## 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"?

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

Not sure how to do (b)

Thanks!

13. ## 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

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

Originally Posted by leehuan
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

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

Always good to draw a diagram

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

Originally Posted by davidgoes4wce
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

17. ## 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

18. ## 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 betterScreen Shot 2016-04-13 at 11.58.28 PM.png

19. ## 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

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

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

$Is it right to say$

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

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

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

Originally Posted by Paradoxica
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.

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

Originally Posted by davidgoes4wce
EX 4D
Q18 c

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

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

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

$Is it right to say$

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

$=Q(x) (x^2-5)+Q(-x)(x^2-5)+8$
For some people who do not have access to the textbook you should include the original question as well.

Side note good to see you've picked up LaTeX
_______________________________

You missed one step.

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

After that you can draw your conclusion

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

Originally Posted by Paradoxica
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"?
That doesn't look like SHM though...

$Definition of simple harmonic motion: \ddot { x } =-{ k }^{ 2 }{ x }^{ 1 }$
_______________________________________

Part d) looks like it wants to talk about the whole thing. If motion is in a way periodic then you'd probably have to refer to every say 2 seconds.
Part c) should be fine by just finding one case where v>0 and v<0

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

Originally Posted by leehuan
That doesn't look like SHM though...

$Definition of simple harmonic motion: \ddot { x } =-{ k }^{ 2 }{ x }^{ 1 }$
_______________________________________

Part d) looks like it wants to talk about the whole thing. If motion is in a way periodic then you'd probably have to refer to every say 2 seconds.
Part c) should be fine by just finding one case where v>0 and v<0
I should just use elliptic integrals to find the position-time equation...

Also that is a rather bland approach to part c)

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

Originally Posted by Paradoxica
I should just use elliptic integrals to find the position-time equation...

Also that is a rather bland approach to part c)
It is. But I mean, it looks like you got this question out of the HSC. So what did you really expect lol

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

Originally Posted by leehuan
For some people who do not have access to the textbook you should include the original question as well.

Side note good to see you've picked up LaTeX
_______________________________

You missed one step.

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

After that you can draw your conclusion
I'll keep that in mind, didn't want to be rude or anything as the student only posted a link.

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