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

[leehuan]

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

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

 

[leehuan]

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.



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...


_______________________________________

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

 

[Paradoxica]

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

That doesn't look like SHM though...


_______________________________________

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)

 

[leehuan]

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

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

 

[davidgoes4wce]

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

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.

 

[wu345]

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



By the way, thanks for making this thread David

 

[davidgoes4wce]

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

View attachment 33103

By the way, thanks for making this thread David

Your question was

13 (c) In how many ways can one yellow, two red and four green beads be placed on a bracelet if the beads are identical apart from colour? [Hint : This will require a listing of patterns to see if they are identical when turned over.]

To arrange 1 yellow, 2 red, and 4 green objects in a line, the number of possible ways is:
7! / (1! * 2! * 4!)
= (7*6*5*4*3*2*1) / (1 * 2*1 * 4*3*2*1)
= 105

However, since the objects are not in a line but in a circlular way (e.g. on a bracelet), the circle can be rotated to that what appears to be 7 possibilities is actually just 1, i.e. ABCDEFG = BCDEFGA = CDEFGAB = DEFGABC = EFGABCD = FGABCDE = GABCDEF. So instead of 105 possibilities, there are actually 105 divide 7 = 15 ways.

But since you can also FLIP the bracelet, not just rotate it, you'll find that of those 15 possibilities, 3 of them are symmetrical (so flipping them has no effect), and the other 12 are actually just 6 pairs of equivalent possibilities. So the actual answer is 15 - 6 = 3 + (12/2) = 3 + 6 = 9

 

[davidgoes4wce]

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

I had a problem with this question tonight EX 3A, Q 5 (b)







Here is my effort of drawing the displacement-time graph:



What confused me was the answer should the graph distances being accumulated? Is this supposed to be? Im treating the base of the hill at its initial position, the top of the hill as its maximum, and returning back down the hill as back to where it initially started.

 

[InteGrand]

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

I had a problem with this question tonight EX 3A, Q 5 (b)







Here is my effort of drawing the displacement-time graph:



What confused me was the answer should the graph distances being accumulated? Is this supposed to be? Im treating the base of the hill at its initial position, the top of the hill as its maximum, and returning back down the hill as back to where it initially started.

It says that he goes down the other side of the hill, so he doesn't come back to where he starts; his final displacement should be 2 m.

 

[davidgoes4wce]

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

It says that he goes down the other side of the hill, so he doesn't come back to where he starts; his final displacement should be 2 m.

ok thanks, personally felt that question was pretty badly worded but maybe its just me. Could accept something along the lines of 'total distance-time' graph.

 

[dlau]

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

Can someone please help me with question 20

Sent from my iPhone using Tapatalk

 

[jathu123]

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

http://imgur.com/uMddJgF

That's part a. Not entirely sure about part b though

 

[wu345]

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

part b... I think...
I'm not sure that you can just assume the altitudes meet at E
http://i.imgur.com/9qgFLtr.jpg

 

[dlau]

Year 12 Mathematics 3 Unit Cambridge Question &amp; Answer Thread

part b... I think...
I'm not sure that you can just assume the altitudes meet at E
http://i.imgur.com/9qgFLtr.jpg

But isn't AC 5x^2 not 4x^2 in part a

 

[Paradoxica]

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

It is not obvious at all to me that the altitudes intersect on the edge.

(If it did, I would have already used my signature phrase)

 

[leehuan]

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





I've forgotten how to binomial probability completely

 

[InteGrand]

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

I've forgotten how to binomial probability completely

Use standard binomial probability formulas with p = 18/30 if you want to define 'success' as a rainy day, or p = 1 – 18/30 = 12/30, if you want to define 'success' as a fine day.

 

[leehuan]

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

Use standard binomial probability formulas with p = 18/30 if you want to define 'success' as a rainy day, or p = 1 – 18/30 = 12/30, if you want to define 'success' as a fine day.

Didn't work when I tried because I forgot what nCr is

 

[InteGrand]

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

Didn't work when I tried because I forgot what nCr is

n!/(r!.(n-r)!)

n will be 5 because we have 5 days total.

 

[leehuan]

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

Oops, my bad on the wording. I meant what to use as n and r.

Basically, two clumsy attempts whilst being tired weren't correct.

30C3.(3/5)^3.(2/5)^27
+30C4.(3/5)^4.(2/5)^26
+30C5.(3/5)^5.(2/5)^25 which I realised was obviously wrong but

5C3(3/5)^3 (2/5)^2 + 5C4 (3/5)^4 (2/5)^1 + 5C5 (3/5)^5 (2/5)^0. still didn't work