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STEP 2016 Solutions

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Original post by riquix
page 1.JPGpage 2.JPGpage 3.JPGpage 4.JPGQ9 from STEP 2. If someone could verify this I'd be grateful. About 90% certain I got it right.




By a completely different method, I got the same answers for a and c, but [my b] is [your b] + [our c]
I think you put b as the distance the bullet moves relative to the block, and I put it as the absolute distance the bullet moves.
I remember being unsure which it wanted, because the question said b was the distance the bullet traveled before coming to rest relative to the block.
What do people think?
Edit: Also, did it want b and c in terms of a? Arrrgh

And side note, anybody have a question paper?
(edited 7 years ago)
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IMG_1982.JPGIMG_1983.JPGIMG_1984.JPGIMG_1985.JPGIMG_1986.JPGQ1 Solution
Q3 was beautiful.


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Original post by farryharnworth
By a completely different method, I got the same answers for a and c, but [my b] is [your b] + [our c]
I think you put b as the distance the bullet moves relative to the block, and I put it as the absolute distance the bullet moves.
I remember being unsure which it wanted, because the question said b was the distance the bullet traveled before coming to rest relative to the block.
What do people think?

And side note, anybody have a question paper?


Wasn't b 'the distance the bullet moves in the block'? In that case, it would be [your b] - [our c]?
Original post by Zacken
Yep, that was Q3. And Q6 was the DE, the last part of Q6 was the bit about y_(mn).


I am a bit confused - was q6 really that difficult. I have possibly got myself confused but I thought that you just repeated the previous method and showed that the expression you obtain for applying (*) to y_n(Y_m(x)) = m^2n^2, which can be done by subbing in the dy/dx values you can obtain from (*) when applied using just y_n(y_m)) and y_m.
Original post by riquix
Wasn't b 'the distance the bullet moves in the block'? In that case, it would be [your b] - [our c]?


Honestly I'm not sure. I think the wording was unclear, but maybe it would turn out that I was just panicking a bit at the time if I read it again.
Regardless, there must be some credit for either answer.
Original post by gasfxekl
i liked it, what was your answer?


Let's just say I didn't like it. I did a foolish thing in the first part where to show that y^2 + 1 >= I just said we can choose theta to be 0 and hence y^2 >=. I realised this was completely stupid when I then had to find tan(theta).
I always thought deduce meant to use the previous part but I now think that is hence.

How did you go about deducing the y^2 + 1 >= part?
Original post by computerkid
For the last integration I found a neat trick, split 1/cosx(cosx+sinx) into (sinx-cosx)/cosx + 2cosx/(sinx+cosx)

Yeh, that's what I did, or you could split it to sin(x)/cos(x) + (cos(x)-sin(x))/(cos(x)+sin(x))= tan(x) +tan(pi/4-x).
Reply 108
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Original post by farryharnworth
Honestly I'm not sure. I think the wording was unclear, but maybe it would turn out that I was just panicking a bit at the time if I read it again.
Regardless, there must be some credit for either answer.


Hmmm. Also, I didn't see that at the end of part (ii) it asked for b and c to be in terms of a, m, M and u (i.e. that you had to eliminate R). I left both b and c in terms of m, M, u and R. How many marks do you think I'd lose for this?
Original post by tridianprime
Let's just say I didn't like it. I did a foolish thing in the first part where to show that y^2 + 1 >= I just said we can choose theta to be 0 and hence y^2 >=. I realised this was completely stupid when I then had to find tan(theta).
I always thought deduce meant to use the previous part but I now think that is hence.

How did you go about deducing the y^2 + 1 >= part?


need to resee the question, but when you rearranged it it was equivalent to a square being greater or equal to zero - (ycostheta+sintheta)^2 or something.
Original post by riquix
Hmmm. Also, I didn't see that at the end of part (ii) it asked for b and c to be in terms of a, m, M and u (i.e. that you had to eliminate R). I left both b and c in terms of m, M, u and R. How many marks do you think I'd lose for this?


Before looking at the solutions you posted, I didn't know that either - I'm in the same boat there. I'm not so good at judging mark distribution stuff though, so no idea.
I call dibs on 13. It was a gorgeous question. 7 was lovely too
Any predictions for STEP 3 after seeing STEP 1/2?

There weren't really any geometry or vectors questions on STEP 2, so I'm worried STEP 3 will be like the 2013 paper - almost all vectors/complex numbers :frown:
Am I the only person who did 12? Also, did I make a mistake in not trying 4 or 13?
How many marks would one get for the d.e. q without the last bit¿
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Original post by tridianprime
Let's just say I didn't like it. I did a foolish thing in the first part where to show that y^2 + 1 >= I just said we can choose theta to be 0 and hence y^2 >=. I realised this was completely stupid when I then had to find tan(theta).
I always thought deduce meant to use the previous part but I now think that is hence.

How did you go about deducing the y^2 + 1 >= part?


Missed out the iff symbols in the picture. Also missed the >= 0 in the 3rd line hahaha.
(edited 7 years ago)
IMG_1987.JPG93.9KB
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Original post by farryharnworth
Before looking at the solutions you posted, I didn't know that either - I'm in the same boat there. I'm not so good at judging mark distribution stuff though, so no idea.


:////// I got told by one person that the question asked for b and c in terms of a. No-one else can verify this. It seemed strange to me that they'd ask for b and c in terms of a, since they arise from two completely different scenarios (fixed block, moving block), but the solution looks quite nice when R is eliminated, so I'm not sure...
Original post by ln(sec(x))
Any predictions for STEP 3 after seeing STEP 1/2?

There weren't really any geometry or vectors questions on STEP 2, so I'm worried STEP 3 will be like the 2013 paper - almost all vectors/complex numbers :frown:


I'm thinking there will be a standard differential equation question, because the one on II certainly wasn't standard.
Original post by gasfxekl
need to resee the question, but when you rearranged it it was equivalent to a square being greater or equal to zero - (ycostheta+sintheta)^2 or something.


I obtained (ycostheta + sintheta)^2 >= the expression on the RHS(?)
(via the discriminant of the original equation in x)
and then for the next part it said deduce the same for y^2 + 1 >=.

Do you mean rearrange from the original equation again?
Original post by Zacken
Q1 and 3 were trivial. Q6 was near impossible. I've heard of only 1 person managing the last part of Q6 out of 30 or so of the more able people. Any guesses for the mark distribution of Q6?

Edit to add: you've said it was on the easier side and then given lower boundaries for a 1 than 2010-2014?


I must've meant 99 / 75 / 65 (I can't find the PM I sent to Insight on this, which had my best estimate at the time). I can only remember the 99 boundary as that was the one I spent the most time estimating.

Q6 I went "differential equations" and hence easy :tongue:

Let me look at Q3 again, from memory I couldn't see how to do the second part immediately :colondollar:
(edited 7 years ago)

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