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# STEP 2016 Solutions

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1. General thoughts on the difficulty? I thought it was fairly average, no obvious gift questions but quite a few questions that it was easyish to get started with.
2. I think I've got two ~fulls (Q3 and Q12), significant chunks of Q1, Q7 (I think that was the integration one?), and the differential equation question, and 2-3 marks on Q5. On the integration, I did everything up to getting an integral of 1/cos x + sin x + 1 in the last part, so hopefully that will be 15ish, and on d.e. I did everything up to the last part. Hopefully that'll be a 1.
3. (Original post by sweeneyrod)
I got to your last line, but couldn't get any further.
before you use the double angle formulae you can just divide through by (cos)^2 and then use sub u = tanx i think
4. (Original post by sweeneyrod)
General thoughts on the difficulty? I thought it was fairly average, no obvious gift questions but quite a few questions that it was easyish to get started with.
Slightly easier then last year. I guess
95/70 for S/1.
I was horrified tbh, no vectors and geometry set me back massively. ****inf ********.

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5. (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?
Sorry, what was q3 again? Was that the f_n(x) one and proving that there are one or no solutions.

Also, which one was q6? I thought q6 was the DE one but I may be completely wrong.

On another note, how did people find the question where for the last part you had to find tan(theta) and x given y =(3+sqrt(7))/2, or something like that.
6. Q2 STEP II Solution
Attached Images

7. (Original post by tridianprime)
Sorry, what was q3 again? Was that the f_n(x) one and proving that there are one or no solutions.

Also, which one was q6? I thought q6 was the DE one but I may be completely wrong.

On another note, how did people find the question where for the last part you had to find tan(theta) and x given y =(3+sqrt(7))/2, or something like that.
Yep, that was Q3. And Q6 was the DE, the last part of Q6 was the bit about y_(mn).
8. (Original post by physicsmaths)
Slightly easier then last year. I guess
95/70 for S/1.
I was horrified tbh, no vectors and geometry set me back massively. ****inf ********.

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I was actually sad about no vectors, because I did some vectors questions the day before and felt super prepared.
9. For the last integration I found a neat trick, split 1/cosx(cosx+sinx) into (sinx-cosx)/cosx + 2cosx/(sinx+cosx)
10. (Original post by tridianprime)
Sorry, what was q3 again? Was that the f_n(x) one and proving that there are one or no solutions.

Also, which one was q6? I thought q6 was the DE one but I may be completely wrong.

On another note, how did people find the question where for the last part you had to find tan(theta) and x given y =(3+sqrt(7))/2, or something like that.
i liked it, what was your answer?
11. (Original post by riquix)
Attachment 551619Attachment 551621Attachment 551623Attachment 551625Q9 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?
12. Q1 Solution
13. Q3 was beautiful.

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14. (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]?
15. (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.
16. (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.
17. (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?
18. (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).
19. (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?
20. (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.

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