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# STEP 2016 Solutions

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Why bother with a post grad course - waste of time? 17-10-2016
1. (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.
2. I call dibs on 13. It was a gorgeous question. 7 was lovely too
3. 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
4. Am I the only person who did 12? Also, did I make a mistake in not trying 4 or 13?
5. How many marks would one get for the d.e. q without the last bit¿
6. (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.
Attached Images

7. (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...
8. (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
I'm thinking there will be a standard differential equation question, because the one on II certainly wasn't standard.
9. (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?
10. (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

Let me look at Q3 again, from memory I couldn't see how to do the second part immediately
11. (Original post by tridianprime)
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?
i did what riquix wrote
12. q4 solution:
Spoiler:
Show

13. (Original post by shamika)
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.

Let me look at Q6 and Q3 again...
I think you said it was similar to 2009 and had 99 / 70 / 61 (which I'd be ecstatic with) since that might mean I could actually scrape a 1.
14. (Original post by Zacken)
I think you said it was similar to 2009 and had 99 / 70 / 65 (which I'd be ecstatic with) since that might mean I could actually scrape a 1.
70 / 65 would be weird boundaries, with such a narrow range of marks for a 2.
15. Hey,

For the last integral on question 7, I simply divided top and bottom by cos^2(x) leaving (xsec^2(x))/(1+\tanx) using parts, as u = x, v ' as the the rest, it turns out as pi/4(ln2) - previous answer. Giving you the previous answer.

Sorry, LaTeX isn't working for me :/
16. (Original post by sweeneyrod)
70 / 65 would be weird boundaries, with such a narrow range of marks for a 2.
Sorry, I meant 61 - not 65.

...although, STEP II 2015 had 68 for a 1 and 60 for a 2.
17. (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?

Hmm, i thought 1 and 3 were rather easy too. I feel very silly for not attemoting 3. Using induction twice works for the last part of 6, that's what I did. But i was running out of time and the working eas taking far too long so I wrote it in a very haphazard way and I'm probably getting no marks for it
18. (Original post by Zacken)
Sorry, I meant 61 - not 65.

...although, STEP II 2015 had 68 for a 1 and 60 for a 2.
Yeup, i saw that yesterday too. Its a bit odd isnt it?
19. (Original post by shamika)
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

Let me look at Q3 again, from memory I couldn't see how to do the second part immediately
That is too high.
Although they were nice topics. Questions like the DE were hard.
96?,70 is my guess.

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20. All I was doubting myself because Zacken said I didn't originall estimate 99 / 70 / 60 (I actually said 61 instead but whatever).

But I still think that is my best guess to date: 99 / 70 / 60. I'm also not sure comparing only to 2010 onwards is right either. Especially if Q1 and Q3 were easy then I think that is a reasonable guess.

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