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# STEP 2016 Solutions Watch

1. (Original post by physicsmaths)
Your S boundary is too high since.
When in 2014 it was 95/74
In 2013 it was 100/79

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They're not set as a multiple of each other (or requiring 21 marks between them). I'm saying the best candidates will find it easy but the 1/2 boundary seems to be around 70 because it wasn't quite as easy as some of the easiest papers. I could be way off but think the boundaries are a reasonable indication of that paper
2. (Original post by farryharnworth)
Are you sure that is wrong? That's how I interpreted the question.
It says "The bullet travels a distance b inside the block before coming to rest relative to the block."
I took that to mean "In the time from when the bullet enters the block to when it comes to rest relative to the block, it travels an absolute distance of b."
I did wonder at the time, because I can see both interpretations, but I took that one.
You could be right, I took it to mean that it travels a distance b relative to the block, but I forgot to substract c in the end.

(Original post by YonRamires)

2: complete, except I got a solution x=5 instead of x=4 on part (ii) (apparently i'm not good at adding and substracting one digit ints)
3: complete, except for checking double roots in the even case in the last part)
6: did parts (i), (ii), and (iii), not (iv)
7 (that was the question w/ four parts and integrals right?): only part (i)
9: complete, but in the last part I calculated the path of the bullet relative to the table (so b+c instead of b), so I got the value of b wrong
12: complete
can somebody estimate my marks pls…
3. Zacken I know you must be absolutely sick of going through people's responses and predicting marks, but could you please please do that for me too?
Spoiler:
Show

Q2) I got everything else, but I didn't find the factors of the last equation. I started off, but the algebra became too dense so I left it halfway

Q6) Again I got everything except for the last part. I started a proof by induction for the last bit, but I was running out of time so it was very haphazard, and I don't think it was very coherent

Q7) Full

Q9) Full except I forgot to substitute R and u in terms of of a in the final answer

Q12) The first two subparts were completely correct. I got the first half of the 3rd part completely,but the second half was me using dodgy maths to get the given answer. Part 4 was absolutely pathetic in mathematical terms, but I did write a footnote telling the examiner that I know my answer is wrong and what I was trying to do in english.

Q13) Full

4. (Original post by shamika)
They're not set as a multiple of each other (or requiring 21 marks between them). I'm saying the best candidates will find it easy but the 1/2 boundary seems to be around 70 because it wasn't quite as easy as some of the easiest papers. I could be way off but think the boundaries are a reasonable indication of that paper
You mentioned a while ago that you didn't do the DE question when deciding the boundaries and just saw it and assumed it was easy. I feel like first parts were easy but then (iii) required a bit more work and overall the question would kind of take longer time to get through. I don't know if it is only me, I think I spent a bit over 30 minutes on it and I usually do DE questions a bit faster than other questions.

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5. (Original post by Insight314)
You mentioned a while ago that you didn't do the DE question when deciding the boundaries and just saw it and assumed it was easy. I feel like first parts were easy but then (iii) required a bit more work and overall the question would kind of take longer time to get through. I don't know if it is only me, I think I spent a bit over 30 minutes on it and I usually do DE questions a bit faster than other questions.

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I have literally only seen a handful answer that part.

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6. (Original post by physicsmaths)
I have literally only seen a handful answer that part.

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What do you mean?

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7. (Original post by krishdesai7)
Zacken I know you must be absolutely sick of going through people's responses and predicting marks, but could you please please do that for me too?
Spoiler:
Show

Q2) I got everything else, but I didn't find the factors of the last equation. I started off, but the algebra became too dense so I left it halfway

Q6) Again I got everything except for the last part. I started a proof by induction for the last bit, but I was running out of time so it was very haphazard, and I don't think it was very coherent

Q7) Full

Q9) Full except I forgot to substitute R and u in terms of of a in the final answer

Q12) The first two subparts were completely correct. I got the first half of the 3rd part completely,but the second half was me using dodgy maths to get the given answer. Part 4 was absolutely pathetic in mathematical terms, but I did write a footnote telling the examiner that I know my answer is wrong and what I was trying to do in english.

Q13) Full

16 + 12 + 20 + 18 + 12(?) + 20 > 95, maybe an S.

(Original post by Insight314)
What do you mean?
Very few people successfully did (iv) of Q6.
8. (Original post by Zacken)
16 + 12 + 20 + 18 + 12(?) + 20 > 95, maybe an S.

Very few people successfully did (iv) of Q6.
Nah, I skipped that one. I thought physicsmaths was referring to (iii). How many marks was that anyway? I assume 5 max but I have no idea how much work had to be done for it.

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9. (Original post by Insight314)
Nah, I skipped that one. I thought physicsmaths was referring to (iii). How many marks was that anyway? I assume 5 max but I have no idea how much work had to be done for it.

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Around 7.

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10. (Original post by physicsmaths)
Around 7.

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Oh damn. I skipped that one because I assumed it wasn't that many marks and I was already 30 minutes into the question. Agh..

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11. (Original post by Zacken)
16 + 12 + 20 + 18 + 12(?) + 20 > 95, maybe an S.
Thanks so much I sincerely hope that you do very well, and I'm absolutely sure you're going to ace STEP III
12. q9 Solution:

Spoiler:
Show
Part (i):

KE lost by bullet is (mu^2)/2, work done on it by block is aR, hence

aR = (mu^2)/2 => a = (mu^2)/2R

Part (ii):

Let the common speed of the bullet and block afterward be v. Then:

KE gained by block = (Mv^2)/2

and the bullet is providing a force R on it (Newton's Third Law) over a distance c, hence work done = cR, hence:

cR = (Mv^2)/2 => c = (Mv^2)/2R (1)

For the bullet:

KE lost = (mu^2)/2 - (mv^2)/2,

and the bullet's travelled b + c subject to a resistive force R, hence work done is (b+c)R, hence:

(b+c)R = (mu^2)/2 - (mv^2)/2 => b+c = (mu^2)/2R - (mv^2)/2R (2)

Finally, conservation of momentum:

mu = (m+M)v => v = mu/(m+M)

We can plug that into (1) and use the expression from (i) to get:

c = amM/(m+M)^2

and use (2) similarly to get:

b = aM/(m+M)
13. Wish I could answer these questions
14. (Original post by Insight314)
You mentioned a while ago that you didn't do the DE question when deciding the boundaries and just saw it and assumed it was easy. I feel like first parts were easy but then (iii) required a bit more work and overall the question would kind of take longer time to get through. I don't know if it is only me, I think I spent a bit over 30 minutes on it and I usually do DE questions a bit faster than other questions.

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But conversely I thought 3 was harder than it was, which is why I'm sticking to the original estimate. I'm not doing anything rigorous: I'm going by gut feel after seeing the questions for about 20 minutes and figuring out how to do them. Dont take what I'm saying as gospel, but I haven't seen anything yet to make me move from that estimate. As I keep saying I could be completely wrong!
15. (Original post by riquix)
Q9 from STEP 2. If someone could verify this I'd be grateful. About 90% certain I got it right.
lol sorry didn't see that :PP nice to have the two different approaches tho
16. (Original post by mathsman22)
Anyone have a solution for 9?
I posted one. Page 4 I think

Edit: so did strangebanana.
17. STEP II Q11 - See attached.
Attached Images
18. solution.pdf (70.7 KB, 157 views)
19. Alternate solution to STEP II Q7 (iv).
Attached Images
20. STEP_2_2016_AlternateQ7.pdf (55.0 KB, 128 views)
21. (Original post by Farhan.Hanif93)
STEP II Q11 - See attached.
How many marks do you think the last part will be? (the alpha>beta part)
22. (Original post by matthewdjones)
How many marks do you think the last part will be? (the alpha>beta part)
I'd expect around 5 or 6, as most of the question comes together in that last part and it's arguably the trickiest part. Although, I haven't really looked at the mark schemes that they've released in recent years so make of that what you will.

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