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# STEP 2016 Solutions

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1. (Original post by shamika)
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.
I didn't think Q 1 was super easy, and Q 3 required more creativity than typical easy questions. That said, I think your estimates might be slightly too low if anything, I'd say maybe 71-75 for a 1. I don't really know though.
2. Could somebody predict my mark:
I managed question three but my reason for the even case was wrong.
I did the integral question but didn't manage the last integral.
I managed questions 9 and 10.
I did question 12 but got the final part incorrect.
I did the question about approximating the sum of 1/x^2 and 1/x^4 which I think was right.
3. (Original post by shamika)
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.
I hope you're correct. Many thanks!
4. (Original post by Ewanclementson)
Could somebody predict my mark:
I managed question three but my reason for the even case was wrong.
I did the integral question but didn't manage the last integral.
I managed questions 9 and 10.
I did question 12 but got the final part incorrect.
I did the question about approximating the sum of 1/x^2 and 1/x^4 which I think was right.
18, 15, 20, 20, 17, 20 by the sounds of it (if the last question was a full). Certainly an S.
5. Q8 Solution
Attached Images

6. Hmmm... I think I made really strange things at Q6. Attached my solution for the (iv) part

For overall I solved completely Q1, Q3, Q4, Q5. I did this at Q6 and started Q7 but only reached the (i) part.
7. (Original post by Ewanclementson)
Could somebody predict my mark:
I managed question three but my reason for the even case was wrong.
I did the integral question but didn't manage the last integral.
I managed questions 9 and 10.
I did question 12 but got the final part incorrect.
I did the question about approximating the sum of 1/x^2 and 1/x^4 which I think was right.
Q9: Could you go back to page 4 and check if the solution I posted is correct or not? Also, did the question ask for b and c in terms of a, m, M, and u, and NOT R, m, M, and u?
8. What was Q11? I'm sure I did it, but I can't remember what it was.

Edit: Ooh, was it particles? Bullet fired from the top of a tower, target fired from the ground.
9. (Original post by farryharnworth)
What was Q11? I'm sure I did it, but I can't remember what it was.

Edit: Ooh, was it particles? Bullet fired from the top of a tower, target fired from the ground.
Yep
10. I cant find the question paper? Can someone post a link to it please
11. q3 Solution
Spoiler:
Show

(there can't be any repeated roots, because for any root x, f'_n(x) is -(x^n)/n!, which is only 0 for x = 0. But x = 0 is clearly not a root.)

mall mistake in part (iii), the n! should be (n!)^2
12. Seriously, has nobody got a copy of the paper? I want to get my teeth into it over the weekend!
13. Here is my solution to Q10; a real gem of a question (both short and easy).
14. (Original post by StrangeBanana)
q3 Solution
Spoiler:
Show

(there can't be any repeated roots, because for any root x, f'_n(x) is -(x^n)/n!, which is only 0 for x = 0. But x = 0 is clearly not a root.)

mall mistake in part (iii), the n! should be (n!)^2
Exactly how i did the question with explanation on the complex roots aswell with some justification odd degree polynomials have atleast 1 root hence exactly 1 since this has atmost one.

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15. (Original post by physicsmaths)
Exactly how i did the question with explanation on the complex roots aswell with some justification odd degree polynomials have atleast 1 root hence exactly 1 since this has atmost one.
awesum

Yeah I was trying to be succinct in the solution, in the exam I was more careful. I think you might need to mention that there can't be repeated roots, though.
16. \$x\$
17. Anyone willing to estimate my marks?

1) (Curve C1 and C2 one) Done completely.
3) (f_n(x) polynomial one) Got all of it, except at the very end I didn't explain why f_n(x)=0 has 0 roots if n is even and 1 root if odd (I just stated that there's 0 roots if n even and 1 root if n odd).
4) Got all of it except I couldn't find x and tan(theta) in part (iii).
6) (Differential Equation one) Got all of it except part (iii).
8) (Approximating sum from r=1 to r=infinity of 1/r^2 and 1/r^4) Done completely.
9) (Bullet and block mechanics one) Done completely... BUT at the last part, I had b and c in terms of R, m, M, and u. I've heard one person saying the question asked for b and c in terms of a, m, M and u, and multiple people saying it didn't ask for this. Eliminating R in place of a just involved substituting in R = 1/2 * mu^2/a; but I'll assume the question DID ask for b and c in terms of a, m, M and u.
18. Q5 STEP II Solution
Spoiler:
Show

Correction: (1-x)^(m+n) should be (1+x)^(m+n) in part ii
19. Q7
Attached Images

20. Solution to Q12
Attached Images

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