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# STEP Prep Thread 2016 (Mark. II)

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1. (Original post by EricPiphany)
Just do maths that you'll never see on a STEP paper again. I want to learn some group theory over the summer.
Above average minds think alike

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2. (Original post by jneill)
we?

nigel garage
3. (Original post by jneill)
we?

We, the people of Britain, voted for a Brexit

You are, I presume, an advocate for democracy, in which case you are partially responsible for this travesty too
4. (Original post by Mathemagicien)
There won't be a future, we voted for Brexit
lol what BS, we have to make this work. The apocalypse preachers will come around eventually.
5. Might as well attempt a PhD now that We've pulled out of the EU, failing that, McDonald's?

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6. I find it so hard to estimate my own grade without bias, so would someone mind?

Q1: Did part (i), somehow couldn't get part (ii) to work and got to integral of cos^(2n)(u) = integral of cos^(2n-2)(u) - integral of cos^(2n-2)(u)sin^2(u) (or something like that - not even sure that's in the right direction so i might not get any for this part) Then did the last part assuming the result from part (ii) but i was in a hurry and didn't do it by induction, just wrong In in terms of In-1, so In in terms of In-2, and repeated 'till In in terms of I1 which gives the result (might give no marks since it's not really induction)

Q3: I did fully assuming my argument works but i made little errors along the way that didn't affect the validity of the argument as a whole (like a sign error when adding fractions, but it didn't change the degrees of the polynomials), or writing that lim(x->-1) of 1/(1+x) = +-inf when it should just be undefined. Also I said some stuff which might've needed some justification: that if Q'(x) has a factor of (1+x)^2 and Q(x) has a factor of (1+x), then Q(x) has a factor of (1+x)^3. Idk how harshly they'll penalise this stuff

Q4: I did the first part fully and changed the sech(2ry)sech(2(r+1)y) sum into a similar form and broke it up into two simpler fractions but didn't actually get around to evaluating anything

Q5 (i think it's Q5 i'm not sure - the one which was about primes between r and s): Did this one fully.

Q8: I did it until h(x), there i found that with M(x) = 1/(1-x), M(M(M(X))) = -x, and found its values for iterations up to 6 (it then repeats). Played around, cancelled some h(x) things by using that and h(-x), but in the end nothing came from it.

Thank you
7. Will GBs be low for this paper? I did 3 fulls (which are most likely not fulls) and 3 partials, one terrible, two possibly terrible...
8. Let me use a nice analogy. STEP III was to me as the EU referendum was to David Cameron.
9. (Original post by drandy76)
Above average minds think alike

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I'm only very slightly above average. You most probably shouldn't associate yourself with me
10. (Original post by IrrationalRoot)
Will GBs be low for this paper? I did 3 fulls (which are most likely not fulls) and 3 partials, one terrible, two possibly terrible...
Having sat this and last years in exam conditions(so people can't say ur bias blah blah blah).
This year was harder, Induction was harder. Q3 was probably the easiest and Q8 to pick up he most marks other then that the questions weren't easy to pick up marks on. I guess
62 for Grade 1, 85 for an S. I was on the money with my predictions last year. Tbh it could stump lower then this.

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11. (Original post by physicsmaths)
Having sat this and last years in exam conditions(so people can't say ur bias blah blah blah).
This year was harder, Induction was harder. Q3 was probably the easiest and Q8 to pick up he most marks other then that the questions weren't easy to pick up marks on. I guess
62 for Grade 1, 85 for an S. I was on the money with my predictions last year. Tbh it could stump lower then this.

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Why did people find Q3 so easy? I couldn't do part (ii)... This was the P(x),Q(x) question right? Regardless any ideas how many marks I'd get for just doing (i) of Q3?
Btw those predictions are reassuring .
12. (Original post by IrrationalRoot)
Why did people find Q3 so easy? I couldn't do part (ii)... This was the P(x),Q(x) question right? Regardless any ideas how many marks I'd get for just doing (i) of Q3?
Btw those predictions are reassuring .
Part i) should get 10-12.

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13. Could someone estimate this please?

1: Did (i) and (iii) but didn't do part (ii) (the inductive step)

2: Did part (i) only

Series question with x^r (can't remember the number): did everything up to finding the final sum to infinity

8: Couldn't do the final part involving h(x), did the rest

9: Got up to the equation of motion but couldn't find the approximation to show SHM

Thanks
14. (Original post by EricPiphany)
I'm only very slightly above average. You most probably shouldn't associate yourself with me
Will need a sounding bound while I try wrap my head around group theory doe

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15. (Original post by jweo)
Q1: Did part (i), somehow couldn't get part (ii) to work and got to integral of cos^(2n)(u) = integral of cos^(2n-2)(u) - integral of cos^(2n-2)(u)sin^2(u) (or something like that
I swear I'm the only one who didn't have use single trig function whatsoever in their solution to (ii)...
16. (Original post by physicsmaths)
Part i) should get 10-12.

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Ok thanks, and what was the method for (ii)? I differentiated and deduced that Q(x) must have a factor of 1+x and further deduced that degP=degQ-1 (not sure if correct, pretty sure pointless anyway). Any marks at all for that?
17. (Original post by IrrationalRoot)
I swear I'm the only one who didn't have use single trig function whatsoever in their solution to (ii)...
No
I didnt either. I just did parts once.

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18. Anybody got final answer for the last part of 4? The sum from infinity to negative infinity
19. (Original post by physicsmaths)
No
I didnt either. I just did parts once.

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Ah I see, I also did parts but then took like a side and a half of crazy manipulations to get the answer lol.
20. (Original post by Gunawardana)
Good luck with your Cambridge Offer - I hope you got what you needed (and did better than you expected)
Oof, I wish my grades were as good as yours. I really flopped STEP II. Anywho, thanks. Good luck to you.

(Original post by jweo)
Q1: Did part (i), somehow couldn't get part (ii) to work and got to integral of cos^(2n)(u) = integral of cos^(2n-2)(u) - integral of cos^(2n-2)(u)sin^2(u) (or something like that - not even sure that's in the right direction so i might not get any for this part) Then did the last part assuming the result from part (ii) but i was in a hurry and didn't do it by induction, just wrong In in terms of In-1, so In in terms of In-2, and repeated 'till In in terms of I1 which gives the result (might give no marks since it's not really induction)
Don't think you'd get marks for the non-induction, but you were very close with your reduction formulae, all you needed to do was use parts with dv = sin x cos^(2n-2) x and u = sin x.

I'd say 14 here.

Q3: I did fully assuming my argument works but i made little errors along the way that didn't affect the validity of the argument as a whole (like a sign error when adding fractions, but it didn't change the degrees of the polynomials), or writing that lim(x->-1) of 1/(1+x) = +-inf when it should just be undefined. Also I said some stuff which might've needed some justification: that if Q'(x) has a factor of (1+x)^2 and Q(x) has a factor of (1+x), then Q(x) has a factor of (1+x)^3. Idk how harshly they'll penalise this stuff
16/17 here.

Q4: I did the first part fully and changed the sech(2ry)sech(2(r+1)y) sum into a similar form and broke it up into two simpler fractions but didn't actually get around to evaluating anything
12/13 marks here.

Q5 (i think it's Q5 i'm not sure - the one which was about primes between r and s): Did this one fully.
20.

Q8: I did it until h(x), there i found that with M(x) = 1/(1-x), M(M(M(X))) = -x, and found its values for iterations up to 6 (it then repeats). Played around, cancelled some h(x) things by using that and h(-x), but in the end nothing came from it.
Should be 16/17-ish. (btw, m^(3)(x) = x, not -x).

Thank you
This is most likely a very high 2 or a very low 1.

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