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STEP Prep Thread 2016 (Mark. II)

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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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Cnoel
Anybody got final answer for the last part of 4? The sum from infinity to negative infinity
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.
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Zacken
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Original post by Gunawardana
Good luck with your Cambridge Offer - I hope you got what you needed (and did better than you expected) :smile:


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 :smile:


This is most likely a very high 2 or a very low 1.
(edited 7 years ago)
Original post by drandy76
Will need a sounding bound while I try wrap my head around group theory doe


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please do... :smile:
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Original post by IrrationalRoot
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?


Yeah, all along the right lines. Reckon you'd pick up 16 marks or so on Q3.
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Zacken
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Original post by IrrationalRoot
Ah I see, I also did parts but then took like a side and a half of crazy manipulations to get the answer lol.


I was considering going along that route but then saw that if I applied the trig sub, the reduction formula fell out in 5 lines. :tongue:
Original post by Zacken
Yeah, all along the right lines. Reckon you'd pick up 16 marks or so on Q3.


Wow that's brilliant, thanks :biggrin:. What was the rest of the solution then if you don't mind? I didn't know where I was going with it lol.
Reply 2208
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Original post by Mathemagicien
Zacken (and myself) got 2 cosech y


Welp did not get that, thank you anyways haha
Original post by Zacken
I was considering going along that route but then saw that if I applied the trig sub, the reduction formula fell out in 5 lines. :tongue:


FFS. I considered the trig sub for a split second and was like nah. Whyyyyyy.

Anyway, I found the induction to be very short. Just a little manipulation of the factorials was all, so that made up for the mass of algebra for (ii) lol.
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Original post by mathsman22
Could someone estimate this please?


13 + 5 + 16 + 15 + Q9 = 49 + Q9 - so a high 2 or low 1 depending on Q9.
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Original post by IrrationalRoot
Wow that's brilliant, thanks :biggrin:. What was the rest of the solution then if you don't mind? I didn't know where I was going with it lol.


I think what I then did was subbed in Q(x) = (x+1)R(x) and worked along there to get a contradiction about the degrees of Q and P but I don't think what I did was correct, so I'm in the dark here as well. :tongue:

And yeah, the induction bit was pretty nice - I took up a page outlining every step because I wanted to ensure full marks on that Q at least. :lol:
Original post by Zacken
Oof, I wish my grades were as good as yours. I really flopped STEP II. Anywho, thanks. Good luck to you.


Np, and thanks :smile:

EDIT : And just to add it's unlikely I've done better than you haha ( and I am still 16 :tongue: )
(edited 7 years ago)
But seriously it's over for me haha. Can we discuss it yet?
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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Oh forgot to tell you that shamika predicts the same like you: 65 for grade 1 and 85 for an S grade.


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Okay sorry been busy how did everyone find it! Would love to know how you all went on.

I surprisingly found it decent, but I cannot for the life of me remember the questions. I think I did Q1,2,3,8 or something like that.
Just realised I took sech to be an ODD function for the whole of Q4. I can't believe this. Properly annoyed now, I won't even get method marks because what I did was so stupid, I subbed x=e^2y to get an equation and then I said replace y with -y and using the fact that sech is odd, you get the result. Will I lose all the marks? :frown:
What would I get with this?

1 - full
2 - did everything up to showing that the minimum distance was whatever (at least I think I got it right, I ended up with T being x = -a).
3 - did part (i), and showed that Q had a factor of (x +1) and that its degree was one more than P's.
7 - showed the first part in what seemed like a bit of a dodgy way, basically just quoting the roots of unity expression from the formula booklet
8 - did (i) and (ii), but verified g(x) by subbing it in rather than deriving it.
12 - full
Original post by Zacken
I think what I then did was subbed in Q(x) = (x+1)R(x) and worked along there to get a contradiction about the degrees of Q and P but I don't think what I did was correct, so I'm in the dark here as well. :tongue:

And yeah, the induction bit was pretty nice - I took up a page outlining every step because I wanted to ensure full marks on that Q at least. :lol:


Yeh i did the induction very clearly outloning 4=2^2 n wverything haha


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Anyone estimate my score/grade please?

Q1- did part i fully (the substitution) but thats it
Q2- completed (thought this was the easiest question on the paper, surprised more people didn't do it, or maybe I'm just better with parabolas than I thought)
Q3- completed
Q5- only had like 5 mins left so wrote out the binomial expansion and a few inequalities in the hope it might be worth some marks
Q6- did up to part ii fine, attempted part iii but don't feel very confident about it and don't think i really proved the conditions were N & S
Q8- did all but the last part however i proved the equations by taking what they said g(x) was and putting it into the equation to prove it worked, which i thought would be ok as they didn't tell you specifically how to show it, but i'm sure there was probably a 'better' way that also made the last part doable

I'm actually quite disappointed with myself, I got the solution to Q2 in under half an hour and got all excited like I could be on to a really good score, then i just kept starting questions and not seeing them through. Poor question choice and lack of time management let me down I think.

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