STEP II 2012 discussion thread

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Reply 20

TheMagicMan

Original post by ben-smith

I have solution to the last part but it seems way too simple.

I just ran out of time. I might have a crack at the last part now as I like having full sets of pure :biggrin:

Reply 21

TheMagicMan

Original post by Peter8837

The first part of Q1...

Oh sorry...it was 15

Reply 22

Farhan.Hanif93

Original post by TheMagicMan

I wasn't really sure what they wanted in the last part to be honest

I got

(1+1/n)^n < e< (1+1/n)^{n+1/2}

1 < e(1+1/n)^{-n}< (1+1/n)^{1/2}

The RHS has a limit of one so want we want follows by the squeeze theorem...the real question is is there a simpler way (tbh I'm never quite sure how STEp wants you to approach limits)

You could have got it directly I think. I don't think there's anything wrong with saying that e is sandwiched between two quantities with the same limit so those limits must both be e. It is just STEP after all, don't need to do much other than giving a reasonable written explanation.

Reply 23

SParm

Original post by TheMagicMan

I wasn't really sure what they wanted in the last part to be honest

I got

(1+1/n)^n < e< (1+1/n)^{n+1/2}

1 < e(1+1/n)^{-n}< (1+1/n)^{1/2}

The RHS has a limit of one so want we want follows by the squeeze theorem...the real question is is there a simpler way (tbh I'm never quite sure how STEp wants you to approach limits)

I said n + 0.5 approaches n as n goes to infinity and so the two outer expressions tend towards each other so they both definitely tend towards e because e is in the middle of them with regards to that inequality. Is that a bit too simplistic?

Original post by TheMagicMan

Wasn't that a show that question? 55 wasn't it?

I got 15 for the first part. 55 was the proof on the second part.

Reply 24

TRLMaths

Well... I'll give my run down I suppose. Hopefully someone can give me a little confidence after reading everyone else's.

Q1 : Did it all, I think.
Q2 : I think i missed a +c off one of the solns in part i), and may have got a little jumbled on the last part. I got 4 solutions for p(x). I think they were 1/2x^2, -x^2, 1/2x^2 + 1 and 2-x^2.
Q3 : Again, i got to the end of this with the correct answer.
Q4 : I showed the (k+1) inequality and did the deduction. I'm thinking only a couple of marks.
Q5 : First sketch was fine. Other 2 were also fine, although I think i drew a small part of the graph above the axis when it should have been below. I'm thinking 17?
Q8 : I showed the very first inequality.

Any ideas on a total? :')

Reply 25

TheMagicMan

Favourite Question? Mine was 8...thought it was really nice. My least favourite was 1 because it was just plain ugly (closely followed by 6 but only cause 6 was a stock olympiad problem and I've seen way too many of those :sick:

)

Reply 26

LucasJ94

Found it difficult :/

Started on 1, but it just wasn't working out for me and I couldn't get the formula for the coefficient, I'm not even sure why I went for it, it looked simple, but binomial is never a hot spot for me in STEP.

After that I got 8 out to near the end, but I couldn't complete the second proof :/. (I did go through and do the final part)

I got 2 to the end, but I feel like I made a silly algebra slip on the last part.

I got 3 to the last part of the final integration, but I couldn't find the form of the function.

I rushed through 5 near the end, because it looked simple, I'm sure I overlooked some details but I think I did ok.

And for the first time ever in STEP II, I did a mechanics question (found the pure too hard, not enough trig/calculus/differential stuff), and I finished 9 with the required solution.

Really hoping that's good for a 1 :/, any ideas on what I'm looking at?

Reply 27

DFranklin

Original post by ben-smith

I have solution to the last part but it seems way too simple.

It's simple enough that I think it's obviously OK.

The hard bit was getting the result before the last part, I think.

Reply 28

Intriguing Alias

Original post by Farhan.Hanif93

Responding to you here, I believe you were supposed to consider

\ln \left(1 + \dfrac{1}{2y}\right) - \ln \left(1 - \dfrac{1}{2y}\right)

from the start.

That's what I did.

Hmm, thinking probably a high 2 for me, how many marks do you (anyone, not farhan specifically) think I would've got for doing both sketches on the graph sketching question correctly but not writing the 3 stationary points on the second graph?

Other than that I got 2 fulls, 1 full with a small arithmetic error and half way through the last part of the integral question (so 12 marks-ish for that one)?

Oh and I personally found it harder than 2011 BUT that's probably largely down to exam pressure.

I predict boundaries to be somewhere between 2010 and 2011 :ahee:

but seriously around 68 is my guess.

(edited 11 years ago)

Reply 29

SParm

Original post by TheMagicMan

)

I think you can probably tell given how quickly my solution for 8 was up that it was my favourite as well :P

Reply 30

romtom55

Did Qn1 fully but messed up the coefficient of X^66

got middle integral out in 3

showed very first inequality in 4

got pretty much all of 5 but think i messed up the final graph a bit--rushing :frown:

got 8 pretty much all the way there.

Overally, not that happy :frown:

normally get 4 full solutions out pretty comfortably.... think this was even harder than Jun 11, but maybe exam pressure got to me :/

Any ideas what this could give me?

(edited 11 years ago)

Reply 31

TheMagicMan

Original post by SParm

I think you can probably tell given how quickly my solution for 8 was up that it was my favourite as well :P

I used three inductions in it and I love inductions so :biggrin:

What do you think you got score wise?

(edited 11 years ago)

Reply 32

Peter8837

Original post by DFranklin

It's simple enough that I think it's obviously OK.

The hard bit was getting the result before the last part, I think.

What do you think of the paper and the grade boundaries?

Reply 33

DFranklin

Original post by Peter8837

What do you think of the paper and the grade boundaries?

My honest feeling is it was average to slightly easier than average. Like last year, there were some attractive applied questions and people sticking exclusively to pure may have been forced to tackle some of the nastier questions.

Reply 34

Peter8837

Original post by DFranklin

And grade boundaries...? Would 64/65 be enough for a 1?

Reply 35

SParm

Original post by TheMagicMan

I used three inductions in it and I love inductions so :biggrin:

What do you think you got score wise?

I personally preferred my methods in that particular question :colondollar:

In terms of score: full solutions in 3 and 8
Got everything but the formula for the co-efficient when the power of x was in the form of 6n - 3 for question 1. Did most of 2 but f-ed up the algebra right at the end for both p(x) bits. And I got everything but the middle inequality proof for 4 with the "1/y".

So: 20 + 20 + 16 + 12 + 14 maybe? 82 I'm guessing? I don't really know. Do you think that would be an accurate appraisal?