STEP III 2011 Discussion Thread

It's that time again. How did it go for everyone else? Here are the three that I managed... My fragments were pretty terrible outside these three, though. That paper was definitely not suited to my strengths. Couldn't save myself with the applied questions either. :s-smilie:

It was about as hard as the 2010 paper, in my opinion, except there were more questions that I actually liked on there...

Q1 - Differential equations

Q6 - Four integrals

Q7 - Square roots of consecutive numbers

Hope you guys had better luck than I did! :erm:

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Reply 1

Zuzuzu

So, after monday's fiasco, I was determined to go in and get a decent number of solutions out for this - whilst remembering the advice I'd been given to stay calm throughout and not get too wound up if something didn't initially work. Maybe, as it turned out, I was too calm.

I opened the paper straight to the applied section in the hope of finding something I could get out with just M1, M2 and S1... No luck there, although q10 did look appealing for a few seconds before seeing that the string received an impulse, rather than a push or some other standard force. I suppose I could have attempted it with A2 physics and a bit of lateral thinking, but deemed it not worth the risk in the end. Now I went straight back to the pure and question 1 was the first that immediately caught my eye (well, naturally, but you know...), and after a minute of thought I could see straight through it and was feeling happy. After that, 6 became the focus of my attention and eventually I managed to find two pairs of integrals that I could see were equivalent and noted them down before moving back to continue browsing the paper... Then on, 2, 3 and 5 looked like I might be able to get a little stuck into them, but I wasn't feeling too confident about the paper on the whole.

The first question I did was 1 and after some careful differentiating, collecting of like terms (and a little panic when I forgot a +c and didn't have it in the required form), it fell out after about 45 minutes. Now, an hour and 5 into the exam, I almost began to panic again after only having one solution out and swiftly moved to question 6. The first two integrals that I showed were equivalent were fairly standard and were quite simple to see by using the definition of hyperbolics. Finding a link between these two pairs seemed to have stumped me for a while, until I considered the typical t substituion for the log and artanh integrals. I was delighted to see the limits fell out as they should have done and proceeded to show equivalence for all of the 4, as required. Now, here's where things start to go down hill...

I revisited 2, 3 and 5 to see if I could see anything extra from the questions - no luck, and there was only an hour left. So I ploughed on into 2 with the hope of something falling out if I stuck at it for long enough (and because I could vaguely remember a proof for the irrationality of the nth root of 2). The first bit was probably the hardest part of the question, actually, but stupidly, I didn't realise that if all of the roots were integers and the leading co-efficient was 1, all roots divided the constant term... I proved that the only root of the equation in part ii) was not an integer graphically and by considering the interval [-2, -1], and hence it was not rational. The final part was where I became unstuck, and obviously I realised that my graphical approach was obviously not what they were looking for in the last part. Again, with only half an hour left, I chose to keep it as it was, because it did show what they wanted albeit in a wrong way... I eventually settled on rearranging the equation to be x^n - x = 4x - 7, and then writing some piss weak and likely invalid statement about divisors of the LHS and RHS, not expecting any marks for that...

The last 10 minutes saw a rushed start to question 3, and getting a and b to resemble something that reminded me of a vectors question for some reason, but with time waning a way, I was too rushed to make any decent progress into something that looked quite standard.

Overall, a fair paper, and it's was timekeeping this time that made it turn out as it did. No complaints at all here.

Reply 2

Phil_Waite

I found it a lot better than STEP II, I managed to get four solutions. Here's the paper:

(edited 12 years ago)

STEP III 2011.pdf206.2KB

Reply 3

Slowbro93

I hated the paper, felt similar to last years

Reply 4

jameswhughes

It went better than Monday, 3 good solutions and two partial ones... hard to say what mark I'll get though.

Reply 5

anttooking

I am worried I have done the whole of 2 Wrong. Is it me or are part ii,iii just trivial when related to the first part?

Reply 6

LtCommanderData

I did really awfully. Only finished one question. At least I managed three of them on STEP 2 :frown:

I think I went wrong by giving up on the questions too soon, I probably could have done more but I was so tired, and I don't actually need STEP for anything, that I didn't persist enough

Reply 7

username219321

Looks fairly normal at first glance - going to do question 2 now as it looks interesting

Reply 8

Zuzuzu

Original post by anttooking

I am worried I have done the whole of 2 Wrong. Is it me or are part ii,iii just trivial when related to the first part?

That's what I thought after revisiting the paper last night. The first bit was definitely harder than the following parts of the question.

Reply 9

Slowbro93

Did all of 6, half of 1, most of 7, half of 3 and beginning bits of 2 and 8

Overall, I think I have half marks, which I hope is a 1

Reply 10

anttooking

Original post by Zuzuzu

That's what I thought after revisiting the paper last night. The first bit was definitely harder than the following parts of the question.

My answers to ii and iii where literaly like: let an-1,an-2... a2 = 0 ... Hense result. With a bit more waffle :smile:

Reply 11

Schnecke

Well I completed 1, 2, 6, 7 but now realise I messed up the last part of 1 and the first part of 2. Made brief attempts at 3, 4, and 8 but didn't really get anywhere.

A much more positive experience than Monday all round however.

Reply 12

Piecewise

Well, it went significantly better than II for me; that's all I've to say! :tongue:

I took heavy approach to 6 in the sense that I kept manipulating V:

Heartless Assessment

Without evaluating any of them explicitly, show that the following integrals are all equal

\displaystyle \begin{aligned} & T =\int_{1/2}^{1/3}\frac{\tanh^{-1}{t}}{t}\;{dt} ~~~~~~~~~~~~~~~~~ U = \int_{\ln{2}}^{\ln{3}}\frac{u}{2\sinh{u}}\;{du} \\& V= -\int_{1/3}^{1/2}\frac{\ln{v}}{1-v^2}\;{dv} ~~~~~~~~~~~~~~~~~ X = \int_{\frac{1}{2}\ln{2}}^{\frac{1}{2}\ln{3}}\ln\left( \coth{x}\right)\;{dx}.\end{aligned}

Spoiler

Reply 13

Slowbro93

what do you think the grade boundaries will be?

Reply 14

AnonyMatt

I finished 1 and 2, but apparently my solution to 1 is wrong... I didn't use an integrating factor. I used the standard way of solving an inhomogenous equation using what I was taught for M3...
Hmm.

As for 2, it's definitely wrong. Did anyone get q = 1?
I bull****ted my way through, not accepting or understanding what I was saying, but it seemed to work!

I tried 6, but failed. I knew not remembering tanh in terms of exponentials would screw me. I tried to show T = V and got really close but to no avail.

7 was so annoying. I thought I could make good progress as it's just induction, but I couldn't see how to show the k + 2 case was of the form of the kth case, so gave up.

3 was just an algebraic nightmare, and I stopped soon after.

I really want to know how these are done!

Mechanics section was awful. :frown:

Reply 15

tobyc

Original post by anttooking

I am worried I have done the whole of 2 Wrong. Is it me or are part ii,iii just trivial when related to the first part?

Did you remember to check that the equations had no integer solutions? That would have made it seem more trivial than it was, although it was still relatively straightforward I thought.

Overall this paper went a LOT better than Monday for me. I started off on questions 1 and 2 and managed to do them both in under an hour, which was a big confidence boost, but then I had a minor panic attack for about 15 minutes when I realised that all the other pure questions looked awful :tongue:

I managed to recover by doing question 4 though, then did 10 from the mechanics section, and had about 45 mins left at the end in which I was unable to complete 3, but I managed to do around half of it.

Hopefully I did enough to meet my offer, because I definitely didn't on monday :/

Reply 16

anttooking

Oh dear, did nobody do a particular integral for 1?

I got: y = Ax + Be^(-x) + x^2 + Dx + 1?

Reply 17

Zuzuzu

Original post by anttooking

Oh dear, did nobody do a particular integral for 1?

I got: y = Ax + Be^(-x) + x^2 + Dx + 1?

Yeah, I did. Complementary function was whatever from the last part, then the PI was just standard DEs and rearrangement.

Reply 18

Schnecke

Original post by tobyc

Did you remember to check that the equations had no integer solutions? That would have made it seem more trivial than it was, although it was still relatively straightforward I thought.

Huh? Am I completely missing the point or did the first part tell you that any rational solutions would be integers? So you could show there were no integer solutions which means no rational solutions?