2013 STEP thread mark II

For questions involving infinite series (Maclaurin, Taylor etc.) is it always a good idea to work with the general term if you're trying to prove a given relationship? Often you can 'see' the result is true by explicitly working with the first few terms, but I'm guessing that's probably not rigorous enough? Also, are there any handy series results that might save some time come STEP III on Wednesday? It seems pretty likely that a series question will come up in one form or another, given recent papers.

Reply 981

bogstandardname

5

Original post by ian.slater

A couple of thoughts for anyone here holding a standard Cambridge offer of 1/1 and who didn't think that STEP II went that well:

(1) Many students who end up with 1/2 are offered places perhaps by another college via the Summer Pool. It's hard to call exactly, but a decent 1/middling 2 is normally about the dividing line. So if you think you might be on a reasonable 2 after last week, there is still everything to play for. Don't feel discouraged - give III your best shot.

(2) A typical trajectory for those who just get in with borderline grades is to be on the 2:1/2:2 boundary later on. So the experience is about working hard to get that 2:1! Those who fall just below the boundary go on to Warwick or Durham or Bristol (or somewhere) and find themselves in good company alongside others with similar experiences. They often then get Firsts.

So are you saying someone who scrapes a 1,1 is likely to be on for a 2.1 2.2 or someone he gets let in with 1,2?

Reply 982

Pyoro

8

Original post by shamika

What I mean is, does your argument make logical sense? A classic is assuming the thing you're trying to prove and then showing it is equivalent to something you already know is true. Unless each step is reversible, your 'proof' isn't actually anything at all.

My experience is that it can quite often be incredibly difficult to reverse an implication, particularly when solving things like coupled pairs of simultaneous equations, functional equations etc. I get the impression that the marking tolerates deducing possible solutions in place of actually solving, unless extraneous solutions are introduced. It's often easier to see if solutions are extraneous rather than to prove there are none.

Quite often, I also find myself dividing by possibly-zero factors when solving DEs, under the guise that they are atypically zero in some way, or are perhaps limits so that setting them to zero causes the result to be trivially zero anyway. Or something. Such problems actually cause massive delays in my STEP solutions where I can otherwise tell how to do the question, but I try to not let them get me down.

A classic is the solution of the SHM DE (and similar), where you get the solution by limiting the time domain, and then somehow extrapolate. As my maths teacher said, "we'll just breeze over that problem..." :smile:

Reply 983

ian.slater

12

Original post by bogstandardname

So are you saying someone who scrapes a 1,1 is likely to be on for a 2.1 2.2 or someone he gets let in with 1,2?

A few years ago the standard offer was 1/2 in either order. Gradually 1/1 offers have taken over, although a few 1/2's remain. My comment was about the marginal entrant on a 1/2 not a 1/1. I'd say an average 1/1 typically expects a mid-high 2:1

(edited 10 years ago)

Reply 984

_Georgie

How important is doing papers in mock conditions? I've got experience from the II exam now but I hate doing mocks, and I find it hard to sit and do it without distractions when I don't have to.
I did III 09, though I didn't time myself and was watching a film...:

Spoiler

I'd like an idea of the grade - I'm hoping it would have been enough for a 1? Even better if it was comfortably into a 1 because I probably wouldn't have been able to do that much in a timed mock :/ I didn't realise how nice Q8 was until the end!

(edited 10 years ago)

Reply 985

Nayim2

Woah, only just noticed that the highest mark for a 1 in STEP III so far is 67.
I'm feeling ready. :hoppy:

Reply 986

_Georgie

Original post by Nayim2

Woah, only just noticed that the highest mark for a 1 in STEP III so far is 67.
I'm feeling ready. :hoppy:

Awesome!
Little bit more attainable than previously thought. Only a little though, haha.

Spoiler

Original post by Appeal to reason

Spoiler

I hope that that makes sense :s-smilie:

Reply 989

sa6opopov

Can we use modular arithmetic in the number theory problems,or we have to consider the last digits?

Reply 990

Appeal to reason

14

Original post by dragonrabbit

Spoiler

I hope that that makes sense :s-smilie:

Spoiler

My scores fluctuate so badly...
The only thing I'm certain of for Tuesday, is if there isn't at least 1 DE question, I'm completely and utterly screwed.

(edited 10 years ago)

Reply 991

Appeal to reason

14

Original post by sa6opopov

Can we use modular arithmetic in the number theory problems,or we have to consider the last digits?

Yes, from the examiners report for I 2010, Q8:
"It was nice to see that a fair number of candidates knew about modular arithmetic and
could use it to construct effective arguments both here and in part (ii)."

Reply 992

sa6opopov

Original post by Appeal to reason

Yes, from the examiners report for I 2010, Q8:
"It was nice to see that a fair number of candidates knew about modular arithmetic and
could use it to construct effective arguments both here and in part (ii)."

Thank you! I also have another question about Q2 from STEP I 2010. In the solution,for the graph-sketching part is given that when x tends to infinity, y tends to e^x. Now,my question is,can I say that y also tends to infinity given the fact that e^x -> infinity as x->infinity or I have to say specifically that y->e^x

Reply 993

metaltron

11

STEP I 2004 Q7 is wonderful, my favourite STEP question so far! :biggrin:

Reply 994

LShirley95

Original post by ian.slater

A few years ago the standard offer was 1/2 in either order. Gradually 1/1 offers have taken over, although a few 1/2's remain. My comment was about the marginal entrant on a 1/2 not a 1/1. I'd say an average 1/1 typically expects a mid-high 2:1

And we don't talk of 3rd scum here.

Edit: it appears I wasn't clear enough that this was a joke. I am obviously not in any position to make a serious comment like this. Sorry.

(edited 10 years ago)

Reply 995

tommyridges

I was just doing Q5 from STEP I 2006 and it got me thinking about when we can/should just use the given integrals in the formula book. Because in part (i) in the answers it does partial fractions rather than just jump straight to the answer like I did (by using the formula book) so would I lose marks for using the formula book or is it perfectly fine?

Posted from TSR Mobile

Reply 996

shamika

16

Original post by LShirley95

And we don't talk of 3rd scum here.

I assume you're joking otherwise that's an awful thing to say

Reply 997

Zorgz

Original post by DJMayes

Just did STEP III 2012 as a half-mock (Finished after 2 hours 20 mins with 5 solutions to 2, 4, 6, 7 and 8 and a partial to Q1 that I abandoned due to poor arithmetical errors. That's questions done from every single STEP paper now. Made an arithmetical mistake in the last part of 4) but I think the other solutions are fine. Roll on Wednesday!

Sounds great- looks like your more than ready! Sort of the same, did STEP III 2012 as a mock, and scraped an S (marked by my teacher), so I feel like I'm ready; just hope it's nothing out of the ordinary on Wednesday and a 1 should be ok.

What sort of questions/topics you looking to do?

Reply 998

Appeal to reason

14

Original post by sa6opopov

Thank you! I also have another question about Q2 from STEP I 2010. In the solution,for the graph-sketching part is given that when x tends to infinity, y tends to e^x. Now,my question is,can I say that y also tends to infinity given the fact that e^x -> infinity as x->infinity or I have to say specifically that y->e^x

I'm not sure if I'm honest, the solution seems to make a big thing of y being asymptotically equal to e^x, if they did penalise you, it'd only be a couple of marks I imagine.

Reply 999

mathsymathsy

2

Hi Can anyone estimate the mark i would get for step iii 2012. Many thanks

Spoiler

2013 STEP thread mark II

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