Submitted by michael on Sun, 04/16/2017 - 13:51
I've been doing the STEP 3 2015 paper and having been running out of time, I wanted to ask for advice about how much I had to write; i.e. how much I can assume is obvious. Would a 10 in the British Maths Olympiad equate to full marks in STEP?
For a specific example, in Q2ii, I gave a quite obvious answer: the question was to give two sequences s and t such that neither s_n > t_n for all n>m nor s_n < t_n for all n>m (for some m).
My example was s_n = 0, t_n = {1 for n odd, -1 for n even}.
It's clear that this works, but having seen all the M1 marks in the 2015 mark scheme for other questions, I wrote proofs by contradiction just in case.
Would I be able to state that this is obvious? And in general, at what sort of level am I able to assume? Maybe a certain competition level?
Thanks!
Q2ii
You don't necessarily need a full blown proof by contradiction here, what you need to do is say that the statement is "False" and then explain why your sequences are a counter example - in your case every odd value of $n$ has $s_n \lt t_n$ and for every even value of $n$ we have $s_n > t_n$.
As for how much do you need to write, that depends on the question! If you are asked to prove something, so show that something is true then you need to show every step (or at least not leave the examiner to fill in any gaps). If the answer is not given (e.g. to an integration) then missing steps will probably not be penalised (but is not to be encouraged as that way it is easy to make mistakes!). Usually results given in the formula book can just be quoted, but occasionally you are asked to prove (or show) one of these, in which case you have to justify the result.
BMO is very different to STEP. It is hard to equate them!