Slight ambiguity in STEP questionWatch
So in this very lovely STEP question, I find the wording a little strange in part (ii). Is it asking for a proof or just for me to state the values? I asked a maths teacher and he is of the opinion that it is NOT asking for a proof. But the thing is, the next part is so easy after this part is completed, and therefore if it isn't asking for a proof then this is an extremely short STEP III question. I'm not sure what to make of it, I'd appreciate thoughts on what part ii means.
Anyway the "mark scheme" (it doesn't show where marks are allocated) implies a proof. It basically says that by considering and applying the recurrence relation, the expression is zero and then it makes the conclusion. It doesn't explicitly say how many marks (if any) is given to that bit of algebra.
As a side note where did you find this wonderful mark scheme?
In my humble opinion, I don't think a question should be difficult to actually understand the intention of the author from if possible (rather than the actual maths). The examiner's report for this question makes an interesting read: 83% of candidates attempted this question (most popular), and on average half marks were scored (third most well attempted). Part (i) "caused no problems" and part (iii) was "generally fairly well done", but part (ii) was "not well attempted, with a number stating the two values the expression can take but failing to do anything else or failing with the algebra".
In my humble opinion, I don't think a question should be difficult to actually understand the intention of the author from if possible (rather than the actual maths).
On the other hand, a huge part of doing really well in these kinds of exams (and the Tripos, for that matter) is getting into the mind of the examiner and having a good idea of what is expected for each part of a question.
And to be honest I'm very much doubting you had many people scoring well in their other question choices and at the same time thinking that writing "0 x 3 - 1 x 1 = -1 = 1 x 5 - 2 x 3" and "-1 when n is even, 1 when n is odd" was going to be sufficient to answer two parts of a 3 part STEP question.
Basis true by part (i).
By principle of mathematical induction bla bla bla true for . Then some stuff about the different cases.
I wish I could write in LaTeX better and make that stuff come down in the middle of the page and add comments on the side without it going all janky but I can't. Anyway this is why I initially thought the question was strange, seeing as the proof was this easy (and recurrence relation induction is bog standard FP1). It was a combination of that and the word "find". But yeah, silly to assume they'll let a mere stating of the result slide so you're still right of course.
EDIT: I talk too much about maths and probably shouldn't have wasted your time on this haha. Thanks though I feel like I've gained stuff from this thread.