A lot of the material I'm seeing in the complex section for STEP III is completely new. Any suggestions for a good resource to learn this stuff? For instance, I had never seen De'Moivres theorem.

We have to answer 6 questions in 3 hours, which gives us 30 minutes per question. How is this supposed to work? It seems like a lot of the STEP III questions are designed to take 2 hours each. :(

In part ii) I used the same approach and got two different values of p. When I subbed them back into the real equation though, I was unable to get the answer.

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}.

To what extent are we allowed to assume results e.g. Leibniz' rule for differentiating products etc?

I am stuck on part ii) and was wondering if I could have hint on the right direction to go in.
So far I have tried doing substitution of x=u-1/2 in order to get the limits similar to part i), and then was trying to do integration by parts. However I am struggling to simplify the sin(1/x) part into f(a-x).

Thank you.

In question 5 of the STEP II Calculus support module, the solutions jump from:
$$\ln |v| = -x + \ln |x-1| +c$$
to
$$v=Ae^{-x}(x-1)$$

$c$ and $A$ are arbitrary constants with $c=\ln A$

There is no obvious domain on v or x so I'm struggling to see how the removable of the absolute value signs was justified. Is this just a simplification to make the question appropriate for STEP I (that's the paper it came from) or am I missing the reason why this is okay to do?

In part ii), my expression for w is the required but without the factor of cos(alpha) squared multiplying m in the denominator... where does it come from?? Perhaps I reached a similar expressions why a wrong method...

Hello

I have a doubt concerning mainly the especification (both STEP II and III). The syllabus states that use of partial fractions to integrate rational functions is required (and I´m okay with that). When I learnt this at school (i'm not doing Alevels), we also saw how to proceed in case we found a denominator (with degree two) with complex roots. I would like to know if this is included on A-levels, so that it would be possible to find it on any of the step papers...If it has ever appeared, do you remember the year and paper??

Hey so I was able to do the preamble bit of the question without too much difficulty but when I get to part (i) I get stuck trying to find neat expressions for |PX2|,|PX3| etc. I have found |OP| = cos(pi/n) and found |PX0| = |PX1| = sin(pi/n) but using cosine rule to find the other lengths creates something that currently looks horrible. Ideas please?