I got problem (i) right off the bat. It was such a fun thinking exercise. However, as soon as I saw part (ii) my mind went blank. I've never seen anything relating the angles between faces. I thought about for about 30 minutes and I still couldn't get it. I haven't looked at the solutions yet (I think that would just ruin the learning experience).

I successfully completed part (ii), driving at the desired result of $I_{n+1} = -\frac{n+1}{m+1}I_n$. Using this recurrence relation and the fact that $I_0 = \frac{1}{m+1}$, I calculated $$I_n = (-1)^n \frac{(n+1)!}{(m+1)^{n+1}}$$

For part (iii), I wrote $x^x$ as $e^{x\log(x)}$, which I then wrote as the power series $\sum_{n=0}^{\infty} \frac{(x\log(x))^n}{n!}$. Then I swapped the integral and the sum, which led to me integrating $\frac{(x\log(x))^n}{n!}$. Given the result from part (ii), this was really easy.

Hi
If I find the mechanics and stats questions easier than the pure questions, is it a bad strategy to aim to answer these and only 1 or 2 pure questions?
If I were to miss my offer would having answered mainly applied questions rather than pure then look bad to tutors looking at my script to see if I should still get a place?
Thanks

Hi!

The Integral solution (from MEI website) says that "y or x is a dummy variable" and use y and x interchangeably, why is this possibly? I understand that sine that sin(pi - x) = x so if y = pi - x then sin(y) = sin(x) but I thought this was only possible within the sine function?

Thanks

Question 4 is about non-uniform circular motion. I worked out the $x$ and $y$ coordinates on point $P$ to be \[\mathbf{P}=\begin{bmatrix} a(\theta-\sin\theta) \\ a(1-\cos\theta) \end{bmatrix}\] But the question asks for position of $P$ in cartesian coordinates. Can I have the parameter $\theta$ in 'cartesian coordinates'? I can eliminate $\theta$ and obtain \[x=a\cos^{-1}\left(\frac{a-y}{y}\right)-\sqrt{2ay-y^2}\] but that's not really what I think of as 'coordinates'.

Is it possible to get the year of the paper for which the STEP III Hyperbolic Functions Module questions are taken from? I've tried to Google the questions themselves but because of the LaTeX formatting it's proved difficult for me. Thanks for any help!

I have been working through the support modules and the past papers, and both have been quite helpful. But I'm still struggling in geometry/trigonometry and some aspects of the pure math questions despite the extra practice. Can anyone recommend any more resources for these topics (or any topics really). That would be a huge help!

I have been working on Question #4 from the calculus step II module for a while. For part (i) the solutions say that after separating variables and integrating we should arrive at the solution $-\frac{1}{u} = \frac{1}{3} (1+x^2)^{\frac{1}{2}} + c$. I've reworked this problem a few times but I keep ending up at the solution $-\frac{1}{u} = \frac{1}{3} (1+x^2)^{\frac{3}{2}} + c$. Has anyone else had to same problem and can point me in the right direction? Thanks in advance!

https://www.thestudentroom.co.uk/showthread.php?t=3411533#post57155081

How do you deduce that a=r3(r1-r2), b = ..., c = ... ?

Thanks!

I am currently stuck on part (i). I have considered that for the maximum L there will be a position where the rod is in contact with two walls and the corner of the corridor and labelled an angle theta between the top wall and the rod. From this I have found an equation resembling first one (with theta instead of alpha and not an inequality since considering the maximum case) however I am not sure how to show that the angle also satisfies the second equation. Hints on where to go please?