I would be glad if anyone can give me a hint on the above.I tried different substitutions,but they only seem to be leading this to a more complicated one.

Here are a few websites that might be useful in your STEP preparation (not including this one!)

The Admissions Testing Service has lots of past papers, the STEP specification, Examiner's reports etc. It also has the details of when the STEP exams will be and how to register for them.

I've started working on the Step 1 stats sheet. Hopefully they start to get easier after a while b/c I found the first question quite tough.

I think I got there after persisting for while and putting it down and coming back to it later, but I have a couple of questions (I appreciate you're not step examiners, but any advice will be gratefully received):

Three new "Foundation modules" have been released. These are selections of Pure, Statistics and Mechanics questions, each one with a preparation questions leading into the STEP question. These are currently draft assignments, and there are no "hints and partial solutions" documents to accompany them yet, but you can find solutions via the Admissions Testing Service website.

A new STEP II module has also been released.

Slight issue with Q2 (ii) : I understand how the question's supposed to be answered but I'd like to know why my method doesn't work :

I wonder if anyone could give me a hint on the best approach for Q5(ii) of 2012 Step 2. The question asks me to sketch \[g(x)=\frac{1}{((x-a)^2-1)((x-b)^2-1)}\] for the case of $b>a+2$. I've tried writing $g(x)$ as partial fractions in two different ways: \[\frac{Ax+B}{(x-a)^2-1}+\frac{Cx+D}{(x-b)^2-1}\] and \[\frac{A}{x-a+1}+\frac{B}{x-a-1}+\frac{C}{x-b+1}+\frac{D}{x-b-1}\] The second way leads to a sketch of a symmetrical curve, which is about right, but I am struggling to find the coordinates of the stationary points (which the question asks for).

For the last part of the STEP Question I tried the following - please excuse the basic formatting

(1 + sin 2θ)/(1+cos 2θ) = (cos²θ + sin²θ + 2sinθ cosθ)/(2cos²θ)

which, if you take good care of the stray ½, you can basically rewrite as

((sinθ + cos θ)/(cos θ))²

Remembering that this lives inside a ln (), from here I used the laws of logs and the first part of the question.

Is this a valid approach?

The last of the Foundation Assignments has now been published. In a couple of weeks we will publish some mixed STEP I questions (with preparation sections).

STEP papers can be downloaded via the Admissions Testing Service. Even if you are not sitting STEP II you might find that the STEP II modules are helpful in your preparation for STEP I as the two papers have the same specification.

Good luck!

Every time I finish one of your Step 2 sheets I feel that I have gained knowledge and improved problem solving skills but there are then no more questions on the sheet on which to deploy my new skills/knowledge.

I'm sure it takes a lot of time to make the sheets, so if it's not possible for you to make longer sheets, I wonder if you could maybe add some references to similar/relevant questions from past papers. Eg 'If you liked these questions, you may also like Step 2, 2012, Q6, etc...'

Keep up the great work.

I noticed that the triangle is a right-angled triangle and remembered a result from the warm down of assignment 21 about incircles of right-angled triangles, namely that there's a square of side length $r$ (the radius of the incircle) in the corner of the triangle. I found the length of the hypotenuse along the $x$-axis to be 5, and in part (i) I had noticed that the circle is tangent to the $x$-axis at $x=2t$.