The STEP format

Two papers, each 3 hours and 12 questions worth 20 marks. Your six best answers count.

Papers	STEP 2 and STEP 3, each 3 hours
Questions	12 a paper: 8 Pure, 2 Mechanics, 2 Probability and Statistics
Marking	20 marks a question; your six best answers count, out of 120
Allowed	No calculator and no formulae booklet

What each paper covers

STEP 2: A-level Maths with some changes and additions, plus the Pure content of AS Further Maths, and some extra Mechanics and Statistics.
STEP 3: everything in STEP 2, plus the Pure content of A-level Further Maths, with more Mechanics and Statistics.
Questions may go beyond the specification, with guidance given in the question.

There is no limit on how many you attempt from any section.

Section	Questions
A: Pure Mathematics	8
B: Mechanics	2
C: Probability and Statistics	2

Paper 2 · Integration · Accessible · 20 marks

(i)
Let $a$ $>0$ , let $g$ be a continuous even function and let $h$ be a continuous odd function, both defined on $[-a,a]$ . By using the substitution $x$ $=-u$ , show that $\int_{-a}^{a}\frac{g(x)}{1+e^{h(x)}}\,\mathrm{d}x=\int_0^a g(x)\,\mathrm{d}x.$
7 marks
(ii)
Find $\displaystyle\int_{-1}^{1}\frac{1}{(1+x^2)(1+e^{x^3})}\,\mathrm{d}x$ .
3 marks
(iii)
Find $\displaystyle\int_{-\pi/3}^{\pi/3}\frac{\sec x}{1+e^{\tan x}}\,\mathrm{d}x$ .
4 marks
(iv)
By adapting the method of part (i) to the substitution $x$ $=\pi-u$ , find $\displaystyle\int_{0}^{\pi}\frac{\sin x}{1+e^{\cos x}}\,\mathrm{d}x$ .
6 marks

The STEP specification on OCR's site, on the OCR website

Can I use a calculator in STEP?

No. Calculators are not permitted, and no formulae booklet is given; the specification lists the formulae you are expected to know.

Do I have to answer questions from every section?

No. You can answer any questions; the six you answer best count.