STEP Preparation

What the STEP actually tests

How to prepare for it

• Finish fewer questions, properly. A complete, well-written answer to two questions beats fragments of five. Most candidates lose more to abandoning questions than to being unable to do them.
• Read all the parts before starting. The last part usually tells you what the first part was for. Reading forwards changes what you do with the opening.
• Write as though someone will read it. Because they will. Say what you are doing and why, state where each assumption comes from, and do not leave the reader to reconstruct your reasoning.

Practice material on this site

These papers were drafted with AI assistance and have not been through the review process the ESAT material goes through. The answer keys were checked by computer algebra where the notice on each paper says so; the difficulty and the explanations were not. They are extra practice, not a predictor, and not a substitute for real past papers.

• Mock Paper 1: Long-form Questions

Found an error in one of them? Tell me and it will be fixed or withdrawn.

What the practice material covers

Counted from the questions themselves, not transcribed from a specification. For what is actually examinable in your cycle, check the official specification: it is revised between cycles and no tutor's summary of it should be trusted over the source.

4 questions across 4 topics. Thin coverage of a topic here does not mean it is unimportant in the real test; it means this practice set is small.

Common questions

• Is STEP just a harder A-level paper? No, and treating it as one is the common mistake. STEP asks for a small number of long questions where the marks are for the argument you write. A complete, well-written answer to two questions beats fragments of five.
• How do I choose which questions to attempt? Read all the parts of a question before starting, not just the first. The last part usually reveals what the first part was for, and a question that looks impossible at part three is often reachable through what you proved at part one.
• Are marks for the answer or the working? The working. An unjustified step loses marks even when it leads somewhere true, and a well-argued partial attempt scores better than most candidates expect.
• Do I need Further Maths? In practice yes for most STEP papers, and the offers that require STEP generally assume it. Check the specification for the paper your offer names.
• Are the practice questions on this site official? No. They are AI-drafted and were generated by a panel of independent agents: one set each question, two solved it from the statement alone, and a fourth reviewed the set adversarially. Two questions failed that review and were rebuilt and re-judged before publication. The reviewer found no mathematical error in any of them, but its remaining reservations, mostly about difficulty and mark allocation, are printed with each question.

Sitting more than one of these?

Candidates often sit two admissions tests in the same cycle, and the overlap is larger than it looks: the pure mathematics is shared, and the habits that earn marks in one paper usually earn them in another. Each page below covers what its test rewards and what free practice exists for it.

• TMUA: Test of Mathematics for University Admission Two papers and Multiple choice and Pure mathematics
• MAT: Mathematics Admissions Test Oxford and Imperial and Multiple choice and long-form
• PAT: Physics Aptitude Test Oxford and Physics and mathematics
• ESAT: Engineering and Science Admissions Test The deepest library on this site, written and checked by hand