STEP Maths preparation: STEP 2 and STEP 3
STEP (Sixth Term Examination Paper) is a pair of long, hard written maths papers that some universities make part of an offer, most often for Mathematics at Cambridge. This page sets out what is on them, how they are marked and when they are, then gives topic guides with original STEP-style problems, hints and full solutions.
- 2 papers: STEP 2 and STEP 3
- 3 hours each
- 12 questions, best 6 count
- No calculator
- Grades S, 1, 2, 3, U
Start with a topic guide Official past papers
Who asks for STEP?
OCR says STEP is used by the University of Cambridge, the University of Warwick and Imperial College London, and that other universities sometimes ask for it. For Mathematics at Cambridge, STEP is part of almost all offers: STEP 2 and STEP 3, with a minimum of grade 1 in each (University of Cambridge: STEP ). Offers say which papers and grades you need, so check each course page. Not sure which test you need? See TMUA vs MAT vs STEP.
The two papers
| Paper | Based on | Length | Questions |
|---|---|---|---|
| STEP 2 | A Level Mathematics and AS Level Further Mathematics | 3 hours | 12 (8 pure, 2 mechanics, 2 probability and statistics) |
| STEP 3 | A Level Mathematics and A Level Further Mathematics | 3 hours | 12 (8 pure, 2 mechanics, 2 probability and statistics) |
OCR's archive has STEP 1 papers up to 2019; the 2020 to 2025 papers are STEP 2 and STEP 3 only, and OCR now describes STEP as two papers. No formula booklet since 2019; a formula that you could not be expected to know is given in the question. Calculators are not allowed.
How STEP is marked
Every question is marked out of 20. The grade for a paper uses the best six answers only. All attempted questions are marked. The grades are S (Outstanding), 1 (Very good), 2 (Good), 3 (Satisfactory), U (Unclassified). Results come out in August, on A Level results day, and are passed to universities through UCAS. For Cambridge, OCR also sends the answer booklets to the university.
Dates and fees
| Registration (through your school or a test centre) | 1 March 2026 to 4 May 2026 |
|---|---|
| STEP 2 | 4 June 2026, 9am UK time |
| STEP 3 | 10 June 2026, 9am UK time |
| Results to candidates | 13 August 2026 |
| Fee per paper | £102.50 per paper in the UK; £142.25 / $179.75 / €166 per paper outside the UK |
Topic guides and practice problems
Each guide gives the key ideas, the common traps and original STEP-style problems with two hints and a full solution. 8 topics, 24 problems; the first in each topic is free.
- Algebra and inequalitiesSTEP algebra is rarely hard because of new facts. 3 problems, 1 free.
- Functions and curve sketchingMany STEP questions ask you to sketch a curve and then use the sketch to count solutions. 3 problems, 1 free.
- IntegrationSTEP integration is about choosing the right substitution or spotting the symmetry, then carrying out a long calculation without slips.. 3 problems, 1 free.
- Sequences, series and inductionSequences and series questions reward you for finding the pattern early and then proving it properly, usually by induction or telescoping.. 3 problems, 1 free.
- Complex numbers and polynomialsComplex numbers turn trigonometry into algebra. 3 problems, 1 free.
- TrigonometrySTEP trigonometry tests whether you can move fluently between identities, equations and geometry.. 3 problems, 1 free.
- MechanicsThe two mechanics questions on each STEP paper use A Level mechanics, but they expect you to set up your own equations from a description, with no diagram given.. 3 problems, 1 free.
- Probability and statisticsSTEP probability questions are about careful counting and clear arguments, often with a neat idea such as symmetry or linearity of expectation.. 3 problems, 1 free.
How to prepare
- A 12-month STEP study timeline: what to do from Year 12 to results day.
- Problem-solving strategies that work on STEP and MAT questions.
- The free STEP Support Programme from the Cambridge Faculty of Mathematics.
- Official STEP past papers (links to OCR), once you have worked through the topics.
- Applying to Oxford or Imperial too? Both ask for the TMUA for Mathematics (2027 entry): see our TMUA preparation.
- Writing your application: personal statement and interview guides, with original interview problems.
Questions
Is STEP 1 still running?
No. OCR's archive has STEP 1 papers up to 2019; since 2020 only STEP 2 and STEP 3 have been set.
What is the difference between STEP 2 and STEP 3?
Both are 3-hour papers with 12 questions (8 pure, 2 mechanics, 2 probability and statistics). STEP 2 is based on A Level Mathematics and AS Further Mathematics; STEP 3 on A Level Mathematics and the full A Level Further Mathematics.
How is STEP marked?
Each question is out of 20, and your grade uses your best six answers. The grades are S (outstanding), 1, 2, 3 and U.
Can I use a calculator in STEP?
No. Calculators are not allowed, and there is no formula booklet.
How do I register for STEP?
You cannot register yourself. Ask your school's exams officer, or another authorised test centre, to enter you before OCR's deadline, with your UCAS ID.
Are your STEP questions real past paper questions?
No. Every problem on our pages is original, written in the style of STEP. For real papers, use OCR's official past papers, which we link to.
STEP is run by OCR. A Level Math Revision is independent: it is not affiliated with or endorsed by OCR, the University of Cambridge or any university. Every problem here is our own, written in the style of STEP; for real papers use OCR's official past papers.