What STEP is
STEP (Sixth Term Examination Papers in Mathematics) is the long-standing problem-solving exam used by Cambridge Mathematics for conditional offers, plus Imperial College, Warwick, and others for some Maths-heavy courses. STEP 1 was discontinued from 2021; STEP 2 and STEP 3 remain in active use. From 2027 entry, Cambridge Maths applicants also sit the TMUA at application stage; STEP keeps its role as the offer-stage requirement, so the preparation described here still applies.
Each paper is 3 hours and structured around a choice of around 12 substantial questions of which the student answers 6. Each question is a full multi-part problem requiring creative mathematical insight, substantial algebraic and calculus manipulation, and clean written argumentation.
STEP 2 vs STEP 3
STEP 2
Content drawn from the A-level Maths syllabus: algebra, calculus, trigonometry, coordinate geometry, sequences and series, vectors, basic statistics. Problem-solving difficulty significantly above standard A-level Maths exam questions.
STEP 3
Content drawn from A-level Further Maths: further calculus (hyperbolic functions, more advanced techniques), complex numbers, matrices, polar coordinates, more advanced proof. Problem-solving difficulty further raised above STEP 2.
Typical Cambridge offer combinations
Cambridge Maths offers vary but typical combinations include S,1 (STEP 2 grade S, STEP 3 grade 1) as a common offer, 1,1 as a slightly less demanding combination, and other formats specific to individual colleges. Always confirm the exact offer with the relevant Cambridge college admissions office. Imperial, Warwick, and other universities have their own STEP requirements which may differ.
Preparation approach
Year 12 (foundation)
Strong A-level Maths and Further Maths foundation. Engagement with extension material: Maths Olympiad routes (UK Junior, Intermediate, Senior, BMO) and Cambridge's STEP Support Programme materials. Some students start working through STEP 2 past papers in late Year 12 or summer holidays.
Year 13 autumn-spring
Systematic STEP past-paper practice. Cambridge's STEP Support Programme is exceptional: structured progression through past-paper questions with worked solutions and tutor support. Use it.
Many students benefit from working in cycles: attempt a question for 30+ minutes, write up the attempt, compare against the worked solution, identify where the insight was missed, work a similar question. STEP rewards deep engagement, not racing through questions.
Year 13 spring-summer
Full-length timed past papers. Build the stamina for 3-hour papers; this is genuinely tiring, and many students fade in the last hour. Refine question-selection strategy (which 6 questions to choose from the 12 available).
What tutoring adds
Worked-problem coaching: tutors demonstrate problem-solving technique on STEP-style questions, then watch the student attempt similar problems with feedback. Insight identification: strong tutors articulate the "what made this tractable" moment that students often miss when checking solutions alone. Written-argumentation coaching: STEP marks reward clean mathematical writing, and tutors help students develop the discipline of writing proofs and arguments that mark schemes credit fully. Question-selection strategy: knowing when to abandon a partial attempt and try a different question.
Choosing a STEP tutor
Tutors who themselves achieved S grades in STEP (or first-class in Cambridge Maths Tripos or equivalent) bring directly applicable experience, and this matters more than for most other tutoring. Tutors with strong competition-maths backgrounds (Maths Olympiad, Putnam, IMO) bring directly relevant problem-solving fluency. Recent Cambridge Maths Tripos graduates often make excellent STEP tutors; they're recently in the headspace and remember the techniques that worked. Stay realistic about preparation time: strong tutors recommend months of consistent practice, not crash-prep weeks before exams, and tutors promising rapid STEP lifts in 4-6 weeks should be treated with skepticism.
Free official resources
STEP past papers and mark schemes are on ocr.org.uk/students/step-mathematics, going back many years (delivery moved from the former Cambridge Assessment Admissions Testing to OCR in 2024). The STEP Support Programme is a free Cambridge-run programme with structured progression and tutor support. The Cambridge Maths department publishes selected past-paper solutions and commentary. Use the free resources before any paid tutoring; they're substantial, and going through them helps clarify whether tutoring is needed and where the marginal value is.