tutorperch

Test prep · STEP

STEP preparation

STEP (Sixth Term Examination Papers) is the admissions test required for Cambridge Mathematics and used by Imperial, Warwick, and others. STEP 2 and STEP 3 are 3-hour problem-solving exams sat in June, considerably harder than A-level Maths in problem-solving demand.

Quick reference

Full name
Sixth Term Examination Papers (in Mathematics)
Two papers in active use
STEP 2 · STEP 3 (STEP 1 was discontinued from 2021)
Used by
Cambridge Mathematics (typical offer S+1+1 or 1+1) · Imperial · Warwick · others — verify per course
Format
3-hour written exams · choose 6 from ~12 questions · sit at school
Test window
June of Year 13 — alongside A-level exam season
Grading
S (Outstanding) · 1 · 2 · 3 · U

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.

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 / 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) — common offer
  • 1, 1 — slightly less demanding combination
  • 1+1+1 (some colleges with the older format) — specific to college

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), Cambridge's STEP Support Programme materials. Some students start working through STEP 2 past papers in late Year 12 / 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 — 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. 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

  • STEP-success background — tutors who themselves achieved S grades in STEP (or first-class in Cambridge Maths Tripos / equivalent) bring directly applicable experience. This matters more than for most other tutoring.
  • Maths Olympiad / Putnam / IMO backgrounds — tutors with strong competition-maths backgrounds 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.
  • Realistic about preparation time — strong tutors recommend months of consistent practice, not crash-prep weeks before exams. Tutors promising rapid STEP lifts in 4-6 weeks should be treated with skepticism.

Free official resources

  • STEP past papers and mark schemes — admissionstesting.org (Cambridge Assessment), going back many years.
  • STEP Support Programme — free Cambridge-run programme with structured progression and tutor support.
  • Cambridge Maths department resources — 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.

Ready to find a tutor?

Free to browse, free to message. £20 one-off to unlock contact details.

Find a STEP tutor

Common questions

  • How is STEP different from A-level Maths? +

    Substantially harder problem-solving. STEP questions are deliberately long and unfamiliar — most are 20+ minute problems requiring multiple insights and substantial algebraic / calculus dexterity. A typical STEP 3 question demands more sustained problem-solving than any A-level Maths question. Students who score A* in A-level Maths and Further Maths can still struggle on STEP if they haven't practised problem-solving in this style. Cambridge Maths offers are typically conditional on STEP grades because STEP is a significantly more discriminating signal.

  • STEP 2 vs STEP 3 — what's the difference? +

    STEP 2 covers A-level Maths content depth at problem-solving difficulty; STEP 3 covers A-level Further Maths content depth at higher problem-solving difficulty. Cambridge Maths offers typically require both (e.g. S in STEP 2 and 1 in STEP 3, or 1 + 1). Some courses (Cambridge Mathematical Tripos) require both; others (some Imperial / Warwick offers) may require just one. Confirm per offer.

  • When should we start preparing? +

    Early Year 12 is not too soon for genuinely Cambridge-Maths-track students. Most students benefit from 6+ months of consistent STEP preparation; some prepare for over a year. STEP problem-solving fluency builds slowly — there's no shortcut. The Cambridge-recommended Maths Olympiad route (UK Junior, Intermediate, Senior, BMO) builds the same skills earlier and gives students problem-solving exposure before STEP itself. Tutoring can compress this timeline somewhat but not by a lot — STEP rewards practice volume.

  • How does tutoring help? +

    STEP tutoring is mostly worked-problem coaching: a tutor demonstrates problem-solving technique on STEP-style questions, then watches the student attempt similar problems and gives feedback. The differentiator is the tutor's own STEP-equivalent ability — tutors who scored S in STEP themselves (or first-class in Cambridge Maths Tripos) bring directly applicable problem-solving experience. Generic A-level Maths tutors usually can't deliver useful STEP coaching above a certain level.

  • Where are the official resources? +

    STEP is run by Cambridge Assessment Admissions Testing. Past papers and mark schemes for STEP 1, 2, 3 are freely available on admissionstesting.org going back many years — substantial practice material. The Cambridge Maths department also publishes useful supporting material and the STEP Support Programme is highly regarded.

Related

Find a STEP tutor

Browse free, message tutors directly, unlock contact details when you're ready.

Find a STEP tutor Other admissions tests

Last reviewed: 2026-04-29