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How to prepare for STEP — a teacher's guide to the Oxbridge maths admissions test

Mike Vuu · 1 June 2026

STEP (the Sixth Term Examination Paper) is the admissions maths test for Cambridge and several other top mathematics departments. It is not "harder A-Level" — it is a different kind of exam. A-Level rewards reliable execution of known methods; STEP rewards depth, persistence, and the ability to construct a complete argument to an unfamiliar problem. Here's how to prepare.

What STEP actually is

PapersSTEP 2 and STEP 3 (STEP 1 has been phased out — confirm your offer's exact requirement)
Format3 hours; a small number of long questions — you choose which ~6 to attempt
MarkingFull solutions, marked out of 20 each; you're rewarded for complete, rigorous arguments
GradesS, 1, 2, 3, U
ContentSTEP 2 ≈ A-Level + AS Further; STEP 3 ≈ full A-Level Further — stretched far beyond routine

STEP 2 builds on standard A-Level; STEP 3 assumes Further Maths content. Check exactly which papers and grades your university offer requires.

How STEP differs from A-Level

  • Few questions, deeply explored. One STEP question can take 30–45 minutes and unfold in stages.
  • Partial progress is rewarded — and a few complete, correct solutions beat many half-finished ones.
  • It tests mathematical maturity: choosing a strategy, spotting structure, and writing a clean argument — not recalling a method.
  • Unfamiliar dressing of familiar content. The syllabus is small; the difficulty is in how ideas are combined.

The skills it rewards (train these directly)

  1. Problem-solving stamina — staying with a hard problem past the first dead end.
  2. Writing rigorous solutions — every claim justified, no hand-waving, clear logical flow.
  3. Algebraic fearlessness — long, careful manipulation without slips.
  4. Pattern-spotting — recognising a substitution, symmetry, or known structure in disguise.
  5. Proof technique — induction, contradiction, inequalities, and careful case analysis.

A realistic plan (≈6 months out)

  1. Months 1–2: Get A-Level + (for STEP 3) Further content genuinely fluent. STEP exposes weak fundamentals instantly.
  2. Months 2–4: Work through STEP questions by topic, slowly, writing full solutions and comparing to the official mark scheme and examiner reports. Quality over speed.
  3. Months 4–5: Build a personal library of "techniques that recur" (substitutions, standard tricks, proof patterns).
  4. Month 5–6: Full timed papers. Practise question selection (read all, start with your strongest) and pacing.
  5. Throughout: keep a log of problems you couldn't finish and return to them — the second attempt is where growth happens.

Common pitfalls

  • Rushing to full papers before the foundations and technique are there.
  • Reading solutions too early. The struggle is the training; give each problem a real fight first.
  • Sloppy write-ups. A correct idea with gaps in the argument loses marks — STEP wants the whole chain.
  • Chasing many questions shallowly instead of completing a few.

How IvyfordMath helps

The hardest STEP skill — constructing and judging a rigorous argument — is exactly what IvyfordMath's reasoning practice trains: identifying the missing step, spotting the invalid one, and choosing the right strategy. Combined with deep A-Level and Further coverage, it builds the foundations STEP stretches.

— Mike Vuu, Oxford Mathematics graduate and founder of IvyfordMath.