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
| Papers | STEP 2 and STEP 3 (STEP 1 has been phased out — confirm your offer's exact requirement) |
| Format | 3 hours; a small number of long questions — you choose which ~6 to attempt |
| Marking | Full solutions, marked out of 20 each; you're rewarded for complete, rigorous arguments |
| Grades | S, 1, 2, 3, U |
| Content | STEP 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)
- Problem-solving stamina — staying with a hard problem past the first dead end.
- Writing rigorous solutions — every claim justified, no hand-waving, clear logical flow.
- Algebraic fearlessness — long, careful manipulation without slips.
- Pattern-spotting — recognising a substitution, symmetry, or known structure in disguise.
- Proof technique — induction, contradiction, inequalities, and careful case analysis.
A realistic plan (≈6 months out)
- Months 1–2: Get A-Level + (for STEP 3) Further content genuinely fluent. STEP exposes weak fundamentals instantly.
- 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.
- Months 4–5: Build a personal library of "techniques that recur" (substitutions, standard tricks, proof patterns).
- Month 5–6: Full timed papers. Practise question selection (read all, start with your strongest) and pacing.
- 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.