Work · Oxbridge STEM · STEP
STEP preparation
STEP is the hardest school-level mathematics paper in the world, and unlike the MAT it sits after the offer, which changes everything about how it should be prepared for.
Free practice: 20 STEP problems with full solutions, or a timed paper.
The problem with STEP is when it happens
The MAT decides whether you are interviewed. STEP decides whether the offer you already hold survives.
A typical Cambridge mathematics offer is A*A* at A-level with grade 1 in STEP 2 and grade 1 in STEP 3. The candidate has an offer in January, sits A-levels in May and June, and sits STEP in mid-June, days after everything else finishes. Most of them have spent the spring on A-levels, because A-levels have deadlines that feel closer.
Then June arrives and the paper is nothing like an A-level, and there is no time left. Every year a number of people with offers miss on STEP alone. That is the failure mode, and it is a planning failure rather than a mathematical one.
What makes STEP different
A STEP question runs to forty minutes and you answer six in three hours. There are no marks for method fragments. You either get a question substantially out or you do not, and a half-finished question is worth very little.
The syllabus is small. STEP 2 sits on A-level content, STEP 3 on Further Maths. Nothing on either paper requires knowledge you do not have. What it requires is sustaining a single argument for forty minutes without losing the thread, which is a stamina nobody at school has ever asked you to develop.
- STEP 2 — A-level content, taken by most Cambridge mathematics offer holders
- STEP 3 — Further Maths content, harder, and usually the binding condition
- Grade 1 is roughly half the paper. Full marks is not the target and pursuing it wastes preparation.
The five archetypes
Most STEP questions are one of a small number of shapes wearing different costumes. The candidates who do well recognise the shape in the first two minutes and choose accordingly, because choosing badly costs more marks than solving badly.
- The scaffolded proof. Part (i) establishes a lemma you will need in part (iv). Rushing (i) throws away the ladder.
- The disguised standard. A familiar technique behind an unfamiliar substitution. Finding the substitution is the whole question.
- The generalisation. Prove a case, then the general result. The general proof usually reuses the specific one structurally.
- The exploration. Deliberately open. Marks for systematic investigation, including cases that fail.
- The long grind. Genuinely just difficult and long. Recognising these early and not choosing them is a skill in itself.
How I teach it
- Start in January, the week the offer arrives, at one question a week alongside A-levels. Not June.
- Full questions, timed, marked hard. Fragments teach nothing because fragments score nothing.
- Question selection as its own skill. Twenty minutes of every mock spent only on choosing which six.
- Writing to be marked. A correct argument badly communicated loses marks that were genuinely earned.
- Stamina. Three hours of continuous mathematics is a physical problem as much as an intellectual one.
Common questions
When should I start preparing for STEP?
January, when the offer arrives, at roughly one question a week alongside A-level work. Candidates who start in April are in trouble and usually do not know it yet. The paper rewards accumulated exposure rather than intensity, and there is no way to compress that.
How much of STEP do I need to get right for a grade 1?
Broadly half the paper, though boundaries move each year. Three questions substantially complete generally beats six half-done, which is why question selection matters as much as technique.
Is STEP 3 much harder than STEP 2?
Yes, and it is usually the binding condition on the offer. STEP 3 draws on Further Maths and its questions run longer. Most candidates who miss an offer miss on STEP 3.
Do I need STEP for Oxford?
No. Oxford uses the MAT before interview and does not require STEP. STEP is Cambridge, plus Warwick and Imperial for some offers.
Do you teach STEP yourself?
Yes, every session. This is the part most consultancies subcontract, and it is the part that decides whether the offer holds.
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