STEP (Sixth Term Examination Paper) Cambridge

If you are applying for mathematics at Cambridge, sooner or later you will run into four letters that strike more fear into maths applicants than almost anything else: STEP. This is not another admissions test in the style of the MAT or TMUA. STEP is a separate mathematics exam sat after you have already been accepted — as a condition of your offer. If you do not hit the required grade, Cambridge withdraws your place.

This guide explains exactly what STEP covers, how to register (in the UK and internationally), how grade boundaries work in practice, and how to realistically prepare from A-level Maths over 6-12 months. No fluff, no “magic methods” — just concrete sources: Cambridge Assessment Admissions Testing, the Cambridge Faculty of Mathematics, and the AMSP programmes.

BLUF — what STEP is, who has to sit it, and the two papers

STEP (Sixth Term Examination Paper) is a conditional mathematics exam required by Cambridge for its maths courses. Historically there were three levels — STEP 1, STEP 2 and STEP 3 — but since 2021 STEP 1 is no longer offered. Today you sit STEP 2 and STEP 3.

The key facts up front:

• Who sits it: applicants holding a Cambridge conditional offer for Mathematics, Mathematics with Physics, and selected applicants for Computer Science (maths option). Imperial College London and Warwick also accept or require STEP on some routes.
• When: June, two papers a few days apart. You sit it after you have your offer, not before.
• Format: 3 hours each, 13 questions to choose from, with your best ~6 counted.
• Required grade: a typical Cambridge offer reads “Grade 1 in STEP 2 AND STEP 3” or, more leniently, “Grade 1 in STEP 2, Grade 2 in STEP 3”.
• Calculator: not allowed. Pure mathematical thinking, pen, paper.
• Cost: around £99-£102.50 per paper in the UK (≈£200 for both), with international fees of roughly €166 or $179.75 per paper, plus a centre fee.

STEP is not a knowledge test in the style of a national school-leaving exam. It is a problem-solving exam — the questions are long (often a full A4 page of prompt), they demand constructing proofs, creative use of familiar tools, and a tolerance for problems you cannot crack in the first 15 minutes. A-level Mathematics teaches you technique; STEP teaches you to think like a mathematician.

“This exam does not test how much you know. It tests whether you can use what you know to solve a problem you have never seen before.” — Stephen Siklos, Advanced Problems in Mathematics

If you are aiming for mathematics at Cambridge, STEP will be the hardest exam of your life to that point. The good news: it is manageable if you start on time and work from the right materials. That is the goal of this guide.

Which Cambridge courses require STEP?

Courses with a conditional offer requiring STEP (2025/2026 season, source: Cambridge Faculty of Mathematics, maths.cam.ac.uk):

1. Mathematics (the main Tripos) — STEP 2 and STEP 3 required, no exceptions.
2. Mathematics with Physics — STEP 2 and STEP 3 required.
3. Computer Science (maths option) — STEP 2 required at some colleges; check the specific college you are applying to.
4. Engineering — STEP is not normally required, but some applicants sit it as an application booster.
5. Natural Sciences — STEP is not required, though the first-year Mathematics paper in NatSci draws on the same problem pool.

What a conditional offer typically looks like

The most common Cambridge formula for mathematics in the 2025/2026 season:

“A in A-level Mathematics, A* in A-level Further Mathematics, A in a third A-level subject, AND Grade 1 in STEP 2, AND Grade 1 in STEP 3.”*

For applicants who are not taking A-levels, Cambridge converts the A-level requirement into an equivalent in your own qualification — typically top grades in advanced mathematics, plus requirements in other subjects. Your school-leaving qualification does not replace STEP — STEP is an additional, independent condition.

What if you apply for maths through a different college?

Cambridge has 31 colleges, and each can tweak the standard offer slightly. Trinity and St John’s (the most selective for mathematics) often require Grade 1 in both papers, sometimes with Grade S preferred. Smaller, less selective colleges may offer Grade 1 + Grade 2.

For the full picture of Cambridge requirements, see the Cambridge University guide for international applicants and the best Cambridge courses — Natural Sciences and Engineering.

What does the STEP format look like — time, questions, marking?

Each STEP paper is 3 hours. 13 questions. You choose 6. Sounds simple. It is not.

Paper structure

Each question is worth 20 marks. Marking is all-or-nothing-ish — either you solve a question completely and earn the full 20, or you stall somewhere along the way and pick up 8-12 marks for substantial work, or 2-4 for starting with the right idea. There is no filling in “B” as on a multiple-choice test.

The sections

• Pure Mathematics (8-9 questions) — algebra, geometry, trigonometry, differential and integral calculus, proofs, induction, complex numbers, differential equations.
• Mechanics (2-3 questions) — kinematics, Newtonian dynamics, energy, momentum, rotational motion.
• Statistics / Probability (1-2 questions) — distributions, expectation, variance, Markov chains (less frequently).

Selection strategy: most candidates aim for 6 Pure questions and ignore Mechanics/Stats. That is rational — STEP counts only your best 6 questions, so a strong Pure base is enough. But if you are good at mechanics, a single Mechanics question can be the fastest 20 marks in the whole paper.

What does “13 questions, choose 6” mean?

The idea is this: you get a lot of questions of varying difficulty and topic, and you choose what to focus on. A realistic scenario:

1. First 30 minutes: read all 13 questions, mark the 6-8 that suit you best.
2. Next 2.5 hours: attack 4-6 questions, 25-40 minutes each.
3. Last 15 minutes: check, finish off, salvage partial marks.

Hitting a full 6 × 20 = 120 marks is extremely rare. Grade 1 is typically reached around 70-90 marks — that is 4-5 questions solved well, plus one started.

No calculator and no formula sheet

This is the biggest shock for many candidates. In most school exams you get a formula sheet. In STEP, you get nothing. Every trigonometric identity, integral, binomial expansion and hyperbolic function — you have to know it by heart.

That means preparing for STEP is not just about solving problems, but about mastering your toolkit to the point of automaticity.

How do you register for STEP?

STEP registration runs through Cambridge Assessment Admissions Testing, via the admissionstesting.org portal. Test centres are operated globally through the Pearson VUE network; internationally, that usually means the British Council network and selected international schools.

Step by step

1. Check the dates for the 2026 season on admissionstesting.org — registration usually opens in February/March.
2. The standard deadline is early May (typically 4-6 May).
3. Late entry deadline — usually mid-May, but at a higher fee (an extra ~£50).
4. Choose a test centre — most commonly:
   • Your own school or college, if it is registered for Cambridge exams
   • A British Council office (the standard route for international candidates)
   • An international school in a major city, in many countries
5. Your centre approves the entry — STEP requires formal centre approval. If your school is not authorised for Cambridge exams, register as a private candidate through the British Council — internationally, that is the standard path.
6. Fee — 2025/2026 season: around £99-£102.50 per paper in the UK (check current rates). Two papers total roughly £200; international fees run to about €166 or $179.75 per paper. Add the centre fee and any late fee.

Exam dates

STEP 2 and STEP 3 are sat in June, on two different days 3-7 days apart. The exact dates are published by Cambridge Assessment Admissions Testing a year in advance. They usually fall in the second and third weeks of June (for 2026, STEP 2 on 4 June and STEP 3 on 10 June).

What to bring to the exam

• Photo ID (a passport is preferred for candidates outside the UK).
• Your statement of entry from the admissionstesting portal (proof of registration).
• Black pens (×2-3, just in case) and a pencil for diagrams.
• A ruler and an eraser.
• No calculator. No phone. No smartwatch.

Results

STEP results are published in the second half of August — typically 13-21 August, in parallel with A-level results day in the UK. Cambridge automatically checks whether you have met the conditions of your offer and confirms your place through UCAS Track.

If you are applying in the 2025/2026 cycle, the other admissions exams are a parallel concern — see the MAT Oxford exam guide if you are also considering Oxford.

How do STEP grade boundaries work — what do Grade S, 1, 2, 3 mean?

STEP does not use the A*/A/B/C system of A-levels, nor a 0-100% percentage like many school exams. STEP uses a five-point system:

• Grade S (Outstanding) — the highest, usually around 75-85% of the raw score.
• Grade 1 — the typical “standard Cambridge offer” target, usually around 55-70%.
• Grade 2 — lower; accepted in some Cambridge offers (e.g. Maths with Physics lower than pure Maths).
• Grade 3 — low; rarely meets a Cambridge offer, accepted by Warwick and below.
• Grade U (Unclassified) — a fail.

Real grade boundaries (example — STEP 2, June 2024)

Cambridge Assessment Admissions Testing publishes grade boundaries after each session. The specific thresholds from STEP 2, the 2024 session (source: admissionstesting.org, reports published in the autumn):

Important note: the thresholds change every year depending on the difficulty of the session. In a harder year Grade 1 may sit as low as 45%; in an easier one, around 60%. Cambridge deliberately does not reveal the thresholds before the exam, so candidates do not strategically undershoot.

What the grades mean for Cambridge

• Standard Maths offer: Grade 1 in STEP 2 AND Grade 1 in STEP 3.
• More lenient Maths with Physics offer: sometimes Grade 1 + Grade 2.
• Highly selective colleges (Trinity, St John’s, for the strongest candidates): sometimes Grade S on one paper preferred (but rarely as a hard requirement).

Why this system surprises students used to percentages

A student used to a percentage-based exam, where 70% is “fine”, sees 53% = Grade 1 and thinks it is easy. It is not. That 53% is 4-5 of the 13 questions solved almost completely — which, at this level of difficulty, is extremely demanding. STEP is designed so that even the best candidates do not finish everything.

How to prepare for STEP — past papers, Siklos and AMSP

The best STEP preparation starts 12 months before the exam. A realistic minimum is 6 months of intensive work. Less than 4 months = Grade 3 or U, regardless of talent.

Hierarchy of materials (most important first)

1. STEP past papers (1987-2024) — the only genuine source.

All STEP past papers are freely available on maths.org / admissionstesting.org. You have 35+ years of material, roughly 70+ papers, each with 13 questions = ~900 questions to draw on. You will not get through them all even in 12 months.

Strategy: start with papers from 2015-2020 (closest in difficulty to current STEP 2), then work back to older ones as extension. STEP from the 1990s was easier, but the techniques shown there are timeless.

2. Stephen Siklos — Advanced Problems in Mathematics: Preparing for University.

A free book (PDF from Cambridge University Press) written specifically to prepare for STEP. Around 50 problems at STEP 2/3 level, with extensive commentary by Siklos — what to try, where the typical student gets stuck, what the “elegant” approach is.

This is the single most important book for a Cambridge Maths candidate. It should be worked through completely in the first 3-4 months of preparation.

3. Advanced Problems in Core Mathematics — Siklos’s second volume.

An easier level — STEP 1 / an introduction to STEP 2. A good warm-up before the main volume if you are starting from A-level Maths without Further Maths.

4. AMSP (Advanced Mathematics Support Programme) — support programmes for applicants to UK mathematics degrees.

The AMSP runs an online STEP support course — a 6-month programme (October-June) led by tutors, with weekly sessions and marked assignments. Part of the programme is free for UK candidates; international candidates usually pay — check current terms on amsp.org.uk.

For applicants outside the UK, the AMSP is the most realistic point of contact with the British STEP-preparation environment short of classic 1-1 tutoring.

5. NRICH STEP-style problems (nrich.maths.org) — a free problem bank from the Cambridge Maths Faculty, excellent for training creative thinking.

A 12-month plan (example)

June-August (the year before the exam) — diagnosis and foundations:

• Do you know the whole A-level Mathematics syllabus? (If not — that is your first task.)
• Work through Siklos’s Advanced Problems in Core Mathematics (the second volume).
• Start A-level Further Maths content — complex numbers, hyperbolics, matrices, differential equations.

September-November — Siklos main volume + first STEP papers:

• Work through Advanced Problems in Mathematics completely (~50 problems, 1-2 a week with the commentary).
• Start STEP 2 papers from 2010-2014, one paper a month under timing.

December-February — intensifying STEP 2:

• 1 paper every 10-14 days, full timing.
• Review of weak question types.
• Begin STEP 3 (once Further Maths material is finished).

March-May — peak training:

• 1 paper a week (a mix of STEP 2 and 3).
• Mock conditions: full 3 hours, no calculator, in silence.
• AMSP weekly sessions (if registered).

June — the exam:

• Final week: light review, no new problems.
• 8 hours of sleep.

National olympiads as preparation

A national mathematics olympiad (such as the British Mathematical Olympiad, or the IMO at the top end) is excellent preparation for STEP. Olympiad difficulty is often higher than STEP, and the type of thinking (proofs, creative approaches) is very similar. If you have reached the later rounds of a national olympiad, STEP will feel technically easier, though different in style (STEP uses more “calculus-heavy” tools).

A junior mathematics olympiad (lower secondary / early upper secondary) is also a great early start. See subject olympiads and applications abroad — being a finalist or medallist in a national olympiad is a strong signal for Cambridge admissions beyond STEP itself.

How does A-level Maths translate into STEP readiness?

This is the question every applicant asks. The honest answer: A-level Mathematics alone covers about 40-50% of the STEP 2 syllabus. The rest is A-level Further Maths material, which not every school teaches — and which students outside the UK often have to source independently.

What A-level Maths gives you for STEP

• Strong algebra and algebraic manipulation.
• Solid trigonometry and identities.
• Solid differential and integral calculus within the A-level Maths range.
• Analytic geometry (lines, circles, parabolas).
• Proof at a basic level — simple algebraic proofs.
• Logarithms, sequences, limits — covered properly.

What A-level Maths does not cover (what you have to add yourself)

1. Complex numbers — not in A-level Maths; core in STEP 3 (this is Further Maths).
2. Full matrix algebra — larger determinants, transformations, eigenvalues (STEP 3, Further Maths).
3. Hyperbolic functions (sinh, cosh, tanh) — STEP 2/3 assumes familiarity.
4. Differential equations — first and second order, separable, linear, homogeneous (STEP 2/3).
5. Mathematical induction in full — A-level Maths has the basics; STEP demands full fluency.
6. Mechanics (Newton’s laws applied) — limited or absent in many curricula.
7. A-level-level statistics — distributions, expectation, variance, hypothesis testing.
8. Advanced calculus — integration by substitution and by parts in many variants, partial fractions, polar coordinates.

A realistic route

1. September-December (the year before the exam): A-level Maths (or your national equivalent) = passing benchmark. If you do not know that material, do it first.
2. January-June (the year before the exam): add A-level Further Maths content — best resources: the Edexcel Further Maths textbook + ExamSolutions.net + Khan Academy.
3. July-December (exam year): only now do you go full STEP mode — past papers, Siklos.
4. January-June (exam year): intensify, mock papers.

Time estimate: for a student with a strong grounding in A-level Maths, that is ~600-1,000 hours of extra work to reach Grade 1 in STEP. Yes. A thousand hours. That is why we talk about 12 months of preparation, not 3.

Is school-leaving achievement “enough proof of talent” for Cambridge?

The answer is twofold. Cambridge requires top grades in advanced mathematics as a condition, but that does not replace STEP. A school-leaving qualification is a measure of technical knowledge — STEP is a measure of problem-solving ability. They are two different dimensions, and Cambridge wants to see the second.

Even students from the most selective schools, with perfect grades in advanced mathematics, have to prepare for STEP separately. A school’s ranking does not exempt you from this.

STEP vs MAT (Oxford) vs TMUA — which is right for you?

The three main UK admissions exams for mathematics differ in philosophy, format, timing and who they are for. If you are applying to a single university, the choice is obvious. If you are weighing up Oxbridge + Imperial + Warwick, you may have to sit all three.

Quick comparison

Which exam applies to you?

• Applying only to Cambridge Maths → STEP (June, after the offer).
• Applying only to Oxford Maths/CS → MAT (October, before applying).
• Applying to Cambridge + Oxford → MAT (autumn) AND STEP (summer). Two full preparation tracks.
• Applying to Imperial Maths → STEP (usually required for some offers); check Imperial’s requirements carefully.
• Applying to Warwick Maths → TMUA preferred, sometimes STEP instead.
• Applying to LSE / UCL Maths/Econ → usually A-level Maths (or equivalent) is enough, with no separate maths admissions test.

What to do if you are applying to Oxbridge + a safety option

A realistic plan for an ambitious candidate:

1. October: sit the MAT (Oxford + some Imperial offers).
2. November: Cambridge interview (if shortlisted).
3. January: offers from Cambridge / Oxford.
4. June: STEP (if you hold a Cambridge offer).

These are two very different styles of preparation. The MAT rewards speed and cleverness in MCQ. STEP rewards stamina and depth on long problems. If you apply to both universities, plan for 18 months of combined preparation — from September of your penultimate school year to the following June.

Plan B if STEP did not go well

In practice Cambridge does not allow a resit within the same season — you sit STEP once a year. Realistic plan Bs:

1. Gap year + retake — take a year out, resit STEP the following June; most Cambridge colleges will agree to deferred entry conditional on passing.
2. Imperial / Warwick / UCL — lower STEP requirements, or none. Imperial Maths often has an offer of “STEP 2 Grade 2” instead of “Grade 1 × 2”.
3. A strong degree at home + a UK Master’s — many countries have mathematics departments at a very high level. A UK Master’s (Cambridge Part III, the Oxford Mathematics MSc) is an alternative route without STEP.
4. The USA — Princeton, MIT, Stanford. A different system — US mathematics admissions rest on the SAT/AP, not STEP. See Oxford vs Cambridge — comparison and courses if you are weighing up alternatives.

If you are applying to several universities and want to understand how different mathematics grading systems compare, the GPA calculator can help you convert your school-leaving results into a US-university equivalent.

Sources and methodology

This guide was built on three main public sources, independent and regularly updated:

1. Cambridge Assessment Admissions Testing — admissionstesting.org. The official STEP registration portal, which publishes:
   • Exam dates (a year in advance).
   • The specification and syllabus for each paper.
   • Past papers 1987-2024 (free to download in PDF).
   • Grade boundaries after each session (published in August).
   • The current fee per paper.
2. Faculty of Mathematics, University of Cambridge — maths.cam.ac.uk. The official page of the Cambridge Faculty of Mathematics, which publishes:
   • Standard conditional offer wording.
   • Requirements per course (Mathematics, Maths with Physics, CS).
   • Recommended preparation materials (Siklos’s books, NRICH).
3. Advanced Mathematics Support Programme (AMSP) — amsp.org.uk. The UK government-backed programme supporting mathematics at A-level and above:
   • The online STEP support course (October-June).
   • Free resources and webinars.
   • Tutorials led by experienced STEP teachers.

Financial data (fees) are drawn from the official 2025/2026 figures published by Cambridge Assessment Admissions Testing. Real costs paid from a foreign account may differ slightly because of bank spreads on currency conversion.

What this guide deliberately does not include:

• Specific “insider tips” or “STEP secrets” — they do not exist. Every strategy that works is public.
• Suggestions to “buy” private tutoring at £500/hour — it is not essential. Candidates reach Grade 1 with free materials (Siklos + past papers + AMSP free content).
• The results of named candidates — Cambridge does not publish national STEP data.

Data freshness: this guide was prepared for the 2025/2026 season. Cambridge dates, fees and policies can change between seasons — always verify the latest information on admissionstesting.org and maths.cam.ac.uk before registering.

If you are planning the full Cambridge application route — interview, college choice, the supervision system — start with how to get into Cambridge — admissions and interview 2026.