United Kingdom · Year 13 · STEP 2 on 14 June 2027 and STEP 3 on 21 June 2027

STEP maths preparation: STEP 2 (9470) and STEP 3 (9475)

STEP is the paper that tells a student what university mathematics feels like before they get there. Each paper lasts three hours and contains twelve questions, and only the six highest-scoring answers count towards the result, so the first skill is not solving but choosing. The University of Cambridge uses STEP in almost every conditional offer for Mathematics, and OCR, which sets and runs it, names Warwick and Imperial as users too. For a student applying in October 2026, the papers fall in June 2027: STEP 2 on the 14th and STEP 3 on the 21st. Below are the papers, the 2027 calendar, what the 2026 grade boundaries actually required, one long question of our own worked through, and how to use the free material the Faculty of Mathematics publishes.

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In short

STEP (Sixth Term Examination Paper) is a mathematics exam set by OCR and used by the University of Cambridge, the University of Warwick and Imperial College London. There are two papers, STEP 2 and STEP 3, each three hours long with twelve questions; only the six highest-scoring answers count, each marked out of 20, and grades run S, 1, 2, 3, U. In 2027 STEP 2 is on 14 June and STEP 3 on 21 June. Modern Age Coders runs live online STEP classes for Year 13 students, as a group of fifteen to twenty or one-to-one, as part of its admissions-test course for TMUA, MAT and STEP.

Where to start

Three courses for a STEP candidate

One for the papers themselves, one for the Further Maths that STEP 3 assumes, and one for problems that go further still.

TMUA and STEP Preparation (Oxford MAT Now TMUA) course thumbnail

STE / 01

STEP, TMUA and MAT course

For 16 to 18 year olds. Question choice, long chains of algebra, and solutions read in full every week.

Open the syllabus →
A Level Further Maths course thumbnail

STE / 02

A Level Further Maths

STEP 3 is built on the Further Mathematics A Level. Gaps here cost whole questions.

Open the syllabus →
Maths Olympiad & Competition Course course thumbnail

STE / 03

Olympiad and competition maths

Invariants, inequalities and number theory for the student who wants harder still.

Open the syllabus →

The two papers

How are STEP 2 and STEP 3 structured?

Each paper lasts three hours and has twelve questions in three sections: eight pure, two mechanics and two probability or statistics. OCR marks every attempted question out of 20 and counts the top six, so the maximum on either paper is 120.

STEP 2 and STEP 3 as OCR and the University of Cambridge describe them (read 31 October 2026)
STEP 2 (STEP Mathematics II, 9470)STEP 3 (STEP Mathematics III, 9475)
Based onA Level Mathematics and AS Level Further MathematicsA Level Mathematics and A Level Further Mathematics
LengthThree hoursThree hours
Section A8 pure questions8 pure questions
Section B2 mechanics questions2 mechanics questions
Section C2 probability/statistics questions2 probability/statistics questions
MarkingEach question out of 20; top six count; 120 maximumEach question out of 20; top six count; 120 maximum
Date in 202714 June 2027, 9am in the UK21 June 2027, 9am in the UK

Why only six count

OCR's FAQ is plain about it: a candidate may answer as many questions as they wish, every answer is marked, and the six highest marks are added. Then comes the advice that matters: "it is not advisable to attempt more than six questions, and candidates who do so rarely score as well as those who concentrate on answering six questions."

Our arithmetic makes the reason obvious. Cambridge contrasts A Levels, where students "are expected to answer 11-14 questions in two hours", with STEP's "no more than 6 questions in three hours". That is roughly nine to eleven minutes a question at A Level against thirty minutes a question on STEP. A STEP question is three A Level questions long, and it wants to be finished.

What a question rewards

OCR says questions "may test a candidate's ability to apply mathematical knowledge in novel and unfamiliar ways" and that solutions "will frequently require insight, ingenuity, persistence and the ability to work through substantial sequences of algebraic manipulation". The last phrase is the one students underestimate.

Two more rules shape how to write. "Correct answers always receive full marks, whatever the method used", unless a question demands a specific method. And crossed-out work is not marked, so a student who scraps an approach should leave it legible until sure.

STEP 1 no longer exists. The current specification states that "From the June 2021 sitting onwards, STEP Mathematics 1 has not been offered." Old STEP 1 papers are still good practice at roughly A Level Mathematics depth, as the Faculty of Mathematics notes, but no offer will ask for one.

Sources: OCR scoring and results, FAQs and the STEP specification for June 2026 onwards; the Faculty of Mathematics STEP page; all read 31 October 2026. The per-question minutes are our calculation. Modern Age Coders has no connection with OCR, Cambridge University Press and Assessment or the University of Cambridge.

The 2027 calendar

When is STEP in 2027, and how do you register?

STEP 2 is on 14 June 2027 and STEP 3 on 21 June 2027. Registration runs from 1 March to 4 May 2027 and is made by a test centre, usually the student's own school; OCR says a candidate cannot register themselves.

STEP key dates 2027, from OCR (OCR reserves the right to change them)
DateEvent
1 March 2027STEP registration opens; centres can register candidates from this date
21 April 2027Last date to request modified question papers
4 May 2027STEP registration closes; last date to request access arrangements
14 June 2027STEP paper 2, 9am in the UK
21 June 2027STEP paper 3, 9am in the UK
12 August 2027Results released at 8am UK time
19 August 2027Last date for results enquiries
  1. Check the offer. OCR says the university usually names the papers in its offer letter. Cambridge says Mathematics applicants are normally asked to take both, and that the grades required vary by College.
  2. Find the centre early. A school that is not yet a STEP centre can apply to become one, OCR says, "even if you are the only person taking a test". Students outside school may be able to sit at their old school or another authorised centre.
  3. Give the exams officer the details. Name, gender, date of birth and UCAS number exactly as on the UCAS application, the universities and course codes, and any access arrangements with evidence.
  4. Ask for the entry number. OCR tells candidates to ask the exams officer for a candidate entry number as proof the registration is complete. Centres may set an internal deadline well before 4 May.
  5. Sit both papers a week apart. Take black pens, a pencil for diagrams, a ruler, a protractor and compasses. No calculator and no bilingual dictionary.
  6. Results reach universities through UCAS. For Cambridge, OCR sends the answer booklets themselves to the admissions team, so a near miss can be judged on the actual work.

Timing within the application matters. Cambridge's guidance is that a student "should normally expect to take STEP in the summer following your application", and gives the example: apply in October 2026, sit STEP in June 2027. A student who has already sat STEP before applying may be asked to sit it again. Cambridge Mathematics applicants for 2027 entry also took the TMUA in the 12 to 16 October 2026 window, according to Cambridge's TMUA page, so the two tests sit at opposite ends of Year 13.

Sources: OCR key dates and fees and how to register; Cambridge undergraduate STEP guidance and TMUA page; read 31 October 2026. OCR publishes its registration fees on the key dates page; we do not repeat them.

What the grades required

What were the STEP grade boundaries in 2026?

In 2026 a grade 1 needed 62 out of 120 on STEP 2 and 56 on STEP 3; an S needed 84 and 80. OCR publishes the boundaries and the share of candidates at each grade every August.

STEP 2026 grade boundaries (minimum marks out of 120) and cumulative percentages, from OCR's Explanation of Results for STEP 2026
PaperS123Reached grade 1 or better
STEP Mathematics II (9470)8462523428.14%
STEP Mathematics III (9475)8056483035.73%

Reading the numbers

Our arithmetic: a grade 1 on STEP 2 in 2026 needed 62 marks, a little over half of 120. Since each question is out of 20, that is three complete solutions and a few marks more. An S needed 84, which is 70 per cent, or four complete solutions and real progress on two others.

Put the other way round, a student who finished three questions properly and wrote nothing else of value would have fallen just short of grade 1 on STEP 2 and just reached it on STEP 3. Boundaries move every year, and these are 2026 figures only, not a target.

What follows for practice

Finishing matters more than starting. Six half-done questions at ten marks each make 60; three finished and three abandoned can make the same, with far less risk. Students who practise reaching the end of a question, rather than sampling many, build the habit the boundaries reward.

Cambridge adds a reason not to panic: the Faculty calls STEP "supposed to be difficult", aimed "at the top 5% or so of all A-level mathematics candidates", and reminds students that colleges can read the scripts and make allowances for a near miss.

Boundaries and percentages from OCR's Explanation of Results for STEP 2026 (PDF), read 31 October 2026. The percentages of 120 and the "three complete solutions" reading are our own arithmetic. We promise no grade.

Worked question, ours

A STEP-style question worked through, start to finish

This is our own question, written for this page in the long, linked style STEP uses: each part leans on the last, and the final part is where the marks separate. It is not taken from any STEP paper.

Our question. For n = 0, 1, 2, ..., let In be the integral of xnex from x = 0 to x = 1. (i) Show that In = e − nIn−1 for n ≥ 1, and find I0, I1 and I2. (ii) Show that 1/(n + 1) ≤ In ≤ e/(n + 1). (iii) Hence find the limit of nIn as n tends to infinity.

Part (i): the recurrence

Integrate by parts with u = xn and dv = exdx: In = [xnex] from 0 to 1 minus n times the integral of xn−1ex, which is e − nIn−1. Then I0 = e − 1, I1 = e − (e − 1) = 1 and I2 = e − 2.

Part (ii): the squeeze

On 0 ≤ x ≤ 1 we have 1 ≤ ex ≤ e, so xn ≤ xnex ≤ exn. Integrating each side from 0 to 1 gives 1/(n + 1) ≤ In ≤ e/(n + 1). One line, but only once you think to bound ex rather than the whole integrand.

Part (iii): the payoff

Rewrite part (i) with n + 1 in place of n: (n + 1)In = e − In+1. By part (ii), In+1 tends to 0, so (n + 1)In tends to e. Since In itself tends to 0, nIn = (n + 1)In − In tends to e as well.

Our check in Python: the true values against the recurrence started from a rounded I0
nTrue In (6 d.p.)Bounds 1/(n+1) to e/(n+1)Recurrence from I0 = 1.718
11.0000000.5 to 1.3591.0003
30.5634360.25 to 0.6800.5651
50.3956000.167 to 0.4530.4294
7about 0.310.125 to 0.3401.7259
8about 0.270.111 to 0.302−11.089
100.2280020.091 to 0.247−1022.47

Why the last column goes wrong

Rounding I0 to 1.718 introduces an error of about 0.0003. Each step of the recurrence multiplies the error by n, so by n = 8 it has been multiplied by 8 × 7 × ... × 1 = 40,320, and the computed value is negative, which part (ii) proves impossible. Our run on 31 October 2026 shows exactly that.

This is the kind of extension STEP enjoys: a short "explain why" at the end that tests whether a student understood what they proved rather than only how. The bound from part (ii) is the tool that catches the error.

What the question trains

Three habits, all of which the 2026 boundaries reward. Reuse earlier parts: part (iii) is impossible without parts (i) and (ii), and STEP questions are usually built that way. Bound before you compute: the squeeze needs no integration at all. Finish: a candidate who stops after part (i) has done the routine third.

A teacher's job here is mostly reading. Most STEP marks are lost in the linking sentences, the "hence" that does not quite follow, and a student needs someone who reads the whole solution, not only the answer at the bottom.

Question, solution and Python check are ours, written and run on 31 October 2026; the values for n = 7 and 8 are given to two places because the point is the sign. For the real thing, OCR publishes STEP 2 and STEP 3 past papers and examiner reports from 2019 to 2025 on its preparing for STEP page; we link to them and reproduce none.

Preparing honestly

How should you prepare for STEP, and do you need a tutor?

The Faculty of Mathematics says the way to prepare is past papers, and offers a free STEP Support programme with NRICH from the summer of Year 12. It also says, of commercial resources, that it "neither endorses nor recommends" them "since there are more than enough free resources". We are a commercial resource, so here is what that means in practice.

Free STEP material named by OCR and the Faculty of Mathematics (read 31 October 2026)
ResourceWho offers itWhat it is for
STEP Support programmeFaculty of Mathematics with NRICHStructured problem sets from the summer of Year 12, with a discussion forum
Advanced Problems in MathematicsDr Stephen Siklos, free PDFRecent STEP questions analysed, each with comment and full solution
STEP past papers and examiner reportsOCRSTEP 2 and STEP 3 papers from 2019 to 2025, plus legacy papers
STEP databaseFaculty of MathematicsA searchable set of questions from the 1986 specimens to 2018
Full solutions 1996 to 2019MEIWorked solutions when a student is stuck
Advanced problem-solvingNRICH and Underground MathematicsA gentler start and selected STEP questions with explanations

Where a class helps

A student working alone through the Support programme has the problems and the solutions. What they lack is a reader. Nobody tells them that their part (ii) assumed what it set out to prove, or that their "hence" used a different method from the one the question asked for, which OCR warns can earn few marks.

A class also helps where the school cannot: a sixth form without Further Maths, or one where STEP is new. Cambridge itself says not to worry if a school cannot provide much help, because plenty of material exists. We add a teacher who reads every line.

Where it does not

If a school already runs STEP sessions with a teacher who marks full solutions, and the student is working steadily through the Support programme, a paid class adds little. We would rather say that than sell a course that duplicates good free provision.

And no class makes STEP easy. The Faculty's own words are that the papers "look daunting; but you should not be daunted", and that with enough practice students get better at them. Enough practice, finished and read, is all we teach.

Resources listed on the Faculty of Mathematics STEP page and OCR's preparing for STEP page; Warwick's use of STEP from its admissions tests page; read 31 October 2026.

From Year 12 to June

Four stages to STEP 2 and STEP 3

A typical path for a student applying in October of Year 13. Move on when the habit is reliable, not when the month changes.

Our STEP plan, alongside the 2026 to 2027 calendar
WhenStageThe sign it is secure
Year 12, summer1. STEP Support foundation workCan finish a multi-part problem without hints, even slowly
Year 13, autumn2. Further Maths content in placeComplex numbers, matrices, further calculus and series no longer interrupt a question
Year 13, January to April3. Single questions, timed at 30 minutesPicks a question in two minutes and reaches the end in most attempts
Year 13, May to June4. Full papers, six questions in three hoursWrites six finished answers, then stops

If June is weeks away

Sit two or three recent papers under full conditions, then rework every question you abandoned until you can finish it. The finishing is the practice.

Decide your sections. Many candidates aim at the eight pure questions; a student strong in mechanics or probability should know in advance that those two-question sections are an option.

If the offer is still to come

Start with the Further Maths A Level done properly, because STEP 3 assumes all of it, and with the free Support programme for problem solving.

Students who enjoy long, linked problems often enjoy the British Mathematical Olympiad in November of Year 13 as well.

The full list

What we teach a STEP candidate

Four groups, chosen by which gap is costing questions.

I

The papers

STEP 2 and STEP 3

STE / P / 01

Admissions tests: STEP, TMUA, MAT

Choosing six, and finishing them.

Open the syllabus

STE / P / 02

Olympiad and competition maths

Inequalities, invariants and proof.

Open the syllabus

STE / P / 03

Statistics and probability

For Section C, two questions a paper.

Open the syllabus
II

The content underneath

Years 12 and 13

STE / C / 02

A Level Maths

Pure, mechanics and statistics, all assumed.

Open the syllabus
III

Beyond the exam

First-year university mathematics

STE / U / 01

College mathematics

Calculus and algebra at university pace.

Open the syllabus

STE / U / 02

Maths through coding

Test a recurrence numerically, as above.

Open the syllabus

STE / U / 03

Python for teens

Check a numerical answer in a few lines.

Open the syllabus
IV

Related applications

Computer science and data

STE / R / 01

Problem solving and algorithms

Proof meets running time.

Open the syllabus

STE / R / 02

Competitive programming

The informatics olympiad route.

Open the syllabus

STE / R / 03

Data science with Python

Probability put to work on datasets.

Open the syllabus

How lessons run

Live STEP classes from the autumn of Year 13 to June

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Weekday evenings

One question, thirty minutes, then the write-up.

Weekend mornings

Room for a full three-hour paper.

1-on-1

For a candidate with a specific offer to meet.

Choose, then solve

Every lesson starts by reading several questions and choosing, the skill the paper tests first.

Finished answers

Solutions are written to the end and read in full, linking sentences included.

All three sections

Pure, mechanics and probability, so a student knows which of the twelve are really open to them.

A batch of 15 to 20

Several routes through one question, compared side by side.

Our own questions

Questions in class are composed by our teachers; OCR's papers are for students to sit on their own.

No grade promised

We do not promise an S, a 1 or an offer, and no one honestly can.

Student work

What our students build

Published student work from our school in mathematics, programming and AI. The student labs page gathers the rest.

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Fees

Fees

OCR charges the STEP entry through the centre, and some centres add an administration fee; our monthly fee is only for the classes, with no joining fee, and ends whenever the student chooses, usually after 21 June.

Free first class

USD 0

no card required

  • A free first class
  • One long question, read line by line
  • No card details
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Group batch

USD 100

a month, billed in US dollars

  • A batch of 15 to 20
  • One teacher through to June
  • Weekly solutions read in full
  • Monthly, stop any time
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One to one

USD 150

a month, billed in US dollars

  • One student, one teacher
  • Built around the offer conditions
  • Mock papers marked by hand
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STEP questions

What STEP candidates and parents ask

What is STEP maths?

STEP, the Sixth Term Examination Paper, is a mathematics exam set by OCR. OCR says it is used by the University of Cambridge, the University of Warwick and Imperial College London, and that some students sit it just for the challenge.

When is STEP in 2027?

OCR lists STEP 2 on 14 June 2027 and STEP 3 on 21 June 2027, both at 9am in the UK. Results are released on 12 August 2027 at 8am UK time.

How many questions do you answer in STEP?

Each paper has twelve questions and lasts three hours. Every answer is marked out of 20 but only the top six count. OCR advises against attempting more than six.

What is the difference between STEP 2 and STEP 3?

STEP 2 is based on A Level Mathematics and AS Level Further Mathematics; STEP 3 on A Level Mathematics and the full Further Mathematics A Level. Both have eight pure, two mechanics and two probability or statistics questions.

What were the STEP grade boundaries in 2026?

OCR's 2026 results explanation gives, out of 120, STEP 2: S 84, grade 1 62, grade 2 52, grade 3 34; and STEP 3: S 80, grade 1 56, grade 2 48, grade 3 30. Boundaries change every year.

Is STEP 1 still available?

No. The STEP specification says STEP Mathematics 1 has not been offered from the June 2021 sitting onwards. Old STEP 1 papers remain useful practice at roughly A Level Mathematics depth.

Can I register for STEP myself?

No. OCR says a candidate must be registered by an authorised centre, usually their school, between 1 March and 4 May 2027. A school that is not yet a centre can apply to become one even for a single candidate.

Can I use a calculator in STEP?

No. OCR says calculators are not allowed. Candidates may bring rulers, protractors and compasses, must write in black pen and use pencil only for diagrams.

Does Warwick accept STEP instead of the TMUA?

Yes, for Mathematics. Warwick says applicants typically take the TMUA or STEP, and that offers to applicants without a TMUA score are conditional on grade 2 in any STEP paper, alongside A Level or equivalent grades.

Do I need a tutor for STEP?

Not necessarily. The Faculty of Mathematics says free resources are more than enough and offers the STEP Support programme with NRICH. A teacher helps most when nobody else is reading full solutions or the school does not teach Further Maths.

When are classes held?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Are you part of OCR or Cambridge?

No. We teach independently, online, and OCR, Cambridge University Press and Assessment and the University of Cambridge have no part in our classes. Entries are made through a school or authorised centre.

Related pages

More for STEP candidates

The A Levels STEP rests on, a competition beside it, and the city itself.

Further Maths tuition online

Every topic STEP 3 takes for granted.

A Level Maths tuition online

STEP 2 rests on all of it.

Is A Level Further Maths worth it?

For a Year 11 student weighing up sixth-form options.

British Mathematical Olympiad

Long problems in November, a good rehearsal for June.

Further Maths tutor cost in the UK

What families pay for help at this level, and why it varies.

Maths tuition in Cambridge

For families living in the city.

Related pages in this guide

Part of the guide: UK university admissions: maths tests and computing applications

Admissions tests and interviews

Computer science applications

More guides: UK maths exam boards and specification codes · UK maths year by year, Reception to Year 11 · UK selective school maths tests: 7+, 11+, 13+ and 16+ · UK maths enrichment, competitions and able pupils

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Tell us which papers your offer names, or which you expect, and how far through Further Maths you are. The free class takes one long question to its last part with you and reads every line you write.

Want to look around first? Each course has its own syllabus, all listed here, and how we teach walks through a lesson.

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