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STEP

Sixth Term Examination Paper

The university-level mathematics examination administered by OCR — STEP 2 and STEP 3, each 3 hours and 12 questions, graded on your six best answers.

Format
2 papers (STEP 2/3)
Per paper
3 hrs, 12 questions
Strategy
Best 6 answers count
Grades
S / 1 / 2 / 3 / U
Start practisingPrep guides
STEP (Sixth Term Examination Paper) is administered by OCR, the exam board within the Cambridge family, and is one of the most demanding written admissions tests for mathematics degrees in the UK. It is used chiefly for Mathematics at Cambridge and for mathematics-related offers at universities such as Warwick and Imperial College London. There are two papers, STEP 2 and STEP 3, each lasting 3 hours with 12 questions (Section A: 8 pure, Section B: 2 mechanics, Section C: 2 probability and statistics), 20 marks per question, and the grade is based on your six best answers only, out of a maximum of 120. STEP is not a race against the clock: it rewards sustained progress through long, open-ended problems — deep mathematical problem-solving and rigorous proof — and is the key bridge from A-level to university mathematics.
PRACTICE

STEP past papers and original mocks, all timed online

Past papers
111+
Questions
1532+
Every paper is sat under time in an interface built to mirror the real computer-based test, not a PDF that gets downloaded and forgotten. Alongside the past papers, the original mocks follow the current exam structure exactly and target the syllabus points that come up most. Submit and you get worked solutions for every question, AI-classified error causes, accuracy tracked topic by topic and a weakness report that tells you what to practise next. Register free to sit 2 papers per subject.
Free tools
By the numbers

What the STEP bank holds today

questions
1532
papers
111
official past papers
111
with worked solutions
100%
Four difficulty tiers
Easy
3
Standard
328
Hard
1198
Very hard
3
By module
  • STEP 133 papers · 462 questions
  • STEP 239 papers · 535 questions
  • STEP 339 papers · 535 questions

Counted live from published content. Every paper and question can be checked in the catalogue.

PRACTICE

No multiple choice in STEP. Start with a real paper.

STEP is a three-hour written paper of long proofs, where every question needs a full derivation, so there is no multiple-choice taster. Register to sit past papers under the clock, each one with a full worked solution written by us.

Browse past papersRead the prep guides first
How it works

From a first taste to test day, in four steps

  1. 01

    Start from a whole past paper

    STEP is entirely open-ended proof questions, with no options to mark on the spot, so there is no five-question taster on this page. You start by opening a whole paper for one year, with STEP 1, 2 and 3 listed separately. The counts are in the numbers above.

  2. 02

    Sign up free

    Signing up opens the two most recent papers for free, each question with a worked solution that spells out the key steps. Earlier years unlock when you buy the subject.

  3. 03

    Answer by hand

    STEP marks the argument you can actually write out, so you write here too: use the on-screen pad, photograph your working on paper and upload it, or pair an iPad to use as a writing tablet.

  4. 04

    Review against the solution

    Proof questions are not auto-marked. Work through your answers against the solutions: where the key steps are, which step you stalled on, which ones you can skip. Students in a class are marked question by question by their teacher.

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What you get

Six things STEP preparation needs

  • Official past papers + originals

    Every officially released paper organised by year, plus original papers written to the current format. Counts are in the numbers above.

  • A worked solution for every question

    The right method, and why each wrong option is wrong. Solutions are verified, not generated once and left.

  • Topic radar and weak spots

    Mastery by topic updates after every session; weak topics go straight into your study plan.

  • A timed, true-to-exam interface

    Same timing, navigation and flagging as the real computer-based test, so nothing is new on the day.

  • Mistake book and review

    Mistakes are grouped by cause; the review centre rebuilds a set of similar questions to try again.

  • English and Chinese

    Questions, solutions and the interface in both languages, switchable at any time.

SCHEDULE

Test dates

June 2026 sitting
Registration opens
1 March
Registration closes
4 May
Test date
STEP 2 on 4 June, STEP 3 on 10 June
Results
13 August (boundaries published the same day)
Register now
The table above gives the exact dates OCR has published for the 2026 series. Dates for 2027 have not been published yet, and OCR reserves the right to change dates and fees, so do not treat 4 June and 10 June as a fixed annual pattern (the weekdays move every year). Note too that you cannot enter yourself: entries must be made through an authorised centre, and some centres charge an administration fee on top of the entry fee. Always work from the dates on the official OCR website.
STRUCTURE

Paper structure

01STEP 2

A-level Maths + Further Maths level — mainly pure

12 questions, best 6 count3 hours
Officially based on A Level Mathematics and AS Level Further Mathematics, centred on pure mathematics with mechanics and probability/statistics alongside. Questions are longer and more open-ended than A-level, demanding multi-step reasoning and proof.
02STEP 3

Harder still — full Further Maths syllabus

12 questions, best 6 count3 hours
Harder than STEP 2 and based on A Level Mathematics and A Level Further Mathematics. The specification describes it as the prescribed pure content of Further Mathematics with some topics removed and others added, so it is not a straight copy, with pure questions of greater depth and abstraction — the core component of a Cambridge Mathematics offer.
SCORING

Scoring

  1. 01
    Each paper is graded on a five-band scale: S / 1 / 2 / 3 / U (S is the highest, U unclassified).
  2. 02
    Each question carries 20 marks and only your six best answers count, for a maximum of 120. Anything beyond six is still marked, but attempting more than six is not advised.
  3. 03
    Cambridge writes STEP into the offer as a condition, and the minimum offer level is grade 1 in both STEP 2 and STEP 3. The exact grades vary by College, so check the page for the College you are applying to.
  4. 04
    Results are released in mid-August (for the 2026 series, 13 August at 08:00 UK time, with the grade boundaries published alongside them) and passed to universities through UCAS.
Grade boundaries · 2026 series (published by OCR)
GradeSTEP 2STEP 3Reached (STEP 2 / 3)
S84 / 12080 / 1208.27% / 9.27%
162 / 12056 / 12028.14% / 35.73%
252 / 12048 / 12041.97% / 48.73%
334 / 12030 / 12073.52% / 83.18%

Boundaries are published each results day and move every year; 2026 is the latest published series.

UNIVERSITIES

Universities & requirements

RequirementUniversityCoursesNotes
RequiredUniversity of CambridgeMathematics, and the Mathematics with Physics route
STEP is a condition of the offer, not a pre-application test: you sit it in the summer after you apply. The published minimum offer level is grade 1 in both STEP 2 and STEP 3, with the exact grades set by each College. There is also a flexible offer scheme (eight Colleges for 2027 entry), under which you still sit both papers. Individual Colleges may set STEP for other maths-heavy courses too.
RequiredUniversity of WarwickMathematics (TMUA or STEP — one of the two is required)
Warwick Mathematics requires either the TMUA or STEP (it is not an optional extra). On the STEP route, the typical offer carries an added condition of grade 2 in any one STEP paper (STEP 2 or 3) — check the offer terms for the year.
RecommendedImperial College LondonMathematics
Imperial Mathematics uses the TMUA as its main written test; applicants without a TMUA score usually receive a conditional offer with a STEP condition attached. Check each course’s admissions page for the current year.
SupplementaryUniversity of Bristol / University of BathMathematics
Bristol: a STEP grade can feed into an alternative (reduced) offer. Bath: from 2025 entry, STEP is no longer considered for standard applicants taking Further Mathematics; only applicants without Further Maths may be asked for it (e.g. grade 2 in any STEP paper).
GUIDES

Prepare module by module

10 in-depth guides for the STEP: what each module actually tests, how to build a revision plan around it, how the marks work, and what to do on test day.

COMPETITIVENESS

How scores compare

  • Cambridge Mathematics: the published minimum offer level is grade 1 in both STEP 2 and STEP 3. The widely repeated claim that certain colleges ask for an S has no source on either the OCR or Cambridge pages; Cambridge states only that the grades required vary by College, so the thing to check is the College you are applying to, not a threshold circulating online.
  • Warwick: one of TMUA/STEP is compulsory — the STEP route needs grade 2 in any one paper. Imperial: TMUA is the primary test, with a STEP condition typically attached when no TMUA score is offered.
  • STEP is hard and the grade distribution moves year on year, with boundaries adjusted to the cohort; always check each university’s website for the latest policy.
Grade boundaries · 2026 series

Minimum mark out of 120 for each grade (published by OCR)

Boundaries move every year; grades are based on your six best answers (20 marks each).

ANALYSIS

Exam analysis

  • STEP uses the S / 1 / 2 / 3 / U grade scale. There is a real maximum of 120 marks (six questions at 20), but no fixed pass mark: grades come from boundaries published each year, set with reference to the intake of the universities that use STEP, so they move from year to year. Question selection therefore shapes your grade directly, and finishing your strongest questions properly beats spreading yourself thinly.
  • Questions are long and open-ended, usually building through several linked parts; they are proof-heavy and reasoning-heavy, with high demands on written presentation and logical rigour.
  • STEP 2 leans pure with foundational mechanics/statistics; STEP 3 steps up markedly in difficulty and abstraction, covering the full Further Maths syllabus — train for the two papers separately.
  • Time management is decisive: 3 hours for roughly 6 questions — fewer, done properly, wins. Use past papers for timed full runs and rehearse your selection rhythm.
Score distribution

Share of candidates by STEP 2 grade, official 2026 series data

Official OCR Explanation of Results data for the 2026 series (STEP 2): 28.14% of candidates reached grade 1 or above, and 8.27% achieved an S. The gold line marks the published Cambridge minimum offer level (grade 1 in both STEP 2 and STEP 3; exact grades vary by College).

The heart of STEP preparation is volume of past papers plus disciplined error review: master your A-level and Further Maths foundations, then work systematically through past STEP 2/3 papers, polishing your written reasoning on the long proof questions. Keep an error log, revisit it regularly, and add timed mock exams. For a structured pathway, see our prep guides.
FAQ

Frequently asked questions

What is the difference between STEP 2 and STEP 3?
STEP 2 targets A-level Maths + Further Maths level and is mainly pure with some mechanics and statistics; STEP 3 is harder, covering the full Further Mathematics syllabus with markedly greater abstraction and depth. Cambridge Mathematics offers usually require both papers.
Do I have to answer all 12 questions?
No, and the rule is not “pick six and commit”: everything you attempt is marked, but only your six best answers count towards the grade. So if a question stalls you can move on without having wasted the slot. Finishing six properly in three hours is the usual shape, and attempting more than six is not advised.
How is STEP graded, and what does Cambridge ask for?
Each paper is graded S / 1 / 2 / 3 / U (S highest), with grades set by boundaries published each year. For the 2026 series, grade 1 fell at 62 out of 120 on STEP 2 and 56 on STEP 3, and the proportion reaching grade 1 or above was 28.14% on STEP 2 and 35.73% on STEP 3. The Cambridge minimum offer level is grade 1 in both papers, with exact grades set by each College.
Is STEP much harder than A-level? How should I prepare?
Yes — STEP is hard, with longer, more open-ended questions centred on proof and multi-step reasoning. Build solid Further Maths foundations first, then work through plenty of past papers with thorough error review, plus timed mock exams. See our prep guides and practice modules.
When is STEP sat, and when do results come out?
STEP is sat in June with results in mid-August, passed to universities through UCAS. The official 2026 dates were: registration open 1 March, close 4 May, STEP 2 on 4 June, STEP 3 on 10 June, results on 13 August with the grade boundaries published the same day. Entries must be made through an authorised centre; you cannot register yourself. Check the official OCR website for the 2027 dates.

Process

How It Works

01

Sign Up

02

Choose Your Exam

03

Start Practicing

There is no waiting step in between. You can open a paper the moment you register.

See the papers for this exam
Pricing

How far free goes for STEP, and what a purchase adds

Free

£0/ forever
  • 10 questions a day per subject, each with a full solution
  • 2 free papers per subject, plus a 5-question taster before you sign up
  • Analytics, mistake book and review centre fully open
Sign up free

Pay once per subject

£58.80/ STEP · permanent access
  • Every STEP past paper and original paper
  • Full mock exams (twice a year by the Frontier team)
  • New content included for a year, then renew the update window annually
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STEP

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