STEP preparation guide

STEP 3: What It Tests, How Hard It Is, and How to Prepare

If Cambridge Mathematics is the goal, STEP 3 is close to unavoidable: it is the deeper of the two current STEP papers, built on the full A level Further Mathematics course, and the published minimum offer level asks for grade 1 in both STEP 2 and STEP 3. This guide covers STEP 3 alone: its official positioning and syllabus basis, the best-six scoring rule, the 2026 grade boundaries and the proportion of candidates who cleared them, where the extra difficulty over STEP 2 actually lives, and how to pace a year of preparation around the official STEP Support Programme.
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STEP 3 at a Glance
Syllabus basis
A level Maths plus full A level Further Maths, with pure topics added and removed
Paper and scoring
Twelve questions in three hours; all marked, best six count, out of 120
2026 boundaries
S=80, 1=56, 2=48, 3=30; 35.73% reached grade 1 or above
Cambridge offer
Minimum offer level A*A*A with grade 1 in both papers; exact grades set by College
Key 2026 dates
Entry opened 1 March and closed 4 May; STEP 3 sat on 10 June

Boundaries are set so successful offers match the places available at Cambridge, Warwick and Imperial, so they move with the cohort and serve only as a reference frame; the 2027 dates are unpublished and OCR reserves the right to change dates and fees.

In short
  • STEP 3 is based on A level Mathematics plus full A level Further Mathematics, and the specification adds and removes pure topics, so map your revision to the syllabus itself, not your textbook.
  • Every attempt is marked and only your six best answers count, out of 120. In 2026 grade 1 fell at 56, below the value of three perfect questions, so depth beats coverage.
  • In 2026, 35.73% of STEP 3 candidates reached grade 1 or above and the S boundary of 80 equalled four perfect questions; boundaries move with the cohort and are published on results day.
  • The Cambridge minimum offer level is grade 1 in both STEP 2 and STEP 3; the exact grades vary by College, so the College website is the authority.
  • The official STEP Support Programme starts its STEP 3 modules in January of Year 13, followed by timed past papers, with official worked solutions available from 2019 onwards.
I

Part 1 of 3

Sections 01 to 03

01

What STEP 3 is

Modern STEP consists of exactly two papers: STEP 2 (paper code 9470) and STEP 3 (paper code 9475), and candidates sit one or both depending on what the universities they applied to require. STEP 1 has not been offered since the June 2021 sitting, so any STEP 1 past paper you find online predates that change. It works as warm-up material, but it no longer represents a live examination.

Paper code

9475

One of the two live papers, alongside STEP 2 (9470)

Board and format

Administered by OCR, paper-based

OCR is the exam board within the Cambridge family

Duration

Three hours per paper

Handwritten at an authorised centre

Knowledge base

A level Maths plus full A level Further Maths

STEP 2 assumes only AS level Further Maths

Current specification

Version 1.3

For examinations from June 2026 onwards

The specification is explicit: the pure content of STEP 3 builds on the prescribed pure content of A level Further Mathematics with modifications, some topics removed and others added. Completing your Further Maths course therefore does not mean you have covered the STEP 3 syllabus. Work through the current specification line by line rather than assuming your school textbook maps neatly onto it.
CambridgeWarwickImperial College London
Where the test sitsWrites STEP 3 into its typical offerRequires one of TMUA or STEPCentres on the TMUA
STEP requirementApplicants normally sit both STEP 2 and STEP 3Grade 2 in either STEP paper is enoughAttaches STEP conditions only in particular circumstances

These three are STEP's official user universities, and how seriously you need to take STEP 3 is largely a function of whether Cambridge is on your UCAS form.

02

Structure and the best-six rule

STEP 3 shares its structure exactly with STEP 2: a three-hour paper of twelve questions in three sections, every question carrying the same maximum of 20 marks. There is no restriction on how many you attempt from any section, so answering six pure questions and nothing else is entirely within the rules.

The STEP 3 paper

Three hours · twelve questions · 120 marks

Section A: PureEight questions
  • 20 marks each
  • No limit on how many you attempt
  • Six pure answers is a legal paper
Section B: MechanicsTwo questions
  • 20 marks each
  • Weighted the same as the pure questions
Section C: Probability and statisticsTwo questions
  • 20 marks each
  • Weighted the same as the pure questions
Scoring: your best sixOut of 120
  • Every attempt is marked
  • The best six are selected afterwards
  • No bonus marks for completing a question

Tap a branch to unfold

The scoring rule deserves precise reading, because it is widely misquoted. Everything you attempt is marked, and your final score is the sum of your six best-answered questions. This is not "choose six at the start and commit": if a question stalls halfway you can abandon it and start another, and the marks already earned are not wasted, because examiners reward good progress towards a solution even when the final answer is incorrect. A correct answer earns full marks whatever method produced it.
Two further official points close the common loopholes. There are no bonus marks for completing a question: each is marked strictly against a 20-mark scheme. And attempting more than six questions is officially not advised, because candidates who spread themselves across seven or eight attempts rarely score as well as those who concentrate on finishing six properly. Time, not access to questions, is the binding constraint.
03

The 2026 grade boundaries and distribution

STEP is unusually open about its numbers: the grade boundaries and score distribution are published every year, released alongside results by 08:00 UK time on results day (13 August in 2026), and the annual Explanation of Results documents are available online back to 2019. For the 2026 sitting of STEP 3, out of a maximum of 120, the figures were these.

Grade S

80 marks

9.27% cumulative

Grade 1

56 marks

35.73% cumulative

Grade 2

48 marks

48.73% cumulative

Grade 3

30 marks

83.18% cumulative

56 marks

The grade 1 boundary, below the value of three perfect questions (60)

80 marks

The grade S boundary, exactly four perfect questions

35.73%

Share of candidates reaching grade 1 or above in 2026

Two pieces of arithmetic are worth internalising. Grade 1 sat at 56, less than half the paper, so three questions done thoroughly plus scattered part-marks elsewhere secures it, while four near-perfect solutions with a little extra reaches an S. The official advice to concentrate on six questions, and within those to finish your strongest work properly, is not a platitude; it falls straight out of the numbers.
The boundaries are not fixed. They are set so that the number of successful offers closely matches the places available at the official user institutions (Cambridge, Warwick and Imperial College London), which means they move with the cohort's performance from year to year. Treat the 2026 figures as a reference frame, not a promise, and aim with a margin of safety rather than at the line itself.
II

Part 2 of 3

Sections 04 to 06

04

How STEP 3 differs from STEP 2

Structurally the two papers are identical twins; every difference lives in the content. That additional further pure material gives STEP 3 questions a higher platform to launch from: for the same 20 marks, a STEP 3 question will typically involve less familiar objects, more abstract definitions and longer chains of algebra, and it leans harder on your ability to stay rigorous inside a structure you have never met before.
STEP 2STEP 3
BasisA level Maths + AS Further MathsA level Maths + full A level Further Maths
Grade 1 boundary6256
Grade 1 or above28.14%35.73%
Grade S boundary8480
Grade S8.27%9.27%

Published 2026 figures for both papers, each marked out of 120.

Notice the apparent paradox: STEP 3 has lower boundaries and a higher proportion of candidates reaching each grade. The more plausible reading is that the STEP 3 cohort is strongly self-selected, made up of candidates who have completed full Further Maths, most with Cambridge in their sights, so the field is stronger, while the harder content pulls raw scores down and the boundaries follow.
Never infer difficulty from boundary heights: STEP 3's lower line does not make it the easier paper. Train for the two papers separately rather than treating STEP 3 as STEP 2 with a few extra topics bolted on.
05

What STEP 3 questions actually demand

The official description of STEP's question character rewards repeated reading: questions may test the ability to apply mathematical knowledge in novel and unfamiliar ways, frequently draw on several specification topics at once, and typically require insight, ingenuity, persistence and the capacity to work through substantial sequences of algebraic manipulation. None of those four words describes fluent formula application; all four describe mathematical behaviour under uncertainty. For STEP 3 that carries extra weight, because the examiner has the whole Further Mathematics toolkit available and can braid together strands your course taught in separate terms.

Presentation

Clear, logical and legible

Working fully set out

Part-marks

Paid for good progress towards a solution

Earned even when the final answer is wrong

Method

A correct answer earns full marks

Whatever route produced it

Where marks leak

Marks may be lost if the examiner cannot follow you

Even when a correct answer appears at the end

Two further rules amplify the premium on fundamentals: calculators are neither permitted nor required, and there has been no formulae booklet since 2019, with the formulae you are expected to know listed in the appendix to the specification. Knowing how to solve a problem and being able to write the solution as a proof another mathematician can follow are two different skills, and the second has to be practised deliberately, on paper and against the clock. Accurate long-form hand computation and instant recall of standard results are trainable, and they need to be your default state well before exam day.
06

STEP 3 in a Cambridge offer

Almost every conditional offer for Mathematics at Cambridge (including the Mathematics with Physics route) includes STEP, and applicants are normally asked to take both papers. The published minimum offer level is A level A*A*A together with at least grade 1 in both STEP 2 and STEP 3. The grades actually required vary by College, so the authoritative source is the website of the College you are applying to, not a threshold circulating on forums.

A*A*A

The A level half of the published minimum offer level

Grade 1, twice

Required in STEP 2 and STEP 3 alike

Eight Colleges

Operate a flexible offer scheme for 2027 entry

How is the flexible offer met?
Eight Colleges run it for 2027 entry: Downing, Emmanuel, Girton, Jesus, Newnham, Robinson, Sidney Sussex and Trinity Hall. The condition is met either by A*A*A with grade 1 in both STEP papers, or by A*A*A* with grade 1 in either paper, with both papers still to be sat.
When is STEP sat, before or after applying?
STEP is a condition of the offer rather than a pre-application test: apply in October 2026 and you would expect to sit STEP in June 2027. You therefore submit your application without a STEP score, and what the result decides is whether the offer converts.
What happens if I narrowly miss the condition?
One detail few applicants know: copies of candidates' answer booklets are sent directly to the Cambridge admissions team, precisely so that decisions about students who narrowly miss their offer can be made on the actual mathematics rather than the bare grade. A result just short of the condition can still be rescued by the quality of the solutions in the booklet, which is one more hard reason to write your working properly.
For contrast, Warwick accepts grade 2 in either STEP paper, whichever you prefer, and Imperial attaches STEP conditions only in particular circumstances. Full-intensity STEP 3 preparation, though, has always had Cambridge applicants as its core audience.
III

Part 3 of 3

Sections 07 to 09

07

A preparation timeline that follows the official sequence

The Faculty of Mathematics at Cambridge has developed a free official preparation programme, the STEP Support Programme, open to everyone and built from online modules with hints and full solutions. It has also published fully worked solutions to every STEP 2 and STEP 3 paper from 2019 onwards, written specifically so you can assess your own timed attempts. Students on an accelerated Further Maths track, common in international schools in China, can reasonably start earlier, but the order below is worth preserving.
01From Year 12

Foundation modules

Designed to be worked weekly over about six months, and the entry point to the whole official path.
02September of Year 13

STEP 2 modules

The stage after Foundation, placed before the STEP 3 modules in the official order.
03January of Year 13

STEP 3 modules

Starting in January is the pacing the programme itself recommends; students further ahead in Further Maths can reasonably begin sooner.
04After the modules

Timed full papers

Entered once all the modules are complete, checked against the official worked solutions for papers from 2019 onwards.
2026Timeline
Mar 26
Apr 26
May 26
Jun 26
Entry opens
1 Mar
Entry for the 2026 series opened. Entry is made through an authorised centre; you cannot register yourself.
Entry deadline
4 May
Entries for the 2026 series closed.
STEP 2 sat
4 Jun
The two papers fall less than a week apart.
STEP 3 sat
10 Jun
Final rehearsals should simulate that double-header intensity.
Hard deadline Event WindowThese are the actual dates for the 2026 series; the 2027 timetable has not been published.

How to enter

Through an authorised centre

You cannot register yourself

Fee in the UK

£102.50

Per paper

Fee elsewhere

£142.25

Per paper, or $179.75 / €166

Extra charges

Some centres add an administration fee

One caution to end on: dates for the 2027 series have not been published, and OCR reserves the right to change dates and fees, so treat the 2026 calendar as an example rather than an annual pattern.
08

Exam-room rules: a different discipline from on-screen tests

Students who have sat the ESAT or TMUA on screen need to recalibrate: STEP is a handwritten, paper-based examination, and its rules are spelt out in the official instructions in unusual detail.

Calculators

Not permitted

And not required either

Formulae booklet

None issued

The formulae you must know are in the specification appendix

Graph paper

Not permitted

Every graph required is a sketch, drawn inside the answer booklet

Rough paper

None given; rough work goes in the booklet

Extra sheets attached are removed unmarked, and crossed-out work is not marked unless you clearly indicate that you want it to be

Equipment

Answers in black pen, diagrams in pencil

Rulers, protractors and compasses are allowed

Dictionaries

Bilingual dictionaries not permitted

A rule candidates from China in particular should know well before the day

The common thread is that the answer booklet is your entire output channel. The efficient response is to practise the way you will be examined: no calculator, no formula sheet open in another tab, rough work managed alongside the fair copy on the same pages. Make examination-conditions writing your default months in advance, not a two-week conversion project at the end.
09

Exam strategy and five common misconceptions

01Step 1

Read all twelve quickly at the start

The aim is six questions done properly, and the read-through is how you find the best entry point.
02Step 2

Begin with the question you understand best

Given the rules, sound strategy is almost boringly simple: start where you can see the most.
03Step 3

Switch without guilt when an attempt stalls

The part-marks stay banked, so abandoning an attempt wastes nothing you have already written.
04Step 4

Write every step so a stranger could follow it

The mark scheme pays for visible progress towards a complete solution, and reasoning nobody can follow cannot collect it.
Myth 1: you must commit to six questions at the start
False: everything attempted is marked, and your best six are selected afterwards automatically.
Myth 2: attempting extra questions can only help
Officially not advised: candidates who attempt more than six rarely score as well as those who concentrate on six, because time, not access, is the binding constraint.
Myth 3: STEP 3's lower boundaries mean it is the easier paper
Boundaries reflect the cohort and the paper's difficulty together; the STEP 3 field is stronger and the content deeper, so the numbers are not comparable across papers.
Myth 4: there are bonus marks for a complete solution
There are none; every question is marked strictly out of 20.
Myth 5: STEP always falls on the same June dates
In 2026 the papers fell on 4 June and 10 June, but the 2027 timetable has not been published and OCR reserves the right to change dates, so always work from the current year's official calendar.
Each of these directly changes behaviour in the exam room, which is why they are worth correcting before your first timed paper rather than paying for them on the results slip.
FAQ

Frequently asked questions

What does STEP 3 cover? Is finishing Further Maths enough?
Officially it is based on A level Mathematics plus full A level Further Mathematics, but the specification states that the further pure content comes with modifications: some topics removed, others added. Finishing the course is therefore not the same as covering the syllabus. Check the current specification (Version 1.3, from June 2026) line by line, including the appendix of formulae you are expected to memorise.
What score gets a grade 1 in STEP 3? Are boundaries the same every year?
In 2026, out of 120, the STEP 3 boundaries were S=80, 1=56, 2=48 and 3=30, and 35.73% of candidates reached grade 1 or above. Boundaries change every year: they are set so that successful offers closely match the places available at Cambridge, Warwick and Imperial, move with the cohort's performance, and are published alongside results. Aim with a margin of safety rather than at last year's line.
How much harder is STEP 3 than STEP 2, and why are its boundaries lower?
The structures are identical; the difficulty gap is in content. STEP 2 assumes only AS Further Maths, while STEP 3 is based on the full course, with more abstract objects and longer algebra. In 2026 the STEP 3 grade 1 boundary (56) was lower than STEP 2's (62), yet a higher proportion cleared it (35.73% against 28.14%), because the STEP 3 cohort is strongly self-selected and the harder paper pulls raw scores down. Boundaries cannot be used to compare difficulty across papers.
What STEP 3 grade does a Cambridge Mathematics offer require?
The published minimum offer level is A level AAA with at least grade 1 in both STEP 2 and STEP 3, and applicants normally sit both papers. The exact grades vary by College, so check the College you are applying to. For 2027 entry, eight Colleges run a flexible offer: AAA with grade 1 in both papers, or AAA* with grade 1 in either, with both papers still taken.
When should I start preparing for STEP 3?
The official STEP Support Programme (free and open to everyone) recommends: Foundation modules from Year 12, worked over about six months; STEP 2 modules from September of Year 13; STEP 3 modules from January of Year 13; then timed full papers, with official worked solutions to STEP 2 and STEP 3 papers available from 2019 onwards. Students on an accelerated Further Maths track can start earlier, but keep the order intact.
Can I use a calculator or formulae booklet in STEP 3?
Neither. Calculators are not permitted or required, and the formulae booklet was discontinued in 2019; the formulae you must know are listed in the specification appendix. Graph paper is not allowed (sketches go in the answer booklet), no extra rough paper is issued (rough work goes in the booklet; attached sheets are not marked), answers are in black pen with diagrams in pencil, rulers, protractors and compasses are allowed, and bilingual dictionaries are banned.
SOURCES

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