STEP preparation guide

STEP Section A pure mathematics: the eight questions that decide your grade

On both STEP 2 and STEP 3, eight of the twelve questions are pure mathematics, and your grade rests on your six best answers. Put those two facts together and the conclusion is blunt: Section A is where your marks will come from. This guide covers what a STEP pure question actually looks like, how far it sits beyond A level, how the syllabus is drawn, which exam-room rules shape your written work, and why the writing itself earns marks.
9 sections2,239 words12 min read5 official sources
Practise 111 STEP papers (2 free)Full STEP guide
Papers
111
Questions
1532
Free to try
2
STEP Pure Maths at a Glance
Paper structure
Three hours, twelve questions: eight pure, two mechanics, two statistics, 20 marks each
How it is scored
Everything is marked, your best six count automatically out of 120, with no cap per section
Syllabus base
STEP 2: A level Maths plus AS Further; STEP 3: A level Maths plus A level Further, with pure amendments
Grade 1 in 2026
62 out of 120 on STEP 2, 56 out of 120 on STEP 3
Exam-room kit
No calculator, no formulae booklet, no graph paper, no extra rough paper

Structure, scoring, syllabus and presentation rules come from the STEP specification v1.3 (for examinations from June 2026) together with OCR's scoring pages and official FAQ; boundaries and distributions come from OCR's explanation of results for STEP 2026.

In short
  • Eight of the twelve questions on each paper are pure; mechanics and statistics offer only four between them, so at least two of your six counting answers must come from Section A, and in practice pure usually supplies most of them.
  • Everything you attempt is marked and your best six count automatically; you never commit to six in advance, so abandoning a stalled question costs nothing and partial progress still banks marks.
  • STEP pure questions demand complete written arguments: OCR states that solutions must be clear, logical and legible, and that marks may be lost when examiners cannot follow the working, even if the final answer is right.
  • Prepare against the specification, not your school course: STEP 2 is based on A level Mathematics plus AS Further Mathematics, STEP 3 on A level Mathematics plus A level Further Mathematics with amendments, so the current specification is the boundary.
  • Calibrate with the published boundaries: grade 1 on STEP 2 in 2026 was 62 out of 120, roughly three questions done properly plus partial credit elsewhere, not six perfect solutions.
I

Part 1 of 3

Sections 01 to 03

01

Eight against four: why Section A carries your grade

8

Pure questions in Section A, out of twelve on the paper

4

Mechanics and statistics questions combined

6

Answers that actually count towards your grade

120

Maximum total, at 20 marks per question

STEP 2 and STEP 3 share an identical structure: three hours, twelve questions, eight pure in Section A, two mechanics in Section B and two probability and statistics in Section C, each worth 20 marks. The scoring rule is the part that matters. Everything you attempt is marked, your grade rests only on your six best answers out of 120, and OCR places no restriction on how many questions you may attempt from any section.
Put those rules together and the arithmetic is stark. Sections B and C offer four questions between them, so even a candidate who answers every applied question in full must still draw at least two of their six counting answers from Section A. The reverse is entirely legitimate: answer six pure questions and nothing else, and your grade is computed exactly as normal. Pure is not a section you can route around; the only question is whether it supplies two of your six or all six.
Most candidates end up much closer to the second case. With only two questions each, Sections B and C carry an element of luck about whether the year's models suit you, while Section A's eight questions give you real freedom to choose and let you sidestep a weak topic.
Let your preparation time mirror that structure. Pure mathematics is the main front; the applied sections are options you add from strength, never obligations.
02

What a STEP pure question actually looks like

OCR describes the character of its questions plainly: they test the ability to apply mathematics in novel and unfamiliar ways, they often draw on several specification topics at once, and solutions demand insight, ingenuity, persistence and the stamina to push through long sequences of algebraic manipulation. That is not marketing copy but an accurate structural description of Section A.
In practice a 20-mark pure question is built in linked parts. An early part establishes a result or demonstrates a technique; a later part expects you to recognise that earlier work as scaffolding and redeploy it somewhere new. Questions rarely stay inside a single topic either, so revising in isolated chunks only carries you half the distance.
What counts as an answer matters just as much. Most Section A questions resolve into proof and sustained argument rather than a single numerical value, and the marking is built to match.

Progress

Rewarded on its own

OCR rewards good progress towards a full solution even when the final answer is wrong

Method

Full marks whatever you use

A correct answer scores full marks however it was reached

Finishing bonus

None

There are no bonus marks for completing a whole question

Mark scheme

Strictly 20 marks per question

Each question is marked strictly against a 20-mark scheme

Your goal is not to conjure a conclusion but to build a chain of reasoning an examiner can verify step by step.
03

The gap from A level pure mathematics

The near-universal first experience of a STEP past paper runs like this: every technique on the page is one you have met, yet the question will not move. The gap is not in the list of topics; it is in the shape of the questions.
A level pureSTEP pure
Length of one questionA few minutes each, arriving pre-sliced into small steps20 marks each, roughly half an hour at the pace of six questions in three hours
SignpostingSignposts planted throughout: find this, hence show thatOften only a starting point and a destination, with the bridge left to you
The examined skillExecuting prescribed stepsJudging which manipulation to try, when to reach back for an earlier result, and how to structure the middle of an argument
A third difference is the working environment. Calculators are neither permitted nor required, and the formulae booklet was discontinued in 2019, with everything you are expected to know listed in the appendix to the specification. There is no external crutch for weak algebra or shaky recall.
The right response is not to relearn content but to retrain: move from executing prescribed steps to planning whole solutions yourself. That capacity grows only by attempting entire questions and writing entire solutions.
II

Part 2 of 3

Sections 04 to 06

04

The syllabus, read from the top down

The boundary of Section A is drawn by the current specification, and the official framing is two sentences long: STEP 2 is based on A level Mathematics plus AS level Further Mathematics, STEP 3 on A level Mathematics plus A level Further Mathematics. Both papers share the whole of A level Mathematics as their foundation; what separates them is how deep into Further Mathematics they reach. The current document is the STEP specification version 1.3, for examinations from June 2026 onwards.

STEP specification v1.3

For examinations from June 2026; it draws the boundary of Section A

What STEP 2 is based onA level Maths plus AS level Further Maths
  • A level Mathematics, the foundation both papers share
  • AS level Further Mathematics
What STEP 3 is based onA level Maths plus A level Further Maths
  • A level Mathematics, the same foundation
  • A level Further Mathematics, with the pure content amended
What the amendments meanNot a verbatim copy of the Further Maths course
  • Some topics have been removed
  • Other topics have been added in
  • Audit yourself against the specification, not your school's scheme of work
The appendixThe part you commit to memory
  • It lists the formulae you are expected to know
  • No booklet is issued in the exam; it was discontinued in 2019
Auditing versus trainingThe syllabus is a checklist, not a training unit
  • Working through the topic list for gaps is a necessary first pass
  • A STEP question routinely reaches for several entries at once
  • It gives no warning about which combinations appear, so train on whole questions

Tap a branch to unfold

Candidates sitting both papers get a bonus from this: every piece of pure groundwork laid for STEP 2 remains fully load-bearing in STEP 3.
05

Playing the best-six rule inside Section A

Get the rule exactly right first, because a common misreading costs real marks. STEP never asks you to nominate six questions. Everything you attempt is marked and the six highest scores are combined automatically. OCR adds two pieces of guidance worth taking literally: you may attempt as many questions as you wish, but going beyond six is not advisable and candidates who do rarely score as well as those who concentrate on six; and there are no bonus marks for completing a question.
01Step 1

Read all twelve before writing anything

Spend the opening minutes ranking the eight Section A questions by confidence. No other few minutes of the exam pay better.
02Step 2

Walk away from a stalled question

There is no structural penalty. You have not wasted a slot, the progress already on the page still earns marks, and the best-six calculation settles it in your favour at the end.
03Step 3

Spend your freedom of choice in Section A

Pure supplies eight of the twelve questions, so nearly all genuine selection freedom lives there; with only two questions each, the applied sections are take-it-or-leave-it.
The published boundaries turn this into arithmetic. Grade 1 on STEP 2 in 2026 fell at 62 out of 120. Three questions finished properly gets you close to 60, and partial progress on one or two others covers the rest. Fewer questions done thoroughly is not a mindset slogan; it is the strategy the scoring rule directly rewards.
06

Presentation is marks, not manners

The specification is blunt about presentation: solutions must be clear, logical and legible, working must be fully set out, standard notational conventions should be followed, and final answers simplified.
Marks may be lost if examiners are unable to follow a candidate's working, even when a correct final answer appears. That is an official marking rule in black and white, not a teacher's plea for neatness.
The rule fits the nature of the paper. Since Section A resolves into proof and argument, what an examiner pays for is verifiable reasoning. Skipped steps, ambiguous references and conclusions that appear from nowhere all convert mathematics you actually did into marks you do not receive.
There is a further audience most candidates never hear about. Copies of answer booklets go directly to the Cambridge admissions team, which uses them to judge applicants who narrowly miss their offer on the strength of their actual work rather than the bare marks or grade. Every page you write may be read not only by an examiner but by the people deciding your place.

Before you start

State what you will prove

Every step

Give a reason for anything non-obvious

Reusing an earlier part

Say explicitly which earlier result you are invoking

Long algebraic chains

Write the extra line rather than skip it

Closing a proof

End with a clear concluding sentence

Practise to this standard from your very first past paper, because exam pressure never improves anyone's handwriting or discipline.
III

Part 3 of 3

Sections 07 to 09

07

Exam-room rules that shape your written work

STEP is a pen-and-paper examination, and a handful of physical rules shape how Section A work actually gets written. Rehearse under them from the start rather than discovering them on the day.

Calculators

Not permitted, not needed

The numbers are designed for hand computation

Formulae booklet

None issued

What you must know is listed in the specification's appendix

Pens and instruments

Black pen for answers, pencil for diagrams

Rulers, protractors and compasses are allowed

Graph paper

Not permitted

Every graph a question asks for is a sketch, drawn in the booklet

Extra paper

None issued

Only work inside the official booklet is marked; attached sheets are removed unmarked

Rough working therefore lives in the booklet too. Under OCR's official FAQ guidance, crossed-out work is not marked unless you clearly indicate that you want it to be, and pages containing answers need to be flagged as the booklet instructs.
Taken together, these rules impose one training requirement: your exploration and your fair copy share the same booklet. Practise thinking on the page within limited space, keeping trial calculations compact, crossing out cleanly and decisively, and laying the final argument out in tidy, readable blocks. Anyone used to sprawling across loose A4 finds the first booklet-constrained paper genuinely uncomfortable, so get that adjustment done months ahead.
08

A training route for Section A

There is an official, free route for pure preparation: the STEP Support Programme, developed by the Faculty of Mathematics at Cambridge and open to everyone. It consists of online modules for individual study, with hints and full solutions provided, and the recommended rhythm is concrete.
01From Year 12

Foundation modules

Designed to be studied weekly over about six months.
02September of Year 13

STEP 2 modules

Picked up after the Foundation work, moving into pure at STEP 2 level.
03January of Year 13

STEP 3 modules

The suggested starting point, matching STEP 3's extra layer of abstraction.
04After the modules

Timed past papers

Fully worked solutions exist for STEP 2 and STEP 3 papers from 2019 onwards, written so you can assess your own timed attempts against them.
Along that route, discipline matters more than volume, and four habits do most of the work:
  • Write every solution in full rather than stopping once you can see the idea. The writing is the examined skill, and it does not improve by being skipped.
  • Debrief against the worked solutions step by step. The point is not whether you were right but which observation you were missing at the moment you stalled.
  • Run timed papers under the real rules: read all twelve questions, rank them, choose, and practise abandoning a question mid-flow, until best-six decisions become reflex.
  • If you are sitting both papers, stagger the effort: consolidate written pure work at STEP 2 level before climbing into STEP 3's abstraction, and keep the earlier material warm.
09

Calibrate with the published boundaries

Unlike many admissions tests, STEP publishes its grade boundaries and mark distributions every year, released alongside results by 08:00 UK time on results day. That makes Section A targets refreshingly quantifiable.
STEP 2STEP 3
Grade S8480
Grade 16256
Grade 25248
Grade 33430

The 2026 boundaries, out of a maximum of 120 per paper.

28.14%

STEP 2 candidates reaching grade 1 or above in 2026

35.73%

STEP 3 candidates reaching grade 1 or above in 2026

About 60

Three questions taken close to full marks, already near the STEP 2 grade 1 line

Boundaries are not fixed. OCR sets them with reference to the places available at the institutions that formally use STEP, namely Cambridge, Warwick and Imperial College London, and to how that year's cohort performs, so they move from year to year. Historical numbers are a reference point, never a promise.
Translated into Section A workload, the message is encouraging. Take the 2026 STEP 2 grade 1 boundary of 62: three questions taken close to full marks is already around 60, with partial credit elsewhere closing the gap. The grade 2 in any one paper that Warwick's STEP route asks for sits lower still (52 on STEP 2 and 48 on STEP 3 in 2026), while the Cambridge minimum offer level is grade 1 in both papers, with exact grades varying by College. None of these targets requires six perfect solutions. What they require is the reliable production of three or four high-quality written arguments in three hours, and that reliability is exactly what sustained pure practice builds.
FAQ

Frequently asked questions

How many pure maths questions are there in STEP, and can I answer only those?
Eight of the twelve questions on each paper are pure (Section A), with two mechanics and two probability and statistics questions. OCR places no restriction on how many you attempt from any section, so answering only pure questions is entirely permitted. Conversely, even answering all four applied questions in full leaves at least two of your six counting answers to come from Section A.
Do you pick six questions in STEP, and what happens if you attempt more?
No. Everything you attempt is marked, and your six highest-scoring answers are combined automatically. OCR says you may attempt as many as you wish but advises against going beyond six, noting that candidates who do rarely score as well as those who concentrate on six. There are also no bonus marks for completing a question.
Is the pure maths syllabus the same for STEP 2 and STEP 3?
No. STEP 2 is based on A level Mathematics plus AS level Further Mathematics, while STEP 3 is based on A level Mathematics plus A level Further Mathematics. The specification also notes that the Further Maths pure content for STEP 3 carries modifications and additions, so audit yourself against the current specification (version 1.3, for examinations from June 2026 onwards) rather than your school course.
Are calculators allowed in STEP, and is there a formulae booklet?
No to both. Calculators are not permitted or required, and the formulae booklet was discontinued in 2019, with the formulae you must know listed in the specification's appendix. You may bring rulers, protractors and compasses; answers go in black pen and diagrams in pencil. Graph paper is not permitted either, all sketches go inside the answer booklet, and no extra rough paper is issued.
How many questions do you need to get a grade 1 in STEP?
Using 2026 as the reference: the grade 1 boundary was 62 out of 120 on STEP 2 and 56 on STEP 3. Roughly, three questions done thoroughly gets you near 60, with method marks elsewhere closing the gap. Boundaries are set each year against cohort performance and the places available at the universities that use STEP, so they move annually; treat past figures as a guide only.
Do you lose marks in STEP for messy or hard-to-follow working?
Yes. The specification requires solutions to be clear, logical and legible with working fully set out, and states that marks may be lost when examiners cannot follow a candidate's working, even if a correct final answer appears. Copies of answer booklets also go directly to the Cambridge admissions team for judging near-miss applicants on their actual work, so your writing can matter beyond the marking itself.
Are there free official resources for STEP pure maths preparation?
Yes. The STEP Support Programme, developed by the Faculty of Mathematics at Cambridge, is free and open to everyone, offering online modules with hints and full solutions; the suggested rhythm starts the Foundation modules in Year 12, the STEP 2 modules in September of Year 13 and the STEP 3 modules in January of Year 13. Fully worked solutions are also available for STEP 2 and 3 papers from 2019 onwards, ideal for reviewing timed attempts.
SOURCES

Official sources

MORE GUIDES

Other STEP preparation guides

FrontierVUE is an independent practice platform. It is not affiliated with or endorsed by UAT-UK, Pearson, OCR, the University of Cambridge, Imperial College London, or any official admissions-test owner.

Put it into practice

111 STEP papers on FrontierVUE, every question with a worked solution. The first 2 papers are free.

Practise STEP papersSee pricing