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

STEP 2 and STEP 3 share an identical structure: each paper lasts 3 hours and contains 12 questions, with eight pure mathematics questions in Section A, two mechanics questions in Section B and two probability and statistics questions in Section C. Every question carries the same maximum of 20 marks. The scoring rule is the part that matters: everything you attempt is marked, but your final grade is based only on your six best answers, out of a maximum 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 mechanics and statistics question in full must still draw at least two of their six counting answers from Section A. Going the other way is entirely legitimate: you may answer six pure questions and nothing else, and your grade is computed exactly as normal.

In practice, most candidates lean far harder on pure than the minimum. With only two questions each, Sections B and C carry an element of luck: the year's applied questions may or may not land on models you know well. Section A's eight questions give you genuine freedom to choose, and a weak topic can simply be avoided. Your preparation time should mirror that structure: pure mathematics is the main front, and the applied sections are options you add from strength, not obligations.

OCR describes the character of STEP questions directly: they test the ability to apply mathematical knowledge in novel and unfamiliar ways, they often require knowledge of several different specification topics, and solutions frequently demand insight, ingenuity, persistence and the stamina to work through substantial sequences of algebraic manipulation. That is not marketing copy; it is an accurate structural description of Section A.

A typical 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 the earlier work was scaffolding and to deploy it in a new setting. Questions rarely stay inside one topic either: a single problem can move between several areas of the syllabus as a matter of course, which is why revising topics in isolation only takes you so far.

Just as important is what counts as an answer. Most Section A questions resolve into proof and sustained argument rather than a single numerical value. The marking reflects this: OCR rewards good progress towards a full solution even when the final answer is wrong, correct answers receive full marks whatever the method used, and there are no bonus marks for finishing a complete question, since each is marked strictly to a 20-mark scheme. Your goal is therefore not to conjure a conclusion but to construct a chain of reasoning an examiner can verify step by step.

The near-universal first experience of a STEP past paper goes like this: every individual 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.

The first difference is length. An A level question typically takes a few minutes and arrives pre-sliced into small steps. A STEP question is worth 20 marks, and at the natural pace of six questions in three hours you are budgeting roughly half an hour for a single problem. One question is a complete mathematical journey with its own arc.

The second is openness. A level papers plant signposts: find this, hence show that. STEP frequently gives you a starting point and a destination and leaves the bridge to you. Deciding which manipulation to try, when to reach back for the result proved in an earlier part, and how to structure the middle of an argument is itself the examined skill.

The third is the working environment. Calculators are neither permitted nor required, and the formulae booklet was discontinued in 2019, with the formulae 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 entire solutions yourself. That capacity only grows through attempting whole questions and writing whole solutions, which is precisely what your practice should look like.

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 and AS level Further Mathematics, while STEP 3 is based on A level Mathematics and A level Further Mathematics. The two papers share the whole of A level Mathematics as their foundation; what separates them is how deep into Further Mathematics they reach.

One detail is easy to miss. The specification states that the Further Mathematics pure content used for STEP 3 carries modifications and additions: some topics have been removed and others included, so it is not a verbatim copy of the Further Maths course you sat at school. The document to audit yourself against is therefore the specification itself, currently the STEP specification for examinations from June 2026 onwards, version 1.3, whose appendix also lists the formulae you are expected to know from memory.

Keep the cross-topic character from the previous section in mind as you read it. The specification tells you what is in the toolbox, but a STEP question routinely reaches for several tools at once, and the syllabus gives no warning about which combinations will appear. Working through the topic list to find gaps is a necessary first pass; the real unit of training after that is the whole question, not the isolated topic. Candidates sitting both papers should also note that the habit pays twice over, since everything built for STEP 2 remains fully load-bearing in STEP 3.

Get the rule exactly right first, because a common misreading costs real marks. STEP does not ask you to nominate six questions. Every question you attempt is marked, and the best six marks are combined automatically into your total. OCR adds two pieces of guidance worth taking literally: you may attempt as many questions as you wish, but doing more than six is not advisable, and candidates who do so rarely score as well as those who concentrate on six; and there are no bonus marks for completing a question.

The tactical consequences are concrete. First, spend the opening minutes reading all twelve questions and ranking the eight in Section A by confidence; no other few minutes of the exam pay better. Second, walking away from a stalled question carries no structural penalty. You have not wasted a slot, the progress already on the page still earns marks, and the best-six calculation settles everything in your favour at the end. Third, because pure supplies eight of the twelve questions, nearly all of your genuine selection freedom lives in Section A; with only two questions each, the applied sections present binary take-it-or-leave-it choices.

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.

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. And then comes the sentence worth reading twice: marks may be lost if examiners are unable to follow a candidate's working, even if 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 questions resolve into proof and argument, what an examiner is paying 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 are sent 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.

Turning this into habit takes only a few standing orders: open by stating what you are about to prove; give a reason for each non-obvious step; say explicitly when you are invoking a result from an earlier part; in long algebraic chains, write the extra line rather than skip it; and close every proof with a clear concluding sentence. Practise to this standard from your first past paper, because exam pressure never improves anyone's handwriting or discipline.

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.

Taken together, these rules impose one training requirement: your exploration and your fair-copy argument share the same booklet. Practise thinking on the page within a limited space, keeping trial calculations compact, crossing out cleanly and decisively, and laying out the final argument in tidy, readable blocks. Anyone used to sprawling across loose A4 sheets finds the first booklet-constrained paper genuinely uncomfortable, so get that adjustment done months before the exam, not during it.

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. The recommended rhythm is concrete: the Foundation modules are designed to be started in Year 12 and studied weekly over about six months, the STEP 2 modules from September of Year 13, and the STEP 3 modules from January of Year 13. After the modules comes timed past-paper work, and fully worked solutions exist for STEP 2 and STEP 3 papers from 2019 onwards, written precisely 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:

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.

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

In 2026, 28.14% of STEP 2 candidates reached grade 1 or above, and 35.73% did so on STEP 3. Bear in mind that 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 (the 2026 grade 2 boundaries were 52 on STEP 2 and 48 on STEP 3), 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.