Writing STEP Solutions: Turning Maths You Can Do into Marks You Get

In most examinations, writing is merely how you present your result. In STEP, the writing is the result. OCR's published marking guidance is unusually explicit: candidates are rewarded for making good progress towards a solution, even where the final answer is wrong, and a correct answer receives full marks whatever the method used. The specification then adds the sentence every candidate should pin above their desk: solutions must be clear, logical and legible, with working fully set out, and marks may be lost if examiners are unable to follow a candidate's working, even if a correct final answer appears. Read those two statements together and the conclusion is stark. What gets marked is not the mathematics in your head but the record of reasoning in your answer booklet, as understood by a stranger reading it cold.

One further fact raises the stakes considerably. Copies of candidates' answer booklets are sent directly to the Cambridge admissions team, so that judgements about students who narrowly miss their offer can be made on the actual work rather than the bare mark or grade. Your handwriting, your structure and your logical chain may therefore be read a second time, after results day, by the very people deciding whether to take you. For a STEP candidate, solution writing is not a soft skill that polishes the real work. It sits alongside question selection and mathematical technique as a third, fully load-bearing skill, and unlike the other two it is almost never practised deliberately.

Every sentence OCR publishes about marking maps onto a decision you will make in the exam room, so it is worth taking them one at a time.

First: every question you attempt is marked, and good progress towards a solution is rewarded even if the final answer is incorrect. STEP has genuine partial credit. A half-finished question is not worth nothing; the marks follow you as far as your argument genuinely reaches.

Second: correct answers always receive full marks, whatever the method used. The markers are not betting on one intended route. If you find an unorthodox path and it holds, it is worth the same twenty marks as the model solution.

Third: there are no bonus marks for answering a complete question, and the markers adhere strictly to the mark scheme. Completion is not rewarded in itself; each verifiable step of progress is what carries the value.

Fourth: each question is marked out of 20, your grade rests on your six best answers, and although everything you write is marked, OCR explicitly advises against attempting more than six questions.

Finally, the specification's presentation clause: standard notational conventions should be followed, final answers should be simplified, and marks may be lost where examiners cannot follow the working. Put together, these five statements are the whole legal basis of solution writing in STEP: progress pays, method is free, completion earns no bonus, six answers count, and unclear writing costs.

STEP is a pen-and-paper examination, and its paper rules are unlike almost any other exam a sixth-former will have sat. Each one changes how you should write.

All of these rules point the same way: from the moment your pen touches the page, everything you write is part of the official record. Managing rough work and managing pages are themselves examinable skills, in the very real sense that doing them badly costs marks.

A level training optimises for reaching correct answers quickly. STEP marks a chain of reasoning that a stranger can verify. OCR describes the questions candidly: they test the ability to apply mathematical knowledge in novel and unfamiliar ways, often drawing on several specification topics at once, and solutions frequently require insight, ingenuity, persistence and the ability to work through substantial sequences of algebraic manipulation. Turning that kind of problem into a markable solution usually demands three distinct shifts in habit.

The first shift is from calculating to justifying. Every non-obvious step needs a stated reason, not just a result. The steps you were allowed to skip at A level are, in STEP, marks left on the table, because the reward is attached to visible progress rather than to the destination.

The second shift is from steps to structure. A long solution needs a skeleton: say what you are about to do, define your notation, advance in clearly separated stages, and close with an explicit conclusion. At any line on the page, the marker should know exactly where they are in your argument.

The third shift is from private scratch work to public document. What you produce is not a record of calculation for your own eyes but an exposition written for a tired examiner who has never met you. Standard notation, simplified final answers and legible handwriting are the typesetting conventions of that document, and the specification names all three explicitly.

Without quoting any particular question, high-scoring solutions share a remarkably consistent skeleton. The table below sets an answer-driven write-up against a markable one.

The closing row matters most on "show that" parts. There the target is printed on the paper, so every mark lives in the working: the final step must land exactly on the stated result, and any "clearly it follows" leap is a voluntary donation of marks back to the exam board. The opposite discipline matters just as much: because the destination is known, your argument must genuinely flow from the given conditions to the conclusion, not be assembled backwards from the answer and dressed up as a derivation. Writing the logic in its true direction is both mathematically honest and, under a rubric that rewards progress the marker can follow, the only reliable way to collect what your work has already earned.

The official rules give partial credit a firm footing: everything you attempt is marked, and good progress towards a solution is rewarded. For a candidate, at least four practical conclusions follow.

First, never abandon a stalled question by leaving a heap of fragments. Before you move on, write up cleanly the part that genuinely stands: the reformulation of the given conditions, the intermediate results you have actually proved, the special cases you have verified. Those are marks that can be banked; an untidy half-attempt is not.

Second, label your break points honestly. "It remains to show X, which I have not done" is worth more than a bluffed ending, because it lets the marker see precisely how far your argument reaches, and pay you for exactly that distance.

Third, be slow to cross out. Crossed-out work is not marked unless you indicate otherwise, so until you have something strictly better, an imperfect argument beats an empty page.

Fourth, a half-question can sit among your six best answers. Your grade rests on the best six, and in 2026 the grade 1 boundary on STEP 2 fell at 62 out of 120. As rough arithmetic, three questions done properly plus two or three attempts showing real, well-presented progress puts you in that region. Partial credit is not a consolation prize; for most candidates it is a structural component of the grade they end up with.

"No rough paper" sounds like a logistical footnote. In practice it reshapes how you work for the whole three hours, because every exploratory calculation happens inside the same booklet as your formal solutions. Some concrete tactics help.

Practise under exactly these constraints at home: one set of pages, black pen, no calculator, rough work crossed out. Composure in the exam room is entirely a product of having rehearsed the format until it feels boring.

Most candidates check their answers and move on. In STEP that is training the wrong muscle. The write-up needs its own practice loop, and the official materials for it already exist.

The STEP Support Programme, developed by the Cambridge Faculty of Mathematics, is free and open to everyone, with online modules, hints and full solutions. Alongside it, fully worked official solutions exist for STEP 2 and STEP 3 papers from 2019 onwards, and the Faculty recommends timed papers once you have completed the STEP 3 modules. Together these form a complete training loop for solution writing.

Run that loop weekly and the change in your written style becomes visible within months. It is slower than doing three extra questions per session, and considerably more valuable.

Every line in this checklist corresponds to an explicit risk in the official rules, and it is worth walking through it in the final week before the exam.

Minutes are expensive in a three-hour paper, but nothing on this list costs more than seconds. These habits defend precisely the marks you can least afford to lose: the ones your mathematics has already earned and only tidy writing can bank.