STEP question selection: finding your best six out of twelve

STEP 2 and STEP 3 each contain 12 questions, each marked out of 20, in a three-hour paper. The scoring rule fits in one sentence, and almost everyone misreads it at first: every question you attempt is marked, and your final score is the sum of your six best-scoring answers, out of a maximum of 120. This is not a system where you nominate six questions at the start and forfeit the rest. The OCR FAQ is explicit that you may answer as many questions as you wish and that all of your answers will be marked, with only the best six counting towards your total. The same FAQ adds something just as important: it is not advisable to attempt more than six, and candidates who spread themselves across more questions rarely score as well as those who concentrate on six. There is also no completion bonus of any kind; a finished question earns exactly what the mark scheme awards out of 20, and nothing extra. Put those three facts together and the shape of the exam becomes clear. STEP hands you a menu of twelve and pays you for your best six choices. Ordering more dishes does not add marks; it only dilutes the time you can spend on each. Question selection is therefore not a minor piece of exam technique. It sits alongside mathematical ability as a core skill that the paper is quietly testing.

Each paper splits its twelve questions across three sections: Section A carries eight pure questions, Section B two mechanics questions, and Section C two probability and statistics questions. The specification adds a line that matters more than it looks: no restriction is placed on the number of questions you may attempt from any section. That freedom should shape your preparation. Pure alone offers eight questions and you only need six to count, so a candidate who never touches mechanics or statistics can, in principle, assemble a full set from Section A with two questions to spare. Equally, if applied maths is your strength, all four questions in Sections B and C are available to you. The practical conclusion is to stop preparing for coverage and start preparing for your intended portfolio. Train hardest on the question types you actually plan to rely on in the exam room, and choose on the day by the same logic. One caution: a pure-only strategy means finding six workable questions out of eight, a margin of just two. In a year where the pure section runs hard, that margin feels thin. The robust configuration for most candidates is pure as the main engine, with at least one of mechanics or statistics trained to exam standard as a release valve for the day Section A does not cooperate.

If extra attempts cost nothing on the mark sheet, why not attempt eight and take out insurance? The arithmetic answers the question. Three hours is 180 minutes. Spread across eight attempts, each question gets roughly 22 minutes; concentrated on six, each gets close to 30. STEP questions are long, multi-part climbs that demand sustained chains of algebraic manipulation, and 22 minutes typically buys you the early parts only, which means the early marks only. Suppose eight shallow attempts earn 12 marks each: the best six of those total 72. Six deeper attempts at 16 marks each total 96. On the published 2026 STEP 2 boundaries, 72 sits at grade 1 (which began at 62) while 96 clears the S boundary of 84, so the gap is a full grade. OCR's own guidance points the same way: attempting more than six is not advised, and candidates who do so rarely score as well as those who concentrate on six. One clarification is worth making. The advice concerns questions you invest real time in. Reading all twelve at the start, or writing two exploratory lines before abandoning a question, is not attempting a seventh question in any meaningful sense, and the opening read-through is positively necessary. What you are avoiding is the version of the exam where questions seven and eight each swallow twenty minutes and each stalls around ten marks. You are not collecting half-finished pieces. You are trying to hand in six well-made ones.

The best use of the first 10 to 15 minutes is not mathematics but reconnaissance: read all twelve questions before committing to any. That is roughly seven per cent of the exam spent deciding how the other ninety-three per cent will go, and it is the highest-return investment available to you. As you read, tag each question into one of three piles: yes (you can see a route to the end), maybe (the early parts look secure, the later parts uncertain), and no (unfamiliar territory or tools you have not practised). Two habits improve the quality of the tagging. First, read whole questions, including the later parts. STEP questions are built so that early parts feed later ones, and the structure of the parts is often a map of the intended solution; judging a question by its first line is how misgrading happens. Second, remember what OCR says about the style of the questions: they apply mathematical knowledge in novel and unfamiliar ways and frequently cut across several specification topics, demanding insight, ingenuity and persistence. First impressions deceive in both directions. A strange-looking question may have a familiar engine under the bonnet, and a comfortable opening can turn sharply at part three. Treat your tags as an initial ranking to be revised, not a verdict. When the read-through ends, you should hold a definite batting order, and you begin with the surest question on your list.

Working in descending order of confidence does two jobs at once: it banks your most reliable marks early, and a clean opening settles the nerves for the harder middle of the paper. The other half of the strategy is the courage to switch. The marking principle here is documented and worth internalising: examiners reward good progress towards a solution even when the final answer is wrong, and a correct answer earns full marks whatever the method used. So a question you abandon halfway keeps every mark you have already earned, and it remains in the pool from which your best six are chosen, automatically, with no action needed from you. Switching costs far less than it feels like it costs. The genuinely expensive thing is sunk-cost thinking, the reluctance to leave a question because twenty-five minutes have already gone into it. A useful discipline is a hard trigger: if a fixed number of minutes passes with no real progress (no new equation, no reduction, no part completed), you switch, mark the question as one to return to, and come back only once your core set is secure. One consequence of the marking rules belongs in the same breath: since everything left uncrossed is marked, never cross out an abandoned attempt. Those stranded lines of working may quietly be worth several marks, and we return to this in the section on booklet mechanics.

Here is a workable frame for the 180 minutes. Spend about 12 on the opening read-through. That leaves roughly 158 for solving, which across six questions comes to about 26 minutes each, and keep 10 at the end for checks. Thirty minutes per question is the right order of magnitude, not a fixed ration: some questions will close in 18 minutes and some will deserve 40. What matters is that the average lands in the 26-to-30 band. Two checkpoints keep the plan honest. At the 90-minute mark you want two to three questions substantially complete. If you have only one, your selection ran too ambitious or you overstayed on a single question, and the second half should aim for breadth of progress marks rather than complete solutions. In the final 30 minutes, only open a new question if it is short or you can already see the route; otherwise return to questions you have progressed and finish an unclaimed part, close a final step, or tighten a justification. Three to five extra marks on an existing attempt are almost always cheaper than starting from zero. The last ten minutes go on procedure: page markings, legibility, final answers simplified. None of that earns new marks, but it stops marks you have already earned from leaking away, and near STEP boundaries a handful of marks is frequently a grade.

STEP publishes its grade boundaries every year, which means a target grade converts directly into a picture of what your six answers must look like. Take 2026. On STEP 2, out of 120, the S boundary was 84, grade 1 was 62 and grade 2 was 52; on STEP 3, S was 80, grade 1 was 56 and grade 2 was 48. Now do the conversions. Grade 1 on STEP 2 needed 62 marks: three complete questions give 60, so three full solutions plus a couple of marks anywhere clears the line. Grade 1 on STEP 3, at 56, sits below the value of three complete questions. The grade 2 that Warwick's STEP route asks for (in any one paper) is more forgiving still: 52 on STEP 2 is roughly two complete questions plus one solid half. S is a different animal altogether: 84 on STEP 2 means averaging 14 out of 20 across six answers, typically four near-perfect solutions and two substantial halves, while 80 on STEP 3 is exactly four complete questions' worth. The 2026 cumulative percentages tell the same story: 28.14 per cent of STEP 2 candidates reached grade 1 or better and only 8.27 per cent reached S, with 35.73 and 9.27 per cent the corresponding figures on STEP 3. Two caveats. Boundaries move with the cohort, since they are set against the places available at Cambridge, Warwick and Imperial, so treat these figures as a scale rather than a promise. And start from your offer: Cambridge's minimum offer level is grade 1 in both papers, so fix the grade you actually need first, then work backwards to how many near-20 answers your six must contain.

In the exam, the time available to judge whether a question is yours works out at perhaps 30 to 60 seconds per question. That judgement cannot be taught in the abstract; it is trained on past papers, and it can be trained deliberately rather than left to grow as a by-product of practice. Try this drill. Take a past STEP 2 or STEP 3 paper. Give yourself ten minutes to read all twelve questions and write down a predicted ranking. Then sit the paper under full timed conditions. Afterwards, set your predicted ranking against your actual scores and log every misjudgement: did you overrate a question because it looked familiar, or underrate one because its setting was strange? After a dozen papers the log will show your personal bias pattern, and both the speed and the accuracy of your triage will climb. On materials, the STEP Support Programme, developed by the Cambridge Faculty of Mathematics, is free and open to everyone, with modules, hints and full solutions; and official fully worked solutions exist for STEP 2 and STEP 3 papers from 2019 onwards, with the recommendation being to sit timed papers after finishing the STEP 3 modules. Timed full papers are precisely where selection instinct gets built. One practical note: STEP 1 has not been offered from the June 2021 sitting onwards. Old STEP 1 papers are fine as warm-up material, but the twelve-into-six rehearsal must happen on STEP 2 and 3 papers, because only there does the difficulty distribution match what you will face.

Several answer-booklet rules interlock with selection strategy, and they are worth knowing cold before the day. First, STEP provides no rough paper: all working goes inside the official answer booklet, and any extra paper attached is removed and not marked. The habit of solving on scrap and copying up neatly does not transfer to STEP; your exploration happens on the official page, so practise thinking on paper legibly from the start. Second, crossed-out work is not marked unless you clearly indicate that you want it marked, whereas everything left uncrossed is marked and competes for your best six. The corollary could not be more direct: do not cross out an abandoned attempt. Those half-finished lines may be free marks. Third, every page you write on must carry the required question marking; a missed marking can leave that work unassessed, so a page check belongs on your final ten-minute list. Fourth, answers go in black pen with diagrams sketched in pencil, calculators are not permitted, and no formulae booklet is issued: the formulae you are expected to know are listed in the specification's appendix and must be memorised in advance. That last point feeds back into triage, because every computation a question demands will be done by hand, so weigh the computational load during the read-through. Finally, the specification warns that solutions must be clear, logical and legible, and that marks may be lost where examiners cannot follow the working, even with a correct final answer. Selection strategy puts your time in the right places; these mechanics make sure every minute you invest is converted into marks.