Practice & Past Papers
Over thirty years of past papers exist. Used in the wrong order they will crush you; used in the right order they are the best training material in mathematics. Here is the right order for someone starting from Matemática A.
The ladder
| Rung | Material | When |
|---|---|---|
| 1 | Bridge-course exercises (this site) + STEP Support Foundation modules — 25 assignments, each built around one STEP 1–style question with warm-ups and hints. | Phase A (Sep–Jan) |
| 2 | Old STEP 1 questions (the discontinued easiest paper, 1987–2020) by topic, from the questions database. Pure questions only at first. | Late Phase A → B |
| 3 | STEP 2 questions by topic + the Support Programme STEP 2 modules + Siklos's book. | Phase B (Jan–Mar) |
| 4 | STEP 3 questions by topic + Support Programme STEP 3 modules. | Phase C (Mar–Apr) |
| 5 | Full timed STEP 3 (and STEP 2) papers, 2019 onwards first — they match the current specification and format exactly; older papers as extra volume. | Phase D (May–June) |
Why not straight to STEP 3 papers?
The 2019 specification change matters: pre-2019 papers have a slightly different syllabus split (some current STEP 3 topics were then in STEP 2 and vice versa), and STEP 1 was discontinued in 2020 — which is exactly why its huge back-catalogue makes perfect training material. Treat pre-2019 papers as question banks, and 2019+ papers as the true mock exams.
Topic order for past-paper practice
When you reach rungs 2–4, take topics in this order — highest STEP 3 frequency and best return first. For each, the database's topic filter finds dozens of questions; do them after the corresponding bridge lesson.
- Algebra & inequalities (Lessons 1–2) — appears inside every other topic too.
- Curve sketching & functions (Lessons 3, 12) — the classic STEP opener; a good sketch is half a solution.
- Integration (Lessons 5–6) — reduction formulae and integral estimation are near-guaranteed on STEP 3.
- Complex numbers (Lessons 7–8) — de Moivre / roots of unity questions are a STEP 3 signature.
- Series & Maclaurin (Lesson 13).
- Differential equations (Lesson 14) — usually with a supplied substitution.
- Vectors, matrices (Lessons 9–10).
- Hyperbolics, polar (Lessons 11–12) — often embedded in integration questions.
- Probability — after your 12.º ano combinatorics/probability term, if you want the two stats questions as backup options.
How to work a single question
- Read it all. Later parts tell you where the question is going — and earlier parts are tools for later ones.
- Fight for 45 minutes. Try small cases, sketch, specialise, look for the connection to the previous part. Being stuck is the training.
- Stuck after a real fight? Take the smallest hint possible (one line of the solution, or the relevant bridge lesson), then put the solution away and continue alone.
- Write it up properly. Full sentences, justified steps, checked edge cases — as trained in Lesson 1.
- Log it. One line in the mistakes notebook: what would have unlocked it?
How to run a mock (Phase D)
- 3 hours, printed paper, no notes, no pauses. Use the real rubric: answer at most 6 questions properly.
- First 10 minutes: read all 12 questions, shortlist ~8, rank them. Choosing well is a skill — train it explicitly.
- Mark yourself against the official mark scheme/examiner report (on the OCR site) or community solutions; be harsh about unjustified steps.
- Track marks per question and per topic across mocks — your last month of study is aimed by this data.
Don't collect, solve
Downloading thirty papers feels like progress; it isn't. One question fought for an hour beats ten skimmed with solutions. At a realistic rate — three to four questions properly fought per week from January, plus mocks in May — you'll touch maybe 120 questions before the exam. That is plenty; make each one count.