STEP Past Papers and Worked Solutions
The Sixth Term Examination Paper is the post-offer mathematics exam used by Cambridge for Mathematics offers, and as a fallback alternative at Warwick and Imperial for applicants who did not sit the TMUA. Sat alongside A-Levels in June, it is the hardest pre-university Maths exam in the UK.
This archive has seven years of recent STEP 2 and STEP 3 past papers (2019 to 2025) with detailed worked solutions, a question database covering 1986 to 2018, and links to the official Cambridge STEP Support Programme.
What STEP is and who needs it
STEP is administered by OCR and developed by the University of Cambridge. It is the post-offer mathematics test for Cambridge Mathematics. Warwick and Imperial moved to TMUA as the primary admissions test from 2026 entry; STEP at those universities is now a fallback requirement for applicants who did not sit the TMUA.
Inside each paper
Universities that use STEP
Cambridge
All Mathematics applicants. Standard offer is grade 1 in STEP 2 and grade 1 in STEP 3. STEP is the post-offer requirement on top of A-Levels.
Warwick
Mathematics. From 2026 entry, TMUA is the primary admissions test. STEP grade 2 is the FALLBACK requirement only if you did not sit the TMUA — and not guaranteed even then.
Imperial
Mathematics. TMUA is the primary admissions test. Imperial states "typical offers may include STEP requirements where TMUA has not been taken" — STEP is the fallback, not the default.
Other Maths departments
STEP is accepted by Bath, Bristol, Durham, and others as a strong supporting qualification, usually optional.
Recent STEP 2 and STEP 3 Past Papers
Seven years of recent STEP 2 and STEP 3 past papers (2019 to 2025) with detailed worked solutions from the Cambridge STEP Support Programme. The "Mock" suffix in the file names reflects that these solutions are written for self-study, not the official OCR mark schemes (which are far less detailed). All files are hosted by Cambridge.
| Year | STEP 2 (Worked) | STEP 3 (Worked) |
|---|---|---|
| 2025 | Solutions PDF | Solutions PDF |
| 2024 | Solutions PDF | Solutions PDF |
| 2023 | Solutions PDF | Solutions PDF |
| 2022 | Solutions PDF | Solutions PDF |
| 2021 | Solutions PDF | Solutions PDF |
| 2020 | Solutions PDF | Solutions PDF |
| 2019 | Solutions PDF | Solutions PDF |
Looking for the original OCR question papers? OCR keeps live papers behind a delayed-release policy. The Cambridge worked-solution PDFs above include the original questions inline so you can work them without needing to retrieve the OCR PDF separately.
STEP question database and full archive
For pre-2019 STEP material the Cambridge STEP team maintains a searchable question database covering 1986 to 2018, and a full Google Drive archive of every past STEP paper with mark schemes where available. The STEP Support Programme is the official 25-week preparation course Cambridge expects strong applicants to work through.
STEP paper structure
STEP 2
- 3 hours, 12 questions, no calculator
- 8 pure maths, 2 mechanics, 2 probability/statistics
- Designed for A-Level Maths + at least AS Further Maths
- Pitched one step beyond A-Level — heavy on algebraic manipulation, integration techniques, inequalities, sequences
- Cambridge offers typically require grade 1 here
STEP 3
- 3 hours, 12 questions, no calculator
- 8 pure maths, 2 mechanics, 2 probability/statistics
- Assumes full A-Level Further Maths content
- Substantially harder: more abstract manipulation, deeper proof, less obvious starting points
- Cambridge offers typically require grade 1 here too, sometimes S
Grading: S, 1, 2, 3, U
STEP is graded on a five-level scale that compresses the very wide spread of candidate performance. Grade boundaries are set after each sitting; published thresholds historically sit around 60 to 90 marks out of 120 for grade 1 in STEP 2, and around 50 to 70 marks for grade 1 in STEP 3. These are typical ranges, not fixed cutoffs.
How to prepare for STEP
Start the STEP Support Programme early (Year 12 / Grade 11)
Cambridge runs a free 25-week assignment programme at maths.org/step. Foundation modules begin in Year 12 (Grade 11) and intermediate modules over the summer between Year 12 and Year 13 (Grade 12). By the time the exam arrives in June of Year 13, strong candidates have worked through 80 to 100 hours of focused STEP-style problems.
Build endurance: full three-hour mocks
A single STEP paper is much longer than any A-Level paper. Practising in three-hour blocks (no calculator, no breaks) is the only way to build the mental stamina needed. Use the worked-solution PDFs above to mark your own work.
Read solutions even on questions you can solve
STEP rewards elegant arguments. The official worked solutions describe approaches that often shave 20 to 30 minutes off the brute-force route. Build a habit of comparing your method to the model solution every time.
Pick questions strategically: 6 deep beats 12 shallow
Only the best six questions count. Spending 30 to 40 minutes on each of six fully-attempted questions almost always outscores 15-minute fragments across twelve. Read all twelve questions at the start, mark which look tractable, and commit.
Use the question database for topic drilling
The Cambridge STEP question database lets you filter by topic and difficulty. If your weakness is integration by substitution or sequence convergence, you can pull every STEP question that touches it and drill until the pattern is automatic.
Frequently asked questions
Is STEP 1 still examined?
No. STEP 1 was discontinued from 2020. The last STEP 1 sitting was 2019. Only STEP 2 and STEP 3 remain active. Old STEP 1 papers from 1987 to 2019 are still useful warm-up material before STEP 2 and are included in the Cambridge historical archive linked above.
When is STEP sat?
STEP is sat in June, alongside summer A-Level exams. Registration with OCR opens in March via a school or exam centre. STEP is not a pre-application test like the TMUA or ESAT; it forms part of conditional offers, so students sit it only after receiving an offer from Cambridge, Warwick, or Imperial.
Which universities still require STEP in 2026?
Only Cambridge requires STEP by default — every Cambridge Mathematics offer includes STEP grades (typically 1 in STEP 2 and 1 in STEP 3, or A*A*A* + grade 1 in one STEP paper at some colleges). Warwick and Imperial moved to TMUA as the primary admissions test from 2026 entry; STEP is now a fallback requirement at those universities only for applicants who did not sit the TMUA. Bath, Bristol, Durham, and others accept STEP as a strong supporting qualification but do not require it.
Can I sit STEP without Further Maths?
STEP 2 only assumes A-Level Maths plus the AS Further Maths content (mainly complex numbers, matrices, and further calculus). STEP 3 assumes full Further Maths. Strong candidates without Further Maths can sometimes attempt STEP 2, but Further Maths is the realistic preparation route and Cambridge typically expects it.
How does STEP compare to TMUA and MAT?
STEP is much longer (three hours per paper versus two and a half hours total for TMUA), much harder per question (long-form proof, much deeper algebra), and is post-application (sat after an offer, in June). TMUA and MAT are pre-application multiple-choice tests used to shortlist for interview. They serve different purposes: TMUA/MAT decide who gets an offer, STEP decides who meets the offer.
Why are the worked solutions labelled "Mock"?
The Cambridge STEP Support Programme distributes its detailed solutions under the "mock" label to differentiate them from OCR's official mark schemes (which are much terser). The mock solutions include the original questions inline, full working, and pedagogical commentary on alternative methods. They are by far the better resource for self-study.