If you are applying to study Mathematics, Economics, or Engineering at a top UK university, A-level grades are not enough. Most of the best universities — Cambridge, Oxford, LSE, Imperial, Warwick, Durham, UCL — require you to sit a separate mathematics admissions test before they make you an offer.
There are two main tests: STEP (used by Cambridge for Mathematics) and TMUA (now used by most other universities, including Oxford from 2026). This guide explains what each test is, what scores matter where, and how to prepare.
The Landscape: Which Test for Which University?
| University | Test Required | Courses |
|---|---|---|
| Cambridge | STEP 2 + STEP 3 | Mathematics, Mathematics with Physics |
| Cambridge | TMUA | Computer Science, Economics |
| Oxford | TMUA (from 2026) | Mathematics, Computer Science |
| LSE | TMUA (mandatory) | Economics, Econometrics & Mathematical Economics |
| Imperial | TMUA (mandatory) | Mathematics |
| Warwick | TMUA or STEP | Mathematics |
| Durham | TMUA | Mathematics and Statistics |
| UCL | TMUA (mandatory for Economics) | Economics, Mathematics (encouraged) |
Important change for 2026: Oxford has discontinued the MAT (Mathematics Admissions Test) it used for decades. From 2026 entry, all Oxford Mathematics and Computer Science applicants take TMUA instead — the same test as LSE, Imperial, and Warwick.
STEP: Cambridge's Own Mathematics Test
STEP stands for Sixth Term Examination Paper. It is taken in June, after your A-level exams, and the results come back in time to confirm or adjust conditional offers.
Structure
There are two papers: STEP 2 and STEP 3. (STEP 1 was discontinued in 2021.)
- Each paper is 3 hours long
- Each paper contains 12 questions
- You only need to answer 6 questions — your 6 best-marked answers count
- Each question is marked out of 20
- Maximum score per paper: 120 marks
The questions are long-form problem-solving questions, not multiple choice. You show all your working. A correct answer with no working gets very little credit; strong partial solutions score well.
Grades
STEP uses five grades: S, 1, 2, 3, U (from highest to lowest). S is Outstanding, 1 is very good, and these are what Cambridge expects.
What Cambridge Offers Look Like
A standard Cambridge Mathematics offer is A*A*A at A-level (usually Mathematics, Further Mathematics, and one other) plus grades 1,1 in STEP 2 and STEP 3.
Some colleges offer an alternative: A*A*A* with only a grade 1 in one STEP paper. College-specific requirements vary — check the individual college websites.
Around two-thirds of places are filled by students who meet their STEP grades outright. The remaining third are filled after a review of full applications, including STEP scripts, from students who narrowly missed.
Key Dates 2026
- STEP 2: 4 June 2026
- STEP 3: 10 June 2026
- Cost: £102.50 per paper in the UK; £142.25 internationally
What STEP Actually Tests
STEP tests deep mathematical thinking, not just technique. A-level Mathematics teaches you procedures. STEP asks you to solve problems you have never seen before using those procedures — and then some.
The questions are long, multi-part, and require you to spot structure, make connections between different areas of mathematics, and construct arguments from first principles. A student who has only worked through past papers without understanding the underlying ideas will struggle. A student who understands why mathematical results work will make progress even on unfamiliar questions.
Topics Covered
STEP 2 covers: Pure mathematics (calculus, algebra, coordinate geometry, trigonometry, vectors, functions), Mechanics, and Statistics — all at A-level content plus STEP-specific depth.
STEP 3 covers similar areas but at significantly higher difficulty, with questions that overlap with first-year university mathematics in some places.
TMUA: The Unified Test for Everyone Else
TMUA (Test of Mathematics for University Admission) has become the standard admissions test across most leading UK universities for mathematics-heavy degrees. From 2026, Oxford has joined LSE, Imperial, Warwick, Durham, and UCL in using it.
Structure
- Total duration: 2 hours 30 minutes
- Format: Computer-based, multiple choice
- 40 questions split into two papers of 20 questions each
Paper 1 (75 minutes): Applications of Mathematical Knowledge Tests whether you can apply A-level mathematics in unfamiliar situations. Focuses on accuracy and efficient technique.
Paper 2 (75 minutes): Mathematical Reasoning Tests logical reasoning in mathematical contexts. Requires you to analyse arguments, identify flaws, construct proofs, and work with abstract ideas.
No marks are deducted for wrong answers.
Scoring
TMUA scores run from 1.0 to 9.0 in 0.5 increments. The distribution is heavily skewed toward lower scores: the most common score nationally is around 3.5, and the median is approximately 4.0–4.5.
A score of 7.0+ is genuinely exceptional and places you among the very top candidates nationally.
Key Dates 2025/2026
There are two sittings:
October sitting (for Cambridge, Oxford, and most Russell Group universities):
- Registration: 31 July – 29 September 2025
- Test dates: 13–14 October 2025
- Results: late November 2025
January sitting (for mature applicants and deferred entry):
- Registration: 27 October – 19 December 2025
- Test dates: 8–9 January 2026
- Results: late February/early March 2026
Cost: £78 in the UK, £133 internationally
Note: Cambridge and Oxford only accept the October sitting. If you are applying to either, you must sit TMUA in October 2025 for 2026 entry.
What Score Do You Need?
Universities do not universally publish cutoffs, but the competitive benchmarks are well-established:
| University | Competitive TMUA Score |
|---|---|
| Cambridge | 6.5+ |
| Oxford | 6.5+ (estimated, first year of TMUA) |
| Imperial | 7.0+ |
| LSE (Economics) | 5.5+ likely |
| UCL | 6.5+ (estimated) |
| Warwick | 5.0 minimum; 6.0+ for strong advantage |
| Durham | 5.0+ (below 3.2–3.5 is a negative signal) |
For context: scoring 6.5 on a 1–9 scale where most candidates score below 4.5 is a substantial achievement. If you are targeting Cambridge or Imperial for Mathematics, you are competing against the strongest mathematicians in the country.
STEP vs TMUA: What's the Difference?
| STEP | TMUA | |
|---|---|---|
| Format | Long-form problem-solving, written | Multiple choice, computer-based |
| Duration | 3 hours per paper | 2 hours 30 minutes total |
| Timing | June (after A-levels) | October or January |
| Universities | Cambridge only (for Maths) | Oxford, LSE, Imperial, Warwick, UCL, Durham, Cambridge (CS/Econ) |
| What it tests | Deep problem-solving over sustained time | Applied technique + logical reasoning |
| Grading | S, 1, 2, 3, U | 1.0–9.0 scale |
If you are applying to Cambridge Mathematics, you need STEP. If you are applying to any other university on the list above, you need TMUA. If you are applying to both Cambridge Mathematics and, say, LSE Economics, you need both.
How to Prepare for STEP
Use the Cambridge STEP Support Programme
Cambridge provides a free online support programme at step.maths.org, developed in collaboration with NRICH. It includes 25 Foundation modules (covering the mathematical background needed for STEP) plus specific STEP 2 and STEP 3 modules. This is the best free preparation resource available.
Work through past papers — but do it properly
OCR publishes past papers from 2014 onwards at their website. MEI has full solutions for STEP papers from 1996 to 2019.
The correct way to use past papers:
- Attempt a question with no help, under timed conditions
- If you get stuck after a genuine effort, look at the solution and understand it
- Come back to similar questions a week later without looking at the solution
Copying out solutions teaches you nothing about STEP. Understanding how to approach a problem — what structure to look for, what technique to try — is what transfers to the actual exam.
Don't neglect Further Mathematics
If your school offers Further Mathematics A-level, take it. Students who sit STEP without Further Maths are at a significant disadvantage on both papers.
Be selective in the exam
You only need to answer 6 out of 12 questions. Do not try to answer all 12 and split your time. In the first 10–15 minutes, read through all questions and identify the 6 (or 7, as a backup) you are most confident about. A complete solution to 6 questions beats half-finished attempts at 12.
How to Prepare for TMUA
Understand what each paper requires
Paper 1 rewards speed and accuracy in applying A-level content. Your preparation should focus on being fast and error-free across the full A-level syllabus — especially algebra, calculus, and coordinate geometry.
Paper 2 rewards logical reasoning and careful reading. Many students find Paper 2 harder because there is less algorithmic technique to apply. Practise reading mathematical arguments, identifying what is being claimed, and finding flaws or counterexamples.
Official practice materials
The UAT-UK website (esat-tmua.ac.uk) provides official practice materials and past questions. Use these. The difficulty and style are calibrated to the real test in a way third-party materials often are not.
Work on your mathematical vocabulary
Paper 2 uses precise mathematical language. If you are not confident distinguishing between "if", "only if", "if and only if", "necessary", and "sufficient" — practise until you are. These distinctions appear regularly.
Time management
40 questions in 150 minutes is 3.75 minutes per question. That sounds comfortable but is not. Many questions require reading, working, and careful checking. Pace yourself with a watch and do not spend more than 4 minutes on any single question in a timed practice session.
A Note on A-Level Requirements
Neither STEP nor TMUA replaces strong A-level grades. They sit on top of them.
For Mathematics at Cambridge and Oxford: A*A*A is the standard A-level requirement, with A* expected in both Mathematics and Further Mathematics.
For Economics at LSE: AAA with A in Mathematics (competitive applicants typically achieve A*).
Taking Further Mathematics A-level is not always officially required outside Cambridge — but students who do not take it are at a structural disadvantage in the TMUA and at university. If your school offers it, take it.
Your Personal Statement Still Matters
Admissions tests are one part of a Mathematics or Economics application. Universities also read your personal statement, and for quantitative subjects it needs to demonstrate genuine intellectual engagement — not just enthusiasm for the subject.
A personal statement for a Maths or Economics degree should reference specific ideas, books, or problems that have shaped your thinking — not simply list your A-level topics. Statementory reviews personal statements against the criteria admissions tutors actually use, with line-by-line feedback and a prioritised improvement plan.
Summary
Cambridge Mathematics requires STEP 2 and STEP 3 — long-form papers sat in June, graded S/1/2/3/U, with typical offers requiring grades 1,1. Oxford has moved from the MAT to TMUA for 2026. TMUA is now the standard admissions test across LSE, Imperial, Warwick, UCL, Durham, and Oxford — a 2.5-hour computer-based multiple choice test scored 1.0–9.0. Competitive TMUA scores start around 5.0–5.5 for most universities and 6.5+ for Cambridge and Oxford. Both tests reward deep preparation over months, not cramming in the last week.