What is the TMUA (Test of Mathematics for University Admission)?
The Test of Mathematics for University Admission (TMUA) tests mathematical thinking and reasoning, not syllabus recall. First used in 2016, it is now part of the UAT-UK testing framework. There are two papers of 20 multiple-choice questions, combined into a single overall score from 1.0 to 9.0:
- Paper 1 — Applications of Mathematical Knowledge20 questions · 75 min
- Paper 2 — Mathematical ReasoningLogic & proof · 20 questions
- Full name
- Test of Mathematics for University Admission, run by UAT-UK; first used in 2016
- Format
- Paper 1: Applications of Mathematical Knowledge; Paper 2: Mathematical Reasoning (logic and proof)
- Timing
- 20 multiple-choice questions in 75 minutes per paper; 2 hours 30 minutes in total
- Scoring
- Papers 1 and 2 combine into one overall score, reported 1.0–9.0 to one decimal place; no pass mark or grade boundaries; no negative marking; scores cannot be appealed
- Score scale
- Equated with the Rasch model, so every version of the test sits on one scale. UAT-UK: “typical candidates will score around 4.5. Approximately 10% of candidates will achieve scores higher than 7.0”
- Resits
- Only once per admissions cycle: you sit the TMUA in October or January, not both
- Who sees your score
- Sent automatically, course by course, to the universities on your UCAS application whose course uses the TMUA; you cannot choose who sees it
- Rules
- Computer-based at Pearson VUE test centres; no calculator or dictionary
- Content level
- Higher-tier GCSE and AS-level mathematics
- Who uses it
- Oxford, Cambridge, Imperial, LSE, UCL, Warwick and Durham, for some Mathematics, Computer Science and Economics courses
- Fee
- £78 at test centres in the UK and Republic of Ireland; £133 elsewhere
ESAT or TMUA: which one does my course need?
For 2027 entry, some engineering and science courses at 4 universities (Cambridge, Imperial, Oxford and UCL) use the ESAT, with each module scored from 1.0 to 9.0. Some mathematics, computer science and economics courses at 7 universities (Oxford, Cambridge, Imperial, LSE, UCL, Warwick and Durham) use the TMUA (compulsory for some courses, recommended for others), with one overall score from 1.0 to 9.0. Cambridge, Imperial, Oxford and UCL use both tests for different courses, and the same subject can differ between universities: Computer Science and Mechanical Engineering at UCL use the TARA, not the TMUA or ESAT, so check the test for your course at each university.
Which universities require the TMUA?
Universities including Oxford, Cambridge and Imperial use the TMUA for some maths, computer science and economics courses. From 2027 entry Oxford replaces its MAT with the TMUA (first sitting October 2026). Here's the course-by-course picture — required versus recommended.
University of OxfordNew for 2027 entry — replaces the MAT · October sitting only
Official page ↗- Required
- Required
- Required
- Required
- Required
Imperial College London
Official page ↗- MathematicsAll Mathematics programmesRequired
- ComputingIncl. joint Mathematics and Computer ScienceRequired
- Required
LSE (London School of Economics)
Official page ↗- Required
- Required
- Mathematics & Economics, Financial Maths, Data Science…Recommended across LSE's quantitative degreesRecommended
University of Warwick
Official page ↗- Computer Science / Discrete MathematicsIncl. Computer Science with Business Studies · except contextual-offer applicantsRequired
- MathematicsBSc G100 / MMath G103 · TMUA or STEP · contextual-offer applicants exemptRequired
- Statistics (Mathematics and Statistics, MORSE, Data Science)Optional · most offers can be met in part with 5.0 in the TMUA or grade 2 in any STEPRecommended
- Economics / Economics and Management / Economics, Politics and International StudiesOptional · requirements under review for 2027 entryRecommended
Durham University
Official page ↗- Mathematics / Mathematics and StatisticsTMUA or STEP · 5.0+ in the TMUA or grade 2 in any STEP can bring a reduced offerRecommended
Requirements change from year to year — always confirm on each university's official course pages before you book. Compiled from the official admissions pages of the universities listed and UAT-UK.
When is the TMUA in 2026–27?
| Sitting | Test dates | Booking | Results | Who it's for |
|---|---|---|---|---|
| Sitting 1 (October) | 12–16 October 2026 | Closed 28 September 2026, 18:00 UK | 16 November 2026 | Most Oxford and Cambridge applicants must sit in October (the exceptions are Cambridge mature-college and Oxford Foundation Year applicants). In mainland China, Hong Kong and Macau the TMUA runs only on 15–16 October (and 8 January in the January sitting): UAT-UK cut the dates there after reports in October 2024 of candidates trying to obtain and sell test content — book early |
| Sitting 2 (January) | 4–8 January 2027 | Opened 28 October 2026, 15:00 UK; closes 21 December 2026, 18:00 UK | 8 February 2027 | Not for Oxford or Cambridge applicants, except mature applicants to a Cambridge mature college with a January deadline and Oxford Foundation Year applicants. In mainland China, Hong Kong and Macau: 8 January only |
Updated 5 November 2026 · Source: UAT-UK ↗
Fees are set by test-centre location: £78 at centres in the UK and Republic of Ireland, £133 elsewhere. A bursary and any access arrangements must be arranged before you book.
Both sittings sit on our application timeline, next to the UCAS deadlines, interviews and decisions.
Where can I find official TMUA past papers?
Unlike brand-new exams, the TMUA is well established — UAT-UK publishes eight years of past papers, full worked solutions and on-screen practice, all free. That is the best preparation material there is, so we point you straight to it and our tutors work through it with you. Below are a few original questions to give you a feel for the style.
A taste of the style — pick an answer to reveal the worked solution.
Paper 1 · Applications
Q1. How many distinct real values of satisfy ?
Paper 2 · Reasoning
Q2. Consider the statement: "For every real number , if then ." Which of the following is its negation?
Paper 2 · Reasoning
Q3. It is known that "if it rained, then the match was cancelled." You are told only that the match was cancelled. Which conclusion is logically valid?
Original TMUA-style questions, not official past papers. For full practice, use the official papers above.
Learn the TMUA from research mathematicians
One to one with a top-UK maths PhD or postdoc — people who reason and prove for a living, which is exactly what Paper 2 rewards. Pay by the session; see who you'd work with before you commit.
Mentors are joining gradually. To talk first, book a 15-minute call →
TMUA questions, answered
Is the TMUA just harder A-level maths?
No. It tests reasoning and proof-style thinking rather than speed and recall, and Paper 2 (Mathematical Reasoning) is about logic and proof.
What's the difference between Paper 1 and Paper 2?
Paper 1 (Applications of Mathematical Knowledge) applies familiar A-level material to less familiar problems. Paper 2 (Mathematical Reasoning) is about logic and proof — spotting valid arguments, negations and counterexamples. Each is 20 multiple-choice questions in 75 minutes.
Are there official TMUA past papers?
Yes — UAT-UK publishes eight years of past papers (2016–2023) with full worked solutions, plus free on-screen specimen tests. They are the best practice material.
How long is the TMUA and how many questions are there?
The TMUA has two papers, each with 20 multiple-choice questions in 75 minutes — 40 questions and 2 hours 30 minutes in total. It is computer-based at Pearson VUE test centres, and no calculator or dictionary is allowed.
When is the TMUA for 2027 entry, and which sitting should I book?
There are two sittings: 12–16 October 2026 and 4–8 January 2027. Most Oxford and Cambridge applicants must sit in October (bookings closed on 28 September 2026); the January sitting (bookings opened on 28 October 2026 and close on 21 December 2026 at 18:00 UK time) is not open to Oxford or Cambridge applicants, apart from some mature and Foundation Year applicants. Results are released about four weeks after each sitting — on 16 November 2026 for October and 8 February 2027 for January — and are sent automatically to the TMUA universities on your UCAS form.
How is the TMUA scored — is there negative marking?
Your result is reported on a scale from 1.0 to 9.0, to one decimal place, and there is no pass or fail. There is no negative marking, so attempt every question.
What is a good TMUA score?
There is no pass mark and there are no grade boundaries. Paper 1 and Paper 2 are equated and scaled together into one overall score from 1.0 to 9.0, and UAT-UK's explanation of results says the scale is designed so that typical candidates score around 4.5 and approximately 10% of candidates score higher than 7.0. Imperial also publishes 2025-entry TMUA score distributions and mean scores by department, split by fee status into Home, Home WP and Overseas applicants and by outcome, and stresses that this is historic data, not a score requirement. Source: UAT-UK TMUA explanation of results (PDF) ↗ · Imperial: understanding your scores ↗
How are sessions run?
One to one, online or in London, booked by the session from your wallet. Your tutor is an active PhD or postdoc researcher — not a former student teaching on the side.
Keep reading
Can you teach the TMUA? We need you.
If you teach A-level Maths to a high standard and enjoy proof and reasoning, you can teach the TMUA — Paper 2 is reasoning, the part that takes the most skill to teach and where a real mathematician shines. Demand is high and strong tutors are scarce. Apply and start on your own terms.
Apply to teach