TMUA Past Papers & Worked Solutions
Free preparation resources for the Test of Mathematics for University Admission. 8 years of past papers (2016-2023) with official worked solutions, specimen papers, and the essential Logic & Proof guide.
Key dates — 2027 entry cycle
Booking closed 28 September 2026 (6pm UK time). Oxford and Cambridge applicants must sit in October, with limited exceptions. Candidates in China, Hong Kong and Macau sat the TMUA on 15–16 October only. Results are released on 16 November 2026.
Booking: 28 October to 21 December 2026 (closes 6pm UK time). Accepted by most non-Oxbridge universities. Results are released on 8 February 2027.
You sit one window per cycle, not both, so check which sitting your universities require before you book. If you are applying to Oxford, Cambridge, or for medicine, dentistry or veterinary science, the UCAS deadline for 2027 entry was 15 October 2026.
Dates and fees are set by UAT-UK and can change. Check the official UAT-UK key dates → You book and pay for the test yourself through your UAT-UK account, and sit it at a Pearson VUE test centre. Your school is only involved if you need a letter for access arrangements. Check each university's course page for which test it requires.
Official Preparation Guides
Start here. These official guides from UAT-UK define what's tested and how to prepare.
Specimen Papers
Official specimen papers with worked solutions — the closest preview of what you'll face.
Specimen Paper 1
Specimen Paper 2
Practice Test (Pearson VUE)
Experience the actual computer-based test interface used on exam day.
Open Pearson VUE Practice TestPast Papers with Worked Solutions (2016-2023)
All 8 years of TMUA past papers with official worked solutions. The content specification and question style are unchanged for the current computer-based format, so these are directly relevant for 2026/2027 sittings.
| Year | Paper 1 | P1 Solutions | Paper 2 | P2 Solutions | Answer Key |
|---|---|---|---|---|---|
| 2023 | Worked | Worked | Key | ||
| 2022 | Worked | Worked | Key | ||
| 2021 | Worked | Worked | Key | ||
| 2020 | Worked | Worked | Key | ||
| 2019 | Worked | Worked | Key | ||
| 2018 | Worked | Worked | Key | ||
| 2017 | Worked | Worked | Key | ||
| 2016 | Worked | Worked | Key |
What's in Each Paper?
Paper 1: Applications of Mathematical Knowledge
- 20 MCQs in 75 minutes
- Tests how you apply AS-level pure maths and Higher GCSE maths in unfamiliar situations
- Topics: algebra, calculus, geometry, trigonometry, sequences
- No calculator allowed
- The maths is familiar, but the questions test depth of understanding, not just technique
Paper 2: Mathematical Reasoning
- 20 MCQs in 75 minutes
- Tests logical reasoning and mathematical proof
- Topics: logic, proof by contradiction, counterexamples, deduction
- No calculator allowed
- The Logic and Proof guide is essential preparation for this paper
Who Needs the TMUA?
Cambridge
- Mathematics
- Computer Science
- Economics
Oxford (from 2026)
- Mathematics
- Mathematics & Statistics
- Mathematics & Computer Science
- Mathematics & Philosophy
- Computer Science
- Computer Science & Philosophy
Other UAT-UK partners
- Imperial — Mathematics, Computing, and Economics, Finance & Data Science
- UCL — Economics
- LSE — required for Economics and for Econometrics & Mathematical Economics; recommended for its other maths, data science and actuarial courses
- Warwick — required for Mathematics, Computer Science and Discrete Mathematics; recommended for MORSE, Maths & Statistics, Data Science and Economics
- Durham — recommended (not required) for Mathematics and Mathematics & Statistics
Seven universities currently use the TMUA for selection to some Mathematics, Economics or Computer Science courses: Cambridge, Oxford, Imperial, UCL, LSE, Warwick and Durham. Exact course requirements vary — always confirm on each university's course page and on the UAT-UK course list for 2027 entry. Official UAT-UK list →
How to Prepare
Read the Content Specification
Know exactly what's tested. The TMUA is based on AS-level pure maths and Higher GCSE maths, with a few topics from the full A-Level, and tests them at a deeper level. Identify any gaps in your knowledge.
Study the Logic and Proof Guide
Paper 2 tests reasoning skills not covered in A-Level. The official guide is essential — cover proof by contradiction, counterexamples, and deductive reasoning.
Work Through Past Papers Chronologically
Start with 2016 and work forward. Do each paper timed (75 minutes). Review worked solutions for every question — even ones you got right — to learn optimal approaches.
Take the Pearson VUE Practice Test
The real test is computer-based. Practise with the official Pearson VUE interface to get comfortable navigating between questions and managing time on screen.
Frequently Asked Questions
What's the difference between TMUA and MAT?
The MAT was Oxford's own admissions test for Mathematics. From the 2026 admissions round (2027 entry), Oxford has replaced the MAT with the TMUA. The two tests are a similar length (both around 2.5 hours), but the TMUA is entirely multiple-choice (the MAT had long-answer questions) and gives one overall score from 1.0 to 9.0. The mathematical content is at a similar level, though the format is quite different. Oxford Mathematical Institute →
When can I sit the TMUA?
The TMUA runs in two windows — October and January — but you sit only one per admissions cycle (there is no resit within a cycle). Cambridge and Oxford applicants must take the October window; applicants to other universities may choose October or January. For 2027 entry, UAT-UK accounts opened on 1 June 2026 and booking for October opened on 20 July 2026. The fee is £78 for candidates in the UK and Republic of Ireland, and £133 elsewhere. UAT-UK: about the TMUA →
When does booking open and close, and when do results come out?
For 2027 entry the October sitting ran 12–16 October 2026 (15–16 October only in China, Hong Kong and Macau): booking closed 28 September 2026 and results are released on 16 November 2026. The January sitting runs 4–8 January 2027, with booking from 28 October to 21 December 2026 (closes 6pm UK time), and results are released on 8 February 2027. You book through your own UAT-UK account and sit the test at a Pearson VUE test centre, not through us. UAT-UK key dates →
Where do the dates on this page come from?
Every date above is taken from the official source, not from us:
- Sitting windows, booking windows and results dates come from UAT-UK, which runs the TMUA. Key dates → About the TMUA →
- The 15 October application deadline for Oxford, Cambridge and for medicine, dentistry and veterinary courses comes from UCAS. UCAS dates and deadlines →
- Oxford using the TMUA in place of the MAT comes from the Oxford Mathematical Institute. Oxford: TMUA →
Dates and fees are set by UAT-UK and can change, so check the official pages before you book. You book and pay for the test yourself through your UAT-UK account, and sit it at a Pearson VUE test centre. Your school is only involved if you need a letter for access arrangements. Check each university's course page for which test it requires.
Is a calculator allowed?
No. The TMUA is entirely non-calculator. All questions are designed to be solvable with mental arithmetic and algebraic manipulation. Practise working without a calculator from the start.
What score do I need?
You get one overall score for the two papers together, on a scale from 1.0 to 9.0. There is no pass mark, and most universities weigh the score alongside your grades, personal statement and (where applicable) interview. Some do publish a figure: Durham says a score of 5.0 or above makes you eligible for an offer one grade lower. Note for Cambridge Mathematics: the TMUA is a preliminary test, but the conditional offer is based on STEP (usually grade 1 in STEP 2 and 3), not on a TMUA score. Cambridge STEP requirement →
Can I use old TMUA papers to prepare?
Yes. The UAT-UK confirms that "both the content specification and question style are unchanged" for the current computer-based format. All 8 years of past papers (2016-2023) above are directly relevant for your preparation.
Where to focus your TMUA prep
A handful of topics show up reliably on every TMUA paper, while a long tail of others rarely appear. We tiered every topic in the official Content Specification by how often it has been tested across past papers, so you can prioritise prep time.
See the topic priority guideMAT past papers give you 190 more multiple-choice questions
Oxford replaced the MAT with the TMUA from the 2026 admissions round (2027 entry). 19 years of MAT past papers (2007 to 2025) remain freely available from Oxford Mathematical Institute, and MAT Question 1 — the ten-MCQ section sat by every candidate — is the closest direct ancestor of TMUA Paper 1. That is 190 more multiple-choice questions at TMUA level, on top of the 320 in the eight years of TMUA past papers.
Open the MAT archive