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. Oxford and Cambridge applicants must sit in October, with limited exceptions. Results are released on 16 November 2026.
Booking opens 26 October 2026 and closes 21 December 2026. 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, your UCAS application is due by 15 October 2026.
Dates and fees are set by UAT-UK and can change. Check the official UAT-UK key dates → Your school's exams officer or test centre confirms your booking.
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: Mathematical Thinking
- 20 MCQs in 75 minutes
- Tests application of A-Level Maths in unfamiliar contexts
- Topics: algebra, calculus, geometry, trigonometry, sequences
- No calculator allowed
- Questions are harder than A-Level — they 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
Other UAT-UK partners
- Imperial — Mathematics
- UCL — Economics & Maths courses
- LSE — Maths, Econ, Data Science
- Warwick — Maths, MORSE
- Durham — Maths, CompSci
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. Official UAT-UK list →
How to Prepare
Read the Content Specification
Know exactly what's tested. The TMUA covers A-Level Maths content but tests it 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 scored 1–9 per paper. 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. Registration opens around June. 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 runs 15–16 October 2026: booking closed 28 September 2026 and results are released on 16 November 2026. The January sitting runs 4–8 January 2027: booking opens 26 October 2026, closes 21 December 2026, and results are released on 8 February 2027. You book through a 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. Your school's exams officer or your test centre confirms your own booking and what your universities require.
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?
Scores are reported on a 1–9 scale per paper, and universities do not publish a fixed cut-off — the TMUA is assessed holistically alongside your grades, personal statement and (where applicable) interview. 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 are the largest pool of TMUA practice
Oxford replaced the MAT with the TMUA from 2026 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 MCQs of TMUA-grade practice, more than four times the total across all eight TMUA past papers.
Open the MAT archive