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.
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 Universities
- LSE — Maths, Econ, Data Science
- Durham — Maths, CompSci
- Warwick — Maths, MORSE
- Bath, Lancaster, Sheffield
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 2026, Oxford has joined the UAT-UK system and replaced the MAT with the TMUA. The TMUA is shorter (2.5 hours vs 2.5 hours), entirely MCQ (MAT had long-answer questions), and scored 1-9 per paper. The mathematical content is at a similar level but the format is quite different.
When can I sit the TMUA?
The TMUA has two sittings per year: October (for 2027 entry applications) and January (for those who missed the October sitting or want to resit). Registration typically opens in June. The test fee is approximately $78 (UK) or $133 (international).
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. For Cambridge and Oxford Mathematics, a score of 6.5+ on each paper is competitive. Some courses accept lower scores. Your TMUA score is one part of a holistic application — it's not the sole deciding factor.
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.