The official TMUA past papers are free on UAT-UK's TMUA preparation materials page: Papers 1 and 2 for every year from 2016 to 2023, plus early specimen papers, each with an answer key and worked answers. No 2024 or 2025 papers are in the archive; for the current computer-based format, use the free specimen and sample tests on Pearson VUE.
Where to find official TMUA past papers
All official TMUA preparation material is linked from UAT-UK's Prepare page. For the TMUA it lists five things: the test specification, the specimen and practice tests, Notes on Mathematics, Notes on Logic and Proof (for Paper 2), and an Archive of Past Papers. The archive lives on its own TMUA preparation materials page, where every paper is a free PDF. You don't need an account to download them.
UAT-UK runs the test today. It was set up in 2023 by Imperial College London and the University of Cambridge, and the older papers in the archive carry Cambridge copyright notices (for example, the 2023 Paper 1 is marked Cambridge University Press & Assessment). You don't need to hunt through old Cambridge Assessment websites: UAT-UK hosts the full archive itself.
Which TMUA past paper years are available
The archive has the same five files for each year: Paper 1, Paper 1 worked answers, Paper 2, Paper 2 worked answers and an answer key covering both papers.
| Set | Paper 1 | Paper 2 | Worked answers | Answer key |
|---|---|---|---|---|
| Early specimen papers | Yes | Yes | Both papers | Yes |
| 2016 | Yes | Yes | Both papers | Yes |
| 2017 | Yes | Yes | Both papers | Yes |
| 2018 | Yes | Yes | Both papers | Yes |
| 2019 | Yes | Yes | Both papers | Yes |
| 2020 | Yes | Yes | Both papers | Yes |
| 2021 | Yes | Yes | Both papers | Yes |
| 2022 | Yes | Yes | Both papers | Yes |
| 2023 | Yes | Yes | Both papers | Yes |
| 2024 and 2025 | Not published | Not published | No | No |
That gives you nine sets: 18 papers and 360 questions, since each paper has 20 questions. One small detail: the 2016 Paper 1 is labelled "Practice paper" on its cover, so treat it like the other papers but don't be surprised by the label.
Looking for TMUA past papers from 2024? UAT-UK first ran the TMUA in October 2024, and the archive stops at 2023. If you see a "2024 TMUA paper" elsewhere, it is not from the official archive. The closest official practice for the current test is the pair of computer-based TMUA tests on Pearson VUE's UAT-UK page.
How the TMUA has changed since the older papers
UAT-UK says the ESAT and TMUA were first offered in October 2024 and describes both as computer-based tests taken at Pearson VUE test centres. The archive page sums up what this means for past papers: although the TMUA is now computer-based, both the content specification and question style are unchanged, so the archive can be used when preparing.
| Archive papers (2016–2023) | Current TMUA | |
|---|---|---|
| Questions and time | 20 questions in 75 minutes per paper (2023 Paper 1) | 2 papers of 20 questions, 75 minutes each, 2 hours 30 minutes in total (UAT-UK) |
| How you answer | Pencil on a separate answer sheet | On screen at a Pearson VUE test centre |
| Rough work | On the question paper | Erasable sheets or a whiteboard and pen (UAT-UK FAQ) |
| Calculator | Not allowed | Not allowed (UAT-UK FAQ) |
| Wrong answers | No penalty | No penalty (UAT-UK) |
The other change is the score scale. Since 2024 you get one overall score on a scale from 1 to 9, reported to one decimal place. Our TMUA scores explained guide covers the scale and the latest averages.
Answer keys, worked answers and scoring yourself
Each year has two kinds of solutions. The answer key is a one-page list of correct letters, which is all you need to mark a paper. The worked answers explain how to reach each answer, so use them when you got a question wrong or guessed.
You cannot turn a past-paper mark into a TMUA score. UAT-UK does not provide grade boundaries or a pass mark, and its online practice tests deliberately don't give a score, because each year's scale is based on that year's candidates. It also warns that practice performance won't necessarily match performance under exam conditions. So track your raw marks out of 20 per paper and look at the trend, not a predicted score.
The official computer-based TMUA practice tests
UAT-UK says it provides free practice tests in the Pearson system that replicate the test system you will see on the day. On Pearson VUE's UAT-UK page there are two TMUA tests:
- Specimen test: each question comes with an explained answer, so it works well for learning.
- Sample exam: at the end you can review which questions you got right. Sit this one under timed conditions.
Pearson says the questions are meant to be viewed on a desktop, not a phone. Do at least one of these tests before your exam so the on-screen layout and moving between questions don't surprise you on the day.
A practical plan for using TMUA past papers
Nine sets is plenty if you use them well. UAT-UK's own advice is to read the specification and Notes on Logic and Proof, then answer the practice test under timed conditions. Here is one way to order it:
- Check the content. Read the TMUA content specification and revise anything you haven't covered yet. For Paper 2, work through the Notes on Logic and Proof; for wider revision, UAT-UK also publishes Notes on Mathematics.
- Learn on the early papers. Do the early specimen and 2016–2017 papers untimed or loosely timed. Read the worked answers for every question you missed or guessed.
- Drill by topic. Use our TMUA Paper 1 practice and TMUA Paper 2 logic and reasoning practice to target weak areas between past papers.
- Move to timed pairs. From 2018 onwards, sit Paper 1 and Paper 2 back to back at 75 minutes each, without a calculator, writing working on a single sheet rather than all over the paper.
- Keep a mistake log. For each wrong answer, note whether it was a content gap, a logic slip or a timing problem. Redo those questions a week later.
- Save the newest for last. Keep 2022, 2023 and the Pearson sample exam for the final weeks, so your last practice is closest to the real thing.
Alongside the past papers, our free TMUA practice test gives you two timed papers in the same multiple-choice format with worked solutions, which is useful once you've used up the official sets or want fresh questions. For test dates and booking windows, see our UAT-UK test dates guide.
Free practice tests
Complete, timed, in the official format, with a worked solution for every question. No account needed.
Frequently asked questions
Where can I download TMUA past papers as PDFs?
On UAT-UK's TMUA preparation materials page (esat-tmua.ac.uk). It has Papers 1 and 2 from 2016 to 2023 and early specimen papers, each with an answer key and worked answers, all free.
Are there TMUA past papers for 2024 or 2025?
No. The official archive stops at 2023. UAT-UK first ran the TMUA in October 2024 and has not added later papers. For the current format, use the free specimen test and sample exam on Pearson VUE's UAT-UK page.
Are old TMUA papers still relevant now the test is computer-based?
Yes. UAT-UK says that although the TMUA is now computer-based, the content specification and question style are unchanged, so the archive can be used for preparation.
Can I convert my TMUA past paper mark into a score out of 9?
No. UAT-UK publishes no grade boundaries, and the scale is set each year from that year's candidates. Track your raw mark out of 20 per paper instead.
Next steps
Link to this guide
Using these figures on your site or in class? You're welcome to quote them with a link back:
<a href="https://www.keiko.study/blog/tmua-past-papers">TMUA Past Papers: Official PDFs, Answers and How to Use Them</a>
Sources
Every source below was accessed on the listed date. Pages — especially department admissions pages — change without notice; the links go to the live versions.
- Prepare — UAT-UK. Accessed 2026-10-01.
- TMUA Preparation Materials — UAT-UK. Accessed 2026-10-01.
- TMUA – The Test of Mathematics for University Admission — UAT-UK. Accessed 2026-10-01.
- About UAT-UK — UAT-UK. Accessed 2026-10-01.
- Test Results — UAT-UK. Accessed 2026-10-01.
- FAQs — UAT-UK. Accessed 2026-10-01.
- UAT-UK University Admission Tests: specimen and sample tests — Pearson VUE. Accessed 2026-10-01.
- TMUA Content Specification — UAT-UK. Accessed 2026-10-01.
- Notes on Logic and Proof – for TMUA Paper 2 — UAT-UK. Accessed 2026-10-01.
- Notes on Mathematics for TMUA Paper 1 and ESAT Mathematics 2 — UAT-UK. Accessed 2026-10-01.
- TMUA 2023 Paper 1 — UAT-UK. Accessed 2026-10-01.
- TMUA 2016 Paper 1 — UAT-UK. Accessed 2026-10-01.
Related guides
Sources and corrections
Sources last checked 2026-10-01Every source cited on this page was checked on the date shown, and we update the page when a source changes. If something looks wrong, tell us and we'll recheck it.