TMUA Past Papers
The TMUA is the mathematics admissions test used across seven UK universities for mathematics, economics, and computer science degrees. Below is every public TMUA past paper from the UAT-UK archive, from the 2023 papers back to 2016, with worked answers and answer keys. The papers are theirs. SummitPapers adds the index, the score notes, and, when original questions are published, the practice.
- 2 × 75 minPaper 1 and Paper 2
- 40 questions20 multiple choice on each paper
- 1.0–9.0One overall score, one decimal
- £78 / £133UK & Ireland / elsewhere
TMUA past papers by year
UAT-UK describes these as historic papers. The content specification and question style are unchanged, but the live TMUA is sat on computer at a Pearson test centre, and papers from 2024 onward are not released. Specimen and practice tests on the Pearson player give right-or-wrong feedback and deliberately do not award a score.
| Paper | Question paper | Worked answers | Answer key |
|---|---|---|---|
| Early specimen 1 | Early specimen 1 Open | Early specimen 1 Open | Early specimen 1 Open |
| Early specimen 2 | Early specimen 2 Open | Early specimen 2 Open | Early specimen 2 Open |
These files are hosted by UAT-UK. SummitPapers links to the current official copy and does not re-host the PDFs. TMUA preparation materials
What is the TMUA?
Paper 1 is Applications of Mathematical Knowledge. Paper 2 is Mathematical Reasoning, and it is the paper that also draws on logic and proof. The mathematical content sits at Higher Level GCSE and AS mathematics. Both papers are equated together into a single score. You do not receive a separate Paper 1 or Paper 2 score.
Sittings for 2027 entry are 12–16 October 2026 and 4–8 January 2027. Most Oxford and Cambridge applicants sit in October. UAT-UK’s exceptions are a Cambridge mature college with a January deadline, and Oxford’s Astrophoria Foundation Year. You sit the test once in a cycle. Results are released to your UAT-UK account. The dedicated results page says this is about four weeks after the sitting. The TMUA overview page still says about six weeks, so treat the date in your account as the one that applies.
How to prepare for the TMUA
- Read the content specification, including the logic and proof section for Paper 2.
- Sit a past paper without a time limit and mark it from the official worked answers.
- Revise the topics you missed. The topic list on the practice page follows the specification codes.
- In the last month, sit full papers in 75 minutes each. There is no negative marking, so answer every question.
Free official TMUA resources
- TMUA specification, topic by topic
- TMUA content specification (PDF)
- Notes on mathematics
- Notes on logic and proof
- Specimen and practice tests (Pearson)
- Explanation of Results, October 2025 and January 2026
- Course list for 2027 entry
The same body runs the ESAT. Oxford also uses the TARA for a different set of courses.
Common questions
What is the TMUA?
The Test of Mathematics for University Admission is a UAT-UK test used by some mathematics, economics, and computer science courses. UAT-UK’s April 2026 course list names seven universities. Check that list for your course, because the test can be compulsory or recommended.
How long is the TMUA?
Two papers of 75 minutes each, 2 hours 30 minutes in total. Each paper has 20 multiple-choice questions. Calculators and dictionaries are not allowed, and wrong answers are not penalised.
What is a good TMUA score?
There is no pass mark. UAT-UK’s Explanation of Results for October 2025 and January 2026 says a typical candidate scores around 4.5, and about 10% score higher than 7.0. Scores run from 1.0 to 9.0.
Which universities require the TMUA?
The April 2026 course list names Durham, Imperial, LSE, Cambridge, Oxford, Warwick, and UCL for at least one test. Durham’s listed mathematics courses describe the TMUA as recommended. Other courses vary. Use the official course list before you book.
Can I use a calculator?
No. UAT-UK states that a calculator or dictionary cannot be used.
Where are the official TMUA past papers?
On UAT-UK’s TMUA preparation materials page. The public paper archive runs from 2016 to 2023, with worked answers and a yearly answer key, plus two early specimen papers. The live test is computer-based, so there is no 2024 or 2025 paper PDF.