Admissions tests / TMUA
UAT-UK, delivered by Pearson VUE
TMUA: Test of Mathematics for University Admission
The TMUA is a two-paper, no-calculator, multiple-choice mathematics test sat by applicants to mathematics, computer science, economics and engineering-adjacent courses at a growing list of universities. From 2027 entry it is also the test Oxford mathematics and computer science applicants sit, having replaced Oxford's own MAT. There are 444 original practice questions with full worked solutions below.
The TMUA is not a harder A level paper. It tests whether you can use school-level mathematics fluently and reason with it, which is a different skill from executing a taught method on demand. The syllabus stops at AS-level pure mathematics plus Higher-tier GCSE, and it says so explicitly: there is no content on the test that a Year 13 mathematician has not met.
What makes it difficult is that the route to the answer is not signposted. A TMUA question rarely tells you which technique to reach for, frequently has a short elegant solution and a long grinding one, and gives you an average of three minutes and forty-five seconds per question with no calculator and no formulae booklet.
Paper 2 adds something A level does not teach at all: the logic of arguments, mathematical proof, and spotting the exact step where a purported proof goes wrong. This is the half of the test most candidates neglect, and it is the half where preparation moves a score furthest.
Format
| Module | Questions | Time | Format | Scored |
|---|---|---|---|---|
| Paper 1: Applications of Mathematical Knowledge | 20 | 75 min | Multiple choice | Scored |
| Paper 2: Mathematical Reasoning | 20 | 75 min | Multiple choice | Scored |
Who needs the TMUA
| University | Courses | Status |
|---|---|---|
| University of Oxford | Mathematics, Mathematics and Statistics, Mathematics and Philosophy, Mathematics and Computer Science, Computer Science, Computer Science and Philosophy | Check the course page |
| University of Cambridge | Economics | Check the course page |
| Imperial College London | Mathematics, Mathematics and Computer Science, Mathematics with Statistics, Computing | Check the course page |
| University of Warwick | Mathematics, Mathematics and Statistics | Check the course page |
| London School of Economics | Mathematics and Economics, Economics | Check the course page |
| Durham University | Mathematics | Check the course page |
| University of Southampton | Mathematics | Check the course page |
How the TMUA is scored
- Each paper is 20 multiple-choice questions. Every correct answer scores one mark and nothing is deducted for a wrong one, so there is never a reason to leave a question blank.
- The two papers are combined into a SINGLE overall score reported on a scale from 1.0 to 9.0, to one decimal place. Separate paper scores are not reported.
- The scale is set so that a typical candidate scores around 4.5, and roughly 10 per cent of candidates score above 7.0. Scores are capped at 1.0 at the bottom and 9.0 at the top.
- There is no pass mark. Universities use the score alongside everything else in your application, and each sets its own expectations, which most do not publish.
Key dates
- Registration opens: Late spring, ahead of the October sitting. You register through Pearson VUE, not through your school in most cases. Check the official site for the exact opening date for your cycle. Check the official site for your cycle.
- Registration closes: Roughly two weeks before the sitting. Registration closes well before the test date and late entry is not generally available. Missing it is the single most common avoidable failure in this process. Check the official site for your cycle.
- Test sitting: October, ahead of the 15 October UCAS deadline for Oxford and Cambridge. Sat at a Pearson VUE test centre on screen. Check the official site for your cycle.
What official practice actually exists
- UAT-UK publishes a content specification, an explanation of results, and companion notes on logic and proof. Read the logic and proof notes before attempting Paper 2 practice: they set the conventions the test uses.
- Specimen papers are published on the UAT-UK preparation pages.
- Legacy TMUA papers from 2016 to 2023 remain available and are genuinely useful, because the syllabus is substantially continuous.
- IMPORTANT: UAT-UK does not release live questions from the 2024 sitting onwards. Any site advertising a complete or current TMUA past-paper archive is describing something that does not exist. The authentic corpus ends in 2023 and is not growing.
- Official material provides an ANSWER KEY, giving the correct option letter, rather than a worked solution. That is the gap this library exists to fill.
Moving from the MAT to the TMUA
What carries over
- Most of the mathematical content. Both tests stop at AS-level pure plus GCSE, so the algebra, graphs, calculus, sequences and trigonometry you revised for the MAT is the same body of knowledge the TMUA assesses.
- The habit of looking for a short route. Both tests are built so that the elegant solution exists and the grinding one does not fit in the time.
- Graph sketching and transformations, which carry heavily on both.
- Reasoning about proofs. The MAT's longer questions asked you to justify, and TMUA Paper 2 asks you to reason about arguments, so the underlying habit transfers even though the format does not.
What does not
- The format. The MAT ended with typed free-response questions worth most of the marks. The TMUA is multiple choice throughout, so writing out a full argument is no longer how marks are earned.
- The pacing. MAT longer questions ran to fifteen or twenty minutes each. TMUA questions average under four minutes, so the rhythm of the paper is completely different.
- The logic of arguments. Conditionals, quantifiers, negation and identifying errors in purported proofs are TMUA Section 2 content with no MAT equivalent, and they are Paper 2 only. This is the largest single thing a former MAT candidate has not covered.
MAT papers from 2007 onwards remain good mathematics and are worth using for the multiple-choice opening section, which is close in spirit to TMUA Paper 1. Do not use the long MAT questions to practise TMUA pacing, and do not treat MAT preparation as covering Paper 2, because it covers none of it.
How to prepare for the TMUA
Start with the specification, not with a paper. The TMUA syllabus is short and completely explicit, and roughly a third of it is Higher-tier GCSE content that most Year 13 students have not touched in two years. Bounds, ratio, circle theorems and vectors all appear, and all of them are easier to lose marks on than the AS-level content precisely because nobody revises them.
Then split your preparation in two, because the TMUA is two different tests wearing one name. Paper 1 rewards fluency: the ability to see, quickly, that a problem about a circle is really a problem about a quadratic discriminant. That comes from volume, and from always asking after a question whether there was a shorter route.
Paper 2 rewards something you have probably never been taught. Working through the logic and proof strands deliberately, in order, is worth more than any number of extra Paper 1 questions, because most candidates arrive at Paper 2 having never had to decide whether a statement's converse follows from it.
Sit the legacy 2016 to 2023 papers late rather than early. There are only eight of them and they are the closest thing to the real experience you will get, so spending them as diagnostics in September wastes them.
Why Paper 2 is where scores are made
Every A level mathematician arrives able to do some of Paper 1. Almost nobody arrives able to do Paper 2, because the logic of arguments is not on any A level specification and proof at A level is a small, procedural topic rather than a way of thinking.
The concrete asymmetry: on Paper 1 you are competing against candidates who have all done the same two years of practice as you. On Paper 2 you are competing against candidates who mostly have not prepared for it at all. A month spent on Section 2 moves a TMUA score further than a month spent on anything else.
The three things to get right are conditionals, quantifiers and negation. Most Paper 2 errors reduce to one of three confusions: treating 'A only if B' as though it meant 'A if B'; assuming a statement's converse follows from it; or negating a quantified statement wrongly, so that the negation of 'all swans are white' comes out as 'no swans are white' rather than 'some swan is not white'.
Practise identifying errors in proofs as a separate skill. It is not the same as proving something. You are being asked to read someone else's argument sceptically and name the exact line where it fails, and the failures are drawn from a small, learnable set: dividing by something that might be zero, squaring both sides and gaining a root, taking a square root and losing one, and assuming the converse.
Technique in the test itself
Three minutes and forty-five seconds per question is the average, not the target. A TMUA paper contains questions that take forty seconds and questions that take eight minutes, and the whole skill of the sitting is deciding quickly which one you are looking at. Get the fast ones banked first.
Use the options. This is a multiple-choice test, and on a good proportion of questions substituting the options, testing a small case, or ruling out answers on grounds of sign, magnitude or units is faster and safer than solving forwards.
There is no negative marking, so an unanswered question is a wasted mark. Leave nothing blank, and if you abandon a question, guess before you move on rather than promising to come back.
Work on the erasable booklet properly. The test is on screen but the mathematics is not, and candidates who try to hold algebra in their head to save time lose more to slips than they gain in seconds.
The mistakes that cost the most marks
Revising A level content instead of the TMUA syllabus. Anything beyond AS-level pure is not on the test, and time spent on it is time not spent on the GCSE content that is.
Treating Paper 2 as Paper 1 with harder algebra. It is a different subject and it needs separate preparation.
Grinding a long method when a short one exists. The TMUA is designed so that the elegant route is available; the papers are not long enough to reward the grinding one.
Learning the formulae you would normally look up too late. There is no formulae booklet, and the ones candidates most often find missing are the trigonometric identities, the binomial expansion and the sum formulae for arithmetic and geometric series.
Registering late. Registration closes well before the test and there is generally no late entry.
TMUA questions students ask
- Is the TMUA harder than A level maths?
- It is not harder in content: the syllabus stops at AS-level pure plus Higher-tier GCSE. It is harder in that the questions do not tell you which method to use, there is no calculator or formulae booklet, and Paper 2 assesses reasoning about arguments that A level does not teach.
- Do I have to sit both papers?
- Universities set their own requirement, and Oxford requires both papers. Check the course page for every course you are applying to before you register.
- What is a good TMUA score?
- There is no pass mark. The scale runs from 1.0 to 9.0 with a typical candidate around 4.5 and roughly 10 per cent above 7.0, so a score above 7.0 places you in about the top tenth of a strong self-selecting field. Most universities do not publish a threshold.
- Is there negative marking?
- No. Nothing is deducted for a wrong answer, so you should answer every question.
- Can I use a calculator?
- No, and there is no formulae booklet either. You are expected to recall every formula the specification lists.
- Are there recent past papers?
- No. UAT-UK does not release live questions from the 2024 sitting onwards. Official practice is the specimen material plus the legacy 2016 to 2023 papers, which is why original practice written to the specification matters more for this test than for most.
- I was preparing for the MAT. Is that wasted?
- Most of the mathematics carries over directly. The format, the pacing and the whole of Paper 2's logic and proof content do not. See the transition section on this page for what to keep and what to add.
Sources
Every fact on this page is checked against the official specification and the administering body. Status: Currently sat. Last verified 2026-09-05.
- TMUA Content Specification (UAT-UK, read 2026-09-05). The content specification every strand on this page is quoted from. Section 1 Part 1 is AS-level pure content, Part 2 is Higher-tier GCSE content, and Section 2 (logic, proof and errors in proofs) is Paper 2 only.
- TMUA Explanation of Results, October 2025 (UAT-UK, read 2026-09-05). Source for the 1.0 to 9.0 scale, the typical score of about 4.5 and the roughly 10 per cent of candidates above 7.0.
- Notes on Logic and Proof (UAT-UK, read 2026-09-05). The official companion notes for Section 2. Read before attempting Paper 2 practice: the notation conventions in it are the ones the test uses.
- About the TMUA (UAT-UK, read 2026-09-05). Format, timing and registration information.
- TMUA preparation materials (UAT-UK, read 2026-09-05). The official specimen material. UAT-UK does not release live questions from the 2024 sitting onwards, so this plus the 2016 to 2023 legacy papers is the whole official corpus.
Practice by module
Paper 1: Applications of Mathematical Knowledge
Paper 1 asks you to apply mathematics you already know in unfamiliar contexts. The content is Section 1 of the specification: AS-level pure mathematics plus Higher-tier GCSE. Nothing on Paper 1 is beyond that syllabus, so every question you find hard is hard because of the route to the answer, not because of missing content.
11 strands. 276 practice questions across 23 sets.
Paper 2: Mathematical Reasoning
Paper 2 is the paper that decides most TMUA scores, because it is the one nothing at A level prepares you for. It assumes all of the Paper 1 content and adds Section 2: the logic of arguments, mathematical proof, and identifying errors in purported proofs. You are asked to reason about arguments rather than to execute a method.
4 strands. 168 practice questions across 14 sets.
37 printable TMUA sets, no login
Original questions written to the published specification, each with a full worked solution and a reason every wrong option is wrong.