The Test of Mathematics for University Admission is a 2 hour 30 minute computer-based admissions test used by seven UK universities for selection to Maths, Economics and Computer Science courses.

How long is the TMUA?

2 hours 30 minutes total, split into two 75 minute papers of 20 multiple-choice questions each.

Is there negative marking in the TMUA?

No. You get 1 mark for a correct answer and 0 for a wrong or blank answer, so it is always worth attempting every question.

What TMUA score do I need for Cambridge?

There is no formal pass mark, but a score around 6.5 is generally competitive for the most selective courses, with 7.0 or above considered elite (the top ~10 percent).

Can I use a calculator in the TMUA?

No. Calculators, formula booklets and dictionaries are not permitted. Every formula and identity must be memorised.

Is the TMUA harder than A-level?

Yes, the questions are noticeably harder than standard A-level papers, but easier than STEP or MAT. The difficulty comes from speed, abstraction and logical reasoning, not from new content.

When is the TMUA 2026?

The 2026/27 cycle has two sittings: 12 to 16 October 2026 (required for Cambridge and Oxford applicants, and the main sitting for everyone) and 4 to 8 January 2027 (accepted by Imperial, LSE, Warwick, Durham and UCL; Oxbridge accepts it only for Cambridge mature colleges and Oxford's Astrophoria Foundation Year).

What Is the TMUA? Format, Syllabus & Scoring (2026/27)

Overview

What the TMUA actually is.

The TMUA is a paper-based skills test sat at Pearson VUE centres, designed to measure how well you can apply standard A-level mathematics in unfamiliar contexts and how cleanly you can reason with logical arguments. It is not a knowledge test. The content sits inside Higher Level GCSE and AS-level mathematics, so the difficulty comes from question style, not new theory.

You sit it if you are applying to Maths, Economics or Computer Science courses at one of seven UAT-UK universities. For most courses it is compulsory; for a few it is recommended. Always check the specific course page on the university website.

The TMUA is normally taken in October of Year 13, alongside your UCAS application. There is also a January sitting, accepted by most TMUA universities; Cambridge and Oxford accept it only from mature-college and Astrophoria Foundation Year applicants respectively.

Seven universities use the TMUA

University of Cambridge
University of Oxford
Imperial College London
London School of Economics
University of Warwick
Durham University
University College London

Test format

Two papers, both 75 minutes, both 20 MCQs.

Paper 175 min · 20 MCQs

Applications of Mathematical Knowledge

Apply standard A-level mathematics to new and unfamiliar situations. Often combines two topics in one question.

Flavour

Find the values of

k

such that…

Δ = k^{2} - 4 (k + 3) < 0

Paper 275 min · 20 MCQs

Mathematical Reasoning

Evaluate, deduce and justify mathematical arguments using elementary logic and proof.

Flavour

Which of the following is the contrapositive of…

P \Rightarrow Q \Leftrightarrow \neg Q \Rightarrow \neg P

No calculatorNo formula bookletNo dictionaryNo negative markingComputer-based at Pearson VUE

Reading about the format only gets you so far.

Try a TMUA-style question

Scoring

One score from 1.0 to 9.0.

Each paper is marked out of 20. Raw marks are combined and converted to a single overall score reported on a 1.0 to 9.0 scale, to one decimal place. There is no pass mark. Universities read your score alongside your application.

6.5

competitive

7.0+

elite (top ~10%)

1.02.03.04.05.06.07.08.09.0

Reported to one decimal place. No pass/fail. Used alongside your UCAS application.

ScorePercentileWhat it means

8.0 – 9.0Top 3–5%

Exceptional

A standout score anywhere, above the offer-holder average for even the most competitive courses.

8.0 – 9.0

Top 3–5%

Exceptional

A standout score anywhere, above the offer-holder average for even the most competitive courses.

7.0 – 7.9Top 10%

Outstanding

Strongly competitive for Cambridge, Imperial and Oxford, Imperial Maths offer-holders averaged about 7.6 in 2025. The unspoken target for top-tier maths offers.

7.0 – 7.9

Top 10%

Outstanding

Strongly competitive for Cambridge, Imperial and Oxford, Imperial Maths offer-holders averaged about 7.6 in 2025. The unspoken target for top-tier maths offers.

6.5 – 6.9Top 11–15%

Highly competitive

Around or above the Cambridge offer-holder average (~6.3 across its TMUA courses). Strong for most top destinations.

6.5 – 6.9

Top 11–15%

Highly competitive

Around or above the Cambridge offer-holder average (~6.3 across its TMUA courses). Strong for most top destinations.

5.5 – 6.4Top 17–33%

Strong

Ahead of most of the cohort and competitive for many top courses; comfortably clears the Warwick and Durham reduced-offer lines.

5.5 – 6.4

Top 17–33%

Strong

Ahead of most of the cohort and competitive for many top courses; comfortably clears the Warwick and Durham reduced-offer lines.

4.5 – 5.4Top 33–50%

Around average

The typical range, 4.5 is the median score. A 5.0 here clears the Durham and Warwick reduced-offer thresholds.

4.5 – 5.4

Top 33–50%

Around average

The typical range, 4.5 is the median score. A 5.0 here clears the Durham and Warwick reduced-offer thresholds.

3.5 – 4.4Top 50–65%

Just below average

A little under the typical 4.5. Still read as positive evidence of ability for optional uses such as Durham.

3.5 – 4.4

Top 50–65%

Just below average

A little under the typical 4.5. Still read as positive evidence of ability for optional uses such as Durham.

1.0 – 3.4Bottom third

Below average

Generally unlikely to strengthen a competitive application at TMUA-requiring institutions.

1.0 – 3.4

Bottom third

Below average

Generally unlikely to strengthen a competitive application at TMUA-requiring institutions.

Key dates

The 2026/27 cycle.

Sitting 1

12–16 October 2026

The main sitting. Required for standard Cambridge and Oxford applicants; keeps every university option open.

Sitting 2

4–8 January 2027

Accepted by Imperial, LSE, Warwick, Durham and UCL. Oxbridge accepts it only for Cambridge mature colleges and Oxford's Astrophoria Foundation Year.

Always confirm registration deadlines on the official UAT-UK site before you book.

Syllabus

The full content specification.

Every topic the test can examine, drawn from the official April 2025 content specification. Open any topic to see the identities, results and traps that come up.

Know the syllabus. Now drill it.

690+ questions tagged to every topic on this page, 26+ mock papers, full worked solutions, FSRS spaced repetition. £49 one-time, no subscription.

See pricing

Logic & proof

The spine of Paper 2.

Most A-level students arrive at the TMUA without ever formally studying logic. These identities recur in almost every Paper 2. Commit them to memory.

Paper 2 cheat sheet

Implication

P \Rightarrow Q

Converse

Q \Rightarrow P

Contrapositive (≡ original)

\neg Q \Rightarrow \neg P

Biconditional

P \Leftrightarrow Q

P

sufficient for

Q

P \Rightarrow Q

P

necessary for

Q

Q \Rightarrow P

Negation of

\forall x, P (x)

\exists x, \neg P (x)

Negation of

\exists x, P (x)

\forall x, \neg P (x)

Proof methods

DirectContradictionCounter-example

Universities

Where the TMUA is used.

Seven UAT-UK universities use the TMUA for selection on at least one of their Maths, Economics or Computer Science courses. Whether it is compulsory or recommended varies by course, so always check the specific course page.

University of Cambridge

University of Oxford

Imperial College London

London School of Economics

University of Warwick

Durham University

University College London

Resources

Official sources, in one place.

Official syllabus (PDF)

The April 2025 content specification. The same document this page summarises.

Official TMUA site

Registration, test centres, access arrangements and bursaries from UAT-UK.

Preparation materials

Past papers, the specimen test and the Notes on Logic and Proof.

Score reporting

How the 1.0 to 9.0 scale is calibrated and what universities receive.

Now go and train for it.

Reading the syllabus gets you a 4.0. Drilling 690+ topic-tagged questions with worked solutions and spaced repetition gets you a 7.0.

See pricing

Or go deeper with our in-depth TMUA guides on scores, papers and strategy.

What is the TMUA?

What the TMUA actually is.

Two papers, both 75 minutes, both 20 MCQs.

Applications of Mathematical Knowledge

Mathematical Reasoning

One score from 1.0 to 9.0.

The 2026/27 cycle.

The full content specification.

Algebra

Coordinate geometry

Trigonometry

Sequences and series

Differentiation

Integration

Exponentials and logarithms

Know the syllabus. Now drill it.

The spine of Paper 2.

Where the TMUA is used.

Official sources, in one place.

Official syllabus (PDF)

Official TMUA site

Preparation materials

Score reporting

Now go and train for it.

What is the TMUA?

What the TMUA actually is.

Two papers, both 75 minutes, both 20 MCQs.

Applications of Mathematical Knowledge

Mathematical Reasoning

One score from 1.0 to 9.0.

The 2026/27 cycle.

The full content specification.

AlgebraQuadratics, polynomials, indices, surds, logarithms and exponentials.

Algebra

Coordinate geometryLines, circles, intersections, tangents and parameter problems.

Coordinate geometry

TrigonometryRadians, exact values, identities and equations in a range.

Trigonometry

Sequences and seriesArithmetic, geometric, sigma notation, convergence.

Sequences and series

DifferentiationGradients, tangents, normals, stationary points.

Differentiation

IntegrationDefinite and indefinite integrals, area under curves.

Integration

Exponentials and logarithmsGrowth, decay and equation solving.

Exponentials and logarithms

Know the syllabus. Now drill it.

The spine of Paper 2.

Where the TMUA is used.

Official sources, in one place.

Official syllabus (PDF)

Official TMUA site

Preparation materials

Score reporting

Now go and train for it.