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The Test of Mathematics for University Admission

What is the TMUA?

The 2h 30m admissions test for Maths, Economics and Computer Science at Cambridge, Oxford, Imperial, Warwick, LSE, Durham and UCL. Format, syllabus, scoring, and how to prepare.

2h 30m
Total duration
0
Multiple-choice questions
1.0–9.0
Score scale
+1 / 0
Marking, no penalties
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 reserved for mature applicants to specific Cambridge mature colleges and to Oxford's Astrophoria Foundation Year.

Seven universities use the TMUA
  • University of Cambridge logo
    University of Cambridge
  • University of Oxford logo
    University of Oxford
  • Imperial College London logo
    Imperial College London
  • London School of Economics logo
    London School of Economics
  • University of Warwick logo
    University of Warwick
  • Durham University logo
    Durham University
  • University College London logo
    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 such that…
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…
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
7.0+
1.02.03.04.05.06.07.08.09.0

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

8.0 – 9.0Top 3–5%

Exceptional

A standout score at any university. Comfortably above the average applicant for even the most competitive courses.

7.0 – 7.9Top 10%

Outstanding

Strongly competitive for Cambridge, Imperial and LSE. The unspoken target for top-tier offers.

6.5 – 6.9Top 15–20%

Highly competitive

Historically the Cambridge interview benchmark. Solid for Warwick and Durham.

5.5 – 6.4Top 25–35%

Strong

Likely sufficient for Durham, UCL or Warwick with a strong application overall.

4.5 – 5.4Top 40–50%

Above average

The typical applicant range. Competitive for mid-tier Russell Group; less so for Oxbridge.

3.5 – 4.4~50th percentile

Average

The modal score range. Roughly half of all candidates score 3.8 or lower.

1.0 – 3.4Bottom 50%

Below average

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

Key dates

The 2026/27 cycle.

Sitting 1
12–16 October 2026

Required for all 2027 entry, including Cambridge and Oxford applicants.

Sitting 2
4–8 January 2027

Mature applicants to a Cambridge mature college with a January deadline, or Oxford Astrophoria Foundation Year applicants only.

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.

400+ questions tagged to every topic on this page, 18+ mock papers, full worked solutions, SM-2 spaced repetition. £37 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
Converse
Contrapositive (≡ original)
Biconditional
sufficient for
necessary for
Negation of
Negation of
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 logoUniversity of Cambridge
University of Oxford logoUniversity of Oxford
Imperial College London logoImperial College London
London School of Economics logoLondon School of Economics
University of Warwick logoUniversity of Warwick
Durham University logoDurham University
University College London logoUniversity 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 400+ 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.