What is the TMUA? Format, papers and scoring

The TMUA, or Test of Mathematics for University Admission, is the admissions test several UK universities use for maths-heavy courses like mathematics, computer science and economics. It is run by UAT-UK, a partnership between Imperial College London and the University of Cambridge, and you sit it on a computer at a Pearson VUE test centre rather than on paper at school.

What the TMUA is for

The TMUA does not test advanced material. It is drawn from Higher Level GCSE and AS-level mathematics, so the content is familiar. What it measures is whether you can apply that maths fluently to unfamiliar problems and reason carefully about it, which is exactly the skill competitive courses want to see before they make an offer. Your score sits alongside your predicted grades, personal statement, reference and, at Cambridge, your interview.

TMUA format and papers

The TMUA is two papers, and they test different things. Both are multiple choice, both have 20 questions, and both last 75 minutes, so the whole test runs to 2 hours 30 minutes. Neither allows a calculator, and nothing is deducted for a wrong answer.

Paper	Full name	Questions	Time
Paper 1	Applications of Mathematical Knowledge	20	75 min
Paper 2	Mathematical Reasoning	20	75 min

Paper 1 gives you maths you already know and asks you to use it on problems you have not seen before. Paper 2 is about arguments rather than calculations: whether a statement follows from another, whether a proof is sound, whether a claim survives a counterexample. Most students find Paper 2 stranger, because school maths rarely trains it directly. Our guide to Paper 1 vs Paper 2 covers the difference in full, and the TMUA exam format sets out the mechanics.

TMUA scoring explained

Unlike the modular ESAT, the TMUA produces a single number. Your answers across both papers are marked and then scaled together into one overall score from 1.0 (low) to 9.0 (high), to one decimal place. The scaling adjusts for how hard a particular sitting was, so a 6.0 means the same thing across years. There is no pass mark and no "X out of 40" to aim for, because the reported score, not the raw mark, is what universities see. For what a strong result looks like, see what is a good TMUA score.

Which universities require the TMUA

For 2027 entry the TMUA is used by Cambridge, Imperial, LSE, Oxford, Warwick, Durham and UCL, with the courses and whether it is required or optional varying by university. The full list, and what each course needs, is on our university requirements pages.

TMUA vs ESAT

The two tests share an administrator and a scoring scale but not much else. The TMUA is one maths and reasoning test that produces a single score. The ESAT is modular, covers sciences as well as maths, and gives you a separate score for each subtest. A few applicants take both, because their course list spans universities that use different tests, so check every course you are applying to rather than assuming one test covers all of them.

Getting ready

Timed practice on real questions, followed by honest review, is what raises a score. Work through past papers, close the gaps you find with the topic-by-topic textbook, and follow the plan in how to prepare for the TMUA.

Official TMUA resources

The TMUA is set and run by UAT-UK, a partnership between Imperial College London and the University of Cambridge. Its pages are the authoritative source for the test itself, and the practice tools on tmua.fyi are supplementary to them.

• TMUA test and content specification, UAT-UK
• TMUA preparation materials, including Notes on Mathematics and Notes on Logic and Proof, UAT-UK
• Booking and specimen tests, Pearson VUE
• University requirements from the source: Cambridge and Imperial