The TMUA has become the gateway for maths applicants in the UK. Cambridge requires it for Mathematics, Computer Science and Economics; Oxford, since 2026, for all its maths and computer science courses; other universities, such as Imperial, LSE, UCL, Warwick and Durham, require or recommend it for some courses. A student at a French lycée aiming for one of these courses takes it in October of their final year.
On paper, it is an easy test for a good student in the French maths specialism: the syllabus stops at roughly the level of the penultimate year. In practice, it often surprises French students, for reasons that have more to do with the format than the level.
TMUA: format and scoring
The test lasts two and a half hours, in two papers of 75 minutes and twenty multiple-choice questions each. The first, Applications of Mathematical Knowledge, checks that you can apply what you know in new situations. The second, Mathematical Reasoning, covers reasoning and logic. Calculators and dictionaries are not allowed. Wrong answers lose no marks, so every question should be answered.
The result is a score on a scale from 1 to 9, to one decimal place, with no pass mark. The test is taken on computer at an approved centre: in France for a student living in France, for £133.
What the TMUA covers, compared with the French syllabus
| TMUA topic | In France | Where it catches students |
|---|---|---|
| Algebra: indices, surds, quadratics, polynomials, inequalities | Ages 15 to 17 | Calculating without a calculator, especially with surds |
| Exponentials and logarithms | Penultimate and final year | Logarithms to any base and change of base, little practised in France |
| Trigonometry | Penultimate year | Equations over a given interval, in degrees as well as radians |
| Arithmetic and geometric sequences | Penultimate year | Little difficulty |
| Differentiation | Penultimate year | Little difficulty |
| Integrating xn, area under a curve | Final year | The chapter may not have been taught yet at test time |
| Logic and proof | Spread across the syllabus | English vocabulary and the multiple-choice format |
The most treacherous point is integration. The official TMUA specification requires simple integrals and the distinction between an integral and an area. In France, this chapter comes in the final year, and it is not always covered by mid-October, when the test takes place. It needs to be studied over the summer.
Logic, the paper students underestimate
The second paper draws on a part of the specification devoted to logic: statements of the form "A if B", "A only if B", "A if and only if B", the converse and the contrapositive, necessary and sufficient conditions, "for all" and "there exists", negating a statement. It also asks students to follow a proof, by contradiction or by counterexample, and sometimes to spot the faulty step.
A French student has an advantage here: they are used to writing proofs. But they are not used to reasoning about reasoning, with multiple-choice options offering several almost identical phrasings. Half an hour on the difference between "if" and "only if" earns several questions. The body that runs the test publishes a document on logic and proof; it is the first thing I give students to read.
How Cambridge and Oxford use the TMUA
For Mathematics at Cambridge, the TMUA is used to shortlist for interview. The faculty explains that it mainly helps identify applicants who would not be competitive, rather than pick the best, and that it has historically interviewed between 75% and 80% of applicants. So the test does not secure admission, but a poor score closes the door. The offer then depends on the interview and, for maths, on the STEP papers sat in June.
Oxford uses it, alongside the rest of the application, to decide whom to invite to its December interviews. For a French student, the stakes are clear: a solid TMUA score, then an interview that shows how they approach a problem.
Preparing for the TMUA from a French lycée
I work with students over ten to twelve weeks, ideally from June to early October:
- A full mock paper from the start, timed and without a calculator, to measure the gap.
- The missing chapters, integration and logarithms first, and calculation by hand.
- Logic, with the official document, then sets of questions in the style of the second paper.
- Official papers in real time, at least one a week in the final month, reviewed together.
Students who have done olympiads arrive with a head start, because they have already learnt to work on unfamiliar problems; I explain this in Maths olympiads on a university application. For the other tests and the full application calendar, see Oxford and Cambridge admissions tests.
I prepare students for the TMUA in private lessons, and with Carmine we build the rest of the application, the UCAS form, the personal statement and the interview, so that the test fits into a coherent plan.