The TMUA format
The TMUA is 2 papers and you sit both. Each is 20 multiple-choice questions in 75 minutes, taken on screen at a test centre. There is no calculator and no negative marking, which means a wrong answer costs exactly what a blank costs: nothing.
The 2 papers
| Paper | Questions | Time | Per question |
|---|---|---|---|
| Paper 1 — Applications of Mathematical Knowledge | 20 | 75 min | 3 min 45 s |
| Paper 2 — Mathematical Reasoning | 20 | 75 min | 3 min 45 s |
What each paper actually asks
Paper 1 — Applications of Mathematical Knowledge
Paper 1 hands you familiar A-level pure content and asks you to apply it quickly. The mathematics is not the hard part: the difficulty is spotting which tool the question wants and reaching the answer by hand. Questions are built so that a well-chosen route takes under a minute and a brute-force route takes five.
Paper 2 — Mathematical Reasoning
Paper 2 tests how you reason about mathematics rather than how much of it you can do. Questions turn on logic and proof: what follows from what, whether a condition is necessary or sufficient, what a single counterexample destroys, and where a printed argument breaks down. Very few candidates are taught this explicitly at school, which makes it the paper where deliberate preparation moves a score most.
How much time you get per question
Paper 1 gives you 3 min 45 s a question, Paper 2 gives you 3 min 45 s a question. That average is the whole shape of the test. The content is not beyond A-level, but a method that takes twice the average has already cost you the question after it. Practising under the real clock, rather than untimed, is the single change that most reliably shows up in a score.
The rules that change how you prepare
- No calculator
- Every question is written to be answered by hand. That rewards exact values over decimals, factorising over expanding, and estimating an answer to eliminate options over computing it precisely. If your A-level habit is to reach for a calculator, the first thing to fix is arithmetic fluency.
- No negative marking
- A wrong answer and a blank score identically, so leaving anything unanswered is simply a mark thrown away. Two minutes before the end, fill in every remaining question, and rule out whatever options you can first: a guess down to two options is worth far more than a blind one.
- Multiple choice, no working marked
- Nobody reads your method, which makes backwards work legitimate: substituting the options into the question, testing a value, or ruling out answers by sign or magnitude are all full-credit routes. Under this much time pressure they are often the fastest ones.
- Sat on screen at a test centre
- You register yourself with UAT-UK / Pearson VUE and book a slot at a test centre rather than sitting it at school. Slots at individual centres are limited, so registering early gives you more choice of location and time. See TMUA dates and deadlines.
How the TMUA is scored
Each paper is reported on a scale from 1.0 to 9.0, in steps of 0.1. Raw marks are converted onto that scale so that a given score means the same thing from one year to the next, which is why there are no grade boundaries to look up and no pass mark to clear. What counts as a good TMUA score depends entirely on where you are applying.
What is on it
The content is fixed and published, and it is narrower than most candidates assume. The full TMUA syllabus lists every topic that can come up, with notes on each one.
Sit a real one under real timing
The format stops being abstract the first time you run out of time on question 14. Every past paper on this site can be sat to the clock, with a full worked solution for each question afterwards.
TMUA format: frequently asked questions
- What is the TMUA?
- The TMUA is the Test of Mathematics for University Admission, a multiple-choice admissions test run by UAT-UK / Pearson VUE and used by UK universities to help decide who to make offers to. It is sat on screen at a test centre in the autumn of the year you apply, and it is separate from your A-levels.
- How long is the TMUA?
- 75 minutes per paper, so 150 minutes in total across the 2 papers.
- How many questions are on the TMUA?
- 40 in total: 20 on Paper 1 and 20 on Paper 2.
- Is the TMUA multiple choice?
- Yes, every question. You select an answer rather than write out a method, and no working is marked, so a correct answer reached by a shortcut scores the same as one reached the long way.
- Can you use a calculator in the TMUA?
- No. Every question is designed to be answered by hand, which changes which methods are worth using: exact values, factorising and sensible estimation beat decimal arithmetic almost every time.
- Is there negative marking in the TMUA?
- No. A wrong answer scores the same as no answer, so there is never a reason to leave a question blank. Eliminating even one or two options before you guess turns a blank into real expected marks.
- How is the TMUA scored?
- Each paper is reported on a scale from 1.0 to 9.0, in steps of 0.1. There are no grade boundaries and no pass mark: universities read the score alongside the rest of your application.