The Test of Mathematics for University Admission (TMUA) is a 2-hour-30-minute admissions test used by several UK universities for maths-heavy courses such as Mathematics, Computer Science and Economics. It is run by UAT-UK and sat at Pearson VUE test centres. There are two sittings a year — an October sitting and a January sitting — and this guide explains exactly what each paper asks of you.
The format in 30 seconds
Two papers, 20 multiple-choice questions each, 75 minutes per paper. That works out at 225 seconds (3 minutes 45 seconds) per question — generous compared with some admissions tests, but the questions are designed so that only sharp, well-drilled candidates finish comfortably. Papers are usually sat on the same day with a short break between them. Start with our syllabus checklist to see what each paper covers, then try five timed questions to feel the pace.
Who sits the TMUA
You sit the TMUA if a course you are applying to requires it. Current users include Cambridge (Computer Science, Economics), Imperial College London, LSE, Durham, Lancaster and Warwick for selected courses — but requirements shift, so treat university course pages as the source of truth and this guide as orientation. Most candidates sit in Year 13 in the October sitting so their score arrives in time for admissions decisions; the January sitting suits gap-year applicants and later decisions. Bursary support is available for eligible UK candidates — see our dates, fees and registration guide for the £75 / £133 fee bands and how to claim support.
The two papers
Paper 1 — Mathematical thinking (Applications of Mathematical Knowledge). Twenty questions on pure and applied school maths: algebra, sequences, geometry, trigonometry, exponentials and logs, calculus, plus number, geometry and statistics strands. No calculator, so fluency with fractions, surds and standard results matters enormously. Our topic hubs break every strand into drills.
Paper 2 — Mathematical reasoning (Reasoning and Logic). Twenty questions on argument and proof: identifying conclusions and flaws, necessary and sufficient conditions, quantifiers, direct proof, contrapositive and contradiction, and spotting the first invalid step in a purported proof. You do not need A-level Further Maths to do well — you need precision with language. Read our Paper 2 logic and proof guide and compare the papers in Paper 1 vs Paper 2.
How scoring works
Each paper is reported on a 1–9 scale (one decimal place), with an overall score combining both sittings of questions. Scores are statistically equated so that a 6.0 means the same standard from year to year, and the scale was recalibrated in 2024. The modal (most common) overall score sits around 4.5; scores of 6.0–6.5+ are typically described as competitive for the most selective courses. There is no pass mark — universities interpret scores alongside UCAS forms and interviews. Our scores explained guide and score calculator walk through bands honestly, including the limits of any raw-to-scaled estimate.
How universities use it
Universities use TMUA scores differently: some set guideline thresholds for interview shortlisting, others combine the score with predicted grades, personal statement and interview. A strong score rarely guarantees an offer, and a middling score rarely sinks an otherwise excellent application — but because the test is designed to separate strong mathematicians, moving from 4.5 to 6.0+ is one of the highest-leverage things a Year 13 applicant can do. Browse realistic practice questions, sit a full timed mock, and read how to prepare for week-by-week plans.
Your first 7 days
Turn orientation into action this week. Day 1–2: read the syllabus checklist and grade every strand green, amber or red. Day 3: drill one red topic — say MM1 algebra — with five timed questions, and open an exemplar such as TMUA-P1-MM1-002 to see the house style up close. Day 4: meet Paper 2 with the arguments hub and an exemplar like TMUA-P2-ARG1-001. Day 5–6: sit half of a timed mock (one paper, strict 75 minutes, no calculator) and log every miss. Day 7: rest, then review the log and convert your band with the score calculator. That single week of evidence beats a month of vague “I should revise” — and tells you exactly which of the 22 topic hubs deserves week two.
No calculator, no formulae
Two rules shape all preparation: calculators are banned and no formula booklet is provided. Every identity you need must be memorised, and every arithmetic step must be doable by hand. That sounds harsh, but it is also an opportunity — candidates who drill mental maths and standard results (exact trig values, log laws, differentiation rules) bank easy marks while others burn time. The test is sat at Pearson VUE centres with photo ID required; details are in the dates and registration guide. For official past papers and mark schemes, UAT-UK publishes verbatim PDFs — we link out rather than reproducing them, and all our questions are original paraphrase-style practice.
Common slip & diagram reading
| Slip | What happens | Fix in 30 seconds |
|---|---|---|
| Common slip: treating 6.0 as 60 percent | Reads the 1–9 equated scale as a percentage and panics at 4.5, missing that 4.5 is the modal hump and 6.0+ is already competitive | Recite scale not percent before every mock; convert raw marks only to band ranges with the score calculator and track trends |
Diagram description: picture a horizontal exam-day timeline for this guide. A left block labelled Paper 1 spans 75 minutes with twenty tick marks for questions and a small no-calculator icon, then a narrow hatched break block sits in the middle labelled short reset with stand-up and snack symbols, followed by an equal right block labelled Paper 2 with its own twenty ticks and a magnifier icon for exact reading. Below the timeline a bell-shaped score curve peaks at 4.5 with shaded bands at 6.0 and 6.5 marked competitive, showing why the scale is a standard of performance rather than a percentage. The reading habit is to trace the day left to right — two equal papers, one reset, one equated scale — before revising any single topic.