Test of Mathematics for University Admission 対策ガイド

75 minutes.

20 multiple-choice questions.

This section tests how well students can apply school-level mathematics in unfamiliar settings. Expect algebraic manipulation, functions, graphs, trigonometry, exponentials and logarithms, sequences, coordinate geometry, and calculus-style reasoning from the specification. The challenge is usually not raw content recall but choosing the right method quickly and executing it cleanly under time pressure.

75 minutes.

20 multiple-choice questions.

This section focuses more on reasoning, argument structure and elementary logic. It still uses mathematical content, but the emphasis is on interpreting statements, testing implications, spotting invalid steps, and handling proof-style thinking. This is the section many students neglect because it feels less like standard school maths, but it is often the bigger separator.

You cannot use a calculator or dictionary. There is no formula booklet, so students are expected to know and recall the required mathematics directly. The TMUA is taken on computer at a Pearson VUE test centre.

There is no negative marking. Both papers carry equal weight, and scores are based on the number of correct answers. That means blank answers are usually a mistake: if you can eliminate options or make a sensible inference, guessing is rational.

Cambridge says there is no pass or fail for TMUA, and performance is considered as part of the wider application rather than as a standalone hurdle. More broadly, Cambridge states that admissions test performance is taken into account alongside the other elements of the application. Cambridge does not publish a universal TMUA cutoff across all colleges and courses, so students should avoid aiming for a mythical safe score and instead treat every mark as useful.

LSE uses TMUA differently by course. For BSc Economics and BSc Econometrics and Mathematical Economics, taking TMUA is mandatory. LSE states that there is no set minimum score and that the score forms part of a holistic assessment alongside the UCAS application, academic record, contextual information, reference and personal statement. For its other listed quantitative courses, TMUA is recommended rather than mandatory, and a strong score can make an application more competitive.

TMUA reports a score on a 1.0 to 9.0 scale to one decimal place.

For the latest fully confirmed cycle, October 2025 booking opened on 31 July 2025 and closed on 29 September 2025. January 2026 booking opened on 27 October 2025 and closed on 19 December 2025. Access-arrangements deadlines were earlier than the final booking deadline. You may sit each UAT-UK test only once per admissions cycle; for 2026 entry, that means you cannot take TMUA in both October and January.

The confirmed sittings were 13 to 14 October 2025 and 8 to 9 January 2026. Cambridge applicants who needed TMUA had to use the October sitting. For the 2026 entry cycle, in China, Hong Kong and Macau, TMUA was offered on only one day per sitting for security reasons: 14 October 2025 or 9 January 2026.

TMUA results are released on the official published release dates, roughly 4 to 6 weeks after the sitting. UAT-UK’s TMUA page says results are available approximately six weeks after the test sitting, while the published 2025 to 2026 release dates were 14 November 2025 for the October sitting and 11 February 2026 for the January sitting.

The test is sat at a Pearson VUE test centre. UAT-UK says there are over 5,000 centres in 180 plus countries. Students needing access arrangements must apply before booking, and UAT-UK will not make unapproved on-the-day adjustments. Book early because centres and preferred slots fill up; earlier booking improves your chance of getting your preferred Pearson VUE test centre.

You have 75 minutes for 20 questions, so the average is 3.75 minutes per question. That does not mean equal time per question. The best approach is to take easy marks immediately, flag slow questions fast, and come back later. Most strong candidates lose marks not because the paper is impossible, but because they let one awkward question consume six or seven minutes.

In Section 1, prioritise efficient setup: translate the problem, choose the cleanest method, and avoid over-algebra. In Section 2, read with forensic care. Small wording shifts matter, and many traps are logical rather than computational. When reviewing, check assumptions, domains, signs and whether a statement is always, sometimes or never true.

Because there is no negative marking, you should aim to answer every question. The best order is: solve fully if quick, eliminate where possible, then make the most evidence-based guess you can. Blind guessing is a last resort; educated guessing after eliminating one or two options is often worth it.

This matters more than many students realise. UAT-UK says TMUA is based on mathematics typically covered within Higher Level GCSE mathematics courses or AS level mathematics. That still does not guarantee your school will have taught every topic by the time you sit it. Download the specification early, compare it with your school scheme of work, identify gaps, and self-study them before you start heavy timed practice.

TLMaths is excellent for clean A-level and Further Maths explanations. ExamSolutions is strong for fast topic repair and worked examples. Dr Frost Maths is useful for extra practice and topic drilling. Bicen Maths is helpful for accessible A-level and Further Maths walkthroughs. Use these to fix weak topics, not as a substitute for timed TMUA practice.

Use the official TMUA Preparation Materials archive first. UAT-UK says historic papers remain useful because the test is now computer-based but the content specification and question style are unchanged. UAT-UK also provides the TMUA specification, specimen and practice tests, Notes on Mathematics, and Notes on Logic and Proof. Official papers run out quickly, so use them carefully under timed conditions and review them properly.

Oxbridge Mentors also has its own TMUA-style question bank with extra practice beyond the official papers, available to students working with our tutors. That matters because official papers are finite and high scorers usually need more volume than the archive provides. Students can enquire via our contact page.

For print resources, a strong A-level or Further Maths revision text can help plug content gaps, but books should be secondary to official TMUA materials and timed question practice. The most useful books are usually standard A-level and Further Maths problem-solving texts, not hack the TMUA books.

Download the specification, compare it with your school syllabus, and start filling content gaps. Build fluency in algebra, functions, graphs, trigonometry and proof-style thinking. Keep practice untimed at first.

Move into weekly timed sets. Start separating errors into three buckets: content gaps, method choice, and time-management mistakes. Begin Paper 2-specific work on logic and proof.

Use official papers under full exam timing. Focus on question selection, pacing and review discipline. At this stage, improvement usually comes more from error analysis than from random new practice.

Do light timed work, review recurring traps, and protect sleep. Make sure your booking, ID, route and test-centre logistics are sorted.

Ignoring Paper 2 logic and proof; treating TMUA like a normal school maths test; spending too long on one question; leaving blanks despite no negative marking; weak algebra under pressure; and doing official papers too early without proper review.

Our tutors help students diagnose weak topics, build a realistic revision plan, sharpen pacing, and learn how to review mistakes properly rather than just doing more questions. We also support students with extra TMUA-style practice beyond the official archive. See our tutors for subject specialists and contact us for TMUA support.