TMUA Guide: Format, Scoring and Which Courses Require It

The Test of Mathematics for University Admission (TMUA) is run by UAT-UK, a collaboration between Imperial College London and the University of Cambridge, with sittings held at Pearson test centres, and it is used by seven UK universities to help assess applicants to mathematics, economics and computer science degrees. The test sits alongside A-level or equivalent grades, and its official website publishes the current format and practice material for applicants preparing to sit it.

Requirements vary by course as well as by university, and Oxford's Mathematical Institute has replaced its Mathematics Admissions Test (MAT) with the TMUA for Mathematics, Computer Science and joint honours applicants. Cambridge asks for the TMUA from applicants to Mathematics, Computer Science and Economics, while Imperial College London, the London School of Economics, Warwick, Durham and UCL also draw on it for some mathematics, economics or computer science courses, so checking the exact course page at each university remains essential.

What is the TMUA and which organisation runs it?

The TMUA is a subject-specific admissions test assessing mathematical thinking beyond standard school qualifications, used by universities to help differentiate between strong applicants to mathematics, economics and computer science courses. UAT-UK, described on its own site as a collaboration between Imperial College London and the University of Cambridge, manages the test alongside the Engineering and Science Admissions Test (ESAT) and the Test of Academic Reasoning for Admissions (TARA). All three are delivered through Pearson VUE's network of test centres, outside the school system.

• TMUA: mathematics, economics and computer science courses
• ESAT: engineering, physical sciences and related courses
• TARA: a non-subject-specific test of undergraduate-level reasoning

Which universities and courses require or recommend the TMUA?

UAT-UK's own TMUA page lists seven universities drawing on the test for admission to mathematics, economics or computer science courses, though whether it is compulsory or simply considered differs by course and can change between admissions cycles, so each university's own course page settles the point. Cambridge requires it for Mathematics, Computer Science and Economics applicants, used alongside the rest of the application to help identify candidates unlikely to be competitive, and Oxford requires it for Mathematics, Computer Science, Mathematics & Computer Science and Computer Science & Philosophy applicants, having replaced the MAT.

• Cambridge: mandatory for Mathematics, Computer Science and Economics
• Oxford: mandatory from the current admissions round for Mathematics, Computer Science, Mathematics & Computer Science and Computer Science & Philosophy
• Imperial: mandatory for the Department of Computing, the Department of Mathematics and BSc Economics, Finance and Data Science
• LSE: mandatory for BSc Economics and BSc Econometrics and Mathematical Economics; recommended for several other mathematics, data science and actuarial science courses
• Warwick: mandatory for Computer Science and Discrete Mathematics; Mathematics applicants typically choose between the TMUA and STEP; optional for some Economics and statistics-related courses
• Durham: strongly encouraged, as an alternative to STEP, for Mathematics and Mathematics and Statistics applicants
• UCL: mandatory for Economics BSc (Econ) and Economics with a Year Abroad BSc (Econ); UCL's Mathematics degrees use STEP or the AEA instead

What do the two TMUA papers cover?

The TMUA lasts two hours thirty minutes in total, split into two multiple-choice papers of seventy-five minutes each, sat back to back with no calculator or dictionary permitted throughout. Each paper carries 20 questions.

Paper 1, Applications of Mathematical Knowledge, tests how far a candidate can apply GCSE and AS-level mathematics to unfamiliar problems, while Paper 2, Mathematical Reasoning, tests logical reasoning and the structure of mathematical argument, built on that same content base. Both papers are marked identically, a point for each correct answer and none deducted for a wrong one.

• Paper 1, Applications of Mathematical Knowledge: 75 minutes, 20 questions
• Paper 2, Mathematical Reasoning: 75 minutes, 20 questions
• No calculator or dictionary permitted in either paper

How are TMUA scores reported and used?

Each TMUA paper is scored separately on a scale running from 1.0 to 9.0, reported to one decimal place, with a mark awarded for every correct answer and none deducted for an incorrect one. There is no pass mark.

Cambridge's own admissions guidance states plainly that there is no pass or fail for the TMUA, and universities weigh the score alongside predicted or achieved grades, the personal statement and, where relevant, an interview. Results are sent automatically to the UCAS-listed universities requiring the test once released, and UAT-UK confirms that a score is passed only to a course that lists the TMUA as an entrance requirement.

A few universities publish more specific score guidance on their own course pages, treating particular scores as evidence for a reduced offer, distinct from a pass mark in themselves.

• Warwick sets out its own score guidance for Mathematics applicants on its course pages, so applicants should check there for the current position.
• Durham: a score of 5.0 or above makes a Mathematics applicant eligible for a reduced offer, with lower scores down to a yearly threshold still counted as positive evidence

When can the TMUA be sat, and how does it relate to the UCAS deadline?

UAT-UK runs two TMUA sittings within each admissions cycle, one earlier in the autumn and one in the new year, timed around the two UCAS deadlines that TMUA universities use. Applicants to Oxford or Cambridge must sit the earlier sitting, since Cambridge's own guidance describes Mathematics, Computer Science and Economics applicants taking the TMUA as part of the application submitted to the October UCAS deadline; applicants to the other TMUA universities can generally choose between the two sittings, though UAT-UK's FAQ makes clear that a candidate must sit within the cycle in which they apply, so a result cannot be carried forward to a later year.

Registration runs through an online UAT-UK account, created before booking a place at a Pearson VUE test centre, with each candidate permitted to register once per sitting. UAT-UK advises registering as early as possible once booking opens, since test centre places are limited, and recommends confirming directly with the relevant university's own admissions pages whether the TMUA is required before committing to a sitting.

• Earlier sitting: aligned with the October UCAS deadline used by Oxford and Cambridge
• Later sitting: aligned with the January UCAS deadline used by the other TMUA universities

How does the TMUA relate to the MAT and STEP?

Oxford's Mathematical Institute confirms that the TMUA has replaced the Mathematics Admissions Test (MAT) for its Mathematics courses; the TMUA is a different test from the MAT, with its own format and specification published on the TMUA's official website. STEP, the Sixth Term Examination Paper, sits at a different stage of a Cambridge application: Mathematics applicants take the TMUA in the mid-October sitting, used alongside the rest of the application to help shape interview shortlisting, and may then face a conditional offer requiring STEP papers sat the following summer. Applicants to Warwick and Durham should check each university's Mathematics course page for how it treats TMUA and STEP results.

• Oxford: the TMUA has replaced the Mathematics Admissions Test (MAT), which it no longer uses for admission to its mathematics-related courses
• Warwick and Durham: a TMUA score of 5.0 is treated as equivalent to grade 2 in a STEP paper for a Mathematics offer

How should students prepare, and what mistakes are worth avoiding?

UAT-UK's own preparation page hosts an archive of past TMUA papers and two specimen papers, each with worked answers and an answer key, noting that although the test is now sat on screen, the content specification and question style are unchanged, so the archive remains directly useful for practice. Working through full papers under timed conditions, seventy-five minutes each, builds the pace the test demands, since marks are awarded for correct answers alone, with working shown earning no credit. No topic beyond GCSE and AS level is tested.

• Treating Paper 2 as easier because it reads as logic, not mathematics, though it draws on the same content base as Paper 1
• Leaving questions unanswered, despite there being no penalty for an incorrect answer
• Preparing only from general GCSE revision material without practising UAT-UK's own past and specimen papers
• Assuming a university's presence on UAT-UK's TMUA page means every course there requires it, without checking the specific course page

University admissions support from Taylor Tuition

Applicants who work with us on university admissions usually start in the spring or summer before they apply, which leaves time for admissions-test practice, personal statement drafts and mock interviews to build on each other. Our tutors, who include graduates of Russell Group universities including Oxford and Cambridge alongside experienced exam-board examiners, plan the work around the course's actual requirements and the deadlines that apply.

Sessions run online for families across the UK and internationally, and in person in central London. Fees start from £50 per 50-minute session and depend on tutor level and subject, with no registration fee and a free initial consultation. Every tutor who works with children holds an enhanced DBS check, families receive progress reports after sessions, and we reply to enquiries within one working day with tutor recommendations.

Read more about our TMUA tutors, or send an enquiry and we will come back with tutor recommendations.