TMUA vs ESAT: what is the difference, and which do you need?
The TMUA is a mathematics-only test of two 75-minute papers, used for mathematics, computer science and economics courses. The ESAT is modular: Mathematics 1 plus, for most candidates, two further 40-minute modules in science or mathematics, used for engineering and science courses. Your course decides which you sit, not you.
By Archie Dyer, founder of Cognivia Tutoring · Last checked 11 October 2026
TMUA: mathematics onlyTwo papers, 75 minutes and 20 questions each.
ESAT: modules40 minutes and 27 questions per module. Most candidates sit three.
No calculator in eitherBoth are multiple choice and taken on a computer at a test centre.
Scored 1 to 9One overall score for the TMUA; one score per ESAT module.
£78 or £133 per test£78 in the UK and Republic of Ireland, £133 elsewhere.
What is the difference between the TMUA and the ESAT?
The TMUA tests mathematics alone in two long papers, while the ESAT tests mathematics and science in short separate modules. Both are run by UAT-UK, both are multiple choice, and neither allows a calculator. The table sets the two side by side for 2027 entry.
TMUA and ESAT compared, for 2027 entry
Feature
TMUA
ESAT
Full name
Test of Mathematics for University Admission
Engineering and Science Admissions Test
Subjects
Mathematics only
Mathematics 1, Mathematics 2, Physics, Chemistry and Biology modules
Structure
Two papers: Paper 1, Applications of Mathematical Knowledge, and Paper 2, Mathematical Reasoning
Everyone takes Mathematics 1; most candidates take two further modules, and some courses specify which
Length of each part
75 minutes per paper
40 minutes per module
Questions
20 multiple-choice questions per paper
27 multiple-choice questions per module
Total time
2 hours 30 minutes
120 minutes for most candidates
Calculator
Not allowed
Not allowed
Scoring
One overall score from 1 to 9, to one decimal place
A separate score from 1 to 9, to one decimal place, for each module
Wrong answers
No marks deducted
No marks deducted
Pass mark
None
None
Fee per test
£78 in the UK and Republic of Ireland, £133 elsewhere
£78 in the UK and Republic of Ireland, £133 elsewhere
Sittings for 2027 entry
12–16 October 2026 and 4–8 January 2027
12–16 October 2026 and 4–8 January 2027
Universities using it
Seven: Cambridge, Durham, Imperial College London, LSE, Oxford, UCL and Warwick
Four: Cambridge, Imperial College London, Oxford and UCL
The single most important structural difference is breadth against depth. An ESAT candidate switches subject every 40 minutes and gets a score for each module. A TMUA candidate stays in mathematics for two and a half hours, and Paper 2 is given over to what UAT-UK calls “mathematical reasoning, and simple ideas from elementary logic”.
Format, timings, scoring, calculator rules and fees taken from UAT-UK’s official pages, About the TMUA and About the ESAT; sitting dates from its Key Dates page. Checked on 11 October 2026.
Do I need the TMUA or the ESAT?
You need whichever test your course names: broadly, the TMUA for mathematics, computer science and economics degrees, and the ESAT for engineering, physics and other science degrees. The summary below is taken from UAT-UK’s course list for 2027 entry. The test is compulsory unless marked recommended.
Which universities and courses use the TMUA and the ESAT for 2027 entry
University
TMUA courses
ESAT courses
Cambridge
Computer Science, Economics, Mathematics.
Engineering, Natural Sciences, Chemical Engineering and Biotechnology, Veterinary Medicine.
Oxford
Computer Science, Computer Science and Philosophy, Mathematics and Computer Science, Mathematics and Philosophy, Mathematics / Mathematics and Statistics.
Engineering Science and the named engineering courses, Physics, Physics and Philosophy, Biomedical Sciences.
Imperial College London
The Computing degrees, the Mathematics degrees, and Economics, Finance and Data Science.
Aeronautical, Chemical, Civil, Design, Electrical and Electronic, Electronic and Information, and Mechanical Engineering; the Physics degrees; Biochemistry, Biological Sciences, Biotechnology, Microbiology, and Ecology and Environmental Biology.
UCL
BSc Economics and BSc Economics with Study Abroad.
BEng and MEng Electronic and Electrical Engineering.
LSE
Compulsory for BSc Economics and BSc Econometrics and Mathematical Economics. Recommended for its other listed courses.
None listed.
Warwick
Compulsory for Computer Science, Computer Science with Business Studies, Discrete Mathematics and Mathematics, except for applicants eligible for a contextual offer. Recommended for a further list including Data Science, Economics, Mathematics and Statistics, and MORSE.
None listed.
Durham
Recommended for Mathematics, and Mathematics and Statistics.
None listed.
Subject names alone can mislead. UAT-UK runs a third test, the TARA, and the same list shows UCL using it for Computer Science and Mechanical Engineering, and Oxford using it for courses such as Philosophy, Politics and Economics. For ESAT courses the list also names the modules: for example, Mathematics 1, Mathematics 2 and Physics for Cambridge Engineering. The ESAT page sets the module combinations out in full.
Check your own course page before you book. UAT-UK states: “Candidates must check the relevant course pages on the website of the institution(s) to which they are applying before booking a test.” Requirements change between cycles, and this table is a summary, not a substitute.
Taken from the UAT-UK Course List 2027 Entry (last updated April 2026), published on the UAT-UK site, and cross-checked for Cambridge against its own admissions tests page. Checked on 11 October 2026.
Do some applicants need both the TMUA and the ESAT?
Yes, if their UCAS choices include a course that names the TMUA and another that names the ESAT. An applicant choosing Physics at Imperial and Mathematics at Warwick, for instance, has one course on each list.
UAT-UK’s candidate handbook covers this case: a candidate who needs two tests for two different courses can sit both in the same sitting, or one in October and one in January, subject to the rules for Cambridge and Oxford applicants. Each test can be sat only once in an admissions cycle, and the fee is charged per test.
Source: the UAT-UK Candidate Handbook 2027 Entry and FAQs, on the UAT-UK site. Checked on 11 October 2026.
How does preparing for the TMUA differ from preparing for the ESAT?
The pace and the breadth differ, so the practice does too. Dividing the official timings by the official question counts gives roughly 90 seconds a question on an ESAT module, and 3 minutes 45 seconds a question on a TMUA paper.
ESAT: short, fast modules across two or three subjects. Module choice is fixed at booking: UAT-UK states that “module selection cannot be changed or added after booking”.
TMUA: fewer, longer questions in one subject, with a whole paper on reasoning and logic rather than on applying methods.
Both: no calculator, no marks for working, and no penalty for a wrong answer, so no question should be left blank.
UAT-UK publishes a specification, practice materials and practice tests for each test free of charge, and those are the place to start. It also says it does not endorse any commercial tutoring service. Cognivia Tutoring is independent, and is not affiliated with or endorsed by UAT-UK, Pearson or any university.
How Cognivia can help
Archie Dyer, a second-year Theoretical Physics student at UCL and the only tutor at Cognivia, teaches both tests one to one: the TMUA, and the ESAT modules Mathematics 1, Mathematics 2, Physics and Chemistry. He does not teach the Biology module. Lessons are one hour and cost £45 online on Google Meet or £55 in person around Marylebone, London. A 5-pack of five lessons saves £15, at £210 online or £260 in person, and a 30-minute online trial is free with no card needed. None of this is a promise about a score.
Timings and rules from UAT-UK’s TMUA and ESAT pages; preparation materials and the statement on tutoring from its Candidate Handbook 2027 Entry. Checked on 11 October 2026.
FAQ
TMUA vs ESAT questions, answered
The TMUA is mathematics only: two papers of 75 minutes and 20 multiple-choice questions each. The ESAT is modular: every candidate sits Mathematics 1, and most sit two further 40-minute modules of 27 questions chosen from Mathematics 2, Physics, Chemistry and Biology. Neither test allows a calculator.
In UAT-UK’s course list for 2027 entry, the TMUA appears for mathematics, computer science and economics courses at Cambridge, Durham, Imperial, LSE, Oxford, UCL and Warwick. The ESAT appears for engineering, physics and other science courses at Cambridge, Imperial, Oxford and UCL. Always confirm on the university’s own course page.
Yes. UAT-UK’s candidate handbook says a candidate who needs two tests for two different courses can sit both in the same sitting, or one in October and one in January, subject to the rules for Cambridge and Oxford applicants. Each test can be sat only once in an admissions cycle.
UAT-UK states that each test costs £78 for candidates in the UK and Republic of Ireland and £133 for candidates elsewhere. It runs a bursary scheme for UK candidates in financial need, which must be applied for before booking.
No. UAT-UK states that calculators are not permitted in either test.
Both are reported on a scale from 1 to 9, to one decimal place. The TMUA gives one overall score; the ESAT gives a separate score for each module. UAT-UK says there is no pass or fail for either test, and no marks are deducted for wrong answers.
Yes. Archie Dyer teaches the TMUA and the ESAT modules Mathematics 1, Mathematics 2, Physics and Chemistry, but not Biology. Lessons are one hour and one to one, at £45 online or £55 in person around Marylebone, London, with a free 30-minute online trial.
Where to go next
Once you know which test your course names, the pages below cover each one in more detail.
