MAT, TMUA, ESAT & PAT Explained: Maths, Physics & Engineering Admissions Tests

The most competitive STEM courses in the country — Maths at Cambridge, Engineering Science at Oxford, Physics at Imperial — receive many applications from students who hold or are predicted straight A and A* grades. A grades are an entry requirement, not a differentiator. Universities need another data point to shortlist for interview, and admissions tests provide it.

Where A-level exams test whether a student has learned the curriculum reliably, admissions tests probe something different: mathematical reasoning, problem-solving under pressure, and the ability to apply knowledge in unfamiliar ways. A student who has memorised the A-level content thoroughly but cannot reason flexibly will find the TMUA unexpectedly hard. A student who thinks mathematically but has a few syllabus gaps can still score well if their reasoning is sharp.

For courses at Oxford and Cambridge, test scores are used alongside the personal statement and reference to shortlist roughly three candidates per available interview place. At Imperial, scores inform offers directly. This is why preparation matters — and why starting early matters more than most families realise.

In January 2026, Oxford University announced it was ending all eight of its own admissions tests. The Mathematics Admissions Test (MAT), which had been running since 2007, and the Physics Aptitude Test (PAT), which had been used since approximately 2001, were both discontinued after the 2025 sitting. So were the TSA, BMSAT, CAT, MLAT, AHCAAT and PhilAT.

From the 2026/27 cycle — meaning students applying in autumn 2026 for entry in October 2027 — Oxford now uses the same three UAT-UK tests as Cambridge and Imperial:

• TMUA — for Maths, Computer Science and joint courses at Oxford
• ESAT — for Engineering Science, Physics and Biomedical Sciences at Oxford
• TARA— for Economics & Management, PPE, Psychology and similar courses (not covered in depth here — see the official Oxford admissions tests page)

Why does this matter if your family has been researching Oxford applications for a year or two? Because a great deal of preparation advice online — and some school guidance — still refers to the MAT and PAT as though they are live tests. They are not. Any student who prepared for the 2026/27 cycle using only MAT-specific resources and expecting the old format would have been heading for a shock.

The good news is that the content overlap between the old tests and the new ones is substantial. MAT past papers remain among the best preparation resources for TMUA; PAT past papers are explicitly recommended by Oxford's Physics department for ESAT preparation. The format has changed; the underlying maths and physics has not.

The table below covers every test relevant to maths, physics and engineering applicants for 2027 entry. Verify all dates against the official sources listed at the foot of this article — dates shift each cycle.

The TMUA is the test that replaced the MAT and is now the primary admissions test for maths and computer science courses at Oxford and Cambridge. It is a computer-based test delivered at a Pearson VUE test centre and consists of two papers of 20 multiple-choice questions each, 75 minutes per paper, with no calculator and no formula booklet. Paper 1 tests application of mathematical knowledge; Paper 2 tests mathematical reasoning and proof. Total sitting time is two hours and thirty minutes.

Who requires TMUA for 2027 entry?

Seven universities use TMUA for specific courses in the 2026/27 cycle. The confirmed list includes:

• University of Oxford— Mathematics, Mathematics & Statistics, Mathematics & Computer Science, Mathematics & Philosophy, Computer Science, Computer Science & Philosophy. October sitting only. (New from the 2026 cycle; replacing the MAT.)
• University of Cambridge — Mathematics, Computer Science, Economics. October sitting only for standard applicants. Cambridge Maths applicants also sit STEP as an offer condition after interview (see Section 6).
• Imperial College London— Mathematics (all pathways), Mathematics & Computer Science, Computing/Computer Science (all pathways), BSc Economics Finance & Data Science. October or January sitting accepted.
• London School of Economics— BSc Economics and BSc Econometrics & Mathematical Economics (mandatory); recommended for approximately eight additional quantitative degrees.
• University of Warwick — Computer Science and Data Science (mandatory); Mathematics, Statistics and MORSE (TMUA or STEP accepted as alternative).
• Durham University — Maths applicants strongly encouraged; a score of 5.0 or above may qualify for reduced grade requirements.
• University College London — Economics BSc and Economics with a Year Abroad BSc only. (UCL Maths and Computer Science use different tests — check the official course pages.)

Other universities — including Bath, Southampton, Sheffield and Lancaster — appeared on some 2025/26 participation lists but their status for the 2026/27 cycle could not be confirmed from official sources. If your child is applying to any of these, check the official course page directly before assuming TMUA is or is not required.

Scoring and what the numbers mean

TMUA scores are reported on a scale of 1.0 to 9.0, to one decimal place. There is no pass or fail, and no penalty for wrong answers — attempt every question. The UAT-UK scoring system is designed so that the October sitting median is anchored at 4.5 and the 90th percentile at 7.0 — meaning approximately 10% of October candidates score above 7.0. Third-party analysis combining October and January sittings produces a blended figure closer to 3.87, but since Oxford, Cambridge and Imperial require the October sitting only, the more relevant benchmark is the October-only scale where the median is 4.5 and the top quarter score approximately 5.2 or above. A score in the region of 6.5 or above is widely regarded as competitive for Oxbridge shortlisting, though no official threshold is published by either university. Treat all such figures as indicative only.

Key TMUA dates — October 2026 sitting

• 1 Jun 2026UAT-UK account registration opens
• 20 Jul 2026Slot booking opens at Pearson VUE
• 14 Sep 2026Access arrangements deadline
• 21 Sep 2026Bursary application deadline (October sitting)
• 28 Sep 2026Final booking deadline — 6pm UK time. No exceptions; this is the hardest date in the calendar.
• 12–16 Oct 2026Test window at Pearson VUE centres

The ESAT replaced Cambridge's Natural Sciences Admissions Assessment (NSAA) and Engineering Admissions Assessment (ENGAA) when it launched in autumn 2024, and from 2026 it also replaced Oxford's PAT. It is now the standard admissions test for engineering, physics and natural sciences courses at Oxford, Cambridge and Imperial.

The ESAT is structured around five modules: Mathematics 1 (compulsory for all candidates), Mathematics 2, Physics, Chemistry and Biology. Most candidates sit three modules — Maths 1 plus two subject modules that depend on their course. Each module contains 27 multiple-choice questions in 40 minutes, with no calculator. Three modules means a total sitting time of two hours.

Which modules for which course?

The most common combinations for engineering and physics applicants are Maths 1, Maths 2 and Physics. Here are the key course-module pairings:

• Oxford Engineering Science, Cambridge Engineering, Imperial Aeronautics / Mechanical / Electrical & Electronic / Physics: Maths 1, Maths 2, Physics
• Oxford Physics / Physics & Philosophy: Maths 1, Maths 2, Physics
• Cambridge Natural Sciences (physical): Maths 1 plus two from Physics / Chemistry / Maths 2
• Imperial Chemical Engineering: Maths 1, Maths 2, Chemistry
• Imperial Life Sciences: Maths 1, Chemistry, Biology

ESAT scores are reported on the same 1–9 scale as TMUA, one decimal place per module. No pass/fail is published. Third-party data indicates that successful Cambridge and Imperial applicants typically score in the 6.5–7.0 range or above, but Imperial emphasises that its own published score dashboard (showing 2025 entry data by department, anonymised) should not be taken as indicative of future requirements. There is no opportunity to resit within the same cycle — only your first ESAT score is considered.

ESAT shares the same key deadlines as TMUA: slot booking opens 20 July 2026, the booking deadline is 28 September 2026 at 6pm, and the test window is 12–16 October 2026. Both tests cost £78 for UK candidates — so a student sitting both TMUA and ESAT pays £156 in total.

Students considering engineering courses should note that the Maths 2 module in ESAT has significant overlap with A-Level Further Mathematics content — particularly in mechanics and calculus — making Further Maths a valuable asset even though it is not required. Our guide to A-Level Maths vs Further Maths covers this decision in detail.

STEP is fundamentally different from TMUA and ESAT, and it is important to understand the distinction before a student plans their year. TMUA and ESAT are pre-application tests sat in October before the UCAS deadline. STEP is an offer condition sat in June, after Cambridge (or another university) has already made a conditional offer. A student who has received a Cambridge Maths offer will sit both: TMUA in October 2026, then STEP the following June 2027.

STEP papers are administered by OCR and consist of long-form written problem-solving — not multiple choice. Each paper contains twelve questions (eight pure maths, two mechanics, two statistics). Candidates answer any six, each marked out of 20, giving a maximum of 120 per paper. Papers are three hours long. The grading scale runs S (Outstanding), 1 (Very good), 2 (Good), 3 (Satisfactory), U (Unclassified).

• STEP 2 is based on A-level Mathematics and the Pure content of A-level Further Mathematics (both AS and A2 year material). Cambridge typically requires grade 1 in both STEP 2 and STEP 3.
• STEP 3 is based on the full A-level Further Mathematics content. Sitting STEP 3 without Further Maths is extremely demanding and not recommended.

Warwick Maths accepts either TMUA or STEP — a grade 2 in either STEP paper may substitute for TMUA for applicants who did not sit it. UCL Maths may offer a reduced grade requirement to students who achieve STEP grade 2, though this should be verified on the official UCL course page for the current cycle. Imperial may also accept STEP in exceptional circumstances — again, check the official page.

Registration for STEP goes through the school or college, not directly from students. Schools must be registered OCR test centres. The exact UK sitting dates for 2027 (approximately 4 June for STEP 2 and 10 June for STEP 3) and OCR's registration fees should be confirmed at ocr.org.uk — these figures were not confirmed from official UK sources in time for this guide.

Every year, students miss their admissions test not because they were unprepared but because they missed the booking deadline. Unlike A-level exam entries, which the school handles, students must register for TMUA and ESAT themselves, independently, via the UAT-UK website. The university cannot do it for them. The school cannot do it for them. If a student misses 28 September 2026 at 6pm, they cannot sit the October test.

The situation is made worse by an ordering trap. If a student needs a bursary (fee waiver), they must apply for the bursary first and receive approval before booking the test slot. The bursary deadline is 21 September — a full week before the booking deadline — and approval can take up to five working days. The sequence must be: create account, apply for bursary (if eligible), wait for approval, then book. A student who tries to book before applying for a bursary will be charged the full £78 fee and cannot retrospectively claim a waiver.

Similarly for access arrangements: apply first via UAT-UK, receive confirmation, then book. The access arrangements deadline is 14 September, even earlier than the bursary deadline. School exam-centre adjustments do not transfer automatically.

A common question I hear from families is: “What score does my child need?” The honest answer is that no university publishes an official threshold, and treating third-party estimates as official targets is a mistake.

At Oxford, TMUA scores are used alongside all other application details to shortlist approximately three candidates per available position for December interviews. No published passing mark exists. At Cambridge, the guidance is explicit: “A high score does not mean your application will be successful. A low score does not mean your application will be unsuccessful.” At Imperial, an interactive anonymous score dashboard is available showing 2025-entry score distributions by department — but Imperial cautions that it should not be taken as indicative of future requirements.

What we can say with confidence is this: at the most competitive universities, a score in the lower half of the scale (below 5 for TMUA, below 5 per module for ESAT) is unlikely to produce a strong application from an otherwise typical candidate pool. A score comfortably above 6 is more competitive. But the goal is always to prepare as thoroughly as possible, not to aim for a number someone on a forum has identified as a threshold.

Durham is an exception in publishing specific guidance: a TMUA score of 5.0 or above may qualify for reduced grade requirements. That's a concrete figure, and it is worth noting — but the exact threshold should be confirmed on Durham's official admissions page for the current cycle.

The families I tutor who get the best results from TMUA and ESAT almost always share one thing: they started earlier than they thought they needed to. For a competitive Oxford or Cambridge application, sixteen weeks of focused preparation before the October test is a reasonable target. That means beginning no later than late June — often during the summer between Year 12 and Year 13. Below is the timeline I recommend.

Free resources — where to find them

• UAT-UK official site (esat-tmua.ac.uk): TMUA and ESAT content specifications, specimen papers, past papers (TMUA 2019–2024), timed practice tests via Pearson VUE. All free.
• MAT past papers (2007–2025): Oxford Mathematical Institute website — an archive of 18 years of papers with full solutions. Content overlaps significantly with TMUA Paper 1 and ESAT Maths 2.
• PAT past papers: Oxford Physics Department website — recommended for ESAT Physics module preparation. The 2024–2025 PAT papers are closest in format to the MCQ-based ESAT.
• AMSP — free TMUA preparation course: Available free to students at state-funded schools and colleges in England (amsp.org.uk). Structured, expert-led and comprehensive. There is no reason not to use it.
• ENGAA and NSAA past papers: Cambridge's old tests, useful for ESAT Chemistry and Biology module preparation. Available via Cambridge admissions pages.
• STEP past papers: Available via Cambridge Mathematics and OCR. STEP 1 (discontinued 2020) papers are still freely available for practice. nrich.maths.org also offers excellent free problem-solving resources recommended by Cambridge.

These tests sit in a specific gap that school teaching rarely fills. A-level lessons prepare students for A-level exams; they do not, in general, build the kind of flexible mathematical reasoning that TMUA Paper 2 and ESAT Maths 2 require. The content is nominally “A-level maths” but the questions are applied at a level of abstraction that most candidates have never encountered in a classroom.

In one-to-one sessions, I do three things that school cannot easily do in a group. First, I identify precisely which reasoning patterns a student finds hardest — it is almost never everything; it is usually two or three specific problem types recurring across past papers. Second, I teach them to approach unfamiliar problems by reasoning from first principles rather than by template-matching, because these tests deliberately avoid templates. Third, I build the pacing discipline that multiple-choice tests require — knowing when to spend 90 seconds on a question and when to skip and return.

For A-level Maths and Further Maths support — the foundation for both TMUA and ESAT — I offer weekly one-to-one lessons across Oxford and surrounding areas including Kidlington, Bicester, Abingdon and Witney, and online on request. I am also happy to work through dedicated TMUA or ESAT preparation sessions alongside A-level tuition in the summer and autumn terms of Year 13. A free diagnostic first lesson maps exactly where a student is starting from, so preparation time is spent on what actually matters.

If the decision about whether to take Further Maths alongside A-Level Maths is still unresolved — which it often is at the start of Year 12 for students thinking about engineering or maths degrees — that guide covers the workload reality and the genuine value of Further Maths for university admissions tests in detail.