TMUA vs MAT vs STEP vs ESAT: Key Differences

If you are applying for maths, computer science, economics or engineering at a top UK university, you have probably met an alphabet soup of admissions tests: TMUA, MAT, STEP, ESAT. They are not interchangeable, and the biggest change in years is that Oxford has just retired the MAT and switched to the TMUA. This guide untangles which test you actually need to sit, how the styles differ, and where the TMUA sits on the difficulty scale.

The headline change: Oxford has switched from the MAT to the TMUA

For nearly two decades, Oxford screened its Mathematics and Computer Science applicants with the MAT (the Mathematics Admissions Test), which ran from 2007 to 2025. That test is now discontinued. For 2027 entry, Oxford has adopted the TMUA in its place for Maths, Computer Science and the joint honours degrees.

The practical message is blunt: if you are applying to Oxford for one of these courses, do not prepare for the MAT. It no longer exists as an admissions route. Your test is the TMUA, sat in October, and it has a different format and a different feel from the MAT. We cover the Oxford-specific details in TMUA for Oxford.

This also means the TMUA is now the single most important maths reasoning test for maths and CS across both Oxford and Cambridge. That is the simplest way to remember the new landscape.

What each test is, in one line

Before the detailed comparison, here is the shape of each test:

• TMUA (Test of Mathematics for University Admission): two multiple-choice papers, calculator-free, content roughly at AS-to-A-level but applied indirectly. Used for maths, computer science and economics at the universities below.
• MAT (Mathematics Admissions Test): Oxford's former test, discontinued after 2025 and replaced by the TMUA. You should no longer prepare for it.
• STEP (Sixth Term Examination Paper): a hard written exam of long-answer questions and full proofs, sat in the summer after A-levels, used inside some Cambridge and Warwick conditional offers.
• ESAT (Engineering and Science Admissions Test): a multiple-choice test for science and engineering applicants to Cambridge and Imperial, which replaced the older NSAA and ENGAA tests.

The comparison table

A handful of universities such as Bath, Cardiff, Sheffield, Southampton and Lancaster may reference these tests in various ways, but for the required and most competitive routes the four tests above are the ones that matter.

TMUA in detail: speed and reasoning, not a marathon

The TMUA is run by UAT-UK, a joint venture between the University of Cambridge and Imperial College London, and is delivered at Pearson VUE test centres (it moved to this provider in 2024, having previously been run by Cambridge Assessment through 2023).

It has two papers, 75 minutes each, 20 multiple-choice questions each, so 40 questions in total. There is no calculator on either paper.

• Paper 1, Applications of Mathematical Knowledge, is essentially pure maths. The content sits roughly at AS-level, but the questions apply it indirectly: you have to spot the right method quickly rather than follow a signposted procedure.
• Paper 2, Mathematical Reasoning, is the part most A-level students have never formally met. It tests logic, proof, the difference between necessary and sufficient conditions, finding counterexamples, and spotting the flaw in a faulty proof. These skills are barely touched at A-level, which is exactly why deliberate practice pays off. Our Paper 1 vs Paper 2 guide breaks down both halves.

Each paper is reported on a scale from 1.0 to 9.0 in 0.1 steps. You earn one mark for a correct answer and zero for a wrong or blank one: there is no negative marking, so you should attempt every question. As a rough guide, around 5.0 is an average score, 6.5 and above is upper tier, and 7.5 and above is exceptional.

The headline on difficulty: the TMUA is harder and more indirect than a standard A-level paper, and the reasoning demands genuinely catch people out, but it is not the marathon written-proof challenge that STEP is. It rewards fluency and clean thinking under time pressure rather than the ability to sustain a single proof over a page.

Try a real TMUA question

Descriptions of difficulty only go so far; the best way to judge how the TMUA compares is to attempt one yourself. Here is a genuine question from a past paper, so you can gauge the style and pressure first-hand. Have a go before you reveal the solution:

MAT: a test you should no longer prepare for

The MAT was Oxford's own Mathematics Admissions Test, used to screen applicants for Maths and Computer Science from 2007 right through to 2025. It mixed multiple-choice questions with longer written answers and had a distinctive style of its own.

It is now discontinued. Oxford has replaced it with the TMUA for 2027 entry. The only reason to know about the MAT today is to avoid wasting time on it: old MAT papers are not the right preparation for the test you will actually sit. If a resource is pointing you at MAT practice for an Oxford maths application, it is out of date.

STEP: the long written-proof test

STEP (the Sixth Term Examination Paper) is a different animal entirely. Rather than a pre-application screening test, it usually appears inside a conditional offer: some Cambridge and Warwick maths offers require you to achieve a given STEP grade, which you sit in the summer after your A-level exams.

STEP is written, not multiple-choice. Questions are long, open-ended, and demand full worked solutions and rigorous proofs. The content starts at A-level and reaches well beyond it, and individual questions can take a long time to crack. Of the tests here, STEP asks for the deepest sustained problem-solving.

The contrast with the TMUA is the clearest way to understand both. The TMUA asks: can you reason correctly and quickly across many short multiple-choice problems before you apply? STEP asks: once you already hold an offer, can you construct complete, watertight proofs to long problems under exam conditions? Many Cambridge maths applicants meet both tests at different stages: the TMUA in October as part of the application, then STEP the following summer as part of the offer.

ESAT: the multiple-choice science and engineering test

ESAT (the Engineering and Science Admissions Test) is for applicants to science and engineering courses at Cambridge and Imperial. It replaced two earlier tests, the NSAA (Natural Sciences Admissions Assessment) and the ENGAA (Engineering Admissions Assessment).

Like the TMUA, ESAT is multiple-choice and sat at a test centre. The difference is scope: ESAT covers maths alongside science subjects such as physics, chemistry or biology, depending on your course, whereas the TMUA is purely a maths and mathematical-reasoning test. If your course is engineering or natural sciences rather than maths, CS or economics, ESAT is more likely to be your test, not the TMUA.

Which test do you actually sit?

The quickest way to find your test is by course and university:

• Maths or Computer Science at Oxford or Cambridge: the TMUA. (Cambridge maths offers may also include STEP later, as a condition.)
• Maths, Computing or Economics, Finance and Data Science at Imperial: the TMUA.
• Economics at LSE, or Economics at UCL: the TMUA. Note that most other UCL courses use a different test called TARA, not the TMUA.
• Computer Science at Warwick: the TMUA is compulsory. For Maths, Economics, Statistics and Data Science at Warwick it is optional, and a strong score can support a reduced offer. Some Warwick maths offers separately involve STEP.
• Maths at Durham: the TMUA is recommended.
• Science or engineering at Cambridge or Imperial: ESAT, not the TMUA.

Always confirm the requirement on your specific course's admissions page, because universities adjust these year to year. But the overall pattern is now simple: for maths and computer science at Oxford and Cambridge, the relevant admissions test is the TMUA.

Costs and official practice material

For completeness, the TMUA costs £78 for candidates in the UK and the Republic of Ireland, and £133 internationally. UAT-UK publishes a specimen paper plus every past paper from 2016 to 2023 for free, which is the gold-standard practice resource for the test.

Working through those real papers under timed conditions is the single most effective thing you can do, especially for the Paper 2 reasoning style that has no A-level equivalent. The catch is that the official PDFs give you the answer key but rarely a full method, so when a question beats you, you are left guessing why.

Where to go from here

Now that you know your test is the TMUA, the plan is straightforward: build genuine fluency with the calculator-free maths, then drill the specific question styles until the traps stop working on you. That is exactly what CrackTMUA is built for. It is a free interactive bank of every official TMUA question with in-depth worked solutions that name the trap and the fastest method, filterable by paper, topic and difficulty, with spaced repetition to lock in your weak areas. Premium unlocks everything for £37 one-time, with 12 months of access.

Start practising free, read TMUA for Oxford to see how the switch affects your application, or compare the two papers in detail with our Paper 1 vs Paper 2 guide. The MAT is gone; the TMUA is your test, and the earlier you start on real questions, the further ahead you will be.

Frequently asked questions