TMUA 2026/27: everything you need to know

Everything below expands on those rows, and links to a dedicated guide where there is more to say than a pillar page should carry.

The TMUA is an admissions test for mathematics-heavy degree courses: maths itself, computer science, and economics.

It is run by UAT-UK, a not-for-profit owned jointly by Imperial College London and the University of Cambridge, and delivered on screen at Pearson VUE professional test centres.

Its purpose is narrow and worth understanding, because it explains almost everything else about how it behaves.

The TMUA exists to separate candidates who all have top grades. UAT-UK describe it as helping universities differentiate among a large number of strong candidates with similar academic profiles.

That is why there is no pass mark, why the questions get progressively harder, and why UAT-UK warn candidates directly not to expect to score as highly as they do in school exams.

What it does not test is subject knowledge beyond AS-level. There is no syllabus to learn from scratch.

It tests whether you can apply mathematics you already know to problems you have not seen, quickly, and whether you can reason about mathematical arguments rather than just execute them.

Before anything else, three questions settle whether this guide applies to you.

Is your course on the list? The TMUA attaches to named courses at seven universities.

If none of your five UCAS choices is one of them, you do not need it.

Is it compulsory or recommended for that course? Both exist.

Warwick and LSE each have a compulsory set and a longer recommended set, and Durham's use is recommended throughout.

A recommended test is genuinely optional, but a good score is positive evidence and Durham say so explicitly.

Are you sure it is the TMUA and not another UAT-UK test? This is where people lose weeks.

One thing worth being clear-eyed about: the answer can be yes even when you would rather it were not.

The requirement belongs to the course, not to you. One choice among your five is enough to commit you to sitting it, including a course you are holding only as an insurance.

There is no partial opt-out. You either sit the test or you drop that choice.

If your course does require it, the next question is timing, and there the rule is simple. Oxford and Cambridge applicants sit in October, and because you may only sit once, that decides it for every other choice too.

Everyone else chooses freely, and UAT-UK say there is no advantage either way.

This section exists because a surprising amount of TMUA advice online describes a version of the test that no longer runs.

Here's how that breaks down:

Why there are no past papers after 2023

This is the question the archive raises and almost nobody answers, and the answer is a consequence of the 2024 handover rather than a policy decision about generosity.

Before 2024, there was one paper a year. Everybody sat the same questions on the same day, so once the sitting was over the paper was spent.

Releasing it cost nothing.

That is no longer how the test works.

Today several versions run across a multi-day window, and candidates do not all see the same questions. There is no single "2026 paper" to publish.

There is also a reason the questions cannot simply be retired each year.

UAT-UK's technical report explains that items are anchored at their known difficulty values so that new items can be placed on the same scale, and that placing items on a common scale across years is what makes equivalent forms possible.

Anchoring like that requires reusing questions between cycles. Publishing a paper would destroy the anchors that keep this year's scores comparable with last year's.

UAT-UK have not stated this as their reason, so this is our reading of what their own published method implies. But it does mean the archive is very unlikely to grow, and it explains why UAT-UK instead tell candidates the old papers remain usable.

The practical consequence is a dividing line you should apply to everything you read.

Anything written about the TMUA before late 2024 describes a different test. Not in content, which is unchanged, but in delivery, scoring and how many times a year you can sit it.

That includes forum threads about score targets, blog posts about what to expect on the day, and any conversion table with separate columns for Paper 1 and Paper 2.

It is also why we put a verification date at the top of this page, and why you should look for one on any TMUA page you rely on.

The two papers are sat one after the other in a single session, with no break.

All 40 questions carry equal weight and there is no negative marking, so the specification advises attempting every question.

One claim you will meet repeatedly on other sites is simply wrong, and it is worth correcting.

How each paper examines its content, and what the question styles actually look like, is on the Paper 1 guide and the Paper 2 guide.

This is where most guidance goes wrong, so here is the rule first.

The TMUA is course-led, not institution-led. No university requires it of every applicant.

It attaches to named courses, and the same university will require it for one degree, require a different UAT-UK test for another, and ask for nothing at all for a third.

For 2027 entry, exactly seven institutions use it.

Every course below is taken from the UAT-UK Course List 2027 Entry, last updated April 2026, and checked against the source PDF on 26 August 2026.

Here's how that breaks down:

Three things in that table are worth pulling out, because each one sends people to the wrong test or the wrong preparation.

UCL Computer Science uses TARA, not TMUA. So do UCL Mechanical Engineering and Robotics, while UCL Electronic and Electrical Engineering uses ESAT.

At UCL the TMUA is for the two Economics degrees and nothing else.

Cambridge Mathematics requires TMUA and STEP. The TMUA does not replace STEP there.

Offers typically require grades in two STEP papers as well.

Check the UCAS code, not just the course name. The UAT-UK list gives LSE's BSc Economics as L101, while UCL uses L101 for its year-abroad Economics degree.

The list also gives the same code, N321, for both LSE Actuarial Science degrees. Neither is likely to matter when you book, but both are reasons to confirm against the university's own page rather than any summary, including this one.

One more point that catches people out, and it follows from the tests being course-led.

The full course table with every UCAS code is on the universities guide.

Your result is a single number between 1.0 and 9.0, reported to one decimal place and capped at both ends.

Papers 1 and 2 are equated and scaled together, so there is no separate score for either paper.

The scale is pinned to the cohort rather than to the content. The median candidate is fixed at 4.5 and the 90th percentile at 7.0, both set on the October sitting and then applied to January.

Which leads to the fact people search for most, and the one every competitor gets tangled in.

There are also no appeals. Results reach universities automatically through UCAS matching, course by course, and you cannot choose who sees them.

That is the summary. The mechanism, the real percentile tables from UAT-UK's technical reports, and what a score is actually precise to are all on the scoring and results guide.

If what you are really after is what a raw mark out of 40 converts to, that guide carries our TMUA score conversion table, built three ways because the real conversion is never published.

If your question is whether a particular number is good enough, that is a separate guide.

Four things about that table catch people out.

Oxford and Cambridge applicants must sit in October. There are two narrow exceptions: mature applicants to a Cambridge mature college with a January admissions deadline, and applicants to Oxford's Astrophoria Foundation Year.

For everyone else the October deadline is hard, not preferred.

That rule reaches further than it first appears, because you may only sit once per cycle.

So if any one of your five choices is Oxford or Cambridge, you sit in October. It does not matter that your four other universities would happily accept a January score.

One choice decides the timing for all of them.

You may only sit once per admissions cycle. There is no resit, and UAT-UK state there is no advantage to either session.

Candidates in China, Hong Kong and Macau have a narrower window. Within the broader dates above, the TMUA specifically runs on 15-16 October and 8 January in those territories.

Late bookings are not possible. UAT-UK say plainly that they are unable to accept bookings after the stated deadline.

Booking mechanics, access arrangements and the bursary timeline are covered on the dates and registration guide.

The TMUA costs £78 for candidates sitting in the UK or the Republic of Ireland, and £133 for candidates sitting elsewhere.

The distinction that matters: the fee follows the test centre, not your nationality or where you live. A UK student sitting abroad pays the higher fee.

A bursary exists and is worth knowing about, because two features of it are easy to fall foul of.

It is a full fee waiver, not a reimbursement, and it must be approved before you book. Review takes up to five working days.

Leave it until the week booking closes and the waiver is gone even if you qualify.

Eligibility runs on UK residence, testing at a UK centre, being under 21 in full-time education, and one of free school meals, a 16-19 bursary or EMA, care leaver status, or a parent on means-tested benefits.

There is no overseas bursary.

The specification splits into two sections, and the split decides which paper tests what.

Section 1 is mathematical knowledge, in two parts. Part 1 is described as almost all within AS-level pure mathematics.

Part 2 is almost all within a Higher tier GCSE course.

Section 2 is logic and proof, and it is required for Paper 2 only.

There is no calculator, no formulae booklet and no dictionary, so every formula has to be recalled.

We classified every question in the official 2016 to 2023 archive against the specification. Two findings are worth knowing before you plan any revision.

Here's how that breaks down:

Paper 2 leans on GCSE material far more than Paper 1 does, particularly number: primes, factors, HCF and LCM. That is the part most candidates skip on the assumption that an admissions test would not ask it.

And difficulty climbs steeply through each paper. Question 20 is several times harder than question 1, but worth exactly the same mark, which has consequences for how you spend the 75 minutes.

Every topic is enumerated, with how often each appears, on the specification guide.

The TMUA has changed more in the last two years than in its first eight, and a great deal of advice still circulating describes the old version.

Some of it describes the paper-based Cambridge Assessment version, which stopped running after 2023.

Scores also used to be reported per paper. They are not any more, which is why old conversion tables have separate Paper 1 and Paper 2 columns.

What has not changed is the part that matters most for preparation.

So the old papers transfer. The old scores do not.

Everything above this point is official fact, taken from UAT-UK. This section is GhostPrep's advice, and you should weigh it as such.

The single most useful thing to know is that the official archive is large, free and completely ungated.

Every paper from 2016 to 2023 is published, and each year comes with Paper 1, Paper 2, UAT-UK's own worked answers for both, and an answer key.

That is 320 questions with official solutions, at no cost and with no account required. Any site charging you for TMUA worked solutions is reselling free files.

Three pieces of advice follow from what the archive actually shows.

Start with Section 2, logic and proof. It is the only content with no direct A-level equivalent, and it carries roughly half of Paper 2.

New material is where preparation moves a score furthest.

Practice without a calculator from day one. Not at the end, as a final check.

Every hour spent solving with one is an hour spent on a different exam.

Save 2022 and 2023 for last. They are the two closest to the current test and the most useful as genuine mocks once you have done the work.

Some genuinely useful free material exists outside UAT-UK too. Warwick's mathematics department publishes video walkthroughs of every question on the 2021 paper, plus handwritten solutions and a logic worksheet for Paper 2.

It is a foundation to build on rather than complete preparation, but it costs nothing.

The archive itself is on the past papers page.

Four other tests come up in the same conversations, and confusing them is common enough to be worth a paragraph each.

ESAT is UAT-UK's engineering and science test, sharing the Pearson VUE delivery model and the Notes on Mathematics document. Different content, different courses.

STEP is a long-form written mathematics examination, not multiple choice. Cambridge Mathematics applicants typically need both TMUA and STEP, and Warwick Maths applicants are typically required to take one or the other.

The MAT is retired. It ran from 2007 to 2025 and Oxford replaced it with the TMUA.

Oxford note that MAT preparation is not wasted, since the mathematical topics are very similar.

TARA is UAT-UK's third test, first offered in October 2025, covering critical thinking, problem solving and a writing task. It is not a mathematics test, and UCL Computer Science uses TARA rather than TMUA.

On difficulty relative to school qualifications, the honest answer is that the comparison does not really work: the TMUA is not harder A-level content, it is the same content under time pressure with no calculator and a design intent to spread out candidates who all have top grades.

More on how hard the TMUA really is.

Each of these is stated confidently somewhere on the first page of search results, and each one is wrong.

A sixth is subtler and worth naming: that the pre-2024 papers are out of date and not worth doing.

The opposite is true. UAT-UK state the content specification and question style are unchanged, and the archive is the only source of real questions that exists.

This page is the overview. Everything below goes deeper on one part of it.