GhostPrep TMUA
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TMUA past papers, every official one

Every official TMUA paper from 2016 to 2023, free, with UAT-UK's own worked answers for all of them. Plus Oxford's full MAT archive, which is the largest source of relevant extra practice that exists and which almost nobody points TMUA candidates at.

Get the papersJoin the TMUA waitlist
  • All eight official sittings, both papers, plus the early specimen set.
  • Official worked answers for every question. Free to download, no account, no email.
  • 19 years of Oxford MAT papers with solutions, feedback and syllabus notes.

The official archive

Every official TMUA past paper

Eight sittings from 2016 to 2023, plus the early specimen set. Every one publishes both papers, UAT-UK’s own worked answers for both, and an answer key. All free, all hosted here.

Official TMUA notes and guidance

UAT-UK publish three things alongside the papers, and they are the fastest way into the parts of the test that are unfamiliar. Linked directly, because all three are revised in place.

  • Notes on Logic and Proof

    UAT-UK, June 2025

    The examiner's own document on the Paper 2 logic content, which is the part most candidates have never met before. If you read one thing on this page, read this one.

  • Notes on Mathematics

    UAT-UK

    Companion notes on the mathematical content shared between the TMUA and ESAT Module 2. Useful for checking whether a topic is in scope before you spend time on it.

  • Official sample and practice tests

    UAT-UK, in the Pearson player

    The only way to see the real on-screen interface before test day, and worth doing at least once. One caveat: their questions are the 2018 and 2022 sittings re-served, so working through both spends two of your eight papers without appearing to.

TMUA past papers and worked answers are the copyright of UAT-UK. MAT past papers, solutions and examiner feedback are the copyright of the University of Oxford Mathematical Institute. Both are reproduced here for candidates' personal, non-commercial revision use. GhostPrep is not affiliated with, endorsed by, or connected to UAT-UK, Pearson VUE, Cambridge Assessment, the University of Oxford, the University of Cambridge or Imperial College London.

The frozen archive

Why there are no papers after 2023

This is the first question the archive raises and almost nobody answers it. No paper from 2024 onwards has ever been released, and on the evidence there is no reason to expect one.

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 and publishing it cost nothing.

That is no longer how the test works. Several versions now run across a multi-day window and candidates do not all see the same questions, so there is no single paper to publish. UAT-UK's technical report also explains that questions are anchored at their known difficulty values across years, which is what keeps scores comparable between cycles. Reusing questions that way and publishing them are mutually exclusive.

UAT-UK have not stated this as their reason, so it is our reading of what their own published method implies. What they have stated is the part that matters most: both the content specification and question style are unchanged, so this archive can still be used to prepare.

How to spend them

Why past papers still matter, and why they run out

Past papers are the only material that was actually sat under exam conditions, by real candidates, against a real clock. No practice question, ours included, fully replicates that.

The catch is scarcity, and it is more acute here than it looks. There are eight official sittings and there will never be a ninth, so every paper you spend is gone for good.

It is worse than eight, in fact. The two interactive practice tests in the Pearson player are the 2018 and 2022 sittings re-served, question for question, so doing those spends two of your eight without appearing to.

This is why the MAT archive matters so much. It gives you the volume to build the skill, so you can save the genuinely-TMUA material for the two or three timed run-throughs that actually tell you whether you are ready.

19 more years

Oxford MAT past papers

Oxford retired the Mathematics Admissions Test when it adopted the TMUA, and says the mathematical topics on the two are very similar. Every paper from 2007 to 2025 is published free, with solutions and examiner feedback.

It does nothing for Section 2, the logic and proof content on Paper 2, because the MAT had no equivalent. Use it for Paper 1 style work.

Start with these four

Short multiple-choice-only tests Oxford ran outside the normal round, each 10 questions in an hour. The closest format match to the TMUA in either archive.

The full MAT archive

Newest first. The syllabus changed for the 2018 test, so prefer 2018 onward and read Oxford’s notes before using anything earlier.

How to use them

How to actually use these papers

The difference between a paper that teaches you something and one you simply used up:

  1. 1Do not start with the oldest and work forwards. 2022 and 2023 are the closest to the current test, so they are the two worth protecting as real mocks rather than burning first.
  2. 2Sit both papers back to back, 75 minutes each, with no break. The real session is 2 hours 30 minutes and the fatigue in Paper 2 is part of what is being tested.
  3. 3No calculator, no formulae booklet, no notes. None of the three exists in the real test, and practicing with any of them is practicing a different exam.
  4. 4Work on a whiteboard, not on the paper. The test is on screen at a Pearson VUE centre, so you cannot annotate a diagram or scribble beside the question. This is the change that catches people out.
  5. 5Answer every question, including ones you are guessing. There is no negative marking, so a blank is always worse than a guess.
  6. 6Mark by method, not by letter. Read the official worked answer even on questions you got right, because arriving at the correct option by faulty reasoning is not a mark you can rely on repeating.

Beyond the archive

Free TMUA resources worth knowing about

The archive above is the official material. It is not everything that exists, and some of what else is out there is genuinely good and almost unknown.

None of it is hosted here. These are links to the universities and charities that made them, which is where the credit belongs.

  • Warwick Mathematics Institute: TMUA walkthroughs

    University of Warwick

    The strongest free TMUA resource anywhere, and the least known. Video walkthroughs of past papers that show the thinking rather than just the answer, including every question of both 2021 papers, plus handwritten PDF solutions with the logic questions marked. Warwick also run live sessions for Year 13 before each sitting.

  • Problem Solving Matters

    AMSP, free for state-funded students

    A Year 12 course run with Oxford, Imperial, Durham, Bath, Manchester and Warwick: three study days, summer assignments and four online sessions, at admissions-test difficulty. Free if you are at a state-funded school or college, and it runs once a year from the summer term, so it needs planning a year ahead.

Free material is where preparation starts rather than where it finishes. Between them these give you worked routes through roughly two of the eight sittings and a term of taught problem solving. What neither can do is give you an unlimited supply of questions on the one topic you keep losing marks on.

The gap the archive cannot fill

320 questions, and there will never be another one

UAT-UK publish worked answers for every question in this archive, free, and they are good. This page would be dishonest if it pretended otherwise.

Two things they cannot do. They cannot tell you why the option you actually picked looked right, because they are written to show the correct route rather than to diagnose your error.

And they cannot give you a 321st question. The archive is frozen and finite, so the moment you have worked through it, the one thing you need more of is the one thing that no longer exists.

The papers

Free, no account

What you get from the buttons above.

  • All eight official sittings, both papers, exactly as they were sat
  • UAT-UK's own worked answers for every question
  • The full Oxford MAT archive, with solutions and examiner feedback
  • Yours to print, annotate and keep. You time yourself and you mark yourself

When we open

Join the waitlist

What we are building, and what the account will be for.

  • The archive rebuilt as timed on-screen practice, in the format the real test uses
  • Unlimited questions on whichever topic you keep losing marks on
  • A worked solution for every question, including why each wrong option is tempting
  • Your accuracy tracked by topic across every sitting, so you can see what is improving
Join the TMUA waitlist
Keep reading

Guides to every part of the TMUA

Free, in-depth guides on what the test actually assesses, how it's scored, and which courses require it.

Scoring

TMUA score conversion: what your raw mark out of 40 is actually worth

There is no TMUA conversion table, no grade boundaries and no official calculator, in any year. Here is what UAT-UK do publish, what your raw mark out of 40 is genuinely worth, and why every conversion table you will find online describes a scoring system that no longer exists.

Read the guideStart here

TMUA 2026/27: everything you need to know

The Test of Mathematics for University Admission, in full: what it is, who has to sit it, how the 1.0 to 9.0 score works, what it costs, and how to prepare. Verified against UAT-UK.

Read the guideDates & Registration

TMUA dates, registration and booking for 2027 entry

The October window is 12 to 16 October 2026 and booking closes 28 September 2026. Registering and booking a seat are two separate steps, and the gap between them is where most people come unstuck.

Read the guideSpecification

TMUA specification 2026/27: every topic you need

The full content specification for assessment in October 2026 and January 2027, as a page rather than a PDF - with how often each topic has actually come up across every official paper.

Read the guidePaper 1

TMUA Paper 1: applications of mathematical knowledge

Twenty questions in 75 minutes, which is 3 minutes 45 seconds each. The median candidate uses 2 hours 29 minutes of the 2 hours 30 available, so the clock is not a background worry. It is the exam.

Read the guidePaper 2

TMUA Paper 2: mathematical reasoning, logic and proof

Paper 2 asks for everything Paper 1 asks for, and adds Section 2 on top. About 38% of it tests reasoning that no A-level maths course formally teaches, which is exactly why it is the best place to spend your preparation.

Read the guideUniversities

Which universities require the TMUA for 2027 entry

Seven institutions: Cambridge, Oxford, Imperial, LSE, Warwick, Durham and UCL. The requirement attaches to named courses rather than to universities, so the only question that matters is whether your exact UCAS code is on the list below.

Read the guideScoring

What is a good TMUA score?

The mean for 2026 entry was 4.28 and the median 4.1. So anything above about 4.3 beats the average candidate, 5.3 puts you in the top quarter, and 6.7 in the top tenth. What counts as good, though, depends on the course rather than the test.

Read the guideCambridge

Cambridge TMUA: courses, STEP, and what a competitive score looks like

Three courses need it: Computer Science, Economics and Mathematics. Mathematics is new for 2027, and it needs the TMUA and STEP, not one instead of the other. If you are applying at the 15 October deadline you must sit in the October window.

Read the guideImperial

Imperial TMUA: 19 courses, and the score data Imperial publishes

Imperial is the largest single user of the TMUA, with 19 compulsory courses. It is also the only university that publishes what its applicants actually scored, broken down by department and by outcome. Here is that data, and what it can and cannot tell you.

Read the guideLSE

LSE TMUA: compulsory for two courses, recommended for nine

Two LSE degrees require the TMUA. Nine more "recommend" it, which is the least useful word in admissions. This page answers what recommended actually means at LSE, using LSE figures rather than guesswork.

Read the guideWarwick

Warwick TMUA: courses, exemptions, and what the 5.0 figure really says

Warwick has the most moving parts of any TMUA university: sixteen courses across four subject groups, four different requirements, an exemption for contextual-offer applicants, and the only published score figure in the landscape. Find which of the four you are, and the rest follows.

Read the guideDurham & UCL

Durham and UCL TMUA requirements for 2027 entry

Two universities on one page, because both requirements are narrow. Durham has the clearest published mechanic in the whole landscape: a high enough score earns an offer one grade lower. For 2026 entry that figure was 5.0, and Durham has confirmed the mechanic for 2027 without yet publishing a number. UCL needs the TMUA for two Economics degrees and nothing else, because UCL Computer Science uses a different test entirely.

Read the guide

TMUA past papers: common questions

Are there TMUA past papers for 2024, 2025 or 2026?

No, and there is no sign there ever will be. Since 2024 several versions of the test run across a multi-day window, so there is no single paper to publish, and questions are reused between cycles to keep scores comparable. The archive is permanently frozen at 2023.

Are the pre-2024 papers still worth doing?

Yes, and they are the best material available. UAT-UK state that both the content specification and question style are unchanged, so the archive can be used when preparing. What differs is delivery: those papers were sat on paper in schools, and the test is now on screen at a Pearson VUE centre.

Do the official papers come with worked solutions?

Yes, for every year, free. Each sitting publishes Paper 1, Paper 2, worked answers for both, and an answer key. Anyone charging you for TMUA worked solutions is reselling free UAT-UK files.

Do I need an account to download these?

No. Everything on this page downloads directly, with no signup and no email, and that is not going to change. Some sites ask for your email before handing over files that UAT-UK publish openly.

What is the difference between the specimen paper and the practice tests?

The early specimen is a PDF set, linked above. The specimen and practice tests run inside the real Pearson test player and give right and wrong feedback but deliberately award no score, because the scale depends on the cohort. Worth knowing: their questions are the 2018 and 2022 sittings re-served, so they are not extra material.

How many past papers should I do?

There are only eight real sittings, so the question is how to spend them rather than how many to get through. Two or three timed early, the rest saved as full mocks near the end, and topic work in between using the MAT archive for volume.

Can I work out my TMUA score from a past paper?

No. The conversion depends on which version of the test you sat and on the cohort who sat it alongside you, so no fixed table exists for any year. There are no grade boundaries either. Track your raw mark out of 40 across several papers instead.

Which past paper is closest to the current test?

2023, then 2022. Both are worth saving as genuine mocks rather than spending early. Bear in mind that the official interactive sample test is the 2022 sitting, so doing one spends the other.

Can I use MAT past papers to prepare for the TMUA?

Yes, for Paper 1 style content. Oxford replaced the MAT with the TMUA and say the mathematical topics are very similar, and 19 years of papers with full solutions are free. Start with the four extra tests, each 10 multiple-choice questions in an hour, which are the closest format match to the TMUA of anything in either archive. The MAT had no equivalent of TMUA Section 2, though, so it does nothing for the logic and proof content on Paper 2.

Are there TMUA notes on logic and proof?

Yes, and the best ones are the examiner's. UAT-UK publish Notes on Logic and Proof specifically for Paper 2, free, linked above. Warwick's walkthroughs also mark which past-paper questions are logic questions, which is the fastest way to drill just that content.

What free TMUA resources are there besides past papers?

Four worth knowing, all linked on this page. UAT-UK publish Notes on Logic and Proof, Notes on Mathematics and the official sample tests, which are with the archive above. Warwick Mathematics Institute's walkthroughs and AMSP's Problem Solving Matters course are further down. None are hosted here, because they belong to the people who made them.

Is a calculator allowed?

No, and there is no formulae booklet or dictionary either. Every formula has to be recalled, so practicing with any of them is practicing a different exam.

Coming soon

The papers are free. The practice is next.

A PDF cannot time you, mark you, or find you twenty more questions on the one topic you keep getting wrong. That is what we are building. Join the waitlist and we will tell you the day it opens.

Join the TMUA waitlistRead the guides