questions in the bank
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Get into Imperial.
TMUA, sorted.
Two papers, twenty questions, seventy-five minutes each, no calculator. The whole thing rewards pace and pattern recognition far more than it rewards depth — so the only preparation that moves the needle is a lot of questions, sat under the clock, with everything you get wrong coming back until it sticks.
⌘K anywhere for the command palette
you have answered
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due for review
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day streak
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01 — exam
Sit the 2026 predicted papers
Two fixed papers that everybody sits in the same form, so the scores are comparable between candidates. Twenty questions and seventy-five minutes each, in a replica of the driver the real test runs in.
Free, and you can resit as often as you like — a resit redraws nothing, so the second attempt is a measure of memory rather than of maths.
Or sit a real one
The past papers UAT-UK publishes, transcribed in full and sat in the same driver under the same countdown. Every answer is checked against the official key.
02 — practice
Pick a paper to practise
Sets of five to thirty questions, relaxed or under exam conditions. Anything you get wrong joins the review queue automatically.
or go straight at one topic
03 — method
The road to an offer
Where the TMUA sits in an application, and what is worth doing at each stage.
Now → October
Work through the bank
The TMUA is not a hard syllabus — it is AS-level content under an unreasonable clock. Twenty questions in seventy-five minutes is three and three-quarter minutes each, and the questions are written so that the intended route takes about ninety seconds while the obvious route takes six minutes. Practice is how you learn to spot which is which.
◆ tmua lab
— questions across both papers, each with a full worked answer. Everything you get
wrong returns in your review queue until you have answered it correctly twice, thirty-six hours apart.
Accuracy and timing are tracked per specification point, so the dashboard tells you what to work on next
rather than leaving you to guess.
October
Sit the TMUA
Two papers on the same day at a Pearson VUE test centre, taken on screen. Paper 1 is applications of mathematical knowledge; Paper 2 is mathematical reasoning — logic, necessary and sufficient conditions, proof and counterexample. No calculator, and your working goes on an erasable note board that is physically separate from the screen.
◆ tmua lab
The mock runs in a replica of that driver: the same navy chrome, the same flag-and-review behaviour, the
same Alt+N / Alt+P navigation, and a countdown that does not
pause. Sitting one before October is the cheapest way to find out that transcribing algebra onto a
separate board costs you twenty seconds a question.
October → January
Your score does its work
Results are reported on the TMUA scale from 1.0 to 9.0, one decimal place, as the average of the two papers. Roughly 5.0 is the middle of the cohort; a competitive score at Imperial or LSE is around 6.5 and up. Universities use it differently — some as a threshold, some as one factor among many, some to lower a conditional offer — so read your course's page rather than a forum.
◆ tmua lab
Every set of ten questions or more is scored against the same 1.0–9.0 scale, with the difficulty of the
questions you were actually served taken into account, and each result carries a
“How is my score calculated?” panel showing the working.
December → January
Interviews, where they happen
Most TMUA universities do not interview for mathematics. Cambridge does, and a strong TMUA is one of the things that gets you there. The habit that helps is the same one the test builds: say what you are trying out loud, and be willing to abandon a route quickly when it stops going anywhere.
04 — who runs this
About
T
The TMUA Lab team
built by people who sat it
maths · 2025 entry
TMUA Lab exists because the honest answer to “how do I prepare?” is “do a very large number of questions under time pressure”, and until recently the only way to do that was to burn through the handful of real past papers in a fortnight and then run out.
So this is a bank of — questions. The core of it is every TMUA paper UAT-UK has published — 2016 to 2023, both papers, all sixteen — transcribed question by question, with every answer checked against the official answer key before it was allowed in. Around those sit questions written for this site to the published specification; they are marked as such, and they are easier than the real thing, so practice draws from the real papers unless you ask otherwise.
Sit them in a relaxed study view or in a replica of the real test driver. Nothing is behind a login and nothing leaves your browser: every answer, streak and score lives in this device's local storage, and the “erase all my local data” command in the palette really does erase it.
The bank is still growing, and errors do slip through. If a question looks wrong, it probably is — please say so, and it gets fixed.
05 — questions
FAQs
01What actually is the TMUA?＋
The Test of Mathematics for University Admission, administered by UAT-UK and sat on screen at Pearson VUE centres. Two papers of twenty multiple-choice questions, seventy-five minutes each, no calculator.
Paper 1 — Applications of Mathematical Knowledge is pure AS content: algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation and integration, graphs.
Paper 2 — Mathematical Reasoning uses the same knowledge but asks you to argue with it: necessary and sufficient conditions, converses and contrapositives, proof by contradiction and by counterexample, divisibility, and inequalities. It is the paper most candidates under-prepare for, and the one where the marks are cheapest to pick up.
02Which universities use it?＋
The core users are Imperial College London, the London School of Economics, the University of Warwick and Durham University, with several others — Bath, Cardiff, Lancaster, Sheffield, Southampton among them — taking it for some courses. Cambridge uses it for a small number of routes.
Requirements move year to year, and a course that “considers” the TMUA this cycle may require it next. The only source worth trusting is the course page on the university's own site for your year of entry.
03How is my score out of 9 worked out?＋
Your answers are measured against the difficulty of the questions you were actually served, and the result is placed on the TMUA 1.0–9.0 scale. If your set happened to be a kind one, the same mark is worth slightly less; if it was a brutal one, it is worth more. That is exactly how boundaries move between real sittings.
Every result carries a How is my score calculated? panel showing what the paper was expected to yield, how your mark was adjusted, and where the final figure lands on the published distribution.
Sets under ten questions get no score at all. Five answers place you somewhere between the bottom and the top of the scale, and any single number drawn from that would be guesswork dressed up as a prediction. Between ten and twenty you get a score, deliberately pulled towards the middle and labelled as an indication. A real section is twenty, and a mock is the thing to trust.
04How does the review queue decide what comes back?＋
Get a question wrong and it joins your review queue straight away, due now. A question served but left unanswered counts as wrong.
Leaving the queue takes two correct answers in review, and they have to be 36 hours apart. Answer correctly and the question goes quiet for thirty-six hours rather than disappearing; when it comes back, a second correct answer clears it for good.
A wrong answer at any point sends it back to the start: due immediately, and needing two correct answers again. One right answer followed by a miss counts for nothing, which is the point of asking twice.
Only answers given in review count towards those two. Getting a question right first time in practice or a mock keeps it out of the queue altogether, but cannot clear one already in there.
05What's the difference between practice, a mock and review?＋
Practice is a set of five to thirty questions drawn from one paper, optionally narrowed to a single topic. By default it draws from the real past papers; you can widen it to the whole bank or narrow it to this site's own questions.
Two settings control how it feels, and they are independent. When you see the answer is either as soon as I pick (committal, fastest for drilling), after I confirm (you can change your mind first), or only at the end. Conditions is either relaxed — the timer counts up and can be paused — or exam conditions, a countdown at the real pace of about 3 minutes 45 seconds a question, without pausing. Exam conditions fixes the answers to the end, because that is what exam conditions means.
A mock is a full twenty-question section with a seventy-five minute countdown, sat in the replica test driver. You can sit one paper or both back to back.
Review serves only questions you have previously got wrong, and only once they are due. It does not use up unseen questions, and its answers do not count towards the seen-question pool.
06Why don't I ever see the same question twice?＋
Every question served in practice or a mock is marked as seen, whether you answered it or left it blank, and will not come round again. The setup screen shows how many questions are left in a paper rather than how many it contains.
Abandoning a set is the exception: nothing is recorded and its questions go straight back into the pool. Deleting a sitting from your history does the same.
Reset and practise again makes a whole paper available from the start. It records a cutoff rather than deleting anything, so your dashboard, streak and review queue stay exactly as they are.
07Which keyboard shortcuts work where?＋
It depends on the interface. The test driver is a replica of the player the real TMUA runs in, so it is deliberately sparse. The study view is this site's own layout and is not.
Test driver (and every mock)
Alt+N — next question
Alt+P — previous question
Answers are selected with the mouse. Nothing else is bound.
Study view
A–H — select that answer
↵ — check the answer, then move on
→ or N — next question ← or P — previous
F — flag the question
Alt+N and Alt+P work here as well.
Everywhere: ⌘K (or CtrlK, or just /) opens the command palette. On a Mac, Alt is the Option key.
08Where does the “% answer correctly” figure come from?＋
It is the calibrated facility of the question — the proportion of candidates expected to get it right — and it is what the scoring model uses to decide how kind or cruel your particular draw was.
The scale is anchored on the real past papers. Their difficulty mix is set so that a real paper comes out at a mean facility of 0.50, which is roughly what the published cohort actually averages: about ten marks out of twenty. Everything else is measured against that line. The questions written for this site sit well above it, which is the honest position — they are easier — and the model discounts a set of them accordingly, so a good score on an easy set does not read as a 9.
A question counts as one of the hard questions when the figure is under 25%. The hard-questions toggle filters a set down to them, and only offers ones you have not already sat.
Because this site keeps nothing on a server, these figures do not move with live cohort data — the whole point of the design is that your answers never leave the browser.
09What happens to my data?＋
Nothing leaves this device. Answers, timings, sessions, streaks and preferences are written to your browser's local storage under a single key and never transmitted anywhere. There is no account, no analytics and no cookie banner because there is nothing to consent to.
The practical consequence is that clearing site data, using a private window or switching browser starts you from scratch, and your progress does not follow you between devices. Erase all my local data in the command palette wipes everything immediately.
Enough reading.
Ten questions is about fifteen minutes, and the first set tells you more than an evening of theory.