TMUA Practice Tests: Free Timed TMUA Simulator
Sit full TMUA practice tests under real conditions. The simulator below runs both papers, 20 multiple-choice questions in 75 minutes each, with the same no-calculator, no-formula-booklet constraints as the real test and a clock that keeps running whether you are ready or not. Both papers are compulsory and run back to back, exactly as they do at the test centre, for two and a half hours in total.
If you are still planning your preparation, start with our complete guide to preparing for the TMUA, which covers registration, key dates, scoring and what counts as a good result.
We currently have 3 sets of TMUA practice questions, with more in development.
Note: To replicate the TMUA test environment, complete the practice test in a quiet environment in full screen.
Find these practice tests useful? Check out our other resources for students sitting the TMUA.
How to Prepare for the TMUA
The complete guide: format, key dates, scoring and a preparation timeline.
TMUA Past Papers and Resources
Every paper from 2016 to 2023, plus the official specimen materials.
Personal Statement Guide
Learn how to structure and write a UCAS personal statement.
What the TMUA looks like
The TMUA is two compulsory papers sat one after the other, two and a half hours in total. Paper 1, Applications of Mathematical Knowledge, is 20 multiple-choice questions in 75 minutes. Paper 2, Mathematical Reasoning, is another 20 multiple-choice questions in 75 minutes.
You get no calculator, no dictionary and no formula booklet, which catches people out: anything you would normally look up has to already be in your head. You are given a whiteboard notebook for working. There is no negative marking, so a wrong answer costs exactly what a blank costs, and every question carries equal weight.
The scoring is where the TMUA differs from most admissions tests. The two papers are not scored separately. They are combined and scaled into a single overall result on the 1.0 to 9.0 scale, reported to one decimal place. A strong Paper 1 never appears on your result as a strong Paper 1; it simply raises one number. For a full breakdown of the TMUA’s structure, scoring and which courses require it, read our TMUA preparation guide.
Pacing is the skill that decides your score
Twenty questions in seventy-five minutes gives you just under four minutes each, which is genuinely more thinking time than most admissions tests allow. The danger is the opposite of the usual one: with four minutes on the clock, a question that is nearly working always feels worth staying with.
It usually is not. Every question is worth one mark, and one stubborn proof can quietly swallow the time of three answerable questions. That is the most expensive habit we see in TMUA practice, and it bites hardest in Paper 2, where a reasoning question can look tractable long after it has stopped being so.
Two habits are worth drilling until they are automatic. First, answer everything. Blanks score zero and guesses cost nothing, so a final minute spent filling in the gaps is pure profit. Second, take a fast first pass and bank every question you can do quickly, then return to the difficult ones with whatever time is left.
Neither habit can be learned from an untimed problem set. Working through a proof with no clock develops your mathematics and does nothing whatsoever for your triage, which is why timed practice needs to start earlier than most candidates think. For what those scores need to reach at each university, see what counts as a good TMUA score.
Paper 2 is where the test is won or lost
Paper 2 is half your score, and it is the half almost nobody has studied. Paper 1 applies A-level mathematics to unfamiliar problems, which is uncomfortable but at least recognisable. Paper 2 tests formal logic and proof: necessary and sufficient conditions, converses and contrapositives, negation and quantifiers, counterexamples, and finding the first false step in a proof that looks perfectly reasonable. Most A-level students have never studied any of this explicitly.
That makes Paper 2 the highest-return part of your preparation, and it is also the part candidates skip, because it feels less like revision and more like a foreign language. It is not harder mathematics. It is ordinary mathematics with the reasoning made the object of the question rather than the route to it, and that shift is what needs practising.
The simulator runs both papers in order, so Paper 2 arrives when you are already 75 minutes in and tired, which is exactly when its style is hardest to switch into. Drilling Paper 2 questions cold, on their own, is a different and easier test than the one you will sit.
The 2016 to 2023 papers are still your best practice
The TMUA moved to computer-based delivery at Pearson VUE, which has left a lot of candidates unsure whether the older papers still count. They do. UAT-UK state that the switch changed neither the specification nor the question style, so every paper from 2016 onwards is excellent practice. Unlike the newer admissions tests, that means years of material rather than a handful of specimen papers.
One thing did change, and it is the trap. The scale has shifted. Scores on pre-2024 papers read about a point or so higher than they would today, so a raw mark that once converted to 7.5 is not a 7.5 now. Out-of-date conversion tables are the most misleading thing you can bring to your preparation. Judge yourself on improvement across papers, not on the number an old table gives you.
A sensible order of use: work through the archive oldest first for volume and speed, hold the official computer-based specimen and sample materials back for full timed run-throughs nearer the test, and use the practice tests above as often as you like to rehearse the interface and the pacing. You can download every paper from 2016 to 2023, the official specimen materials and the content specification from our TMUA past papers and resources page.
Common mistakes to avoid
Neglecting Paper 2. It is half the test and the least familiar half. If you under-prepare anywhere, it will be here.
Practising untimed. Comfortable, and almost useless on its own. If every question you attempt has unlimited time, you are training a skill the test does not measure.
Reading the specification instead of drilling problems. The TMUA punishes recall-only preparation. You cannot revise your way into it.
Trusting old conversion tables. Pre-2024 papers scored about a point higher than the current scale. Track your improvement, not the converted number.
Counting on a formula booklet you will not have. There is not one. Anything you would normally look up has to be memorised.
Booking late. The most damaging TMUA errors are administrative rather than mathematical, and there is no late entry.
Not reviewing on the same day. Patterns in your mistakes only register while the attempt is fresh. A paper you never review is a paper you have mostly wasted.
Never seeing the real interface. Sit the official Pearson VUE practice version at least once, so the screen itself holds no surprises on test day.
Want expert help with your TMUA preparation?
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Frequently asked questions
No. These are original questions written to the current specification. The official archive of papers from 2016 to 2023 is on our TMUA past papers page, and UAT-UK confirms those remain valid practice, because the content specification and question style are unchanged despite the move to computer-based delivery.
Yes, free, and no account is needed. We currently have 3 sets of TMUA practice questions, with more in development.
Unusually. Paper 1 and Paper 2 are not scored separately. They are combined and scaled into a single overall result from 1.0 to 9.0, reported to one decimal place. A strong Paper 1 never appears on your result as a strong Paper 1. It simply raises one number.
Only two universities say anything concrete. Warwick Mathematics reports that most offers last cycle went to applicants scoring 5.0 or above, with some made below that after holistic assessment. Durham automatically considers applicants scoring 5.0 or above for a reduced offer, and still treats scores down to roughly 3.2 as positive evidence. Cambridge, Oxford, Imperial, LSE and UCL publish no thresholds at all.
For most people the choice does not exist, because Oxford and Cambridge applicants must sit in October. If you are applying elsewhere, Warwick states there is no advantage to either sitting. January buys preparation time. October gets it done before interviews and coursework pile up.
No calculator, no dictionary and no formula booklet. You are given a whiteboard notebook for working, and nothing else.
No. A wrong answer costs exactly what a blank costs, and every question carries equal weight across both papers. There is never a reason to leave one unanswered.
No. The specification sits at higher-tier GCSE and AS-level pure mathematics, with elementary logic and proof added for Paper 2. Further Maths helps with fluency rather than with content coverage.
No. From 2027 entry, Oxford Mathematics, Maths and Statistics, Computer Science and the joint courses use the TMUA instead. Old MAT papers are still useful for general problem-solving practice, but the format is different, so do not build your preparation around them.