Free preparation resources
TMUA Past Papers
Every released TMUA paper from 2016 to 2023, the official specimen sets, the logic notes Paper 2 quietly assumes, and how to use the archive without wasting the newest years.
The TMUA is unusually well served: every paper set from 2016 to 2023 is published free by UAT-UK, and each one comes with official worked answers as well as an answer key. The sittings from October 2024 onwards are computer-based and are not released, but the specification has not changed, so the archive remains fully representative of the real questions. Used in the right order, it is the core of any serious TMUA plan.
Facts and links checked against the official UAT-UK archive · July 2026 · Oxbridge Mentors editorial team
Start here
The official TMUA archive
UAT-UK, the consortium that runs the TMUA, hosts the complete archive: two papers per year from 2016 to 2023 plus the official specimen and practice sets, each with official worked answers, not just a letter key. These are the only questions written by the people who write the real test, so they beat any third-party material.
The real test is two 75-minute multiple-choice papers in one sitting: Paper 1 applies A-Level-standard mathematics to unfamiliar problems, and Paper 2 tests mathematical reasoning, logic and proof. There is no negative marking, no calculator, and you receive a single overall score on the 1.0 to 9.0 scale, with the two papers equated and scaled together.
Every sitting, every file
The figures on the right of each row are the raw marks out of 20 that first converted to a 6.0, 7.0 and 9.0 in that sitting's official conversion table (we read every table ourselves; 2016 is the sitting the official documents title "Practice papers"). They are paper-era benchmarks: the current computer-based test is equated separately each sitting and reports a single overall score. No official table was published for 2023, so that row carries no benchmarks.
All files are hosted by UAT-UK. If a link stops working, the current copies are always on the official archive page.
Beyond the papers
The rest of the free TMUA toolkit
Three more free resources round out the archive: the official notes that teach the logic Paper 2 assumes, the on-screen practice tests that rehearse the real Pearson VUE interface, and the retired MAT archive for when the TMUA papers run out.
Official notes & on-screen practice
UAT-UK · Pearson VUE
The official Notes on Logic and Proof cover the Paper 2 material most A-Level courses never teach, and the free Pearson VUE sample tests are the only way to rehearse the real on-screen interface before test day.
Official preparation hub →Warwick TMUA Support
Free university programme
Warwick’s Mathematics department runs a free support programme: video walkthroughs of past papers, a logic worksheet, and live online sessions for Year 13 students before each sitting.
Warwick TMUA Support →The MAT archive
Retired 2026 · papers from 2007
Oxford retired the MAT when it moved to the TMUA, but its archive remains the best overflow practice: the multiple-choice questions sit very close to TMUA Paper 1 style, and there are over 15 years of them.
MAT guide →Method
How to use the archive properly
- 1
Oldest first, newest saved
Work forwards from 2016 and treat the newest two or three years plus the specimen sets as full-dress timed mocks for the final month. The newest papers are the closest match to current difficulty: do not spend them early.
- 2
Always timed, always both papers
Each paper is 75 minutes for 20 questions, under four minutes a question. Sit papers whole and timed rather than browsing questions: pacing and triage are the skills the TMUA actually selects for.
- 3
Read the logic notes before Paper 2
Paper 2 assumes comfort with quantifiers, negation, contrapositives and counter-examples, which most A-Level courses never teach. Read the official Notes on Logic and Proof before your first Paper 2, not after it.
- 4
Log errors and rehearse the screen
Keep an error log by topic and re-test weak areas a week later. Late in your preparation, switch to the official on-screen sample tests: the real test is sat at a Pearson VUE centre with an erasable notebook instead of rough paper, and that is worth rehearsing.
TMUA past papers: common questions
Are the old paper-based TMUA papers still relevant now the test is on-screen?
Yes. The specification and question style are unchanged: only the delivery moved on-screen. The 2024 onwards sittings are not released, so the 2016 to 2023 archive plus the specimen sets remain the definitive practice material. Rehearse the on-screen format separately with the official Pearson VUE sample tests.
Do TMUA past papers have worked solutions?
Yes, and this is a real advantage over the ESAT: every released TMUA paper has official worked answers published alongside the answer key, so you can see the intended method for every question, not just the right letter.
What raw mark do I need for a 7.0?
For the current test there is no fixed conversion table: scores are equated for each sitting, anchored so the median candidate scores about 4.5 and roughly the top tenth score 7.0 or above. For marking practice papers, the archive above shows the raw marks that converted to a 6.0, 7.0 and 9.0 in each sitting's official paper-era conversion table: typically around 13 to 15 out of 20 for a 7.0. Our free score checker shows what each university actually asks for, with official sources.
What should I do when I run out of past papers?
Most well-prepared students exhaust the archive a few weeks before the test. The best overflow material is the retired MAT archive (especially its multiple-choice questions), Warwick’s free support programme, and our TMUA question bank, which pairs new exam-style questions with full worked solutions.
Can I sit the TMUA twice in the same cycle?
No. Only one attempt counts per admissions cycle, and sitting both windows is treated as misconduct. Cambridge and Oxford applicants must sit the October window; the January sitting exists for some other universities’ applicants.