How to use TMUA past papers: order, marking and a 10-week plan
The official TMUA past papers are the closest practice to the real test, and there are only nine sets of them. Used in the right order, with the worked answers, they show you exactly which skills cost you marks.
On this page
What is available
UAT-UK, which runs the TMUA, publishes past papers free on its preparation materials page. At the time of writing (October 2026) there are nine sets: a specimen paper and the papers from 2016 to 2023. Each set has:
- Paper 1 (Applications of Mathematical Knowledge) and Paper 2 (Mathematical Reasoning), each 20 multiple-choice questions in 75 minutes;
- an answer key for both papers;
- worked answers for every question, written by the test's own team.
We link every one of them, by year, on our TMUA past papers page. The files stay on UAT-UK's site, so you always get the official version.
That is 360 official questions in total. It sounds like a lot, but at 20 questions a sitting it is only 18 timed papers, so plan how you will use them rather than working through them in a rush in the last fortnight.
The test you will sit is on a computer
The published papers are PDFs, but the TMUA is now taken on a computer at a Pearson VUE test centre, with no calculator. The questions are the same kind, but reading them on screen and working on paper beside you feels different. Two things help:
- Try the sample test on the Pearson VUE website, which Oxford's admissions page also recommends, so the screen layout and the way you flag questions are familiar.
- Do your timed past papers from a screen, with rough paper beside you, rather than printing them.
Which order to use them in
- Specimen paper, untimed. Use it to learn the question styles. Check each answer as you go and read the worked answer even when you were right.
- 2016 to 2018, by topic. Do these untimed or loosely timed, a section at a time, while you revise the content in the specification. Paper 2 questions on logic are the ones to slow down on.
- 2019 to 2021, timed. Full papers in 75 minutes each, then a full review. This is where you build pace.
- 2022 and 2023, as mocks. Keep the two most recent years for the last fortnight. Sit both papers back to back, as on test day, and treat the result as your most reliable estimate of where you are.
If you run out, redo the papers you found hardest a month later. You will remember some answers, but not the reasoning, and the reasoning is what you are practising.
How to mark a paper so it helps
Marking right and wrong is not enough. For every question, record one of four outcomes:
- Right and quick: nothing to do.
- Right but slow: read the worked answer for a faster route. Many TMUA questions have a shortcut, such as a sketch, a substitution or an estimate.
- Wrong, and I can see why: write the mistake in your error log in one sentence, such as “forgot that log needs a positive argument”.
- Wrong, and I cannot see why: work through the official worked answer line by line, then try the question again the next day without looking.
After three or four papers the error log shows a pattern: usually a handful of topics or habits that account for most lost marks. Those are what your revision should fix.
Turning raw marks into a target
Your TMUA result is reported on a scale from 1.0 to 9.0, not as a raw mark, and the conversion varies a little from sitting to sitting. So treat raw marks on past papers as a trend, not a precise prediction. What matters is that the number of questions you get right, in time, goes up from paper to paper. For a target, use the typical scores that your chosen universities publish for applicants who received offers.
A 10-week plan using the past papers
- Weeks 1 and 2: specimen paper untimed, then fix your weakest Paper 1 topics without a calculator.
- Weeks 3 and 4: 2016 and 2017 by section. Work through UAT-UK's Notes on Logic and Proof alongside Paper 2.
- Weeks 5 and 6: 2018 and 2019, timed. Start the error log properly.
- Weeks 7 and 8: 2020 and 2021, timed, on screen. Practise moving on from a question after about four minutes.
- Weeks 9 and 10: 2022 and 2023 as full mocks, then re-sit the questions in your error log.
Applying to Oxford? Its admissions page says MAT past papers remain relevant, because the mathematics is very similar. Use them for extra problem-solving practice once you have done the TMUA papers. See our guide to Oxford's switch from the MAT to the TMUA.
Timing on test day
Twenty questions in 75 minutes is 3 minutes 45 seconds each. The questions are not equally hard, so do not spend equal time on them. Work through once, answer everything you can do quickly, and flag the rest. On the second pass, go back to the flagged questions. Never leave an answer blank: an educated guess between two options costs nothing.
Common mistakes
- Using the 2022 and 2023 papers early, and having no unseen papers left for final mocks.
- Marking right and wrong without reading the worked answers.
- Doing papers with a calculator, or printed out, when the real test is on screen with no calculator.
- Spending ten minutes on one question and running out of time for three easier ones.
- Treating Paper 2 as a maths paper and skipping the logic notes.
Practice questions
Try each one before opening the answer.
Q1. You have 6 weeks and have not started. Which papers should you keep for the final week?
Show answer
Q2. You got a question right but took 8 minutes. What should you do?
Show answer
Q3. How many official TMUA questions are there in the published papers?
Show answer
Frequently asked questions
Where can I download TMUA past papers?
From UAT-UK's preparation materials page. We link every paper, answer key and set of worked answers on our TMUA past papers page.
Are there TMUA past papers after 2023?
At the time of writing, the published papers run from 2016 to 2023, plus the specimen paper. Check UAT-UK's page for anything new.
Are the old papers still like the real test?
Yes for the questions: the specification and question styles have stayed the same. The difference is that the test is now taken on a computer, so practise reading questions on screen.
Should I use MAT papers too?
If you are applying to Oxford, its admissions page says MAT past papers remain relevant. For everyone, they are good extra problem-solving practice once the TMUA papers are done.
Key takeaways
- Nine official sets, from the specimen paper to 2023, with worked answers.
- Learn the styles untimed first, then build pace, then sit the newest papers as mocks.
- Mark every question as right-and-quick, right-but-slow, or wrong, and keep an error log.
- Practise on screen and without a calculator, as on test day.