TMUA past papers, mark schemes and worked solutions

You can register and book the TMUA through the official UAT-UK website. You will need to create a UAT-UK account before booking, and the test is sat at an authorised Pearson VUE test centre. Registration windows open ahead of each test sitting, so it is worth registering early to secure your preferred time and location.

The TMUA assesses mathematical thinking and reasoning, rather than how much content a student has memorised. It is used by Cambridge, Oxford, and other universities to help select applicants for Mathematics, Economics, and Computer Science courses.

The TMUA is made up of two papers, each marked out of 20. Your raw marks across both papers are combined and converted to a single overall score, reported on a scale from 1.0 (lowest) to 9.0 (highest), to one decimal place. There is no pass or fail mark.

The TMUA lasts 2 hours and 30 minutes in total, split into two papers of 75 minutes each, with 20 multiple-choice questions per paper.

Since the TMUA uses mathematics most students will already have covered at school, there is no need for a lengthy content-based preparation course. Most students benefit from starting around two to three months before their test date, focusing on the test specification and the Notes on Logic and Proof, then working through past papers under timed conditions.

The TMUA does not require knowledge beyond standard A Level Mathematics. However, many students find it more challenging than their A Level exams because it tests reasoning, logic, and proof in unfamiliar contexts, rather than applying memorised methods to familiar question types.

No. Calculators are not permitted in the TMUA.

No. Your score is based on the number of correct answers you give, with no penalty for incorrect ones, so it is worth attempting every question.

No. You may only sit the TMUA once per admissions cycle. The test runs in two sittings each year, in October and January, but Oxford and Cambridge applicants must sit in the October window, with limited exceptions for mature applicants or Oxford’s Astrophoria Foundation Year.

Paper 1, Applications of Mathematical Knowledge, tests a student’s ability to apply familiar mathematics to new and unfamiliar situations. Paper 2, Mathematical Reasoning, focuses on evaluating mathematical arguments using elementary logic and proof. Both papers are equally weighted and combine into a single overall score.

Every published TMUA past paper is on this page, free and without registration: Paper 1 and Paper 2 for each year from 2016 to 2023, the early specimen set, and the official mark scheme for each sitting. They are the papers UAT-UK publishes; we host the links so the whole archive sits in one place alongside worked solutions and the score conversion.

Yes. UAT-UK publishes an answer key for each sitting, which serves as the mark scheme, and one key covers both Paper 1 and Paper 2. Because the TMUA is entirely multiple choice, the mark scheme gives the correct option for each question rather than a method mark breakdown. For the reasoning behind each answer, use the worked solutions linked beside every paper above.

No. The TMUA became a computer-based test for the 2024 sitting and UAT-UK has not released question papers from 2024 onwards, so the 2016 to 2023 archive on this page is the complete published set. For practice in the current on-screen format, use the official sample tests and our free timed TMUA practice tests.

On the official 2023 conversion, 21 marks out of 40 gave an overall score of 6.5, and 19 marks gave 6.0. That is a little over half the questions, which surprises most candidates the first time they mark a paper. Roughly the top 10% of the field scores 6.5 to 7.0 or above. The exact mapping shifts between test versions, so treat it as accurate to within two or three marks.