Free TMUA & ESAT Maths Practice: Make Past Papers Count

Past papers are one of the best ways to turn maths knowledge into exam-ready problem solving. The value comes from attempting unfamiliar questions, checking your reasoning and returning to the ones you missed. Start here with 599 free MAT, ENGAA and NSAA maths multiple-choice questions—original diagrams, instant answer checks and worked solutions where available, all in one digital question bank for your TMUA and ESAT preparation.

Your next useful practice session starts below. Choose By topic to tackle a weak spot, add a difficulty level, or choose By year for a mixed paper. Want more room for your working? Open the free question bank in a new tab ↗.

Practise maths by topic, difficulty or past-paper year

Select MAT, ENGAA, NSAA or a combination of the three. In topic mode, practise areas such as algebra, trigonometry, coordinate geometry, differentiation, integration, probability and sequences. Add a difficulty level to narrow your selection. In year mode, choose a paper and move through its maths questions in their original order.

539 questions have topic and difficulty labels. Difficulty levels run from 1 to 5 and are indicative practice ratings, not official grades or directly comparable exam scores. The extra MAT specimens and supplementary tests remain available by year; they are not included in topic filtering.

Which MAT, ENGAA and NSAA questions are included?

Only maths multiple-choice questions appear in this bank. Physics, chemistry, biology and long-answer questions are excluded. The original question numbers are retained, so ENGAA and advanced NSAA sets may skip numbers. MAT 2024 and 2025 MCQs are not included because Oxford has not released them in its public PDF archive.

Answers and worked solutions

Every question has an answer checked against its official key. 459 questions have worked-solution images: Oxford’s MAT solutions, plus Physics & Maths Tutor’s available ENGAA 2016–2020 and NSAA 2016–2019 model solutions. The remaining questions show the official answer key and are clearly labelled. Some model solutions are handwritten; multi-page working appears in reading order.

1. Attempt the question first. Work on paper and choose the answer letter shown in the original image.
2. Check and review. Check your answer to see the correct option and available solution. Revealing an answer without attempting it is tracked separately from your score.
3. Build a focused practice set. Use topic and difficulty filters to work on weak areas, then return to year-based practice for a broader mix.

Your answers stay recorded as you switch papers and filters while the page remains open. Restart selection clears only the questions currently selected. A new tab opens the same filters and question, with a fresh practice session.

Turn every past-paper question into progress

MAT questions offer extra practice in mathematical reasoning and unfamiliar problems. ENGAA and NSAA mathematics questions provide a useful pool of historical ESAT-style practice. These are historical MAT, ENGAA and NSAA questions, rather than official TMUA or ESAT past papers. Match your practice to the current specification: some older questions test material outside the current syllabus.

Attempt. Review. Revisit. Start with a topic you want to improve, then use mixed questions to practise choosing the right method. Work against a timer when you are ready. Before opening a solution, commit to an answer; afterwards, identify the clue you missed, the step that cost time or the distractor that caught you. Return to that question a few days later without your notes. This bank supports practice and review; it does not estimate an official TMUA or ESAT score.

Sources and credits

Original papers and answer keys: the Oxford Mathematical Institute MAT archive and UAT-UK ESAT preparation materials. Model solutions: Physics & Maths Tutor ENGAA and Physics & Maths Tutor NSAA. Copyright remains with the respective owners. PMT solutions are credited under CC BY-NC-ND 4.0; source links appear beside each solution. Thriving Scholars is an independent provider.

Continue your TMUA and ESAT preparation with Thriving Scholars

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