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 3,284 free TMUA, MAT, ENGAA, NSAA, AMC 8 and AMC 10 multiple-choice problems—with paper, topic and difficulty filters, instant answer checks and worked solutions where available, all in one digital question bank.

Your next useful practice session starts below. Choose By topic to tackle a weak spot, add a difficulty level, or choose By paper 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 TMUA, MAT, ENGAA, NSAA, AMC 8, AMC 10 or any combination. In topic mode, practise areas such as algebra, geometry, number, combinatorics, trigonometry, coordinate geometry, calculus, probability and sequences. Questions with more than one relevant topic appear under each of those filters. Add a difficulty level to narrow your selection. In paper mode, choose a paper and move through its questions in their original order.

3,224 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. TMUA and AMC questions retain their supplied topic classifications, including secondary topics where a question genuinely tests more than one area. The extra MAT specimens and supplementary tests remain available by paper; they are not included in topic filtering.

Which TMUA, MAT, ENGAA, NSAA and AMC questions are included?

Only maths multiple-choice questions appear in this bank. The TMUA collection keeps Paper 1 and Paper 2 separate within every specimen or annual set, while AMC 8 and AMC 10 papers retain all 25 original problems. Physics, chemistry, biology and long-answer questions are excluded. ENGAA and advanced NSAA sets may therefore 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 a checked answer. All 360 TMUA questions and all 230 MAT questions include official worked-solution images, while all 2,325 AMC problems show a written worked solution. Where a TMUA solution continues onto another page, every relevant part appears in order beneath the answer. The 369 ENGAA and NSAA questions show the official answer key and are clearly labelled, so students can check the correct option without relying on third-party model solutions.

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

The TMUA archive contains the historical official specimen and annual papers released from 2016 to 2023. MAT questions offer extra practice in mathematical reasoning and unfamiliar problems, while ENGAA and NSAA mathematics questions provide a useful pool of historical ESAT-style practice. Match older material to the current specification: some questions may test topics or presentation styles that are no longer central to the current exam.

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

Historical TMUA papers and worked answers were originally released by Cambridge Assessment Admissions Testing and its successor preparation services. MAT papers and worked solutions come from the Oxford Mathematical Institute MAT archive; ENGAA and NSAA papers and answer keys come from UAT-UK preparation materials. AMC contest papers, questions, answer choices and original figures are from the Mathematical Association of America (MAA). This free digital practice presentation organises the material with paper, topic and difficulty filters alongside worked explanations. Copyright remains with the respective owners. Thriving Scholars is an independent provider and is not affiliated with or endorsed by MAA.

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