TMUA Past Papers

Practice makes perfect when preparing for the Test for Mathematics for University Admission (TMUA). Here we’ve compiled TMUA past paper questions, answers and worked solutions to help you with your revision.

Although the TMUA is now computer-based, both the content specification and question style are unchanged.

More details about the TMUA, including format, scoring, and common mistakes can be found on our complete TMUA guide.

If you want support beyond these TMUA questions and solutions, please reach out to our tutoring team.

TMUA Specification

Frequently Asked Questions

  • You can book the TMUA through the official UAT website. You can sit the TMUA at authorised computer-based test centers worldwide. Registration opens several months before each sitting. It’s important to register early and double check that the test date does not clash with other admissions tests or school commitments.


  • Unlike the A levels, IB or APs, the TMUA assesses your mathematical thinking ability, not just syllabus coverage. Universities use it to evaluate how students reason, make decisions under time pressure, and work through unfamiliar problems using core mathematical concepts. The TMUA focuses on logical reasoning, fluency with algebra and functions, precision and accuracy, and the ability to eliminate incorrect options efficiently. 

    For competitive courses at top universities, the TMUA is used before the interview to shortlist candidates.

  • The TMUA is scored from 1.0 to 9.0, with 1.0 being the lowest score and 9.0 being the highest score. 5.4 is the average score in previous years. The scale is designed such that approximately a third of candidates will achieve scores higher than 6.5. Thus applicants should aim for a score of above 7.0 to be competitive. A strong score can significantly strengthen an application, while a weak score can raise concerns even for students with strong academics.

  • The TMUA consists of two papers, each lasting 75 minutes. All questions are multiple-choice and non-calculator. On average, students have just over two minutes per question, which means efficient decision-making is crucial.

  • Most successful applicants prepare for the TMUA over several months, rather than weeks. Because the test focuses on reasoning and problem-solving rather than content revision, improvement takes time. Preparation is most effective when it is consistent, reflective, and supported by feedback, rather than based on last-minute practice alone.

  • The TMUA is not harder in terms of content, but it is more demanding in terms of thinking. Questions are based on material students have typically encountered at school, but they are presented in unfamiliar ways and under tighter time pressure. Many high-achieving A-level or IB students find the TMUA challenging and may benefit from expert guidance.

  • Calculators are not allowed when taking the TMUA.