Test of Mathematics for University Admission (TMUA)

The TMUA is a compulsory exam for Computer Science and Economics applicants to the University of Cambridge.

Next Exam
15th-17th October 2024
Prerequisite knowledge
A level/IB first year
Download our comprehensive TMUA Handbook
For students, parents, and teachers

About the TMUA

The Test of Mathematics for University Admissions (TMUA) is used by some UK universities as part of their undergraduate admissions process for courses in mathematics, computer science, economics, and related subjects. The TMUA allows students to demonstrate the thinking and reasoning skills required to study mathematics or mathematical science courses at university level. It is the most time pressured of the university admissions tests, so requires diligent practice to master.

The test is designed to differentiate between the highest achieving students. There is no pass or fail mark for the test, and a ‘good’ score will depend on the university course applied for. The results of the test are used in different ways by different universities. For example, scores are considered in the process shortlisting Cambridge candidates for interview and determining reduced grade offers. Good TMUA scores generally support a student's university applications by providing additional standardised information.

Our TMUA Handbook is a free resource for students, parents, and teachers. It details the admissions test requirements for each university, our recommended preparation plan, our timing recommendations, and useful exam technique tips.

Format and Content
Key Information
  • Pearson VUE is administering the TMUA from 2024. There may be small changes to the specification, with full details expected in Spring 2024.
  • The TMUA comprises two papers, each lasting 1 hour and 15 minutes, which are taken consecutively. Both papers consist of 20 multiple choice questions.
  • Paper 1 (Applications of Mathematical Knowledge) assesses a candidate’s ability to apply their knowledge of mathematics in unfamiliar situations.
  • Paper 2 (Mathematical Reasoning) assesses a candidate’s ability to deal with mathematical reasoning, and simple ideas from elementary logic.
  • The TMUA is designed to test candidates' problem solving ability rather than breadth of knowledge beyond first year A Level/IB content.

The following universities take the TMUA into consideration as part of their admissions process:

Vantage Preparation Courses for the TMUA

To many students, the TMUA seems like an overwhelming obstacle in the university admissions process, far surpassing any of their previous exams in difficulty and time pressure. With rigorous preparation and practice, students can reliably improve their score. Vantage programmes provide TMUA tuition and personalised preparation strategies, which have led many students to admission at their first-choice university. .

The Vantage TMUA programme consists of five key elements which give students the best chance of success on the TMUA:

TMUA Primer Course

Unique to Vantage, the TMUA Primer Course is the most comprehensive TMUA preparatory course. It bridges the gap between A level (or equivalent) content and the TMUA, both introducing new techniques that go beyond the A level and offering new perspectives on the school-level material used in the exams. It also covers in detail the ideas from logic and proof which feature prominently on Paper Two. The course includes 10 lessons, in video and written form, each providing a systematic and thorough introduction to a prominent theme of TMUA questions. Each lesson has an accompanying worksheet with detailed solutions, and in total there are more than 200 original questions to ensure students master the necessary skills. Please note, our current TMUA Primer Course is designed for the 2023 exam specification. We expect only minimal changes to the specification in 2024 due to the change in administration, and the TMUA Primer Course will be updated accordingly, including for students who have already enrolled on the programme. Details of the new specification are expected by May 2024.

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Past Paper Solutions

Our TMUA programme includes detailed past paper solutions (in video and booklet form) for all TMUA past papers, as well as solutions for over 25 years of MAT multiple-choice questions (1996-2022) for extra practice. The solutions were written and delivered by our founding director, Rowan Wright, and designed in consultation with our team of qualified teachers, admissions test examiners, and Oxbridge supervisors. Rather than merely presenting a method which works, the solutions focus on how a student can generate the required ideas and think through a problem systematically. This enables students to gain the full benefit of past paper practice, coming away from each question with a complete understanding and ready to tackle variations in future. Due to the relatively small number of TMUA past papers available, we also provide an original TMUA-style practice paper, complete with solutions.

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Mentoring Sessions

All Vantage students have the benefit of regular mentoring sessions over the course of their exam preparation, ideally attended along with their parents/guardians. All meetings are held with our founding director and are completely tailored to the student’s specific goals. The aim of these sessions is to review students’ progress, address doubts or concerns, provide motivation, and create actionable plans to resolve any difficulties. Personalised mentoring enables students to ensure they are staying on track for success and provides vital support over what is often a long process of preparation.

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Individual Tuition

Many Vantage students opt to include individual tuition as part of their TMUA course. It is the most personalised support we offer and ensures any and all doubts can be addressed, whether they pertain to specific questions or broader topics and concepts. It also provides an opportunity for students to explore questions further, pursue their own interests, and – most importantly – ask questions. Beyond merely understanding a successful approach to a question, it’s very important for students to understand why their approach to a question didn’t work, which is uniquely well-served by one-to-one discussion with a specialist TMUA tutor. Discussion can be also particularly beneficial for mastering the ideas from Logic and Proof which feature in Paper Two.

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Live Workshops

All Vantage students are invited to attend our interactive online problem solving workshops over the summer. Run each week by Olympiad enthusiast, problem solving aficionado and expert TMUA tutor Carlo Scarian, these classes provide a fun change of pace from the more technical focus of our Primer Courses and the rigidity of past paper problems, instead focusing on general problem solving principles and cultivating the mindset of a mathematician. Students are given access to some problems to think about before each session to gain the most benefit.

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We offer a comprehensive programme for TMUA preparation and individual tuition available to book on an ad hoc basis.

TMUA Programme '24

Course Summary

With access to extensive, high-quality resources, personalised mentoring, and live workshops, students are given the best chance of success on the TMUA.

  • Complete access to the TMUA Primer Course, including worksheets and solutions
  • Additional TMUA practice paper designed by the Vantage team
  • Complete access to solution videos and booklets for all TMUA past papers and MAT multiple-choice questions
  • Access to all live problem solving workshops over Summer 2024
  • Three mentoring sessions with Vantage founding director, Rowan Wright
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Individual Tuition


Our specialist TMUA tutors help students develop an instinct for problem solving and build confidence. Most students benefit from some individual support.

  • One tuition credit costs £150 and is redeemed for 1 hour of individual tuition.
  • Tuition can be used for troubleshooting any concerns with past papers, to fortify weaker topics, or for hands-on training in problem solving.
  • Tuition is provided by highly qualified members of the Vantage team, including admissions test examiners, Oxbridge supervisors, and qualified teachers. Nothing is outsourced to undergraduate students.
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Book a free consultation with our founding director, Rowan Wright, and:

Discuss your university course choices

Determine the most advantageous admissions test combination for your chosen courses

Formulate a personalised preparation strategy and receive actionable advice

Discuss Vantage course options

Hear from our students

"Rowan from Vantage is the real deal, a rare blend of being a sufficiently brilliant mathematician to have a complete, deep and intuitive grasp on the difficult problems set in admissions tests, but also a great teacher who is able to explain the thought process in a way students can understand. I cannot recommend him highly enough."

Achieved 1 in STEP II and S in STEP III