Test of Mathematics for University Admission (TMUA)

"Beyond a thorough understanding of A Level Mathematics and Further Mathematics, a student needs two qualities to thrive on a demanding university Mathematics degree. The first is the ability to solve problems and apply knowledge in unfamiliar settings. The second is the capacity to cope with abstraction and generality, and to understand proofs. Preparing for TMUA is a great way of nurturing these qualities, and getting ready for university mathematics."

Professor Samir Siksek,
University of Warwick

About TMUA

Select students with the best chance of success on challenging undergraduate Mathematics courses with our Test of Mathematics for University Admission (TMUA).

This maths admissions test focuses on the mathematical thinking and reasoning skills needed for progression to university mathematics. It gives students an extra opportunity to prove their potential, whatever their background.

Why use TMUA?

TMUA focuses on skills crucial for success in mathematics, such as applying standard knowledge in unfamiliar situations and mathematical reasoning – skills not typically tested in school qualifications.
Our research shows a positive relationship between test scores and the first year of undergraduate academic performance, helping you identify students with the best possible chance of success on-course.
Developed in consultation with leading UK universities, the test meets university requirements and has been trialled to confirm its effectiveness.
It is used as a trusted benchmark in a changing educational landscape, helping you to fairly compare students across a broad range of changing qualifications at home and overseas. Our global network of test centres also enables many applicants to take the test in their home country.

Who uses TMUA?

The test is currently taken by students applying to undergraduate Mathematics and related courses. Leading institutions that use the test include Durham University, the University of Warwick, the University of Bath, the University of Cambridge, the University of Nottingham, Lancaster University, Cardiff University, the University of Sheffield, the University of Southampton and the London School of Economics and Political Science.

Consider making TMUA an optional part of a student’s application (e.g. to support alternative offer-making), or a compulsory requirement of your admissions process.

Test format
Test delivery and costs
Preparing for the test
Test research

Test format

The Test of Mathematics for University Admission is 2 hours 30 minutes long and includes two multiple-choice papers which are taken consecutively. Find the full test format and its content in our Test of Mathematics for University Admission test specification.

Paper	What does it test?
Paper 1: Applications of Mathematical Knowledge	Focuses on assessing candidates’ ability to apply knowledge of mathematics in new situations. View a Paper 1 sample paper
Paper 2: Mathematical Reasoning	Focuses on assessing candidates’ ability to deal with mathematical reasoning, and simple ideas from elementary logic. View a Paper 2 sample paper

Test delivery and costs

Our global network of test centres allows applicants to typically take the test in their own country. This means your selection procedure is accessible to all applicants, and quick and convenient for your staff.

There is currently one test date per year – in late October/early November.

We believe all applicants should have an equal opportunity to prove they have what it takes and we ensure test fees are affordable, so they do not present a barrier to students entering university. We can also make arrangements with universities to provide reimbursement of test fees for financially disadvantaged students, as we do for UK/EU students applying to UK universities.

Preparing for the test

We support test-takers with free preparation materials to help them prepare for the test, including past papers and an introductory video. There is no need for students to attend additional courses.

To ensure that the test is accessible to all applicants and minimise the amount of new learning needed, it focuses on knowledge and skills that should already be familiar to applicants.

The Test of Mathematics for University Admission is designed to have a positive impact for test-takers. Any time spent preparing for the test helps test-takers develop skills directly beneficial for their future academic studies.

Test research

We conduct extensive research to ensure the validity and fairness of the Test of Mathematics for University Admission. Our test is guided by an established mathematical taxonomy which divides mathematics questions into three skill groups:

dealing with routine questions and procedures, similar to those likely to have been encountered before
applying standard knowledge in unfamiliar situations
reasoning, justifying, and proving assertions couched in a broadly mathematical manner.

While school mathematics qualifications tend to focus on group A, the Test of Mathematics for University Admission is designed to assess a student’s potential to deal with groups B and C, which are key for success in university study.

To ensure accessibility for students, the knowledge required to tackle the test questions is restricted to foundational pure mathematics.

Initial research has shown a positive relationship between scores on the test and first year academic performance. An ongoing programme of research will help to ensure the validity and reliability of the test.

Find out more about our research agenda and approach here.