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Test of Mathematics for University Admission (TMUA)

The TMUA is taken by applicants for Economics and Computer Science courses at many of the UK’s most competitive universities. But what does the TMUA involve and how can you prepare for it?

What is the TMUA?

The Test of Mathematics for University Admission (TMUA) is a Maths assessment used by some universities to assess applicants for the following courses:

  • Computer Science
  • Economics

Universities will use the results of the TMUA, alongside the other aspects of your application, to help them decide which students to make offers to. Scoring well might also mean that universities make you an offer with lower entry requirements.

Currently, the universities which use the test are:

  • University of Cambridge
  • University of Bath
  • Cardiff University
  • Durham University
  • Lancaster University
  • London School of Economics and Political Science
  • University of Nottingham School of Mathematical Sciences
  • University of Sheffield
  • University of Southampton
  • University of Warwick

What does the test involve?

The TMUA lasts for 2 hours and 30 minutes, and is divided into two parts:

  • Part 1: Applications of Mathematical Knowledge
  • Part 2: Mathematical Reasoning

Both parts last 75 minutes, and consist of 20 multiple-choice questions. Calculators and dictionaries are not allowed.

Part 1 assesses your ability to apply your existing mathematical knowledge to new contexts and problems. The first paper will test the candidate’s ability to apply their mathematical knowledge in a variety of contexts. Topics you will be expected to know include:

  • Algebra and functions
  • Coordinate geometry in the (x, y) plane
  • Differentiation
  • Exponentials and Logarithms
  • Geometry
  • Graphs of Functions
  • Integration
  • Measures
  • Number
  • Probability
  • Sequences and series
  • Statistics
  • Trigonometry

Part 2 focuses on mathematical logic and reasoning. As well as the content above, you will need to know:

  • The Logic of Arguments
  • Mathematical Proof
  • Identifying Errors in Proofs

Sitting the TMUA

Registration and costs

To sit the TMUA, you need to be registered in advance. The assessment must be taken at a Pearson VUE test centre – there are locations in 180 countries. You register via the Pearson VUE website.

The entry fee for the test is £75 in the UK or Republic of Ireland, or £130 elsewhere. Bursaries are available for UK candidates in financial need.

Exam dates

For the 2024/25 application cycle, there are two sittings of the TMUA.

  1. 15 or 16 October 2024
  2. 7 or 8 January 2025

Cambridge applicants must take the test in the October sitting. Applicants to other universities can take it in either the October or January sitting.

If you are sitting the TMUA in October 2024, you will need to register between 1st August and 16th September 2024. If you are sitting it in January 2025, register between 24th October and 9th December 2024.

What is a good TMUA result?

There is no set pass or fail mark. Applicants will have their score considered alongside the other elements of their application – like the personal statement, A Level or equivalent predicted grades, and possibly interview.

The test is scored on a scale of 1.0 to 9.0. The average score is around 5.4, with the top third of applicants scoring above 6.5. Above 6.5 would therefore be considered a strong result.


The Mathematics Admissions Test (MAT) is an assessment for students applying to Maths and related courses at the University of Oxford and Imperial College, London. There is no need to take it unless you are applying for relevant courses at these universities.

The Sixth Term Examination Paper (STEP) is a Maths assessment, taken in the summer term of Year 13 by applicants who have been given a conditional offer to study Maths at the University of Cambridge. It is not compulsory for any other universities.

Anecdotally, the MAT and STEP are often considered more challenging than the TMUA.

How to prepare

The foundation of the test will be Maths which is covered at the higher level of the school curriculum (for instance, A Level Maths and Further Maths, or IB Higher Level Maths). Revising your school Maths curriculum will therefore be a vital first step. However, as the test is designed to sift between very strong Maths students, the highest marks will be reserved for those who are working at a level beyond the school curriculum.

You can read the TMUA specification here to find out what may be asked. You should review this carefully and consider which areas you are weaker on in order to target your revision. Then make use of the official practice materials to familiarise yourself with the format of the test and the type of questions asked in the TMUA. Doing this in timed conditions will help you get used to what you will be facing on the day itself.

One-to-one preparation from a private tutor experienced in the TMUA can make all the difference. Our tuition is delivered by expert tutors who have years of experience in helping students secure top grades in the TMUA. They know the requirements of the assessment inside-out and are familiar with the common challenges students face, enabling them to target their preparation effectively and to help applicants achieve outstanding results.

Private tutors for the TMUA

  • Alex H

    Alex H

    Alex is a specialist Maths tutor who works with students from 11+ to Oxbridge level. Additionally, he works with students on their Oxbridge admissions.

  • Samuel


    Samuel is a qualified teacher and highly experienced tutor who specialises in Physics, Biology, Chemistry, Mathematics, Study Skills and 11+ preparation.

  • Greg


    Greg specialises in Maths tuition up to Undergraduate level and Physics up to A-level and both the IB Standard Level and Higher Level.

  • Mustafa


    Mustafa is Mathematics and Entrance Examination tutor who specialises in online teaching. He has worked with Simply Learning Tuition for over three years.

  • Imran


    Imran is a Maths specialist, supporting students from Key Stage 3 up to A Level.

  • Haris J

    Haris J

    Haris specialises in Business Studies, Economics, Accounting and Statistics tuition and is a qualified Chartered Accountant.

  • Ritchard


    Ritchard is a highly experienced tutor who prepares students from 11+ to A-Levels and IB, in a range of subjects.

  • Luke


    Luke specialises in Maths and Physics tuition. He also teaches Economics, Chemistry, Biology and competitive Entrance Exam preparation.

How to get the test results

You will receive your results in the Pearson VUE test portal around 6 weeks after taking the test. These results will be automatically shared with the universities you are applying for.

Past and practice papers

Official TMUA practice materials are available here. You can also access TMUA past papers here.

Frequently asked questions

  • Which universities use TMUA?

    A number of universities use the TMUA to assess applicants for Computer Science and Economics courses. These include Cambridge, Bath, Durham, Lancaster, Warwick and several others.

  • Is 7 a good TMUA score?

    Around a third of TMUA applicants score above 6.5/9.0, so a score of 7 would put you in the upper bracket of students.

  • Is 5.1 a good TMUA score?

    A score of 5.1 in the TMUA is a little below the average score of 5.4. Bear in mind that the TMUA is used to sift between very strong Maths students, so a score slightly below average can still be taken as a positive by universities. For instance, Durham University use a score of above 4.5/9.0 as positive evidence of mathematical ability.

  • What is the average TMUA result?

    The average TMUA score is around 5.4/9.0.

  • How much does the TMUA cost?

    The entry fee is £75 in the UK or Republic of Ireland, or £130 elsewhere in the world.