How to Prepare for the TMUA

The TMUA (Test of Mathematics for University Admission) is a Maths-based admissions test used by a handful of top universities, including Cambridge. The aim of the TMUA exam is to help universities assess your ability to understand A-level Maths and your suitability for a Maths-based degree.

Preparing for the TMUA exam can be a challenging and demanding undertaking. The assessment not only tests your mathematical knowledge, but also your logical thinking skills and ability to solve mathematical problems.

That’s where The Profs’ experienced TMUA tutors can help. With first-hand experience of the exam content and skills required and an understanding of how it fits into the wider admissions process for top universities, our tutors are able to help you get the best possible TMUA grade and secure a place on your first choice Mathematics-based course.

What is the TMUA?

The Test of Mathematics for University Admission (TMUA) is an admissions test used by a handful of top universities, including Cambridge, to assess your mathematical ability – both your subject knowledge and mathematical thinking skills. While the content is based on A level Maths, it is designed to separate out the most competent applicants to the top universities in the UK, so it is challenging and requires plenty of preparation.

Which universities require the TMUA?

The TMUA is only required for courses at Cambridge and Imperial College London.

However, the TMUA is recommended in some instances for the following universities:

  • The University of Bath.
  • Durham University.
  • London School of Economics (LSE).
  • The University of Sheffield.
  • Lancaster University.
  • The University of Warwick.
  • The University of Southampton.

Either way, when it comes to competitive courses, taking the TMUA could help your application stand out from other applicants. It’s especially a good idea if you’re looking for a reduced grade offer.

The table below shows some of the universities and courses that the TMUA is required/recommended for.

UniversityCourses the TMUA is required forCourses the TMUA is recommended for
University of CambridgeComputer Science


Imperial College LondonUndergraduate courses in the Department of Computing, including joint Mathematics and Computer Science plus the BSc Economics, Finance and Data Science.
University of Bath*Mathematical Sciences

Mathematics and Statistics

Mathematics, Statistics and Data Science


Durham University*Mathematics

Mathematics and Statistics

Lancaster UniversityMathematics

Mathematics and Philosophy

Mathematics and Statistics

Mathematics, Operational Research, Statistics

and Economics (MORSE)

Financial Mathematics

Computer Science and Mathematics

London School of Economics (LSE)Mathematics and Economics

Mathematics with Economics

Financial Mathematics and Statistics

University of Nottingham*Mathematics

Financial Mathematics

Mathematics and Economics

University of Sheffield**Mathematics

Mathematics and Statistics

Economics and Mathematics

Mathematics and Philosophy

Financial Mathematics

Mathematics with French/Spanish/German

University of Southampton*Mathematical Physics


Mathematical Sciences

Mathematics with Computer Science

Mathematics with Actuarial Science

Mathematics with Finance

Mathematics with French/Spanish/German

Mathematics, Operational Research, Statistics and

Economics (MORSE)

University of Warwick*Mathematics

Mathematics and Statistics

Mathematics, Operational Research, Statistics and


Data Science

* STEP and/or MAT are also accepted

Top tip: In many cases, the TMUA is just one of two or more admissions tests accepted by a university for Maths-based courses. You should therefore do your research into each of the tests before you commit to taking the TMUA. Each admissions test has a slightly different format and contains different content, and it may well be the case that you feel that one is slightly better suited to your skills.

It’s also worth noting that while Cambridge uses the TMUA for Economics and Computer Science, other universities tend to use it explicitly for Mathematics or joint Maths courses. Cambridge, by contrast, uses STEP for Mathematics admissions, so if you’re applying to both Cambridge and other universities for Maths, STEP may be the better option.

If you’d like some advice on which admissions test to take for the courses and universities you’re applying to, get in touch with our team. We can match you up with a professional TMUA tutor who can provide personalised advice on which test to take, what score you’ll need to be aiming for, and how to prepare.

What is included in the TMUA exam?

The TMUA is a non-calculator Mathematics test which lasts for 2 hours 30 minutes. It has two papers which are taken consecutively.

Paper 1 tests your ability to apply your mathematical knowledge in new situations. It consists of 20 multiple-choice questions and lasts for half of the total exam time (75 minutes).
Paper 2 tests your mathematical reasoning skills and apply your conceptual knowledge to
constructing and analysing mathematical arguments. It also consists of 20 multiple-choice questions and lasts for the remaining 75 minutes of the exam.

The content you are expected to know for section 1 of the TMUA is listed in the 2021 Test Specification. It includes:

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

Section 2 requires candidates to understand how to think in a mathematical way, including the logic of arguments, mathematical proof and identifying errors in proofs. This content is detailed in the TMUA Notes on Logic and Proof. More information on this can be found in tip 1 under ‘How to prepare for the TMUA’ below.

How is the TMUA exam marked?

Each question in the TMUA is worth 1 mark, meaning there are a maximum of 40 marks available in the whole exam. This number of marks will then be converted into a scale from 1.0 (low) to 9.0 (high). The scale has been designed so that approximately one third of candidates will achieve overall scores higher than 6.5, therefore the grade boundaries differ from year to year depending on the particular cohort of students.

The formal score you will be given in the TMUA will be based on your overall performance across both papers. You will also be given scores for each of the two papers using the same scale, however these are just for your information.

The TMUA is not negatively marked, so it is recommended that you answer as many questions in the allotted time as possible.

What TMUA score do you need to get?

What is considered a ‘good’ TMUA score depends on the university you’re applying for. Some universities specify a cut-off score for considering applicants and, in most cases, the TMUA is not a requirement but a recommendation, so you can choose whether or not to submit your result based on what score you get. The table below shows the TMUA cut-off scores for each university.

UniversityTMUA cut-off score
University of Cambridge
University of Bath
Durham University6.5 or above = automatically eligible for a reduced offer
Below 6.5 to a certain threshold (around 4.5) = used as positive evidence of your mathematical ability
London School of Economics (LSE)
University of Sheffield5.0 or above

Cambridge does not publish cut-off scores for the TMUA, however there is some data on the average score of offer holders in previous years. See the table below for the most recent average scores of applicants and offer holders on Cambridge’s Computer Science course.

Average score of applicantAverage score of offer holder
Computer Science (2021)4.76.9

When is the TMUA exam?

The TMUA usually takes place in October. You must ensure you have registered for the test through an authorised test centre (see below) before the end of September to ensure that you are eligible.

How do you register for the TMUA?

To register for the TMUA, you will need an authorised test centre to register you on your behalf. For most candidates, their authorised test centre is their school or college, however, you should check this with your Exams Officer to make sure. If your school or college is not authorised, they can register to become a test centre at any time before the specified date in September. Alternatively, you can find an open test centre to register with. You can find your nearest test centre via the Pearson VUE website.

You can register from early September, and you must have your candidate entry number as proof of entry by the end of September.

Please note that while registration is automatic for some admissions assessments at Cambridge, it is not automatic for the TMUA, so you must register through a test centre before the end of September.

Dates can change year to year so ensure that you check the dates for your application year and circumstances.

How much does the TMUA cost?

Pearson VUE does charge candidates to take the TMUA. The costs differ depending on where you are planning on taking the test. There are also additional costs if you choose to enquire about your results or apply for an appeal. See the table below for TMUA costs (these prices are subject to change as the TMUA has been adopted by Pearson VUE from the CAAT).

Registration fee within the UK and EU£75/€88
Registration fee outside of the EU£100/$137
Application for results enquiries£38/€45/$52
Application for appeals£38/€45/$52

Note that some test centres may also have an additional administration fee. Speak to your local test centre for details on this.

When can you find out your TMUA results?

The TMUA results are released on 29th November. You can find out your TMUA results by logging onto the Metritests system and entering the details from your Confidential Results Information sheet given to you on the day of your test.

If you would like to apply for a Results Enquiry, you will need to do this by 5th December.

How do your chosen universities receive your TMUA results?

Unlike almost all other admissions tests, TMUA results are not automatically shared with most universities. You will therefore need to share your results with your chosen universities manually. You can do this by logging onto the Metritests system and selecting which universities you want to receive your results.

It’s best to share your results with your chosen universities as soon as possible once the results have been released. This will help to ensure the universities receive them in good time and are able to take them into consideration during the deliberation process.

The only exception to this is for the University of Cambridge. TMUA results will be sent directly to Cambridge if you have applied there. You won’t find Cambridge on the Metritests system for that reason.

4 tips on how to prepare for the TMUA

1. Focus on developing your mathematical thinking skills

The focus of the TMUA is not only on your specific subject knowledge (section 1), but on your logical and mathematical thinking skills (section 2). It may be tempting to leave out preparation for section 2, assuming that you have the necessary skills simply through studying Maths at school, however it is extremely important to prepare just as you would for section 1.

You should use the TMUA Notes on Logic and Proof as a key resource when you’re preparing and treat it with equal importance to the subject content you’ll need to revise. The Notes on Logic and Proof is a 67-page document that details the concepts and skills you’ll need to have in order to succeed in the exam. These are:

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

It’s best to read through this resource and familiarise yourself with the concepts above before attempting any past papers so that you have a solid understanding of what is expected and how to go about answering the questions. You may not have encountered questions like those in section 2 before, so we suggest leaving yourself plenty of time to develop the necessary skills and avoid leaving it until the last minute!

2. Go through the content specification closely

Cambridge Assessment Admissions Testing (CAAT) also releases a content specification for section 1 of the TMUA which details the topics you are expected to know for the exam. Now that the test has been taken over by Pearson VUE, you should also keep an eye on their website. You should go through this specification carefully, checking off what you have covered previously in school and making a note of any areas you have not covered. This will ensure that you can pay closer attention to those topics which you have not covered, haven’t covered in as much depth, or that you don’t understand as well, during your preparation.

3. Practise past papers under timed conditions

Once you’re familiar with the style of TMUA questions and know how to go about answering them, start attempting past papers under timed conditions. This will help you to gauge what sort of pace you work at and how long you should be spending on each question in order to complete the paper in the 2.5 hours provided.

Once you’ve finished a past paper, it’s also a good idea to mark your answers. CAAT provides worked solutions to each of the past papers which will not only help you gauge what marks you’re getting and what score you might expect in the real exam, but also help you to learn the correct solutions to the questions.

4. Seek help from a TMUA expert

How you perform in the TMUA will impact how likely you are to be offered a place by top universities, so it’s really important that you are prepared to do as well as possible in the exam. Unfortunately, schools and colleges are oftentimes not equipped to provide specialist TMUA preparation due to a lack of experience, expertise or resources. As a result, we advise seeking a professional TMUA tutor to help you through the process.

The Profs’ TMUA tutors have many years of experience preparing students for the TMUA exam, with many having actual experience as exam and admissions officers as well. Over these years, they have built a bank of previous questions and developed in-depth knowledge of the mark scheme, so they know exactly what examiners will be looking for.

If you work with one of The Profs’ tutors, you are more than three times more likely to get into Cambridge, which is ranked as the best university in the UK to study Computer Science. You’ll also have a 95% chance that you will receive an offer from your first or second choice university to study your chosen Maths, Statistics or Economics degree course when working with us.

Plus, you can trust us to guide you through every stage of the admissions process to ensure that you don’t just succeed in the TMUA, but also achieve top A level or IB grades and perform well in your interview. Reach out to our experienced team today to get started.