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Test of Mathematics for University Admission (TMUA) Guide

Everything you should know before taking the TMUA and how to be successful!

**Please be aware that from the 2024 application cycle onwards, the TMUA is no longer being run by Cambridge Assessment Admissions Testing (CAAT), the company which has previously administered it. The test is now being administered by UAT (University Admissions Tests) UK. This guide is for the TMUA as administered by UAT UK.**


The Test of Mathematics for University Admission (TMUA) is an admissions test used by Cambridge University for applicants to degree courses where mathematical skills are required (but not the mathematics course itself). The TMUA is tailored specifically for candidates applying to maths-intensive courses at Cambridge. By focusing on mathematical concepts, problem-solving abilities, and analytical thinking, the TMUA enables Cambridge University to identify students who not only possess a passion for mathematics but also demonstrate the intellectual acumen required to excel in their chosen courses.


Applicants for Cambridge University wishing to study Computer Science or Economics will be required to sit the TMUA as part of their application. Other UK universities also use the TMUA for various maths-related courses. These are: University of Bath, Cardiff University, Durham University, Lancaster University, LSE, University of Nottingham, University of Sheffield, University of Southampton, and University of Warwick.

If you’re applying for Cambridge and have heard of the ECAA Cambridge, or Economics Admissions Assessment, then you might be asking yourself why we haven’t mentioned this test. The ECAA is an older, Cambridge-specific admissions test that Cambridge University used to use for its economics applicants but, from the ECAA 2022 onwards, it has been replaced by the TMUA. If you’ve been preparing for the ECAA either by mistake or for a precious year’s application, don’t be disheartened! Prepping for this test or going through ECAA past papers will still help prepare you for the TMUA and an economics course in general.


The TMUA is made up of two sections, each 75-minutes in length and consisting of 20 multiple-choice questions. The first paper is on Applications of Mathematical Knowledge, whilst the second paper is on Mathematical Reasoning. The first paper is aimed at assessing your ability to apply your mathematical knowledge to new situations, whilst the second paper gives admissions tutors the chance to see your ability to deal with mathematical reasoning, and simple ideas from elementary logic.


Applicants do not have a choice of questions as part of the TMUA exam.


Cambridge University uses the TMUA as a standardised format for assessing and benchmarking their applicants. The exam rewards problem solving over knowledge of particular mathematical knowledge such as formulae, so that students taking different qualifications at school can access the syllabus.

Cambridge uses students’ marks in the TMUA to make decisions about which applicants they should invite to interview, giving them a further indicator in addition to predicted and achieved grades. Whilst the TMUA is important in their selection processes, it is always used as part of a matrix and considered alongside other factors submitted with the application, such as predicted grades and personal statement.


The raw points achieved on the TMUA are converted into a score between 1.0 and 9.0, with 9.0 being the highest score. A score over 6.5 is generally considered to be a good TMUA score, with only the most exceptional students achieving above this. A grade of 6.5 or above makes for a very competitive university application. The average TMUA score is between 4.0 and 6.5, so a score in this range will not make you stand out, but likewise probably will not become a barrier to being invited to interview.


The TMUA syllabus is designed so that students taking a wide variety of qualifications or have a background in international education systems can access the mathematic content. However, it is more focused around the UK education system and the general concepts covered in GCSE and A-level. We recommend that students cross-reference their knowledge with past TMUA papers. We also have specialist tutors who have experience of advising students taking other qualifications and help them fill in knowledge gaps.

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How to register for the TMUA


The test date for the TMUA in 2024 is the 16th and 17th of October, meaning that all applicants will have to sit the test on one of these two days. This may be during half term, but with plenty of advanced notice this hopefully shouldn’t prevent your school or college from holding the test. Be aware that if you miss this date for whatever reason you will not be able to take the test on another day and your application will not be considered.


The TMUA, like many UK university Admissions Tests, requires applicants to register in advance of sitting the test. 2024 applicants will have to register between the 1st of August and the 16th of September to be able to sit the test (although the deadline for many access arrangements is the 29th August, so be sure to register early if you’re likely to need special arrangements of any kind!).

An applicant cannot register themselves for the test, but must be registered through an official test centre. For most candidates this will be their school or college, but if not it can be done through an open test centre. We recommend reading the Cambridge Assessment Admissions Testing website for more details on how to register. However you register, make sure that you have submitted all your details to the test centre and have received your candidate entry number as proof of entry by midnight on the 16th of September, but ideally at least a few days before to account for emergencies! If you have extenuating circumstances (i.e. a situation beyond your control) that prevented you from registering on time, get in touch with the University or college you applied to immediately and alert them of your situation.

If you’re struggling to keep on top of dates and deadlines, head to our website to download our free University Application Calendar, which features registration deadlines and test dates for all major UK admissions tests, as well as other key dates such as UCAS deadlines, interview dates, open days, and more.


Registration for the TMUA costs £75 for students applying in the UK and Republic of Ireland, and £130 for those anywhere else in the world. Some independent test centres also charge an additional administration fee for candidates to cover costs such as room hire and invigilation. Get in touch with your chosen test centre to clarify if this cost will apply to you.

Tips from a successful Cambridge student


  1. Master Core Mathematical Concepts: Thoroughly revise fundamental mathematical concepts, focusing on topics typically covered in the TMUA.
  2. Practice Problem-Solving: Regularly work on maths problems that require analytical thinking and application of mathematical principles.
  3. Time Management: Practise answering questions under timed conditions to improve your ability to manage time effectively during the TMUA. Practise answering questions under timed conditions to improve your ability to manage time effectively during the PAT. For access to bespoke, true-to-life mock papers with which to practise your timing skills, head to our Admissions Test Resources hub and browse our exclusive collections.
  4. Seek Guidance: Consider seeking guidance from teachers or mentors experienced in TMUA preparation to receive valuable feedback and insights. Previous Cambridge students who sat the TMUA themselves, such as our mentors here at Oxbridge Applications, are also a great source of knowledge to draw on, as they can give you an accurate picture of what it means to perform like a real Cambridge student.
  5. Stay Confident and Composed: Approach the TMUA with confidence in your mathematical abilities, knowing that your preparation has equipped you for success.


In addition to TMUA past papers on the Cambridge Assessment Admissions Testing website, we at Oxbridge Applications have written a series of additional mock papers. Our students have 33% more questions to practise with. Our mock TMUA papers can be found here and are included with our admissions test tuition. All of our TMUA tutors are highly-trained Cambridge graduates who can share their personal insights of having sat the test. You can contact our Oxbridge-graduate Consultants on +44 (0) 20 7499 2394 or email [email protected] to discuss which of our test training would suit you best. We also have an online testing portal for students who want to sit the exam in timed, test conditions.

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