TMUA support & links

It is vital to take the time to properly prepare for the TMUA exam, as its format and style of questions may be unfamiliar to you. We've pulled together a range of video and written walkthroughs of past TMUA papers, as well as some general information about TMUA and useful links, to help you feel confident about tackling the exam.

Jump to the past paper walkthroughs

Information about TMUA

What is the TMUA?

TMUA stands for the Test of Mathematics for University Admissions and is used by a number of UK universities, including Warwick, as part of the admissions and applications process. The test has been designed to let you demonstrate your mathematical thinking and reasoning skills – both of which are vital for a demanding mathematics undergraduate course, such as what we offer here at Warwick.

How hard is the TMUA?

The specification for the exam is available on the UATUK websiteLink opens in a new window and it goes through everything that the exam could assess. The volume of content, as well as the topics covered, is comparable to a UK AS level in Mathematics. However, the level of understanding needed in order to be able to answer the questions is often at a greater depth. In addition to the topics on the syllabus, the test includes elements of elementary mathematical logic. This is often new to many students when they are preparing for the test and it is explained in Section 2 of the specification.

Is the TMUA harder than MAT and STEP?

The Mathematics Admissions Test (MAT) and Sixth Term Examination Papers (STEP) are often both considered to be harder than the Test of Mathematics for University Admission (TMUA). This is mainly due to two factors; the content covered and the length of the questions.

• The TMUA exam requires students to be able to answer questions using topics that are mainly from AS level mathematics content and is made up entirely of shorter, multiple-choice style questions, which students would typically be expected to take between 2-5 minutes to answer.
• The MAT exam requires students to be able to answer questions using topics from AS level mathematics as well as A level mathematics.
• STEP requires students to be able to answer questions using topics from AS level mathematics, A level mathematics, AS level further mathematics and A level further mathematics (STEP 3 only).
• STEP is made up entirely of longer questions which students would typically be expected to take approximately 30 minutes each to answer, and the MAT exam includes 2 longer questions, along with a number of shorter, multiple-choice style questions.

What is the format of the TMUA?

The TMUA exam lasts 2 hours and 30 minutes in total and is divided into two papers. You have up to 75 minutes to complete each paper, both of which contain 20 multiple choice questions.

The focus of the TMUA is on mathematical thinking. It uses mathematics you will have already learned in your school studies, but the test format and question style might be unfamiliar to you. In your preparation, it is important to look at TMUA past papers, using a significant portion of your preparation to practice working through the exam questions, so that you can familiarise yourself with the style, format and best ways of approaching the questions. Make sure you check through the specification, which you can find on the UAT UK websiteLink opens in a new window. This give details of the topics that the exam could assess.

There is no formula booklet for the test and you cannot use a calculator or dictionary. Your overall scores are based on the number of correct answers you give, but you don’t lose marks for wrong answers, so it’s worth attempting all of the questions.

Keep scrolling on this page for video walkthroughs of a number of TMUA past papers and past questions, where we not only show you the answers but also take you through the thinking process involved, as well as highlighting certain techniques you can use and drawing out the level of understanding needed when answering the questions.

What’s the best way to revise and prepare for TMUA Paper 1?

Paper 1 is 75-minutes long and features 20 multiple choice questions. This paper, Applications of Mathematical Knowledge, assesses your ability to apply your knowledge of the mathematical content in a variety of situations, some of which may be new to you. The best way to revise is to attempt to answer questions from the available past papers, reflecting on the techniques and understanding needed for each question. Even if you are able to find a solution to a question without needing any hints, it is important to reflect and take note of the learning points from each question. You might like to attempt a number of questions that cover the same topic so that you can explore that topic in more depth, but you should consider reserving at least 2 full papers so that you can practice under exam conditions, as the test date approaches.

The UATUK websiteLink opens in a new window provides a sample test that you can use as a mock exam, that mimics the same format and interface that you will experience in the actual exam.

What’s the best way to revise and prepare for TMUA Paper 2?

Paper 2 is 75-minutes long and features 20 multiple choice questions. This paper, Mathematical Reasoning, assesses your ability to reason mathematically, and to deal with ideas from elementary mathematical logic.

Here are some examples of aspects of mathematical logic that are key to achieving success on this paper:

• You may be required to investigate whether one statement is necessary and/or sufficient for another statement. It’s valuable to have an efficient way to approach these questions such as the approach demonstrated in our video solution to 2021 Paper 2 Question 9 (see also Question 6 of the same paper).
• You need to be confident with ideas and terms such as the ones listed below:
  • A counterexample – see our video on 2021 Paper 2 question 4
  • The contrapositive of a statement
  • The converse of a statement
  • The term or (meaning inclusive or) – we reflect on this in our video on 2021 Paper 2 question 4 (also seen in Q10 of the same paper)

As with paper 1, the following advice also applies: the best way to revise is to attempt to answer questions from the available past papers, reflecting on the techniques and understanding needed for each question. Even if you are able to find a solution to a question without needing any hints, it is important to reflect and take note of the learning points from each question.

You might like to attempt a number of questions that cover the same topic so that you can explore that topic in more depth, but you should consider reserving at least 2 full papers so that you can practice under exam conditions as the test date approaches. The UATUK websiteLink opens in a new window also provides a sample test that you can use as a mock text, that mimics the same format and interface that you will experience in the actual exam.

As mentioned above, paper 2 of the exam has a particular focus on logic, and UAT UK have provided a comprehensive booklet to explore the ideas involved, which you can find on their webpage dedicated to preparation for the examLink opens in a new window. Our Associate Professor, Siri Chongchitnan, has produced a helpful worksheet to introduce the key concepts within mathematical logicLink opens in a new window that we hope you will find complimentary in your preparation for paper 2. You can get in touch with Fiona Kitchen at f.kitchen@warwick.ac.ukLink opens in a new window to request an example of a filled in version of this worksheet.

How is the TMUA scored?

You will receive one single overall score for the TMUA as a number between 1 (low) to 9 (high), given to one decimal place. Your final scores are based on the number of correct answers you give. You do not lose marks for wrong answers, so it’s worth attempting all questions.

Results for each paper are also reported on a scale from 1 (low) to 9 (high), to one decimal place.

When does the TMUA take place?

You can choose to sit the Test of Mathematics for University Admission (TMUA) in either October or January. For 2026 entry, the TMUA test dates were:

October Sitting: 13 – 14 October 2025

January Sitting: 8 – 9 January 2026

You can book your preferred test sitting via the UAT UK websiteLink opens in a new window. We recommend booking early to secure a convenient time and location. There is no advantage to sitting the test in either the first or second sitting, and we only accept the results from one test in each admissions cycle.

How do you register for the TMUA?

Registration for the TMUA must be done via Pearson VUE’s websiteLink opens in a new window.

First, create an account and received your candidate ID, which usually arrives within 24 hours. Then, once the TMUA test booking window is open, you can use your account to book your slot – you’ll be able to use the website to find your nearest test location and pick a date and time to take the test.

Finally, you have to pay to confirm your booking – this can be done via credit card or via a bursary voucher.

How much does the TMUA cost?

The TMUA costs £75 for candidates in the UK and Republic of Ireland. For those sitting elsewhere, it costs £130.

Candidates from the UK in financial need can apply for a UAT UK's bursary scheme to take the TMUA test free of charge. Please refer to the UAT UK websiteLink opens in a new window for information about how to apply, eligibility criteria and the evidence required to qualify.

Past Paper Walkthroughs

Our Mathematics Outreach Centre Manager, Fiona Kitchen, has provided some ways of approaching selected questions below in the form of video walkthroughs and handwritten solutions. You will find videos that cover all questions from 2021 Paper 1 and Paper 2. There are also some additional questions covered and this page will continue to be added to.

The video below is a general introduction explaining what to expect from this webpage, while further down the page you will find videos covering individual questions and some handwritten solutions to selected questions.

Video Walkthroughs for Individual Questions

Below are video walkthroughs for individual past TMUA questions. We currently have videos covering all of 2021 Paper 1 and Paper 2, as well as a small number of questions from other papers. These resources will continue to be added to.

To make a video full screen, click the icon showing four corners of a square - it is located between the volume control and the three vertical dots.

Latest update: 10 November 2025 (18 new handwriting solutions uploaded).

Handwritten Solutions for Individual Questions

We've also prepared some handwritten solutions of questions from past papers - you can download our notes as PDFs and compare to your own attempts. Questions that include an aspect of mathematical logic are marked with (L) for ease of reference.

Other TMUA Support

We offer TMUA support at certain points in the year, for example we give live online sessions for year 13 students in the lead up to each sitting of the exam, and many of the opportunities for students in year 12 also have elements of TMUA support included in them. You can see a list of the opportunities we offer on our outreach webpages, in particular there is a webpage that lists upcoming eventsLink opens in a new window.

Get in Touch

If you would like to get in touch with us then you can email maths-outreach@warwick.ac.ukLink opens in a new window

General Content and Advice

You might also find it useful to explore the following links about TMUA from University Admissions Tests UK (UAT-UK), including general guidance and a bank of past papers for you to attempt yourself, with some solutions provided. It is the UAT-UK website that you will need in order to register to sit the exam itself.