Top 10 TMUA Tips for Preparation

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Top 10 Tips for Preparing for the Test of Mathematics for University Admission (TMUA)

TMUA how to prepare


The Test of Mathematics for University Admission (TMUA) is an admissions test for applicants who are interested in pursuing Mathematics or mathematics-related undergraduate courses such as Economics and Computer Science at certain universities, including the University of Cambridge. In most cases, the test is not compulsory. However, it is a requirement for the University of Cambridge! Furthermore, a good performance on it may result in a reduced offer at your applications to other universities.
For further TMUA preparation, you also could visit our TMUA past papers page, and check the previous years exam questions.

It is a paper-based test that consists of two different papers. Each paper is 75 minutes long, and it is taken one after the other. Both papers consist of 20 multiple choice questions each.

Questions across the two papers carry equal weight. There will be no penalty for incorrect answers, so candidates are advised to attempt all questions. There is no formulae booklet for this test. Students are expected to understand and recall all relevant formulae. No calculators are allowed in the test.

The content of Part 1 is almost all covered within the pure mathematics specification of an AS level in mathematics. The content of Part 2 is almost all covered within a Higher Level GCSE mathematics course. There is some duplication of content across Parts 1 and 2.

Our Oxbridge application experts have compiled a list of top 10 tips. This includes dos and don’ts for preparing for TMUA for the 2024/25 application cycle. For more information on what is the TMUA test, check out our comprehensive guide.

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General Advice for the Test of Mathematics for University Admission (TMUA)

As with any test that you would be taking, early TMUA preparation is key when taking the Test of Mathematics for University Admission (TMUA). The focus of the TMUA is on mathematical thinking. It uses mathematics you will have already learned in your school studies. So there is no need to take a preparation course or to do much preparation beyond familiarising yourself with the test format and style of questions.

We recommend that you read the test specification and notes on Logic and Proof. This is available on the Cambridge Assessment Admissions Testing (CAAT) and answer the past year’s question papers under timed test conditions. Read on for our top TMUA tips!

how to prepare for TMUA

How to Prepare for the TMUA

1. Practice as many past year papers as possible.

As with any test that you take, doing past year papers would be immensely useful when preparing for the assessment. It would allow you to be familiar with the format of the test, preventing you to waste precious time during the actual test. It will also allow you to do practice essays and be better at it. 

You can access some past year papers/ specimen papers through the official Cambridge Admissions Assessment Testing website, or through the link here: Cambridge Admissions Assessment Testing . When doing past year papers, remember to do it under examination conditions. This includes doing the practice paper under timed conditions. You should also do it under exam conditions– no phones or music. This would help you be more familiar and less anxious about the actual day itself.

2. Having a good pace when doing the test.

The University of Cambridge’s aim when setting the test is that most students will have enough time to complete the questions and to check their answers, so it does not become a test of speed. Therefore, working steadily through the questions and not spending too long on any one question is a good strategy for obtaining the highest mark you can.

In each paper, the later questions are generally harder than the earlier questions. However, different people find different questions easier or harder. For example, it may be that you find question 14 much easier than question 11, so do not be surprised if this is the case.

3. Ensuring that you do the questions carefully and apply as much mathematical knowledge as possible.

Another important thing to point out is that there are no trick questions on this test. There will be hard questions. But The University of Cambridge’s interest is in allowing candidates to show what they are capable of doing Mathematics, and not in catching candidates out. Hence, a question will never deliberately try to mislead candidates.

However, that being said, there will be options offered which are the result of certain common errors. So reaching an answer which is one of the options offered is no guarantee that you have got the correct answer. On this point, another thing to be aware of is that some questions ask which of the following three things are true. The answer would also include options such as none of them and all of them. These two options are genuine options and you may be correct if you reach the conclusion that they’re all true or that none of them is true.

TMUA preparation

4. Being familiar with the format of the examination.

The two papers are different in their focus.

How to Prepare for TMUA Paper 1

Paper one focuses on mathematical thinking. The mathematical content required is similar to the pure mathematics part of the first year of A-level mathematics. It is also fairly similar to the pure mathematics content as many other courses at a comparable level such as the IB or Scottish examinations. These questions generally require you to solve a multi-step problem. You’ll have to use your mathematical knowledge to both decide what steps to take and then work out the answer.

There will be some familiar textbook-like questions early on in the paper but most of the questions will require more than this. For example, you may have to perform integration and then do something with the answer. Another example includes being asked to work out probability but having to think quite carefully to decide how to count the number of possible events. Most mathematics you will encounter in your mathematical career will not be in the form of a standard textbook question. So these questions in this test a design to test how well you can put together what you already know in an unfamiliar context.

How to Prepare for TMUA Paper 2

The second paper focuses on mathematical reasoning. These questions are generally about the components of mathematical arguments. One key component of Mathematics as a discipline is the emphasis on proving that things are true. Rather than just believing things because they seem likely or because they work in a few small cases. The history of mathematics includes many stories of widely believed conjectures which later turned out to be false and this underscores the need for rigorous proof.

This paper, therefore, asks you to decide if one statement follows from another. Or if one statement is necessary for another to be true. It can also ask you if the given proof is correct or erroneous. There are also questions on this paper which are like the paper one questions. They also ask you to devise an argument in an unfamiliar situation. Such questions typically require more creativity than paper one but use simpler Mathematics.

5. Prepare physically (not only mentally!).

You probably would have heard this before every examination. But do try to get a good night’s sleep before your examination. Eat well before the examination and not drink water right before the examination so as to avoid any unnecessary washroom emergencies during your examination. As with every other examination, also do remember to check all your examination arrangements. For example, the venue location, as well as the timing, and to be there at least half an hour before.

Download Your Free TMUA Practice Questions

    Top 5 things to AVOID for TMUA Preparation

    1. Not being familiar with the content.

    You should read through the TMUA syllabus it to ensure that you are familiar with the content being tested and ask your teachers if you are unsure about anything, especially in Section 1. For Paper 2 there is content that you may well not yet be familiar with. This is because as explained in section 2 of the test specification, this content is focused on the ideas of mathematical logic and its use in proof.

    Hence, to prepare for section 2, it is recommended that you read through the notes on logic and proof available from the “Preparing for the test” section of the Cambridge Assessment Admissions Testing website. These notes provide thorough explanations of all the technical terms used on paper. They also show how mathematical proofs use these ideas the questions on paper. These will test your understanding of these terms either alone or within the context of a proof.

    2. Not practising enough.

    When preparing for a Mathematics test of any sort, there is no substitute for doing mathematics questions. It is important to know syllabus content. But just reading through your notes or making revision notes is both inefficient and inadequate as in preparation, you must do questions to test yourself.

    This will not only help you to recall and revise the maths, but it will also develop your ability to answer more difficult questions. Practice, practice, practice! For this to be effective, you must be using questions which challenge you. One good source of such questions is the review questions on the Underground Mathematics website ( these are taken from a variety of old exam papers and were generally chosen for the site because they require more than one step to reach the solution. They are based on A-level content which may be an advantage when preparing for this test.

    preparing for TMUA

    3. Pressurising yourself before the admissions test, or panicking and overthinking during the test.

    Do not feel stressed out or panic if during the admissions examination, the texts would not be a carbon copy of the questions that you are used to. Be confident in your abilities and know that the skills you have honed when practising other essays are still transferable. Furthermore, the actual admissions assessment would be the same for every other applicant, and the resources these applicants would have used would also be similar to yours. Hence, others would also be equally caught off guard, and there would not be any unfair disadvantage by getting difficult questions.

    4. Only having one source of practice.

    Other than the sources of questions listed above, another good source of questions is the UKMT Intermediate and Senior Maths Challenges and Kangaroos (; go to “Individual challenges”). The website is full of questions which require creative thinking to solve though. These questions generally do not require much A-level content, but rather they are good for developing mathematical flexibility that is using what you already know in different ways. On that point, once you’ve studied the notes on logic and proof and worked through some underground mathematics and UKMT questions, it is very important to do some pass test papers under timed conditions without a calculator to familiarise yourself with the style of questions and the speed needed.

    5. Using a calculator when practising.

    Calculators are not allowed in the actual examination, so even if it is difficult or time-consuming, you should do the practice questions without your calculator to mimic examination conditions as much as possible. Practising without your calculator would also allow you to brush up on your mental arithmetics, which could come in useful by helping you avoid careless mistakes, as well as save you time when actually doing the questions on the day itself.


    →What is the TMUA exam, and why is it important to prepare for it?

    The TMUA (Test of Mathematics for University Admission) is an exam that tests mathematical knowledge and skills at a level appropriate for undergraduate study. It is an essential requirement for students wishing to study mathematics or related subjects at top universities in the UK, including the University of Cambridge and the University of Warwick. Preparing for the TMUA is important to ensure that students have the necessary skills and knowledge to succeed in their university studies.

    →How can I prepare for the TMUA?

    There are several ways to prepare for the TMUA, including practicing past papers, reviewing key mathematical concepts and formulae, and seeking guidance from experienced CTMUA tutors. It is also important to develop problem-solving skills, as the exam is designed to test not only mathematical knowledge but also the ability to apply that knowledge in unfamiliar situations.

    →What are some tips for practicing past papers?

    When practicing past papers, it is important to simulate exam conditions as closely as possible, including timing yourself and working under pressure. Start by reviewing the questions and identifying areas where you need to improve your knowledge or skills. Then, work through the questions systematically, focusing on understanding the concepts and applying them to solve the problems. It can also be helpful to review the solutions provided and seek feedback from a tutor or teacher.

    →What should I look for in an experienced TMUA tutor?

    When seeking guidance from an experienced TMUA tutor, look for someone who has a strong track record of helping students succeed on the exam. Ideally, the tutor should have a deep understanding of the exam format and content, as well as experience working with students at your level. They should also be able to provide personalized feedback and support to help you improve your skills and knowledge.

    →What is the content in the TMUA?

    The content in the TMUA (Test of Mathematics for University Admission) includes a range of mathematical topics and skills, with an emphasis on problem-solving and mathematical reasoning. The exam consists of two papers, each lasting 90 minutes.

    →What is a good score for TMUA?

    A good score for TMUA depends on the university and course to which you are applying. The TMUA is one of several factors considered in the admissions process, and universities may have different expectations for minimum scores. As a general guideline, a score of 60% or above is considered a strong result and may improve your chances of being offered a place at a top university. However, it’s important to note that a high score alone does not guarantee admission, as universities consider a range of factors in their decision-making process.

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