Suggested Preparation for the TMUA
I have organised this by the 9 topic areas taken from the official TMUA specification.​ Using the TMUA Topic Menu you can access information relevant to each topic. This includes my thoughts on exam techniques for the topic, the official specification, and links to my resources. The resources currently consist of a topic worksheet and a set of multiple choice questions in the style of TMUA questions, as well as solutions. In order to prepare effectively, I suggest that you work through the following steps:​​
TMUA Topic Menu
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Read my thoughts on exam techniques for each topic.
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Look at the specification for each topic and identify if there are any areas that you need to learn / revise.
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Work through my worksheet on each topic: the initial questions ensure you have the key skills and knowledge required, and they then build in difficulty, introducing typical TMUA style questions. Use the solutions to give yourself hints where needed, but then try to go back and answer the question yourself each time.
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Answer the multiple choice questions for each topic. Again you can use the solutions when you are stuck, but after looking at them, make sure you can now answer the question yourself.
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Answer some of the papers from previous years as well as my 'mock' exam papers - I suggest that initially you do not time yourself. Allow yourself the time to become familiar with the style of questions and time to puzzle over those questions that you can‘t immediately solve. This will really help to improve your problem solving skills rather than just looking at the answers.
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Once you have marked the papers, make a note of those questions that you were not sure about, or got wrong, and check that you now understand them. Then have a go at answering them again after some time has passed, say a week later.
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Finally you are ready to tackle some past papers under timed conditions. My tip here is that you work for 75 minutes and then change pen colour and continue working for as long as it takes to finish. This way you can see what score you would have achieved in the time allowed, but you will still benefit from the ‘puzzling’ time spent thinking about questions.
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In 2024 the test was offered online at Pearson VUE test centres. There are sample tests available online to ensure you are familiar with the format and can use the navigation features. You can access these here:​
Tips For Success
​​My top tip is : DO LOTS OF MATHS
​​No amount of teaching or tuition can help you unless you practise practise practise by yourself.
​​Do questions - spend time puzzling over them - look at the answers to understand them - then do them again!
​​Make sure you really understand the mathematical concepts on the specification, and that you are not just learning ‘tricks’ (unless of course you understand why the trick works!). ​
​Identify where you are prone to making small errors (we all make mistakes), but the key is that you become aware of places where these mistakes can creep in, and be extra vigilant. Do you often make mistakes with minus signs (eg when multiplying brackets or rearranging equations)? or when converting between degrees and radians? If so, be extra careful at these stages of your working.
​If you often make calculation slips, you might want to consider doing calculations in two different ways, although you should be careful that this doesn’t take up too much time. Can you do a quick inverse calculation to check your answer?
TMUA Overview
The TMUA, or Test of Mathematics for University Admission, is a test that focuses on the mathematical thinking and reasoning skills needed for a degree in maths or a maths-related course such as computer science or economics. Questions are based on topics taught at Higher Level GCSE and the first year of A Level, but also includes ‘Sequences and Series’ which is usually taught at the start of Year 13.
There are 2 papers, taken consecutively on the same day in either October or January. Dates for the 2025/26 academic year are 13th & 14th October 2025, and 8th & 9th January 2026. Note that you can only take the exam at one of these sittings, and Cambridge applicants must take the exam in October.
Each paper is 75 minutes long and consists of 20 multiple choice questions.
Paper 1 focuses on application of mathematical knowledge to new situations - while the subject content should be familiar, it is very likely that the style of questions will be new. For example a question might require you to sketch the graph of two different functions in order to work out how many solutions there are to an equation (by counting the number of intersections). You may be able to sketch these graphs but may not realise that this technique could be helpful in this question.
Paper 2 tests mathematical reasoning and ability to deal with simple ideas using elementary logic. This is often an area that students have not had much experience of, and they will need to learn some new terminology and practise analysing mathematical arguments and thinking ‘logically’.