TMUA Resources
First of all I want to say that if you heard from other people that the TMUA exam is ‘really hard’ or have looked at a past paper and thought it looked difficult, or even completed a past paper and not scored as highly as you hoped, please don’t be disheartened. The TMUA questions are a very different style to A Level questions, and it takes a while to get used to them. My worksheets are designed to introduce many of these styles and allow you to practise a variety of typical techniques. By practising these questions you should improve your overall mathematical understanding and competence which will help with your A Levels, but you will also become familiar with typical TMUA questions. My hope is that you will also develop the skills to tackle unfamiliar questions where you might have to use mathematical reasoning with a known concept in a new scenario.
These resources are organised by the 9 main topic areas taken from the official TMUA specification.
Each section includes my thoughts on exam techniques for the topic, a topic worksheet which covers core knowledge and a set of multiple choice questions in the style of TMUA questions. There is also a copy of the official specification for that topic.
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Start with the worksheet to ensure you have all the core knowledge required.
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Then move on to the multiple choice questions.
1. Algebra and Functions
indices / surds / quadratics / equations / inequalities / polynomials / modulus function
2. Sequences and Series
arithmetic / geometric / convergence / recurrence relations / sigma notation / binomial expansion / choose function
3. Coordinate Geometry
straight lines / parallel and perpendicular / equation of circle / circle theorems
4. Trigonometry
sine and cosine rules / ambiguous case / radians / exact values / sine, cosine and tangent functions / graphs / equations
5. Exponentials and Logs
exponential graphs / log laws / equations
6. Differentiation
tangent to a graph / rate of change / second order derivatives / stationary points / increasing and decreasing functions
7. Integration
integrals vs area under curve / integrals of powers of x / link to differentiation / trapezium rule / differential equations
8. Graphs of Functions
graphs of common functions / transformations / stationary points and roots / link to solution of simultaneous equations
9. Proof and Logic
logic of arguments / if then statements / necessary and sufficient / negation / counter-examples / errors in proofs
10. Extra
abstract functions / probability / combinatorics / number theory
TMUA Exam Papers
When you are used to the style of the TMUA questions and are confident with your subject knowledge you should start working through exam papers. To start with I suggest you allow yourself unlimited time, and spend time puzzling over those questions that you can't immediately solve. This will really help to improve your problem solving skills.
​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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As well as the official past papers available from 2016 to 2023, I have written a series of 'mock' papers which are available below. There are a number of other 'mock' papers available online, and these are often good practice, but just a slight word of caution that these do not always stick to the specification. One exception is the excellent series of papers available on JZMaths which are genuine TMUA style questions but unashamedly contain only "hard, very hard, and occasionally unreasonably hard" questions!
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You should also practise answering papers online, just like the real exam. There is an official sample test offered by Pearson to ensure you are familiar with the format and can use the navigation features. There is also a free 'exam simulator' on JZMaths which allows you to practise any of the official past papers, all of the original papers written by JZMaths as well as my Tyler Tutoring mock papers.
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Official Past Papers
Link to papers from 2016 to 2023 on the UAT UK Website. Most of these papers are also available on the Physics and Maths Tutor website with worked solutions as well as the official answers.
Tyler Tutoring Mock Papers
These are TMUA style papers I have written, that mimic the style and difficulty of the real exam papers.
Each set has Paper 1 and Paper 2 and full worked solutions. You can now also answer these online at JZMaths.
JZMaths Papers
Link to a set of papers written by Joe Zhou of JZMaths featuring a selection of only "hard, very hard, and occasionally unreasonably hard" questions. These are great way to challenge yourself in preparation for harder questions that may come up in the exam.