University Entrance Test
TMUA Tutoring & PreparationTest of Mathematics for University Admission
Specialist one-to-one preparation for the TMUA — the admissions test for Maths, Computer Science and Economics at Cambridge, Oxford, Imperial, LSE, Warwick and more. Learn from Oxford and Cambridge mathematicians who've been through it themselves.
Find a TMUA tutorAbout the Test
What is the TMUA?
The TMUA (Test of Mathematics for University Admission) is the admissions test for maths-heavy courses — Mathematics, Computer Science and Economics — at Cambridge, Oxford, Imperial, LSE, Warwick, Durham and UCL. It tests how well you apply A-level maths in unfamiliar contexts and reason with logic and proof, not how much you've memorised.
Who takes the TMUA
- Mathematics, Computer Science and Economics applicants
- Cambridge: Maths, Computer Science, Economics
- Oxford (new for 2027): the Maths and Computer Science family of courses
- Also Imperial, LSE, Warwick, Durham and UCL for selected courses
Format & scoring
- Two papers, 75 minutes each: Paper 1 (Applications of Mathematical Knowledge) and Paper 2 (Mathematical Reasoning)
- 20 multiple-choice questions per paper; no calculator and no formula booklet
- No marks lost for wrong answers
- One overall score on a 1.0–9.0 scale; no pass or fail
Key dates (2026 cycle, 2027 entry)
- Registration opens: 1 June 2026
- Booking opens 20 July 2026; deadline 28 September 2026
- Test window: 12–16 October 2026 (Oxford & Cambridge must sit in October)
- Results released: 16 November 2026
- Fee: £78 (UK & Ireland) / £133 (elsewhere); bursaries available
What's changed?
- From 2027 entry, Oxford has replaced the MAT with the TMUA for all its Maths and Computer Science courses (as has Imperial)
- The TMUA is now part of the shared UAT-UK framework, delivered at Pearson VUE centres
- The format is unchanged, so recent TMUA past papers remain ideal practice
- Old MAT papers are less aligned, but the underlying problem-solving overlaps
Dates, fees and course requirements are set by UAT-UK and the universities — always confirm the latest at esat-tmua.ac.uk and your course page before registering.
Applying for Cambridge Maths? You'll likely sit both — the TMUA before interview, and STEP as part of your offer.
See our STEP pageYour Tutors
Meet our TMUA tutors
Oxford and Cambridge mathematicians who sat these admissions tests themselves — and know exactly what the TMUA rewards.

Mingxuan
Ongoing A-Level tuition with this tutor: £85/hr
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I studied Mathematics at the University of Cambridge, completing both my undergraduate degree and Part III of the Mathematical Tripos. I achieved First Class results throughout my undergraduate studies and ranked within the top 20% of my year.
I have around five years of tutoring experience, amounting to approximately 1,000 hours of teaching. My admissions teaching has included Oxbridge mathematics interview preparation, STEP, TMUA and advanced problem-solving, as well as supporting students with the mathematical thinking and communication skills required for highly selective university applications.
My teaching style is highly interactive and closely aligned with the Oxbridge interview format. I focus not only on whether a student can solve a problem, but on how they structure their reasoning, respond to hints, communicate their ideas and adapt when an initial approach does not work. My aim is to help students become more confident, flexible and precise problem-solvers in unfamiliar situations.
Admissions tutoring experience
I have supported around 30 students with Oxbridge Mathematics admissions, with most of my work focused on interview preparation, mock interviews, STEP and TMUA.
For interview preparation, I work with students through Oxbridge-style mathematical questions in a one-to-one setting. I focus on how clearly they explain their reasoning, how they respond when they are given a hint, whether they can adjust their approach when their first idea does not work, and how confidently they communicate under pressure. After each mock interview, I give detailed feedback on both the mathematics and the way the student approaches and presents their thinking.
I have also supported students preparing for STEP and TMUA, helping them improve both accuracy and efficiency when tackling unfamiliar problems. This includes identifying weaknesses in their existing approach, reviewing difficult questions in detail and helping them develop more reliable problem-solving habits.
Overall, I have around five years of tutoring experience and approximately 1,000 hours of teaching. My admissions experience has been primarily focused on Mathematics.
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Abir
Ongoing A-Level tuition with this tutor: £90/hr
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I'm a Mathematics graduate from Sidney Sussex College, Cambridge, currently pursuing an MPhil in Data Intensive Science at Cambridge. I achieved Grade 1 in both STEP II and STEP III, scored 7.4 in the TMUA and earned a Distinction in the British Mathematical Olympiad, alongside seven UKMT Gold Awards, four A*s at A-Level and nine grade 9s at GCSE.
I specialise in Oxbridge Mathematics admissions, STEP, TMUA and interview preparation, alongside GCSE and A-Level tuition. My approach combines strong mathematical expertise with extensive tutoring, mentoring and educational outreach experience, helping students develop the confidence and problem-solving ability to excel.
Admissions tutoring experience
I've mentored over five prospective Oxbridge Mathematics applicants, at least three of whom subsequently received offers. My experience includes 20+ mock Mathematics interviews, 20+ personal statement and application reviews, and personalised guidance across admissions tests, interviews and super-curricular preparation.
I've also developed hundreds of original TMUA and MAT-style questions and practice materials for an admissions preparation company, giving me valuable insight into how challenging admissions problems are designed and assessed.
My tutoring experience began with 11+ preparation in 2016 and has since expanded to over 100 hours of one-to-one tuition across GCSE, A-Level and university admissions. I've additionally worked with an academic summer school provider and Universify Education on academic residential programmes and mentoring initiatives. At Universify, I helped deliver a residential programme for 39 students and provided ongoing individual academic coaching. I've also supported students through Queen Elizabeth's School's Elite Maths Club and Economics Clinic.
GCSE and A-Level tutoring experience
I also teach GCSE Mathematics and Sciences, and A-Level Mathematics, Further Mathematics, Physics and Economics. Having achieved four A*s at A-Level and nine grade 9s at GCSE, I'm familiar with the demands of top-grade preparation and the Edexcel, AQA and OCR specifications.
Above all, I aim to develop genuine mathematical understanding rather than reliance on memorised methods. Whether a student is working towards an A*, tackling STEP or preparing for a Cambridge interview, I focus on building the confidence, independence and problem-solving skills needed to succeed.
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Ziji
Ongoing A-Level tuition with this tutor: £70/hr
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Hello! My name is Ziji and I am studying for a master’s degree in Mathematics at St John's College, Oxford. I achieved First Class Honours in my undergraduate degree and placed in the top 20% of my cohort. I also achieved 3A*s in my A-Levels in Maths, Further Maths and Computer Science, and scored 9s across the board in GCSEs.
I have over 150 hours of tutoring experience, from teaching A-Levels and GCSE to Oxbridge admissions preparation tests such as the TMUA and STEP. I am committed to helping students achieve the very best they can. I create a tailored learning plan for each student, working closely with them to strengthen their weaker areas whilst challenging them in topics they feel more confident in.
Above all, my focus is on encouraging my students to develop deeper problem solving and critical thinking skills. Not only do I aim to help them develop the skills to succeed in their exams, but also to be well prepared for further studies and beyond.
Admissions tutoring experience
I have been helping people with the Oxbridge admissions system for over 6 months. My focus so far has been on support for admissions tests - I have helped over 3 students with preparing for the TMUA and ESAT, with all of them due to take their assessments soon in October/November. I have also been involved with giving taster interviews to over ten yr 12 students as part of a yearly maths open day at St John's College Oxford. As part of this I also led some group collab MAT sessions between students.
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Aidan
Ongoing A-Level tuition with this tutor: £65/hr
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Hi, I'm Aidan! I've just graduated from the University of Cambridge with a degree in Mathematics. I have 5+ years of experience tutoring mathematics, from GCSE level to university entrance exams, and have helped many students of varying abilities. I've helped many students through Cambridge Maths admissions during my degree — giving practice interviews, reviewing personal statements, and working through entrance-exam questions and preparation.
Admissions tutoring experience
I've given practice interviews for Cambridge Maths to five students as well as reviewing their personal statements, and I worked on a residential at my college for state school students, supporting them with entrance-exam questions. Many students I've tutored are those who need extra help to pass GCSE maths, and I've been able to support and encourage them to do exactly that. I've supported many students with SEND, providing tailored and engaging sessions suited to their individual needs. I am kind and supportive, and what I aim to provide for all students, alongside the mathematical knowledge, is the confidence that they are also good at maths — and that they can enjoy it.
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Theo
Ongoing A-Level tuition with this tutor: £55/hr
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I am a recent graduate of Mathematics from Lincoln College, Oxford. I achieved four A*s at A-Level and ten grade 9s at GCSE, as well as a distinction in the British Mathematical Olympiad. I have two years of tutoring experience, including Mathematics, Further Mathematics and Core Maths at A-Level and the Oxford Mathematics admissions process. I deliver a personal style of tutoring which is more collaborative and involved than at school — closer to an Oxford tutorial.
Admissions tutoring experience
I tutored one student through the Oxford Mathematics admissions process, taking them from an initial practice mark of 40 to 60 in their actual exam. I've also helped students with admissions preparation as a university student ambassador, running personal statement workshops, mock interviews and entrance exam preparation. I sat Oxford's maths admissions test myself in 2022, scoring 65, before the TMUA replaced it — the reasoning and unfamiliar problem-solving it demanded is the same thinking these papers reward, and my Olympiad background means I'm comfortable with problems that don't have an obvious route in.
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Arjan
Ongoing A-Level tuition with this tutor: £70/hr
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Hi, I'm Arjan — a First-Class Computer Science graduate from Trinity Hall, Cambridge. Before Cambridge I earned 12 grade 9s at GCSE and 4 A*s at A-Level, including one of the top 50 Computer Science marks in the country. I specialise in Oxbridge Computer Science applications: TMUA preparation, personal statement guidance and mock interviews. Having been through it recently myself, I know what admissions tutors look for — and how overwhelming it can feel from the other side.
Admissions tutoring experience
My style is patient and question-led: rather than handing you answers, I help you build the understanding and confidence to reason through problems yourself — exactly how I was taught in Cambridge supervisions. My degree specialism was artificial intelligence, which I love using to stretch students and show them where the subject leads. I also hold the JLPT N1, the highest level of the Japanese-Language Proficiency Test, from six years of self-teaching — an experience that shaped how I break difficult material down. Beyond admissions I tutor Maths, Further Maths, Computer Science and Japanese.
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Frederick
Ongoing A-Level tuition with this tutor: £70/hr
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I hold a master's degree in Chemistry with Molecular Physics from Imperial College London, as well as a postgraduate master's in Theory and Simulation of Materials from the same university. I have 12 years' tutoring experience in Physics, Maths, Further Maths, Chemistry, and Biology across all academic levels, from GCSE/IGCSE to IB. I also have significant mentoring experience and hold QTS (Qualified Teacher Status). I am currently pursuing a PhD in Pure Mathematics.
My experience includes working with students of varying abilities, helping them master challenging concepts and excel in their coursework. I have successfully prepared students for key exams, including GCSEs, A-Levels, and university entrance assessments, often helping them achieve top grades. I have tutored students from prestigious schools, including St. Paul's School, St. Paul's Girls' School, Tiffin School, Westminster, Eton, and Rugby. This experience has given me a deep understanding of the academic challenges students face and the strategies to overcome them.
I have extensive experience in tutoring A level and GCSE/IGCSE Chemistry, Physics, Maths and Biology, and A level Further Maths, across all the main exam boards; IB Maths, Physics and Chemistry (Higher and Standard); undergraduate Geophysics, Physics, Chemistry, Engineering and Mathematics; postgraduate Mathematics; and the TMUA, ESAT (Biology, Chemistry, Physics, Mathematics 1, Mathematics 2) and STEP (II and III).
My approach is tailored to each student's needs, ensuring they grasp complex concepts and excel in their studies. In addition to tutoring, I have extensive mentoring experience, guiding students not only in their academic pursuits but also in developing effective study strategies, time-management skills, and confidence. My mentoring background has enabled me to support students holistically and help them realise their full potential.
Admissions tutoring experience
I have extensive experience in tutoring the TMUA, ESAT (Biology, Chemistry, Physics, Mathematics 1, Mathematics 2) and STEP (II and III).
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Emilie
Ongoing A-Level tuition with this tutor: £105/hr
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Oxford Mathematics and Statistics student with over three years of experience tutoring admissions tests. I sat both the MAT and the TMUA myself, and having navigated the Oxford process recently, I specialise in TMUA preparation — developing the problem-solving and reasoning the test demands.
Admissions tutoring experience
Alongside admissions support I tutor maths and further maths at every level, personalising sessions to your specific needs and the areas you want to strengthen. I enjoy the learning process as much as the result, and I tailor everything to how you work best.
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Jade
Ongoing A-Level tuition with this tutor: £65/hr
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My name is Jadesola — Jade for short — and I'm a Mathematics Graduate from the University of Oxford, having achieved all A*s at A-Level and all 9s at GCSE. I sat the TMUA myself, scoring around 7.0, so I know exactly what the papers ask of you. I love helping students understand the subjects I loved learning, and I keep sessions engaging and interactive, always making space to ask questions.
Admissions tutoring experience
I've been a self-employed tutor more than 4 years — teaching Maths at GCSE and A-Level has taught me to notice what a student is really struggling with and adapt the next lesson around it, pacing things differently depending on their level. As I've done A-Level Maths and Further Maths myself, I'm equally happy tutoring GCSE Further Maths. I focus on the reasoning and unfamiliar problem-solving the TMUA rewards, built through structured, patient practice.
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Ana
Ongoing A-Level tuition with this tutor: £75/hr
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Oxford mathematics student and European Girls' Mathematical Olympiad bronze medallist, with over a decade of competitive and academic maths behind me. I scored 84 on the MAT — the test the TMUA now replaces at Oxford — and I specialise in TMUA preparation, building the problem-solving and mathematical thinking it rewards.
Admissions tutoring experience
I attended a specialist maths high school focused on problem-solving, and I work patiently and consistently until things click. I tutor TMUA and STEP preparation alongside A-Level and GCSE maths, and I love showing students that hard problems become approachable with the right mindset.
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Nicholas
Ongoing A-Level tuition with this tutor: £65/hr
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I'm Nicholas, a recent graduate Cambridge University studying Computer Science. I sat the TMUA myself as part of my application, so I know what the papers ask of you and how to prepare for them. I've been tutoring for four years at GCSE and A-Level, with A*s of my own in Maths, Further Maths and Computer Science.
Admissions tutoring experience
The TMUA rewards applying A-level maths in unfamiliar situations and reasoning carefully with logic and proof, rather than recalling method — and that's what I focus on in sessions. Alongside TMUA preparation I tutor Maths, Further Maths and Computer Science at GCSE and A-Level, and I'm happy to talk through what Computer Science at Cambridge is actually like from someone currently doing it.
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Hari
Ongoing A-Level tuition with this tutor: £50/hr
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I am a highly motivated engineering student, with a modest, methodical and patient approach to teaching. I am seeking to share my expertise with students, in order to ensure that they achieve their full potential across their qualifications in Science, Mathematics, and Engineering, and to help them gain offers to prestigious institutions through support in personal statement writing, admissions test practice, and interview preparation. Having achieved 4A*s in my A-Levels and 87/100 on Oxford's PAT test, with 2 years of tutoring experience across a range of students, and offers received from institutions such as the University of Oxford, Imperial College London, and the Dyson Institute of Engineering and Technology, I think that I am well equipped to provide both the academic knowledge and practical guidance necessary to help students excel.
Admissions tutoring experience
I helped a student pass his combined science GCSE through a year of tutoring in 2025. I consulted with his teachers about particular areas of difficulty, in order to plan out our weekly tutoring sessions in order to meet his needs. During each session, I took notes on how easily he was able to grasp certain concepts, allowing me to more effectively allocate time in future sessions.
I helped a student write a personal statement that they used in their Oxford application in 2026. I had a large amount of expertise to offer, having attended the highly selective 'Frontier' residential at Oxford's Balliol College, and having been through the application process, receiving offers from Oxford and Imperial College London. Over a few sessions, we worked through the structure and content of her personal statement, to build up an essay that I thought would appeal to the tutors at Oxford.
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Each tutor shows up to three prices. Entrance test support is for students who want tuition for their course's entrance test, with interview and/or personal statement preparation included at the same rate. Interview and/or personal statement only is for students who want help with either or both without entrance test tuition, including students whose course has no entrance test. If you then book entrance test support, those lessons are charged at the entrance test price. Ongoing A-Level tuition is the price if you carry on with A-Level tuition with this tutor.
Free Resources
TMUA past papers & practice
A full archive of past papers with answer keys and worked solutions, plus the official specification and notes. The TMUA format hasn't changed, so every paper below is directly relevant practice.
Study materials
Past papers
2023
2022
2021
2020
2019
2018
2017
2016
Specimen Papers
Past papers from 2016–2023 are from the test's earlier provider but remain directly relevant — the format is unchanged. The newest official paper and the current specification are on the UAT-UK site.
After the test
Next: practise for your interview
Most Oxford and Cambridge interviews happen in December. Each subject page explains how your course is assessed and shows the tutors who can help.
Applying outside Oxford and Cambridge? There's a second TMUA sitting on 4–8 January 2027, for universities that accept it. It isn't open to most Oxford or Cambridge applicants. Booking opens on 26 October at 3pm. Ask about January preparation.
See every Oxford and Cambridge course that uses the TMUA, or our interview practice page.
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