TMUA, ESAT & STEP Maths Admissions Test Tuition
Specialist one-to-one preparation for competitive university Maths admissions tests
Harry Williams offers online preparation for TMUA, ESAT Mathematics 1 and Mathematics 2, and STEP 2 and STEP 3.
Harry is a fully qualified Maths teacher with a PGCE in Mathematics from the University of Reading and Qualified Teacher Status (QTS). He is a former Head of Mathematics at Harrow School Online and Highgrove Education, and a current Pearson Edexcel examiner for International A Level Mathematics and Further Mathematics.
Admissions tests require students to do more than reproduce familiar A Level techniques. They often demand unfamiliar problem-solving, mathematical reasoning, efficient methods, and the ability to work accurately under significant time pressure. Harry’s tuition is therefore focused on helping students become more confident tackling difficult problems, rather than simply working through additional syllabus content.
The free consultation is available if you would prefer to discuss the student’s university plans, admissions-test requirements, current mathematical level, or preparation timetable first.
How Maths Admissions Test Tutorials Work
Lessons are live, one-to-one, and tailored to the student’s chosen admissions test and application timetable.
Strong A Level or International A Level Mathematics results do not automatically translate into strong admissions-test performance.
Students may understand the underlying mathematics but still find it difficult to:
Recognise how familiar ideas can be used in unfamiliar problems
Identify efficient routes through demanding questions
Reason mathematically when a standard method is not obvious
Work accurately under severe time pressure
Decide when to persist with a problem and when to move on
Adapt their approach when an initial method does not work
Tuition with Harry can therefore include:
Diagnostic work using admissions-test-style questions
Explicit development of mathematical problem-solving strategies
Timed practice
Detailed discussion of different possible approaches
Identifying unnecessarily long or inefficient methods
Building confidence with unfamiliar mathematical problems
Reviewing errors and developing strategies to avoid repeating them
Structured preparation around the student’s test date
The emphasis is on developing the mathematical thinking required for the test, rather than memorising a collection of tricks.
Sessions are 55 minutes, delivered live online from the UK.
Tutorials with Harry: Specialist teaching for high-attaining Maths students
Harry is a fully qualified Maths teacher with Qualified Teacher Status (QTS) and a PGCE in Mathematics from the University of Reading.
He has more than ten years’ experience teaching Mathematics and Further Mathematics, including at Abingdon School and as Head of Mathematics at Harrow School Online and Highgrove Education.
Harry holds a First-Class Master’s degree in Mathematics from the University of Sussex and has extensive experience teaching students working at the highest levels of school Mathematics.
He is also a current Pearson Edexcel examiner for International A Level Mathematics and Further Mathematics.
His admissions-test tuition focuses particularly on:
Recognising the mathematical structure behind unfamiliar problems
Developing flexible problem-solving approaches
Selecting efficient methods
Mathematical reasoning and proof
Working accurately under time pressure
Learning from unsuccessful approaches rather than simply being shown a solution
Developing the independence needed for university-level mathematical study
TMUA Tuition: Test of Mathematics for University Admission
Harry offers specialist one-to-one preparation for the TMUA.
The TMUA assesses mathematical knowledge, application, and reasoning rather than simply testing whether a student can reproduce standard A Level methods.
The test consists of two papers:
Paper 1 – Applications of Mathematical Knowledge
Paper 1 assesses a student’s ability to apply mathematical knowledge in unfamiliar situations.
Students answer 20 multiple-choice questions in 75 minutes.
Paper 2 – Mathematical Reasoning
Paper 2 assesses mathematical reasoning and includes ideas from elementary logic.
Students answer 20 multiple-choice questions in 75 minutes.
Calculators are not permitted.
TMUA preparation with Harry can focus on:
Applying familiar mathematics in unfamiliar contexts
Identifying efficient solution routes
Mathematical reasoning and logic
Multiple-choice strategy
Eliminating implausible answers
Working accurately without a calculator
Managing the considerable time pressure of the test
Timed practice using official and appropriate preparation materials
Harry can tailor the programme to the student’s existing mathematical strengths, target universities, and time remaining before the examination.
ESAT Mathematics Tuition: Engineering and Science Admissions Test
Harry offers tuition for the mathematical components of the ESAT, specifically:
Mathematics 1
Mathematics 2
Harry does not provide tuition for the Biology, Chemistry, or Physics modules.
ESAT Mathematics 1
Mathematics 1 is taken by all ESAT candidates.
The module contains 27 multiple-choice questions to be completed in 40 minutes.
The combination of relatively short questions and significant time pressure means that students need both secure mathematical foundations and the ability to recognise efficient methods quickly.
ESAT Mathematics 2
Mathematics 2 is required for some mathematically demanding courses.
It also consists of 27 multiple-choice questions in 40 minutes.
Students should check the current requirements for their specific university and course before choosing their ESAT modules.
Preparing for ESAT Mathematics
Tuition can focus on:
Identifying what a question is really testing
Applying school mathematics in less familiar contexts
Finding efficient approaches under time pressure
Mental and written mathematical accuracy
Multiple-choice strategy
Knowing when to move on from a difficult question
Timed practice
Reviewing errors and developing more reliable approaches
Because ESAT module requirements differ by university and course, families should confirm exactly which modules the student is required to take.
STEP Tuition: STEP 2 and STEP 3
Harry offers preparation for STEP 2 and STEP 3.
STEP is substantially different in style from TMUA and ESAT. Rather than short multiple-choice questions, STEP requires students to engage with long, demanding mathematical problems and construct complete mathematical solutions.
It is designed to assess mathematical reasoning, problem-solving, and the ability to work with unfamiliar material at a level closer to undergraduate Mathematics.
STEP 2
Harry can support students preparing for STEP 2, including work on advanced problem-solving, selecting questions strategically, constructing rigorous solutions, and developing the persistence needed for longer mathematical problems.
STEP 3
Harry also offers preparation for STEP 3, which assumes a broader mathematical background and is particularly relevant to students studying Further Mathematics.
Preparing for STEP
STEP tuition can focus on:
Tackling unfamiliar and extended mathematical problems
Breaking difficult problems into manageable stages
Choosing productive starting points
Mathematical proof and reasoning
Writing complete and coherent solutions
Learning when an approach should be abandoned or adapted
Selecting questions strategically in the examination
Developing stamina for extended mathematical problem-solving
Reviewing past solutions in detail rather than simply checking final answers
STEP preparation is normally most effective when students begin sufficiently early to develop their problem-solving skills gradually rather than treating the examination as a short revision exercise.
Which Maths Admissions Test Do I Need?
The required admissions test depends on the university, course, and year of application.
For example, TMUA is currently used for a number of Mathematics, Computer Science, Economics, and related courses, while ESAT is used for selected Engineering, Physics, Natural Sciences, and other science-based courses.
STEP continues to be used for some highly mathematical university courses and offers.
Admissions-test requirements can change from year to year.
Students should therefore always check the current requirements directly on the official university course page before booking preparation.
Harry can help students understand the mathematical demands of the relevant test, but responsibility for confirming the correct admissions test, registration requirements, and deadlines remains with the student and family.
Oxford Maths Admissions: TMUA Has Replaced MAT
Students applying for Oxford Mathematics and related courses should be aware that Oxford now uses the TMUA rather than the former Mathematics Admissions Test (MAT).
The MAT is no longer used for the current admissions cycle.
Students who have previously worked through MAT material may still find some of the mathematical problem-solving useful, but preparation should now be aligned to the current TMUA specification and format.
Preparing Alongside A Level or International A Level Maths
Admissions-test preparation is separate from normal A Level or International A Level tuition.
However, the two can complement each other.
Students may need to strengthen particular areas of their school Mathematics course while simultaneously developing the much less familiar problem-solving and reasoning skills required for an admissions test.
Harry also offers separate tuition for:
Where a student is receiving both curriculum and admissions-test tuition, the programme can be planned around their school workload, examination timetable, university application, and admissions-test date.
Testimonials and Google Reviews
“I wanted to improve the way I approached ESAT problems. Harry gave incredibly clear explanations and really helpful advice for dealing with the challenging time pressure of the test. Working with him changed the way I approach difficult problems and helped me spot the most time-efficient way of solving them. Harry’s help is 100% worth it. Even after my first session, I could already see ESAT questions differently and felt much more confident.”
Frequently Asked Questions
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Yes. Harry is a fully qualified Maths teacher with a PGCE in Mathematics from the University of Reading and Qualified Teacher Status (QTS).
He is a former Head of Mathematics at Harrow School Online and Highgrove Education, has more than ten years’ experience teaching Maths and Further Maths, and holds a First-Class Master’s degree in Mathematics from the University of Sussex.
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Yes. Harry offers one-to-one preparation for both TMUA papers:
Paper 1 – Applications of Mathematical Knowledge
Paper 2 – Mathematical Reasoning
Tuition can include diagnostic work, mathematical reasoning, unfamiliar problem-solving, multiple-choice strategy, timed practice, and examination technique.
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Yes. Harry offers preparation for ESAT Mathematics 1 and Mathematics 2.
He does not offer tuition for the Biology, Chemistry, or Physics ESAT modules.
Families should confirm which modules are required for the student’s chosen university course before booking.
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Yes. Harry offers preparation for STEP 2 and STEP 3.
STEP tuition focuses on extended mathematical problem-solving, mathematical reasoning, proof, constructing complete solutions, question selection, and examination strategy.
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Yes, where the required admissions test falls within the tests Harry teaches.
For the current admissions system, Oxford Mathematics uses TMUA, while Cambridge Mathematics applicants may encounter TMUA and/or STEP requirements depending on the stage and nature of their application and offer.
Students must check the current requirements for their exact course and year of entry directly with the university.
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There is no single timetable that suits every student.
The appropriate starting point depends on the test, the student’s existing mathematical level, their school workload, and how much unfamiliar problem-solving experience they already have.
In general, admissions-test preparation is more effective when students have enough time to develop their reasoning and problem-solving skills progressively rather than relying on a short period of intensive revision.
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Yes.
Time pressure is particularly important in TMUA and ESAT, where students need to recognise promising approaches and make decisions quickly.
Tuition can include timed practice, analysis of inefficient methods, question-selection strategy, and developing the confidence to move on when a problem is consuming too much time.
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No.
Students considering highly mathematical university courses are usually academically strong, but performance in an admissions test depends on more than an existing school grade.
A student may have strong syllabus knowledge while finding unfamiliar problem-solving or severe time pressure much more difficult.
Harry can assess the student’s current mathematical level and give an honest view of the areas that need development.
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Oxford no longer uses the Mathematics Admissions Test for its current undergraduate admissions process.
Oxford Mathematics and related courses now use the TMUA, so Harry’s current Oxford Maths admissions preparation is focused on TMUA rather than MAT
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Yes.
Some students need both curriculum tuition and specialist admissions-test preparation.
Harry can keep the two strands distinct while planning them around the same wider timetable, helping the student maintain their school Mathematics performance while also developing the problem-solving skills required for university admissions tests.
Ready to begin?
Book a 55-minute one-to-one TMUA, ESAT Mathematics, or STEP preparation session lesson or purchase one of our 10 lesson packages through the online scheduling system.
Alternatively, book a free consultation to discuss the student’s university plans, required admissions test, current mathematical level, preparation timetable, and goals.
You may also contact us if you would prefer to discuss your options with us first.