TMUA · STEP · ESAT · Oxford & Cambridge Preparation
Book a Free Intro MeetingThese exams test mathematical thinking that goes beyond A-Level. Standard revision techniques won't cut it.
The TMUA covers content up to roughly AS-level — but a student who only knows AS-level maths will not score well on it. The same algebra and calculus used at A-Level becomes raw material for problems requiring genuine insight. STEP goes further: its questions are designed to have no obvious starting point and require sustained, creative mathematical thinking from first principles.
Grinding through every past paper while understanding nothing deeply will still be beaten by a student who genuinely understands the underlying mathematics. TMUA and STEP questions alike require the ability to work forward from what you know — not backward from a remembered answer. Recognition is not the same as understanding.
The TMUA’s two 75-minute papers are relentless — multiple-choice questions where the efficient approach saves the time the obvious one wastes. STEP questions are deliberately long — each is designed to take the best students 20–30 minutes. Either way, speed comes from depth of understanding, not from working faster: students who see the structure of a problem reach the answer in a fraction of the time.
Most schools don’t have the expertise to prepare students for the TMUA, STEP, or ESAT. These exams require a tutor who has sat them and understands the style of thinking they reward — not a teacher working through the past papers for the first time alongside their students.
Each admissions test rewards a different kind of mathematical thinking — preparation must be exam-specific.
The Test of Mathematics for University Admission is now the shared maths admissions test for a growing group of universities — Cambridge, Imperial, Warwick, UCL, LSE and Durham, with Oxford adopting it for Maths and Computer Science in place of its former MAT. Two 75-minute papers of multiple-choice questions, designed so pattern-matching from past papers alone does not work. They reward genuine insight: spotting structure, choosing elegant approaches, and reasoning quickly under pressure.
STEP 2 and STEP 3 are each three hours. Candidates attempt any six of twelve questions; only the best six count toward the grade (S, 1, 2, 3, U). Questions are long and multi-part, often building toward a proof or a general result. Cambridge typically makes STEP conditional offers requiring grades in both STEP 2 and STEP 3, and Warwick accepts STEP as an alternative. STEP 1 has been discontinued — only STEP 2 and STEP 3 now run.
The Engineering and Science Admissions Test is now the shared test for science and engineering applicants to Cambridge, Imperial, Oxford and UCL. It replaced Cambridge’s ENGAA and NSAA — and Oxford’s Physics Aptitude Test (PAT), so Oxford physics, engineering and physics & philosophy applicants now sit the ESAT too. Candidates take Mathematics 1 plus two subtests chosen from Mathematics 2, Physics, Chemistry or Biology. Fast, accurate mathematical and physical reasoning is decisive — the Maths and Physics modules are exactly what we prepare students for.
Our founder and tutors come from the universities that set these exams.
Your entrance-exam tutor steers a curated pathway to the top, all the way to test day — keeping a clear picture of your progress, so the teaching always follows where you actually are.
Alex Fraley holds a Distinction in Part III of the Mathematical Tripos at Cambridge — one of the most demanding postgraduate mathematics courses in the world — built on a prize-winning MPhys in Theoretical Physics from the University of Manchester, where he graduated top of his class. He has tutored entrance-exam candidates personally for years, across the TMUA and its predecessor the MAT, STEP, and the Oxford physics tests now folded into the ESAT. That depth of mathematical training is directly relevant to what these exams test. He still takes on the occasional entrance-exam student directly, by request — if you'd like to ask, get in touch.
Our team includes students and graduates from Imperial, Cambridge, UCL, and Warwick — the very universities whose entrance exams we prepare students for. They know what admissions tutors look for.
We don’t just work through past papers. We teach the problem-solving strategies that the TMUA and STEP specifically reward: identifying the hook of a problem, choosing elegant approaches over brute-force computation, constructing proofs step by step, and building the fluency to execute the right approach under time pressure.
Our students have gone on to study mathematics, physics, and engineering at Cambridge, Imperial, and other leading universities. For most students, entrance exam preparation runs alongside A-Level Further Maths — we cover both, so there’s no conflict between the two demands on their time.
Test of Mathematics for University Admission — Cambridge, Imperial, Warwick, UCL, LSE, Durham, and Oxford (Maths & Computer Science)
Sixth Term Examination Paper (2 and 3) — Cambridge maths conditional offers; Warwick also accepts STEP
Engineering & Science Admissions Test — science and engineering at Cambridge, Imperial, Oxford and UCL (replaced the ENGAA, NSAA and Oxford’s PAT)
Any other admissions test — if your exam isn’t listed above, ask us. We support a range of university-specific maths and physics assessments.
Curious where the marks are actually concentrated on the TMUA? See our topic priority breakdown, read our full TMUA practice test guide — paper structure, dates and cost — or take the free TMUA readiness check to see exactly where you personally stand.
For most of our entrance-exam students, the admissions test and A-Level Further Maths are one project, not two — so we teach them with the same tutor.
STEP 3 draws directly on Further Maths content — complex numbers, hyperbolic functions, differential equations — and STEP 2 assumes the start of the course. If a Cambridge or Warwick offer includes STEP, the A-Level and the admissions test are the same preparation, and treating them separately wastes the overlap.
The TMUA officially examines A-Level Maths content rather than Further Maths — but it rewards exactly the problem-solving fluency Further Maths builds. Students taking both arrive at the test with the habits of mind it’s designed to find.
We cover A-Level Further Maths and entrance-exam preparation with the same tutor, moving lesson focus between the two as term deadlines and exam dates demand — so neither preparation is squeezed out by the other.
How much does entrance-exam tutoring cost?
Entrance and admissions-test preparation is charged at our Advanced rate of £105 per hour, reflecting the university-level depth these exams demand. Full platform access, instantly marked practice and Q&A support between lessons are all included, with no contracts. See full pricing details.
Which entrance exams do you cover?
The TMUA, STEP and ESAT, plus other university-specific maths and physics admissions tests. If your exam isn’t one of the main three, ask us — we prepare students for a range of assessments, including the maths and physics elements of Oxford and Cambridge entry.
What happened to the MAT and the PAT?
Both have been retired in the recent admissions-test overhaul. Oxford now uses the TMUA for Maths and Computer Science in place of its former MAT, and the new ESAT has replaced the Physics Aptitude Test (PAT) for Oxford physics applicants — alongside Cambridge’s old ENGAA and NSAA. We prepare students for the current tests, and if you’ve been revising for an older one we’ll get you onto the right syllabus quickly.
When should we start preparing?
Most students begin six to twelve months before the test, usually during Year 12 or early in Year 13. Starting early matters most when entrance-exam preparation runs alongside A-Level Further Maths — the two reinforce each other, so there is a real advantage to building the foundations in good time.
Can you prepare for the entrance exam and A-Level Further Maths at the same time?
Yes — for most of our students these are one project, not two. STEP in particular is built directly on Further Maths content, and we teach both with the same tutor, moving lesson focus between them as deadlines demand so neither preparation is squeezed out. More on Further Maths tutoring.
Do your tutors have experience with these specific exams?
Yes. Our tutors sat these admissions tests themselves and studied at the universities that set them — Cambridge, Imperial, UCL and Warwick. Our founder, Alex Fraley, holds a Distinction in Part III of the Mathematical Tripos at Cambridge and has tutored entrance-exam candidates personally for years.
Entrance and admissions-test preparation is charged at our Advanced rate, reflecting the university-level depth and preparation these exams demand. Full platform access included.
See Full Pricing Details“Alex tutored me for almost a year and brought my maths A-Level from a D to a confident A.”
“…helped her secure her place at UCL!”
“Alex was very knowledgeable beyond the course… he helped me prepare for my admissions exam.”
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