Entrance Exam & Admissions Test Tutoring

Every entrance-exam tutor is vetted by

Alex Fraley — Cambridge-Trained Mathematician

Cambridge Part III Mathematics — Distinction MPhys Theoretical Physics — Top of Class PhD Candidate — Theoretical Particle Physics A* in A-Level Further Maths

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.

Read Alex's Story

Why Entrance Exams Are Different

These exams test mathematical thinking that goes beyond A-Level. Standard revision techniques won't cut it.

Beyond the Syllabus

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.

Past Papers Alone Won’t Cut It

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.

Time Pressure Is Intense

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.

School Can’t Prepare You

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.

What Each Exam Tests

Each admissions test rewards a different kind of mathematical thinking — preparation must be exam-specific.

TMUA — the maths admissions test

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. We classified every question in the published papers from 2016 to 2023 — see what actually comes up in each paper, and why Paper 2 catches out strong mathematicians. Paper 2 tests formal reasoning — necessary vs sufficient conditions, negating quantifiers, proof by contradiction, spotting a flawed proof — that no A-Level course teaches; see how to answer it, with worked examples for each skill.

STEP — Cambridge Maths

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.

ESAT — science & engineering, incl. physics

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 and physics & philosophy applicants now sit the ESAT too. Candidates take Mathematics 1 plus two subtests chosen from Mathematics 2, Physics, Chemistry or Biology — most physics and engineering courses fix that choice at Mathematics 1, Mathematics 2 and Physics. Fast, accurate mathematical and physical reasoning is decisive — the Maths and Physics modules are exactly what we prepare students for, and that preparation runs naturally alongside A-Level Physics lessons with the same tutor. More on our ESAT tutoring, or see our full guide to the ESAT for the module-by-module breakdown and every 2026–27 date.

Why We’re the Right Choice

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.

Taught by the Founder, by Request

Alex still takes on the occasional entrance-exam student directly, alongside vetting every entrance-exam tutor we hire — if you'd like to ask, get in touch. Otherwise you'll be matched with the tutor whose own admissions-test experience fits your target course best.

Tutors from Target Universities

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.

Problem-Solving Focus

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.

Proven Results

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.

Exams We Prepare For

TMUA

Test of Mathematics for University Admission — Cambridge, Imperial, Warwick, UCL, LSE, Durham, and Oxford (Maths & Computer Science)

STEP

Sixth Term Examination Paper (2 and 3) — Cambridge maths conditional offers; Warwick also accepts STEP

ESAT

Engineering & Science Admissions Test — science and engineering at Cambridge, Imperial, Oxford and UCL (replaced the ENGAA, NSAA and Oxford’s PAT). ESAT tutoring →

Other

Any other admissions test — if your exam isn’t listed above, ask us. We support a range of university-specific maths and physics assessments.

Sitting the TMUA? Start with a free readiness check

Before any lessons are booked, find out honestly where you stand. Our free TMUA readiness check takes about 20 minutes, adapts to how you answer, and gives you a readiness band, a topic-by-topic map across both papers, and a prioritised list of what to fix first. No cost, no commitment.

Take the free TMUA readiness check

Curious where the marks are actually concentrated? See our topic priority breakdown — which TMUA topics carry the most marks.

Interviewing at Oxford or Cambridge? Practise it first

Shortlisted maths, computer science, physics, engineering and natural sciences applicants are interviewed in December, on problems they haven’t seen before. Our mock interviews recreate that conversation on a shared whiteboard, with honest feedback afterwards — best booked in November.

Oxbridge interview preparation

Entrance Exams and Further Maths — Taught Together

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 Is Built on Further Maths

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 Rewards the Same Fluency

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.

One Tutor, Both Goals

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.

For the wider picture, our subject directory covers everything we teach alongside entrance-exam preparation.

Online TMUA Tutoring, Paper by Paper

The two TMUA papers reward different work, so lessons treat them differently. Every lesson is online, and each part of it is backed by a free resource you can use between lessons.

Paper 1: speed on the topics that recur

In the published papers, four topics — algebra and functions, sequences and series, integration and trigonometry — carried 64.4% of Paper 1. Lessons build fluency there first, then practise using it on problems the student has not met before, at TMUA pace. See TMUA Paper 1 vs Paper 2: what comes up.

Paper 2: the reasoning school does not teach

43.8% of Paper 2 was logic, proof and spotting errors in proofs — none of it in a standard A-Level. We teach it explicitly: necessary and sufficient conditions, “only if”, negating a statement, choosing a proof. Our free TMUA logic and proof notes are the reference.

Timed mocks, read properly

We use the official 2016–2023 papers under real conditions, then sort every lost mark by type: content, slip, time or reasoning. Here is how to sit a TMUA mock yourself, and our free readiness check shows where to start.

Applying to Oxford? It replaced the MAT with the TMUA for Maths, Computer Science and their joint honours courses. The October 2026 sitting runs 12–16 October, and results are released on 16 November 2026.

Book a Free Intro Meeting Take the free TMUA check

Entrance Exam Tutoring — Common Questions

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. Our full guide to the switch: the MAT has been replaced by the TMUA — what changed.

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. Several of our tutors sat these admissions tests themselves and studied at the universities that set them — Cambridge, Imperial, UCL and Warwick. Our founder, Alex Fraley, brings a different depth: a Distinction in Part III of the Mathematical Tripos at Cambridge, and years spent personally tutoring entrance-exam candidates through the TMUA, STEP and their predecessors.

Do you offer TMUA tutoring online?

Yes — all our lessons are online, so they work the same wherever you live. We teach both papers: fluency and speed on the topics Paper 1 keeps returning to, and the logic, proof and error-spotting that make up much of Paper 2 and that no A-Level teaches. A good first step is our free TMUA readiness check, which shows where you stand on each paper before any lessons are booked.

£105 / hour

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

“If it wasn’t for them I would not have managed to get an A in maths A-Level and a place at my first choice university.”

Tobias Ross

“He gives you a deeper understanding of equations and answers by breaking it down into first principles.”

Julian Paul

“Alex was very knowledgeable beyond the course… he helped me prepare for my admissions exam.”

Joshua Keedy

University Entrance Exam & Admissions Test Tutoring