TMUA · STEP · PAT · 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 PAT. 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 the main maths admissions test for Oxford (Maths & Computer Science, from 2026 entry — replacing the MAT), Imperial, Warwick and a growing list of others. Two 75-minute papers — Mathematical Thinking and Mathematical Reasoning — 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 thirteen 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. STEP 1 has been discontinued — only STEP 2 and STEP 3 now run.
The Physics Aptitude Test covers maths and physics at AS/A2 level but requires applying these in novel, unfamiliar ways under time pressure. It combines multiple-choice and written sections. Strong mathematical reasoning is essential — many PAT questions are as much about applied quantitative reasoning as about physics knowledge, and marks are lost by those who know the physics but can’t execute the maths quickly.
The Engineering and Science Admissions Test replaced the ENGAA and NSAA from 2025 entry, for engineering and science applicants to Cambridge and Imperial. Candidates sit 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.
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. He has sat these admissions tests himself and has tutored entrance-exam candidates personally for years across the TMUA (and its predecessor, the MAT), STEP, and PAT. The depth of Cambridge-level mathematical training is directly relevant to what these exams test.
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 — Oxford (Maths & Computer Science), Imperial, Warwick, Bath, Durham and more
Sixth Term Examination Paper (2 and 3) — Cambridge maths conditional offers; Warwick also accepts STEP
Physics Aptitude Test — Oxford physics, physics & philosophy, and engineering courses
Engineering & Science Admissions Test — Cambridge and Imperial engineering and science (replaced the ENGAA and NSAA)
Any other admissions test — if your exam isn’t listed above, ask us. We support a range of university-specific maths and physics assessments.
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.
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