Entrance exam and admissions test tuition. TMUA, STEP, 11+.
These exams don't test what your child has been taught. That's the point.
A-Level Maths rewards a student who can recognise a question type and execute the method. Admissions tests are built specifically to defeat that. They take familiar material and ask something unfamiliar of it — and a student who has only ever been drilled on procedures will sit there, competent and stuck.
School entrance papers at 11+ and 13+ do the same thing a few years earlier: they reach past the curriculum to find out how a child thinks when they don't already know the answer.
That gap is the whole job. It isn't more content — it's a different habit of mind, and it takes months rather than weeks to build.
I scored 599/600 UMS in A-Level Maths, took Further Maths to A*, and read Mathematics to Master's level at Bristol. I've spent over ten years preparing students for these exams, and I've taught students who went on to Eton, Harrow, Westminster, Winchester and St Paul's.
If your child is sitting one of these, I can prepare them for it.
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Why strong students struggle
An A* student can still fail these papers.
Every year I meet students predicted A* in Maths and Further Maths who open a STEP paper and cannot start a single question. This is not a knowledge problem. They know every technique on the page.
What they've never been asked to do is sit with a problem for twenty minutes without knowing where it's going — to try something, watch it fail, and try something else. School maths almost never requires that, because school maths is examined on time and on syllabus.
The preparation is therefore not revision. It's building tolerance for not knowing, and a repertoire of things to try when nothing is obvious.
What changed for 2026
The MAT is gone.
Oxford ran the Maths Admissions Test from 2007 to 2025 and has now retired it. From the 2026 sitting, every Oxford applicant for Maths, Computer Science and the joint honours courses sits the TMUA instead.
That makes the TMUA the common test across Oxford, Cambridge, Imperial, LSE, Warwick and Durham — a single paper now carrying most of the weight in competitive UK maths admissions.
If your child spent last summer working through MAT past papers, that time wasn't wasted — the material overlaps heavily and the problem-solving spirit is the same. But the timeline and the format have both moved.
Read the full breakdown of what changed →University admissions tests
The tests that decide competitive offers.
For Maths, Computer Science and Economics at the most selective universities, the admissions test is often the single largest factor in whether an application progresses. Grades get you considered. These papers get you shortlisted.
TMUA
Test of Mathematics for University Admission. Two papers: the first applies A-Level content to unfamiliar problems, the second tests mathematical reasoning, logic and proof. Built on A-Level Maths — Further Maths is not required.
STEP 2 & STEP 3
The hardest school-level maths exam in the UK, and the one that most often decides whether a Cambridge offer is met. Long, multi-part problems with no scaffolding, marked on the quality of the full argument rather than the final answer.
MAT past papers
The MAT no longer runs, but nineteen years of papers and full solutions remain freely available from Oxford — and they are still some of the best problem-solving practice a TMUA candidate can get. I use them alongside TMUA-specific work.
Interview preparation
Oxford and Cambridge interviews are, in practice, a supervised problem-solving session. The skill being assessed is the same one the written tests measure — thinking out loud, recovering from a wrong turn, and taking a hint without being led.
How preparation works
A plan mapped back from the exam date.
Admissions test preparation fails when it's treated as a revision sprint. The habits these papers reward take months to form, so the work is structured backwards from the sitting date and paced accordingly.
Assessment first
The first lesson is a diagnostic. I give your child real questions at the right level and watch how they approach them — not just whether they get there. You then receive a written breakdown of where they actually stand.
Close the syllabus gaps
These papers assume total fluency in the underlying A-Level content. Any hesitation there consumes the thinking time the problem itself needs, so we fix that before touching problem-solving technique.
Build the problem-solving repertoire
Substitution, symmetry, extreme cases, working backwards, spotting invariants. These are teachable moves, and the difference between a student who freezes and one who starts is simply knowing what to try.
Real papers, properly marked
Past papers under timed conditions from the moment they're useful — and marked the way examiners mark them, on the argument rather than the answer. Homework is set and returned with written feedback between every session.
School entrance exams
11+, 13+ and Common Entrance.
Senior school entrance maths sits well ahead of the primary curriculum, and it is examined under time pressure that most children have never experienced. The papers vary considerably between schools, so preparation has to be aimed at the specific schools on your list rather than at "11+ maths" in general.
11+ Maths
Independent and grammar school entrance at 11+. Arithmetic fluency, multi-step word problems, ratio and proportion, early algebra, and the timed-accuracy work that decides most marks.
13+ Common Entrance
ISEB Common Entrance at 13+, sat for entry to independent senior schools. Levels 1 to 3 papers, with the harder tiers reaching well into GCSE territory.
ISEB Common Pre-Test
The adaptive online test used by many senior schools to shortlist in Year 6 or Year 7. Adaptive scoring means pacing and early accuracy matter more than on a conventional paper.
School-specific papers
Many senior schools set their own maths paper with a distinct house style. Preparation is targeted at the schools you're actually applying to, using their own past papers where published.
Scholarship papers
Academic and maths scholarship papers are a significant step above Common Entrance — closer in character to an admissions test, with genuine problem-solving rather than curriculum recall.
Exam technique
Working under time, checking efficiently, knowing when to leave a question and come back. For most children this is worth more marks than any additional content.
Schools my students have gone on to attend.
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