Beyond the Syllabus: Olympiad, TMUA, MAT and STEP Pathway

The route

1. Maths challenges

Short, clever multiple-choice and short-answer problems that use the maths you already know in unfamiliar ways. Practise with our Junior, Intermediate and Senior problems; the real competitions (UKMT challenges, MAA AMC 8, 10 and 12, the Australian Mathematics Competition, India’s IOQM) are entered through schools.

Junior · Intermediate · Senior · Official competitions and past papers

2. Olympiad-style problems

Fewer, harder problems where you must write a complete argument. Our Olympiad-style set trains the habits: find the answer, then prove nothing else works. The official next steps are the follow-on rounds of the national competitions (for example UKMT’s olympiad rounds after the Senior Challenge, or the olympiad stages that follow India’s IOQM).

Olympiad-style problems · Problem-solving strategies

3. University admissions tests

Some university maths courses set their own tests. These need the same problem-solving habits, applied to school-level algebra, functions, calculus and logic.

Admissions tests below

University admissions tests

What each test is, in brief, with the official pages. Requirements change every year: check the university’s own admissions page.

TMUA (Test of Mathematics for University Admission)

Run by UAT-UK and used by a number of UK universities for mathematics, computer science, economics and related courses. The University of Oxford’s Mathematical Institute says Oxford uses the TMUA from the 2026 admissions round for Mathematics, Computer Science and their joint courses, in place of the MAT. Check each university’s own admissions page for whether you need it.

TMUA: about the test (UAT-UK) (official)
TMUA at Oxford (Mathematical Institute) (official)
TMUA practice on A Level Math Revision (ours: free topic notes and practice questions)

MAT (Oxford Mathematics Admissions Test)

Oxford’s own maths admissions test, sat by applicants for Mathematics and Computer Science courses up to and including 2025. Oxford’s Mathematical Institute says the MAT will not take place from 2026. Its past papers, published by Oxford, remain excellent problem-solving practice at this level.

Maths Admissions Test past papers (Mathematical Institute, University of Oxford) (official)

STEP (Sixth Term Examination Paper)

Longer, harder written papers (STEP 2 and STEP 3) used mainly by the University of Cambridge as part of conditional offers for Mathematics; the exams are run by OCR. Cambridge’s Faculty of Mathematics and NRICH run a free online STEP Support Programme.

STEP: Faculty of Mathematics, University of Cambridge (official)
STEP Mathematics (OCR) (official)
STEP Support Programme (Cambridge and NRICH, free) (official)

We are independent and are not affiliated with or endorsed by UAT-UK, the University of Oxford, the University of Cambridge, OCR or any competition organiser. Details change every year, so always check the official pages linked here. Our practice problems are original and written in the style only.

Questions

What is the TMUA?