HomeNAME

TMUA

Two 75-minute papers testing mathematical reasoning, not just calculation.

MAT

Oxford's problem-solving test, built on AS-Level content.

STEP

Cambridge's toughest test — depth over breadth, six questions to shine.

TMUA

The TMUA is a computer-based admissions test used by UK universities to assess mathematical reasoning ability beyond A-Level grades alone. It consists of two 75-minute papers taken one after the other (5 minute gap), each made up of 20 multiple-choice questions, with both papers carrying equal weight and no penalty for incorrect answers. Each question offers five answer options with no partial credit. Calculators aren't permitted, and there's no formula sheet - candidates are expected to know and recall the relevant formulae themselves. The two papers test different skills: Paper 1 covers applications of mathematical knowledge, while Paper 2 covers mathematical reasoning - proofs, counterexamples, logical implications, and negation of statements, testing whether a candidate can think like a mathematician rather than just calculate. Scores range from 1.0 to 9.0, and the scoring is statistically adjusted year to year so a given score represents a consistent standard of ability, with roughly 4.5 as average and 7.0+ considered exceptional. It's typically sat in October, with a January window also available - though Oxford and Cambridge applicants must use the October sitting unless covered by specific exceptions. The TMUA is now used by Oxford (for Computer Science), Imperial, UCL, LSE and others - worth double-checking current requirements per university, since they shift year to year.

Cambridge

Oxford

Warwick

LSE

UCL

MAT

The Maths Admissions Test will be replaced by the TMUA

Oxford

STEP

STEP is widely regarded as the most demanding admissions test - it's designed to resemble undergraduate-level mathematical thinking rather than school-level exam technique. Cambridge colleges favour it because it's a stronger predictor of success in the Mathematics Tripos than A-Levels alone, partly because its less standardised questions better distinguish genuine mathematical ability from good exam coaching. STEP 1 has been discontinued - only STEP 2 and STEP 3 are now taken, each a paper-based exam lasting 3 hours. Each paper contains 13 long-form questions (8 Pure, 5 shared between Mechanics and Statistics), each worth 20 marks, but candidates only need to attempt 6 - meaning depth of mastery across chosen topics matters far more than broad coverage. Papers 2 is based on A-Level Mathematics and Paper 3 on A-Level Further Mathematics. Grades run U, 3, 2, 1, S (highest), with boundaries shifting year to year - historically an S has needed around 90 marks and a grade 1 around 70, out of 120 max. It's set and administered by OCR, usually sat in mid-to-late June, and is typically part of a conditional Cambridge offer rather than something sat speculatively. Its official users are Cambridge, Imperial, and Warwick - though since the 2025 entry cycle, Imperial and Warwick have moved to TMUA instead, leaving Cambridge as STEP's primary remaining user, where it's almost always required as part of a conditional offer.

Cambridge

Warwick

Imperial

TMUA

MAT

STEP

TMUA

MAT

STEP

Solution

Worked Example

Solution

Worked Example