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Self-assessment — maths tests & mock protocols

The maths assessments used to gauge current level and the admissions bar — what each is, how to sit a realistic mock at home, and how to read the result. Each test has its own page (rules · papers · how to sit · how to score · how to interpret); the comparison and the shared principles are here.

Which test matters (for a maths target)

  • TMUA is the one that counts — it's the maths-admissions test for Cambridge, Imperial, Oxford (from 2026), Warwick, LSE, Durham and Bath.
  • SMC is for gauging raw aptitude (it's not an admissions test).
  • STEP is the hard ceiling (Cambridge offers; Warwick alternative) — a target to build toward, not a starting point.
  • ESAT matters only if engineering/science is in scope (its Maths 1/2 are good practice regardless).
  • MAT is now legacy for maths — Oxford moves to the TMUA from 2026 — so it's optional practice, not a target.

Comparison

Test Who uses it (the universities here) Format Calc Neg. marking Score Content level
SMC (UKMT) aptitude calibration — not an admissions test 25 MCQ, 90 min No Yes (−1) raw /125 → certificate syllabus-light (no calculus)
TMUA Cambridge · Imperial · Oxford (2026+) · Warwick · LSE · Durham · Bath 2 papers × 20 MCQ × 75 min No No 1.0–9.0 GCSE + AS (light calculus)
ESAT Cambridge Eng/NatSci · Imperial Eng Maths 1 + 2 modules; 27 MCQ × 40 min each No No 1.0–9.0 AS-level
MAT Oxford (until 2025 → TMUA 2026) — legacy 2½ h; 25 MCQ + 2 long; /100 No No /100 AS pure (no FM)
STEP (2 & 3) Cambridge · Warwick (alt) · Imperial (some) 3 h; 12 Qs, best 6 count; /120 No n/a (proof) grades S/1/2/3/U A-level + Further Maths

Shared mock principles (make it like the real sitting)

  1. Replicate conditions: a strict timer, no calculator, no dictionary, no notes, no phone, nothing looked up. Pen + blank paper for working only.
  2. Marking rule differs: on SMC a wrong answer costs −1, so only guess if you can eliminate options; on TMUA / ESAT / MAT there's no penalty, so answer everything (guess the unfinished ones before time runs out).
  3. Mark against the official key/solutions and record the raw score.
  4. Scaled scores: the official 1.0–9.0 (TMUA/ESAT) and STEP grades can't always be reproduced at home (the raw→scale conversion is set per paper). Use raw % / marks, plus any published conversion table or grade boundaries for that specific paper.
  5. Aptitude vs content: SMC needs no calculus (pure reasoning). TMUA, ESAT, MAT and STEP test AS-level → A-level + Further Maths content — so until that content is learned, expect low scores; that's a measure of the content gap, not of ability.

See Qualification levels for where each test sits on the GCSE → AS → A-level → Further Maths ladder.