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TMUA — Test of Mathematics for University Admission

What it is. The maths-admissions test — required or used by Cambridge, Imperial, Oxford (from 2026 entry), Warwick, LSE, Durham and Bath. For a maths target this is the test that matters most, so it's the priority mock. Run by UAT-UK; sat on-screen at a Pearson VUE centre (use PDFs/the practice test for a home mock).

Format & rules

  • Paper 1 — Applications of Mathematical Knowledge: 20 multiple-choice questions, 75 minutes.
  • Paper 2 — Mathematical Reasoning (plus simple ideas from elementary logic): 20 multiple-choice questions, 75 minutes.
  • No calculator, no dictionary.
  • No negative marking — so answer every question (guess the unfinished ones before time runs out).
  • Scored 1.0–9.0 (one decimal), combining both papers. No pass/fail.
  • Content: Higher-GCSE + AS-level pure (algebra, functions, coordinate geometry, sequences, trig, logs, elementary calculus) + logic/proof.

Where to get papers

Free at the TMUA Prepare page: the Test Specification, Notes on Logic and Proof (read this before Paper 2), and an official timed practice test. Older official TMUA past papers (2016–2021) are also widely available and are the best practice.

How to sit it (mock protocol)

  1. Read the Notes on Logic and Proof first (Paper 2 leans on them).
  2. For each paper: 75-minute timer, 20 questions, no calculator/dictionary/notes. Pen + blank paper.
  3. Answer all 20 — no penalty for wrong answers.
  4. Do Paper 1 and Paper 2 as separate 75-minute blocks; mark against the key.

How to score & interpret

  • Raw score = number correct out of 20 per paper (no deductions).
  • The official 1.0–9.0 can't be reproduced exactly at home (per-paper conversion); if the specific past paper publishes a score-conversion table, use it.
  • Rough guide on the scale: ~6.5 is a typical strong / offer-level score (Cambridge, Imperial); 7.0+ is excellent. These are hard tests — a strong applicant might get only ~14/20 raw; the median is lower.
  • For a no-calculus starting point, expect a low score now — TMUA tests AS-level content, so it measures the gap to close (calculus/algebra) rather than aptitude. Re-run after AS-level prep to track progress toward ~6.5.