The Test of Mathematics for University Admission (TMUA) is required or accepted by some universities for mathematics, computer science, economics, and related courses. It tests mathematical thinking, reasoning, and problem-solving without a calculator.
What the TMUA tests
The TMUA has two papers, each 75 minutes long with 20 multiple-choice questions. Paper 1 (Mathematical Knowledge) tests application of A-Level maths topics. Paper 2 (Mathematical Reasoning) tests logical thinking and proof. Both papers require you to work without a calculator. Scores run from 1.0 to 9.0, and most successful applicants score above 6.5.
Which universities require it
The TMUA is required or considered by Cambridge, Durham, Lancaster, LSE, Sheffield, Southampton, and Warwick for mathematics and related courses, among others. Always check the current requirements on the official TMUA website, as participating universities change. Some universities make it optional but give it significant weight.
How to prepare
Use official past papers from the TMUA website. These are free and the most accurate preparation resource. Work through each paper and check your answers against the mark scheme. Identify the A-Level topics where you make errors and revise them. Paper 2 is harder to practise for directly — work on logic and mathematical proof by reading through proof-based questions from your A-Level further maths content if you take it.
Timing and technique
Seventy-five minutes for 20 questions means 3.75 minutes per question. Some questions are quick, others are not. Do not get stuck on one question for too long — move on and return. Multiple choice means you can use elimination strategies if you are unsure. Write out working clearly, even though answers are multiple choice. This helps you avoid careless arithmetic errors.
Checklist
- Download and read the official TMUA specification
- Complete all available official past papers
- Review mark schemes carefully after each paper
- Revise A-Level topics where you make errors
- Practise under timed conditions from early in your preparation
- Work on mathematical proof and reasoning separately
Common mistakes to avoid
- Only practising Paper 1 and neglecting Paper 2 reasoning
- Attempting questions without writing out working
- Not revising the A-Level topics that appear most frequently
- Starting preparation too late in the autumn term