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Free TMUA practice test

Practise for the Test of Mathematics for University Admission (TMUA) with a timed online test in the style of Paper 1, Applications of Mathematical Knowledge: 20 multiple-choice questions in 75 minutes, no calculator. Questions draw on GCSE Higher and AS-level pure maths, and every answer has a worked solution when you finish.

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Paper 1 style

Free TMUA Paper 1 Practice Test

20 questions in 75 minutes applying GCSE and AS-level maths to unfamiliar problems, no calculator.

20 questions · 75 minutes

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Timed like the real test

Each module has its own countdown and ends when time is up.

No calculator

As in the real test: work things out on paper.

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Marked instantly

See your score for each module, your weakest topics and a worked explanation for every question.

The real test at a glance

Paper 1: Applications of Mathematical Knowledge: 20 multiple-choice questions in 75 minutes
Paper 2: Mathematical Reasoning: 20 multiple-choice questions in 75 minutes, including simple ideas from logic
Total time: 2 hours 30 minutes
Calculator: Not allowed (nor a dictionary)
Scoring: 1.0 to 9.0; no negative marking
Test windows: 12–16 October 2026 and 4–8 January 2027, at Pearson VUE test centres

Checked against the official sources below on 27 October 2026.

What our questions cover

Algebra and functions
Composite and inverse functions, the factor and remainder theorems, the discriminant, binomial expansions and graph transformations.
Calculus
Gradients, tangents and normals, stationary points, definite integrals and areas under curves.
Sequences, logs and trigonometry
Arithmetic and geometric series, sums to infinity, exponential equations, logarithm laws and counting solutions of trigonometric equations.
GCSE Higher topics, harder
Indices, surds, quadratic inequalities, coordinate geometry and probability, set as multi-step problems.

Tips for test day

That's 3 minutes 45 seconds a question. Spend the first few seconds deciding the quickest route.
Check options by substitution or estimation when the algebra is long.
Paper 2 tests logic ("if… then", necessary and sufficient conditions, counterexamples), which isn't on the A-level syllabus. Practise it separately with the official materials.
Answer every question: wrong answers don't lose marks.

More help: What is the TMUA? A complete guide, Free ESAT Mathematics 2 practice test and Free ESAT practice tests.

Questions

Is this an official TMUA past paper?

No. It's an original test written by TutorAura in the style of TMUA Paper 1 (20 multiple-choice questions in 75 minutes, no calculator). UAT-UK publishes official practice papers and past papers on its website; use those too.

Does this cover Paper 2?

Not yet. Paper 2 tests mathematical reasoning and logic. This test is in the style of Paper 1, which applies GCSE and AS-level maths to unfamiliar problems.

Which universities use the TMUA?

For 2027 entry these include Imperial (Computing, Mathematics, and Economics, Finance and Data Science) and LSE (required for Economics and for Econometrics and Mathematical Economics, and recommended for several other programmes). Requirements change, so check each course page and the UAT-UK course list.

Do I get a TMUA score from 1 to 9?

No. UAT-UK doesn't publish how raw marks convert to the 1.0 to 9.0 scale, so we show questions correct with a breakdown by topic.

Official sources

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