TMUA preparation: notes, practice questions and timed papers
A number of UK universities ask for the TMUA for some maths, computer science and economics courses. Requirements differ between universities and courses, so check each course's own admissions page. Here are free notes for every topic in the specification, 269 original TMUA-style questions with full worked solutions, and a timed paper simulator.
- 32 topics
- 269 questions
- Free
The test
| Paper | Time | Questions | Content |
|---|---|---|---|
| Paper 1: Applications of Mathematical Knowledge | 75 minutes | 20 multiple choice | Section 1 (Parts 1 and 2) of the specification |
| Paper 2: Mathematical Reasoning | 75 minutes | 20 multiple choice | Sections 1 and 2 of the specification |
No calculator and no formula booklet. There is no penalty for a wrong answer, so answer every question. For test dates and booking deadlines, check UAT-UK's dates and deadlines page . Cambridge and Oxford applicants sit in October.
Paper 2: logic and proof
Paper 2 adds the logic of arguments, proof and errors in proofs, which most A Level courses do not teach. Read the Paper 2 guide.
Topics
MM1: Algebra and functions
- Indices and surds8 questions · Papers 1 and 2
- Quadratics and the discriminant7 questions · Papers 1 and 2
- Simultaneous equations and inequalities8 questions · Papers 1 and 2
- Polynomials, Factor and Remainder Theorems8 questions · Papers 1 and 2
- Functions7 questions · Papers 1 and 2
MM2: Sequences and series
- Sequences and recurrence relations7 questions · Papers 1 and 2
- Arithmetic and geometric series9 questions · Papers 1 and 2
- Binomial expansion8 questions · Papers 1 and 2
MM3: Coordinate geometry in the (x, y)-plane
MM4: Trigonometry
- Sine rule, cosine rule and area8 questions · Papers 1 and 2
- Radians, arcs and sectors7 questions · Papers 1 and 2
- Trig graphs, identities and equations8 questions · Papers 1 and 2
MM5: Exponentials and logarithms
- Exponential graphs and laws of logarithms7 questions · Papers 1 and 2
- Exponential equations9 questions · Papers 1 and 2
MM6: Differentiation
- Differentiating powers of x7 questions · Papers 1 and 2
- Tangents, normals and stationary points9 questions · Papers 1 and 2
MM7: Integration
- Definite integrals and area7 questions · Papers 1 and 2
- Integration: the Fundamental Theorem and the trapezium rule9 questions · Papers 1 and 2
MM8: Graphs of functions
- Sketching and transformations7 questions · Papers 1 and 2
- Roots, intersections and shape8 questions · Papers 1 and 2
M1-M7: GCSE-level knowledge (Part 2)
- Number, units and bounds8 questions · Papers 1 and 2
- Ratio, proportion and percentages7 questions · Papers 1 and 2
- Algebra at GCSE level6 questions · Papers 1 and 2
- Geometry and vectors7 questions · Papers 1 and 2
- Statistics and probability8 questions · Papers 1 and 2
Arg1-Arg4: The logic of arguments
- Converse and contrapositive12 questions · Paper 2
- Necessary and sufficient conditions13 questions · Paper 2
- Quantifiers and negation11 questions · Paper 2
Prf1-Prf5: Mathematical proof
- Types of proof and counterexamples8 questions · Paper 2
- Deductions, conjectures and ordering proofs13 questions · Paper 2
Err1-Err2: Identifying errors in proofs
How we write and check the questions
Every question on these pages is our own: none is copied or paraphrased from UAT-UK's papers. Each answer is re-solved independently by computer (sympy or brute force) before it is published, and every question is compared with the official papers to make sure it is original.
FAQ
What is the TMUA?
The Test of Mathematics for University Admission, run by UAT-UK and taken on screen at Pearson VUE test centres. It has two 75-minute papers of 20 multiple-choice questions each: Paper 1 (Applications of Mathematical Knowledge) and Paper 2 (Mathematical Reasoning).
Is a calculator allowed in the TMUA?
No. There is no calculator and no formula booklet, so you need to recall the formulae in the specification.
What maths does the TMUA test?
Section 1 is almost all AS pure maths plus higher GCSE maths, for both papers. Paper 2 adds Section 2: logic, proof and identifying errors in proofs.
How is the TMUA scored?
There is no penalty for wrong answers. UAT-UK scales Papers 1 and 2 together into one overall score.
Where are the official TMUA past papers?
UAT-UK publishes specimen papers, practice tests and past papers with worked answers. Our past-papers page links to them.
TMUA is run by UAT-UK. A Level Math Revision is independent: it is not affiliated with or endorsed by UAT-UK, Pearson VUE or any university. Every question here is our own.