TMUA Specification
The TMUA specification is the official list of what the test can assess. UAT-UK says the content specification and the question style are unchanged from the paper test, so this list applies to the October 2026 and January 2027 sittings. The tables below use the same topic codes as the practice questions. The official PDF remains the full statement of the syllabus.
Download the official materials
These files are published free by UAT-UK. This page links to them and does not rehost them.
- TMUA content specification (PDF) — the official topic list.
- Notes on Mathematics (PDF) — the mathematics for both papers. The same file is the ESAT Mathematics 2 guide.
- Notes on Logic and Proof (PDF) — Paper 2 only: argument, proof, and identifying errors in proofs.
- Specimen and practice tests — open in the Pearson player.
- 2016–2023 past papers — question papers, worked answers, and answer keys on UAT-UK’s archive.
The topic list
Section 1 is the mathematics, and both papers can test it. Part 1 is MM1–MM8. Part 2 is M1–M7. Those are two parts of one section, not two competing lists. Section 2 is argument, proof, and identifying errors, and it appears only on Paper 2. The codes stop at this level. The PDF goes into more detail inside each topic.
A practice link appears for each topic that already has original questions. Units has none yet. The question and the correct letter are free. Most worked solutions are part of the £59 bank. Every question from the 2016–2023 papers and the two early specimens is classified on the by-topic page, with a solution beside it. The full papers stay on the paper list.
| Code | Topic | Practice |
|---|---|---|
| MM1 | Algebra and functions | Practise this topic |
| MM2 | Sequences and series | Practise this topic |
| MM3 | Coordinate geometry | Practise this topic |
| MM4 | Trigonometry | Practise this topic |
| MM5 | Exponentials and logarithms | Practise this topic |
| MM6 | Differentiation | Practise this topic |
| MM7 | Integration | Practise this topic |
| MM8 | Graphs of functions | Practise this topic |
| Code | Topic | Practice |
|---|---|---|
| M1 | Units | Still being written |
| M2 | Number | Practise this topic |
| M3 | Ratio and proportion | Practise this topic |
| M4 | Algebra | Practise this topic |
| M5 | Geometry | Practise this topic |
| M6 | Statistics | Practise this topic |
| M7 | Probability | Practise this topic |
| Code | Topic | Practice |
|---|---|---|
| Arg | The logic of arguments | Practise this topic |
| Prf | Mathematical proof | Practise this topic |
| Err | Identifying errors in proofs | Practise this topic |
Paper 1 and Paper 2
Paper 1, Applications of Mathematical Knowledge, tests Section 1: MM1–MM8 and M1–M7. Paper 2, Mathematical Reasoning, tests Section 1 and Section 2, so the argument, proof, and error questions are only on Paper 2. Each paper is 75 minutes and 20 multiple-choice questions. The two papers are reported as one score from 1.0 to 9.0.
The two official sets of notes
Notes on Mathematics cover the Section 1 topics: algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration, and graphs, together with the Part 2 material the specification places alongside them. If you are also sitting ESAT Mathematics 2, it is the same document.
Notes on Logic and Proof cover Paper 2’s Section 2: how an argument is structured, how a proof is built, and how to find the error in a proof. That is the Arg, Prf, and Err rows above.
How to use this list
- Mark the topics you cannot yet answer.
- Read the matching section of the notes, then sit a 2016–2023 paper and mark it from UAT-UK’s worked answers.
- Use the practice link where one is listed. The short diagnostic on the practice page is an indicative band, not a predicted score.
- Read how the 1.0–9.0 scale is reported before you treat any practice mark as a result.
Common questions
Where can I download the TMUA specification?
From UAT-UK, free of charge. The download on this page opens the official PDF. SummitPapers does not rehost it.
Has the TMUA syllabus changed for the computer-based test?
UAT-UK says the content specification and question style are unchanged. The topic list on this page is the one for the October 2026 and January 2027 sittings. The live test is sat at a Pearson centre, and papers from 2024 onward are not released.
What are the Notes on Mathematics?
They are UAT-UK’s working notes for the mathematics on both papers. The same file is the ESAT Mathematics 2 guide.
Are the Notes on Logic and Proof only for Paper 2?
Yes. They cover argument, proof, and identifying errors in proofs. Those three topics appear only on Paper 2.
Is there a TMUA formula sheet?
UAT-UK does not publish a separate formula sheet in the TMUA preparation materials indexed here. The specification and the Notes on Mathematics are the official statements of the mathematics, including the standard results you are expected to use.
Do I need paid coaching to prepare?
UAT-UK says candidates do not need anything beyond the materials it and Pearson provide, and that it does not endorse commercial preparation services. Start with the specification, the two sets of notes, and the 2016–2023 papers.