TMUA Syllabus and Specification: What You Need to Know

There is one TMUA specification, and it sits behind both papers. Because the test is not modular, you do not have several syllabuses to track: one content list defines everything that can be assessed. Knowing what it says, and being honest about which parts you are shaky on, is the first real step in TMUA preparation.

One specification, two papers

UAT-UK publishes a single content specification for the TMUA. Both Paper 1, Applications of Mathematical Knowledge, and Paper 2, Mathematical Reasoning, draw on the same underlying mathematics. What differs is what each paper does with it: Paper 1 applies the content to unfamiliar problems, and Paper 2 reasons about arguments, proof and logic built on the same base. So the content revision feeds both papers at once, which is covered in Paper 1 vs Paper 2.

What the specification covers

The specification defines the assumed knowledge as content typically covered in Higher Level GCSE and AS-level mathematics. In practice that means the core of school maths: algebra and functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation and integration at AS level, and the basics of counting and probability. The exact topics, and the depth expected, are defined in the specification itself, which is why it is worth reading in full rather than working from a summary. Paper 2 additionally assumes comfort with elementary logic and proof, which the free UAT-UK Notes on Logic and Proof set out.

Turn the specification into a checklist

The most useful thing you can do with the specification is treat it as an audit. Read through it and mark each topic in one of three ways:

1. Solid, meaning you could answer a question on it now.
2. Shaky, meaning you know it but would need to revise.
3. Forgotten, meaning you would have to relearn it.

That honest pass tells you exactly where your revision time should go, and it stops you spending hours reviewing content you already know. Our topic-by-topic textbook then covers those areas so you can rebuild the shaky and forgotten ones before you move to timed practice.

Why this matters for your score

Every TMUA question sits inside the assumed knowledge in the specification, so a gap there is a gap in your score. Working from the official content, rather than from a general sense of what "AS maths" contains, keeps your revision aligned with what the test actually asks. And because Paper 2 reasons on top of that content, weak foundations hurt you twice. Once your content is solid, how to prepare for the TMUA covers the practice that turns knowledge into marks.

Official TMUA resources

The specification is defined by UAT-UK, which sets and runs the TMUA. Its pages are the authoritative source, and the tools on tmua.fyi are supplementary to them.

• TMUA test and content specification, UAT-UK
• TMUA preparation materials, including Notes on Mathematics and Notes on Logic and Proof, UAT-UK