TMUA Specification: What You Need to Know
The TMUA specification tells you what you may be tested on. It is worth reading before deciding what to revise: otherwise, it is surprisingly easy to spend hours learning something impressive while overlooking something essential.
This is a practical overview for October 2026 and January 2027. Use it alongside the official specification and preparation materials, which remain the full statement of the requirements.
How the syllabus is organised
Section 1 applies to both papers. It combines mathematics largely drawn from AS-level pure maths and Higher GCSE maths. Section 2 adds logic, proof and evaluating arguments for Paper 2. Paper 2 therefore requires mathematical knowledge as well as reasoning.
The main areas are:
| Area | Examples to check |
|---|---|
| Algebra and functions | Indices, surds, quadratics, inequalities, polynomials |
| Sequences and series | Recurrences, arithmetic and geometric series, binomial expansion |
| Coordinate geometry | Straight lines, circles and circle properties |
| Trigonometry | Exact values, radians, equations, sine and cosine rules |
| Exponentials and logarithms | Graphs, log laws and equations |
| Calculus | Differentiation, integration and their interpretations |
| Graphs | Transformations, intersections and composite functions |
| GCSE foundations | Number, ratio, geometry, vectors, probability and statistics |
| Logic and proof | Implications, quantifiers, counterexamples and errors in arguments |
This is a summary, not an exhaustive checklist. The detailed specification includes restrictions: for example, questions requiring the logarithmic change-of-base formula are excluded. Do not assume that every technique in an A-level textbook is required.
Do I need Further Maths?
The TMUA is designed to be approachable without Further Maths. University course entry requirements are a separate question: a course may expect Further Maths even though the test does not require its syllabus. Oxford explains this distinction in its TMUA guidance.
My advice is to make the required mathematics dependable before collecting more advanced methods. A technique is useful if you understand when it works and can recognise when to use it.
Turn the specification into a working checklist
For each item, put yourself into one of three groups:
- Not yet learned: I need teaching and introductory examples.
- Familiar but unreliable: I recognise the idea, but cannot consistently use it independently.
- Comfortable: I can explain it and apply it in unfamiliar questions.
Be honest with the middle category. Recognising a worked solution is not the same as finding one yourself. I suspect most of us have occasionally confused the two.
For instance, you may know the sine rule but overlook the possibility of two triangles. Or you may know how to translate a graph but become uncertain when several transformations are combined. A broad topic can contain quite specific gaps.
What should I do with a gap?
Choose one manageable idea. Watch or read an explanation, attempt focused questions, and then try a different question without help. Make a short note of what you needed to notice.
Return to mixed questions afterwards. Focused practice tells you which method to use; a paper requires you to recognise that for yourself.
Our teaching videos and logic course can help with this. You do not need to rush straight into a full mock every time you sit down to study.
Official reference
- UAT-UK preparation page: current specification, notes and practice tests
- TMUA content specification
- Oxford: TMUA content and preparation
Checked on 27 October 2026. Check the edition on the specification's cover when preparing for a later sitting.