TMUA Syllabus and Topic Breakdown: What You Need to Know
A comprehensive breakdown of the TMUA syllabus covering Paper 1 pure mathematics topics and Paper 2 mathematical reasoning, with full topic codes and descriptions from the official specification.
TMUA Syllabus Overview
The TMUA syllabus is divided into two sections. Section 1 covers the mathematical knowledge required for both papers, split into Part 1 (AS-level pure mathematics) and Part 2 (Higher GCSE mathematics). Section 2 covers the mathematical reasoning skills tested specifically in Paper 2.
Paper 1: Applications of Mathematical Knowledge
Paper 1 tests the mathematical content set out in Section 1 of the specification. The main pure mathematics topics are:
| Code | Topic | Description |
|---|---|---|
| MM1 | Algebra and Functions | Laws of indices, surds, quadratic functions, simultaneous equations, inequalities, polynomials, Factor/Remainder Theorem, function properties |
| MM2 | Sequences and Series | Sequences (formula and recurrence), arithmetic series, geometric series, binomial expansion |
| MM3 | Coordinate Geometry | Straight lines, circle equations, circle properties |
| MM4 | Trigonometry | Sine/cosine rules, radian measure, trig functions, identities, solving trig equations |
| MM5 | Exponentials and Logarithms | Exponential graphs, laws of logarithms, solving exponential/logarithmic equations |
| MM6 | Differentiation | Derivatives as gradients, differentiation of x^n, applications to tangents, normals, stationary points |
| MM7 | Integration | Definite/indefinite integrals, Fundamental Theorem of Calculus, trapezium rule, differential equations |
| MM8 | Graphs of Functions | Sketching common functions, transformations, using differentiation for graph shape |
Section 1 Part 2 Topics
Section 1 Part 2 covers content broadly at Higher GCSE level, with some overlap with Part 1. It includes:
| Code | Topic | Description |
|---|---|---|
| M1 | Units | Standard and compound units, unit conversions |
| M2 | Number | Integers, fractions, surds, standard form, bounds, rounding |
| M3 | Ratio and Proportion | Scale factors, ratio, percentages, direct/inverse proportion, growth and decay |
| M4 | Algebra | Algebraic notation, substitution, equations, inequalities, sequences, graphs, simultaneous equations |
| M5 | Geometry | Angles, polygons, congruence, similarity, Pythagoras, circle theorems, trigonometry, vectors |
| M6 | Statistics | Data representation, averages, scatter graphs, correlation |
| M7 | Probability | Probability calculations, Venn diagrams, tree diagrams, conditional probability |
Paper 2: Mathematical Reasoning
Paper 2 tests mathematical reasoning skills based on both Sections 1 and 2 of the specification. The Section 2 content focuses on three key areas:
The Logic of Arguments
| Code | Topic | Description |
|---|---|---|
| Arg1 | Mathematical Logic | True/false, and/or/not, if-then, if and only if, converse, contrapositive |
| Arg2 | Necessary and Sufficient | Understanding and using necessary and sufficient conditions |
| Arg3 | Quantifiers | For all, for some, there exists |
| Arg4 | Negation | Negating statements with the above terms |
Mathematical Proof
| Code | Topic | Description |
|---|---|---|
| Prf1 | Proof Types | Direct deductive proof, proof by cases, proof by contradiction, disproof by counterexample |
| Prf2 | Deduction | Deduce implications from given statements |
| Prf3 | Conjectures | Make conjectures based on small cases and justify them |
| Prf4 | Proof Ordering | Rearrange statements into correct proof order |
| Prf5 | Sophisticated Reasoning | Problems requiring a sophisticated chain of reasoning |
Identifying Errors in Proofs
| Code | Topic | Description |
|---|---|---|
| Err1 | Error Identification | Identifying errors in purported proofs |
| Err2 | Common Errors | Common mathematical errors in purported proofs (e.g., invalid cancellation, assuming sin A = sin B implies A = B) |
Paper 1 vs Paper 2: Key Differences
Paper 1 focuses on applying mathematical knowledge and uses the Section 1 content. Paper 2 additionally requires Section 2 reasoning skills and tests the ability to construct and analyse mathematical arguments. Both papers are 75 minutes with 20 multiple-choice questions each, and both are taken consecutively on the same day.
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