GCSE MATHEMATICS (9–1)
Complete Revision Notes
Pearson Edexcel 1MA1 Higher & Foundation
All Six Topic Areas Covered
1. Number — 2. Algebra — 3. Ratio, Proportion & Rates of Change
4. Geometry & Measures — 5. Probability — 6. Statistics
Papers 1, 2 & 3 — Foundation & Higher Tier — Syllabus-Matched
All key concepts, definitions, formulae and worked examples
, How to Use These Notes
These notes cover the complete Pearson Edexcel GCSE (9–1) Mathematics specification (1MA1),
matching every topic for both Foundation and Higher tiers. Higher-only content is marked [H only].
Colour Code Key
■ Blue boxes — Key concepts and important explanations
■ Green boxes — Definitions (learn these precisely)
■ Orange boxes — Exam technique and tips
■ Red boxes — Common mistakes to avoid
■ Purple boxes — Formulae (essential to remember)
■ Blue border boxes — Worked examples with step-by-step solutions
Assessment Structure:
Paper 1 (non-calculator) — 1h 30min, 80 marks, 33.3% of total
Paper 2 (calculator) — 1h 30min, 80 marks, 33.3% of total
Paper 3 (calculator) — 1h 30min, 80 marks, 33.3% of total
Grades: Foundation tier — grades 1–5; Higher tier — grades 4–9 (grade 3 allowed).
Exam Tip
Higher tier is worth pursuing if you are aiming for grade 6+. The additional Higher topics
(surds, harder algebra, circle theorems, vectors proofs) are well worth learning and appear
regularly.
, GCSE Mathematics (9–1) — Edexcel 1MA1 Complete Revision Notes
Contents
1 Number 4
1.1 Order of Operations and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Integers, Decimals and Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 The Four Operations with Fractions . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Primes, Factors and Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Powers, Roots and Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Standard Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5.2 Recurring Decimals [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Surds [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.7 Rounding and Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Algebra 8
2.1 Algebraic Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Factorising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Completing the Square [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 Simultaneous Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Graphs and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 Straight Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.2 Quadratic Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.3 Other Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.4 Graph Transformations [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.5 Gradients and Areas Under Graphs [H only] . . . . . . . . . . . . . . . . . . . 11
2.5 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.6 Algebraic Fractions [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.7 Iteration [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Ratio, Proportion and Rates of Change 13
3.1 Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.1 Compound Interest and Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Direct and Inverse Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Speed, Density, Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 Scale and Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Geometry and Measures 14
4.1 Angle Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Triangles and Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 Pythagoras’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4.1 Right-Angled Triangles (SOH CAH TOA) . . . . . . . . . . . . . . . . . . . . . 15
4.4.2 Sine Rule, Cosine Rule and Area [H only] . . . . . . . . . . . . . . . . . . . . 16
4.5 Perimeter, Area and Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.6 Similarity and Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.7 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.8 Circle Theorems [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.9 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2
Complete Revision Notes
Pearson Edexcel 1MA1 Higher & Foundation
All Six Topic Areas Covered
1. Number — 2. Algebra — 3. Ratio, Proportion & Rates of Change
4. Geometry & Measures — 5. Probability — 6. Statistics
Papers 1, 2 & 3 — Foundation & Higher Tier — Syllabus-Matched
All key concepts, definitions, formulae and worked examples
, How to Use These Notes
These notes cover the complete Pearson Edexcel GCSE (9–1) Mathematics specification (1MA1),
matching every topic for both Foundation and Higher tiers. Higher-only content is marked [H only].
Colour Code Key
■ Blue boxes — Key concepts and important explanations
■ Green boxes — Definitions (learn these precisely)
■ Orange boxes — Exam technique and tips
■ Red boxes — Common mistakes to avoid
■ Purple boxes — Formulae (essential to remember)
■ Blue border boxes — Worked examples with step-by-step solutions
Assessment Structure:
Paper 1 (non-calculator) — 1h 30min, 80 marks, 33.3% of total
Paper 2 (calculator) — 1h 30min, 80 marks, 33.3% of total
Paper 3 (calculator) — 1h 30min, 80 marks, 33.3% of total
Grades: Foundation tier — grades 1–5; Higher tier — grades 4–9 (grade 3 allowed).
Exam Tip
Higher tier is worth pursuing if you are aiming for grade 6+. The additional Higher topics
(surds, harder algebra, circle theorems, vectors proofs) are well worth learning and appear
regularly.
, GCSE Mathematics (9–1) — Edexcel 1MA1 Complete Revision Notes
Contents
1 Number 4
1.1 Order of Operations and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Integers, Decimals and Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 The Four Operations with Fractions . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Primes, Factors and Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Powers, Roots and Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Standard Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5.2 Recurring Decimals [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Surds [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.7 Rounding and Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Algebra 8
2.1 Algebraic Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Factorising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Completing the Square [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 Simultaneous Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Graphs and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 Straight Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.2 Quadratic Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.3 Other Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.4 Graph Transformations [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.5 Gradients and Areas Under Graphs [H only] . . . . . . . . . . . . . . . . . . . 11
2.5 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.6 Algebraic Fractions [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.7 Iteration [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Ratio, Proportion and Rates of Change 13
3.1 Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.1 Compound Interest and Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Direct and Inverse Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Speed, Density, Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5 Scale and Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Geometry and Measures 14
4.1 Angle Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Triangles and Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 Pythagoras’ Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4.1 Right-Angled Triangles (SOH CAH TOA) . . . . . . . . . . . . . . . . . . . . . 15
4.4.2 Sine Rule, Cosine Rule and Area [H only] . . . . . . . . . . . . . . . . . . . . 16
4.5 Perimeter, Area and Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.6 Similarity and Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.7 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.8 Circle Theorems [H only] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.9 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2
