Edexcel Pure Mathematics 1
Pearson Edexcel International Advanced Level (IAL) Mathematics
Welcome, students! This academic portal provides unit-specific study materials, syllabus outlines, and exam revision resources to help you master P1 and prepare for your modular exams.
1. Syllabus
The detailed syllabus structure for Edexcel Pure Mathematics 1 (P1) comprises the following topics:
1. Algebra and functions
1.1 Laws of indices.
1.2 Surds.
1.3 Quadratic functions and graphs.
1.4 Discriminant.
1.5 Completing the square & solving quadratics.
1.6 Simultaneous equations.
1.7 Interpret inequalities graphically.
1.8 Represent inequalities graphically.
1.9 Solutions of inequalities.
1.10 Algebraic manipulation of polynomials.
1.11 Cubic and reciprocal functions.
1.12 Graph transformations.
2. Coordinate geometry in the (x, y) plane
2.1 Equation of a straight line.
2.2 Parallel and perpendicular lines.
3. Trigonometry
3.1 Sine rule, cosine rule and triangle area.
3.2 Radian measure.
3.3 Sine, cosine and tangent functions.
4. Differentiation
4.1 The derivative and rates of change.
4.2 Differentiation of polynomials.
4.3 Gradients, tangents and normals.
5. Integration
5.1 Indefinite integration.
5.2 Integration of polynomials.
2. Study Lessons
2.1. Study Notes
Access core study notes and practice worksheets for each subtopic below:
| Subtopic | Revision Notes | Practice Questions |
|---|---|---|
| Algebra & Functions | ||
| Graphs of Functions | Notes | Practice |
| Inequalities | Notes | Practice |
| Laws of Indices and surds | Notes | Practice |
| Polynomials | Notes | Practice |
| Quadratics | Notes | Practice |
| Simultaneous Equations | Notes | Practice |
| Transformations of Functions | Notes | Practice |
| Coordinate Geometry | ||
| Equation of a straight line | Notes | Practice |
| Differentiation | ||
| Differentiation | Notes | Practice |
| Integration | ||
| Integration | Notes | Practice |
| Trigonometry | ||
| Basic Trigonometry | Notes | Practice |
| Radian Measure | Notes | Practice |
| Trigonometric Functions | Notes | Practice |
2.2. Cheat Sheets
Summary cheat sheets and formula revision guides for Edexcel Pure Mathematics 1 (P1):
| Topic / Concept | Cheat Sheet (PDF) |
|---|---|
| Ch.1 Algebraic Expressions | Cheat Sheet |
| Ch.2 Quadratics | Cheat Sheet |
| Ch.3 Equations and Inequalities | Cheat Sheet |
| Ch.4 Graphs and Transformations | Cheat Sheet |
| Ch.5 Straight Line Graphs | Cheat Sheet |
| Ch.6 Circles | Cheat Sheet |
| Ch.7 Algebraic Methods | Cheat Sheet |
| Ch.9 Trigonometric Ratios | Cheat Sheet |
| Ch.10 Trignometric Identities | Cheat Sheet |
| Ch.11 Vectors | Cheat Sheet |
| Ch.14 Exponentials and Logarithms | Cheat Sheet |
| Proof | Cheat Sheet |
3. Practice Questions
Topical worksheets with Question Papers (QP) & Mark Schemes (MS) alongside single-file Practice Question Packs (QP/MS) organized by official syllabus topics for Edexcel Pure Mathematics 1 (P1):
3.1. Topical Worksheets
| Topic / Concept | Worksheet (QP) | Mark Scheme (MS) |
|---|---|---|
| Algebra & Functions | ||
| Algebraic division, the factor theorem and the remainder theorem | QP | MS |
| Graphs of functions | QP | MS |
| Indices | QP | MS |
| Indices and surds − further questions | QP | MS |
| Inequalities | QP | MS |
| Inequalities - further questions | QP | MS |
| Mixed exam-style questions on algebra | QP | MS |
| Mixed exam-style questions on graphs of functions | QP | MS |
| Polynomials | QP | MS |
| Quadratics – completing the square | QP | MS |
| Quadratics – factorising | QP | MS |
| Quadratics – further questions | QP | MS |
| Quadratics – the quadratic formula and the discriminant | QP | MS |
| Simultaneous equations | QP | MS |
| Surds | QP | MS |
| The factor theorem and the remainder theorem − further questions | QP | MS |
| Transformations of graphs | QP | MS |
| Coordinate Geometry | ||
| Circles | QP | MS |
| Coordinate geometry − further questions | QP | MS |
| Equations of straight lines | QP | MS |
| Mixed exam-style questions on coordinate geometry | QP | MS |
| Parallel and perpendicular lines | QP | MS |
| Trigonometry | ||
| The sine rule and the cosine rule | QP | MS |
| Trigonometric Equations | QP | MS |
| Trigonometric ratios and graphs | QP | MS |
| Using trigonometric identities | QP | MS |
| Exponentials & Logarithms | ||
| Exponential graphs and using logarithms to solve equations | QP | MS |
| Laws of logarithms | QP | MS |
| Laws of logarithms − further questions | QP | MS |
| Mixed exam-style questions on exponentials and logarithms | QP | MS |
| e and ln x | QP | MS |
| Differentiation | ||
| Differentiating exponentials and logarithms | QP | MS |
| Gradient of a curve | QP | MS |
| Gradients, tangents, normals and rates of change | QP | MS |
| Increasing and decreasing functions and stationary points | QP | MS |
| Maximum and minimum problems | QP | MS |
| Integration | ||
| Area under a curve − further questions | QP | MS |
| Boundary conditions | QP | MS |
| Definite integrals and the area under a curve | QP | MS |
| Proof | ||
| Mixed exam-style questions on proof | QP | MS |
| Proof | QP | MS |
| Vectors | ||
| Cartesian components of a vector | QP | MS |
| Vectors | QP | MS |
3.2. Practice Question Packs
| Topic / Question Pack | QP/MS |
|---|---|
| Algebra & Functions | |
| Inequalities | QP/MS |
| Quadratics | QP/MS |
| Surds and Indices | QP/MS |
| Transformations and Graphs | QP/MS |
| Coordinate Geometry | |
| Circles | QP/MS |
| Straight Lines | QP/MS |
| Trigonometry | |
| Sine and Cosine Rule | QP/MS |
| Trigonometric Graphs | QP/MS |
| Exponentials & Logarithms | |
| Laws of Logarithms 1 | QP/MS |
| Laws of Logarithms 2 | QP/MS |
| Ch.14 Exponentials and Logarithms | QP/MS |
| Laws of Logarithms | QP/MS |
| Differentiation | |
| Stationary Points 1 | QP/MS |
| Tangents and Normals 1 | QP/MS |
| Stationary Points 2 | QP/MS |
| Tangents and Normals 2 | QP/MS |
| Stationary Points | QP/MS |
| Tangents and Normals | QP/MS |
| Proof | |
| Proof | QP/MS |
4. Topical Past Paper Questions
Official topical past paper question packs (PDF) for Edexcel Pure Mathematics 1 (P1):
| Chapter / Topical Pack | Question Pack (PDF) |
|---|---|
| Chapter 1: Algebra And Functions | Questions |
| Chapter 2: Coordinate Geometry In 2D Plane | Questions |
| Chapter 3: Trigonometry | Questions |
| Chapter 4: Differentiation | Questions |
| Chapter 5: Integration | Questions |
| Chapter 8: Exponentials And Logarithms | Questions |
5. Past Papers Bank
Search and filter official past exam papers. Use the control panel below to filter by year and variant:
Edexcel Pure Mathematics 1 Past Papers
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