Edexcel A Level Maths: Pure
Exam Questions

Language of Proof, Proof by Deduction, Proof by Exhaustion, Disproof by Counter Example

Proof by Contradiction

Laws of Indices, Manipulating Surds, Rationalising the Denominator with Surds

Quadratic Graphs, Discriminants, Completing the Square, Solving Quadratic Equations, Solving Hidden Quadratics using Substitutions

Linear Simultaneous Equations using Elimination, Linear Simultaneous Equations using Substitution, Quadratic Simultaneous Equations

Linear Inequalities, Quadratic Inequalities, Inequalities on Graphs

Expanding Brackets, Polynomial Division, Factor Theorem, Factorisation

Rational Expressions, Improper Algebraic Fractions

Sketching Polynomials, Sketching Reciprocal Graphs, Solving Equations Graphically, Proportional Relationships

Language of Functions, Composite Functions, Inverse Functions, Sketching Graphs of Modulus Functions, Solving Equations with Modulus Functions

Translations, Stretches, Reflections

Combinations of Transformations

Partial Fractions with Linear Denominators, Partial Fractions with Squared Linear Denominators

Modelling with Functions

Further Modelling with Functions

Basic Coordinate Geometry, Equation of a Straight Line, Parallel & Perpendicular Gradients, Modelling with Straight Lines

Equation of a Circle, Finding the Centre & Radius, Bisection of Chords, Angle in a Semicircle, Radius & Tangent

Binomial Expansion

General Binomial Expansion, Subtleties of the General Binomial Expansion, Multiple General Binomial Expansion, Approximating Values using the Binomial Expansion

Arithmetic Sequences, Arithmetic Series

Geometric Sequences, Geometric Series

Language of Sequences & Series, Sigma Notation, Recurrence Relations

Modelling with Sequences & Series

Definitions of Trigonometric Functions, Right-Angled Triangles, Non-Right-Angled Triangles

Graphs of Trigonometric Functions, Transformations of Trigonometric Functions

Simple Trigonometric Identities, Linear Trigonometric Equations, Quadratic Trigonometric Equations, Strategy for Trigonometric Equations

Radian Measure, Trigonometry Exact Values, Small Angle Approximations

Definitions of Reciprocal Trigonometric Functions, Graphs of Reciprocal Trigonometric Functions, Identities with Reciprocal Trigonometric Functions, Inverse Trigonometric Functions

Compound Angle Formulae, Double Angle Formulae, Harmonic Form

Strategy for Further Trigonometric Equations

Trigonometric Proof

Modelling with Trigonometric Functions

Exponential Functions, Logarithmic Functions, "e", Derivatives of Exponential Functions

Laws of Logarithms, Exponential Equations

Exponential Growth & Decay, Using Exponentials & Logarithms in Modelling, Logarithmic Graphs

Definition of Gradient, Differentiation from First Principles, Differentiating Powers of x

Gradients, Tangents & Normals, Increasing & Decreasing Functions, Second Order Derivatives, Stationary Points & Turning Points, Sketching Gradient Functions, Modelling with Differentiation (Optimisation)

Differentiation of Trigonometric Functions from First Principles, Differentiating Other Functions, Chain Rule, Product Rule, Quotient Rule, Differentiating Reciprocal and Inverse Trig Functions

Concave & Convex Functions, Points of Inflection, Connected Rates of Change

Implicit Differentiation

Fundamental Theorem of Calculus, Integrating Powers of x, Definite Integration, Area Under a Curve, Area between a curve and a line

Integration as the limit of a sum, Integrating Other Functions, Reverse Chain Rule, Integrating f'(x)/f(x), Integration by Substitution, Harder Substitution, Integrating with Trigonometric Identities, Integration by Parts, Integration using Partial Fractions, Area between 2 curves, Integration Decision Making

General Solutions, Particular Solutions, Separation of Variables, Modelling with Differential Equations, Solving & Interpreting Differential Equations

Basics of Parametric Equations, Eliminating the Parameter of Parametric Equations, Sketching Graphs of Parametric Equations

Parametric Differentiation, Parametric Integration, Modelling with Parametric Equations

Change of Sign Method, Failure of the Change of Sign Method, x = g(x) Iteration, Newton-Raphson Method, Trapezium Rule (Numerical Integration)

Numerical Methods in Context

Basic Vectors, Magnitude & Direction, Vector Addition, Position Vectors, Problem Solving using Vectors

Vectors in 3 Dimensions, Problem Solving using 3D Vectors