AQA · A-Level

Your journey to excellence inMathematics

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Structure of Mathematical Proof

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Proof by Deduction

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Proof by Exhaustion

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Disproof by Counterexample

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Proof by Contradiction

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Laws of Indices

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Manipulating Surds

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Quadratic Functions and Graphs

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Simultaneous Equations

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Inequalities and Graphical Solutions

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Polynomials and Factor Theorem

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Graphs of Functions

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Composite and Inverse Functions

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Transformations of Graphs

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Partial Fractions

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Equations of Straight Lines

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Circle Geometry

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Parametric Equations

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Applications in Modelling

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Binomial Expansion

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Arithmetic Sequences and Series

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Geometric Sequences and Series

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Sigma Notation

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Sequences in Modelling

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Sine, Cosine, and Tangent

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Radian Measure

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Trigonometric Graphs and Values

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Secant, Cosecant, and Cotangent

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Trigonometric Identities

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Double Angle and Compound Angle Formulae

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Solving Trigonometric Equations

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Applications in Context

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Exponential Functions and Graphs

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Logarithmic Functions and Graphs

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Laws of Logarithms

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Solving Exponential Equations

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Logarithmic Graphs for Modelling

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Exponential Growth and Decay

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Derivative as Gradient and Rate of Change

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Rules of Differentiation

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Second Derivatives

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Applications: Gradients and Stationary Points

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Product, Quotient, and Chain Rules

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Implicit and Parametric Differentiation

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Differential Equations

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Fundamental Theorem of Calculus

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Basic Integration Rules

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Definite Integrals and Areas

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Integration by Substitution

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Integration by Parts

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Integration with Partial Fractions

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Differential Equations with Separable Variables

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Applications in Context

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Locating Roots

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Iterative Methods

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Newton-Raphson Method

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Numerical Integration

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Applications in Modelling

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Vectors in 2D and 3D

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Magnitude and Direction

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Vector Addition and Multiplication

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Position Vectors and Distances

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Applications in Context

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Population and Sample

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Sampling Techniques

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Critiquing Sampling Methods

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Diagrams for Single-Variable Data

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Scatter Diagrams and Correlation

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Measures of Central Tendency

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Outliers and Data Cleaning

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Mutually Exclusive and Independent Events

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Conditional Probability

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Probability Modelling

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Discrete Probability Distributions

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Binomial Distribution

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Normal Distribution

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Selecting Appropriate Distributions

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Language of Hypothesis Testing

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Binomial Distribution Tests

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Normal Distribution Tests

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SI Units and Derived Quantities

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Language of Kinematics

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Graphs of Motion

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Formulae for Constant Acceleration

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Calculus in Kinematics

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Motion Under Gravity

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Concept of Force

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Newton's Laws of Motion

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Weight and Gravitational Acceleration

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Equilibrium of Forces

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Resultant Forces and Dynamics

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Friction and Rough Surfaces

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Moments in Static Contexts

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