1. Number & Algebra

• Number Toolkit

  • Standard Form

  • Laws of Indices

• Exponentials & Logs

  • Introduction to Logarithms

  • Laws of Logarithms

  • Solving Exponential Equations

• Sequences & Series

  • Language of Sequences & Series

  • Sigma Notation

  • Arithmetic Sequences & Series

  • Geometric Sequences & Series

  • Applications of Sequences & Series

  • Compound Interest & Depreciation

• Proof & Reasoning

  • Proof

• Binomial Theorem

  • Binomial Coefficients & Pascal’s Triangle

  • Binomial Theorem

2. Functions

• Linear Functions & Graphs

  • Equations of a Straight Line

  • Parallel & Perpendicular Lines

• Quadratic Functions & Graphs

  • Quadratic Functions

  • Factorising Quadratics

  • Completing the Square

  • Solving Quadratic Equations

  • Quadratic Inequalities

  • Discriminants

• Functions Toolkit

  • Language of Functions

  • Composite Functions

  • Inverse Functions

  • Graphing Functions & Their Key Features

  • Intersecting Graphs

• Further Functions & Graphs

  • Reciprocal & Rational Functions

  • Exponential & Logarithmic Functions

  • Solving Equations Analytically

  • Solving Equations Graphically

  • Modelling with Functions

• Transformations of Graphs

  • Translations of Graphs

  • Reflections of Graphs

  • Stretches of Graphs

  • Composite Transformations of Graphs

3. Geometry & Trigonometry

• Geometry Toolkit

  • Coordinate Geometry

  • Arcs & Sectors Using Degrees

  • Radian Measure

  • Arcs & Sectors Using Radians

• Geometry of 3D Shapes

  • 3D Coordinate Geometry

  • Volume & Surface Area

• Trigonometry

  • Pythagoras & Right-Angled Trigonometry

  • Sine Rule, Cosine Rule & Area of a Triangle

  • Angles of Elevation & Depression

  • Bearings & Constructions

• The Unit Circle & Exact Values

  • The Unit Circle

  • Exact Values

• Trigonometric Functions & Graphs

  • Graphs of Trigonometric Functions

  • Solving Equations Using Trigonometric Graphs

  • Transformations of Trigonometric Functions

  • Modelling with Trigonometric Functions

• Trigonometric Equations & Identities

  • Simple Identities

  • Double Angle Formulae

  • Relationship Between Trigonometric Ratios

  • Linear Trigonometric Equations

  • Quadratic Trigonometric Equations

4. Statistics & Probability

• Statistics Toolkit

  • Sampling & Data Collection

  • Measures of Central Tendency

  • Measures of Dispersion

  • Frequency Tables

  • Linear Transformations of Data

  • Outliers

  • Box & Whisker Diagrams

  • Cumulative Frequency Graphs

  • Histograms

  • Interpreting Data

• Correlation & Regression

  • Scatter Diagrams & Correlation

  • Pearson’s Product-Moment Correlation Coefficient

  • Linear Regression

• Probability

  • Probability & Types of Events

  • Independent & Mutually Exclusive Events

  • Conditional Probability

  • Venn Diagrams

  • Tree Diagrams

• Probability Distributions

  • Discrete Probability Distributions

  • Expected Values

• Binomial Distribution

  • The Binomial Distribution

  • Calculating Binomial Probabilities

• Normal Distribution

  • The Normal Distribution

  • Calculations with Normal Distribution

  • Standardisation of Normal Variables & z-Values

  • Finding Unknown Parameters

5. Calculus

• Differentiation

  • Introduction to Derivatives

  • Differentiating Powers of x

  • Gradients, Tangents & Normals

  • Increasing & Decreasing Functions

• Further Differentiation

  • Differentiating Special Functions

  • Chain Rule

  • Product Rule

  • Quotient Rule

  • Second Order Derivatives

  • Stationary Points

  • Concavity & Points of Inflection

  • Derivatives & Graphs

• Integration

  • Introduction to Integration

  • Integrating Powers of x

  • Finding the Constant of Integration

  • Finding Areas Using a GDC

• Further Integration

  • Integrating Special Functions

  • Reverse Chain Rule

  • Integration by Substitution

  • Definite Integrals

  • Negative Integrals

  • Area Between a Curve and a Line

  • Area Between 2 Curves

• Optimisation

  • Modelling with Differentiation

• Kinematics

  • Displacement, Velocity & Acceleration

  • Calculus for Kinematics