1. Number

Number Operations

Mathematical Symbols

Order of Operations (BIDMAS/BODMAS)

Irrational Numbers

Negative Numbers

Money Calculations

Addition & Subtraction

Multiplication & Division

Related Calculations

Systematic Lists

Product Rule for Counting

Prime Factors, HCF & LCM

Types of Numbers

Prime Factor Decomposition

Uses of Prime Factor Decomposition

HCF & LCM

Powers, Roots & Standard Form

Powers & Roots

Laws of Indices

Converting to & from Standard Form

Operations with Standard Form

Fractions

Basic Fractions

Mixed Numbers & Improper Fractions

Adding & Subtracting Fractions

Multiplying & Dividing Fractions

Percentages

Basic Percentages

Percentage Increases & Decreases

Reverse Percentages

Simple & Compound Interest, Growth & Decay

Simple Interest

Compound Interest

Depreciation

Exponential Growth & Decay

Fractions, Decimals & Percentages

Converting Fractions, Decimals & Percentages

Recurring Decimals

Ordering Fractions, Decimals & Percentages

Rounding, Estimation & Bounds

Rounding & Estimation

Upper & Lower Bounds

Surds

Simplifying Surds

Rationalising Denominators

Using a Calculator

Using a Calculator

2. Algebra

Introduction to Algebra

Algebraic Notation

Algebraic Vocabulary

Substitution

Collecting Like Terms

Algebraic Roots & Indices

Algebraic Roots & Indices

Expanding Brackets

Expanding & Simplifying Single Brackets

Expanding Double Brackets

Expanding Triple Brackets

Factorising

Factorising Out Terms

Factorising by Grouping

Factorising Simple Quadratics

Factorising Harder Quadratics

Difference of Two Squares

Deciding the Factorisation Method

Completing the Square

Completing the Square

Algebraic Fractions

Simplifying Algebraic Fractions

Adding & Subtracting Algebraic Fractions

Multiplying & Dividing Algebraic Fractions

Solving Equations with Algebraic Fractions

Rearranging Formulas

Formulas where Subject Appears Once

Formulas where Subject Appears Twice

Algebraic Proof

Algebraic Proof

Linear Equations

Solving Linear Equations

Quadratic Equations

Solving Quadratics by Factorising

The Quadratic Formula

Completing the Square

Deciding the Quadratic Method

Simultaneous Equations

Linear Simultaneous Equations

Quadratic Simultaneous Equations

Iteration

Iteration

Forming & Solving Equations

Forming Equations from Words

Forming Equations from Shapes

Problem Solving with Equations

Functions

Introduction to Functions

Composite Functions

Inverse Functions

Coordinate Geometry

2D Coordinates

Midpoint of a Line

Gradient of a Line

Length of a Line

Linear Graphs

Equations of Straight Lines (y = mx + c)

Drawing Straight Line Graphs

Parallel Lines

Perpendicular Lines

Graphs of Functions

Types of Graphs

Quadratic Graphs

Drawing Graphs from Tables

Solving Equations Using Graphs

Trigonometric Graphs

Solving Trig Equations

Equation of a Circle

Equation of a Circle

Equation of a Tangent

Estimating Gradients & Areas under Graphs

Finding Gradients of Tangents

Finding Areas under Graphs

Real-Life Graphs

Distance-Time Graphs

Speed-Time Graphs

Conversion Graphs

Rates of Change of Graphs

Solving Inequalities

Solving Linear Inequalities

Solving Quadratic Inequalities

Graphing Inequalities

Representing Inequalities as Regions

Finding Inequalities from Regions

Transformations of Graphs

Translations of Graphs

Reflections of Graphs

Sequences

Introduction to Sequences

Types of Sequences

nth Terms of Linear Sequences

Quadratic Sequences

3. Ratio, Proportion & Rates of Change

Ratios

Introduction to Ratios

Sharing in a Ratio

Working with Proportion

Problem Solving with Ratios

Ratios with Fractions, Decimals & Percentages

Multiple Ratios

Direct & Inverse Proportion

Direct Proportion

Inverse Proportion

Standard & Compound Units

Time

Converting between Units

Squared & Cubic Units

Compound Measures

Speed, Density & Pressure

Exchange Rates & Best Buys

Exchange Rates

Best Buys

4. Geometry & Measures

Symmetry & Shapes

Rotational Symmetry

Lines of Symmetry

Planes of Symmetry

2D Shapes

3D Shapes

Plans & Elevations

Angles in Polygons & Parallel Lines

Basic Angle Properties

Angles in Polygons

Angles in Parallel Lines

Bearings, Scale Drawing, Constructions & Loci

Bearings

Scale

Constructing Triangles

Constructions

Loci

Circle Theorems

Angles at Centre & Circumference

Angle in a Semicircle

Theorems with Chords & Tangents

Angles in Cyclic Quadrilaterals

Angles in the Same Segment

The Alternate Segment Theorem

Circle Theorem Proofs

Area & Perimeter

Perimeter

Area

Adding & Subtracting Areas

Problem Solving with Areas

Circles, Arcs & Sectors

Area & Circumference of Circles

Volume & Surface Area

Volume

Problem Solving with Volumes

Surface Area

Congruence, Similarity & Geometrical Proof

Congruence

Congruent Triangles

Similarity

Similar Lengths

Geometrical Proof

Area & Volume of Similar Shapes

Similar Areas & Volumes

Pythagoras & Trigonometry

Pythagoras Theorem

SOHCAHTOA

Angles of Elevation & Depression

Exact Trig Values

Sine, Cosine Rule & Area of Triangles

The Sine Rule

The Cosine Rule

Area of a Triangle

Deciding the Trigonometric Rule

3D Pythagoras & Trigonometry

3D Pythagoras & Trigonometry

Vectors

Introduction to Column Vectors

Representing Vectors as Diagrams

Length of a Vector

Position & Displacement Vectors

Finding Vector Paths

Problem Solving with Vectors

Transformations

Translations

Reflections

Rotations

Enlargements

Combination of Transformations

5. Probability

Introduction to Probability

Basic Probability

Sample Space Diagrams

Relative & Expected Frequency

Simple Probability Diagrams

Two-Way Tables

Frequency Trees

Set Notation & Venn Diagrams

Tree Diagrams

Probability Tree Diagrams

Combined & Conditional Probability

Combined Probabilities

Conditional Probability

Combined Conditional Probabilities

6. Statistics

Averages, Ranges & Data

Mean, Median & Mode

Calculations with the Mean

Averages from Tables

Averages from Grouped Data

Range & Interquartile Range

Comparing Data Sets

Population & Sampling

Statistical Diagrams

Bar Charts & Pictograms

Pie Charts

Time Series Graphs

Reading & Interpreting Statistical Diagrams

Comparing Statistical Diagrams

Histograms

Frequency Density

Drawing Histograms

Interpreting Histograms

Cumulative Frequency & Box Plots

Cumulative Frequency

Drawing Cumulative Frequency Diagrams

Interpreting Cumulative Frequency Diagrams

Box Plots

Scatter Graphs & Correlation

Scatter Graphs & Correlation

Lines of Best Fit

Exam boards

• AQA GCSE Maths: Foundation
• Edexcel GCSE Maths: Higher
• Edexcel GCSE Maths: Foundation
• OCR GCSE Maths: Higher
• OCR GCSE Maths: Foundation

Study tools

• AQA GCSE Maths · Exam Questions
• AQA GCSE Maths · Flashcards
• AQA GCSE Maths · Past Papers

Related links

• GCSE Maths · Revision Notes
• GCSE Maths · Exam Questions
• GCSE Maths · Flashcards
• GCSE Maths · Past Papers
• GCSE Maths · Glossary