1. Number Operations & Integers

Number Operations

Mathematical Operations

Order of Operations (BIDMAS/BODMAS)

Negative Numbers

Money Calculations

Addition & Subtraction

Multiplication & Division

Related Calculations

Counting Principles

Types of Number, Prime Factors, HCF & LCM

Types of Number

Multiples, Factors & Primes

Squares, Cubes & Roots

Reciprocals

Prime Factor Decomposition

HCF & LCM

2. Fractions, Decimals & Percentages

Fractions

Introduction to Fractions

Fractions of Amounts

Equivalent & Simplified Fractions

Mixed Numbers & Improper Fractions

Adding & Subtracting Fractions

Multiplying & Dividing Fractions

Percentages

Introduction to Percentages

Percentages of Amounts

Percentage Increases & Decreases

Percentage Change

Reverse Percentages

Fractions, Decimals & Percentages

Converting Fractions, Decimals & Percentages

Ordering Fractions, Decimals & Percentages

3. Indices & Surds

Powers, Roots & Standard Form

Powers & Roots

Laws of Indices

Converting to & from Standard Form

Operations with Standard Form

Exact Values

Exact Values

4. Approximation & Estimation

Rounding, Estimation & Error Intervals

Rounding to a Given Place Value

Rounding to Significant Figures

Estimation

Error Intervals

Using a Calculator

Using a Calculator

5. Ratio, Proportion & Rates of Change

Introduction to Ratio

Introduction to Ratios

Equivalent & Simplified Ratios

Sharing in a Ratio

Ratio Problem Solving

Ratios with Fractions, Decimals & Percentages

Multiple Ratios

Direct & Inverse Proportion

Direct & Inverse Proportion

Exchange Rates & Best Buys

Exchange Rates

Best Buys

Simple & Compound Interest, Growth & Decay

Simple Interest

Compound Interest

Depreciation

Exponential Growth & Decay

6. 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

Factorising

Factorising Out Terms

Factorising Quadratics

Difference of Two Squares

Rearranging Formulas

Rearranging Formulas

Algebraic Reasoning

Algebraic Reasoning

Linear Equations

Solving Linear Equations

Equations with Brackets & Fractions

Equations with Unknowns on Both Sides

Solving Inequalities

Interpreting Inequalities

Representing Inequalities on a Number Line

Solving Linear Inequalities

Solving Quadratic Equations

Solving Quadratic Equations

Simultaneous Equations

Simultaneous Equations

Forming & Solving Equations

Forming Equations from Words

Forming Equations from Shapes

Functions

Introduction to Functions

Sequences

Introduction to Sequences

Continuing Sequences

Types of Sequences

nth Terms of Linear Sequences

7. Graphs of Equations & Functions

Coordinate Geometry

Coordinates

Midpoint of a Line

Gradient of a Line

Linear Graphs

Equations of Straight Lines (y = mx + c)

Drawing Straight Line Graphs

Parallel Lines

Graphs of Functions

Types of Graphs

Quadratic Graphs

Drawing Graphs from Tables

Real-Life Graphs

Distance-Time Graphs

Speed-Time Graphs

Conversion Graphs

Rates of Change of Graphs

8. Basic Geometry

Symmetry & Shapes

Introduction to Lines & Angles

Rotational Symmetry

Lines of Symmetry

Planes of Symmetry

Angles in Polygons & Parallel Lines

Angles around Points & Lines

Angles in Triangles

Angles in Quadrilaterals

Angles in Polygons

Angles in Parallel Lines

2D & 3D Shapes

Properties of Polygons

Properties of 3D Shapes

Nets of Solids

Plans & Elevations

9. Congruence, Similarity, Vectors & Transformations

Congruence, Similarity & Geometrical Proof

Congruence

Congruent Triangles

Similarity

Similar Lengths

Geometrical Proof

Vectors

Introduction to Column Vectors

Representing Vectors as Diagrams

Finding Vector Paths

Transformations

Translations

Reflections

Rotations

Enlargements

10. Mensuration, Lengths, Areas & Volumes

Standard & Compound Units

Time

Converting between Units

Squared & Cubic Units

Compound Measures

Speed, Density & Pressure

Bearings, Scale Drawing, Constructions & Loci

Bearings

Scale

Constructing Triangles

Constructions

Loci

Area & Perimeter

Perimeter

Area

Adding & Subtracting Areas

Problem Solving with Areas

Circles, Arcs & Sectors

Properties of Circles

Area & Circumference of Circles

Arc Lengths & Sector Areas

Volume & Surface Area

Volume

Problem Solving with Volumes

Surface Area

Pythagoras & Trigonometry

Pythagoras Theorem

Trigonometry to Find Lengths

Trigonometry to Find Angles

Angles of Elevation & Depression

Exact Trig Values

11. Probability

Introduction to Probability

Basic Probability

Sample Space Diagrams

Relative & Expected Frequency

Simple Probability Diagrams

Two-Way Tables

Frequency Trees

Set Notation & Venn Diagrams

Probabilities from Venn Diagrams

Tree Diagrams & Combined Probability

Probability Tree Diagrams

Combined Probability

12. Statistics

Averages, Ranges & Data

Mean, Median & Mode

Calculations with the Mean

Averages from Tables

Averages from Grouped Data

Range

Comparing Data Sets

Population & Sampling

Statistical Diagrams

Tally Charts & Frequency Tables

Bar Charts & Pictograms

Pie Charts

Time Series Graphs

Reading & Interpreting Statistical Diagrams

Comparing Statistical Diagrams

Scatter Graphs & Correlation

Scatter Graphs & Correlation

Lines of Best Fit

Exam boards

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

Study tools

• OCR GCSE Maths · Past Papers

Related links

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