Number

Number Operations, Rounding & Bounds

Mathematical Symbols

Addition & Subtraction

Negative Numbers

Multiplication & Division

Order of Operations (BIDMAS/BODMAS)

Related Calculations

Number Machines

Rounding & Estimation

Upper & Lower Bounds

Using a Calculator

Prime Factors, HCF & LCM

Types of Number

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, Decimals & Percentages

Basic Fractions

Mixed Numbers & Improper Fractions

Adding & Subtracting Fractions

Multiplying & Dividing Fractions

Basic Percentages

Converting Fractions, Decimals & Percentages

Recurring Decimals

Ordering Fractions, Decimals & Percentages

Percentages Increases & Decreases

Reverse Percentages

Ratio & Proportion

Introduction to Ratios

Sharing in a Ratio

Multiple Ratios

Ratios with Fractions, Decimals & Percentages

Working with Proportion

Information in Tables, Charts & Diagrams

Information in Tables, Charts & Diagrams

Venn Diagrams

Finance, Money & Interest

Money Calculations

Exchange Rates

Best Buys

Simple Interest

Compound Interest

Depreciation & Appreciation

Income & Tax

Savings & Loans

Annual Equivalent Rate (AER)

Annual Percentage Rate (APR)

Budgets, Bank Statements & Bills

Profit, Loss & Price Changes

Surds

Irrational Numbers

Simplifying Surds

Simplifying Fractions with Surds

Algebra

Algebraic Conventions, Expressions & Indices

Algebraic Notation

Algebraic Vocabulary

Substitution

Collecting Like Terms

Algebraic Roots & Indices

Expanding Brackets

Expanding & Simplifying Single Brackets

Expanding Double Brackets

Expanding a Linear & a Quadratic

Factorising

Factorising Out Terms

Factorising by Grouping

Factorising Simple Quadratics

Factorising Harder Quadratics

Difference of Two Squares

Deciding the Factorisation Method

Rearranging Formulas

Formulas where Subject Appears Once

Formulas where Subject Appears Twice

Linear Equations & Inequalities

Solving Linear Equations

Solving Linear Inequalities

Forming Equations from Words

Forming Equations from Shapes

Simultaneous Equations

Linear Simultaneous Equations

Quadratic Equations

Solving Quadratics by Factorising

The Quadratic Formula

Problem Solving with Equations

Algebraic Fractions

Simplifying Algebraic Fractions

Adding & Subtracting Algebraic Fractions

Solving Equations with Algebraic Fractions

Trial & Improvement

Trial & Improvement

Direct & Inverse Proportion

Direct Proportion

Inverse Proportion

Sequences

Introduction to Sequences

nth Terms of Linear Sequences

Quadratic Sequences

Coordinate Geometry & Linear Graphs

Coordinates

Midpoint of a Line

Coordinates on Parallelograms

Coordinates using Distance & Angle

Gradient of a Line

Equations of Straight Lines (y = mx + c)

Drawing Straight Line Graphs

Representing Inequalities as Regions

Finding Inequalities from Regions

Parallel Lines

Perpendicular Lines

Graphs of Curves

Types of Graphs

Quadratic Graphs

Drawing Graphs from Tables

Solving Equations Using Graphs

Estimating Gradients & Areas under Graphs

Rates of Change of Graphs

Finding Gradients of Tangents

Finding Areas under Graphs

Real-life Graphs

Distance-Time Graphs

Speed-Time Graphs

Conversion Graphs

Geometry & Measures

Representation of 2D & 3D Shapes

2D Shapes

3D Shapes & Nets

Plans & Elevations

2D Representations of 3D Shapes

Accurate Drawings, Loci, Maps & Bearings

Constructions

Constructing Triangles

Loci

Scale

Bearings

Angles in Polygons & Parallel Lines

Basic Angle Properties

Angles in Parallel Lines

Angles in Polygons

Geometrical Proof

Circle Theorems

Theorems with Chords & Tangents

Angles at Centre & Circumference

Angle in a Semicircle

Angles in Cyclic Quadrilaterals

Angles in the Same Segment

The Alternate Segment Theorem

Time, Units, Speed & Density

Time

Converting between Units

Squared & Cubic Units

Compound Measures

Speed, Density & Fuel Consumption

Area & Perimeter

Perimeter

Area

Adding & Subtracting Areas

Problem Solving with Areas

Circles, Arcs & Sectors

Area & Circumference of Circles

Arc Lengths & Sector Areas

Volume & Surface Area

Volume

Problem Solving with Volumes

Surface Area

Pythagoras' Theorem & Trigonometry

Pythagoras Theorem

SOHCAHTOA

Angles of Elevation & Depression

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

Trigonometric Graphs & Equations

Trigonometric Graphs

Solving Trig Equations

Transformations & Symmetry

Lines of Symmetry

Rotational Symmetry

Translations

Reflections

Rotations

Enlargements

Combination of Transformations

Similar Shapes & Congruence

Congruence

Congruent Triangles

Similarity

Similar Lengths

Similar Areas & Volumes

Statistics & Probability

Data Collection & Sampling

The Data Handling Cycle

Data, Populations & Samples

Sampling Techniques

Questionnaires

Averages Ranges & Data

Mean, Median & Mode

Calculations with the Mean

Averages from Tables

Averages from Grouped Data

Median from Grouped Data

Range & Interquartile Range

Comparing Data Sets

Statistical Diagrams

Bar Charts & Pictograms

Pie Charts

Time Series Graphs

Frequency Polygons

Reading & Interpreting Statistical Diagrams

Comparing Statistical Diagrams

Graphs in the Media

Histograms

Frequency Density

Drawing Histograms

Interpreting Histograms

Median from a Histogram

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

Probability of Single Events

Basic Probability

Relative & Expected Frequency

Probability of Multiple Events

Mutually Exclusive & Independence

Sample Space Diagrams

Two Way Tables

Probability from Venn Diagrams

Tree Diagrams & Combined Probabilities

Probability Tree Diagrams

Combined Probabilities

Conditional Probability

Combined Conditional Probabilities

Exam boards

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

Study tools

• WJEC GCSE Maths & Numeracy (Double Award) · Past Papers

Related links

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