Number

Number Toolkit

Types of Number

Irrational Numbers

Negative Numbers

Mathematical Operations

Order of Operations (BIDMAS/BODMAS)

Addition & Subtraction

Multiplication & Division

Operations with Decimals

Set Notation & Venn Diagrams

Set Notation & Venn Diagrams

Prime Factors, HCF & LCM

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 Toolkit

Introduction to Fractions

Fractions of Amounts

Equivalent & Simplified Fractions

Mixed Numbers & Improper Fractions

Adding & Subtracting Fractions

Multiplying & Dividing Fractions

Percentages Toolkit

Basic Percentages

Percentage Increases & Decreases

Reverse Percentages

Simple & Compound Interest, Growth & Decay

Simple Interest

Compound Interest

Depreciation

Exponential Growth & Decay

Surds

Simplifying Surds

Rationalising Denominators

Fractions, Decimals & Percentages

Converting Fractions, Decimals & Percentages

Recurring Decimals

Ordering Fractions, Decimals & Percentages

Ratio & Proportion

Introduction to Ratios

Equivalent & Simplified Ratios

Sharing in a Ratio

Problem Solving with Ratios

Working with Proportion

Compound Measures

Compound Measures

Speed, Density & Pressure

Time, Currency & Conversions

Time

Money Calculations

Exchange Rates

Rounding, Estimation & Bounds

Rounding to a Given Place Value

Rounding to Significant Figures

Estimation

Upper & Lower Bounds

Using a Calculator

Using a Calculator

Algebra & Sequences

Algebra Toolkit

Algebraic Notation

Algebraic Vocabulary

Substitution

Collecting Like Terms

Algebraic Roots & Indices

Algebraic Roots & Indices

Expanding & Factorising Brackets

Expanding & Simplifying Single Brackets

Expanding Double Brackets

Expanding Triple Brackets

Factorising Out Terms

Factorising by Grouping

Factorising Simple Quadratics

Factorising Harder Quadratics

Difference of Two Squares

Deciding the Factorisation Method

Linear Equations & Inequalities

Solving Linear Equations

Equations with Brackets & Fractions

Equations with Unknowns on Both Sides

Solving Linear Inequalities

Quadratic Equations

Solving Quadratics by Factorising

The Quadratic Formula

Completing the Square

Deciding the Quadratic Method

Rearranging Formulas

Formulas where Subject Appears Once

Formulas where Subject Appears Twice

Forming & Solving Equations

Forming Equations from Words

Forming Equations from Shapes

Problem Solving with Equations

Simultaneous Equations

Solving Simultaneous Equations

Forming Simultaneous Equations

Algebraic Fractions

Simplifying Algebraic Fractions

Adding & Subtracting Algebraic Fractions

Multiplying & Dividing Algebraic Fractions

Solving Equations with Algebraic Fractions

Functions

Introduction to Functions

Domain & Range

Composite Functions

Inverse Functions

Sequences

Introduction to Sequences

Other Sequences

nth Terms of Linear Sequences

Quadratic Sequences

Proportion

Direct Proportion

Inverse Proportion

Coordinate Geometry & Graphs

Coordinate Geometry

Midpoint of a Line

Coordinates

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

Quadratic Graphs

Quadratic Graphs

Further Graphs & Tangents

Types of Graphs

Drawing Graphs from Tables

Solving Equations from Graphs

Finding Gradients of Tangents

Solving & Graphing Inequalities

Representing Inequalities as Regions

Finding Inequalities from Regions

Real-Life Graphs

Conversion Graphs

Distance-Time Graphs

Speed-Time Graphs

Rates-of-Change Graphs

Geometry

Geometry Toolkit

Rotational Symmetry

Lines of Symmetry

Planes of Symmetry

Properties of Polygons

Properties of Circles

Properties of 3D Shapes

Nets of Solids

Converting between Units

Squared & Cubic Units

Angles in Polygons & Parallel Lines

Angles around Points & Lines

Angles in Triangles

Angles in Quadrilaterals

Angles in Polygons

Angles in Parallel Lines

Bearings, Constructions & Scale Drawings

Bearings

Scale

Constructing Triangles

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

Lengths, Areas & Volumes

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

Congruence & Similarity

Congruence

Similarity

Similar Lengths

Similar Areas & Volumes

Pythagoras & Trigonometry

Pythagoras & Trigonometry with Right-Angled Triangles

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 Trig Rule

3D Pythagoras & Trigonometry

3D Pythagoras & Trigonometry

Vectors & Transformations

Vectors

Introduction to Column Vectors

Representing Vectors as Diagrams

Magnitude of a Vector

Position & Displacement Vectors

Finding Vector Paths

Problem Solving with Vectors

Transformations

Translations

Reflections

Rotations

Enlargements

Probability

Probability Toolkit

Basic Probability

Possibility (Sample Space) Diagrams

Relative & Expected Frequency

Probability Diagrams (Tree & Venn Diagrams)

Two-Way Tables

Probabilities from Venn Diagrams

Probability Tree Diagrams

Combined Probabilities

Statistics

Averages & Range

Mean, Median & Mode

Calculations with the Mean

Averages from Tables

Averages from Grouped Data

Range & Interquartile Range

Comparing Data Sets

Statistical Diagrams

Bar Charts & Pictograms

Pie Charts

Reading & Interpreting Statistical Diagrams

Comparing Statistical Diagrams

Histograms

Frequency Density

Drawing Histograms

Interpreting Histograms

Cumulative Frequency

Cumulative Frequency

Drawing Cumulative Frequency Diagrams

Interpreting Cumulative Frequency Diagrams

Scatter Graphs & Correlation

Scatter Graphs & Correlation

Lines of Best Fit

Study tools

• Cambridge (CIE) O Level Maths · Exam Questions
• Cambridge (CIE) O Level Maths · Past Papers

Related links

• O Level Maths · Revision Notes
• O Level Maths · Exam Questions
• O Level Maths · Past Papers