IGCSEMaths: ExtendedCIERevision Notes

CIE IGCSE Maths: Extended Revision Notes

Concise resources for the CIE IGCSE Maths: Extended course.

Syllabus Edition

First teaching 2021

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Last exams 2024

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1. Number

1.1.1 Types of Number

1.1.2 Mathematical Operations

1.1.3 Number Operations

1.2.1 Set Notation & Venn Diagrams

1.3.1 Prime Factor Decomposition

1.3.2 HCF & LCM

1.4.1 Powers, Roots & Indices

1.4.2 Standard Form

1.5.1 Basic Fractions

1.5.2 Operations with Fractions

1.6.1 Basic Percentages

1.6.2 Working with Percentages

1.7.1 Interest & Depreciation

1.7.2 Exponential Growth & Decay

1.8.1 Converting between FDP

1.8.2 Ordering FDP

1.10.1 Direct & Inverse Proportion

1.11.1 Compound Measures

1.12.2 Currency & Conversion

1.13.1 Rounding & Estimation

1.14.1 Using a Calculator

2. Algebra & Graphs

2.1.1 Algebraic Notation & Vocabulary

2.1.2 Algebra Basics

2.2.1 Algebraic Roots & Indices

2.3.1 Expanding Brackets

2.3.2 Factorising

2.3.3 Factorising Quadratics

2.4.1 Solving Linear Equations

2.4.2 Solving Linear Inequalities

2.5.1 Completing the Square

2.5.2 Solving Quadratic Equations

2.5.3 Quadratic Equation Methods

2.6.1 Rearranging Formulae

2.7.1 Simultaneous Equations

2.8.1 Algebraic Fractions

2.8.2 Solving Algebraic Fractions

2.9.1 Forming & Solving Equations

2.9.2 Equations & Problem Solving

2.10.1 Functions Toolkit

2.10.2 Composite & Inverse Functions

2.11.1 Sequences

2.11.2 nth Term

2.12.1 Coordinate Geometry

2.13.1 Straight Line Graphs (y = mx + c)

2.13.2 Parallel & Perpendicular Lines

2.14.1 Quadratic Graphs

2.15.1 Types of Graphs

2.15.2 Using Graphs

2.16.1 Graphical Inequalities

2.17.1 Conversion Graphs

2.17.2 Distance-Time & Speed-Time Graphs

2.17.3 Rates of Change of Graphs

2.18.1 Differentiation

2.18.2 Applications of Differentiation

2.18.3 Problem Solving with Differentiation

3. Geometry

3.1.2 2D & 3D Shapes

3.1.3 Unit Conversions

3.2.1 Basic Angle Properties

3.2.2 Angles in Polygons

3.2.3 Angles in Parallel Lines

3.3.3 Constructing a Triangle

3.4.1 Angles at Centre & Semicircles

3.4.2 Chords & Tangents

3.4.3 Cyclic Quadrilaterals

3.4.4 Segment Theorems

3.5.1 Area & Perimeter

3.5.2 Problem Solving with Areas

3.6.1 Area & Circumference of Circles

3.6.2 Arcs & Sectors

3.7.2 Surface Area

3.8.1 Congruence

3.8.2 Similarity

3.9.1 Pythagoras Theorem

3.9.2 Right-Angled Trigonometry

3.10.1 Sine & Cosine Rules

3.10.2 Area of a Triangle

3.10.3 Applications of Trigonometry

3.11.1 3D Pythagoras & Trigonometry

3.12.1 Trigonometric Graphs

3.12.2 Solving Trig Equations

3.13.1 Introduction to Vectors

3.13.2 Working with Vectors

3.14.1 Translations

3.14.2 Reflections

3.14.3 Rotations

3.14.4 Enlargements

4. Probability & Statistics

4.1.1 Basic Probability

4.1.2 Relative & Expected Frequency

4.2.1 Two Way Tables

4.2.2 Probability & Venn Diagrams

4.2.3 Probability Tree Diagrams

4.3.1 Conditional Probability

4.4.1 Mean, Median & Mode

4.4.2 Averages from Tables

4.4.3 Range & Quartiles

4.4.4 Comparing Distributions

4.5.1 Stem & Leaf Diagrams

4.5.2 Bar Charts & Pictograms

4.5.3 Pie Charts

4.5.4 Frequency Polygons

4.5.5 Working with Statistical Diagrams

4.6.1 Histograms & Frequency Density

4.7.1 Cumulative Frequency Diagrams

4.7.2 Box Plots

4.8.1 Scatter Graphs

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