IGCSEMathsCambridge (CIE)International MathsExtendedRevision Notes

Cambridge (CIE) IGCSE International Maths: Extended
Revision Notes

Concise resources for the Cambridge (CIE) IGCSE International Maths: Extended course.

Number

Types of Numbers

Irrational Numbers

Negative Numbers

Mathematical Symbols

Order of Operations (BIDMAS/BODMAS)

Addition & Subtraction

Multiplication & Division

Operations with Decimals

Prime Factor Decomposition

Uses of Prime Factor Decomposition

Set Notation & Venn Diagrams

Laws of Indices

Converting to & from Standard Form

Operations with Standard Form

Basic Fractions

Mixed Numbers & Improper Fractions

Adding & Subtracting Fractions

Multiplying & Dividing Fractions

Basic Percentages

Percentage Increases & Decreases

Reverse Percentages

Simple Interest

Compound Interest

Simplifying Surds

Rationalising Denominators

Converting Fractions, Decimals & Percentages

Recurring Decimals

Ordering Fractions, Decimals & Percentages

Problem Solving with Ratios

Working with Proportion

Compound Measures

Money Calculations

Converting between Units

Squared & Cubic Units

Rounding & Estimation

Algebra & Sequences

Algebraic Notation

Algebraic Vocabulary

Collecting Like Terms

Algebraic Roots & Indices

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

Solving Linear Equations

Solving Linear Inequalities

Solving Quadratics by Factorising

The Quadratic Formula

Solving Quadratics using a Calculator

Formulas where Subject Appears Once

Formulas where Subject Appears Twice

Linear Simultaneous Equations

Quadratic Simultaneous Equations

Simplifying Algebraic Fractions

Adding & Subtracting Algebraic Fractions

Multiplying & Dividing Algebraic Fractions

Solving Equations with Algebraic Fractions

Forming Equations from Words

Forming Equations from Shapes

Problem Solving with Equations

Introduction to Functions

Composite Functions

Inverse Functions

Introduction to Sequences

nth Terms of Linear Sequences

Quadratic Sequences

Other Sequences

Direct Proportion

Inverse Proportion

Variation Models

Exponential Growth & Decay

Coordinate Geometry & Graphs

Midpoint of a Line

Gradient of a Line

Length of a Line

Equations of Straight Lines (y = mx + c)

Drawing Straight Line Graphs

Perpendicular Lines

Quadratic Graphs

Reciprocal Graphs

Exponential Graphs

Using Calculators to Sketch Graphs

Using Calculators to Solve Equations

Using Calculators to Solve Inequalities

Representing Inequalities as Regions

Finding Inequalities from Regions

Translations of Graphs

Geometry

Rotational Symmetry

Lines of Symmetry

Planes of Symmetry

Basic Angle Properties

Angles in Polygons

Angles in Parallel Lines

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

Adding & Subtracting Areas

Problem Solving with Areas

Area & Circumference of Circles

Arc Lengths & Sector Areas

Problem Solving with Volumes

Similar Lengths

Similar Areas & Volumes

Pythagoras & Trigonometry

Pythagoras Theorem

Angles of Elevation & Depression

Exact Trig Values

The Cosine Rule

Area of a Triangle

Deciding the Trig Rule

3D Pythagoras & Trigonometry

Trigonometric Graphs

Periods & Amplitudes

Solving Trig Equations

Vectors & Transformations

Introduction to Column Vectors

Representing Vectors as Diagrams

Magnitude of a Vector

Probability

Basic Probability

Relative & Expected Frequency

Possibility (Sample Space) Diagrams

Probabilities from Venn Diagrams

Probability Tree Diagrams

Combined Probabilities

Conditional Probability

Combined Conditional Probabilities

Statistics

Discrete & Continuous Data

Mean, Median & Mode

Calculations with the Mean

Averages from Tables

Averages from Grouped Data

Using Calculators to Find Averages

Range & Interquartile Range

Comparing Data Sets

Stem & Leaf Diagrams

Bar Charts & Pictograms

Reading & Interpreting Statistical Diagrams

Comparing Statistical Diagrams

Cumulative Frequency

Drawing Cumulative Frequency Diagrams

Interpreting Cumulative Frequency Diagrams

Scatter Graphs & Correlation

Lines of Best Fit

Linear Regression Lines

Exam boards

Study tools

Related links