IGCSE Maths Notes

Distance – Time Graphs

Cumulative Frequency Curves, Quartiles, Interquartile Range and Median


Calculating the Dimensions of Histogram Bars

When Hour and Minute Hands of a Clock Coincide


Rational and Irrational Numbers

Simultaneous Equations With One a Quadratic

Domain, Range, Inverse

Composing Functions and Finding Inverses

Velocity - Time Graphs

Transformations of Graphs

The Laws of Indices

Completing the Square and Solving Quadratic Equations

Sketching Quadratic Curves

Proof of Formula for Chord Bisecting a Diameter at Right Angles

Speeds There and Back

Identifying Regions on a Two Set Venn Diagram

Scale Factors and Negative Enlargements

Solving Equations Involving Algebraic Fractions

Proof of the Quadratic Formula

Proving Triangles are Congruent

Working With Column Vectors

Profit and Loss

Solving Exponential Simultaneous Equations Algebraically

Volumes of Frustrums

Simple Interest

Nets and Surface Areas

Length, Gradient and Midpoint of a Line

Ratios and Similar Shapes

Relations Between Lengths of Solids With Volumes in a Certain Ratio

Similar Triangles Formed Between Parallel Lines

Advanced Indices

Finding the Rules or nth Terms for Quadratic Sequences

Finding the Rules or nth Terms for Simple Sequences

Direct and Inverse Proportion

Summary of Terms Used in Probability

Drawing a Line of Best Fit

Trigonometry - Right Angled Triangles - Finding a Side

Vectors 1

Rules of Inequalities

Definition of a Function

Stretch With Invariant x Axis

Stretch With Invariant y Axis

Determining the Equation of a Quadratic From a Graph

The Vertex of a Quadratic Graph


Problem Solving 1

Problem Solving 2

Finding the Locus of Points Equidistant From Two Given Points

Constructing a Set of Points a Fixed Distance From a Given Line

Constructing a Triangle With Given Sides

Constructing a Thirty Degree Angle

Constructing an Angle of 45 Degrees

Constructing a Right Angle

Constructing an Equilateral Triangle/60 Degree Angle

Venn Diagram Problems

Mode, Median and Mean

Designing a Good Questionaire

Continued Square Roots

Intervals and Directed Numbers


Parallel Chords Formed By Lines Drawn in Intersecting Circles

Proof That Common Tangent From Meeting Point of Two Circles Bisects Other Common Tangent

Solving Inequalities Algebraically

Standard Deviation

Chain Percentages

Finding Quartiles and Median of a List of Numbers

Proof Of Formula Relating Intersecting Chords

Area and Perimeter of a Sector of a Circle

Surface Areas of Frustums

Solving Cosine Equations for More Than One Solution

Solving Sine Equations for More Than One Solution

Proof of Formula Relating extended Chords

Proof Length of Tangent Squared Equals Product of Chord With Chord Extended to Meet Tangent

Additional Maths

Simplifying Logarithmic Expressions

Tangents and Normals

Finding a Polynomial With Given Roots

Displacement, Velocity and Acceleration

2 by 2 matrices - Adding, Subtracting, Multiplying and Inverses

Matrices and Scalings

Matrices and Transformations

Differentiation – The Product, Quotient and Chain Rules

Solving Simple Differential Equation

Integration and The Area Between Two Curves

Symbols and Notation

Solving Trigonometric Equations

The Factor and Remainder Theorems

Solving Logarithmic Equations

Relative Velocities and Relative Positions

Combinations and Permutations

Curves, Maxima, Minima, Stationary Points and Turning Points


Optimisation – Maximising a Function

Plotting Lines From Exponential Equations

Practical Vectors

Venn Diagrams – A Summary

Using Matrices to Solve Simultaneous Equations

Proof of Formula for Curved Surface Area of Cone

Matrices and Practical Problems

Minima and Maxima of Quadratics and Reciprocals of Quadratics

The Binomial Expansion

Finding a Polynomial With Given Roots

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