IGCSE Mathematics:
Geometry & Trigonometry

Cambridge IGCSE (0580) & Edexcel IGCSE (4MA1) · Updated March 2026 · 8 Chapters

This course covers every Geometry and Trigonometry topic examined in Cambridge IGCSE Mathematics (0580) and Edexcel International GCSE (4MA1). Each chapter is a self-contained textbook unit with clear concept explanations, interactive diagrams, fully worked examples, and graded practice exercises with solutions.

Foundation & Extended Tiers

Chapters 1–5 and 6–8 cover both Foundation and Extended content. Topics exclusive to the Extended tier — such as the Sine and Cosine Rule (Ch 4), 3D trigonometry (Ch 3), and geometric vector proofs (Ch 7) — are clearly labelled within each chapter.

Prerequisites

Ability to use a protractor and ruler accurately
Basic arithmetic: fractions, decimals, percentages, rounding
Understanding of square roots and squares
Familiarity with coordinate axes (x and y)

Course Chapters

Angles and Shapes

Types of angles · Angle relationships · Parallel lines (Z, F, C angles) · Triangles · Quadrilaterals · Regular polygons · Bearings

Foundation & Extended

Pythagoras' Theorem

Finding the hypotenuse · Finding a shorter side · Real-world applications · 3D Pythagoras · Converse · Distance between two points

Foundation & Extended

Right-Angled Trigonometry

SOHCAHTOA ratios · Finding sides · Finding angles · Exact values · Elevation & depression · Bearings · 3D trigonometry

Foundation & Extended

Sine Rule & Cosine Rule

Sine rule · Ambiguous case · Cosine rule · Area = ½$ab$sin$C$ · Choosing the right rule · Mixed problems

Circle Theorems

Circle vocabulary · 7 circle theorems · Tangent properties · Alternate segment theorem · Combining theorems · Exam technique

Foundation & Extended

Transformations

Translation · Rotation · Reflection · Enlargement (positive, negative, fractional) · Describing transformations · Combined transformations

Foundation & Extended

Vector notation · Addition & subtraction · Scalar multiplication · Magnitude & unit vectors · Position vectors · Geometric proofs

Foundation & Extended

Constructions and Loci

Perpendicular bisector · Angle bisector · Standard angles · Constructing triangles · Four standard loci · Compound loci

Foundation & Extended

How to Use This Course

📖

Read each section carefully before looking at examples

✏️

Work through each example yourself before checking the solution

🔢

Attempt all exercises — use "Show Solution" only to check

📐

Use interactive Desmos figures to explore diagrams dynamically