Cambridge IGCSE · 0580 Extended

Mathematics • Notes

1. Number

• Types of Number
• Sets & Venn Diagrams
• Powers & Roots
• Fractions, Decimals & Percentages
• Four Operations
• Indices
• Standard Form
• Estimation & Rounding
• Limits of Accuracy
• Ratio & Proportion
• Rates
• Percentages
• Time, Money & Calculator
• Exponential Growth & Decay
• Surds

2. Algebra and graphs

• Introduction to Algebra
• Algebraic Manipulation
• Algebraic Fractions
• Indices II
• Equations
• Inequalities
• Sequences
• Algebraic Proportion
• Graphs in Practical Situations
• Graphs of Functions
• Sketching Curves
• Differentiation
• Functions

3. Coordinate geometry

• Coordinates
• Drawing Linear Graphs
• Gradient
• Length & Midpoint
• Equations of Lines
• Parallel Lines
• Perpendicular Lines

4. Geometry

• Geometrical Terms
• Constructions
• Scale Drawings & Bearings
• Similarity
• Symmetry
• Angles
• Circle Theorems I
• Circle Theorems II

5. Mensuration

• Units of Measure
• Area & Perimeter
• Circles, Arcs & Sectors
• Surface Area & Volume
• Compound Shapes & Parts of Shapes

6. Trigonometry

• Pythagoras’ Theorem
• Right-angled Triangles
• Exact Trigonometric Values
• Trigonometric Functions
• Non-right-angled Triangles
• Pythagoras & Trigonometry in 3D

7. Transformations and vectors

• Reflection
• Rotation
• Translation
• Enlargement
• Combined Transformations
• Column Vectors
• Vector Geometry

8. Probability

• Introduction
• Relative & Expected Frequencies
• Combined Events
• Tree Diagrams
• Venn Diagrams
• Conditional Probability

9. Statistics

• Classifying Data
• Interpreting Data
• Averages & Spread
• Grouped Data
• Charts & Diagrams
• Scatter Diagrams
• Cumulative Frequency
• Histograms