Cambridge Notes
IGCSE
Mathematics

IGCSE Mathematics Notes (0580)

Cambridge IGCSE Mathematics (0580) revision notes by topic — syllabus-aligned key concepts and revision for CAIE exam preparation.

1. Number

1.1 Types of number
1.2 Sets
1.3 Powers and roots
1.4 Fractions decimals and percentages
1.5 Ordering
1.6 The four operations
1.7 Indices I
1.8 Standard form
1.9 Estimation
1.10 Limits of accuracy
1.11 Ratio and proportion
1.12 Rates
1.13 Percentages
1.14 Using a calculator
1.15 Time
1.16 Money
1.17 Exponential growth and decay
1.18 Surds

2. Algebra and graphs

2.1 Introduction to algebra
2.2 Algebraic manipulation
2.3 Algebraic fractions
2.4 Indices II
2.5 Equations
2.6 Inequalities
2.7 Sequences
2.8 Proportion
2.9 Graphs in practical situations
2.10 Graphs of functions
2.11 Sketching curves
2.12 Differentiation
2.13 Functions

3. Coordinate geometry

3.1 Coordinates
3.2 Drawing linear graphs
3.3 Gradient of linear graphs
3.4 Length and midpoint
3.5 Equations of linear graphs
3.6 Parallel lines
3.7 Perpendicular lines

4. Geometry

4.1 Geometrical terms
4.2 Geometrical constructions
4.3 Scale drawings
4.4 Similarity
4.5 Symmetry
4.6 Angles
4.7 Circle theorems I
4.8 Circle theorems II

5. Mensuration

5.1 Units of measure
5.2 Area and perimeter
5.3 Circles arcs and sectors
5.4 Surface area and volume
5.5 Compound shapes and parts of shapes

6. Trigonometry

6.1 Pythagoras’ theorem
6.2 Right-angled triangles
6.3 Exact trigonometric values
6.4 Trigonometric functions
6.5 Non-right-angled triangles
6.6 Pythagoras’ theorem and trigonometry in 3D

7. Transformations and vectors

7.1 Transformations
7.2 Vectors in two dimensions
7.3 Magnitude of a vector
7.4 Vector geometry

8. Probability

8.1 Introduction to probability
8.2 Relative and expected frequencies
8.3 Probability of combined events
8.4 Conditional probability

9. Statistics

9.1 Classifying statistical data
9.2 Interpreting statistical data
9.3 Averages and measures of spread
9.4 Statistical charts and diagrams
9.5 Scatter diagrams
9.6 Cumulative frequency diagrams
9.7 Histograms