Cambridge IGCSE & O Level Mathematics

Mathematics • Purple & Green Course

Table of Contents

Follow the complete Mathematics course in textbook order. The course is presented on IGCSE360 as Cambridge IGCSE & O Level Mathematics, with the 46 chapters organised into clear mathematical areas for easier navigation and revision.

46 chaptersComplete course sequence
9 areasNumber to statistics
IGCSE & O LevelOne Mathematics subject on IGCSE360

Course structure

This contents page follows the chapter order of the Mathematics textbook. All 46 chapter notes pages are now available for revision and practice.

The book formally maps its chapters across number, algebra, coordinate geometry, geometry, measures, trigonometry, transformations and vectors, probability, and statistics. IGCSE360 will present this material under the combined subject name Cambridge IGCSE & O Level Mathematics.

1

Number

Core number skills, accuracy, ratio, rates, percentages and numerical reasoning.

1

Chapter 1 – Number

Course mapping 1.1Notes available

Types of number, prime factors, HCF and LCM.

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2

Chapter 2 – Sets

Course mapping 1.2Notes available

Set notation, Venn diagrams, complements, subsets and three-set problems.

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3

Chapter 3 – Powers and roots

Course mapping 1.3Notes available

Squares, square roots, cubes and cube roots.

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4

Chapter 4 – Fractions, decimals and percentages

Course mapping 1.4Notes available

Fractions, equivalent forms, recurring decimals and percentage conversion.

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5

Chapter 5 – Ordering

Course mapping 1.5Notes available

Ordering integers, decimals, fractions and percentages; inequalities.

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6

Chapter 6 – The four operations

Course mapping 1.6Notes available

Negative numbers, order of operations, decimals and fraction operations.

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7

Chapter 7 – Indices 1

Course mapping 1.7Notes available

Index notation, multiplication/division laws, negative and fractional indices.

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8

Chapter 8 – Standard form

Course mapping 1.8Notes available

Writing and calculating with numbers in standard form.

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9

Chapter 9 – Estimation

Course mapping 1.9Notes available

Decimal places, significant figures, estimation and sensible accuracy.

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10

Chapter 10 – Limits of accuracy

Course mapping 1.10Notes available

Measurement bounds and bounds in calculations.

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11

Chapter 11 – Ratio and proportion

Course mapping 1.11Notes available

Ratio, sharing in a ratio and proportional reasoning.

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12

Chapter 12 – Rates

Course mapping 1.12Notes available

Common rates, speed and other measures of rate.

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13

Chapter 13 – Percentages

Course mapping 1.13Notes available

Percentage change, reverse percentages, profit/loss and compound interest.

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14

Chapter 14 – Using a calculator

Course mapping 1.14Notes available

Efficient calculator use, standard form, checking accuracy, time and fractions.

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15

Chapter 15 – Time

Course mapping 1.15Notes available

24-hour time, time calculations, decimal hours and time zones.

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16

Chapter 16 – Money

Course mapping 1.16Notes available

Value for money and currency conversion.

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17

Chapter 17 – Exponential growth and decay

Course mapping 1.17Notes available

Exponential growth and exponential decay.

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18

Chapter 18 – Surds

Course mapping 1.18Notes available

Simplifying surds, manipulating surd expressions and rationalising denominators.

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2

Algebra

Algebraic manipulation, equations, sequences, proportion, graphs and functions.

19

Chapter 19 – Introduction to algebra

Course mapping 2.1Notes available

Using letters, substitution and evaluating algebraic expressions.

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20

Chapter 20 – Algebraic manipulation

Course mapping 2.2Notes available

Simplifying, expanding, factorising algebraic expressions and completing the square.

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21

Chapter 21 – Algebraic fractions

Course mapping 2.3Notes available

Simplifying and combining algebraic fractions.

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22

Chapter 22 – Indices 2

Course mapping 2.4Notes available

Index laws with numerical and algebraic expressions.

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23

Chapter 23 – Equations

Course mapping 2.5Notes available

Linear, simultaneous and quadratic equations; rearranging formulae.

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24

Chapter 24 – Inequalities

Course mapping 2.6Notes available

Solving inequalities and representing regions graphically.

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25

Chapter 25 – Sequences

Course mapping 2.7Notes available

Linear, quadratic, cubic and exponential sequences; nth-term rules.

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26

Chapter 26 – Proportion

Course mapping 2.8Notes available

Direct and other forms of proportion expressed algebraically.

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27

Chapter 27 – Graphs in practical situations

Course mapping 1.27Notes available

Conversion graphs, travel graphs, rate of change and area under speed–time graphs.

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28

Chapter 28 – Graphs of functions

Course mapping 2.10Notes available

Quadratic, cubic, reciprocal and exponential graphs; graphical solutions and gradients.

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29

Chapter 29 – Sketching curves

Course mapping 2.11Notes available

Recognising and sketching linear, quadratic, cubic, reciprocal and exponential families.

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30

Chapter 30 – Functions

Course mapping 2.12Notes available

Function notation, domain/range, inverse and composite functions.

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3

Coordinate geometry

Straight-line geometry, gradients, distances and relationships between lines.

31

Chapter 31 – Coordinate geometry

Course mapping 3.1–3.7Notes available

Gradient, line segments, distance, straight-line equations, parallel and perpendicular lines.

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4

Geometry

Geometrical language, constructions, similarity, symmetry, angle properties and circles.

32

Chapter 32 – Geometrical terms

Course mapping 4.1Notes available

Angles, lines, bearings, polygons, solids, nets, congruence, similarity and circles.

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33

Chapter 33 – Geometrical constructions

Course mapping 4.2Notes available

Measuring and constructing angles/figures, including compass constructions and nets.

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34

Chapter 34 – Scale drawings

Course mapping 4.3Notes available

Scale drawings, maps and bearings.

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35

Chapter 35 – Similarity

Course mapping 4.4Notes available

Similar shapes and relationships between corresponding lengths, areas and volumes.

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36

Chapter 36 – Symmetry

Course mapping 4.5Notes available

Line symmetry, rotational symmetry and symmetry of shapes/solids.

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37

Chapter 37 – Angles

Course mapping 4.6Notes available

Straight-line, parallel-line, quadrilateral and polygon angle properties.

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38

Chapter 38 – Circle theorems

Course mapping 4.7–4.8Notes available

Circle symmetry, angle theorems and the alternate segment theorem.

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5

Measures and mensuration

Units, perimeter, area, circumference, surface area and volume.

39

Chapter 39 – Units of measure

Course mapping 5.1Notes available

Length, mass, capacity, area and volume units.

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40

Chapter 40 – Mensuration

Course mapping 5.2–5.5Notes available

Perimeter, area, circumference, surface area and volume.

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6

Pythagoras and trigonometry

Right-angled and non-right-angled trigonometry, including three-dimensional problems.

41

Chapter 41 – Pythagoras’ theorem and trigonometry

Course mapping 6.1–6.4Notes available

Pythagoras, trigonometric ratios, obtuse angles, non-right triangles and 3-D problems.

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7

Transformations and vectors

Geometric transformations and vector methods in two-dimensional geometry.

42

Chapter 42 – Transformations

Course mapping 7.1Notes available

Reflection, rotation, translation, enlargement with integer, fractional and negative scale factors, describing and combining transformations.

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43

Chapter 43 – Vectors

Course mapping 7.2–7.4Notes available

Vectors and translations, vector notation, scalar multiplication, column vector operations, position vectors, magnitude and vector geometry.

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8

Probability

Single and combined events, relative frequency and dependent/independent probability.

44

Chapter 44 – Probability

Course mapping 8.1–8.3Notes available

Single events, complements, expected frequency, relative frequency, combined events, independent events and dependent-event trees.

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9

Statistics and data

Data collection, averages, grouped data and statistical diagrams.

45

Chapter 45 – Categorical, numerical and grouped data

Course mapping 9.1–9.3Notes available

Data collection, questionnaires, two-way tables, averages and grouped/continuous data.

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46

Chapter 46 – Statistical diagrams

Course mapping 9.4–9.7Notes available

Bar/pie charts, scatter diagrams, cumulative frequency, quartiles and histograms.

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Build status: the Mathematics subject and full Table of Contents are established. Chapter 1 notes are now available; later chapter links will be activated only when those notes are completed, preventing dead links to unfinished pages.