Mathematics--A Complete Introduction provides an invaluable, step-by-step introduction to the subject. Packed full of worked examples and useful exercises, it will guide you through the essentials quickly and easily, giving you the knowledge you need to gain math confidence.

Table of Contents

• Welcome to Complete Mathematics!
• Introduction
• 1 Number
• 1.1 Introduction – place value
• 1.2 Arithmetic – the four operations
• 1.3 Order of operations
• 1.4 Problems which use arithmetic
• 1.5 Special numbers
• 1.6 Multiples, factors and primes
• 2 Angles
• 2.1 Introduction
• 2.2 Angles
• 2.3 Measuring and drawing angles
• 2.4 Using angle facts
• 2.5 Parallel lines
• 2.6 Bearings
• 3 Fractions
• 3.1 Introduction
• 3.2 What is a fraction?
• 3.3 Which fraction is bigger?
• 3.4 Simplifying fractions
• 3.5 Improper fractions
• 3.6 Adding and subtracting fractions
• 3.7 Multiplication of fractions
• 3.8 Fractions of quantities
• 3.9 Division of fractions
• 3.10 A number as a fraction of another number
• 4 Two-dimensional shapes
• 4.1 Introduction
• 4.2 Triangles
• 4.3 Constructing triangles
• 4.4 Quadrilaterals
• 4.5 Polygons
• 4.6 Interior and exterior angles
• 4.7 Symmetries of regular polygons
• 4.8 Congruent shapes
• 4.9 Tessellations
• 5 Decimals
• 5.1 Introduction
• 5.2 Place value
• 5.3 Converting decimals to fractions
• 5.4 Converting fractions to decimals 1
• 5.5 Addition and subtraction
• 5.6 Multiplication of decimals
• 5.7 Division of decimals
• 5.8 Converting fractions to decimals 2
• 6 Statistics
• 6.1 Introduction
• 6.2 Collection of data
• 6.3 Pictograms
• 6.4 Bar charts
• 6.5 Pie charts
• 6.6 Line graphs
• 6.7 Scatter graphs
• 6.8 Discrete and continuous data
• 6.9 Grouping data
• 7 Directed numbers
• 7.1 Introduction
• 7.2 Ordering directed numbers
• 7.3 Addition and subtraction
• 7.4 Multiplication and division
• 7.5 Using a calculator
• 8 Graphs
• 8.1 Coordinates
• 8.2 Straight-line graphs
• 8.3 Lines parallel to the axes
• 9 Measurement
• 9.1 The metric system
• 9.2 Imperial units
• 9.3 Converting between metric and imperial units
• 9.4 Choosing suitable units
• 10 Perimeter and area
• 10.1 Perimeter
• 10.2 Area
• 10.3 Area of a rectangle
• 10.4 Area of a parallelogram
• 10.5 Area of a triangle
• 10.6 Area of a trapezium
• 11 Algebraic expressions
• 11.1 Introduction – what is algebra?
• 11.2 Writing expressions
• 11.3 Simplifying expressions
• 11.4 Evaluating expressions
• 11.5 Squaring
• 11.6 Brackets
• 11.7 Factorizing expressions
• 11.8 Indices
• 11.9 Laws of indices
• 11.10 Simplifying expressions with indices
• 12 Approximation
• 12.1 Introduction
• 12.2 Rounding whole numbers
• 12.3 Rounding with decimals
• 12.4 Significant figures
• 12.5 Estimates
• 12.6 Rounding in practical problems
• 12.7 Accuracy of measurements
• 13 Equations
• 13.1 Introduction
• 13.2 Finding missing numbers
• 13.3 Solving linear equations
• 13.4 Equations with brackets
• 13.5 Solving problems using equations
• 13.6 Solving inequalities
• 14 Percentages
• 14.1 Introduction
• 14.2 Percentages, decimals, fractions
• 14.3 Percentages of quantities
• 14.4 Increasing and decreasing quantities
• 14.5 One quantity as a percentage of another quantity
• 14.6 Percentage increases
• 14.7 Using multipliers
• 15 Formulae
• 15.1 What is a formula?
• 15.2 Evaluating terms other than the subject
• 15.3 Changing the subject of a formula
• 16 Circles
• 16.1 Introduction
• 16.2 Circumference of a circle
• 16.3 Area of a circle
• 16.4 Two properties of circles
• 17 Probability
• 17.1 Introduction
• 17.2 Relative frequency
• 17.3 Probability of a single event
• 17.4 Two events
• 17.5 Tree diagrams
• 17.6 Expected frequency
• 18 Three-dimensional shapes
• 18.1 Introduction
• 18.2 Nets and surface area
• 18.3 Volume of a cuboid
• 18.4 Volume of a prism
• 18.5 Weight of a prism
• 19 Ratio and proportion
• 19.1 What is a ratio?
• 19.2 Scales
• 19.3 Using ratio
• 19.4 Direct proportion
• 19.5 Inverse proportion
• 20 Pythagoras’ theorem and trigonometry
• 20.1 Pythagoras’ theorem
• 20.2 Using Pythagoras’ theorem
• 20.3 Proof of Pythagoras’ theorem
• 20.4 Pythagoras’ theorem problems
• 20.5 Trigonometry
• 20.6 The tangent ratio
• 20.7 Values of the tangent
• 20.8 Using tangents
• 20.9 Sine and cosine
• 21 Indices and standard form
• 21.1 Indices
• 21.2 Laws of indices
• 21.3 Prime factors
• 21.4 Highest common factor
• 21.5 Lowest common multiple
• 21.6 Standard form – large numbers
• 21.7 Standard form – small numbers
• 21.8 Standard form calculations
• 22 Statistics
• 22.1 Averages
• 22.2 The mode
• 22.3 The median
• 22.4 The mean
• 22.5 The range
• 22.6 Frequency tables
• 22.7 Grouped frequency tables
• 23 Graphs
• 23.1 Equations of straight lines
• 23.2 Drawing straight-line graphs
• 23.3 The gradient of a straight line
• 23.4 Curved graphs
• 24 Equations
• 24.1 Simultaneous equations
• 24.2 Algebraic methods
• 24.3 Quadratic expressions
• 24.4 Factorizing quadratic expressions
• 24.5 Quadratic equations
• 24.6 Solution by factorizing
• 24.7 Cubic equations
• Taking it further
• Reading List