# Online Maths GCSE Textbook

The textbook contains 19 sections. Scroll down to find the section you are looking for below and then click on the links to download that part of the textbook and also the answers to the textbook questions.

**Textbook Sections:**

**1 Indices**

- 1.1 Multiplication and Division
- 1.2 Squares, Cubes, Square Roots and Cube Roots
- 1.3 Index Notation
- 1.4 Factors
- 1.5 Prime Factors
- 1.6 Further Index Notation
- 1.7 Standard Form
- 1.8 Calculations with Standard Form

**2 Formulae**

- 2.1 Using Formulae
- 2.2 Construct and Use Simple Formulae
- 2.3 Revision of Negative Numbers
- 2.4 Substitution in Formulae
- 2.5 More Complex Formulae
- 2.6 Changing the Subject (of a formula)
- 2.7 Further Change of the Subject (of a formula)
- 2.8 Expansion of Brackets
- 2.9 Factorisation
- 2.10 Algebraic Manipulation
- 2.11 Algebraic Fractions

**3 Angle Geometry**

- 3.1 Measuring Angles
- 3.2 Line and Rotational Symmetry
- 3.3 Angle Geometry
- 3.4 Angles with Parallel and Intersecting Lines
- 3.5 Angle Symmetry in Polygons
- 3.6 Symmetry Properties of 3D Shapes
- 3.7 Compass Bearings
- 3.8 Angles and Circles 1
- 3.9 Angles and Circles 2
- 3.10 Circles and Tangents

**4 Trigonometry**

- 4.1 Squares and Triangles
- 4.2 Pythagoras’ Theorem
- 4.3 Further Work with Pythagoras’ Theorem
- 4.4 Sine, Cosine and Tangent
- 4.5 Finding Lengths in Right Angled Triangles
- 4.6 Finding Angles in Right Angled Triangles
- 4.7 Mixed Problems with Trigonometry
- 4.8 Sine and Cosine Rules
- 4.9 Angles Larger than 90 Degrees

**5 Probability**

- 5.1 Probabilities
- 5.2 Simple Probabilities
- 5.3 Outcome of Two Events
- 5.4 Finding Probabilities Using Relative Frequency
- 5.5 Determining Probabilities
- 5.6 Probability of Two Events
- 5.7 Use of Tree Diagrams
- 5.8 Multiplication for Independent Events
- 5.9 Mutually Exclusive Events
- 5.10 Tree Diagrams and Conditional Probability
- 5.11 Using Venn Diagrams to Find Probabilities

**6 Number System**

- 6.1 Decimals
- 6.2 Multiplying and Dividing with Decimals
- 6.3 Fractions and Decimals
- 6.4 Long Multiplication and Division
- 6.5 Estimating Answers
- 6.6 Using Brackets and Memory on a Calculator
- 6.7 Upper and Lower Bounds
- 6.8 Number System
- 6.9 Surds

**7 Mensuration**

- 7.1 Units and Measuring
- 7.2 Estimating Areas
- 7.3 Making Solids Using Nets
- 7.4 Constructing Nets
- 7.5 Conversion of Units
- 7.6 Squares, Rectangles and Triangles
- 7.7 Area and Circumference or Circles
- 7.8 Volumes of Cubes, Cuboids, Cylinders and Prisms
- 7.9 Plans and Elevations
- 7.10 Using Isometric Paper
- 7.11 Discrete and Continuous Measures
- 7.12 Areas of Parallelograms, Trapeziums, Kites and Rhombuses
- 7.13 Surface Area
- 7.14 Mass, Volume and Density
- 7.15 Volumes, Areas and Lengths
- 7.16 Dimensions
- 7.17 Areas of Triangles

**8 Data Handling**

- 8.1 Tables and Timetables
- 8.2 Pictograms and Bar Charts
- 8.3 Pie Charts
- 8.4 Line Graphs
- 8.5 Questionnaires and Surveys
- 8.6 Frequency Graphs
- 8.7 Histograms with Unequal Class Intervals
- 8.8 Sampling

**9 Data Analysis**

- 9.1 Mean, Median, Mode and Range
- 9.2 Finding the Mean from Tables and Tally Charts
- 9.3 Calculations with the Mean
- 9.4 Mean, Median and Mode for Grouped Data
- 9.5 Cumulative Frequency
- 9.6 Standard Deviation

**10 Equations**

- 10.1 Negative Numbers
- 10.2 Arithmetic with Negative Numbers
- 10.3 Simplifying Expressions
- 10.4 Simple Equations
- 10.5 Solving Equations
- 10.6 Trial and Improvement Method
- 10.7 Expanding Brackets
- 10.8 Simultaneous Linear Equations
- 10.9 Factorisation 1
- 10.10 Factorisation 2
- 10.11 Solving Quadratic Equations by Factorisation
- 10.12 Solving Quadratic Equations Using the Formula
- 10.13 Algebraic Fractions
- 10.14 Completing the Square
- 10.15 Algebraic Fractions and Quadratic Equations

**11 Fractions and Percentages**

- 11.1 Fractions, Decimals and Percentages
- 11.2 Fractions and Percentages of Quantities
- 11.3 Quantities as Percentages
- 11.4 More Complex Percentages
- 11.5 Percentage Increase and Decrease
- 11.6 Addition and Subtraction of Fractions
- 11.7 Multiplication and Division of Fractions
- 11.8 Compound Interest and Depreciation
- 11.9 Reverse Percentage Problems

**12 Number Patterns**

- 12.1 Simple Number Patterns
- 12.2 Recognising Number Patterns
- 12.3 Extending Number Patterns
- 12.4 Formulae and Number Patterns
- 12.5 General Laws
- 12.6 Quadratic Formulae

**13 Graphs**

- 13.1 Positive Coordinates
- 13.2 Coordinates
- 13.3 Plotting Straight Lines
- 13.4 Plotting Curves
- 13.5 Gradient
- 13.6 Applications of Graphs
- 13.7 Scatter Plots and Lines of Best Fit
- 13.8 The Equation of a Straight Line
- 13.9 Horizontal and Vertical Lines
- 13.10 Solution of Simultaneous Equations by Graphs
- 13.11 Graphs of Common Functions
- 13.12 Graphical Solutions of Equations

**14 Loci and Transformations**

- 14.1 Drawing and Symmetry
- 14.2 Scale Drawings
- 14.3 Constructing Triangles and Other Shapes
- 14.4 Enlargements
- 14.5 Reflections
- 14.6 Construction of Loci
- 14.7 Enlargements which Reduce
- 14.8 Further Reflections
- 14.9 Rotations
- 14.10 Translations
- 14.11 Combined Transformations
- 14.12 Congruence
- 14.13 Similarity
- 14.14 Enlargements with Negative Scale Factors

**15 Variation**

- 15.1 Simple Ratios
- 15.2 Proportion and Ratio
- 15.3 Map Scales and Ratios
- 15.4 Proportional Division
- 15.5 Direct Proportion
- 15.6 Inverse Proportion
- 15.7 Functional and Graphical Representations
- 15.8 Further Functional Representations

**16 Inequalities**

- 16.1 Inequalities on a Number Line
- 16.2 Solution of Linear Inequalities
- 16.3 Inequalities Involving Quadratic Terms
- 16.4 Graphical Approach to Inequalities
- 16.5 Dealing With More Than One Inequality

**17 Using Graphs**

- 17.1 Transformations of Graphs
- 17.2 Areas Under Graphs
- 17.3 Tangents to Curves
- 17.4 Finding Coefficients

**18 3D Geometry**

- 18.1 Using Pythagoras’ Theorem and Trigonometry in Three Dimensions
- 18.2 Angles and Planes

**19 Vectors**

- 19.1 Vectors and Scalars
- 19.2 Applications of Vectors
- 19.3 Vectors and Geometry
- 19.4 Further Work with Vectors
- 19.5 Commutative and Associative Properties