Complete Additional Mathematics for Cambridge IGCSE® & O Level

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Description

Contents

Reviews

Language

English

ISBN

9780198376736

Front Cover

Title Page

Introduction

Contents

1 Set language and notation

1.1 Describing sets

1.2 Sets of numbers

1.3 Set properties

1.4 Combining sets

1.5 Putting elements in sets

1.6 Converting from English to Mathematics

1.7 Identifying regions

1.8 Using sets to solve problems

Summary

Chapter 1 Summative Exercise

Chapter 1 Test

2 Indices and surds

2.1 Introduction

2.2 Laws of indices

2.3 Powers of small numbers

2.4 Surds

2.5 The arithmetic of surds

2.6 Mixed numbers

2.7 The conjugate

2.8 Rationalising the denominator

2.9 Square roots of mixed numbers

2.10 Geometric applications

Summary

Chapter 2 Summative Exercise

Chapter 2 Test

3 Permutations and combinations

3.1 Introduction

3.2 Orderings

3.3 Factorial notation

3.4 Restrictions

3.5 Permutations and combinations

3.6 0!

Summary

Chapter 3 Summative Exercise

Chapter 3 Test

4 Functions

4.1 Introduction

4.2 Mappings

4.3 Functions

4.4 Defining functions

4.5 Finding the value of a function

4.6 Composite functions

4.7 Inverse functions

4.8 Many - one functions

4.9 The inverse of a composite function

4.10 The modulus function

Summary

Chapter 4 Summative Exercise

Chapter 4 Test

Term test 1A (Chapters 1–4)

5 Quadratic functions

5.1 Introduction

5.2 Completing the square

5.3 Interpreting the expression

5.4 Sketching the graph of a quadratic function

5.5 Solving a quadratic equation

5.6 The discriminant

Summary

Chapter 5 Summative Exercise

Chapter 5 Test

6 Simultaneous equations and inequalities

6.1 Introduction

6.2 Simultaneous linear equations

6.3 Simultaneous equations: one linear, one non-linear

6.4 The sign diagram

6.5 Quadratic inequalities

Summary

Chapter 6 Summative Exercise

Chapter 6 Test

7 The binomial theorem

7.1 Introduction

7.2 Powers of (a + b)

7.3 Pascal’s triangle

7.4 Combinations

7.5 Expanding binomial expressions

7.6 The binomial theorem for a positive integer index

7.7 More complicated expressions

Summary

Chapter 7 Summative Exercise

Chapter 7 Test

8 Polynomial factorisation

8.1 Introduction

8.2 Polynomial division

8.3 The division algorithm

8.4 The remainder theorem

8.5 The factor theorem

8.6 Factorising polynomials

Summary

Chapter 8 Summative Exercise

Chapter 8 Test

Examination Questions

Term test 2A (Chapters 5–8)

9 Straight lines

9.1 Introduction

9.2 Lines and line segments

9.3 Basic coordinate geometry

9.4 The equation of a line

Summary

Chapter 9 Summative Exercise

Chapter 9 Test

Examination Questions

10 The derived function

10.1 Introduction

10.2 Function diagrams

10.3 The derived function

10.4 The function f(x) = x2

10.5 Higher indices

10.6 More complicated functions

10.7 Other powers of x

10.8 The gradient function

10.9 A third interpretation of the derivative

10.10 The second derivative

10.11 Tangents and normals

Summary

Chapter 10 Summative Exercise

Chapter 10 Test

11 Trigonometric functions

11.1 Introduction

11.2 Trigonometric ratios

11.3 Defining sine and cosine

11.4 Symmetries of the unit circle

11.5 Graphs of the trigonometric functions

11.6 The tangent function and its graph

11.7 Properties of the trigonometric functions

11.8 Inverse trigonometric functions

11.9 The periodic properties of trigonometric functions

11.10 Solving trigonometric equations

Summary

Chapter 11 Summative Exercise

Chapter 11 Test

Term test 3A (Chapters 9–11)

12 Circular measure

12.1 Measuring an angle

12.2 Mensuration of the circle

12.3 The radian

12.4 Equivalent angle measurements

12.5 Circle geometry

12.6 Solving equations

Summary

Chapter 12 Summative Exercise

Chapter 12 Test

Examination Questions

13 Applications of the derivative

13.1 Introduction

13.2 Stationary points

13.3 The nature of stationary points

13.4 Identifying the nature of stationary points

13.5 Small increments

13.6 The chain rule

13.7 Connected rates of change

13.8 Composite functions

13.9 Maximising and minimising

Summary

Chapter 13 Summative Exercise

Chapter 13 Test

Examination Questions

14 Matrices

14.1 Introduction

14.2 Notation

14.3 Matrix algebra

14.4 More matrix algebra

14.5 The algebra of (2 by 2) matrices

14.6 Solving matrix equations

14.7 Solving simultaneous equations

Summary

Chapter 14 Summative Exercise

Chapter 14 Test

Examination Questions

15 Integration

15.1 Introduction

15.2 The integration process

15.3 Integral notation

15.4 Rules of integration

15.5 Integrating polynomial functions

15.6 Problems that we often encounter

15.7 Looking at the gradient function

15.8 The arbitrary constant (constant of integration)

15.9 The area function

15.10 The area of the region between x = a and x = b

15.11 The area of the region between two curves

15.12 Curves below the x-axis

15.13 Integrating composite functions

Summary

Chapter 15 Summative Exercise

Chapter 15 Test

Examination Questions

Term test 4A (Chapters 12–15)

16 Further trigonometry

16.1 Introduction

16.2 Reciprocal trigonometric functions

16.3 Identities

16.4 Trigonometric identities

16.5 Using trigonometric identities

16.6 Graphs of trigonometric functions

16.7 Transforming the graphs of trigonometric functions

16.8 Maximising trigonometric functions

Summary

Chapter 16 Summative Exercise

Chapter 16 Test

Examination Questions

17 Further differentiation

17.1 Introduction

17.2 The product rule

17.3 The quotient rule

Summary

Chapter 17 Summative Exercise

Chapter 17 Test

Examination Questions

18 Exponential and logarithmic functions

18.1 Introduction

18.2 Exponential functions

18.3 Logarithmic functions

18.4 Laws of exponential and logarithmic functions

18.5 Problem solving with logarithms

18.6 Changing the base of logarithms

18.7 Straightening curves

Summary

Chapter 18 Summative Exercise

Chapter 18 Test

Examination Questions

19 Calculus and trigonometry

19.1 Introduction

19.2 sin(A + B), cos(A + B)

19.3 The derivative of sin x

19.4 The derivative of cos x

19.5 The derivative of tan x

19.6 Applications

Summary

Chapter 19 Summative Exercise

Chapter 19 Test

Term test 5A (Chapters 16–19)

20 The number e and its applications

20.1 Introduction

20.2 The derivative of the exponential function y = ax

20.3 Natural logarithms

20.4 The derivative of the logarithmic function y = ln x

20.5 Graphs of exponential and logarithmic functions

20.6 Applications of ex and ln x

Summary

Chapter 20 Test

Examination Questions

21 Vectors

21.1 What is a vector?

21.2 Describing translations (vectors)

21.3 Unit vectors

21.4 Base vectors

21.5 Position vectors

21.6 Vector geometry

21.7 Velocities

21.8 Currents and winds

21.9 Relative velocity

Summary

Chapter 21 Summative Exercise

Chapter 21 Test

Examination Questions

22 Kinematics

22.1 What is kinematics?

22.2 Rates of change

22.3 Mathematical modelling

22.4 Motion with uniform acceleration

22.5 Displacement-time and velocity-time graphs

Summary

Chapter 22 Summative Exercise

Chapter 22 Test

Examination Questions

Term test 6A (Chapters 20–22)

Revision practice paper

Answers

Index

Back Cover

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