 \$37.49

# Complete Additional Mathematics for Cambridge IGCSE® & O Level

US\$ 37.49
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Book Description

Equip your top achievers to excel in their Cambridge exams with the practice-based, rigorous approach of Complete Additional Mathematics for Cambridge IGCSE. It completely covers the latest Additional Mathematics Cambridge IGCSE & O Level syllabus. In addition to a wealth of practice, it includes clear and concise explanations and worked examples, to fully prepare students for top exam achievement and the step up to further study.

• 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)
• 5.1 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
• 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
• 10.9 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
• 12.4 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
• Index
• Back Cover
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