Complete Additional Mathematics for Cambridge IGCSE® & O Level
$37.49

Complete Additional Mathematics for Cambridge IGCSE® & O Level

By Tony Beadsworth
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.

Table of Contents
  • 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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