Oxford University Press Education & Teaching
Complete Additional Mathematics for Cambridge IGCSE® & O Level
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Description
Contents
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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.

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)
5.1 Introduction
5.2 Completing the square
5.3 Interpreting the expression
5.4 Sketching the graph of a quadratic function
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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