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1.2 Completing the square
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1.3 The quadratic formula
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1.1 Solving quadratic equations by factorisation
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1.4 Solving simultaneous equations (one linear and one quadratic)
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1.5 Solving more complex quadratic equations
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1.8 The number of roots of a quadratic equation
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2.3 Inverse functions
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2.4 The graph of a function and its inverse
2.7 Stretches
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3.2 Parallel and perpendicular lines
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3.3 Equations of straight lines
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3.1 Length of a line segment and midpoint
82
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3.4 The equation of a circle
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3.5 Problems involving intersections of lines and circles
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End-of-chapter review exercise 3
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End-of-chapter review exercise 2
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2.8 Combined transformations
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2.5 Transformations of functions
3 Coordinate geometry
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2.1 Definition of a function
2.2 Composite functions
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End-of-chapter review exercise 1
2.6 Reflections
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1.9 Intersection of a line and a quadratic curve
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1.7 Solving quadratic inequalities
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1.6 Maximum and minimum values of a quadratic function
2 Functions
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1 Quadratics
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Acknowledgements
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How to use this book
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vi
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Series introduction
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Contents
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Contents
Copyright Material - Review Only - Not for Redistribution
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Cambridge International AS & A Level Mathematics: Pure Mathematics 1
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Cross-topic review exercise 1
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121
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5.2 The general definition of an angle
123
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5.3 Trigonometric ratios of general angles
127
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5.4 Graphs of trigonometric functions
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5.5 Inverse trigonometric functions
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5.6 Trigonometric equations
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5.7 Trigonometric identities
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6.3 Arithmetic progressions
6.4 Geometric progressions
156
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6.2 Binomial coefficients
155
171
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6.1 Binomial expansion of ( a + b )
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6 Series
175
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6.5 Infinite geometric series
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6.6 Further arithmetic and geometric series
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End-of-chapter review exercise 6
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7.1 Derivatives and gradient functions
198
7.3 Tangents and normals
7.4 Second derivatives
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7.2 The chain rule
209
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End-of-chapter review exercise 7
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7 Differentiation
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180
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Cross-topic review exercise 2
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153
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End-of-chapter review exercise 5
140
149
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5.8 Further trigonometric equations
136
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5.1 Angles between 0° and 90°
116
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5 Trigonometry
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End-of-chapter review exercise 4
107
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4.3 Area of a sector
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104
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4.2 Length of an arc
99
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4.1 Radians
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4 Circular measure
Copyright Material - Review Only - Not for Redistribution
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Contents
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8 Further differentiation
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8.1 Increasing and decreasing functions
8.3 Practical maximum and minimum problems
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End-of-chapter review exercise 8
230
9 Integration
238
9.1 Integration as the reverse of differentiation
239
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9.3 Integration of expressions of the form ( ax + b )
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9.2 Finding the constant of integration
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247
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9.4 Further indefinite integration
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9.5 Definite integration
9.8 Improper integrals
264
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Pr
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Glossary
Index
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Answers
v
280
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Cross-topic review exercise 3
Practice exam-style paper
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250
9.7 Area bounded by a curve and a line or by two curves
End-of-chapter review exercise 9
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253
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9.6 Area under a curve
9.9 Volumes of revolution
y
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8.5 Practical applications of connected rates of change
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8.4 Rates of change
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216
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8.2 Stationary points
211
Copyright Material - Review Only - Not for Redistribution