Complete Pure Mathematics 1 for Cambridge International AS & A Level
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Description
Contents
Reviews
Language
English
ISBN
9780198427469
Front Cover
Title Page
Contents
1 Quadratics
1.1 Solve quadratic equations by factorising
1.2 Solving quadratic inequalities
1.3 The method of completing the square
1.4 Solving quadratic equations using the formula
1.5 Solve more complex quadratic equations
1.6 The discriminant of a quadratic equation
1.7 Solving simultaneous equations
1.8 Graphs of quadratic functions
2 Functions and transformations
2.1 Mappings
2.2 Composite functions
2.3 Inverse functions
2.4 Transformations: translations
2.5 Transformations: reflections
2.6 Transformations: stretches
3 Coordinate geometry
3.1 Line segments
3.2 Parallel and perpendicular lines
3.3 Equation of a straight line
3.4 Circles
3.5 Points of intersection and circle properties
Maths in real-life
4 Circular measure
4.1 Radians
4.2 Arc length and sector area
4.3 Further problems involving arcs and sectors
5 Trigonometry
5.1 Exact values of trigonometric functions
5.2 Graphs of trigonometric functions
5.3 Inverse trigonometric functions
5.4 Composite graphs
5.5 Trigonometric equations
5.6 Trigonometric identities
6 Binomial expansion
6.1 Pascal’s triangle
6.2 Binomial notation
6.3 Binomial expansion
6.4 More complex expansions
7 Series
7.1 Sequences
7.2 Finite and infinite series
7.3 Arithmetic progressions
7.4 Geometric progressions
7.5 Infinite geometric progressions
Maths in real-life: Infinity
8 Differentiation
8.1 The gradient of the tangent
8.2 Gradient of a tangent as a limit
8.3 Differentiation of polynomials
8.4 Differentiation of more complex functions
8.5 The chain rule (differentiating a function of a function)
8.6 Finding the gradient of the tangent using differentiation
8.7 The second derivative
8.8 Equation of the tangent and the normal
9 Further differentiation
9.1 Increasing and decreasing functions
9.2 Stationary points
9.3 Problems involving maximum and minimum values
9.4 Connected rates of change
10 Integration
10.1 Integration as the reverse process of differentiation
10.2 Finding the constant of integration
10.3 Integrating expression of the form (ax + b)n
10.4 The definite integral
10.5 Finding area using definite integration
10.6 Area bounded by two curves or a curve and a line
10.7 Improper integrals
10.8 Volumes of revolution
Maths in real-life: Describing change mathematically
Exam-style paper A
Exam-style paper B
Answers
Glossary
Index
Back Cover
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