$37.49

# Complete Pure Mathematics 1 for Cambridge International AS & A Level

By Jean Linsky, Brian Western, James Nicholson

US$ 37.49

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Book Description

Providing complete syllabus support (9709), this stretching and practice-focused course builds the advanced skills needed for the latest Cambridge assessments and the transition to higher education. Engaging, real world examples make mathematics relevant to real life.

Table of Contents

- 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 Pascalâ€™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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