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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