Oxford International AQA Examinations: International AS Level Mathematics

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Description

Contents

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Language

English

ISBN

9780198411260

Contents

About this book

1 Expanding Brackets, Surds and Indices

1.1 Algebraic expressions

1.2 Expansion of Two Brackets

1.3 Square roots and other roots

1.4 Surds

1.5 Indices

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2 Quadratic Polynomials and Equations

2.1 Quadratic polynomials

2.2 Quadratic equations

2.3 Solution by completing the square

2.4 The formula for solving a quadratic equation

2.5 Properties of the roots of a quadratic equation

2.6 Simultaneous equations

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3 Algebraic Division

3.1 Division of a polynomial by x − a

3.2 The remainder theorem and thefactor theorem

3.3 The factors of a3 − b3 and a3 + b3

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4 Functions and Graphs

4.1 Functions

4.2 Graphical interpretation of equations

4.3 Inequalities

4.4 Transformations of graphs

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5 Coordinate Geometry

5.1 Lines joining two points

5.2 Gradient

5.3 The equation of a straight line

5.4 Intersection

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6 Differentiation

6.1 Chords, tangents, normals and gradients

6.2 Differentiation

6.3 Gradients of tangents and normals

6.4 Increasing and decreasing functions

6.5 Stationary points

6.6 Maximum and minimum points

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7 Integration

7.1 Indefinite integration

7.2 Using integration to find an area

7.3 The trapezium rule

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8 Sequences and Series

8.1 Defining a sequence

8.2 Series

8.3 Arithmetic series

8.4 Geometric series

8.5 The Binomial theorem

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9 Coordinate Geometry and Circles

9.1 The equation of a circle

9.2 Geometric properties of circles

9.3 Tangents to circles

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10 Trigonometry

10.1 Trigonometric ratios of acute angles

10.2 The sine rule and cosine rule

10.3 The area of a triangle

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11 Trigonometric Functions and Equations

11.1 Angle units

11.2 The length of an arc

11.3 The area of a sector

11.4 The trigonometric functions

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12 Exponentials and Logarithms

12.1 Exponential functions

12.2 Logarithms

12.3 The laws of logarithms

12.4 Equations containing logarithmsor x as a power

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13 Probability

13.1 Introduction to probability

13.2 Combined events

13.3 Conditional events

13.4 Tree diagrams

13.5 Further applications

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14 Discrete Random Variables

14.1 Discrete variables

14.2 Discrete random variables

14.3 E(X), the expectation of X

14.4 The variance and standard deviation of X

14.5 Sum or difference of two independent random variables

14.6 Further applications

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15 Bernoulli and Binomial Distributions

15.1 The Bernoulli distribution

15.2 The binomial distribution

15.3 The cumulative binomial distribution function

15.4 Mean, variance and standard deviation of a binomial distribution

15.5 Further applications

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16 Displacement, Speed, Velocity and Acceleration

16.1 Displacement, speed, velocity and acceleration

16.2 Displacement-time and velocity-time graphs

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17 Motion in a Straight Line

17.1 Equations of motion with constant acceleration

17.2 Free fall motion under gravity

17.3 Motion in a straight line with variable acceleration

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18 Forces and Newton’s Laws

18.1 Types of force

18.2 Newton’s first law of motion

18.3 Connected particles

18.4 Dynamic friction

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19 Momentum and Impulse

19.1 Momentum and impulse

19.2 Conservation of linear momentum

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Glossary

Answers

Index

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