Oxford International AQA Examinations: International A2 Level Mathematics Pure and Statistics

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Description

Contents

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Language

English

ISBN

9780198411215

Front Cover

Title Page

Contents

About this book

1 Functions

1.1 Functions

1.2 Composite functions

1.3 Inverse functions

1.4 Modulus functions

1.5 Combinations of transformations

1.6 Simplification of rational functions

1.7 Algebraic division

1.8 Partial fractions

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2 Binomial Series

2.1 The binomial series for any value of n

2.2 Approximations

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3 Trigonometric Functions and Formulae

3.1 The inverse trigonometric functions

3.2 The reciprocal trigonometric functions

3.3 Trigonometric formulae

3.4 Compound angle formulae

3.5 Expressions of the formf(θ) = a cos θ + b sin θ

3.6 Double angle formulae

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Assessment

4 Exponential and Logarithmic Functions

4.1 Exponential growth and decay

4.2 The exponential function

4.3 Natural logarithms

4.4 The logarithmic function

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5 Differentiation

5.1 The derivative of ex

5.2 The derivative of ln x

5.3 The derivatives of sin x and cos x

5.4 Differentiating products, quotients and composite functions

5.5 Implicit functions

5.6 Parametric equations

5.7 Finding dy/dx using parametric equations

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6 Integration

6.1 Standard integrals

6.2 Integrating products by substitution

6.3 Integration by parts

6.4 Integrating fractions

6.5 Special techniques for integrating some trigonometric functions

6.6 Volume of revolution

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7 Differential Equations

7.1 First order differential equations with separable variables

7.2 Natural occurrence of differential equations

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8 Numerical Methods

8.1 Approximately locating the roots of an equation

8.2 Using the iteration xn + 1 = g(xn)

8.3 Rules to find the approximate value of an area under a curve

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9 Vectors

9.1 Properties of vectors

9.2 Position vectors

9.3 The location of a point in space

9.4 Operations on cartesian vectors

9.5 Properties of a line joining two points

9.6 The equation of a straight line

9.7 Pairs of lines

9.8 The scalar product

9.9 The coordinates of the foot of the perpendicular from a point to a line

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10 The Poisson Distribution

10.1 The Poisson distribution

10.2 Cumulative Poisson probability tables

10.3 The Poisson distribution as a limiting case of the binomial distribution

10.4 The sum of independent Poisson variables

10.5 Further applications

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11 Continuous Random Variables

11.1 Continuous random variables

11.2 Cumulative distribution function

11.3 Expectation of X

11.4 Variance of X

11.5 Independent continuous random variables

11.6 Further applications

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12 The Exponential Distribution

12.1 The exponential distribution

12.2 Link between Poisson and exponential distributions

12.3 ‘No memory’ property

12.4 Further applications

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13 The Normal Distribution

13.1 The normal distribution

13.2 The standard normal variable, Z

13.3 Standardising any normal variable

13.4 Finding the z-value that gives a known probability

13.5 Finding x for any normal variable

13.6 Finding an unknown mean or standard deviation or both

13.7 Sum of independent normal random variables

13.8 Further applications

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14 Estimation

14.1 Sampling

14.2 The sample mean X

14.3 Distribution of the sample mean

14.4 Further applications

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15 Hypothesis Tests

15.1 Testing a population proportion, p

15.2 Testing a Poisson mean, λ

15.3 Type I and Type II errors

15.4 Introduction to testing a population mean μ

15.6 Case 1: Testing the mean of a normal distribution with known variance

15.7 Case 2: Test for the mean of adistribution using a normal approximation

15.8 The t-distribution

15.9 Case 3: Test for the mean of anormal distribution with unknown variance and small sample size

15.10 Further applications

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Assessment

Glossary

Answers

Index

Index

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