Oxford International AQA Examinations: International A2 Level Mathematics Pure and Statistics
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Description
Contents
Reviews
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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Assessment
2 Binomial Series
2.1 The binomial series for any value of n
2.2 Approximations
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Assessment
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
Summary
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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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Assessment
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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Assessment
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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Assessment
7 Differential Equations
7.1 First order differential equations with separable variables
7.2 Natural occurrence of differential equations
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Assessment
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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Assessment
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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Assessment
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
Summary
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Assessment
Glossary
Answers
Index
Index
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