Oxford International AQA Examinations: International A Level Further Mathematics with Statistics
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Description
Contents
Reviews
Language
English
ISBN
9780198411314
Front Cover
Title Page
Contents
AS Pure
1 Loci, Graphs and Algebra
1.1 Loci
1.2 Rational functions
1.3 Conic sections
Summary
Review exercises
Practice examination questions
2 Complex Numbers
2.1 What is a complex number?
2.2 Calculating with complex numbers
2.3 Argand diagram
2.4 Loci in the complex plane
Summary
Review exercises
Practice examination questions
3 Roots and Coefficients of a Quadratic Equation
3.1 Roots of a quadratic equation
3.2 Finding an equation with roots that area function of existing roots
Summary
Review exercises
Practice examination questions
4 Series
4.1 Summation formulae
4.2 Method of differences
Summary
Review exercises
Practice examination questions
5 Trigonometry
5.1 General solutions of trigonometric equations
5.2 Solving equations involving more complicated terms
Summary
Review exercises
Practice examination questions
6 Calculus
6.1 Gradient of a tangent to a curve
6.2 Rates of change
6.3 Improper integrals
Summary
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Practice examination questions
7 Matrices and Transformations
7.1 Introduction to matrices
7.2 Transformations
7.3 Common transformations
7.4 Invariant points and lines
Summary
Review exercise
Practice examination questions
8 Linear Graphs
8.1 Relationship between data
8.2 When the power of x is unknown, or when x is in the exponent
Summary
Review exercises
Practice examination questions
9 Numerical Methods
9.1 Solutions of polynomial equations
9.2 Step-by-step solution of differential equations
Summary
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Practice examination questions
AS Statistics
10 Bayes’ Theorem
10.1 Tree diagrams
10.2 Bayes’ Theorem
Summary
Review exercises
Practice examination questions
11 Discrete Uniform and Geometric Distributions
11.1 Discrete uniform distribution
11.2 Geometric distribution
Summary
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Practice examination questions
12 Probability Generating Functions
12.1 Probability generating functions and their properties
12.2 Some standard distributions
12.3 Sums of independent random variables
Summary
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Practice examination questions
13 Linear Combinations of Discrete Random Variables
13.1 Linear combinations of discrete random variables
13.2 Independent discrete random variables
Summary
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Practice examination questions
14 Constant Velocity in Two Dimensions
14.1 Vectors in component form
14.2 Position, displacement, distance, velocity and speed
14.3 Resultant velocity
14.4 Relative velocity, closest approach and interception
Summary
Review exercises
Practice examination questions
15 Dimensional Analysis
15.1 Dimensions and dimensional consistency
15.2 Finding a formula
Summary
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Practice examination questions
16 Collisions in One Dimension
16.1 Impulse and momentum
16.2 The principle of conservation of linear momentum
16.3 Elastic impact
16.4 Multiple collisions
Summary
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Practice examination questions
A2 Pure
17 Roots and Polynomials
17.1 Roots of higher-order equations
17.2 Complex roots of a polynomial equation
Summary
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Practice examination questions
18 Proof by Induction and Finite Series
18.1 Proof by induction
18.2 Finite series
Summary
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Practice examination questions
19 Series and Limits
19.1 Convergence
19.2 Maclaurin’s theorem
19.3 Finding the limits of a series
19.4 Improper integrals
Summary
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Practice examination questions
20 De Moivre’s Theorem De Moivre’s Theorem
20.1 De Moivre’s theorem
20.2 Further applications of de Moivre’s theorem to complex numbers
20.3 Trigonometric identities
Summary
Review exercises
Practice examination questions
21 Polar Coordinates
21.1 Position of a point
21.2 Sketching curves given in polar coordinates
21.3 Area of a sector of a curve
Summary
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Practice examination questions
22 The Calculus of Inverse Trigonometrical Functions
22.1 Inverse trigonometric functions
22.2 Differentiation and integration of inverse trigonometric functions
Summary
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Practice examination questions
23 Arc Length and Area of Surface of Revolution
23.1 Arc length
23.2 Area of a surface of revolution
Summary
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Practice examination questions
24 Hyperbolic Functions
24.1 Hyperbolic functions
24.2 Differentiation of hyperbolic functions
24.3 Inverse hyperbolic functions
Summary
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Practice examination questions
25 Differential Equations of First and Second Order
25.1 First-order linear equations
25.2 Second-order differential equations
25.3 Using a complementary function and particular integral to solve a first order equation
Summary
Review exercises
Practice examination questions
26 Vectors and Three-Dimensional Coordinate Geometry
26.1 Vectors
26.2 Vector product
26.3 Applications of vectors to coordinate geometry
26.4 Equation of a line
26.5 Equation of a plane
26.6 Scalar triple product and its applications
Summary
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Practice examination questions
27 Solutions of Linear Equations
27.1 Simultaneous linear equations
27.2 Using determinants to find the number of solutions of three simultaneous equations
Summary
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Practice examination questions
28 Matrix Algebra
28.1 Inverse matrices
28.2 Transformations
28.3 Invariant points and lines
Summary
Review exercises
Practice examination questions
A2 Statistics
29 Moment Generating Functions
29.1 Moment generating functions of random variables
29.2 Moment generating functions of some standard distributions
29.3 Sums of independent random variables
Summary
Review exercises
Practice examination questions
30 Estimators
30.1 Review of key concepts
30.2 Estimators and estimates
Summary
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Practice examination questions
31 Estimation
31.1 Confidence intervals for the mean of a distribution
31.2 Finding the sample size for a given confidence interval width
31.3 Inferences from confidence intervals
Summary
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Practice examination questions
32 Further Hypothesis Testing 1 – Means and Variances
32.1 Power of a hypothesis test
32.2 Tests for the difference between the means of two independent distributions
32.3 Tests for the difference between the means of two non-independent distributions
32.4 Tests related to population variances
Summary
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Practice examination questions
33 Further Hypothesis Testing 2 − Goodness of Fit Tests and Tests of No Association
33.1 Goodness of fit tests
33.2 Tests of no association
Summary
Review exercises
Practice examination questions
Answers
Index
Back Cover
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