$38.13

# Oxford International AQA Examinations: International A Level Further Mathematics with Statistics

By John Rayneau, Mark Gaulter, Brian Gaulter, Brian Jefferson

US$ 38.13

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Book Description

The only textbook that completely covers the pure and statistics parts of the Oxford AQA International Oxford AQA International AS & A Level Further Mathematics specifiction (9665), for first teaching in September 2017.

Written by experienced authors, the rigorous, international approach ensures advanced mathematical understanding and challenges your most able students. This textbook helps students develop the complex mathematical, reasoning and problem solving skills needed for the Oxford AQA International A Level exams and provides an excellent grounding for university study.

Table of Contents

- 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
- Review exercises
- 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
- Review exercises
- Practice examination questions

- 1 Loci, Graphs and Algebra
- 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
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- Practice examination questions

- 10 Bayes’ Theorem
- A2 Pure
- 17 Roots and Polynomials
- 17.1 Roots of higher-order equations
- 17.2 Complex roots of a polynomial equation
- Summary
- Review exercises
- Practice examination questions

- 18 Proof by Induction and Finite Series
- 18.1 Proof by induction
- 18.2 Finite series
- Summary
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- Practice examination questions

- 24 Hyperbolic Functions
- 24.1 Hyperbolic functions
- 24.2 Differentiation of hyperbolic functions
- 24.3 Inverse hyperbolic functions
- Summary
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- 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

- 17 Roots and Polynomials
- 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
- Review exercises
- 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
- Review exercises
- 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
- Review exercises
- 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

- 29 Moment Generating Functions
- Answers
- Index
- Back Cover

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