IB Mathematics: applications and interpretation Higher Level eBook

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Description

Contents

Reviews

Language

English

ISBN

9780198427094

Contents

Introduction

How to use your enhanced online course book

1 Measuring space: accuracy and geometry

1.1 Representing numbers exactly and approximately

1.2 Angles and triangles

1.3 Three dimensional geometry

Chapter review

Modelling and investigation activity

2 Representing and describing data: descriptive statistics

2.1 Collecting and organizing data

2.2 Statistical measures

2.3 Ways in which you can present data

2.4 Bivariate data

Chapter review

Modelling and investigation activity

3 Dividing up space: coordinate geometry, Voronoi diagrams, vectors, lines

3.1 Coordinate geometry in 2 and 3 dimensions

3.2 The equation of a straight line in 2 dimensions

3.3 Voronoi diagrams

3.4 Displacement vectors

3.5 The scalar and vector product

3.6 Vector equations of lines

Chapter review

Modelling and investigation activity

Paper 3 question and comments

4 Modelling constant rates of change: linear functions and regressions

4.1 Functions

4.2 Linear models

4.3 Inverse functions

4.4 Arithmetic sequences and series

4.5 Linear regression

Chapter review

Modelling and investigation activity

5 Quantifying uncertainty: probability

5.1 Reflecting on experiences in the world of chance. First steps in the quantification of probabilities

5.2 Representing combined probabilities with diagrams

5.3 Representing combined probabilities with diagrams and formulae

5.4 Complete, concise and consistent representations

Chapter review

Modelling and investigation activity

6 Modelling relationships with functions: power and polynomial functions

6.1 Quadratic models

6.2 Problems involving quadratics

6.3 Cubic functions and models

6.4 Power functions, direct and inverse variation and models

Chapter review

Modelling and investigation activity

7 Modelling rates of change: exponential and logarithmic functions

7.1 Geometric sequences and series

7.2 Financial applications of geometric sequences and series

7.3 Exponential functions and models

7.4 Laws of exponents – laws of logarithms

7.5 Logistic models

Chapter review

Modelling and investigation activity

8 Modelling periodic phenomena: trigonometric functions and complex numbers

8.1 Measuring angles

8.2 Sinusoidal models: f(x) = a sin (b (x − c)) + d

8.3 Completing our number system

8.4 A geometrical interpretation of complex numbers

8.5 Using complex numbers to understand periodic models

Chapter review

Modelling and investigation activity

9 Modelling with matrices: storing and analysing data

9.1 Introduction to matrices and matrix operations

9.2 Matrix multiplication and Properties

9.3 Solving systems of equations using matrices

9.4 Transformations of the plane

9.5 Representing systems

9.6 Representing steady state systems

9.7 Eigenvalues and eigenvectors

Chapter review

Modelling and investigation activity

10 Analyzing rates of change: differential calculus

10.1 Limits and derivatives

10.2 Differentiation: further rules and techniques

10.3 Applications and higher derivatives

Chapter review

Modelling and investigation activity

11 Approximating irregular spaces: integration and differential equations

11.1 Finding approximate areas for irregular regions

11.2 Indefinite integrals and techniques of integration

11.3 Applications of integration

11.4 Differential equations

11.5 Slope fields and differential equations

Chapter review

Modelling and investigation activity

12 Modelling motion and change in two and three dimensions

12.1 Vector quantities

12.2 Motion with variable velocity

12.3 Exact solutions of coupled differential equations

12.4 Approximate solutions to coupled linear equations

Chapter review

Modelling and investigation activity

13 Representing multiple outcomes: random variables and probability distributions

13.1 Modelling random behaviour

13.2 Modelling the number of successes in a fixed number of trials

13.3 Modelling the number of successes in a fixed interval

13.4 Modelling measurements that are distributed randomly

13.5 Mean and variance of transformed or combined random variables

13.6 Distributions of combined random variables

Chapter review

Modelling and investigation activity

14 Testing for validity: Spearman’s, hypothesis testing and χ2 test for independence

14.1 Spearman’s rank correlation Coefficient

14.2 Hypothesis testing for the binomial probability, the Poisson mean and the product moment correlation coefficient

14.3 Testing for the mean of a normal distribution

14.4 χ2 test for independence

14.5 χ2 goodness-of-fit test

14.6 Choice, validity and interpretation of tests

Chapter review

Modelling and investigation activity

15 Optimizing complex networks: graph theory

15.1 Constructing graphs

15.2 Graph theory for unweighted graphs

15.3 Graph theory for weighted graphs: the minimum spanning tree

15.4 Graph theory for weighted graphs: the Chinese postman problem

15.5 Graph theory for weighted graphs: the travelling salesman problem

Chapter review

Modelling and investigation activity

16 Exploration

Practice exam paper 1

Practice exam paper 2

Practice exam paper 3

Answers

Index

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