IB Mathematics: applications and interpretation Standard Level eBook

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Description

Contents

Reviews

Language

English

ISBN

9780198427032

Contents

Introduction

How to use your enhanced online course book

1 Measuring space: accuracy and 2D geometry

1.1 Measurements and estimates

1.2 Recording measurements, significant digits and rounding

1.3 Measurements: exact or approximate?

1.4 Speaking scientifically

1.5 Trigonometry of right-angled triangles and indirect measurements

1.6 Angles of elevation and depression

Chapter review

Modelling and investigation activity

2 Representing space: non-right angled trigonometry and volumes

2.1 Trigonometry of non-right triangles

2.2 Area of a triangle formula: applications of right- and non-right angled trigonometry

2.3 3D geometry: solids, surface area and volume

Chapter review

Modelling and investigation activity

3 Representing and describing data: descriptive statistics

3.1 Collecting and organizing univariate data

3.2 Sampling techniques

3.3 Presentation of data

3.4 Bivariate data

Chapter review

Modelling and investigation activity

4 Dividing up space: coordinate geometry, lines, Voronoi diagrams

4.1 Coordinates, distance and the midpoint formula in 2D and 3D

4.2 Gradient of a line and its applications

4.3 Equations of straight lines: different forms of equations

4.4 Parallel and perpendicular lines

4.5 Voronoi diagrams and the toxic waste dump problem

Chapter review

Modelling and investigation activity

5 Modelling constant rates of change: linear functions

5.1 Functions

5.2 Linear models

5.3 Arithmetic sequences

5.4 Modelling

Chapter review

Modelling and investigation activity

6 Modelling relationships: linear correlation of bivariate data

6.1 Measuring correlation

6.2 The line of best fit

6.3 Interpreting the regression line

Chapter review

Modelling and investigation activity

7 Quantifying uncertainty: probability, binomial and normal distributions

7.1 Theoretical and experimental probability

7.2 Representing combined probabilities with diagrams

7.3 Representing combined probabilities with diagrams and formulae

7.4 Complete, concise and consistent representations

7.5 Modelling random behaviour: random variables and probability distributions

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

7.7 Modelling measurements that are distributed randomly

Chapter review

Modelling and investigation activity

8 Testing for validity: Spearman's, hypothesis testing and χ2 test for independence

8.1 Spearman’s rank correlation coefficient

8.2 χ2 test for independence

8.3 χ2 goodness of fit test

8.4 The t-test

Chapter review

Modelling and investigation activity

9 Modelling relationships with functions: power functions

9.1 Quadratic models

9.2 Problems involving quadratics

9.3 Cubic models, power functions and direct and inverse variation

9.4 Optimization

Chapter review

Modelling and investigation activity

10 Modelling rates of change: exponential and logarithmic functions

10.1 Geometric sequences and series

10.2 Compound interest, annuities, amortization

10.3 Exponential models

10.4 Exponential equations and logarithms

Chapter review

Modelling and investigation activity

11 Modelling periodic phenomena: trigonometric functions

11.1 An introduction to periodic functions

11.2 An infinity of sinusoidal functions

11.3 A world of sinusoidal models

Chapter review

Modelling and investigation activity

12 Analyzing rates of change: differential calculus

12.1 Limits and derivatives

12.2 Equations of tangent and normal

12.3 Maximum and minimum points and optimization

Chapter review

Modelling and investigation activity

13 Approximating irregular spaces: integration

13.1 Finding areas

13.2 Integration: the reverse process of differentiation

Chapter review

Modelling and investigation activity

14 Exploration

Practice exam paper 1

Practice exam paper 2

Answers

Index

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