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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