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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