OXFORD UNIVERSITY PRESS

# Oxford IB Mathematics: Applications & Interpretation, Course Companion (Higher Level)

## Oxford IB Mathematics: Applications & Interpretation, Course Companion (Higher Level)

Featuring a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: analysis and approaches SL syllabus, for first teaching in September 2019. Each **Enhanced Online Course Book Pack** is made up of **one full-colour, print textbook **and **one online textbook** - packed full of investigations, exercises, worksheets, worked solutions and answers, plus assessment preparation support.

**[ TABLE OF CONTENTS ]**

**Measuring space: accuracy and geometry**

1.1: Representing numbers exactly and approximately

1.2: Angles and triangles

1.3: three-dimensional geometry

**Representing and describing data: descriptive statistics**

2.1: Collecting and organizing data

2.2: Statistical measures

2.3: Ways in which we can present data

2.4: Bivariate data

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

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

**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

**Quantifying uncertainty: probability**

5.1: Theoretical and experimental probability

5.2: Representing combined probabilities with diagrams

5.3: Representing combined probabilities with diagrams and formulae

5.4: Complete, concise and consistent representations

**Modelling relationships with functions: power and polynomial functions**

6.1: Quadratic models

6.2: Quadratic modelling

6.3: Cubic functions and models

6.4: Power functions, inverse variation and models

**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

**Modelling periodic phenomena: trigonometric functions and complex numbers**

8.1: Measuring angles

8.2: Sinusoidal models: f(x) = asin(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

**Modelling with matrices: storing and analyzing 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

**Analyzing rates of change: differential calculus**

10.1: Limits and derivatives

10.2: Differentiation: further rules and techniques

10.3: Applications and higher derivatives

**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

**Modelling motion and change in 2D and 3D: vectors and differential equations**

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

**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

**Testing for validity: Spearman's hypothesis testing and x2 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: Chi-squared test for independence

14.5: Chi-squared goodness-of-fit test

14.6: Choice, validity and interpretation of tests

**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

**Exploration**

## **[ SPECIAL FEATURES ]**

- Address all aspects of the new DP Mathematics: analysis and approaches SL syllabus via an Enhanced Online Course Book Pack - made up of one full-colour, print textbook and one online textbook, including extensive teacher notes.
- Ensure learners are ready to tackle each topic with targeted 'Prior Knowledge' worksheets, linked to 'Before You Start' summaries and exercises at the start of every chapter.
- Deliver in-depth coverage of all topics through clear explanations and worked solutions, animated worked examples, differentiated exercises and worksheets, with answers provided.
- Adopt a concept-based approach with conceptual lenses and microconcepts woven into every chapter, plus rich investigations that integrate factual and conceptual questions - leading to meaningful, content-specific conceptual understanding.
- Deepen mathematical understanding via inquiry-based tasks that relate to the content of each chapter, 'international mindedness' features, regular links to Theory of Knowledge, and activities that target ATL skills.
- Support students' development of a mathematical toolkit, as required by the new syllabus, with modelling and investigation activities presented in each chapter, including prompts for reflection, and suggestions for further study.
- Thoroughly prepare students for IB assessment via in-depth coverage of course content, overviews of all requirements, exam-style practice questions and papers, and a full chapter supporting the new mathematical exploration (IA).
- Includes support for the most popular Graphic Display Calculator models.
- This Online Course Book will be available on Oxford Education Bookshelf until 2029. Access is facilitated via a unique code, which is sent in the mail. The code must be linked to an email address, creating a user account.
- Access may be transferred once to an additional user.

GRADES / AGES |
GRADES 11 - 12 |

ANSWER KEY |
UNDEFINED |

AUTHOR(S) |
OXFORD UNIVERSITY PRESS |

PUBLISHER |
OXFORD UNIVERSITY PRESS |

PAGES |
832 PAGES |

SAMPLE |
N/A |

ISBN |
9780198427049 |

SERIES |
IB DIPLOMA SERIES |