OXFORD UNIVERSITY PRESS

# Oxford IB Mathematics: Analysis & Approaches, Course Companion (Higher Level)

## Oxford IB Mathematics: Analysis & Approaches, 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 ]**

**From patterns to generalizations: sequences and series**

1.1: Sequences, series and sigma notation

1.2: Arithmetic and geometric sequences and series

1.3: Proof

1.4: Counting principles and the binomial theorem

**Representing relationships: introducing functions**

2.1: Functional relationships

2.2: Special functions and their graphs

2.3: Classification of functions

2.4: Operations with functions

2.5: Function transformations

**Expanding the number system: complex numbers**

3.1: Quadratic equations and inequalities

3.2: Complex numbers

3.3: Polynomial equations and inequalities

3.4: The fundamental theorem of algebra

3.5: Solving equations and inequalities

3.6: Solving systems of linear equations

**Measuring change: differentiation**

4.1: Limits, continuity and convergence

4.2: The derivative of a function

4.3: Differentiation rules

4.4: Graphical interpretation of the derivatives

4.5: Applications of differential calculus

4.6: Implicit differentiation and related rates

**Analysing data and quantifying randomness: statistics and probability**

5.1: Sampling

5.2: Descriptive statistics

5.3: The justification of statistical techniques

5.4: Correlation, causation and linear regression

**Relationships in space: geometry and trigonometry**

6.1: The properties of 3D space

6.2: Angles of measure

6.3: Ratios and identities

6.4: Trigonometric functions

6.5: Trigonometric equations

**Generalizing relationships: exponents, logarithms and integration**

7.1: Integration as antidifferentiation and definite integrals

7.2: Exponents and logarithms

7.3: Derivatives of exponential and logarithmic functions; tangents and normals

7.4: Integration techniques

**Modelling changes: more calculus**

8.1: Areas and volumes

8.2: Kinematics

8.3: Ordinary differential equations (ODEs)

8.4: Limits revisited

**Modelling 3D space: vectors**

9.1: Geometrical representation of vectors

9.2: Introduction to vector algebra

9.3: Scalar product and its properties

9.4: Vector equations of a line

9.5: Vector product and properties

9.6: Vector equation of a plane

9.7: Lines, planes and angles

9.8: Application of vectors

**Equivalent systems of representation: more complex numbers**

10.1: Forms of a complex number

10.2: Operations with complex numbers in polar form

10.3: Powers and roots of complex numbers in polar form

**Valid comparisons and informed decisions: probability distributions**

11.1: Axiomatic probability systems

11.2: Probability distributions

11.3: Continuous random variables

11.4: Binomial distribution

11.5: The normal distribution

**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 |
9780198427162 |

SERIES |
IB DIPLOMA SERIES |