OXFORD UNIVERSITY PRESS

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

## Oxford IB Mathematics: Analysis & Approaches, Course Companion (Standard 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: Number patterns and sigma notation

1.2: Arithmetic and geometric sequences

1.3: Arithmetic and geometric series

1.4: Modelling using arithmetic and geometric series

1.5: The binomial theorem

1.6: Proofs

**Representing relationships: introducing functions**

2.1: What is a function?

2.2: Functional notation

2.3: Drawing graphs of functions

2.4: The domain and range of a function

2.5: Composition of functions

2.6: Inverse functions

**Modelling relationships: linear and** **quadratic functions**

3.1: Parameters of a linear function

3.2: Linear functions

3.3: Transformations of functions

3.4: Graphing quadratic functions

3.5: Solving quadratic equations by factorization and completing the square

3.6: The quadratic formula and the discriminant

3.7: Applications of quadratics

**Equivalent representations: rational functions**

4.1: The reciprocal function

4.2: Transforming the reciprocal function

4.3: Rational functions of the form ax+b/cx+d

**Measuring change: differentiation**

5.1: Limits and convergence

5.2: The derivative function

5.3: Differentiation rules

5.4: Graphical interpretation of first and second derivatives

5.5: Application of differential calculus: optimization and kinematics

**Representing data: statistics for univariate data**

6.1: Sampling

6.2: Presentation of data

6.3: Measures of central tendency

6.4: Measures of dispersion

**Modelling relationships between two data sets: statistics for bivariate data**

7.1: Scatter diagrams

7.2: Measuring correlation

7.3: The line of best fit

7.4: Least squares regression

**Quantifying randomness: probability**

8.1: Theoretical and experimental probability

8.2: Representing probabilities: Venn diagrams and sample spaces

8.3: Independent and dependent events and conditional probability

8.4: Probability tree diagrams

**Representing** **equivalent quantities: exponentials and logarithms**

9.1: Exponents

9.2: Logarithms

9.3: Derivatives of exponential functions and the natural logarithmic function

**From approximation to generalization: integration**

10.1: Antiderivatives and the indefinite integral

10.2: More on indefinite integrals

10.3: Area and definite integrals

10.4: Fundamental theorem of calculus

10.5: Area between two curves

**Relationships in space: geometry and trigonometry in 2D and 3D**

11.1: The geometry of 3D shapes

11.1: Right-angles triangle trigonometry

11.3: The sine rule

11.4: The cosine rule

11.5: Applications of right and non-right angled trigonometry

**Periodic relationships: trigonometric functions**

12.1: Radian measure, arcs, sectors and segments

12.2: Trigonometric ratios in the unit circle

12.3: Trigonometric identities and equations

12.4: Trigonometric functions

**Modelling change: more calculus**

13.1: Derivatives with sine and cosine

13.2: Applications of derivatives

13,3: Integration with sine, cosine and substitution

13.4: Kinematics and accumulating change

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

14.1: Random variables

14.2: The binomial distribution

14.3: 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 |
672 PAGES |

SAMPLE |
N/A |

ISBN |
9780198427100 |

SERIES |
IB DIPLOMA SERIES |