Oxford IB Diploma Programme IB Mathematics: Analysis and Approaches, Higher...

Description: 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 HL syllabus, for first teaching in September 2019.FeaturesAddress all aspects of the new DP Mathematics: analysis and approaches HL syllabus via an Enhanced Online Course Book Pack - made up of one full-colour, print textbook and one online textbook, including extensive teacher notesEnsure 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 chapterDeliver in-depth coverage of all topics through clear explanations and worked solutions, animated worked examples, differentiated exercises and worksheets, with answers providedAdopt 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 understandingDeepen 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 skillsSupport 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 studyThoroughly 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 modelsThis 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 a new user, once the initial user no longer requires access. You will need to contact your local Educational Consultant to arrange this.Table of ContentsFrom 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

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