Oxford IB Diploma Programme: IB Mathematics: analysis and approaches, Higher Level, Print and Enhanced Online Course Book Pack

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