Oxford IB Diploma Programme: IB Mathematics: analysis and approaches, Higher Lev

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