Oxford IB Diploma Programme: IB Mathematics: analysis and approaches, Standard L

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