IB Maths: Applications and Interpretation

Standard form, arithmetic and geometric sequences, compound interest and depreciation, approximation and percentage error, amortization and annuities, and solving equations with technology. At HL: the laws of logarithms, rational exponents, infinite geometric series, complex numbers, matrices, and eigenvalues and eigenvectors.

Straight lines, the language of functions, key features of graphs, the library of models — linear, quadratic, exponential, direct and inverse variation, cubic and sinusoidal — and the modelling cycle itself. At HL: composite and inverse functions, transformations, logarithmic, logistic and piecewise models, and linearising data with logarithms.

Three-dimensional solids, the sine and cosine rules, bearings, arcs and sectors, perpendicular bisectors and Voronoi diagrams. At HL: radians, the unit circle, matrix transformations and fractals, vectors and vector kinematics, and a substantial graph theory strand ending in the Chinese postman and travelling salesman problems.

The biggest topic in the course. Sampling and bias, summary statistics, correlation and regression, Spearman’s rank, probability, the binomial and normal distributions, and hypothesis testing with chi-squared and \(t\)-tests. At HL: data collection design, non-linear regression and \(R^{2}\), the central limit theorem, confidence intervals, the Poisson distribution, Type I and II errors, and Markov chains.

The derivative as a rate of change, tangents and normals, stationary points, optimisation, integration and area, and the trapezoidal rule. At HL: the further derivatives and the three rules, related rates, concavity, integration by substitution, volumes of revolution, kinematics, differential equations, slope fields, Euler’s method and phase portraits.