Mathematics:Applications & interpretation

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Measuring space: accuracy and geometry1.1: Representing numbers exactly and approximately1.2: Angles and triangles1.3: three-dimensional geometryRepresenting and describing data: descriptive statistics2.1: Collecting and organizing data2.2: Statistical measures2.3: Ways in which we can present data2.4: Bivariate dataDividing up space: coordinate geometry, lines, Voronoi diagrams, vectors3.1: Coordinate geometry in 2 and 3 dimensions3.2: The equation of a straight line in 2 dimensions3.3: Voronoi diagrams3.4: Displacement vectors3.5: The scalar and vector product3.6: Vector equations of linesModelling constant rates of change: linear functions and regressions4.1: Functions4.2: Linear models4.3: Inverse functions4.4: Arithmetic sequences and series4.5: Linear regressionQuantifying uncertainty: probability5.1: Theoretical and experimental probability5.2: Representing combined probabilities with diagrams5.3: Representing combined probabilities with diagrams and formulae5.4: Complete, concise and consistent representationsModelling relationships with functions: power and polynomial functions6.1: Quadratic models6.2: Quadratic modelling6.3: Cubic functions and models6.4: Power functions, inverse variation and modelsModelling rates of change: exponential and logarithmic functions7.1: Geometric sequences and series7.2: Financial applications of geometric sequences and series7.3: Exponential functions and models7.4: Laws of exponents - laws of logarithms7.5: Logistic modelsModelling periodic phenomena: trigonometric functions and complex numbers8.1: Measuring angles8.2: Sinusoidal models: f(x) = asin(b(x-c))+d8.3: Completing our number system8.4: A geometrical interpretation of complex numbers8.5: Using complex numbers to understand periodic modelsModelling with matrices: storing and analyzing data9.1: Introduction to matrices and matrix operations9.2: Matrix multiplication and properties9.3: Solving systems of equations using matrices9.4: Transformations of the plane9.5: Representing systems9.6: Representing steady state systems9.7: Eigenvalues and eigenvectorsAnalyzing rates of change: differential calculus10.1: Limits and derivatives10.2: Differentiation: further rules and techniques10.3: Applications and higher derivativesApproximating irregular spaces: integration and differential equations11.1: Finding approximate areas for irregular regions11.2: Indefinite integrals and techniques of integration11.3: Applications of integration11.4: Differential equations11.5: Slope fields and differential equationsModelling motion and change in 2D and 3D: vectors and differential equations12.1: Vector quantities12.2: Motion with variable velocity12.3: Exact solutions of coupled differential equations12.4: Approximate solutions to coupled linear equationsRepresenting multiple outcomes: random variables and probability distributions13.1: Modelling random behaviour13.2: Modelling the number of successes in a fixed number of trials13.3: Modelling the number of successes in a fixed interval13.4: Modelling measurements that are distributed randomly13.5: Mean and variance of transformed or combined random variables13.6: Distributions of combined random variablesTesting for validity: Spearman's hypothesis testing and x2 test for independence14.1: Spearman's rank correlation coefficient14.2: Hypothesis testing for the binomial probability, the Poisson mean and the product moment correlation coefficient14.3: Testing for the mean of a normal distribution14.4: Chi-squared test for independence14.5: Chi-squared goodness-of-fit test14.6: Choice, validity and interpretation of testsOptimizing complex networks: graph theory15.1: Constructing graphs15.2: Graph theory for unweighted graphs15.3: Graph theory for weighted graphs: the minimum spanning tree15.4: Graph theory for weighted graphs - the Chinese postman problem15.5: Graph theory for weighted graphs - the travelling salesman problemExploration

Written to support the new DP Mathematics: application and interpretation HL syllabus, for first assessment in 2021