Mathematics : applications and interpretation. Higher level course companion / created by Paul Belcher, Jennife Chang Wathall, Suzanne Doering, Phil Dixbury, Panayiotis Enonomopoulos, Jane Forest, Peter Gray, Tony Halsey, David Harris, Lorraine Heinrichs, Ed Kemp, Paul La Rondie, Palmira Mariz Seiler, Michael Ortman, Muriye Sirinoglu Singh, NAdia Stoyanova Kennedy and Paula Waldman [and sixteen others].

Includes bibliography and index

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.