§-Mathematics Applications Q&A
TAS · TASC← Mathematics Applications
Mathematics Applications Q&A by dot point
A short Q&A bank for every TAS Mathematics Applications syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Unit 3
Use arithmetic and geometric sequences, including their nth-term and sum rules, to model practical situations.
Identify and find Eulerian trails and circuits and Hamiltonian paths and cycles in networks.
Apply simple and compound interest, depreciation, and recurrence relations to financial situations.
Use first-order linear recurrence relations of the form V(n+1) = R V(n) + d to model and analyse practical situations.
Formulate and solve linear programming problems graphically to optimise an objective function.
Perform matrix operations and analyse graphs, paths and networks
Recognise planar graphs and apply Euler's formula relating vertices, edges and faces.
Calculate residuals and use a residual plot to assess the appropriateness of a linear model.
Construct and interpret two-way frequency tables to investigate association between categorical variables.
Unit 4
Model annuities and perpetuities using recurrence relations and analyse the regular payments they support.
Model annuity investments and superannuation where regular contributions are added to a fund that earns compound interest.
Solve allocation problems using the Hungarian algorithm to find an optimal assignment.
Analyse bivariate data using scatterplots, correlation, and least-squares regression lines.
Use activity networks, forward and backward scanning, and float to identify the critical path of a project.
Determine the maximum flow through a network using the maximum-flow minimum-cut theorem.
Model and analyse linear and geometric growth and decay using recurrence relations and rules.
Find minimum spanning trees of weighted networks using a systematic algorithm.
Model reducing-balance loans with recurrence relations and amortisation tables.
Analyse time series using smoothing and trend lines, then forecast future values.