§-Mathematics Applications syllabus
TAS · TASC← Mathematics Applications
Mathematics Applications syllabus, dot point by dot point
Every dot point in the TAS Mathematics Applications syllabus, with a focused answer for each. Click any dot point for a worked explainer, past exam questions and links to related points.
Unit 3
Module overview →How do we describe and sum sequences that grow by a constant amount or a constant factor?
Use arithmetic and geometric sequences, including their nth-term and sum rules, to model practical situations.
When can we trace every edge, or visit every vertex, of a network exactly once?
Identify and find Eulerian trails and circuits and Hamiltonian paths and cycles in networks.
How does money grow or shrink over time, and how are loans and investments modelled?
Apply simple and compound interest, depreciation, and recurrence relations to financial situations.
How do we model a process that both multiplies and adds a fixed amount each step?
Use first-order linear recurrence relations of the form V(n+1) = R V(n) + d to model and analyse practical situations.
How can we find the best decision when choices are limited by constraints?
Formulate and solve linear programming problems graphically to optimise an objective function.
How do matrices and networks model connected systems?
Perform matrix operations and analyse graphs, paths and networks
When can a network be drawn with no crossings, and how do its faces, edges and vertices relate?
Recognise planar graphs and apply Euler's formula relating vertices, edges and faces.
How do we check whether a straight line is the right model for bivariate data?
Calculate residuals and use a residual plot to assess the appropriateness of a linear model.
How do we detect and describe association between two categorical variables?
Construct and interpret two-way frequency tables to investigate association between categorical variables.
Unit 4
Module overview →How does an investment pay out a regular income, and when can it last forever?
Model annuities and perpetuities using recurrence relations and analyse the regular payments they support.
How does a fund grow when we both earn interest and add regular contributions?
Model annuity investments and superannuation where regular contributions are added to a fund that earns compound interest.
How do we assign workers to tasks to minimise total cost or time?
Solve allocation problems using the Hungarian algorithm to find an optimal assignment.
How do we describe and model the relationship between two numerical variables?
Analyse bivariate data using scatterplots, correlation, and least-squares regression lines.
How do we schedule a project and find the shortest time in which it can finish?
Use activity networks, forward and backward scanning, and float to identify the critical path of a project.
What is the greatest amount that can flow through a network from source to sink?
Determine the maximum flow through a network using the maximum-flow minimum-cut theorem.
How do we model quantities that grow or decay by a constant factor over time?
Model and analyse linear and geometric growth and decay using recurrence relations and rules.
How do we connect every site in a network at the lowest total cost?
Find minimum spanning trees of weighted networks using a systematic algorithm.
How does a loan balance fall as repayments are made, and how is interest split out?
Model reducing-balance loans with recurrence relations and amortisation tables.
How do we describe patterns in data over time and forecast future values?
Analyse time series using smoothing and trend lines, then forecast future values.