§-Mathematics Applications syllabus

Mathematics Applications syllabus, dot point by dot point

Every dot point in the TAS Mathematics Applications course document, in syllabus order, with a focused answer for each. Open any dot point for the answer, exam-style questions and links to related points.

Unit 3

Section overview →

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.

7 min read →

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.

8 min read →

How do we detect and describe association between two categorical variables?

Construct and interpret two-way frequency tables to investigate association between categorical variables.

7 min read →

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.

8 min read →

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.

8 min read →

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.

7 min read →

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.

8 min read →

How do matrices and networks model connected systems?

Perform matrix operations and analyse graphs, paths and networks

8 min read →

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.

8 min read →

Unit 4

Section 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.

8 min read →

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.

8 min read →

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.

8 min read →

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.

8 min read →

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.

8 min read →

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.

8 min read →

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.

8 min read →

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.

8 min read →

How do we describe and model the relationship between two numerical variables?

Analyse bivariate data using scatterplots, correlation, and least-squares regression lines.

8 min read →

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.

8 min read →