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Mathematics Applications syllabus, dot point by dot point
Every dot point in the TAS Mathematics Applicationssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.7, Anthropic's latest AI, published by Better Tuition Academy.
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.8 min answer →
- 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 answer →
- 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.7 min answer →
- 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 Vn+1 = R Vn + d to model and analyse practical situations.8 min answer →
- 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.7 min answer →
- How do matrices and networks model connected systems?Perform matrix operations and analyse graphs, paths and networks8 min answer →
- 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.6 min answer →
- 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 answer →
- 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 answer →
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.8 min answer →
- 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.7 min answer →
- 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 answer →
- 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 answer →
- 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 answer →
- 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 answer →
- 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.7 min answer →
- 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.7 min answer →
- 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 answer →
- 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 answer →