TCE Mathematics Applications: 2026 study notes for TASC General Mathematics Level 3 (MTG315123)

Study notes for TASC General Mathematics

TASC does not offer a course called Mathematics Applications. The notes on this page match General Mathematics Level 3 (MTG315123), the Tasmanian pre-tertiary course that applies mathematics to data, finance and networks. We file them under Mathematics Applications, the name of the equivalent WACE course, so that existing links keep working.

Our notes are still grouped as Unit 3 and Unit 4 in the site menu. Below they are listed by the TASC module they belong to.

Module 1: modelling, problem solving and statistical investigation

Module 1 is taught alongside Modules 2 and 3 rather than as separate content. The statistical investigation process runs through the statistics notes below.

Module 2: statistical analysis

• Bivariate data and regression: scatterplots, correlation, the coefficient of determination, and least-squares lines.
• Residual analysis: calculating residuals and reading residual plots to test a linear model.
• Two-way frequency tables: row and column percentages and association between categorical variables.
• Time series and forecasting: trend, seasonal and irregular components, moving averages, seasonal indices, and forecasting.

Module 2: growth and decay in sequences

• Arithmetic and geometric sequences: nth-term and sum rules for linear and geometric patterns.
• First-order linear recurrence relations: the general form Vn+1 = R Vn + d and steady-state behaviour.
• Growth and decay: linear and geometric models, recurrence relations, and closed-form rules.

Module 3 core: investment, loans and annuities

• Financial mathematics: simple and compound interest, depreciation, effective rates, and recurrence relations.
• Reducing-balance loans and amortisation: loan recurrence, amortisation tables, and total interest.
• Annuities and perpetuities: drawing a regular income from a fund, and perpetual payments.
• Annuity investments and superannuation: building a fund with contributions plus compound interest.

Module 3 elective: networks and decision mathematics

• Planar graphs and Euler's formula: planarity, faces, and v - e + f = 2.
• Eulerian and Hamiltonian paths: trails and circuits over edges, and paths and cycles over vertices.
• Minimum spanning trees: the minimum connector problem solved by Prim's algorithm.
• Critical path analysis: activity networks, float, and the minimum completion time.
• Flow networks: capacities, cuts, and the maximum-flow minimum-cut theorem.
• Assignment and matching: optimal allocation with the Hungarian algorithm.
• Matrices and networks: adjacency matrices are in the course; general matrix operations and inverses go beyond it.

The other Module 3 elective, applications of trigonometry and Earth geometry, is not yet covered by our notes.

Beyond the TASC course

• Linear programming: defining variables and constraints, graphing feasible regions, and the corner-point method. This is not part of TASC General Mathematics, so treat it as extension reading.

How to use these notes

Each dot-point note opens with a quick answer, then works through the ideas with at least one fully worked numeric example and a common-mistake warning. Read the note, then reproduce the worked example without looking, checking your method and units against the model answer.