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TAS · TASC2026

TCE Mathematics Applications (Tasmania): complete 2026 guide to the pre-tertiary Units 3 and 4

Study-note hub for TCE Mathematics Applications (TASC Level 3, pre-tertiary). Covers Unit 3 (financial maths, matrices and networks, linear programming) and Unit 4 (bivariate data and regression, time series and forecasting, growth and decay), with assessment guidance.

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TCE Mathematics Applications study hub

This hub links the ExamExplained study notes for TCE Mathematics Applications, a TASC Level 3 pre-tertiary course in Tasmania. The course builds practical mathematical skills for finance, data analysis, networks, and optimisation.

Unit 3

  • Financial mathematics: simple and compound interest, depreciation, effective rates, and recurrence relations.
  • Bivariate data and regression: scatterplots, correlation, the coefficient of determination, and least-squares lines.
  • Two-way frequency tables: row and column percentages and association between categorical variables.
  • Residual analysis: calculating residuals and reading residual plots to test a linear model.
  • 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.
  • Matrices and networks: matrix operations, inverses, adjacency matrices, spanning trees, and shortest paths.
  • 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.
  • Linear programming: defining variables and constraints, graphing feasible regions, and the corner-point method.

Unit 4

  • Time series and forecasting: trend, seasonal and irregular components, moving averages, seasonal indices, and forecasting.
  • Growth and decay: linear and geometric models, recurrence relations, and closed-form rules.
  • 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.
  • 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.

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.

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Common questions about Mathematics Applications

What is TCE Mathematics Applications and what level is it?
It is a TASC Level 3 pre-tertiary course in the Tasmanian Certificate of Education. It is designed for students who want to apply mathematics to practical, real-world contexts such as finance, data, and optimisation, rather than the more abstract focus of Mathematics Methods.
How is the course assessed and does it count towards ATAR?
Assessment combines school-based internal assessment against the course criteria with a TASC external examination. As a Level 3 pre-tertiary course it contributes to the ATAR.
What topics are in Unit 3 and Unit 4?
Unit 3 covers financial mathematics, matrices and networks, and linear programming. Unit 4 covers bivariate data and regression, time series and forecasting, and growth and decay.
Do I need a calculator for the external exam?
Yes. A calculator (and often graphics or CAS technology where permitted) is expected for regression, interest calculations, matrix operations, and smoothing. Always check the current TASC exam specifications for the approved technology.
What is the difference between linear and geometric growth in this course?
Linear growth adds a constant amount each step and graphs as a straight line, while geometric growth multiplies by a constant factor each step and graphs as a curve. Simple interest and flat-rate depreciation are linear; compound interest and reducing-balance depreciation are geometric.
How should I structure exam answers for full marks?
Show the formula or rule you use, substitute clearly, give units, and interpret the result in the context of the question. For predictions, state whether you are interpolating or extrapolating and comment on reliability.