Mathematics Applications ATAR Year 12 syllabus — effective January 2025
School assessment comprises Response 40%, Investigation 20% and Examination 40%. The external examination has two papers: Calculator-free allows 5 minutes reading and 50 minutes working, while Calculator-assumed allows 10 minutes reading and 100 minutes working. A changeover period of up to 15 minutes permits no work. The 2025 reference papers carry 51 and 100 raw marks respectively, weighted at 35% and 65% of the examination. The original practice models retain those raw totals; historical totals may vary. Both papers use written responses. The examination mark and moderated school mark contribute equally to the combined mark. A supervisor-supplied formula sheet is available for both papers; no calculator or notes are permitted in Calculator-free. Calculator-assumed permits the specified drawing equipment, two unfolded A4 sheets of notes and up to three calculators, with CAS capability assumed. Check the official instructions for the sitting being used.
Past papers on this subject span more than one syllabus. Papers written under an older one still work as practice, but the units and content areas they test have changed — the index labels every paper with the syllabus it was set under.
Syllabus effective January 2025 · 2025–presentEarlier syllabus — check current alignment · 2020–2024
The units and content areas, one by one
Each area below lists the concepts named in the syllabus, what the SCSA exam asks of them, and the mistake that most often costs marks.
- Unit 3 — Bivariate data analysis
- Unit 3 — Growth and decay in sequences
- Unit 3 — Graphs and networks
- Unit 4 — Time series analysis
- Unit 4 — Loans, investments and annuities
- Unit 4 — Networks and decision mathematics
Area 1 of 6
Unit 3 — Bivariate data analysis
Investigate associations using appropriately percentaged two-way tables, scatterplots, correlation and least-squares models. Identify explanatory and response variables, interpret slope and intercept in context, and connect the coefficient of determination to explained variation.
What the syllabus lists under this area · 4 points
- The statistical investigation process and describing association in percentaged two-way tables
- Scatterplots, direction-form-strength, the correlation coefficient r and the coefficient of determination
- Fitting and interpreting the least-squares line, residual plots, interpolation and extrapolation
- Association versus causation: coincidence, confounding and common response
What the exam asks
Describe direction, form and strength, use fitted models for predictions and judge whether a linear model is appropriate. Communicate the statistical investigation and distinguish interpolation from extrapolation.
Where marks go missing
A strong association does not establish causation. Keep r and r squared distinct, and compare percentages using the denominator appropriate to the question.
Area 2 of 6
Unit 3 — Growth and decay in sequences
Generate arithmetic and geometric sequences recursively and represent their terms in tables and graphs. Deduce nth-term rules from patterns and use first-order linear recurrence relations to model discrete growth, decay and steady-state behaviour.
What the syllabus lists under this area · 3 points
- Arithmetic sequences: recursion, nth-term rules and linear growth and decay
- Geometric sequences: recursion, nth-term rules and exponential growth and decay
- First-order linear recurrence relations, long-term behaviour and steady state
What the exam asks
Define the initial value and time index, generate terms, compare models and bracket a first threshold crossing with consecutive terms. Practical recurrence analysis uses numerical or graphical methods.
Where marks go missing
The initial value may be indexed by zero or one. A model value at a fractional time does not identify the first whole-period threshold, and a mathematical long-term prediction can become unrealistic in context.
Area 3 of 6
Unit 3 — Graphs and networks
Represent connected systems with vertices, edges and appropriate matrices. Analyse degree, connectivity, walks, trails, paths, circuits and cycles, including Eulerian and Hamiltonian features and planar graphs.
What the syllabus lists under this area · 3 points
- Graphs, digraphs and networks: terminology, adjacency matrices and multi-stage matrices
- Planar graphs, faces and Euler's formula v + f − e = 2
- Walks, trails, paths, cycles, shortest paths, Eulerian and Hamiltonian graphs
What the exam asks
Translate a written network into a valid representation, justify route classifications and use the handshaking rule or Euler’s planar relationship under their required conditions.
Where marks go missing
Eulerian routes concern edges; Hamiltonian routes concern vertices. Degree parity alone does not decide Hamiltonian existence, although a degree-one vertex rules out a Hamiltonian cycle.
Area 4 of 6
Unit 4 — Time series analysis
Identify the components of a time series, smooth data with moving averages and centre even-period averages. Use the average percentage method for seasonal indices, deseasonalise observations and make contextual forecasts.
What the syllabus lists under this area · 3 points
- Time series plots: trend, seasonality, irregular fluctuations and outliers
- Smoothing a time series with simple moving averages
- Seasonal indices by the average percentage method, deseasonalising and predicting from the trend line
What the exam asks
Show the time location of centred values, distinguish trend from seasonal variation and apply the appropriate seasonal index when converting between observed and deseasonalised values.
Where marks go missing
A four-period moving average initially lies between observation times. Do not multiply by a seasonal index when the required step is deseasonalisation, and keep seasonal indices normalised consistently.
Area 5 of 6
Unit 4 — Loans, investments and annuities
Model compound interest, depreciation, reducing-balance loans and annuities with recurrence relations. Use numerical tables, graphs and financial technology to compare rates, payments, balances and durations, including perpetuities.
What the syllabus lists under this area · 4 points
- Compound interest loans and investments: recurrence relations and the effective annual rate
- Solving compound interest and depreciation problems with the finance solver
- Reducing balance loans: recurrence models, repayments and time to repay
- Annuities and perpetuities: recurrence models and finance-solver problems
What the exam asks
State payment timing, interest period and initial balance. Rebase at a change of rate or payment, and identify the last full payment and any smaller final payment using the remaining balance.
Where marks go missing
An annual quoted rate is not automatically the monthly rate. Keep payment and compounding frequencies consistent, use the correct finance-solver signs and distinguish a fractional solver period from the actual payment schedule.
Area 6 of 6
Unit 4 — Networks and decision mathematics
Solve small shortest-path and flow problems, find minimum spanning trees, schedule projects through critical-path analysis and optimise one-to-one assignments. Relate every mathematical result to the constraints represented by the network.
What the syllabus lists under this area · 3 points
- Trees, spanning trees, Prim's algorithm and minimum connector problems
- Project networks, forward and backward scanning, critical paths and float
- Maximum flow-minimum cut and assignment problems with the Hungarian algorithm
What the exam asks
Use trial-and-error for shortest paths, inspection or Prim’s algorithm for minimum spanning trees, and inspection or the Hungarian algorithm for assignments as appropriate. Calculate earliest and latest times, float and project duration; justify a maximum flow with a matching cut.
Where marks go missing
The shortest route and minimum spanning tree solve different problems. A feasible flow needs capacity and conservation checks, and independent row or column choices can violate the one-to-one assignment constraint.