Year 12 · Units 3 and 4
WACE Mathematics Applications, Year 12 (Units 3 and 4)
Unit 3 and 4 Mathematics Applications moves from single-variable statistics into genuinely applied territory: bivariate analysis and regression, recurrence relations for growth and decay, and network and graph theory — the mathematics behind scheduling, logistics and shortest-path problems. Unit 4 shifts into finance and networks specifically, including compound interest, loan calculations and critical path analysis, all directly applicable outside the classroom. It's the most visibly "useful" maths course on offer, and that's a genuine strength, not a consolation prize.
Unit 3
Bivariate statistics, sequences and the first look at networks.
Scatterplots and correlation
Displaying and describing the relationship between two numerical variables.
Least-squares regression (line of best fit)
Fitting a least-squares regression line to bivariate data and using it for prediction.
Residuals and how well a model fits
Analysing residuals to assess how well a regression model actually fits the data.
Where students get stuck: Assuming a high correlation coefficient automatically means the linear model is a good fit. A residual plot showing a clear pattern reveals a non-linear relationship even when the correlation looks strong — this is the actual test the course wants a student to apply.
Arithmetic sequences and recurrence relations
Representing arithmetic sequences using recurrence relations, connecting to real stepwise growth.
Geometric sequences
Working with geometric sequences and their recurrence relations.
Geometric growth and decay
Modelling real growth and decay situations using geometric sequences.
Linear recurrence relations
Working with recurrence relations that combine both additive and multiplicative change.
Graphs and networks (vertices and edges)
Learning the formal terminology of graph and network theory — vertices, edges, degree.
Adjacency matrices and network paths
Representing networks using adjacency matrices and analysing paths through them.
Planar graphs, Euler's formula and trees
Working with planar graphs, Euler's formula, and tree structures within network theory.
Unit 4
Time series, finance and network optimisation — the most applied content in the course.
Time series, trends and seasonality
Analysing time series data for trends and seasonal patterns.
Smoothing and seasonal indices
Using smoothing techniques and seasonal indices to analyse and adjust time series data.
Compound interest
Calculating compound interest and future value for real investment and savings scenarios.
Loan repayments and amortisation
Calculating loan repayments and amortisation schedules for reducing-balance loans.
Annuities and regular investments
Calculating the future and present value of annuities and regular investments.
Finding the shortest path in a network
Finding the shortest path through a network using systematic algorithms.
Minimal spanning trees
Finding the minimal spanning tree of a network — the cheapest way to connect every point.
Critical path analysis
Using critical path analysis to schedule a project and identify which tasks control its minimum completion time.
Where students get stuck: Assuming every task on a long project needs monitoring equally. The critical path method exists precisely to identify the small subset of tasks — the critical ones — where a delay genuinely delays the whole project, and that's the actual point of the technique.
How it is assessed
- Unit 3 and Unit 4 combine school assessment, moderated by SCSA, with an external written examination set by SCSA at the end of the year.
- The combined school and examination result is what contributes to the ATAR for this course.
- A course must be completed to at least a C grade average across Units 3 and 4 for the result to count toward the WACE.
Common questions
- Has this syllabus changed recently?
- WACE senior secondary syllabuses are reviewed by SCSA on a rolling basis rather than all at once — there's no single blanket revision date the way there is for the P-10 curriculum. Check senior-secondary.scsa.wa.edu.au for the current syllabus version of this specific course before relying on unit content for assessment planning.
- How is Unit 3 and 4 Applications different in character from Unit 1 and 2?
- Unit 1 and 2 are built around everyday calculation — money, measurement, trigonometry. Unit 3 and 4 shift toward genuinely modern applied mathematics — network and graph theory in particular is closer to how logistics and scheduling problems are actually solved in industry than anything earlier in the WA maths sequence.
- Are the finance topics in Unit 4 just an extension of Unit 1's money maths?
- They build on the same foundation but go considerably further — compound interest, amortisation and annuities involve genuine formulas and multi-step calculations, not just percentage arithmetic. A student who found Unit 1's financial maths easy shouldn't assume Unit 4's finance content will be equally straightforward.
Related year levels
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Start learning for freeWritten from the current WACE course syllabus. Requirements change — check SCSA for the official syllabus.