SACE Stage 2:
General Mathematics

Modelling with Linear Relationships in SACE Stage 2 General Mathematics extends the Stage 1 linear functions and graphs content to the more sophisticated modelling and graphical analysis expected at Stage 2 level — including solving simultaneous linear equations algebraically and graphically, applying systems of equations to practical situations such as break-even analysis and resource allocation, linear programming including setting up a system of linear inequalities to define a feasible region, identifying corner points of the feasible region, and using an objective function to find the optimal solution for maximisation and minimisation problems in practical settings such as production planning and scheduling, interpreting and communicating the results of a linear programming solution in context, and understanding the effect of changing constraints on the feasible region and the optimal solution. Modelling with Linear Relationships is assessed in both the school-assessed coursework and the external examination, and rewards students who can set up and solve practical optimisation problems systematically and communicate their reasoning clearly in context.

Modelling with Matrices in SACE Stage 2 General Mathematics extends the Stage 1 matrix content to the more powerful modelling applications that are distinctive to the General Mathematics course at Stage 2 level — including matrix arithmetic including addition, subtraction, scalar multiplication, and matrix multiplication and their practical applications, representing communication and connection networks as adjacency matrices, using matrix powers to analyse multi-step connections and reachability in networks, transition matrices and their use in modelling discrete dynamic systems that change state over time such as population migration, market share, and ecosystem transitions, raising transition matrices to successive powers to analyse short-run and long-run behaviour, finding the steady-state distribution of a transition system and interpreting it in context, and using matrix equations and technology to solve systems of practical problems efficiently. Modelling with Matrices is assessed in the school-assessed coursework and the external examination, and directly applies the matrix skills developed at Stage 1 to more complex and realistic mathematical models.

Statistical Models in SACE Stage 2 General Mathematics is one of the most substantial topics in the course and develops statistical reasoning and data analysis at Stage 2 level directly from the Stage 1 Statistical Investigation foundation — including the normal distribution as a continuous probability model, the empirical rule for data within one, two, and three standard deviations of the mean, standardising data using z-scores and using z-scores to compare data from different distributions, using technology to calculate normal distribution probabilities and find values corresponding to given probabilities, bivariate data analysis including scatter plots, calculating and interpreting the Pearson correlation coefficient, the least-squares regression line and its equation, making and evaluating predictions using regression equations, understanding the distinction between correlation and causation, and the concept of a sample proportion as a random variable, its approximate sampling distribution for large samples, and the construction and interpretation of confidence intervals for a population proportion. Statistical Models is consistently one of the most heavily assessed topics in the external examination and requires students to reason statistically with precision and interpret results clearly in practical contexts.

Financial Models in SACE Stage 2 General Mathematics is the most directly practical topic in the course and extends the Stage 1 Investing and Borrowing content to more sophisticated financial modelling at Stage 2 level — including compound interest and the future value formula A = P(1 + r)ⁿ applied to investments and loans, reducing balance loans including setting up recurrence relations to model the outstanding balance, calculating regular repayment amounts, determining the total interest paid over the life of a loan, and comparing the effect of changing repayment amounts or interest rates on the loan term and total cost, annuities including future value annuities and present value annuities modelled using recurrence relations and geometric series, using technology to construct and analyse financial models including spreadsheets, and applying financial mathematics to informed personal and household financial decision-making in contexts such as home loans, superannuation, and investment strategies. Financial Models is assessed in both school-assessed coursework and the external examination, and directly reflects the SACE Board subject outline emphasis on applying mathematics to practical financial situations that students will encounter in adult life.

Discrete Models in SACE Stage 2 General Mathematics covers the graph theory and network optimisation content that is a distinctive and applied feature of the General Mathematics course at Stage 2 — including the language and properties of graphs and networks including vertices, edges, degree, paths, cycles, and connected graphs, Eulerian trails and Hamiltonian paths and circuits and the conditions for their existence, minimum spanning trees found using Prim’s and Kruskal’s algorithms and their practical applications in network design, the shortest path problem and Dijkstra’s algorithm applied to routing and logistics problems, and critical path analysis including constructing activity network diagrams from activity tables, identifying all paths through a network, calculating the critical path and the minimum project completion time, determining earliest start times, latest start times, and float times for each activity, and interpreting results in practical project management contexts. Discrete Models is assessed in the school-assessed coursework and the external examination, and rewards students who can read and interpret network diagrams accurately, apply algorithms methodically, and communicate results clearly in the context of realistic planning and optimisation problems.