§-General Mathematics syllabus
SA · SACE Board← General Mathematics
General Mathematics syllabus, dot point by dot point
Every dot point in the SA General Mathematics syllabus, with a focused answer for each. Click any dot point for a worked explainer, past exam questions and links to related points.
Topic 1: Modelling with Linear Relationships
Module overview →How do we use a straight-line equation to model and predict from a real situation?
Construct and interpret linear functions of the form y = mx + c to model practical situations, identifying the meaning of the gradient and intercept.
How do we find the best decision when several linear constraints limit our choices?
Formulate linear programming problems with constraints and an objective function, identify the feasible region, and find the optimal solution at a vertex.
How do we model a situation whose rate of change shifts at certain points?
Construct, graph and interpret piecewise-linear models in which the rule changes over different intervals of the domain.
How do we find the point where two linear models meet, and what does break-even mean?
Solve pairs of simultaneous linear equations algebraically and graphically, and interpret the solution as a break-even point in cost and revenue models.
Topic 2: Modelling with Matrices
Module overview →How can matrices store the connections in a network and count routes between vertices?
Represent networks with adjacency matrices and use matrix powers to count walks of a given length between vertices.
How do we add, scale and multiply matrices, and when is each operation defined?
Perform matrix addition, subtraction, scalar multiplication and matrix multiplication, applying the order and conformability rules correctly.
How do we predict the future state of a system that moves between categories at fixed rates?
Use transition matrices and an initial state vector to predict future states and to find the long-term steady state of a system.
Topic 3: Statistical Models
Module overview →How do we measure the strength and direction of a relationship between two variables?
Display bivariate data in a scatterplot and describe the association using form, direction, strength and the correlation coefficient r.
How do we fit the best straight line to data and use it to predict?
Determine and interpret the least-squares regression line, use it to make predictions, and assess fit using residuals.
How do we describe and compare values within a bell-shaped distribution?
Use the normal distribution, the 68-95-99.7 rule and z-scores to describe data and compare values from different distributions.
Topic 4: Financial Models
Module overview →How does money grow when interest compounds, and how do regular savings build an investment?
Apply the compound interest formula and model annuities with regular contributions to find future values of investments.
How do we model the loss in value of an asset over time?
Model depreciation using flat-rate, reducing-balance and unit-cost methods, and find the value of an asset over time.
How does a loan balance fall as we make regular repayments against compounding interest?
Model a reducing-balance loan with a recurrence relation, track the balance after each repayment, and analyse the effect of changing the repayment.
Topic 5: Discrete Models
Module overview →How do we assign workers to tasks for the lowest total cost or time?
Solve assignment problems using the Hungarian algorithm to allocate agents to tasks for minimum total cost.
How do we find the shortest time to complete a project of dependent tasks?
Use forward and backward scanning on an activity network to find the critical path, the minimum project time and the float of each activity.
How do we find the cheapest route through a network and the greatest flow it can carry?
Find shortest paths through weighted networks and determine the maximum flow using the minimum cut in a capacitated network.