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SA · SACE BoardQ&A
General MathematicsQ&A by dot point
A short Q&A bank for every SA General Mathematics syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Topic 1: Modelling with Linear Relationships
- Construct and interpret linear functions of the form y = mx + c to model practical situations, identifying the meaning of the gradient and intercept.0Q&A pairs
- Formulate linear programming problems with constraints and an objective function, identify the feasible region, and find the optimal solution at a vertex.0Q&A pairs
- Construct, graph and interpret piecewise-linear models in which the rule changes over different intervals of the domain.0Q&A pairs
- Solve pairs of simultaneous linear equations algebraically and graphically, and interpret the solution as a break-even point in cost and revenue models.3Q&A pairs
Topic 2: Modelling with Matrices
- Represent networks with adjacency matrices and use matrix powers to count walks of a given length between vertices.0Q&A pairs
- Perform matrix addition, subtraction, scalar multiplication and matrix multiplication, applying the order and conformability rules correctly.0Q&A pairs
- Use transition matrices and an initial state vector to predict future states and to find the long-term steady state of a system.0Q&A pairs
Topic 3: Statistical Models
- Display bivariate data in a scatterplot and describe the association using form, direction, strength and the correlation coefficient r.0Q&A pairs
- Determine and interpret the least-squares regression line, use it to make predictions, and assess fit using residuals.0Q&A pairs
- Use the normal distribution, the 68-95-99.7 rule and z-scores to describe data and compare values from different distributions.0Q&A pairs
Topic 4: Financial Models
- Apply the compound interest formula and model annuities with regular contributions to find future values of investments.0Q&A pairs
- Model depreciation using flat-rate, reducing-balance and unit-cost methods, and find the value of an asset over time.0Q&A pairs
- Model a reducing-balance loan with a recurrence relation, track the balance after each repayment, and analyse the effect of changing the repayment.0Q&A pairs
Topic 5: Discrete Models
- Solve assignment problems using the Hungarian algorithm to allocate agents to tasks for minimum total cost.0Q&A pairs
- Use forward and backward scanning on an activity network to find the critical path, the minimum project time and the float of each activity.0Q&A pairs
- Find shortest paths through weighted networks and determine the maximum flow using the minimum cut in a capacitated network.0Q&A pairs