§-General Mathematics Q&A
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General Mathematics Q&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.
Formulate linear programming problems with constraints and an objective function, identify the feasible region, and find the optimal solution at a vertex.
Construct, graph and interpret piecewise-linear models in which the rule changes over different intervals of the domain.
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
Represent networks with adjacency matrices and use matrix powers to count walks of a given length between vertices.
Perform matrix addition, subtraction, scalar multiplication and matrix multiplication, applying the order and conformability rules correctly.
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
Display bivariate data in a scatterplot and describe the association using form, direction, strength and the correlation coefficient r.
Determine and interpret the least-squares regression line, use it to make predictions, and assess fit using residuals.
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
Apply the compound interest formula and model annuities with regular contributions to find future values of investments.
Model depreciation using flat-rate, reducing-balance and unit-cost methods, and find the value of an asset over time.
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
Solve assignment problems using the Hungarian algorithm to allocate agents to tasks for minimum total cost.
Use forward and backward scanning on an activity network to find the critical path, the minimum project time and the float of each activity.
Find shortest paths through weighted networks and determine the maximum flow using the minimum cut in a capacitated network.