§-Mathematics Applications Q&A
WA · SCSA← Mathematics Applications
Mathematics Applications Q&A by dot point
A short Q&A bank for every WA Mathematics Applications 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.
Unit 3
Recognise arithmetic sequences, use the recursive and explicit rules, and apply them to simple interest and linear depreciation.
Distinguish association from causation, identify confounding and coincidence, and place bivariate analysis within the statistical investigation process.
Model compound interest with a recurrence relation, convert nominal annual rates to the period rate, and find balances and effective rates.
Model and solve problems involving compound interest, depreciation, annuities, loans and investments using recursion and the financial solver.
Calculate and interpret Pearson's correlation coefficient r and the coefficient of determination r squared, and state their limitations.
Apply squared, logarithmic and reciprocal transformations to linearise data, fit a least-squares line to the transformed data and use it to predict.
Recognise geometric sequences, use the recursive and explicit rules with the common ratio, and apply them to growth and decay.
Use vertex, edge, degree, loop and multiple-edge terminology, apply the handshake rule, and represent a graph with an adjacency matrix.
Fit a least-squares line using technology, interpret the slope and intercept in context, and predict while distinguishing interpolation from extrapolation.
Formulate linear programming problems, graph feasible regions, and locate the optimal solution at a vertex of the feasible region.
Perform matrix operations, find determinants and inverses of 2x2 matrices, solve matrix equations, and apply transition matrices to model systems.
Represent situations with graphs and networks, use terminology and matrices, and solve shortest path, minimum spanning tree and connection problems.
Identify planar graphs, count vertices, edges and faces, and verify and apply Euler's formula v minus e plus f equals 2.
Use first-order linear recurrence relations to generate sequences and recognise the patterns of growth and decay they produce.
Model reducing-balance depreciation with a recurrence relation, compare it with flat-rate depreciation, and find book value and scrap-value timing.
Calculate residuals, construct and interpret a residual plot, and use it to judge whether a linear model is appropriate.
Identify response and explanatory variables, construct a scatterplot, and describe the association in terms of direction, form, strength and outliers.
Distinguish walks, trails, paths, cycles and circuits, and determine when Eulerian and Hamiltonian routes exist.
Unit 4
Model annuities and annuity-investments with recurrence relations and find balances, payments and the time to exhaust or reach a target.
Model an assignment problem as a bipartite graph and solve it with the Hungarian algorithm to minimise total cost.
Construct and interpret scatterplots, calculate the correlation coefficient and least-squares regression line, and use the line to make predictions.
Construct an activity network, compute earliest and latest starting times and float, and identify the critical path and minimum completion time.
Recognise geometric growth and decay, use recurrence relations and the explicit rule for geometric sequences, and model compound and reducing situations.
Model flow in a directed network, find the maximum flow, and use the maximum-flow minimum-cut relationship.
Solve connector problems by finding a minimum spanning tree using Prim's algorithm and interpret its total weight.
Model a perpetuity, find the payment that keeps the balance constant, and relate it to the interest earned each period.
Use the normal distribution and the 68-95-99.7 rule, standardise to z-scores, and construct and interpret sample proportions and confidence intervals.
Model a reducing-balance loan with a recurrence relation, build an amortisation table, and find balances, repayments and total interest.
Calculate seasonal indices, deseasonalise and reseasonalise a time series, and interpret seasonal indices in context.
Find the shortest path between two vertices in a weighted network and interpret it in context.
Smooth a time series using moving averages, including centred even-order averages, and using median smoothing.
Plot and describe time series, smooth with moving averages, deseasonalise with seasonal indices, fit a trend line and forecast future values.
Construct a time series plot and identify trend, seasonal, cyclic and irregular components.
Fit a least-squares trend line to a time series, forecast future values, and reseasonalise forecasts for seasonal data.