QCE General MathematicsPractice Examination 1

This paper covers

• Time series analysis: 4-quarter centred moving averages, ratio-to-moving-average seasonal indices, deseasonalising (divide by SI), and reseasonalised next-year forecasting of Queensland seasonal rainfall across four weather stations
• Bivariate data: scatterplots, Pearson's r, coefficient of determination R², least-squares regression and prediction (rainfall vs reservoir inflow)
• Arithmetic and geometric sequences and recurrence relations modelling annual rainfall trend and drought storage decay
• Earth geometry and time zones: distance along a parallel of latitude, longitude-to-time conversion, and an International Date Line travel problem
• Financial mathematics: compound interest with non-annual compounding via recurrence, reducing-balance loans and amortisation, future-value annuities (sinking funds) and perpetuities
• Graphs and networks: terminology, adjacency matrices, Euler's formula, Eulerian/Hamiltonian graphs, Dijkstra's shortest path and the travelling salesman problem
• Decision mathematics: minimum spanning trees (Kruskal/Prim), maximum-flow minimum-cut, Hungarian assignment, and critical path analysis with forward/backward passes and float
• Assessment objectives 1-6 across simple familiar (60%), complex familiar (20%) and complex unfamiliar (20%) demand, with explicit contextual interpretation and justification for Band A

Students are permitted to bring into the examination the materials normally allowed for this subject. Answer all questions in the spaces provided.

This is an ATARMAxxing practice paper. It is not an official examination and is not affiliated with, endorsed by, or produced by the VCAA, NESA or the QCAA.