ATARMAxxing · General Mathematics
QCE General Mathematics Practice Exams with Worked Solutions
20 full-length papers · worked solutions for every question
The 20 practice exams inside the QCE General Mathematics Mastery Pack, each set out like the real paper with a separate worked-solution guide. Open any paper to see what it 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
- Bivariate data analysis: scatterplots, Pearson's r, coefficient of determination R-squared, least-squares regression, residuals, correlation vs causation (reef health score vs water temperature)
- Time series analysis: trend/seasonal/cyclical/irregular components, 4-point centred moving averages, ratio-to-moving-average seasonal indices, deseasonalising, regression-based forecasting (Great Barrier Reef visitor numbers)
- Growth and decay in sequences: arithmetic and geometric rules and recurrence relations, simultaneous equations for unknown terms, threshold/doubling problems
- Earth geometry and time zones: distance along a parallel of latitude (D = 111.2 cos(theta) x angular distance), longitude-to-time conversion, International Date Line and flight-time problems
- Investing: compound interest with non-annual compounding, reducing-balance loans via recurrence relations, future-value annuities using the QCAA formula sheet
- Graphs and networks: adjacency matrices, degree, Euler's formula, Dijkstra's shortest path
- Decision mathematics: minimum spanning trees (Kruskal's), critical path analysis (forward/backward pass, float, critical activities), maximum-flow minimum-cut
- Band A skills: contextual interpretation, justification of model suitability, evaluating reasonableness and model limitations across complex familiar and complex unfamiliar items
- Bivariate data: Pearson r, R-squared, least-squares regression, residuals (cane yield vs rainfall)
- Time series: trend/seasonal/cyclical/irregular, centred moving averages, seasonal indices, deseasonalising, forecasting (quarterly cane crush)
- Arithmetic and geometric sequences and recurrence relations (annual sugar cane harvest growth; machinery depreciation)
- Earth geometry: latitude/longitude, great-circle distance, nautical miles, time zones and the International Date Line
- Compound interest with varied compounding periods via recurrence relations (agribusiness loan)
- Reducing-balance loans and amortisation; annuities and perpetuities using the QCAA formula sheet
- Graphs and networks: terminology, adjacency matrices, Euler's formula, Eulerian/Hamiltonian graphs, Dijkstra's shortest path, travelling salesman problem
- Decision mathematics: minimum spanning trees (Kruskal/Prim) for irrigation pipelines, maximum-flow minimum-cut, Hungarian assignment, critical path analysis with forward/backward passes and float
- Unit 4 Networks: weighted directed graphs, adjacency matrices, Dijkstra's shortest path, Euler/Hamilton, TSP
- Unit 4 Decision maths: minimum spanning trees (Kruskal/Prim), max-flow min-cut, Hungarian assignment, critical path analysis (forward/backward pass, float)
- Unit 4 Finance: compound interest with varied compounding, reducing-balance loans and amortisation, annuities (FV) and perpetuities
- Unit 3 Bivariate data: scatterplots, Pearson's r, R squared, least-squares regression and prediction
- Unit 3 Time series: centred moving averages, seasonal indices, deseasonalising, trend lines and forecasting
- Unit 3 Sequences: arithmetic and geometric sequences, recurrence relations, growth/decay modelling
- Unit 3 Earth geometry: latitude/longitude distances (great-circle and parallels), time zones and the International Date Line
- Integrated complex-unfamiliar problem solving combining Dijkstra routing with critical-path depot scheduling, with contextual justification and evaluation of reasonableness
- Project network critical path analysis: precedence table to activity network, dummy activities, forward/backward pass, EST/EFT/LST/LFT, float, critical activities, crashing
- Graph and network theory: adjacency matrices, Euler's formula, Eulerian/Hamiltonian graphs, Dijkstra shortest path, travelling salesman
- Decision mathematics: minimum spanning trees (Kruskal/Prim), maximum-flow minimum-cut, bipartite assignment
- Financial mathematics: compound interest via recurrence, reducing-balance loans and amortisation, annuities, perpetuities, sinking funds
- Sequences: arithmetic and geometric recurrence relations modelling crew growth and equipment depreciation
- Bivariate data: scatterplots, Pearson's r, R-squared, least-squares regression and prediction
- Time series: trend vs seasonal vs cyclical components, moving averages, seasonal indices, deseasonalising, forecasting
- Earth geometry: latitude/longitude, great-circle distance, time zones and the International Date Line
- Bivariate data: least-squares regression, Pearson r and r-squared interpretation in context
- Time series: 4-quarter centred moving averages, seasonal indices, deseasonalising actual data
- Arithmetic and geometric sequences: equipment depreciation and ore-stockpile decay modelling
- Earth geometry and time zones: great-circle distance along a meridian and AEST/AWST shift scheduling across the Mount Isa-Townsville-Perth supply chain
- Financial mathematics: compound interest with varied compounding periods, reducing-balance loan amortisation tables, annuities and sinking funds
- Networks and graphs: adjacency matrices, Euler's formula, Dijkstra's shortest path
- Decision mathematics: maximum-flow minimum-cut, minimum spanning trees, critical path analysis (forward/backward passes, float), and Hungarian-algorithm assignment
- Complex unfamiliar multi-step problems: two-phase investments, loan refinancing with rate change, and reasonableness/limitation evaluation in a mining-logistics context
- Unit 4 Topic 1 financial mathematics as the spine — compound interest with monthly compounding (A=P(1+r/n)^nt and recurrence An+1
- Full seven-topic EA coverage: bivariate data (Pearson's r, R2, least-squares line), time series (seasonal indices, deseasonalisation, centred moving averages, reseasonalised forecasts), arithmetic and geometric sequences and recurrence relations, earth geometry (parallel and meridian distances) and time zones
- Networking and decision mathematics: graph terminology and degree/edge counting, Euler's formula, Dijkstra shortest path, minimum spanning tree (Kruskal/Prim), and critical path analysis with full forward/backward pass, float times and critical-activity identification
- QCAA EA architecture and cognitions: Paper 1 Section A (15 MC) + Section B (42-mark short response) and Paper 2 Section C (38-mark short response), assessing all six objectives across a 60% simple-familiar / 20% complex-familiar / 20% complex-unfamiliar spread with explicit contextual interpretation and justification for Band A
- Unit 4 Topic 1 financial mathematics as the spine — compound interest with monthly compounding (A=P(1+r/n)^nt and recurrence An+1
- Earth geometry: latitude/longitude positions, great-circle and same-meridian/same-parallel distances using the QCAA formula (R = 6400 km)
- Longitude-based time differences (15 degrees = 1 hour) and International Date Line day changes across the Pacific
- Bivariate data: scatterplots, Pearson's r, the coefficient of determination R squared, and least-squares regression with contextual interpretation
- Time series: seasonal indices, deseasonalising (dividing by the index), centred moving averages, trend lines and forecasting
- Arithmetic and geometric sequences and recurrence relations for growth/decay
- Financial mathematics: compound interest with non-annual compounding, reducing-balance loans and amortisation, annuities and perpetuities (QCAA formula sheet)
- Graphs and networks: 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, the Hungarian assignment method, and critical path analysis (forward/backward pass, float, critical activities)
- Geometric sequences and recurrence relations (herd growth with culling)
- Arithmetic sequences and series
- Time series: seasonal indices, deseasonalising, moving-average smoothing, trend forecasting
- Bivariate data: Pearson's r, R-squared, least-squares regression
- Earth geometry: great-circle distance, time zones, International Date Line
- Compound interest, reducing-balance loans and amortisation, annuities and perpetuities
- Graphs and networks: adjacency matrices, Euler's formula, Dijkstra's shortest path
- Decision mathematics: minimum spanning trees, maximum flow, Hungarian assignment, critical path analysis
- Bivariate data analysis (Pearson's r, R squared, least-squares regression, prediction, correlation vs causation)
- Time series analysis (4-point centred moving averages, seasonal indices, deseasonalising, forecasting, seasonal vs cyclical vs structural change)
- Arithmetic and geometric sequences and recurrence relations (growth/decay modelling, simultaneous equations)
- Earth geometry and time zones (latitude-distance formula D = 111.2 cos(theta) x angular distance, longitude-to-time conversion, AEST/AWST, International Date Line)
- Loans, investments and annuities (compound interest with varied compounding, reducing-balance recurrence, annuity FV/PV from QCAA formula sheet, repayments, perpetuities)
- Graphs and networks (degree/handshake, adjacency matrices, Euler's formula, Eulerian and Hamiltonian graphs, Dijkstra's shortest path)
- Decision mathematics (Kruskal's/Prim's minimum spanning tree, maximum-flow minimum-cut, Hungarian algorithm bipartite assignment, critical path analysis with forward/backward pass and float)
- Stimulus context: Queensland State of Origin stadium ticketing, vendor-to-zone assignment via the Hungarian algorithm, and an Eulerian security-patrol circuit
- Bivariate data: scatterplots, Pearson's r, R-squared, least-squares regression and prediction (solar install cost vs panel count)
- Time series: trend/seasonal/cyclical/irregular components, 4-quarter centred moving averages, seasonal indices, deseasonalising and forecasting
- Arithmetic and geometric sequences and recurrence relations modelling panel installation rates and output degradation
- Earth geometry: latitude/longitude, great-circle distance, time zones and the International Date Line
- Financial mathematics: compound interest with varied compounding, reducing-balance loans and amortisation, annuities and perpetuities (20-year solar funding) via the QCAA formula sheet
- Graphs and networks: terminology, adjacency matrices, Euler's formula, Eulerian/Hamiltonian graphs, Dijkstra's shortest path, travelling salesman
- Decision mathematics: minimum spanning trees (Kruskal/Prim), maximum-flow minimum-cut, Hungarian assignment, and critical path analysis (forward/backward passes, float, critical activities) for the Rockhampton solar panel installation
- Networks and decision mathematics (graph terminology, adjacency matrices, Euler's formula, Eulerian and Hamiltonian paths/circuits, Dijkstra's shortest path, travelling salesman, minimum spanning trees via Kruskal's and Prim's, maximum-flow minimum-cut, critical path analysis) applied to a South-East Queensland multimodal public transport network
- Bivariate data and least-squares regression, Pearson's r and R-squared
- Time series analysis: trend, seasonal indices, centred moving averages, deseasonalising and forecasting
- Arithmetic and geometric sequences modelling patronage growth and fleet depreciation
- Earth geometry: latitude/longitude distances and time-zone calculations
- Financial mathematics: compound interest by recurrence, reducing-balance loans and amortisation, annuities and perpetuities using the QCAA formula sheet
- Bivariate data: Pearson's r, R-squared and least-squares regression with contextual interpretation (Q16, Q27)
- Time series: 3-point moving averages, seasonal indices, deseasonalising by division, and forecasting (Q17, Q18, Q26, Q27)
- Arithmetic and geometric sequences via recurrence relations for passenger/route growth (Q6, Q7, Q19)
- Earth geometry: latitude/longitude distances along a meridian and Australian time-zone problems (Q11, Q12, Q20)
- Financial mathematics: compound interest with varied compounding periods, reducing-balance loans/amortisation, and annuities (Q5, Q21, Q23, Q24, Q28)
- Graphs and networks: adjacency matrices, Euler's formula, Eulerian/Hamiltonian conditions, Dijkstra's shortest path (Q1, Q2, Q3, Q22)
- Travelling salesman problem and the nearest-neighbour heuristic on the Brisbane hub-and-spoke flight network (Q4, Q25, Q32)
- Decision mathematics: minimum spanning trees (Kruskal and Prim), maximum-flow minimum-cut, and critical path analysis with forward/backward passes (Q13, Q14, Q15, Q29, Q30, Q31)
- Earth geometry: latitude/longitude positions, great-circle meridian arc distance (d = angle/360 x 2 pi R, R = 6400 km), three-figure bearings and reverse bearings
- Time zones and the International Date Line: AEST (UTC+10) to Vanuatu (UTC+11) conversions, longitude-to-time, eastbound IDL day adjustment
- Bivariate data: scatterplots, Pearson r, coefficient of determination R-squared, least-squares regression line, interpolation/extrapolation and contextual interpretation
- Time series: trend/seasonal/cyclical/irregular components, 4-quarter centred moving averages, seasonal indices, deseasonalising (divide by index), trend forecasting and reseasonalising
- Arithmetic and geometric sequences and recurrence relations modelling charter fees, fuel use and equipment decay
- Financial mathematics: compound interest with varied compounding periods, reducing-balance loans and amortisation, future-value annuities, perpetuities
- Networks: terminology, adjacency matrices, vertex degree, Euler's formula, Eulerian/semi-Eulerian conditions, Dijkstra's shortest path
- Decision mathematics: Kruskal/Prim minimum spanning trees, maximum-flow minimum-cut, Hungarian bipartite assignment, and critical path analysis (forward/backward pass, float, critical activities)
- Bivariate data: two-way frequency tables, association between categorical variables, Pearson's r, least-squares regression and R-squared evaluation (UQ research-funding context)
- Time series: centred moving averages, seasonal indices, deseasonalisation and forecasting of quarterly grant income
- Sequences: arithmetic and geometric models with recurrence relations for research output growth and funding
- Earth geometry: latitude/longitude great-circle distance, time zones and the International Date Line
- Financial mathematics: compound interest with varied compounding, reducing-balance loans and amortisation, annuities and perpetuities
- Networks and decision mathematics: adjacency matrices, Euler's formula, Dijkstra's shortest path, minimum spanning trees, maximum flow-minimum cut, Hungarian assignment, and critical path analysis
- Cognition spread: ~60% simple familiar, ~20% complex familiar, ~20% complex unfamiliar across QCAA objectives 1-6 with contextual justification
- Time series analysis: trend, seasonal indices, deseasonalisation and deseasonalised-trend forecasting (Queensland Health flu vaccination context)
- Bivariate data: Pearson's r, coefficient of determination R2, least-squares regression, residuals and two-way tables
- Arithmetic and geometric sequences and recurrence relations (dose delivery and cold-chain decay)
- Earth geometry and time zones: distance along a parallel of latitude, longitude-to-time conversion
- Financial mathematics: compound interest recurrence, reducing-balance loans, annuities (future value) and perpetuities
- Graphs and networks: adjacency matrices, Euler's formula, Dijkstra shortest path, walks
- Decision mathematics: minimum spanning trees (Kruskal/Prim), maximum-flow minimum-cut, and critical path analysis with forward/backward pass and float
- Sequences & recurrence relations (arithmetic/geometric, loan-balance modelling)
- Financial mathematics: perpetuities, annuities, reducing-balance loans, amortisation, compound interest with varied compounding
- Bivariate data & least-squares regression (Pearson's r, prediction)
- Time series: seasonal indices, deseasonalising, trend forecasting
- Earth geometry (latitude/longitude great-circle distance)
- Networks: adjacency, Euler's formula, Dijkstra shortest path, MST (Kruskal/Prim), max-flow/min-cut, TSP
- Critical path analysis: forward/backward pass, EST/EFT/LST/LFT, float, critical activities
- Toowoomba grain-storage investment context across all seven Units 3&4 topic areas
- Bivariate data: scatterplots, Pearson's r, R-squared, least-squares regression, residuals (Mackay cable cost vs length)
- Time series: seasonal indices, deseasonalising, centred moving averages, trend and forecasting (desalination water demand)
- Arithmetic and geometric sequences and recurrence relations (cable-laying schedule, maintenance cost escalation)
- Earth geometry: latitude/longitude, great-circle distance, time zones (marina sensor network)
- Compound interest with non-annual compounding via recurrence (infrastructure bond)
- Reducing-balance loans, amortisation, annuities and perpetuities (marina financing)
- Graph and network theory: adjacency matrices, Euler's formula, Eulerian/Hamiltonian graphs, Dijkstra's algorithm, TSP
- Minimum spanning trees (Kruskal's and Prim's) for underwater cable installation
- Network flow: maximum-flow minimum-cut theorem (desalination plant pipe network)
- Critical path analysis: forward/backward passes, EST/EFT/LST/LFT, float, critical activities
- Bivariate data analysis: scatterplots, Pearson's r, coefficient of determination R-squared, least-squares regression, interpolation vs extrapolation, residuals (athlete age vs finish time)
- Time series analysis: trend/seasonal/cyclical/irregular components, 4-point centred moving averages, seasonal indices, deseasonalising, forecasting (annual triathlon entries)
- Arithmetic and geometric sequences: nth-term and recurrence relations, series sums (entry growth, prize pools)
- Earth geometry: latitude/longitude, great-circle/arc distance, time zones and the International Date Line
- Financial mathematics: compound interest with varied compounding, effective rates, reducing-balance loans and amortisation, annuities (future value) and perpetuities
- Graphs and networks: terminology, adjacency matrices and walks, Euler's formula, Dijkstra's shortest path, minimum spanning trees (Kruskal/Prim), bipartite assignment
- Project network critical path analysis: forward/backward passes (EST, EFT, LST, LFT), float, critical activities, and crashing (event set-up)
- Financial mathematics: simple and compound interest, reducing-balance loans, annuities/savings plans, effective interest rates, depreciation, GST, CPI/inflation
- Applied trigonometry: Pythagoras, right-angled trig, sine rule, cosine rule, area of triangles, bearings, angles of elevation/depression
- Graphs and networks: minimum spanning trees, shortest path, vertex degree/handshake lemma, connected weighted graphs
- Matrices: order/dimensions, matrix multiplication, real-world cost/flow modelling
- Univariate statistics: five-number summary, IQR, outlier fences, mean, z-scores, frequency tables
- Bivariate data: least-squares regression line, correlation coefficient r, interpolation/extrapolation prediction
- Rates, ratios, percentages, scale, unit conversion and modular/sequence reasoning in real-world bus-network and savings/loan contexts
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