ATARMAxxing · General Mathematics
VCE General Mathematics Practice Exams with Worked Solutions
20 full-length papers · worked solutions for every question
The 20 practice exams inside the VCE 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.
- Data analysis: normal distribution and z-scores, boxplot outliers, least squares regression with CAS (slope/intercept interpretation, r, r2, prediction, residual), and seasonal time series forecasting
- Recursion and financial modelling: flat-rate, unit-cost and reducing-balance depreciation, reducing-balance loan via Finance Solver (repayment, recurrence, total interest), annuity drawdown and perpetuity
- Matrices: matrix product and element interpretation, determinant and inverse for simultaneous equations, transition matrices including S(n+1) = T.S(n) + B and steady state, dominance ranking with D + D2
- Networks and decision mathematics: Eulerian trails, minimum spanning tree, shortest path, maximum flow / minimum cut, and project scheduling with float and crashing
- Original Exam-2 written paper for VCE General Maths U3&4, retail/small-business flavour, exactly 4 questions x 15 marks = 60.
- Every numerical answer independently verified in Python (z-scores, finance, matrices, project network, MST, shortest path).
- Full worked sample solutions for every labelled part, with mark-by-mark criteria summing to 15 per question.
- CAS-assumed, Australian conventions, internally consistent retail data; no VCAA/textbook content copied.
- Q1 Data analysis: 68-95-99.7 rule with z-scores, boxplot/outlier (IQR fence), least-squares interpretation/prediction/residual, and a 4-quarter time series (seasonal index, deseasonalise, trend-line forecast, reseasonalise) - all using clean verified numbers.
- Q2 Recursion & finance: arithmetic recurrence (Myki balance), reducing-balance depreciation as a geometric sequence, compound interest, a reducing-balance loan via Finance Solver (payment, balance, total interest) and a perpetuity scholarship fund.
- Q3 Matrices: revenue by matrix product, 2x2 determinant/inverse to solve simultaneous equations, regular transition matrix with steady state, and the S(n+1)=T*S(n)+B recurrence with an added constant matrix.
- Q4 Networks & decision maths: graph terminology and Euler path condition, minimum spanning tree (Prim/Kruskal) total weight, and full project scheduling - forward/backward pass, float, critical path A-C-F-G (17 weeks) and crashing.
- Q1 Data analysis: z-scores, 68-95-99.7 rule, least-squares regression with slope/intercept interpretation, residuals, and quarterly seasonal indices (deseasonalising)
- Q2 Recursion & finance: flat-rate vs reducing-balance depreciation recurrence relations, reducing-balance loan via Finance Solver, perpetuity and annuity
- Q3 Matrices: 2x2 determinant/inverse to solve simultaneous equations, transition matrix with state iteration and steady state
- Q4 Networks: minimum spanning tree (Kruskal), project scheduling with EST/LST/float, critical path, and crashing cost analysis
- Data analysis: summary statistics, outliers, z-scores and the 68-95-99.7 rule, least-squares regression with coefficient of determination, and deseasonalising time series
- Recursion and financial modelling: recurrence relations, compound interest, flat-rate depreciation, reducing-balance loans and perpetuities
- Matrices: operations, 2x2 determinant and inverse, solving simultaneous equations, and transition matrices with steady-state behaviour
- Networks and decision maths: graph terminology, minimum spanning tree, shortest path, and project scheduling with critical path and float
- Data analysis: five-number summary and boxplot outlier test, 68-95-99.7 rule and z-scores, least-squares regression from summary statistics, slope interpretation, residuals, coefficient of determination, and seasonal indices with trend forecasting - set in a community nutrition study
- Recursion and financial modelling: compound-interest recurrence and explicit rule, flat-rate vs reducing-balance vs unit-cost depreciation, reducing-balance loan amortisation with Finance Solver, and a retirement annuity including perpetuity - set around a health-food cafe
- Matrices: order and product of matrices for revenue, determinant and inverse of a 2x2 to solve simultaneous equations, a three-state transition matrix with steady state and the S(n+1) = T.S(n) + B growth model, and dominance ranking - set in a wellness centre
- Networks and decision mathematics: Euler trail/circuit conditions, minimum spanning tree, shortest path, maximum flow and minimum cut, and project scheduling with earliest start times, float and crashing - set in a community health precinct
- Q1 Data analysis: normal distribution and the 68-95-99.7% rule, z-scores, five-number summary and outlier testing, least-squares regression (slope interpretation, prediction, residuals, coefficient of determination), seasonal indices and deseasonalisation
- Q2 Recursion and financial modelling: unit-cost and reducing-balance depreciation, recurrence relations, compound interest investments, effective annual interest rate, reducing-balance loan amortisation with Finance Solver, perpetuities
- Q3 Matrices: matrix products and order, determinant and inverse of a 2x2 matrix for simultaneous equations, transition matrices and state matrices, steady state, the rule S(n+1) = T.S(n) + B, communication matrices and two-step connections
- Q4 Networks and decision mathematics: vertex degrees with Euler circuits and trails, minimum spanning tree, shortest path, maximum flow and minimum cut, project scheduling with EST/LST, critical path, float and crashing
- Q1 Data analysis — five-number summary and outlier fences for suburb house prices, normally distributed apartment prices (68-95-99.7 rule, z-scores), least-squares regression of price vs distance from CBD (slope interpretation, prediction, residual, coefficient of determination), and a quarterly house-sales time series (seasonal indices, deseasonalising, trend-line forecasting).
- Q2 Recursion and financial modelling — flat-rate depreciation of rental-property appliances, compound-interest deposit savings, a $480,000 reducing-balance home loan (recurrence relation, step-by-step amortisation, interest vs principal split, Finance Solver repayment count and adjusted final repayment), and a perpetuity funded by a property sale.
- Q3 Matrices — order and matrix product for office sales x commissions, determinant/inverse of a 2x2 to solve marketing-cost simultaneous equations, a three-region rental transition matrix (interpretation, state matrices, steady state, and the S(n+1) = T.S(n) + B extension), and a dominance-matrix ranking using D + D2.
- Q4 Networks and decision mathematics — display-village graph (vertex degree, Euler trail conditions), minimum spanning tree for NBN cabling, shortest path between display homes, and a ten-activity house-construction project: minimum completion time, critical path, float, latest start time and minimum-cost crashing.
- Data analysis: five-number summary and 1.5 x IQR outlier fences, normal distribution (z-scores, 68-95-99.7% rule), least squares regression (slope/intercept interpretation, prediction, residuals, coefficient of determination), seasonal indices, deseasonalising and trend forecasting
- Recursion and financial modelling: flat-rate and unit-cost depreciation recurrences, compound interest and effective annual rate, reducing-balance loan amortisation (balance, interest split, term via Finance Solver), perpetuities and annuity lifetimes
- Matrices: matrix product modelling and order, determinant and inverse of a 2x2 for simultaneous equations, transition matrices S(n+1) = T.S(n), steady state, and the rule S(n+1) = T.S(n) + B
- Networks and decision mathematics: degree sum and Eulerian trails, minimum spanning tree (Prim/Kruskal), shortest path, max-flow min-cut, and project scheduling (EST/LST, float, critical path, crashing)
- Data analysis: rainfall five-number summary and the 1.5xIQR outlier rule, normally distributed January temperatures (68-95-99.7 rule and z-scores), least-squares regression of reservoir evaporation on maximum temperature (slope, r2, prediction, residual), and seasonal indices with deseasonalisation of quarterly rainfall
- Recursion and financial modelling: flat-rate vs unit-cost depreciation of a survey drone, a monthly-compounding investment recurrence, a reducing-balance loan for a Doppler radar (Finance Solver repayment, amortisation split, mid-loan balance, total interest), and a perpetuity research fund
- Matrices: order and element interpretation, a cost matrix product, determinant and inverse of a 2x2 to solve simultaneous equations, a fine/wet weather transition matrix (two-step probability and steady state), and the rule S(n+1) = T.S(n) + B for volunteer numbers
- Networks and decision mathematics: vertex degrees and Euler trail conditions on a station network, minimum spanning tree for cabling, shortest path, max-flow min-cut on a stormwater system, and project scheduling for a flood-siren installation (critical path, float, crashing)
- Q1 Data analysis: normal-distribution z-scores and the 68-95-99.7 rule on practice-exam scores (mean 62, SD 9), IQR outlier test on a five-number summary, least-squares line built from summary statistics (slope 1.89, intercept 39.32), r2 interpretation, prediction and residual, then a termly library-visits time series (missing seasonal index, deseasonalising, trend-line forecast with re-seasonalising).
- Q2 Recursion & financial modelling: flat-rate depreciation recurrence vs unit-cost vs reducing-balance on an $8000 photocopier, compound-interest recurrence and effective annual rate for a building fund, a $400,000 reducing-balance gym loan (first-row amortisation, balance after 60 repayments, 114 repayments with adjusted final repayment $3475.90) and a $150,000 scholarship perpetuity vs annuity drawdown.
- Q3 Matrices: canteen revenue by matrix product with order/definedness, 2x2 determinant and inverse to find production ticket prices, a 3-state weekly lunch-choice transition matrix on 850 students with integer steady state [310, 260, 280] and the S(n+1) = T.S(n) + B rule, plus a four-house debating dominance matrix ranked by one-step + two-step scores.
- Q4 Networks & decision maths: campus path graph (9 edges) - Euler trail condition with start/end vertices, unique minimum spanning tree of 220 m, shortest path 120 m; Open Day one-way corridor network with cut capacity and max flow = min cut = 480 people/min; school-musical project network - forward/backward pass, critical path A-C-E-G-H (16 weeks), float, and crashing E for the cheapest minimum completion time of 12 weeks ($1600).
- Data analysis: normal distribution (68-95-99.7 rule), 1.5 x IQR outlier testing, least squares regression and interpretation, seasonal time series and trend forecasting
- Recursion and financial modelling: flat-rate, unit-cost and reducing-balance depreciation, reducing-balance loan amortisation with Finance Solver, perpetuities and annuities
- Matrices: matrix product and element interpretation, inverse-matrix solution of simultaneous equations, transition matrices with steady state and S(n+1) = T.S(n) + B, dominance ranking
- Networks and decision mathematics: Euler trails, minimum spanning tree, shortest path, maximum flow and minimum cut, critical path analysis with float and crashing
- Data analysis: normal distribution (68-95-99.7), z-scores, boxplot outlier test, least squares regression with r2 and residuals, seasonal indices, deseasonalising and trend forecasting - applied to parcel delivery data
- Recursion and financial modelling: flat-rate and unit-cost depreciation, compound interest with effective annual rate, reducing-balance loan amortisation via Finance Solver, annuity withdrawals and perpetuities - delivery fleet and warehouse finance
- Matrices: order and elements, cost matrix products, 2x2 determinant/inverse solution of simultaneous equations, transition matrices with steady state and S(n+1) = T.S(n) + B, one-step and two-step dominance - dispatch operations
- Networks and decision mathematics: Eulerian trails and Hamiltonian cycles, minimum spanning tree, shortest path, max-flow min-cut, project scheduling with earliest start times, float and crashing - warehouse logistics
- Data analysis: five-number summaries and outlier fences, the 68-95-99.7% rule and z-scores, least squares regression from summary statistics with residuals, and seasonal indices with trend-line forecasting.
- Recursion and financial modelling: flat-rate vs reducing-balance depreciation, reducing-balance loan recurrences and amortisation components, Finance Solver balances and total interest, and perpetuities vs annuities.
- Matrices: matrix products for revenue, determinants and inverses for solving simultaneous equations, transition matrices with state predictions and steady state, and Leslie matrix population modelling.
- Networks and decision mathematics: vertex degrees and Euler trails, minimum spanning trees, shortest paths, maximum flow-minimum cut, and project scheduling with critical paths, float and crashing.
- Q1 Data analysis: normal distribution and z-scores, outlier fences, least-squares regression (slope, prediction, residual, r2), seasonal indices, deseasonalising and trend forecasting
- Q2 Recursion and financial modelling: flat-rate, reducing-balance and unit-cost depreciation, reducing-balance loan recurrence and amortisation, annuity exhaustion with Finance Solver, perpetuities
- Q3 Matrices: matrix equations, determinant and inverse of a 2x2, matrix products and order, transition matrices with steady state and S(n+1) = T.S(n) + B, dominance ranking with M + M2
- Q4 Networks and decision maths: Hamiltonian cycles, Euler trail conditions, minimum spanning tree, shortest path, max-flow min-cut, critical path analysis with float and crashing
- Data analysis: normal distribution and z-scores (68-95-99.7), boxplot outlier test, least-squares regression with CAS (slope/intercept interpretation, prediction, residual, r and coefficient of determination), seasonal indices, deseasonalising and trend forecasting
- Recursion and financial modelling: flat-rate, unit-cost and reducing-balance depreciation as recurrence relations, reducing-balance loan amortisation (interest/principal split), Finance Solver for repayments and total interest, annuity duration and perpetuity condition
- Matrices: order and matrix product with interpretation, determinant and inverse of a 2x2 to solve simultaneous equations, transition matrices (interpretation, state matrices, steady state, two-step transitions), the rule S(n+1) = T.S(n) + B, dominance matrices and ranking
- Networks and decision mathematics: vertex degree and Euler trail/Hamiltonian cycle conditions, minimum spanning tree, shortest path, maximum flow with cut capacities and min-cut justification, project scheduling (EST/LST, critical path, float, crashing)
- Data analysis: normal distribution and z-scores, 1.5xIQR outlier testing, least-squares regression with slope/r2 interpretation and residuals, seasonal indices and trend-line forecasting
- Recursion and financial modelling: flat-rate vs unit-cost depreciation recurrences, compound interest, reducing-balance loan amortisation on the Finance Solver, perpetuities and annuities
- Matrices: order and matrix products in context, determinant/inverse solution of simultaneous equations, transition matrices with steady state and the rule S(n+1) = T.S(n) + B, Leslie matrix population projection
- Networks and decision mathematics: vertex degree and Euler trails, minimum spanning tree, shortest path, max-flow/min-cut, and project scheduling with float and crashing
- Original Exam-2 written paper (Exam 18 of 20) for VCE General Maths U3&4, hospitality flavour: exactly 4 questions x 15 marks = 60, CAS assumed, extended-response with labelled parts.
- Q1 waterfront-bistro data analysis (normal model, 1.5xIQR outlier, least-squares regression with residuals, seasonal indices); Q2 espresso-cafe finance (flat-rate and unit-cost depreciation, savings annuity, reducing-balance loan with final-payment adjustment, perpetuity).
- Q3 hotel matrices (order/product revenue, determinant-inverse solve of simultaneous equations, transition matrix with steady state and S(n+1)=T.S(n)+B); Q4 resort networks (Euler trail, minimum spanning tree, shortest path, max-flow min-cut, project scheduling with float and crashing).
- Every numerical answer independently verified in Python (regression coefficients, amortisation table, matrix powers, Kruskal/Dijkstra/cut enumeration/CPM passes); criteria sum to 15 per question; original content, Australian conventions.
- Data analysis: median, IQR and the 1.5 x IQR outlier rule, normal distribution (68-95-99.7 rule and z-scores), least squares regression with slope/intercept interpretation, prediction, residuals and coefficient of determination, plus seasonal indices, deseasonalising and trend-line forecasting for quarterly construction data.
- Recursion and financial modelling: flat-rate, unit-cost and reducing-balance depreciation of construction plant, recurrence relations, reducing-balance loan amortisation with Finance Solver (number of repayments, final adjusted repayment, total interest), and an annuity drawdown including the perpetuity condition.
- Matrices: matrix order and multiplication for site materials costing, determinant and inverse of a 2 x 2 matrix to solve equipment-hire equations, transition matrices with state matrices, steady state, the rule S(n+1) = T x S(n) + R for a workforce with recruitment, and one- and two-step dominance ranking of tendering firms.
- Networks and decision mathematics: vertex degree and Euler trail conditions for a site inspection, minimum spanning tree for power cabling, shortest path, maximum flow and minimum cut for concrete deliveries, and project scheduling with earliest start times, critical path, float and crashing.
- Data analysis: normal distribution and z-scores, boxplot outliers, least-squares regression (interpretation, prediction, residuals, r2), seasonal indices and trend forecasting
- Recursion and financial modelling: flat-rate vs reducing-balance depreciation, compound interest recurrence, effective interest rate, reducing-balance loan amortisation with final payment, perpetuities
- Matrices: matrix products in context, determinant and inverse for simultaneous equations, transition matrices with steady state and the rule S(n+1) = T.S(n) + B, dominance ranking
- Networks and decision mathematics: Euler trails, minimum spanning tree, shortest path, maximum flow and minimum cut, critical path analysis with float and crashing
Included in the VCE General Mathematics Mastery Pack
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
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