VCE General Mathematics past exams 2023–2025

Every question from the last three VCE General Mathematics exams, matched to the lesson that teaches it, with class averages from the examiners' reports and worked solutions. VCE General Mathematics (Year 12) lessons.

2025 Exam 1

MC 1 (1 mark, class average 75%): Median from a histogram of a discrete variable. Lesson: Investigating Data Distributions
MC 2 (1 mark, class average 76%): Total quantity from a frequency histogram. Lesson: Investigating Data Distributions
MC 3 (1 mark, class average 82%): Compare two boxplots using quartiles, medians and spread. Lesson: Associations Between Two Variables
MC 4 (1 mark, class average 52%): Place a calculated value in the right column of a log-scale histogram. Lesson: Investigating Data Distributions
MC 5 (1 mark, class average 81%): Mean and standard deviation from two tail percentages. Lesson: The Normal Distribution and z-Scores
MC 6 (1 mark, class average 79%): Count low outliers using the lower fence. Lesson: Investigating Data Distributions
MC 7 (1 mark, class average 86%): Row percentage from a two-way table. Lesson: Associations Between Two Variables
MC 8 (1 mark, class average 79%): Choose a suitable display for two categorical variables. Lesson: Associations Between Two Variables
MC 9 (1 mark, class average 66%): Find the equation of a least squares line drawn on a scatterplot. Lesson: Least Squares Regression
MC 10 (1 mark, class average 63%): Interpret a negative correlation without assuming causation. Lesson: Scatterplots and Correlation
MC 11 (1 mark, class average 81%): Least squares equation after a log transformation of the response. Lesson: Data Transformations — Linearising Relationships
MC 12 (1 mark, class average 61%): Prediction from a least squares line after squaring the explanatory variable. Lesson: Data Transformations — Linearising Relationships
MC 13 (1 mark, class average 76%): Five-median smoothed value for one week. Lesson: Time Series — Features and Smoothing
MC 14 (1 mark, class average 85%): Describe the features of a time series plot. Lesson: Time Series — Features and Smoothing
MC 15 (1 mark, class average 81%): Four-mean smoothing with centring for one day. Lesson: Time Series — Features and Smoothing
MC 16 (1 mark, class average 50%): Percentage change that deseasonalises a value with a given seasonal index. Lesson: Seasonal Indices and Forecasting
MC 17 (1 mark, class average 53%): Expression for a balance after three years of simple interest. Lesson: Compound Interest and Effective Interest Rates
MC 18 (1 mark, class average 52%): Type of sequence from a recurrence with R between 0 and 1 and d equal to 0. Lesson: Recurrence Relations — Linear and Geometric Growth
MC 19 (1 mark, class average 49%): When flat rate depreciation first gives a lower value than reducing balance. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
MC 20 (1 mark, class average 55%): Depreciation per hour using the unit cost method. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
MC 21 (1 mark, class average 69%): When total payments from a perpetuity first exceed the amount invested. Lesson: Annuities, Perpetuities and Annuity Investments
MC 22 (1 mark, class average 68%): Interest rate needed for a savings plan with regular deposits to reach a target. Lesson: Annuities, Perpetuities and Annuity Investments
MC 23 (1 mark, class average 41%): Interest earned over five years given an effective rate. Lesson: Compound Interest and Effective Interest Rates
MC 24 (1 mark, class average 52%): Total length of an annuity whose payment changes partway through. Lesson: Annuities, Perpetuities and Annuity Investments
MC 25 (1 mark, class average 83%): Classify a matrix of zeros and ones. Lesson: Matrices — Types, Operations and Inverses
MC 26 (1 mark, class average 84%): Which products give one element of a matrix product. Lesson: Matrices — Types, Operations and Inverses
MC 27 (1 mark, class average 76%): Values that stop a 2 by 2 matrix from having an inverse. Lesson: Matrices — Types, Operations and Inverses
MC 28 (1 mark, class average 93%): Find a valid communication route using a communication matrix. Lesson: Matrices — Types, Operations and Inverses
MC 29 (1 mark, class average 84%): Build a Leslie matrix from a life-cycle diagram. Lesson: Transition Matrices and Steady State
MC 30 (1 mark, class average 73%): Count negative elements of a matrix defined by a rule. Lesson: Matrices — Types, Operations and Inverses
MC 31 (1 mark, class average 70%): Decide which matrix calculation is defined. Lesson: Matrices — Types, Operations and Inverses
MC 32 (1 mark, class average 63%): Complete a dominance matrix from clues, then find one-step plus two-step totals. Lesson: Matrices — Types, Operations and Inverses
MC 33 (1 mark, class average 76%): Count Hamiltonian cycles from a given vertex. Lesson: Graphs — Euler, Hamilton and Planar Graphs
MC 34 (1 mark, class average 85%): Count the bridges in a graph. Lesson: Graphs — Euler, Hamilton and Planar Graphs
MC 35 (1 mark, class average 65%): Length of a minimum spanning tree that must include an unknown edge. Lesson: Trees, Minimum Spanning Trees and Shortest Paths
MC 36 (1 mark, class average 77%): Capacity of a cut that crosses edges in both directions. Lesson: Flow Networks, Matching and the Hungarian Algorithm
MC 37 (1 mark, class average 73%): Maximum flow equals the minimum cut. Lesson: Flow Networks, Matching and the Hungarian Algorithm
MC 38 (1 mark, class average 47%): Shortest route through a road network. Lesson: Trees, Minimum Spanning Trees and Shortest Paths
MC 39 (1 mark, class average 71%): Result of the first two steps of the Hungarian algorithm. Lesson: Flow Networks, Matching and the Hungarian Algorithm
MC 40 (1 mark, class average 39%): Float time of an activity from a precedence table. Lesson: Project Scheduling — Critical Path Analysis and Crashing

2025 Exam 2

Q1a (1 mark, class average 84%): Median price of 20 homes from a table. Lesson: Investigating Data Distributions
Q1b (1 mark, class average 77%): Classify a variable as numerical, nominal or ordinal. Lesson: Investigating Data Distributions
Q1c.i (1 mark, class average 69%): Standard deviation of one group's prices. Lesson: Investigating Data Distributions
Q1c.ii (1 mark, class average 47%): Compare spread using two standard deviations. Lesson: Investigating Data Distributions
Q1d (1 mark, class average 89%): Complete a table of percentages in price ranges for two types of home. Lesson: Associations Between Two Variables
Q2a (1 mark, class average 85%): Range from a boxplot. Lesson: Investigating Data Distributions
Q2b (1 mark, class average 82%): Upper fence from a boxplot. Lesson: Investigating Data Distributions
Q3 (2 marks, class average 55%): Find a standard deviation from a z-score, then a percentage using the 68–95–99.7% rule. Lesson: The Normal Distribution and z-Scores
Q4a (1 mark, class average 94%): Name the explanatory variable in a least squares equation. Lesson: Least Squares Regression, Associations Between Two Variables
Q4b (1 mark, class average 21%): Correlation coefficient from the coefficient of determination and a negative slope. Lesson: Residuals and the Coefficient of Determination, Scatterplots and Correlation
Q4c (1 mark, class average 73%): Predict the sale price at zero distance. Lesson: Least Squares Regression
Q4d (1 mark, class average 27%): Decide whether a prediction is interpolation or extrapolation. Lesson: Least Squares Regression
Q4e (2 marks, class average 75%): Describe a linear association's strength and direction from r. Lesson: Scatterplots and Correlation
Q4f.i (1 mark, class average 41%): Show how a residual is calculated for one home. Lesson: Residuals and the Coefficient of Determination
Q4f.ii (1 mark, class average 45%): Plot a residual on a residual plot. Lesson: Residuals and the Coefficient of Determination
Q5a (2 marks, class average 50%): Least squares line from a table, rounded to four significant figures. Lesson: Least Squares Regression
Q5b (1 mark, class average 44%): Explain r squared in context, rounded to a whole percentage. Lesson: Residuals and the Coefficient of Determination
Q6a (2 marks, class average 55%): Name two qualitative features of a time series plot. Lesson: Time Series — Features and Smoothing
Q6b (2 marks, class average 20%): Seasonal index for one month from four years of data. Lesson: Seasonal Indices and Forecasting
Q7a (1 mark, class average 93%): Amount borrowed from an amortisation table. Lesson: Reducing Balance Loans and the Finance Solver
Q7b (1 mark, class average 65%): Why the interest in a reducing balance loan falls each payment. Lesson: Reducing Balance Loans and the Finance Solver
Q7c (1 mark, class average 40%): Complete the next row of a loan amortisation table. Lesson: Reducing Balance Loans and the Finance Solver
Q7d (1 mark, class average 41%): Number of full repayments before a smaller final payment. Lesson: Reducing Balance Loans and the Finance Solver
Q8a.i (1 mark, class average 73%): Recurrence relation for flat rate depreciation read from a graph. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost, Recurrence Relations — Linear and Geometric Growth
Q8a.ii (1 mark, class average 50%): Rule for the value after n years of flat rate depreciation. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
Q8b (1 mark, class average 69%): Annual flat rate depreciation as a percentage. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
Q9a (1 mark, class average 37%): Weekly interest rate when repayments only cover the interest. Lesson: Reducing Balance Loans and the Finance Solver
Q9b.i (1 mark, class average 40%): Annual interest rate from a loan balance after one year. Lesson: Reducing Balance Loans and the Finance Solver
Q9b.ii (1 mark, class average 30%): Weekly multiplier R from an annual rate. Lesson: Recurrence Relations — Linear and Geometric Growth, Reducing Balance Loans and the Finance Solver
Q10 (2 marks, class average 20%): Recurrence relation for the second half of an annuity. Lesson: Annuities, Perpetuities and Annuity Investments, Recurrence Relations — Linear and Geometric Growth
Q11a (1 mark, class average 96%): Order of a matrix. Lesson: Matrices — Types, Operations and Inverses
Q11b (1 mark, class average 57%): Interpret a row of ones multiplied by a matrix. Lesson: Matrices — Types, Operations and Inverses
Q11c (1 mark, class average 44%): Diagonal matrix that scales each capacity by a different percentage. Lesson: Matrices — Types, Operations and Inverses
Q12a (1 mark, class average 53%): Work back one step through a transition matrix. Lesson: Transition Matrices and Steady State
Q12b (1 mark, class average 13%): Total enrolled two years on with new children added each year. Lesson: Transition Matrices and Steady State
Q13a (1 mark, class average 67%): Meaning of zeros on the leading diagonal of a transition matrix. Lesson: Transition Matrices and Steady State
Q13b.i (1 mark, class average 9%): Percentage in one activity after nine transitions. Lesson: Transition Matrices and Steady State
Q13b.ii (2 marks, class average 20%): Number of children expected to move from one activity to another between two weeks. Lesson: Transition Matrices and Steady State
Q14a (1 mark, class average 65%): Which rows a permutation matrix leaves unchanged. Lesson: Matrices — Types, Operations and Inverses
Q14b (1 mark, class average 27%): Apply a permutation matrix twice to find a later order. Lesson: Matrices — Types, Operations and Inverses
Q14c (1 mark, class average 11%): Meaning of a permutation matrix to the fourth power being the identity. Lesson: Matrices — Types, Operations and Inverses
Q15a (1 mark, class average 88%): Sum of the degrees of a graph. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q15b (1 mark, class average 91%): Fill in Euler's formula for a planar graph. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q15c (1 mark, class average 53%): Name a route that visits every vertex once without returning. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q15d (1 mark, class average 81%): Draw a spanning tree using edges of a graph. Lesson: Trees, Minimum Spanning Trees and Shortest Paths
Q16 (2 marks, class average 45%): Count routes between areas on a map to complete an adjacency matrix. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q17a (1 mark, class average 40%): Explain why a circuit along every edge would need repeats. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q17b (1 mark, class average 27%): Minimum distance to inspect every walkway and return to the start. Lesson: Graphs — Euler, Hamilton and Planar Graphs, Trees, Minimum Spanning Trees and Shortest Paths
Q18a (1 mark, class average 44%): Activities shared by two critical paths. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q18b (1 mark, class average 46%): Latest start time for an activity using a backward scan. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q18c (1 mark, class average 47%): Activity with the longest float. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q18d (1 mark, class average 21%): Cheapest crashing that cuts three days from a project. Lesson: Project Scheduling — Critical Path Analysis and Crashing

2024 Exam 1

MC 1 (1 mark, class average 78%): Read one category's share from a percentage segmented bar chart. Lesson: Investigating Data Distributions, Associations Between Two Variables
MC 2 (1 mark, class average 79%): Classify two survey variables as categorical or numerical. Lesson: Investigating Data Distributions
MC 3 (1 mark, class average 71%): Locate the median column of a log-scale histogram. Lesson: Investigating Data Distributions
MC 4 (1 mark, class average 68%): Convert a log-scale outlier column back to an actual value. Lesson: Investigating Data Distributions
MC 5 (1 mark, class average 80%): Use a five-number summary to test statements about a boxplot of small whole numbers. Lesson: Investigating Data Distributions
MC 6 (1 mark, class average 53%): Smallest whole number that would be an outlier given a five-number summary. Lesson: Investigating Data Distributions
MC 7 (1 mark, class average 82%): Find a standard deviation from a value, the mean and its z-score. Lesson: The Normal Distribution and z-Scores
MC 8 (1 mark, class average 73%): Choose the least squares equation for a line shown on a scatterplot. Lesson: Least Squares Regression
MC 9 (1 mark, class average 52%): Work back to the correlation coefficient from a slope and two standard deviations. Lesson: Least Squares Regression, Scatterplots and Correlation
MC 10 (1 mark, class average 73%): Solve a regression equation for the explanatory variable. Lesson: Least Squares Regression
MC 11 (1 mark, class average 59%): Least squares equation after a log transformation of the explanatory variable. Lesson: Data Transformations — Linearising Relationships
MC 12 (1 mark, class average 48%): Find which point has the largest residual after a reciprocal transformation of the response. Lesson: Data Transformations — Linearising Relationships, Residuals and the Coefficient of Determination
MC 13 (1 mark, class average 72%): Seven-median smoothed value for one year of a time series. Lesson: Time Series — Features and Smoothing
MC 14 (1 mark, class average 68%): Find a missing value from a new mean over 13 years. Lesson: Investigating Data Distributions
MC 15 (1 mark, class average 70%): Six-mean smoothing with centring for one month. Lesson: Time Series — Features and Smoothing
MC 16 (1 mark, class average 58%): Find two missing seasonal indices when one is double the other. Lesson: Seasonal Indices and Forecasting
MC 17 (1 mark, class average 36%): Which values of R and d make a recurrence relation geometric. Lesson: Recurrence Relations — Linear and Geometric Growth
MC 18 (1 mark, class average 74%): Annual interest rate from a weekly recurrence multiplier. Lesson: Compound Interest and Effective Interest Rates, Reducing Balance Loans and the Finance Solver
MC 19 (1 mark, class average 72%): Multiplier for reducing balance depreciation at a given rate. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
MC 20 (1 mark, class average 48%): Simple interest rate that earns the same as a compound interest investment. Lesson: Compound Interest and Effective Interest Rates
MC 21 (1 mark, class average 56%): Total interest paid on a loan from its repayments and term. Lesson: Reducing Balance Loans and the Finance Solver
MC 22 (1 mark, class average 70%): Principal reduction for the second line of a loan amortisation table. Lesson: Reducing Balance Loans and the Finance Solver
MC 23 (1 mark, class average 54%): Time to repay a loan using the finance solver. Lesson: Reducing Balance Loans and the Finance Solver
MC 24 (1 mark, class average 46%): New regular addition needed for an investment to reach a target. Lesson: Annuities, Perpetuities and Annuity Investments
MC 25 (1 mark, class average 79%): Order of a matrix that can be added to a matrix product. Lesson: Matrices — Types, Operations and Inverses
MC 26 (1 mark, class average 76%): Scalar multiple for a 15% discount. Lesson: Matrices — Types, Operations and Inverses
MC 27 (1 mark, class average 50%): Value of an element that makes a 2 by 2 matrix have no inverse. Lesson: Matrices — Types, Operations and Inverses
MC 28 (1 mark, class average 84%): Interpret an element of a product with a column of ones. Lesson: Matrices — Types, Operations and Inverses
MC 29 (1 mark, class average 49%): Apply a permutation matrix repeatedly to find a playing order. Lesson: Matrices — Types, Operations and Inverses
MC 30 (1 mark, class average 78%): Build a Leslie matrix from birth and survival rates. Lesson: Transition Matrices and Steady State
MC 31 (1 mark, class average 53%): Which final ranking is impossible once two remaining games are played. Lesson: Matrices — Types, Operations and Inverses
MC 32 (1 mark, class average 33%): Work backwards through a transition matrix with a constant addition. Lesson: Transition Matrices and Steady State
MC 33 (1 mark, class average 75%): Sum of degrees in a graph with a loop and an isolated vertex. Lesson: Graphs — Euler, Hamilton and Planar Graphs
MC 34 (1 mark, class average 85%): Identify a valid Eulerian trail through a small graph. Lesson: Graphs — Euler, Hamilton and Planar Graphs
MC 35 (1 mark, class average 52%): Count faces of a graph that can be redrawn without crossings. Lesson: Graphs — Euler, Hamilton and Planar Graphs
MC 36 (1 mark, class average 83%): Pick the minimum spanning tree for a cable network. Lesson: Trees, Minimum Spanning Trees and Shortest Paths
MC 37 (1 mark, class average 40%): Choose missing edge lengths that make the shortest path a given length. Lesson: Trees, Minimum Spanning Trees and Shortest Paths
MC 38 (1 mark, class average 18%): Decide which statements must hold for every connected graph with six vertices and six edges. Lesson: Graphs — Euler, Hamilton and Planar Graphs
MC 39 (1 mark, class average 19%): Time saved when a fifth worker joins and the tasks are reallocated. Lesson: Flow Networks, Matching and the Hungarian Algorithm
MC 40 (1 mark, class average 32%): Match an unlabelled activity network to its precedence table. Lesson: Project Scheduling — Critical Path Analysis and Crashing

2024 Exam 2

Q1a.i (1 mark, class average 96%): Read the largest value from a table of winning heights. Lesson: Investigating Data Distributions
Q1a.ii (1 mark, class average 77%): Percentage of values in a table above a given height. Lesson: Investigating Data Distributions
Q1b (1 mark, class average 84%): Standardised score for one value given a mean and standard deviation. Lesson: The Normal Distribution and z-Scores
Q1c (2 marks, class average 85%): Draw a boxplot from 22 values in a table. Lesson: Investigating Data Distributions
Q1d (2 marks, class average 50%): Least squares line for height against year, rounded to three significant figures. Lesson: Least Squares Regression
Q1e (1 mark, class average 52%): Interpret the coefficient of determination in context. Lesson: Residuals and the Coefficient of Determination
Q2a (1 mark, class average 86%): Describe the shape of a distribution from its boxplot. Lesson: Investigating Data Distributions
Q2b (1 mark, class average 3%): Least number of values that could lie below the first quartile shown on a boxplot. Lesson: Investigating Data Distributions
Q2c.i (1 mark, class average 84%): Show how the lower and upper fences are calculated from a boxplot. Lesson: Investigating Data Distributions
Q2c.ii (1 mark, class average 76%): Use the fences to explain why a boxplot has no outliers. Lesson: Investigating Data Distributions
Q3a (1 mark, class average 90%): Name the response variable in a least squares equation. Lesson: Least Squares Regression
Q3b (1 mark, class average 51%): Draw the least squares line on a scatterplot. Lesson: Least Squares Regression
Q3c (1 mark, class average 57%): Coefficient of determination as a percentage from r. Lesson: Residuals and the Coefficient of Determination
Q3d (1 mark, class average 78%): Describe strength and direction of an association from r. Lesson: Scatterplots and Correlation
Q3e (1 mark, class average 54%): Interpret the slope of a least squares line in context. Lesson: Least Squares Regression
Q3f (2 marks, class average 50%): Show how a residual is calculated for one point. Lesson: Residuals and the Coefficient of Determination
Q3g.i (1 mark, class average 47%): Add one point to a residual plot. Lesson: Residuals and the Coefficient of Determination
Q3g.ii (1 mark, class average 40%): Use a residual plot to judge whether a linear model is appropriate. Lesson: Residuals and the Coefficient of Determination
Q3h (1 mark, class average 50%): Explain why a prediction from a least squares line is unreliable. Lesson: Least Squares Regression
Q4a (1 mark, class average 55%): Finish five-median smoothing on a time series plot. Lesson: Time Series — Features and Smoothing
Q4b (1 mark, class average 24%): Name two qualitative features of a time series plot. Lesson: Time Series — Features and Smoothing
Q5a (1 mark, class average 87%): Weekly depreciation from a rule for value after n weeks. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
Q5b (1 mark, class average 72%): Value of equipment after four years of weekly depreciation. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
Q5c (1 mark, class average 59%): Recurrence relation for weekly flat rate depreciation. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost, Recurrence Relations — Linear and Geometric Growth
Q5d (1 mark, class average 42%): Annual flat rate depreciation as a percentage. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
Q6a (1 mark, class average 51%): Nominal annual rate from an effective rate with fortnightly compounding. Lesson: Compound Interest and Effective Interest Rates
Q6b (1 mark, class average 26%): Explain why a nominal rate is lower than the effective rate. Lesson: Compound Interest and Effective Interest Rates
Q7a (1 mark, class average 49%): Use a recurrence relation to find an annuity balance after two months. Lesson: Annuities, Perpetuities and Annuity Investments, Recurrence Relations — Linear and Geometric Growth
Q7b (1 mark, class average 42%): How long an annuity lasts using the finance solver. Lesson: Annuities, Perpetuities and Annuity Investments
Q7c (1 mark, class average 56%): Annual interest rate from a monthly multiplier. Lesson: Compound Interest and Effective Interest Rates, Annuities, Perpetuities and Annuity Investments
Q7d (1 mark, class average 47%): Monthly payment from a perpetuity. Lesson: Annuities, Perpetuities and Annuity Investments
Q8 (2 marks, class average 30%): Number of repayments and total cost of a loan with an adjusted final payment. Lesson: Reducing Balance Loans and the Finance Solver
Q9a (1 mark, class average 88%): Write the transpose of a row matrix. Lesson: Matrices — Types, Operations and Inverses
Q9b (1 mark, class average 78%): Matrix product that gives a week's total pay. Lesson: Matrices — Types, Operations and Inverses
Q9c (1 mark, class average 70%): Find a scalar and a missing element from a scalar multiple. Lesson: Matrices — Types, Operations and Inverses
Q10a (1 mark, class average 54%): Build a row matrix from a rule for its elements. Lesson: Matrices — Types, Operations and Inverses
Q10b (1 mark, class average 50%): Last element of a longer row matrix built from the same rule. Lesson: Matrices — Types, Operations and Inverses
Q11a.i (1 mark, class average 24%): Draw the transition diagram for a Leslie matrix. Lesson: Transition Matrices and Steady State
Q11a.ii (1 mark, class average 61%): Initial and next-year populations from a Leslie matrix. Lesson: Transition Matrices and Steady State
Q11b (1 mark, class average 39%): Years until a population modelled by a Leslie matrix first halves. Lesson: Transition Matrices and Steady State
Q12a (1 mark, class average 25%): Percentage drop in one group over two years using a transition matrix. Lesson: Transition Matrices and Steady State
Q12b (1 mark, class average 24%): Long-term number of staff when leaving is permanent. Lesson: Transition Matrices and Steady State
Q12c (1 mark, class average 12%): Change in staff numbers after one year with new hires added. Lesson: Transition Matrices and Steady State
Q12d (1 mark, class average 26%): First year a group passes a threshold in a recurrence with additions. Lesson: Transition Matrices and Steady State
Q13a (1 mark, class average 88%): Add the missing vertex and edges to a graph of a floorplan. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q13b.i (1 mark, class average 88%): Where a route that visits every department once must end. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q13b.ii (1 mark, class average 75%): Name the type of route that visits each vertex once. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q13c (1 mark, class average 80%): Label a floorplan from an adjacency matrix. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q14a (1 mark, class average 78%): Capacity of a given cut in a flow network. Lesson: Flow Networks, Matching and the Hungarian Algorithm
Q14b (1 mark, class average 29%): Maximum flow through a network from source to sink. Lesson: Flow Networks, Matching and the Hungarian Algorithm
Q14c (1 mark, class average 22%): Which single edge to increase for the biggest gain in flow. Lesson: Flow Networks, Matching and the Hungarian Algorithm
Q15a (1 mark, class average 65%): Find the critical path in an activity network. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q15b (1 mark, class average 34%): Activity with the most float time. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q15c (1 mark, class average 10%): Place a dummy activity to match a new set of latest start times. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q15d (1 mark, class average 27%): New minimum completion time after a dummy is added. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q15e (1 mark, class average 7%): Cheapest crashing that gives the shortest possible project time. Lesson: Project Scheduling — Critical Path Analysis and Crashing

2023 Exam 1

MC 1 (1 mark, class average 90%): Median of 40 race times read from a dot plot. Lesson: Investigating Data Distributions
MC 2 (1 mark, class average 88%): Describe the shape of a dot plot of race times. Lesson: Investigating Data Distributions
MC 3 (1 mark, class average 89%): Find the sixth value needed to reach a target mean. Lesson: Investigating Data Distributions
MC 4 (1 mark, class average 82%): Count visitors within two standard deviations using the 68–95–99.7% rule. Lesson: The Normal Distribution and z-Scores
MC 5 (1 mark, class average 84%): Convert a negative z-score back to a height. Lesson: The Normal Distribution and z-Scores
MC 6 (1 mark, class average 54%): Decide which car prices fall in the modal class of a log-scale histogram. Lesson: Investigating Data Distributions
MC 7 (1 mark, class average 60%): Pick the least squares equation that matches a line drawn on a scatterplot. Lesson: Least Squares Regression
MC 8 (1 mark, class average 43%): Count points whose residual is within two marks of the regression line. Lesson: Residuals and the Coefficient of Determination
MC 9 (1 mark, class average 59%): Slope of a regression line from two predicted points. Lesson: Least Squares Regression
MC 10 (1 mark, class average 59%): Interpret a negative association without claiming causation. Lesson: Scatterplots and Correlation
MC 11 (1 mark, class average 60%): Least squares line after a reciprocal transformation of the explanatory variable. Lesson: Data Transformations — Linearising Relationships
MC 12 (1 mark, class average 76%): Use a log-transformed regression equation to find the age for a given height. Lesson: Data Transformations — Linearising Relationships
MC 13 (1 mark, class average 68%): Seven-median smoothed value for a single year of a time series. Lesson: Time Series — Features and Smoothing
MC 14 (1 mark, class average 37%): Median of all values shown on a time series plot. Lesson: Investigating Data Distributions, Time Series — Features and Smoothing
MC 15 (1 mark, class average 66%): Eight-mean smoothing with centring for one day. Lesson: Time Series — Features and Smoothing
MC 16 (1 mark, class average 43%): Find a seasonal index from the percentage change needed to deseasonalise. Lesson: Seasonal Indices and Forecasting
MC 17 (1 mark, class average 43%): Generate terms of a recurrence relation that changes sign each step. Lesson: Recurrence Relations — Linear and Geometric Growth
MC 18 (1 mark, class average 60%): Rule for the value after n years from a unit cost recurrence relation. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
MC 19 (1 mark, class average 62%): Number of units of use per year from a unit cost depreciation amount. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
MC 20 (1 mark, class average 82%): Flat rate depreciation percentage from a start value, end value and time. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
MC 21 (1 mark, class average 48%): Reducing balance depreciation rate that gives the same four-year value. Lesson: Depreciation — Flat Rate, Reducing Balance and Unit Cost
MC 22 (1 mark, class average 39%): Size of the final adjusted repayment on a reducing balance loan. Lesson: Reducing Balance Loans and the Finance Solver
MC 23 (1 mark, class average 37%): Effective annual rate from the first quarterly balances of a loan. Lesson: Compound Interest and Effective Interest Rates, Reducing Balance Loans and the Finance Solver
MC 24 (1 mark, class average 27%): Express the growth multiplier of a perpetuity in terms of its value and payment. Lesson: Annuities, Perpetuities and Annuity Investments
MC 25 (1 mark, class average 89%): Interpret one element of a matrix built from a table of temperatures. Lesson: Matrices — Types, Operations and Inverses
MC 26 (1 mark, class average 90%): Effect of multiplying a column of letters by a permutation matrix. Lesson: Matrices — Types, Operations and Inverses
MC 27 (1 mark, class average 39%): Long-term behaviour of a transition matrix with one absorbing state. Lesson: Transition Matrices and Steady State
MC 28 (1 mark, class average 69%): Pick a dominance matrix consistent with a final ranking. Lesson: Matrices — Types, Operations and Inverses
MC 29 (1 mark, class average 62%): Build a matrix from a rule for its elements. Lesson: Matrices — Types, Operations and Inverses
MC 30 (1 mark, class average 39%): Decide how many statements about matrix inverses are true. Lesson: Matrices — Types, Operations and Inverses
MC 31 (1 mark, class average 74%): Interpret a survival rate in a Leslie matrix. Lesson: Transition Matrices and Steady State
MC 32 (1 mark, class average 18%): Use a transition diagram to trace how many students stayed on the oval two days running. Lesson: Transition Matrices and Steady State
MC 33 (1 mark, class average 56%): Count the true statements about a small connected graph with no cycles. Lesson: Graphs — Euler, Hamilton and Planar Graphs, Trees, Minimum Spanning Trees and Shortest Paths
MC 34 (1 mark, class average 77%): Which kind of problem a bipartite graph is used for. Lesson: Flow Networks, Matching and the Hungarian Algorithm
MC 35 (1 mark, class average 74%): Weight of the minimum spanning tree of a six-vertex weighted graph. Lesson: Trees, Minimum Spanning Trees and Shortest Paths
MC 36 (1 mark, class average 75%): Minimum total time when four people are each given one of four duties. Lesson: Flow Networks, Matching and the Hungarian Algorithm
MC 37 (1 mark, class average 66%): Use an adjacency matrix and Euler's formula to count faces of a planar graph. Lesson: Graphs — Euler, Hamilton and Planar Graphs
MC 38 (1 mark, class average 60%): Choose the activity network with a correctly placed dummy. Lesson: Project Scheduling — Critical Path Analysis and Crashing
MC 39 (1 mark, class average 62%): Capacity of the minimum cut in a one-way flow network. Lesson: Flow Networks, Matching and the Hungarian Algorithm
MC 40 (1 mark, class average 40%): Which change to one edge increases the maximum flow the most. Lesson: Flow Networks, Matching and the Hungarian Algorithm

2023 Exam 2

Q1a (1 mark, class average 50%): Count the categorical variables in a table of oyster measurements. Lesson: Investigating Data Distributions
Q1b.i (1 mark, class average 86%): Mean weight of a sample of 15 oysters. Lesson: Investigating Data Distributions
Q1b.ii (1 mark, class average 39%): Median weight of only the large oysters in the sample. Lesson: Investigating Data Distributions
Q1c.i (1 mark, class average 88%): Name the response variable in a least squares equation. Lesson: Least Squares Regression, Associations Between Two Variables
Q1c.ii (1 mark, class average 27%): Use the slope to describe the change for a 10 g increase in weight. Lesson: Least Squares Regression
Q1d (2 marks, class average 50%): Find a least squares line from table data and round to four significant figures. Lesson: Least Squares Regression
Q1e (2 marks, class average 30%): Use two percentages and the 68–95–99.7% rule to find a mean and standard deviation. Lesson: The Normal Distribution and z-Scores
Q2a.i (1 mark, class average 95%): Count each size category to complete a frequency table. Lesson: Investigating Data Distributions
Q2a.ii (1 mark, class average 84%): Draw a percentage segmented bar chart from a frequency table. Lesson: Investigating Data Distributions, Associations Between Two Variables
Q2b.i (1 mark, class average 87%): Percentage of all oysters across two farms that were large. Lesson: Associations Between Two Variables
Q2b.ii (2 marks, class average 65%): Use column percentages to compare how many large oysters two farms produce. Lesson: Associations Between Two Variables
Q3a (1 mark, class average 40%): Draw a given least squares line accurately on a scatterplot. Lesson: Least Squares Regression
Q3b (1 mark, class average 69%): Correlation coefficient from the coefficient of determination. Lesson: Residuals and the Coefficient of Determination, Scatterplots and Correlation
Q3c (1 mark, class average 58%): Describe a scatterplot's association by strength, direction and form. Lesson: Scatterplots and Correlation
Q3d (1 mark, class average 43%): Interpret the intercept of a least squares line in context. Lesson: Least Squares Regression
Q3e (1 mark, class average 75%): Predict consumption for a temperature below zero. Lesson: Least Squares Regression
Q3f (1 mark, class average 41%): Decide whether a prediction is interpolation or extrapolation. Lesson: Least Squares Regression
Q4a (1 mark, class average 26%): Point to a feature of a time series plot that shows seasonality. Lesson: Time Series — Features and Smoothing
Q4b (1 mark, class average 72%): Deseasonalise one month's value with a seasonal index. Lesson: Seasonal Indices and Forecasting
Q4c (2 marks, class average 35%): Show how to calculate one month's seasonal index from a year of data. Lesson: Seasonal Indices and Forecasting
Q5a (1 mark, class average 76%): Number of quarterly repayments over six years. Lesson: Reducing Balance Loans and the Finance Solver
Q5b (1 mark, class average 51%): Use a recurrence relation step by step to find a loan balance after two quarters. Lesson: Reducing Balance Loans and the Finance Solver, Recurrence Relations — Linear and Geometric Growth
Q5c (1 mark, class average 25%): Adjust the last repayment so a loan finishes at exactly zero. Lesson: Reducing Balance Loans and the Finance Solver
Q6a (1 mark, class average 70%): Annual interest rate from a monthly rate. Lesson: Compound Interest and Effective Interest Rates, Annuities, Perpetuities and Annuity Investments
Q6b (1 mark, class average 40%): Complete the next line of an annuity amortisation table. Lesson: Annuities, Perpetuities and Annuity Investments
Q6c (1 mark, class average 41%): Write the recurrence relation for a monthly annuity. Lesson: Annuities, Perpetuities and Annuity Investments, Recurrence Relations — Linear and Geometric Growth
Q6d (1 mark, class average 59%): Name an annuity whose balance never changes. Lesson: Annuities, Perpetuities and Annuity Investments
Q7a (1 mark, class average 32%): Show the annual rate implied by a weekly recurrence multiplier. Lesson: Compound Interest and Effective Interest Rates
Q7b.i (1 mark, class average 47%): Weekly payment that keeps a loan balance constant. Lesson: Reducing Balance Loans and the Finance Solver
Q7b.ii (1 mark, class average 40%): Weekly repayment that pays off a loan in five years. Lesson: Reducing Balance Loans and the Finance Solver
Q7c (1 mark, class average 32%): New weekly repayment after a year of smaller repayments. Lesson: Reducing Balance Loans and the Finance Solver
Q7d (1 mark, class average 11%): Value of the subtracted constant that turns the recurrence into a geometric sequence. Lesson: Recurrence Relations — Linear and Geometric Growth
Q8a (1 mark, class average 48%): Name the element of a column matrix that holds one ticket price. Lesson: Matrices — Types, Operations and Inverses
Q8b (1 mark, class average 44%): Complete a matrix expression that compares a family ticket with separate tickets. Lesson: Matrices — Types, Operations and Inverses
Q8c (1 mark, class average 34%): Find the matrix that multiplies each price by its own number of tickets sold. Lesson: Matrices — Types, Operations and Inverses
Q9a (1 mark, class average 25%): Scalar multiple that turns 20-performance totals into averages. Lesson: Matrices — Types, Operations and Inverses
Q9b (1 mark, class average 47%): Scalar that represents a 25% increase in revenue. Lesson: Matrices — Types, Operations and Inverses
Q9c (1 mark, class average 68%): Follow a permutation matrix to find the order of the circus's visits. Lesson: Matrices — Types, Operations and Inverses
Q9d (1 mark): Complete a movement matrix after a new location is added to the cycle. Lesson: Matrices — Types, Operations and Inverses
Q10a (1 mark, class average 74%): Shortest chain of communication from a customer to a director. Lesson: Matrices — Types, Operations and Inverses
Q10b.i (1 mark, class average 66%): Complete the two-step communication matrix. Lesson: Matrices — Types, Operations and Inverses
Q10b.ii (1 mark, class average 25%): Interpret matching elements of a one-step and a two-step communication matrix. Lesson: Matrices — Types, Operations and Inverses
Q11a (1 mark, class average 34%): Transition matrix for workers who either stay or leave for good. Lesson: Transition Matrices and Steady State
Q11b (1 mark, class average 39%): Restocking matrix that keeps the workforce constant. Lesson: Transition Matrices and Steady State
Q12a (1 mark, class average 76%): Sum of the degrees in a small graph. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q12b.i (1 mark, class average 90%): Fill in Euler's formula for a planar graph. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q12b.ii (1 mark, class average 81%): Name the property, besides being connected, that Euler's formula needs. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q12c (1 mark, class average 71%): Match graph vertices to regions on a map using their borders. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q13a (1 mark, class average 71%): Shortest distance between two landmarks in a road network. Lesson: Trees, Minimum Spanning Trees and Shortest Paths
Q13b (1 mark, class average 44%): Write a Hamiltonian cycle that starts and ends at the same landmark. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q13c (1 mark, class average 12%): Choose which two roads to repeat so a route covers every road. Lesson: Graphs — Euler, Hamilton and Planar Graphs
Q14a (1 mark, class average 73%): Immediate predecessors of an activity that follows a dummy. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q14b (1 mark, class average 59%): Earliest start time for an activity with two predecessors. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q14c (1 mark, class average 35%): Count the activities on the critical path. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q14d (1 mark, class average 33%): Reduction in project time when two starting activities are crashed. Lesson: Project Scheduling — Critical Path Analysis and Crashing
Q14e (1 mark, class average 9%): Best crashing plan for a project within a fixed budget. Lesson: Project Scheduling — Critical Path Analysis and Crashing