General Mathematics — past papers by topic

Data types (numerical, categorical: nominal/ordinal)

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Summarising and displaying univariate data (dot plots, stem plots, histograms, boxplots)

• 2025General Mathematics SD (from 2023)Examination 1 Q11 markReading the median value directly off a histogram of bag sizes bought by customers.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 1 Q31 markComparing interquartile range, median and quartile relationships between two parallel boxplots of life expectancy.Official paper ↗Examiner report ↗Work through it with a tutor →

Measures of centre and spread (mean, median, standard deviation, IQR, range)

• 2025General Mathematics SD (from 2023)Examination 2 Q15 marksMulti-part question finding median price, classifying a categorical variable, computing standard deviation and comparing spread, and completing a percentage price-range table for a housing sales dataset.Official paper ↗Examiner report ↗Work through it with a tutor →

The normal distribution and the 68–95–99.7% rule; standardised (z) scores

• 2025General Mathematics SD (from 2023)Examination 1 Q51 markBack-solving mean and standard deviation of a normal distribution from two given percentile cut-offs using the 68-95-99.7 rule.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q32 marksUsing a given standardised z-score and the 68-95-99.7 rule to find the percentage of home sales within a price range.Official paper ↗Examiner report ↗Work through it with a tutor →

Investigating relationships between two variables (scatterplots, two-way frequency tables, segmented bar charts)

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Correlation and coefficient of determination

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Least squares line of best fit, residual analysis and interpolation/extrapolation

• 2025General Mathematics SD (from 2023)Examination 1 Q91 markIdentifying the correct least squares regression equation from a scatterplot of games won versus goals against.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 1 Q101 markCorrectly interpreting a negative correlation coefficient as association rather than causation.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q48 marksExtended regression question: identifying explanatory variable, computing correlation coefficient from a given least squares equation, predicting a value, judging interpolation vs extrapolation, describing association strength/direction, and computing and plotting a missing residual.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q53 marksCalculating a least squares line equation from a raw bivariate dataset and interpreting the coefficient of determination as a percentage in context.Official paper ↗Examiner report ↗Work through it with a tutor →

Data transformation (log and squared transformations) to linearise data

• 2025General Mathematics SD (from 2023)Examination 1 Q111 markSelecting the least squares equation for data after a log base-10 transformation has been applied to the response variable.Official paper ↗Examiner report ↗Work through it with a tutor →

Time series analysis: trend, seasonality, smoothing (moving mean/median), seasonal indices and deseasonalising

• 2025General Mathematics SD (from 2023)Examination 1 Q131 markCalculating a smoothed value at a specific week using five-median smoothing on a time series graph.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 1 Q161 markConverting a seasonal index above 1 into the percentage reduction needed to deseasonalise sales figures.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q64 marksIdentifying qualitative features of a multi-year time series plot and calculating a monthly seasonal index from annual totals.Official paper ↗Examiner report ↗Work through it with a tutor →

First-order linear recurrence relations (u0 = a, un+1 = Run + d)

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Simple interest and compound interest as recurrence relations and rules

• 2025General Mathematics SD (from 2023)Examination 1 Q171 markSelecting the correct closed-form expression for simple interest growth over three years.Official paper ↗Examiner report ↗Work through it with a tutor →

Effective annual interest rate

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Reducing balance loans and amortisation tables

• 2025General Mathematics SD (from 2023)Examination 2 Q74 marksReading and completing rows of a reducing-balance loan amortisation table, including explaining why interest declines and finding remaining payment count before the final payment.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q93 marksDetermining a weekly interest rate for a balance-neutral repayment scenario, then finding the compounding interest rate and recurrence multiplier for a reducing loan balance.Official paper ↗Examiner report ↗Work through it with a tutor →

Annuities and perpetuities

• 2025General Mathematics SD (from 2023)Examination 1 Q211 markFinding when cumulative perpetuity payments first exceed the original invested principal.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 1 Q241 markDetermining total annuity payment duration given a mid-term balance and a changed monthly payment amount.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q102 marksCompleting a matrix-style recurrence relation for the quarterly balance of an annuity partway through its term.Official paper ↗Examiner report ↗Work through it with a tutor →

Flat rate and reducing balance (unit cost) depreciation

• 2025General Mathematics SD (from 2023)Examination 1 Q191 markDetermining the year in which flat rate depreciated value first falls below reducing balance depreciated value from a comparison table.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q83 marksWriting both a recurrence relation and an explicit rule for flat-rate asset depreciation from a graph, then finding the annual depreciation percentage.Official paper ↗Examiner report ↗Work through it with a tutor →

Compound interest investments with regular deposits/withdrawals

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Matrix definition, order, types (row, column, square, diagonal, identity, binary, permutation)

• 2025General Mathematics SD (from 2023)Examination 1 Q251 markClassifying a given square matrix by its structural type (permutation matrix).Official paper ↗Examiner report ↗Work through it with a tutor →

Matrix operations: addition, subtraction, scalar multiplication, matrix multiplication

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Determinant and inverse of a 2×2 matrix; when an inverse exists

• 2025General Mathematics SD (from 2023)Examination 1 Q271 markIdentifying which parameter values make a 2x2 matrix's determinant zero, so its inverse fails to exist.Official paper ↗Examiner report ↗Work through it with a tutor →

Matrices used to represent and solve practical problems (communication/adjacency matrices, permutation matrices)

• 2025General Mathematics SD (from 2023)Examination 1 Q321 markReconstructing a dominance matrix sum (D + D-squared) to rank round-robin tournament results from partial match data.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q113 marksStating matrix order, interpreting a row-sum matrix multiplication result, and constructing a diagonal scaling matrix for room capacity changes.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q143 marksUsing a permutation matrix to project a timetable forward multiple days and interpreting what a matrix power equal to the identity matrix implies about cyclical repetition.Official paper ↗Examiner report ↗Work through it with a tutor →

Transition matrices and Markov chains (regular transition matrices, steady-state behaviour)

• 2025General Mathematics SD (from 2023)Examination 2 Q122 marksWorking backwards through a matrix recurrence relation to find a prior year's state matrix, then projecting forward with an added constant intake matrix.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q134 marksInterpreting leading-diagonal transition probabilities and projecting activity-group membership several transition steps ahead using a transition matrix.Official paper ↗Examiner report ↗Work through it with a tutor →

Matrix recurrence relations of the form Sn+1 = TSn + B

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Leslie matrices for population/age-structured growth

• 2025General Mathematics SD (from 2023)Examination 1 Q291 markConstructing the correct Leslie matrix from a life-cycle diagram showing birth and survival rates across four age groups.Official paper ↗Examiner report ↗Work through it with a tutor →

Graphs, networks, vertices, edges, degree of a vertex, Euler's formula (v + f = e + 2)

• 2025General Mathematics SD (from 2023)Examination 2 Q154 marksSumming vertex degrees, applying Euler's formula, naming the closed walk-type for a start-and-return route, and constructing a spanning tree from a residential location graph.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q162 marksSolving for unknown entries in an adjacency matrix representing a network of connected gym areas.Official paper ↗Examiner report ↗Work through it with a tutor →

Planar graphs, bridges, walks, trails, paths, cycles

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Eulerian trails/circuits and Hamiltonian paths/cycles

• 2025General Mathematics SD (from 2023)Examination 1 Q331 markCounting the number of Hamiltonian cycles starting from a given vertex in a graph.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q172 marksExplaining why an inspection route must repeat edges based on odd-degree vertices, then finding minimum total inspection distance (Chinese postman-style route).Official paper ↗Examiner report ↗Work through it with a tutor →

Weighted graphs, minimum spanning trees (Prim's algorithm)

• 2025General Mathematics SD (from 2023)Examination 1 Q351 markExpressing the total length of a minimum spanning tree in terms of an unknown edge weight variable.Official paper ↗Examiner report ↗Work through it with a tutor →

Shortest path problems in networks

• 2025General Mathematics SD (from 2023)Examination 1 Q381 markFinding the shortest route between two points through a weighted road network.Official paper ↗Examiner report ↗Work through it with a tutor →

Flow problems: capacity, cuts and maximum flow-minimum cut

• 2025General Mathematics SD (from 2023)Examination 1 Q371 markApplying max-flow min-cut to determine maximum water flow through a pipe network from source to sink.Official paper ↗Examiner report ↗Work through it with a tutor →

Assignment problems and the Hungarian algorithm

• 2025General Mathematics SD (from 2023)Examination 1 Q391 markVerifying the correct output table after two row/column reduction steps of the Hungarian algorithm on a cost matrix.Official paper ↗Examiner report ↗Work through it with a tutor →

Critical path analysis: activity networks, earliest/latest start times, float time, critical path, crashing

• 2025General Mathematics SD (from 2023)Examination 1 Q401 markCalculating the float time of a specific activity within a 12-activity project precedence network.Official paper ↗Examiner report ↗Work through it with a tutor →
• 2025General Mathematics SD (from 2023)Examination 2 Q184 marksIdentifying activities common to two critical paths, finding latest start time and greatest float time for named activities, and determining minimum crashing cost to reduce project duration by three days given per-activity cost/day tradeoffs.Official paper ↗Examiner report ↗Work through it with a tutor →