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VCE · VCE Units 3 & 4 · official past papers

VCE Foundation Mathematics past exams 2023–2025, by year and topic

The official VCAA exams, marking guides and examiner reports we index, organised by topic and subtopic and labelled with the study design it was written under. Open the official paper, work the question in your own workspace, or bring a tutor into it live.

Index last synced 19 August 2026.

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ATARMAxxing indexes 3 official VCAA Foundation Mathematics papers from 2023 to 2025, with 116 questions mapped to 5 areas of study. Every paper opens on the VCAA website.

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Mathematics Study Design (from 2023) · 2023–present

VCE Foundation Mathematics exams by year: official papers & marking guidance

Past exams indexed: 2025, 2024, 2023. Open the official VCAA papers, with marking guidance where available.

Year	Study design	Official paper(s)	Marking guidance
2025 VCE Foundation Mathematics exam	Mathematics Study Design (from 2023)	Written examination ↗	Marking guidance ↗
2024 VCE Foundation Mathematics exam	Mathematics Study Design (from 2023)	Written examination ↗	Marking guidance ↗
2023 VCE Foundation Mathematics exam	Mathematics Study Design (from 2023)	Written examination ↗	Marking guidance ↗

3 official papers across 3 years (2023–2025), 3 with marking guidance, published by VCAA.

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Pick a topic, open the exact question in the official paper, then work it in your own workspace — or hand the question straight to a live tutor session.

Units 3 and 4, AOS 1 — Algebra, number and structure · 25 mapped questions

Mathematical conventions, notation and order of operations

2025Mathematics Study Design (from 2023)Written examination Section B Q1a1 markFinds the average water volume per AI query from a total volume and a number of queries.Official paper ↗Marking guidance ↗Check tutors for this question →

Ratio, proportion and rates

2025Mathematics Study Design (from 2023)Written examination Section A Q11 markConverts a fuel price in cents per litre and a litres-per-100-km consumption rate into the fuel cost of a 420 km trip.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section A Q131 markFinds the volume of bleach in 60 litres of a cleaning solution mixed in a 2:13 ratio with water.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q5b2 marksCosts the fertiliser for the paddock from a 1:3 ingredient ratio, bag prices and a coverage rate per hectare.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q11a1 markWrites the simplest whole-number ratio of two OECD household electricity prices read from a bar graph.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q11 markScales a two-colour paint mix stated as a ratio to find the volume of the second colour.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q1c1 markWrites two quantities as a ratio in simplest whole-number form, in the stated order and with labels.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q3b2 marksWorks out the ingredient cost per tart from bulk unit prices and the quantity each recipe uses.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q11 markFinds the volume of water in a 270 mL medicine bottle mixed two parts concentrate to seven parts water.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q151 markCompares five in-game coin bundles on a unit-rate basis to find the best value.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q3a–e5 marksGarden spray recipe: scales a four-ingredient mixture to 5 L, finds the ceiling number of bottles needed, simplifies a ratio, splits a three-part ratio, and finds the minimum whole items to meet a daily nutrient requirement.Official paper ↗Marking guidance ↗Check tutors for this question →

Percentage change, mark-up, discount and percentage error

2025Mathematics Study Design (from 2023)Written examination Section A Q41 markCalculates the percentage increase in Australia's population between two census-era figures more than a century apart.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q2b2 marksApplies a 10 per cent change to a value and explains whether a stated requirement is met.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q21 markFinds the percentage error in a floor area when both room dimensions are rounded to the nearest whole metre.Official paper ↗Marking guidance ↗Check tutors for this question →

Direct and indirect variation

2025Mathematics Study Design (from 2023)Written examination Section B Q9b2 marksUses direct variation between cost share and volume to find the millilitres of milk in a cup, rounded by leading-digit approximation.Official paper ↗Marking guidance ↗Check tutors for this question →

Substitution into formulas

2024Mathematics Study Design (from 2023)Written examination Section B Q1d2 marksSubstitutes given values into a supplied rule and solves it for the remaining unknown.Official paper ↗Marking guidance ↗Check tutors for this question →

Transposition of formulas to find an unknown

2025Mathematics Study Design (from 2023)Written examination Section B Q6c2 marksTransposes a supplied after-tax income rule to recover the annual before-tax income from a fortnightly figure.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q51 markTransposes a square-root pendulum formula to find the length of a swing from its period.Official paper ↗Marking guidance ↗Check tutors for this question →

Simultaneous equations and break-even points

2025Mathematics Study Design (from 2023)Written examination Section A Q141 markReads a sales-versus-total-cost graph for a candle business to identify the break-even number of candles.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q4b2 marksCompares a flat per-head venue charge with a per-head-plus-fixed-cost venue to find the minimum guest count where the second is cheaper.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q51 markExtends two plotted lines to their intersection and uses it to find the distance an ambulance has travelled.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q2c2 marksSets up and solves a pair of simultaneous equations for the number of tickets bought in two reserves.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q31 markSolves two simultaneous ticket-price equations for the cost of one adult and one child cinema ticket.Official paper ↗Marking guidance ↗Check tutors for this question →

Floor and ceiling values and interval estimates

2025Mathematics Study Design (from 2023)Written examination Section A Q21 markFinds the floor value of the percentage error when a brick price is estimated upwards for a 420-brick wall.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q1b2 marksTurns a per-kilowatt-hour water-use range into a volume interval for a stated energy output, recorded as smallest and largest values.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Rational and irrational numbers in measurement contexts · Rounding, significant figures and leading-digit approximation · Checking results for accuracy and reasonableness — question-level mapping in progress; the year table above links every official paper.

Units 3 and 4, AOS 2 — Data analysis, probability and statistics · 35 mapped questions

Categorical, discrete and continuous data; survey design, audience and purpose

2025Mathematics Study Design (from 2023)Written examination Section B Q7c2 marksConverts two survey percentages into numbers of children from the sample size and finds the difference.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q3c2 marksExpresses the fibre in two tarts as a percentage of a stated reference value.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q2a–e5 marksSport participation lists by gender: identifies sports missing from one list, finds the smallest gender gap, rounds a percentage to four significant figures, compares two participation percentages, and reads a missing bar off a divided display.Official paper ↗Marking guidance ↗Check tutors for this question →

Tables, spreadsheets and choosing a form of display

2025Mathematics Study Design (from 2023)Written examination Section B Q7a1 markStates the most common mobile phone use in the earlier survey year from a paired bar display.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q1a1 markReads a data display to state the jurisdiction meeting a described condition.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q5a1 markStates the category identified by a described feature of the data display.Official paper ↗Marking guidance ↗Check tutors for this question →

Contemporary displays: pictogram, bubble, Mekko, radar, sunburst, heat map, stacked area

2025Mathematics Study Design (from 2023)Written examination Section B Q7d1 markPlots a missing data point onto a radar graph comparing mobile phone use across three age bands.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q71 markCompares three employees on one criterion using a multi-axis ratings display.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q81 markReads a stacked market-share chart for two years to identify which streaming services changed as described.Official paper ↗Marking guidance ↗Check tutors for this question →

Mean, median and mode

2025Mathematics Study Design (from 2023)Written examination Section A Q71 markWorks backwards from a required mean across five games to the minimum score needed in the last game.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section A Q201 markIdentifies the quarter holding the median value of a personal-savings percentage read from a time-series graph.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q2a1 markCalculates the mean diameter of five machined pistons.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q11c2 marksApplies a weighted-score rule to a table of criterion weightings and average ratings.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q91 markCalculates and compares two mean point scores and states the difference.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q91 markCalculates the mean of ten daily childcare rates, rounded to the nearest five cents.Official paper ↗Marking guidance ↗Check tutors for this question →

Range, percentiles, quantile intervals and cumulative frequency

2024Mathematics Study Design (from 2023)Written examination Section B Q4a1 markInterprets a 15th percentile on a growth chart as a percentage of the population above that weight.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q4b2 marksNames the two percentile curves a given weight falls between and describes the weight relative to each.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q71 markJudges which statements about a cumulative frequency curve of illness cases on a cruise ship are correct.Official paper ↗Marking guidance ↗Check tutors for this question →

Standard deviation

2023Mathematics Study Design (from 2023)Written examination Section B Q7a–d5 marksUnleaded petrol prices: states the median of 13 weekly values, finds the date of the largest Victoria-versus-national gap and the date prices start rising, then compares the two series using mean, range and standard deviation.Official paper ↗Marking guidance ↗Check tutors for this question →

Shape of distribution and outliers

2023Mathematics Study Design (from 2023)Written examination Section A Q81 markPredicts what adding one extreme speed reading does to the mean and the median of a 20-value data set.Official paper ↗Marking guidance ↗Check tutors for this question →

Interpolation, extrapolation and prediction

2025Mathematics Study Design (from 2023)Written examination Section A Q31 markReads a daily AUD/USD exchange-rate line graph to identify the pair of consecutive dates with the largest decrease.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q3a2 marksReads a days-before-and-after graph of monsoon start dates to name the first season starting after 19 December and its date.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q3b1 markCounts how many monsoon seasons started more than 10 days away from the reference date.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q7b1 markIdentifies the mobile phone use with the largest percentage increase between the two survey years.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q1b1 markFinds the difference between two percentages read off the display.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q4c.i1 markDraws a straight-line extrapolation of a percentile curve out to the right edge of a growth chart.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q4c.ii1 markReads a predicted weight for a three-year-old off the extrapolated line.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q61 markExpresses one account's follower count as a percentage of a stated total, using a most-followed bar chart.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q101 markReads a predicted goal count off a trend line drawn through a practice-time scatterplot.Official paper ↗Marking guidance ↗Check tutors for this question →

Long-term data, relative frequency and likelihood

2025Mathematics Study Design (from 2023)Written examination Section A Q121 markCombines two long-term relative frequencies for independent roads to find the likelihood of heavy traffic on both.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q3c1 markInterprets one plotted financial year of monsoon start-date data in context.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q6a–d5 marksNational electricity supply mix: totals the renewable share for one quarter, finds the combined fall in black and brown coal, describes the renewable versus non-renewable trend, and projects quarters until brown coal reaches zero.Official paper ↗Marking guidance ↗Check tutors for this question →

Errors, limitations and misrepresentation in statistics

2025Mathematics Study Design (from 2023)Written examination Section A Q181 markConverts a percentage quoted in a survey infographic back into a number of respondents from the stated sample size.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q3d1 markCounts the gaps in the series where consecutive recorded start dates are more than one year apart.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q61 markAdds the percentages of a daily recommended salt intake for several foods and finds by how much the maximum is exceeded.Official paper ↗Marking guidance ↗Check tutors for this question →

Units 3 and 4, AOS 3 — Discrete mathematics: financial and consumer mathematics · 28 mapped questions

Loans, mortgages, credit and debt consolidation

2025Mathematics Study Design (from 2023)Written examination Section A Q61 markApplies a 30 per cent of after-tax income guideline to find a suggested maximum monthly mortgage payment.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section A Q191 markApplies a per-annum simple interest rate over 23 days to an overdue credit-card balance and adds it to the principal.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q10a2 marksSeparates interest from principal in the first monthly repayment on a $400 000 loan at a stated monthly rate.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q10b1 markReads a stacked area amortisation chart to give the total number of repayments over the life of the loan.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q10c2 marksFinds the average interest paid per year from the total repaid and the amount borrowed, rounded to the nearest ten dollars.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q141 markCalculates the repayment on a stated borrowed amount.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q131 markReads a 30-year loan amortisation graph to estimate the monthly repayment.Official paper ↗Marking guidance ↗Check tutors for this question →

Investments, returns and superannuation

2025Mathematics Study Design (from 2023)Written examination Section A Q91 markCalculates an employer superannuation contribution at the guarantee rate on one week of casual gross pay.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q121 markChooses the statement correctly describing a long-run graph of annual superannuation returns.Official paper ↗Marking guidance ↗Check tutors for this question →

Personal income tax scales and marginal rates

2025Mathematics Study Design (from 2023)Written examination Section A Q81 markApplies a published Australian resident tax-rate table to find the tax payable on a stated annual taxable income.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q10a–d5 marksBuilder's tax and hire purchase: shows an annual taxable income after deductions, applies a marginal tax table, then finds the flat-rate interest, total paid and monthly repayment on a laptop payment plan.Official paper ↗Marking guidance ↗Check tutors for this question →

GST, invoicing and Business Activity Statements

2025Mathematics Study Design (from 2023)Written examination Section B Q4a3 marksCompletes the Amount column of a partly blank tax invoice, including the GST line, from unit prices excluding GST.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q121 markFinds a selling price by applying a mark-up and then adding GST.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q41 markAdds 10 per cent GST to a restaurant invoice and splits the total equally between three diners.Official paper ↗Marking guidance ↗Check tutors for this question →

Wages, payroll, commission and leave entitlements

2025Mathematics Study Design (from 2023)Written examination Section B Q9c2 marksFinds the minimum number of coffees needed to cover a barista's wage for an eight-hour shift.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q111 markApplies a tiered commission table to a month's sales value.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q111 markCombines ordinary hours with time-and-a-half Saturday hours to find a week's pay before tax.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q141 markApplies a banded commission table to a month's car sales and adds the base salary.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q8a–c5 marksBookstore payslip audit: finds weeks worked from year-to-date pay, shows the corrected weekly gross and superannuation figures, totals a year's superannuation, and finds the extra ordinary hours needed to reach a target net pay.Official paper ↗Marking guidance ↗Check tutors for this question →

Depreciation of assets

2023Mathematics Study Design (from 2023)Written examination Section B Q5a–d5 marksFlat-rate car depreciation: finds the value after one year, the years until the car falls below 10 per cent of its purchase price, the full-tank range from a fuel gauge, and the cost to refill using only $5, $10 and $20 pump buttons.Official paper ↗Marking guidance ↗Check tutors for this question →

Insurance, phone and internet plans, and hire purchase

2023Mathematics Study Design (from 2023)Written examination Section B Q9a–e5 marksZoo pricing: totals a bulk concession ticket sale, shows a mixed-ticket total, finds a senior discount as a percentage, strips GST from a ticket price, and compares annual membership with six single adult entries.Official paper ↗Marking guidance ↗Check tutors for this question →

Inflation, currency fluctuation and economic indicators

2025Mathematics Study Design (from 2023)Written examination Section A Q151 markMatches the percentage rise in a basket of grocery prices to the reported inflation rate of one listed year.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q11b2 marksCosts a year of dishwasher use in Australian dollars from a USD per kilowatt hour price and a stated exchange rate.Official paper ↗Marking guidance ↗Check tutors for this question →

Financial risk, budgeting and long-term financial data

2025Mathematics Study Design (from 2023)Written examination Section B Q6a2 marksShows that a mixed weekly and monthly expense table adds to a stated annual cost for two tenants.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q6b1 markFinds one tenant's maximum monthly savings after an equal share of the annual essential expenses.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q9a1 markShows that a stated percentage slice of a coffee's retail price equals a given cost in cents.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q2a1 markCosts three tickets in the same reserve, keeping the cents component in the total.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q4a–e5 marksElectric vehicle sales: finds two models' combined share of total sales, totals sales revenue for two models, applies a per-$200 stamp duty rate, and uses supplied sales and cost equations to find a break-even volume and a revised sale price.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Renting versus buying — question-level mapping in progress; the year table above links every official paper.

Units 3 and 4, AOS 4 — Space and measurement · 28 mapped questions

Names and properties of shapes and objects

2025Mathematics Study Design (from 2023)Written examination Section B Q8a1 markConverts the diameter of a netball centre circle from millimetres to a radius in metres.Official paper ↗Marking guidance ↗Check tutors for this question →

Plans, maps, elevations, nets and scale drawings

2025Mathematics Study Design (from 2023)Written examination Section A Q111 markUses a map scale bar to approximate the area of a park modelled as a rectangle.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q201 markCounts how many hexagonal shapes of a given side length fit a tessellated area of stated width and height.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q171 markUses a 1:60 model ratio to convert a real car length into the model's length in centimetres.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q12a–d5 marksPark map: measures a path length using the map scale, finds the area of a boundary made of a rectangle and a circular arc, applies a supplied formula for the width of an equilateral triangle section, and finds the resin volume for the tessellated path.Official paper ↗Marking guidance ↗Check tutors for this question →

Transformations, symmetry and similarity

2025Mathematics Study Design (from 2023)Written examination Section A Q51 markUses a set of similar triangles in a bridge-rail diagram to find an unknown height.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section A Q171 markIdentifies the reflected image of a number plate as it would appear in a rear-view mirror.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q181 markUses similar triangles formed by a camera lens to find the real height of a photographed flower.Official paper ↗Marking guidance ↗Check tutors for this question →

Metric conversion, derived and non-metric measures

2025Mathematics Study Design (from 2023)Written examination Section B Q1c2 marksConverts cubic metres to gigalitres and expresses a global AI water forecast as a whole-number percentage of Australia's annual use.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q5a1 markShows that a rectangular paddock of given length and width has an area of 96 hectares.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q161 markConverts a length given in metres to centimetres as part of a measurement comparison.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section A Q191 markConverts a Melbourne time to the corresponding Perth time across a two-hour time difference.Official paper ↗Marking guidance ↗Check tutors for this question →
2024Mathematics Study Design (from 2023)Written examination Section B Q3a1 markConverts a mass between metric units in a recipe context.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q1a–c5 marksMattress size guide: converts between centimetres and feet and inches, gives a missing imperial width, and finds the percentage increase in area from one bed size to the next.Official paper ↗Marking guidance ↗Check tutors for this question →

Rates, density and consumption

2025Mathematics Study Design (from 2023)Written examination Section B Q5c2 marksFinds the total spraying time from a boom width, a tractor speed and an allowance for turning.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q12a2 marksTransposes a density rule to find the volume in litres occupied by 20 kg of dry sand.Official paper ↗Marking guidance ↗Check tutors for this question →

Perimeter and area of compound shapes

2025Mathematics Study Design (from 2023)Written examination Section A Q101 markFinds the area of a rhombus floor tile from its side length and the shorter leg of the four right triangles inside it.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section A Q161 markCosts carpet sold per linear metre plus hourly installation for a compound office floor of a stated area.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q8b2 marksFinds the area of a uniform-width safety clearance zone surrounding a rectangular netball court.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q8c2 marksTotals the length of all painted line markings on a netball court, including two semicircles and the centre circle.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q191 markFinds the area of a uniform-width path surrounding a rectangular swimming pool.Official paper ↗Marking guidance ↗Check tutors for this question →

Surface area of solids

2023Mathematics Study Design (from 2023)Written examination Section A Q201 markFinds the glass needed for an open-topped rectangular fish tank.Official paper ↗Marking guidance ↗Check tutors for this question →

Volume and capacity

2025Mathematics Study Design (from 2023)Written examination Section B Q2c2 marksFinds the volume of an internal cylindrical space from a dimensioned diagram, converting mm³ to cm³ and rounding to three significant figures.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q12b1 markScales the volume of a two-thirds full sandbag up to the volume of a completely full one.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Mathematics Study Design (from 2023)Written examination Section B Q12c2 marksCounts the filled sandbags needed for a wall of given length and height, allowing for a fixed overlap on each bag.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section B Q11a–e5 marksHouse slab and tiling: finds the concrete volume and cost for a 100 mm slab from a floor plan, the capacity of a cylindrical water tank in litres, the minimum tiles for a brick-bond feature wall, and the cost of whole boxes of tiles.Official paper ↗Marking guidance ↗Check tutors for this question →

Tolerance, accuracy, precision and measurement error

2025Mathematics Study Design (from 2023)Written examination Section B Q2b2 marksSelects which of five measured piston diameters fall inside a stated ± tolerance about the specified diameter.Official paper ↗Marking guidance ↗Check tutors for this question →
2023Mathematics Study Design (from 2023)Written examination Section A Q161 markRewrites a minimum-and-maximum machine tolerance for nail length in the ± form.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Angle properties and Pythagoras' theorem — question-level mapping in progress; the year table above links every official paper.

The rest of the study design

Question-level mapping for this area is still being verified. Every official paper covering them is in the year table above.

Units 1 and 2 — assumed knowledge (not externally examined) — Algebra, number and structure: integers, fractions, decimals, ratio, rate and estimation · Data analysis, probability and statistics: collecting, tabulating and representing data · Discrete mathematics: banking, bills, pay rates, payslips, personal tax and superannuation · Space and measurement: metric units, reading scales, time, dates, schedules and timetables

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