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HSC · HSC Year 12 · official past papers

HSC Mathematics Standard 2 past exams 2019–2025, by year and topic

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ATARMAxxing indexes 14 official NESA Mathematics Standard 2 papers from 2019 to 2025, with 63 questions mapped to 5 topics. Every paper opens on the NESA website.

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2017 Mathematics Standard Syllabus (Standard 2 pathway) · 2019–2025

HSC Mathematics Standard 2 exams by year: official papers & marking guidance

Past exams indexed: 2025, 2024, 2023, 2022, 2021, 2020, 2019. Open the official NESA papers.

YearStudy designOfficial paper(s)Marking guidance
2025 HSC Mathematics Standard 2 exam2017 Mathematics Standard Syllabus (Standard 2 pathway)Exam ↗ · Marking guidelines ↗—
2024 HSC Mathematics Standard 2 exam2017 Mathematics Standard Syllabus (Standard 2 pathway)Exam ↗ · Marking guidelines ↗—
2023 HSC Mathematics Standard 2 exam2017 Mathematics Standard Syllabus (Standard 2 pathway)Exam ↗ · Marking guidelines ↗—
2022 HSC Mathematics Standard 2 exam2017 Mathematics Standard Syllabus (Standard 2 pathway)Exam ↗ · Marking guidelines ↗—
2021 HSC Mathematics Standard 2 exam2017 Mathematics Standard Syllabus (Standard 2 pathway)Exam ↗ · Marking guidelines ↗—
2020 HSC Mathematics Standard 2 exam2017 Mathematics Standard Syllabus (Standard 2 pathway)Exam ↗ · Marking guidelines ↗—
2019 HSC Mathematics Standard 2 exam2017 Mathematics Standard Syllabus (Standard 2 pathway)Exam ↗ · Marking guidelines ↗—

14 official papers across 7 years (2019–2025), published by NESA.

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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.

Algebra · 7 mapped questions

Types of relationships (linear, quadratic, exponential, inverse variation modelling)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q91 markMultiple-choice: apply inverse variation to find how long a task takes with a different number of workers.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q223 marksComplete a table comparing two exponential growth/decay population models by finding an initial value, percentage rate of change, and a predicted future population from a graph.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q215 marksCompare two linear electricity-pricing plans by completing a charge table, graphing one plan against the other, and finding the break-even usage and cost difference at a given usage level.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q223 marksDetermine the constant of proportionality in a direct-square variation model (braking distance vs speed) and use it to predict a value at a new speed.Official paper ↗Check tutors for this question →

Simultaneous linear equations

Non-linear relationships and their graphs

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q263 marksUse a quadratic area model and its graph to find the width and corresponding height that maximise the cross-sectional area of a folded gutter.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q203 marksRead a quadratic height-versus-time graph to find a maximum value and the two times at which the function reaches a given fraction of that maximum.Official paper ↗Check tutors for this question →

Measurement · 18 mapped questions

Non-right-angled trigonometry (sine rule, cosine rule, area of triangle, bearings, radial surveys)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q61 markMultiple-choice: select the correct trigonometric expression for an unknown side length in a right triangle diagram.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q364 marksUse the sine rule across two connected triangles on sloping ground to find the heights of two vertical flagpoles.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q403 marksUse a compass radial survey with given distances and bearings, plus a collinearity condition, to find the bearing of one point from the survey origin.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q274 marksUse bearings and given distances between three locations to find one internal distance, then determine the bearing of a third point from the reference point.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q353 marksCalculate the area of a triangle using the two-sides-and-included-angle area formula, given one side length and two angles requiring an angle-sum step.Official paper ↗Check tutors for this question →

Rates and ratios (unit conversion, best buys, mixing ratios, speed)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q172 marksCalculate the cost of running an electrical appliance for a given time at a stated per-kWh electricity rate, converting watts to kilowatts.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q244 marksApply a blood-alcohol-content formula to compute a BAC value from drinks consumed and time elapsed, then use a related formula to find the time for BAC to return to zero.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q333 marksConvert a running speed in km/h and distance in metres to find the time in seconds to cover that distance.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q265 marksFind the area of an L-shaped path around a garden, then use a three-part mixing ratio to determine the quantity of one material (in whole bags) needed for a target mix weight.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q364 marksRearrange and apply a blood-alcohol-content formula to back-calculate the start time of drinking given a known BAC reading at a later time.Official paper ↗Check tutors for this question →

Further applications of area and volume (composite shapes, trapezoidal rule, surface area, volume of solids)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q324 marksFind the area of a shaded circular segment region outside a regular pentagon inscribed in a circle of given radius.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q344 marksFind the total surface area of a composite solid (cylinder with hemispherical ends) sized to exactly contain three spheres of known diameter.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q383 marksUse a given volume ratio between a cylindrical and conical section of a cake to find total volume, then determine how many equal-volume slices can be cut.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q245 marksApply two applications of the trapezoidal rule to estimate a cross-sectional area, then use uniform thickness and material density to find the total weight of concrete required.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q334 marksFind the perimeter of a composite shape formed by a rectangle with a circular arc replacing one side, using arc length and given angle/radius.Official paper ↗Check tutors for this question →

Latitude, longitude and time zones

Rates and ratios

Financial Mathematics · 16 mapped questions

Annuities (future value, present value, annuity tables)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q203 marksUse a future-value annuity factor table to find an investment's value after regular annual deposits, then determine a required six-monthly contribution to reach a savings target.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q414 marksUse present-value annuity factor tables to find the minimum initial deposit needed to fund two different phases of scheduled monthly withdrawals over 25 years.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q255 marksUse a future-value annuity factor table to find the required periodic contribution to reach a savings goal, then compute the final balance for a different quarterly contribution scenario.Official paper ↗Check tutors for this question →

Depreciation (straight-line and declining-balance methods)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q294 marksCalculate total asset depreciation over ten years where the method switches partway from straight-line to declining-balance depreciation.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q283 marksCompare straight-line versus declining-balance depreciation methods over a fixed period to determine which produces the lower salvage value, with supporting calculations.Official paper ↗Check tutors for this question →

Investments and loans

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q213 marksComplete a reducing-balance loan amortisation spreadsheet for two months, then explain why fixed repayments below the interest charged mean the loan is never repaid.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q233 marksGiven total weekly earnings including a base rate and time-and-a-half overtime, solve for the number of overtime hours worked.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q253 marksCompare total interest earned on equal principal amounts under simple interest versus quarterly-compounding interest over the same period to determine which investor ends up ahead.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q273 marksDetermine the extra total amount repaid on a loan when the monthly repayment is reduced partway through the term, extending the repayment period.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q11 markMultiple-choice: calculate simple interest earned over two years on a given principal and annual rate.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q61 markMultiple-choice: back-calculate the GST component included in a stated GST-inclusive price.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q101 markMultiple-choice: select the correct compound-interest expression for an investment compounding quarterly over several years.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q294 marksUse a monthly-repayment-per-$1000 table to compute total repayments on a home loan, then reverse the calculation to find a loan principal from a given monthly repayment.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q303 marksGiven a receipt total and the GST amount charged, work backward to find the value of GST-exempt items on the receipt.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q324 marksCalculate daily-compounding credit card interest on a single purchase repaid after a set number of days, then express that interest as a percentage of the total repaid.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q373 marksUse a marginal income-tax rate table and a known effective tax percentage at a given income to solve for an unknown marginal rate in one tax bracket.Official paper ↗Check tutors for this question →

Also in this topic: Investments and loans (simple and compound interest, GST, income tax, wages/overtime) — question-level mapping in progress; the year table above links every official paper.

Statistical Analysis · 14 mapped questions

Bivariate data analysis (scatterplots, correlation, least-squares regression line)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q193 marksRead the equation of a least-squares regression line from a scatterplot, then use it to judge whether a new data point performed better or worse than predicted.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q303 marksState three qualitative observations about the relationship between age and length for two animal groups shown on a scatterplot, without calculation.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q346 marksPlot the mean point and y-intercept of a least-squares regression line from summary statistics, state the regression equation, and identify a limitation of extrapolating it beyond the data range.Official paper ↗Check tutors for this question →

The normal distribution (z-scores, empirical rule)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q51 markMultiple-choice: compare relative performance across subjects with different normal-distribution means and standard deviations by reasoning about z-scores.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q355 marksUse a standard normal probability table and z-scores to find a percentage of exam scores in a range, explain a symmetry relationship, and estimate a cut-off score for a top percentile.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q384 marksUse a standard normal probability table and known mean/standard deviation to find the expected count of a population exceeding a given weight threshold.Official paper ↗Check tutors for this question →

Sampling and data collection (sampling methods, bias)

Data displays and summary statistics (box plots, histograms, two-way tables, measures of central tendency and spread)

The normal distribution

Bivariate data analysis

Probability

Also in this topic: Probability (relative frequency, tree diagrams, conditional and compound probability) — question-level mapping in progress; the year table above links every official paper.

Networks · 8 mapped questions

Critical path analysis (activity charts, forward/backward scanning, float time, project crashing)

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q393 marksDetermine a project's critical path and an unknown activity duration from partial earliest/latest start time data, then find the maximum float between two other activities.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q314 marksIdentify two critical paths in an activity network, then determine which single task to shorten (and by how much) to reduce the overall project time by a set amount.Official paper ↗Check tutors for this question →

Network concepts

  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q41 markMultiple-choice: count the number of edges needed in a network diagram representing shared borders between regions on a map.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q164 marksFind the shortest path between two towns in a distance network, then re-solve the shortest path between a different pair after one connecting road is removed.Official paper ↗Check tutors for this question →
  • 20242017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q183 marksDraw a minimum spanning tree for a weighted network and state its total weight, then explain whether an alternative minimum spanning tree of equal weight exists.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q141 markMultiple-choice: interpret a network cut to determine bounds on the maximum flow between a source and a sink.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q173 marksComplete a network diagram of flight distances between cities from a partially filled distance table, then compute total travel distance for a two-leg journey.Official paper ↗Check tutors for this question →
  • 20232017 Mathematics Standard Syllabus (Standard 2 pathway)Exam Q194 marksIdentify the shortest-time path between two points in a weighted running-track network, then justify whether a given spanning tree is a minimum spanning tree.Official paper ↗Check tutors for this question →

Also in this topic: Network concepts (network diagrams, shortest path, minimum spanning trees, network flow/maximum flow) — question-level mapping in progress; the year table above links every official paper.

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