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VCE · VCE Units 3 & 4 · official past papers

VCE Mathematical Methods past exams 2010–2025, by year and topic

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Index last synced 19 August 2026.

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ATARMAxxing indexes 34 official VCAA Mathematical Methods papers from 2010 to 2025, with 84 questions mapped to 4 areas of study. Every paper opens on the VCAA website.

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Mathematical Methods (CAS) SD 2006–2015 · 2006–2015SD 2016–2022 · 2016–2022SD 2023–2027 (current) · 2023–2027

VCE Mathematical Methods exams by year: official papers & marking guidance

Past exams indexed: 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010. Open the official VCAA papers, with marking guidance where available.

Year	Study design	Official paper(s)	Marking guidance
2025 VCE Mathematical Methods exam	SD 2023–2027 (current)	Exam 1 ↗ · Exam 2 ↗ · Exam 1 Assessment Guide ↗ · Exam 2 Assessment Guide ↗	Marking guidance ↗
2024 VCE Mathematical Methods exam	SD 2023–2027 (current)	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2023 VCE Mathematical Methods exam	SD 2023–2027 (current)	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2022 VCE Mathematical Methods exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2021 VCE Mathematical Methods exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2020 VCE Mathematical Methods exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2019 VCE Mathematical Methods exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2018 VCE Mathematical Methods exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2017 VCE Mathematical Methods exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2016 VCE Mathematical Methods exam	SD 2016–2022	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2015 VCE Mathematical Methods exam	Mathematical Methods (CAS) SD 2006–2015	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2014 VCE Mathematical Methods exam	Mathematical Methods (CAS) SD 2006–2015	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2013 VCE Mathematical Methods exam	Mathematical Methods (CAS) SD 2006–2015	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2012 VCE Mathematical Methods exam	Mathematical Methods (CAS) SD 2006–2015	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2011 VCE Mathematical Methods exam	Mathematical Methods (CAS) SD 2006–2015	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗
2010 VCE Mathematical Methods exam	Mathematical Methods (CAS) SD 2006–2015	Exam 1 ↗ · Exam 2 ↗	Marking guidance ↗

34 official papers across 16 years (2010–2025), 16 with marking guidance, published by VCAA. These span more than one study design; the most recent is SD 2023–2027 (current). Earlier papers may cover material that has since changed.

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Functions, relations and graphs · 18 mapped questions

Graphs of polynomial functions and their key features

2024SD 2023–2027 (current)Exam 1 Q7b.ii1 markDetermine the range of the derivative function over a restricted sub-interval.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q7c3 marksSketch the derivative graph of an x·sin(x)-type function over a symmetric domain, labelling endpoints.Official paper ↗Marking guidance ↗Check tutors for this question →

Graphs of power, exponential, logarithmic and circular functions and their key features

2024SD 2023–2027 (current)Exam 1 Q3a3 marksSketch a transformed reciprocal-square function labelling its asymptotes and intercepts.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q8a1 markFind the y-intercept of a shifted cube-root function in terms of its parameters.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q11 markMultiple choice: identify the asymptote(s) of a shifted log function.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q151 markMultiple choice: locate the points of inflection of a transformed tangent function.Official paper ↗Marking guidance ↗Check tutors for this question →

Transformations of the plane applied to these functions and their inverse transformations

2024SD 2023–2027 (current)Exam 1 Q5b2 marksIdentify a sequence of two transformations linking an original population model to a modified decreasing version of it.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q121 markMultiple choice: identify the graph resulting from a horizontal dilation-and-translation transformation of a given piecewise-looking curve.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q131 markMultiple choice: find the local minimum of a reciprocal function after a dilation and translation are applied.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1d.i1 markDescribe a translation-only transformation mapping one quartic's local maximum onto another's.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1d.ii2 marksDescribe a dilation-and-translation transformation mapping both local minimums of one quartic onto another's.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q3a.ii2 marksFind translation parameters mapping a cubic sales model onto a shifted version with a specified new local maximum.Official paper ↗Marking guidance ↗Check tutors for this question →

Graphs of sum, difference, product and composite functions of the specified function types

2024SD 2023–2027 (current)Exam 2 Section B Q3b.i2 marksExtend a graph of a linear-plus-cosine-terms sales model over a further time interval, labelling the endpoint.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5a.i1 markFind the coordinates of a local maximum of a sine-of-sine composite function on a restricted interval.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5a.ii1 markState the range of a sine-of-sine composite function over a full period.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5b.iv1 markState the range of the sine-of-double-angle composite over one full period.Official paper ↗Marking guidance ↗Check tutors for this question →

Modelling practical situations using polynomial, power, circular, exponential and logarithmic functions and simple piecewise (hybrid) functions

2024SD 2023–2027 (current)Exam 1 Q5a1 markEvaluate a rational population-growth model at a given time value.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q3b.ii1 markDetermine the annual increase predicted by the linear-trend component of a sales model.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Relation between the graph of an original function and a transformed function, including families of transformed functions — question-level mapping in progress; the year table above links every official paper.

Algebra, number and structure · 16 mapped questions

Solution of polynomial equations with real coefficients of degree n, including numerical solutions

2024SD 2023–2027 (current)Exam 2 Section A Q171 markMultiple choice: trace through a pseudocode algorithm to determine the order in which it prints a cubic's roots.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1a1 markState the x-intercepts of a factorised quartic in terms of a parameter.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1b.i2 marksFind parameter values for which a factorised quartic has exactly three distinct x-intercepts.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1b.ii1 markFind the parameter values for which a factorised quartic has exactly four distinct x-intercepts.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5b.ii2 marksProve that a cosine-of-sine equation has no real solutions by bounding the relevant expressions.Official paper ↗Marking guidance ↗Check tutors for this question →

Functions and their inverses, including conditions for existence of an inverse function

2024SD 2023–2027 (current)Exam 2 Section A Q61 markMultiple choice: find the rule and domain of the inverse of a rational function.Official paper ↗Marking guidance ↗Check tutors for this question →

Composition of functions

2024SD 2023–2027 (current)Exam 2 Section A Q51 markMultiple choice: determine the range of a composite of a restricted quadratic and an exponential decay function.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5d2 marksFind the domain values for which a further composition with a restricted sine function is defined.Official paper ↗Marking guidance ↗Check tutors for this question →

Solution of equations f(x) = g(x) over a specified interval by graphical, numerical and algebraic methods

2024SD 2023–2027 (current)Exam 2 Section B Q2d1 markFind the time at which two competing temperature models predict equal values.Official paper ↗Marking guidance ↗Check tutors for this question →

Solution of literal equations and general solution of equations involving a single parameter

2024SD 2023–2027 (current)Exam 1 Q64 marksSolve a logarithmic equation combining a doubled and a single log term using log laws.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q8c1 markExpress one parameter in terms of another given that a cube-root graph passes through the origin.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q81 markMultiple choice: identify a guaranteed x-intercept of a difference of two functions from a table of values.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2f.i1 markUse continuity of a piecewise power-usage function to solve for an unknown parameter.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q3a.i3 marksFit a cubic sales model's coefficients using given local maximum and minimum conditions.Official paper ↗Marking guidance ↗Check tutors for this question →

Solution of simple systems of simultaneous linear equations, including no-solution and infinite-solution cases

2024SD 2023–2027 (current)Exam 1 Q23 marksFind the parameter value that makes a pair of simultaneous linear equations with a parameter have no real solution.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1c.iv2 marksFind the intersection point of two tangent lines to the quartic at two specified irrational x-values.Official paper ↗Marking guidance ↗Check tutors for this question →

Calculus · 30 mapped questions

Derivatives of polynomial, power, exponential, logarithmic and circular functions, and of sums, products, quotients and composites of these

2024SD 2023–2027 (current)Exam 1 Q1a1 markDifferentiate a product of an exponential and a cosine function using the product rule.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q1b2 marksEvaluate the derivative of a log-of-cubic composite function at a specified point.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q7b.i1 markDifferentiate a product of x and sin(x) using the product rule.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q8b2 marksFind the gradient of a cube-root function at its y-intercept in terms of a parameter.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q161 markMultiple choice: find the tangent gradient to a square-root-of-function graph using given value and derivative data at a point.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1c.i1 markDifferentiate a specific quartic given as a product of two squared linear factors.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2a2 marksExpress the derivative of a two-piece hybrid temperature model as a hybrid function.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2c.i1 markDifferentiate an exponential-decay temperature model.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q3b.iii1 markDifferentiate a sales model combining a linear term with two cosine terms of different periods.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5b.i1 markDifferentiate a composite of sine and sine-of-double-angle functions using the chain rule.Official paper ↗Marking guidance ↗Check tutors for this question →

Application of differentiation to graph sketching, key features and optimisation problems

2024SD 2023–2027 (current)Exam 1 Q7b.iii1 markUse a sign-change argument on the derivative's range to verify a stationary point exists on a sub-interval.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q8d3 marksFind the coordinates of a second point on a cube-root curve where the gradient matches the gradient at the y-intercept.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q101 markMultiple choice: deduce a valid conclusion about a function's behaviour from sign information about its derivative at two points.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q181 markMultiple choice: optimise a trapezium's dimensions to maximise its area subject to a fixed slant-side constraint.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1c.ii1 markFind the coordinates of the local maximum of the specific quartic.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q1c.iii1 markFind the interval(s) on which the specific quartic's derivative is positive.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2c.ii1 markSolve numerically for the time at which the exponential model's instantaneous rate of change equals a target value.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2e1 markFind the time at which the gap between two competing temperature models is greatest.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q3b.iv2 marksFind the maximum instantaneous rate of change of the sales model and the times at which it occurs.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5b.iii1 markFind the x-values of stationary points of a sine-of-double-angle composite over one full period.Official paper ↗Marking guidance ↗Check tutors for this question →

Anti-derivatives of polynomial and other standard functions

2024SD 2023–2027 (current)Exam 2 Section A Q21 markMultiple choice: recover a function value from its cubic-minus-linear derivative and a boundary condition.Official paper ↗Marking guidance ↗Check tutors for this question →

Definite integrals, the trapezium rule, and the fundamental theorem of calculus

2024SD 2023–2027 (current)Exam 1 Q7a3 marksApproximate the area under an x·sin(x)-type curve using the trapezium rule with a specified step size.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q41 markMultiple choice: combine two given definite integrals over adjacent intervals to evaluate a third.Official paper ↗Marking guidance ↗Check tutors for this question →

Application of integration to area under/between curves, average value of a function, and rates of change problems

2024SD 2023–2027 (current)Exam 1 Q3b2 marksFind the area of a region bounded by a vertical line, both axes and a transformed reciprocal-square curve.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q201 markMultiple choice: use a function's average value and periodicity property to evaluate a definite integral over a shifted interval.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2b1 markFind the average rate of change of a temperature model over a specified time interval.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2f.ii1 markFind the time at which cumulative energy usage (area under a power-time graph) reaches a specified value.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q2f.iii2 marksFind the time at which cumulative energy usage reaches a larger specified value, correct to two decimal places.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5c.i1 markWrite a single definite integral for the area between two related sinusoidal composite curves.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q5c.ii1 markState the numerical value of the enclosed area between the two sinusoidal composite curves.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this areas of study: Graphical treatment of limits, continuity and differentiability — question-level mapping in progress; the year table above links every official paper.

Data analysis, probability and statistics · 20 mapped questions

Discrete random variables: probability mass functions, mean, variance and standard deviation

2024SD 2023–2027 (current)Exam 2 Section A Q31 markMultiple choice: compute a conditional probability from a discrete distribution table with an unknown constant.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q91 markMultiple choice: apply Bayes-style reasoning to a two-group scenario to find a conditional probability given a shared outcome.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q111 markMultiple choice: compute a hypergeometric-style seating probability for a fixed-size random selection.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4c.ii2 marksComplete a probability distribution table for the number of heavy luggage pieces per traveller.Official paper ↗Marking guidance ↗Check tutors for this question →

Bernoulli trials and the binomial distribution

2024SD 2023–2027 (current)Exam 1 Q4a1 markFind the standard deviation of a given binomial random variable.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 1 Q4b2 marksCalculate a cumulative binomial probability for a strict-inequality event.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section A Q71 markMultiple choice: find the minimum number of repeated die rolls for a target at-least-once probability threshold.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4c.i1 markVerify a stated binomial probability for a traveller checking in two heavy pieces of luggage.Official paper ↗Marking guidance ↗Check tutors for this question →

Continuous random variables: probability density functions, mean, variance and standard deviation

2024SD 2023–2027 (current)Exam 2 Section A Q141 markMultiple choice: evaluate a probability from a piecewise-linear probability density function with an unknown constant.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4a1 markWrite a definite integral expression for the probability that luggage mass exceeds a threshold.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4b.i1 markFind the mean of a continuous random variable given its probability density function.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4b.ii2 marksFind the standard deviation of the continuous random variable modelling luggage mass.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4b.iii2 marksFind the conditional probability that luggage is labelled heavy given its mass exceeds the mean.Official paper ↗Marking guidance ↗Check tutors for this question →

The normal distribution, including standard and transformed normal distributions

2024SD 2023–2027 (current)Exam 2 Section A Q191 markMultiple choice: use two tail-probability conditions on a normal variable to find a third probability.Official paper ↗Marking guidance ↗Check tutors for this question →

Statistical inference: sample proportions, distribution of sample proportions and simulation

2024SD 2023–2027 (current)Exam 1 Q5c.ii1 markFind the minimum sample size needed for a target standard deviation of the sample proportion.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4d.i2 marksFind the probability that a sample proportion of heavy luggage exceeds a threshold, without a normal approximation.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4d.ii2 marksFind the probability the sample proportion lies within one standard deviation of its mean, without a normal approximation.Official paper ↗Marking guidance ↗Check tutors for this question →

Approximate confidence intervals for a population proportion, including the 95% confidence interval

2024SD 2023–2027 (current)Exam 1 Q5c.i2 marksConstruct an approximate 95% confidence interval for a population proportion from survey data.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4e.i1 markConstruct an approximate 90% confidence interval for a population proportion from a sample of 50.Official paper ↗Marking guidance ↗Check tutors for this question →
2024SD 2023–2027 (current)Exam 2 Section B Q4e.ii1 markDetermine the minimum and maximum sample counts consistent with a wider 90% confidence interval from a second sample.Official paper ↗Marking guidance ↗Check tutors for this question →

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