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HSC · HSC Year 12 · official past papers

HSC Mathematics Extension 1 past exams 2015–2025, by year and topic

The official NESA 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.

Papers, marking guides and examiner reports open on the official NESA website — they stay official and up to date. Question descriptions below are our own; we never republish exam content. Prefer to be walked through it? See the tutor directory →

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ATARMAxxing indexes 22 official NESA Mathematics Extension 1 papers from 2015 to 2025, with 32 questions mapped to 7 topics. Every paper opens on the NESA website.

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Pre-2017 syllabus (3 Unit era Extension 1 course) · 2015–2019Mathematics Extension 1 Stage 6 Syllabus (2017) · 2020–2026Mathematics Extension 1 11-12 Syllabus (2024) · 2027–present

HSC Mathematics Extension 1 exams by year: official papers & marking guidance

Past exams indexed: 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016, 2015. Open the official NESA papers, with marking guidance where available.

Year	Study design	Official paper(s)	Marking guidance
2025 HSC Mathematics Extension 1 exam	SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)	Exam ↗ · Marking Guidelines ↗	Marking guidance ↗
2024 HSC Mathematics Extension 1 exam	SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)	Exam ↗ · Marking Guidelines ↗	Marking guidance ↗
2023 HSC Mathematics Extension 1 exam	SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)	Exam ↗ · Marking Guidelines ↗	Marking guidance ↗
2022 HSC Mathematics Extension 1 exam	SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)	Exam ↗ · Marking Guidelines ↗	Marking guidance ↗
2021 HSC Mathematics Extension 1 exam	SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)	Exam ↗ · Marking Guidelines ↗	Marking guidance ↗
2020 HSC Mathematics Extension 1 exam	SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017) - first year examined under this syllabus	Exam ↗ · Marking Guidelines ↗	Marking guidance ↗
2019 HSC Mathematics Extension 1 exam	Pre-2017 syllabus (final year of the old 3-Unit-era Extension 1 course)	Exam (archive) ↗ · Marking Guidelines (archive) ↗	Marking guidance ↗
2018 HSC Mathematics Extension 1 exam	Pre-2017 syllabus (old 3-Unit-era Extension 1 course)	Exam (archive) ↗ · Marking Guidelines (archive) ↗	Marking guidance ↗
2017 HSC Mathematics Extension 1 exam	Pre-2017 syllabus (old 3-Unit-era Extension 1 course)	Exam (archive) ↗ · Marking Guidelines (archive) ↗	Marking guidance ↗
2016 HSC Mathematics Extension 1 exam	Pre-2017 syllabus (old 3-Unit-era Extension 1 course)	Exam (archive) ↗ · Marking Guidelines (archive) ↗	Marking guidance ↗
2015 HSC Mathematics Extension 1 exam	Pre-2017 syllabus (old 3-Unit-era Extension 1 course)	Exam (archive) ↗ · Marking Guidelines (archive) ↗	Marking guidance ↗

22 official papers across 11 years (2015–2025), 11 with marking guidance, published by NESA. These span more than one study design; the most recent is Mathematics Extension 1 11-12 Syllabus (2024). Earlier papers may cover material that has since changed.

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Trigonometric Functions · 5 mapped questions

Inverse trigonometric functions

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q14(d)3 marksDifferentiate a composite of inverse and ordinary trigonometric functions on a restricted domain.Official paper ↗Marking guidance ↗Check tutors for this question →

Trigonometric equations

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q11(b)3 marksSolve a trigonometric equation involving a double-angle identity over a restricted domain.Official paper ↗Marking guidance ↗Check tutors for this question →
2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q61 markMultiple-choice: find the general solution of a quadratic-in-sine trigonometric equation.Official paper ↗Marking guidance ↗Check tutors for this question →

Applications of trigonometric functions

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q14(c)3 marksModel clock-hand positions with trigonometric parametrisation and find the times the hands are first and second perpendicular after midnight.Official paper ↗Marking guidance ↗Check tutors for this question →

Applications of trigonometric functions - old syllabus SHM

2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q13(a)4 marksModel a tide using simple harmonic motion and find the earliest time the tide rises at its fastest rate. Old syllabus era; SHM sits outside the current topics array.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this topic: Further trigonometric identities — question-level mapping in progress; the year table above links every official paper.

Calculus · 8 mapped questions

Further calculus skills

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q101 markMultiple-choice: apply inverse-function differentiation rules twice to find the second derivative of an inverse function at a point.Official paper ↗Marking guidance ↗Check tutors for this question →

Further applications of calculus

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q12(a)3 marksRelated-rates problem: find the rate of change of a sector's radius given a constant area and a known rate of change of angle.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q12(d)3 marksSolve a separable first-order differential equation with a logistic-type right-hand side, given an initial condition.Official paper ↗Marking guidance ↗Check tutors for this question →
2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q12(a)6 marksRelated-rates problem for a leaking conical container: relate radius to height, derive dV/dh, then find dh/dt and the rate of volume change at a given height.Official paper ↗Marking guidance ↗Check tutors for this question →
2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q12(b)5 marksSet up and solve a first-order differential equation modelling a chemical reaction where mass transfer rate is proportional to the remaining reactant, given an initial rate.Official paper ↗Marking guidance ↗Check tutors for this question →

Further applications of calculus (projectile motion)

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q14(b)4 marksTwo-particle projectile scenario: show that a velocity ratio between two horizontally-launched particles landing at the same point depends only on a height ratio.Official paper ↗Marking guidance ↗Check tutors for this question →

Applications of calculus - old syllabus simple harmonic motion

2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q71 markMultiple-choice: find the maximum velocity of a particle whose displacement is a sum of sine and cosine terms. Old syllabus era; SHM sits outside the current topics array.Official paper ↗Marking guidance ↗Check tutors for this question →

Further applications of calculus - old syllabus projectile motion via parametrics

2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q13(b)7 marksMulti-part projectile-motion problem: prove a maximum-height formula, find the height at which a projectile strikes a wall, then analyse its rebound trajectory to the ground. Old syllabus era; projectile motion via parametrics has no direct current-topic equivalent.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this topic: Rates of change — question-level mapping in progress; the year table above links every official paper.

Combinatorics · 4 mapped questions

Permutations and combinations

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q13(b)2 marksCount circular seating arrangements for a group of guests subject to a must-not-sit-together restriction.Official paper ↗Marking guidance ↗Check tutors for this question →
2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q81 markMultiple-choice: count team selections from a group subject to an at-least-one composition constraint.Official paper ↗Marking guidance ↗Check tutors for this question →

The binomial theorem

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q13(e)3 marksProve a binomial-coefficient telescoping identity using the Pascal's triangle recurrence.Official paper ↗Marking guidance ↗Check tutors for this question →
2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q14(b)3 marksDerive two standard binomial-coefficient identities from the binomial expansion, then combine them to prove a weighted-sum identity.Official paper ↗Marking guidance ↗Check tutors for this question →

Proof · 8 mapped questions

Proof by mathematical induction

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q12(c)3 marksProve a summation identity involving factorials by mathematical induction.Official paper ↗Marking guidance ↗Check tutors for this question →
2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q14(a)4 marksFactorise a cubic expression, then use the result to prove a summation identity by mathematical induction.Official paper ↗Marking guidance ↗Check tutors for this question →

Sum and product of roots (polynomials)

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q11(f)2 marksUse root-coefficient relationships for a cubic to evaluate a symmetric expression in its roots.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q14(e)3 marksUse a cubic's roots expressed as tangents of three angles to find the smallest positive value of the angle sum.Official paper ↗Marking guidance ↗Check tutors for this question →

Proof techniques (divisibility)

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q14(a)2 marksProve a divisibility claim about the product of a chosen set of distinct factors of a fixed integer.Official paper ↗Marking guidance ↗Check tutors for this question →

Sum and product of roots (polynomials) - old syllabus series notation

2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q11 markMultiple-choice: identify which expanded series matches a given sigma-notation summation. Old syllabus era; no direct current-topic equivalent.Official paper ↗Marking guidance ↗Check tutors for this question →

Geometric proof - old syllabus circle geometry

2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q13(c)4 marksCircle-geometry proof: show a quadrilateral formed by two chords and their intersection points is cyclic, then use this to prove a perpendicularity result. Old syllabus era; circle-geometry proof has no direct current-topic equivalent.Official paper ↗Marking guidance ↗Check tutors for this question →

Locus and parametric proof - old syllabus parabola geometry

2016Pre-2017 syllabus (old 3-Unit-era Extension 1 course)Exam Q14(c)7 marksParabola locus problem: find coordinates of a point on the directrix, show a related point traces a second parabola, state its focal length, then minimise the distance between two points on the two parabolas. Old syllabus era; parabola-locus geometry has no direct current-topic equivalent.Official paper ↗Marking guidance ↗Check tutors for this question →

Vectors · 5 mapped questions

Introduction to vectors

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q21 markMultiple-choice: compute the vector projection of one 2D vector onto another.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q81 markMultiple-choice: determine what must be true about the relative position of three collinear points defined by position vectors.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q91 markMultiple-choice: use a vector-sum-to-zero condition and given magnitudes to find the angle between two of three vectors.Official paper ↗Marking guidance ↗Check tutors for this question →
2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q11(e)1 markFind the unknown component that makes one given vector parallel to another.Official paper ↗Marking guidance ↗Check tutors for this question →

Further work with vectors (calculus of vectors)

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q13(c)4 marksGiven a vector-valued position function, find the time at which the angle between the velocity and acceleration vectors equals a specified value.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this topic: Further work with vectors — question-level mapping in progress; the year table above links every official paper.

Statistical Analysis · 2 mapped questions

The binomial distribution

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q41 markMultiple-choice: find the mean and variance of a Bernoulli random variable from a given probability function.Official paper ↗Marking guidance ↗Check tutors for this question →

The sampling distribution of the mean / normal approximation

2025SD 2020-2026 (Mathematics Extension 1 Stage 6 Syllabus, 2017)Exam Q13(d)4 marksUse a normal approximation to a binomial setting, given the mean and a tail probability, to find an unknown threshold value.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this topic: The sampling distribution of the mean — question-level mapping in progress; the year table above links every official paper.

The rest of the syllabus

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

Functions — Further work with functions · Polynomials

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