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QCE Specialist Mathematics past exams 2020–2025, by year and topic

The official QCAA 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 QCAA 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 32 official QCAA Specialist Mathematics papers from 2020 to 2025, with 11 questions mapped to 4 topics. Every paper opens on the QCAA website.

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Specialist Mathematics 2019 syllabus · 2020–2025Specialist Mathematics 2025 syllabus (v1.4) · 2026–present

QCE Specialist Mathematics exams by year: official papers & marking guidance

Past exams indexed: 2025, 2024, 2023, 2022, 2021, 2020. Open the official QCAA papers, with marking guidance where available.

Year	Study design	Official paper(s)	Marking guidance
2025 QCE Specialist Mathematics exam	Specialist Mathematics 2019 syllabus	Paper 1 — Question and response book ↗ · Paper 2 — Question and response book ↗ · Paper 1 — Multiple choice question book ↗ · Paper 2 — Multiple choice question book ↗ · Paper 1 — Marking guide ↗ · Paper 2 — Marking guide ↗	Marking guidance ↗
2024 QCE Specialist Mathematics exam	Specialist Mathematics 2019 syllabus	Marking guide ↗ · Paper 1 — Multiple choice question book ↗ · Paper 1 — Question and response book ↗ · Paper 2 — Multiple choice question book ↗ · Paper 2 — Question and response book ↗	Marking guidance ↗
2023 QCE Specialist Mathematics exam	Specialist Mathematics 2019 syllabus	Paper 1 — Marking guide ↗ · Paper 1 — Multiple choice question book ↗ · Paper 1 — Question and response book ↗ · Paper 2 — Marking guide ↗ · Paper 2 — Multiple choice question book ↗ · Paper 2 — Question and response book ↗	Marking guidance ↗
2022 QCE Specialist Mathematics exam	Specialist Mathematics 2019 syllabus	Marking guide ↗ · Paper 1 — Multiple choice question book ↗ · Paper 1 — Question and response book ↗ · Paper 2 — Multiple choice question book ↗ · Paper 2 — Question and response book ↗	Marking guidance ↗
2021 QCE Specialist Mathematics exam	Specialist Mathematics 2019 syllabus	Marking guide ↗ · Paper 1 — Multiple choice question book ↗ · Paper 1 — Question and response book ↗ · Paper 2 — Multiple choice question book ↗ · Paper 2 — Question and response book ↗	Marking guidance ↗
2020 QCE Specialist Mathematics exam	Specialist Mathematics 2019 syllabus	Marking guide ↗ · Paper 1 — Multiple choice question book ↗ · Paper 1 — Question and response book ↗ · Paper 2 — Multiple choice question book ↗ · Paper 2 — Question and response book ↗	Marking guidance ↗

32 official papers across 6 years (2020–2025), 6 with marking guidance, published by QCAA. These span more than one study design; the most recent is Specialist Mathematics 2025 syllabus (v1.4). Earlier papers may cover material that has since changed.

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Unit 3: Further complex numbers, proof, vectors and matrices · 6 mapped questions

Topic 1: Further complex numbers

2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q196 marksProve a divisibility/integer-membership result about a non-real fifth root of unity using complex number properties.Official paper ↗Marking guidance ↗Check tutors for this question →

Topic 3: Vectors in two and three dimensions

2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q126 marksFind an unknown coordinate on a 3D line and a point-condition on a plane, then extract direction and normal vectors from their symmetric/Cartesian equations.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q165 marksUse vector methods to prove that the two space-diagonals of a parallelepiped bisect each other.Official paper ↗Marking guidance ↗Check tutors for this question →

Topic 5: Further matrices

2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q11a1 markApply a given row operation to transform one row of a 3x3 augmented matrix.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q11b3 marksSolve a 3-variable linear system from a reduced augmented matrix, given one row's equation.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q11c1 markGive a geometric interpretation (in terms of intersecting planes) of a linear system's solution.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this topic: Topic 2: Mathematical induction and trigonometric proofs · Topic 4: Vector calculus — question-level mapping in progress; the year table above links every official paper.

Unit 4: Further calculus and statistical inference · 5 mapped questions

Topic 1: Integration techniques

2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q155 marksProve a given integration-by-parts result for an exponential-times-polynomial integrand.Official paper ↗Marking guidance ↗Check tutors for this question →

Topic 3: Rates of change and differential equations

2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q177 marksRelated-rates problem: find the rate of change of a shrinking cylinder's volume at a given time given a constant rate of radius decrease.Official paper ↗Marking guidance ↗Check tutors for this question →

Topic 4: Modelling motion

2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q135 marksGiven velocity as a function of position for a moving object, find its momentum and acceleration at the origin using calculus.Official paper ↗Marking guidance ↗Check tutors for this question →
2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q186 marksUse vector calculus for projectile motion to find the launch angle given initial speed, height, horizontal range and gravitational acceleration.Official paper ↗Marking guidance ↗Check tutors for this question →

Topic 5: Statistical inference

2025Specialist Mathematics 2019 syllabusPaper 1 — Technology-free Q145 marksConstruct an approximate confidence interval for a population mean from sample statistics and use it to assess compliance with a labelling regulation.Official paper ↗Marking guidance ↗Check tutors for this question →

Also in this topic: Topic 2: Applications of integral calculus — question-level mapping in progress; the year table above links every official paper.

The rest of the syllabus

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

Unit 1: Combinatorics, proof, vectors and matrices — Topic 1: Combinatorics · Topic 2: Introduction to proof · Topic 3: Vectors in the plane · Topic 4: Algebra of vectors in two dimensions · Topic 5: Matrices
Unit 2: Complex numbers, further proof, trigonometry, functions and transformations — Topic 1: Complex numbers · Topic 2: Complex arithmetic and algebra · Topic 3: Circle and geometric proofs · Topic 4: Trigonometry and functions · Topic 5: Matrices and transformations

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