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HSC · HSC Year 12 · official past papers

Mathematics Advanced — past papers by topic

Every official NESA exam and examiner report 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.

Papers 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? Book a tutor →

Mathematics Advanced Stage 6 Syllabus (2017) · 2020–2026Mathematics Advanced 11–12 Syllabus (2024) — new course · 2027–2027

Official papers & examiner reports, year by year

YearStudy designOfficial paper(s)Examiner report
2025SD 2017–2026 (Mathematics Advanced Stage 6 Syllabus 2017)Exam paper ↗Report ↗
2024SD 2017–2026 (Mathematics Advanced Stage 6 Syllabus 2017)Exam paper ↗Report ↗
2023SD 2017–2026 (Mathematics Advanced Stage 6 Syllabus 2017)Exam paper ↗Report ↗
2022SD 2017–2026 (Mathematics Advanced Stage 6 Syllabus 2017)Exam paper ↗Report ↗
2021SD 2017–2026 (Mathematics Advanced Stage 6 Syllabus 2017)Exam paper ↗Report ↗
2020SD 2017–2026 (Mathematics Advanced Stage 6 Syllabus 2017) — first HSC cohort examined under this syllabusExam paper ↗Report ↗

All URLs verified live against official NSW Government pages. NESA's legacy `educationstandards.nsw.edu.au` domain now 301-redirects to `www.nsw.gov.au/education-and-training/nesa/...` — this migration is confirmed and current; both are official NESA/NSW Government infrastructure, and the years[] URLs use the live nsw.gov.au host exactly as served (redirect confirmed via direct WebFetch on multiple original educationstandards.nsw.edu.au URLs). Subject scope: "Mathematics Advanced" as a distinct HSC course began with the 2020 HSC (first cohort examined under the Mathematics Advanced Stage 6 Syllabus 2017); no earlier years exist for this exact subject, so years[] covers 2020–2025 (6 years, all available) rather than a fixed ~10 — this is a genuine ceiling, not a coverage gap. A new "Mathematics Advanced 11–12 Syllabus (2024)" begins Year 11 teaching Term 1 2026, Year 12 Term 4 2026, with first HSC exam in 2027 — noted as a forward-looking sdEra for future badge-readiness but has no exam papers yet. Syllabus/topic structure (topics[]) reflects the CURRENT 2017 syllabus (Year 12 course) as published on the official syllabus page, cross-checked between two independent fetches of the same page (consistent both times): Functions, Trigonometric Functions, Calculus (3 subtopics), Financial Mathematics, Statistical Analysis (2 subtopics). I added "Exponential and Logarithmic Functions" and "Probability" as separate topics because real exam content (verified in the 2023/2024 papers actually read) clearly draws on exponential-growth modelling and conditional-probability/independence content distinctly from the syllabus's headline topic names — this is my own organisational grouping to make browsing easier, not an official NESA topic list restructure; flagging this explicitly as a judgment call. questions[]: all 30 entries were built ONLY after opening and reading the actual PDF text of the 2023 (full paper, Q1–32 read in full, extracted via pypdf from the officially-hosted PDF, metadata confirmed Author="NSW Education Standards Authority") and 2024 (partial, Q1–19 read) exam papers — no verbatim question text or figures were copied; all `desc` fields are my own one-line paraphrases. 2024 Section I (10 multiple-choice questions) and Q20–31, and the full 2020–2022/2025 papers, were NOT opened/read, so no questions[] entries were generated for those — per instructions I did not guess. One genuine anomaly worth flagging to the user: the 2021 marking-feedback PDF has an unusual doubled ".pdf.pdf" filename on NESA's own server — verified as real (not a transcription slip) by directly fetching that exact URL, which returned a valid 19-page PDF. Gaps for a future pass: reading the remaining un-opened papers (2020, 2021, 2022, 2025, and the rest of 2024) would extend questions[] coverage; the reportUrl entries are the "marking feedback" documents (which NESA publishes per-year covering Section II) — I did not find a single consolidated "examination report" as a separate document type distinct from these; marking guidelines (full worked solutions/criteria) exist as a third document type per year and are noted in each year's `notes` field rather than as a fourth structured field, since the schema only allows one reportUrl per year.

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Functions · 2 mapped questions

Graphing techniques (transformations, odd/even functions, sums/products of functions)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Graphing techniques

Trigonometric Functions · 3 mapped questions

Trigonometric functions and graphs (radians, graphing trig functions, trig equations)

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Trigonometric functions and graphs

Calculus · 11 mapped questions

Differential calculus (composite, product, quotient rules)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

The second derivative (concavity, points of inflection, curve sketching)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Integral calculus (indefinite/definite integrals, areas, integration techniques)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Integral calculus

Differential calculus

The second derivative

Exponential and Logarithmic Functions · 2 mapped questions

Applications of exponential and logarithmic functions (growth and decay models, rates of change)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Applications of exponential and logarithmic functions

Financial Mathematics · 3 mapped questions

Modelling financial situations (compound interest, annuities, arithmetic/geometric sequences and series applied to finance)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Modelling financial situations

Statistical Analysis · 5 mapped questions

Descriptive statistics and bivariate data analysis (correlation, least-squares regression, box plots, standard deviation)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Random variables (discrete and continuous probability distributions, expected value)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

The normal distribution (z-scores, standardisation, empirical rule)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Random variables

Descriptive statistics and bivariate data analysis

The normal distribution

Probability · 2 mapped questions

Conditional probability and independence (tree diagrams, multi-stage events)

Question-level mapping for this subtopic is being verified — use the year table above; every official paper is one click away.

Conditional probability and independence

Sequences and series · 2 mapped questions

Modelling financial situations

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