01-NSW · Maths Advanced

Higher School Certificate · NESA· 2026

HSC Mathematics Advanced: complete 2026 guide (2017 and 2024 syllabuses covered)

A complete 2026 guide to HSC Mathematics Advanced. Covers the 2017 syllabus (Year 12 sitting HSC 2026) and the new 2024 syllabus (Year 11 starting HSC 2027 onwards). Topic breakdown, exam structure, scaling, study strategy, and links to every deep guide we have.

Browse guides Syllabus dot points (51)Exam trends ATAR calculator

HSC Mathematics Advanced is the standard university-track maths subject in NSW. It is the most-taken 2-unit Stage 6 maths subject and the single most important determinant of an ATAR for most students aiming at STEM or commerce degrees.

This page is the index. Below you will find a topic-by-topic breakdown, exam structure, scaling notes, and links to every deep guide we have for HSC Mathematics Advanced in 2026.

Critical 2026 note: two syllabuses are live

HSC Mathematics Advanced is currently in a syllabus transition.

If you are sitting the HSC in 2026 (currently Year 12): you follow the 2017 syllabus. Topics: Functions, Trigonometric Functions, Calculus (differentiation and integration), Financial Mathematics, Statistical Analysis.

If you are starting Year 11 in 2026 (HSC 2027 onwards): you follow the new 2024 syllabus. Most content is identical, but the new syllabus adds Vectors as a major topic, expands statistical inference, and updates assessment structures.

Our guides cover both syllabuses where they differ. Check with your school which syllabus your cohort is on if you are unsure.

The Mathematics Advanced topics (2026 cohort, 2017 syllabus)

Functions: Polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions. Composite and inverse functions. Graph transformations.
Trigonometric functions: Definitions, exact values, identities, equations, graphs, applications, radian measure, periodic functions.
Calculus (differentiation): First principles, rules (product, quotient, chain), implicit differentiation, applications including rates of change, related rates, optimisation, and motion.
Calculus (integration): Definite and indefinite integration, integration techniques (substitution, by parts is not in Advanced but is in Extension 1), areas, volumes of revolution, applications.
Financial mathematics: Simple and compound interest, annuities, future and present value, loan repayments. Geometric sequences and series.
Statistical analysis: Discrete and continuous probability distributions, the normal distribution, sampling, descriptive statistics.

The Mathematics Advanced topics (Year 11 from 2026, 2024 syllabus)

The new syllabus retains all the above, with these additions and adjustments:

Vectors: Vector arithmetic, vector geometry, scalar product, projections, applications in two dimensions. (Previously only in Extension 1.)
Expanded statistical inference: More emphasis on sampling distributions, confidence intervals, and hypothesis testing for the mean.
Updated assessment: Internal school-based assessment patterns and external exam emphasis updated.

Exam structure

HSC Mathematics Advanced is sat as a single 3-hour paper plus 10 minutes reading time.

Section I: Multiple choice (~10 questions, worth 10 marks)
Section II: Extended response (the remaining ~90 marks across questions of varying length)

The paper covers every topic in the syllabus. Multi-step extended-response questions in the last third of the paper test sustained problem-solving across multiple topics. Bring an approved scientific calculator (a graphics calculator is not required and not standard).

How Mathematics Advanced scales (2026)

Mathematics Advanced typically scales to a mean scaled mark per unit of around 34-35 out of 50. For comparison:

Mathematics Extension 2: scales to around 46-47 per unit (highest-scaling HSC subject most years)
Mathematics Extension 1: scales to around 41-43 per unit
Mathematics Advanced: scales to around 34-35 per unit
Mathematics Standard 2: scales to around 25 per unit

A raw HSC mark of 90 in Mathematics Advanced typically scales to a per-unit mark of about 42-43, which is competitive for a high ATAR. Try our HSC ATAR calculator to estimate your ATAR from projected Mathematics Advanced marks.

Our 2026 deep guides

We have written in-depth guides for the major Mathematics Advanced topics:

HSC Maths Advanced: calculus (differentiation and integration) at /hsc/math-advanced/guides/hsc-maths-advanced-calculus
HSC Maths Advanced: vectors at /hsc/math-advanced/guides/hsc-maths-advanced-vectors (mostly relevant for the new 2024 syllabus cohort)
HSC Maths Advanced: trigonometric functions at /hsc/math-advanced/guides/hsc-maths-advanced-trigonometric-functions
HSC Maths Advanced: statistical analysis at /hsc/math-advanced/guides/hsc-maths-advanced-statistical-analysis
HSC Maths Advanced practice questions at /hsc/math-advanced/guides/hsc-maths-advanced-practice-questions

Each guide includes worked examples, exam-style questions, and links to the relevant NESA syllabus dot points.

Calculator support

Try the HSC ATAR calculator to estimate your ATAR from Mathematics Advanced and your other subjects. The calculator models UAC scaling means and the best-10-units aggregate.

System context

HSC Mathematics Advanced sits inside the wider HSC system. Related explainers:

How the HSC ATAR is calculated covers UAC's aggregate and scaling mechanics.
How HSC subjects are scaled explains why Advanced scales higher than Standard.
HSC bonus points and EAS covers subject-specific selection-rank bonuses (Mathematics Advanced earns subject-bonus points at many universities for engineering and science degrees).

How to use this hub

If you are a Year 12 student sitting HSC 2026: read the topic guides for the topics you struggle with most. Aim for 8-10 past papers under timed conditions in Term 4.

If you are a Year 11 student on the new 2024 syllabus: read all the topic guides including Vectors. Plan for Year 12 by mapping the new syllabus content to your school's assessment schedule.

For the official NESA syllabus, prescribed reference material, and past papers, refer to educationstandards.nsw.edu.au.

02-Guides

In-depth written guides with paired practice quizzes.

See all →

03-Practice quizzes

Calculus (Year 12 Maths Advanced)12 questions Statistical analysis (Year 12 Maths Advanced)12 questions HSC Mathematics Advanced trigonometric functions14 questions Vectors (Year 12 Maths Advanced, 2024 syllabus)15 questions

04-The HSC system

general10 hardest HSC subjects in 2026 (and what 'hard' actually means)A ranked list of the 10 hardest HSC subjects in 2026 based on cohort strength, content difficulty, time commitment and band distribution. With the data, the honest reasons each subject earns its place, and why the answer to 'what is the hardest HSC subject' is more nuanced than a ranking.scaling10 highest scaling HSC subjects in 2026 (with UAC data)The 10 highest-scaling HSC subjects in 2026, ranked using the most recent publicly-released UAC scaling means. Plus what scaling actually does to your ATAR, when high scaling helps, and when it does not.generalAI and academic integrity in 2026: what you can and cannot doAn honest 2026 guide to how Year 12 students can use AI tools well and where the line is. NESA, VCAA, and QCAA rules, what AI is actually good at, what it is bad at, and how to think about it without panicking.wellbeingExam stress, anxiety, and looking after yourselfAn honest guide to exam stress and mental health in Year 12. What is normal, what is not, when to ask for help, and what to do if it gets really hard. With the numbers you can call.uni pathwaysGap year or uni straight after school?A clear-eyed comparison of going straight to uni versus taking a gap year. Who benefits from each, how to actually defer your offer, common gap-year traps, and how to make either path work for you.

05-Common questions

Which HSC Maths Advanced syllabus applies in 2026?

Year 12 students sitting the HSC in 2026 follow the 2017 syllabus. Year 11 students starting in 2026 follow the new 2024 syllabus and will sit their first HSC under it in 2027. Topics overlap substantially but the new syllabus has updated content emphasis (more statistical inference, more applications) and slightly different assessment structure. Check with your school which syllabus your cohort is on.

How is HSC Mathematics Advanced structured?

Mathematics Advanced is a 2-unit subject covering functions, calculus (differentiation and integration), trigonometric functions, vectors (new in the 2024 syllabus), and statistical analysis. The HSC exam is 3 hours, sat as a single paper with multiple choice plus extended-response questions. It is worth 100 marks total in the exam, weighted with internal school assessments.

How does HSC Mathematics Advanced scale?

Mathematics Advanced typically scales up to roughly 34-35 mean scaled mark per unit (out of 50). It scales higher than Mathematics Standard 2 and lower than Mathematics Extension 1 and 2. A raw HSC mark of 90+ in Advanced typically scales to a per-unit mark of 42-45, which is competitive for a high ATAR.

Should I take Mathematics Standard, Advanced, or Extension?

Mathematics Standard 2 is the broad-cohort option and scales lower. Advanced is the standard university-track maths and scales meaningfully higher. Extension 1 (3 units total with Advanced) and Extension 2 (4 units total) are for students who genuinely enjoy maths and are aiming at STEM degrees. Take the highest level you can sustain at a credit average or better. See our HSC Maths Standard vs Advanced decision guide.

What topics are in HSC Mathematics Advanced?

For the 2017 syllabus (HSC 2026) - Functions, Trigonometric Functions, Calculus (differentiation and integration), Financial Mathematics, and Statistical Analysis. For the 2024 syllabus (HSC 2027 onwards) - similar topics plus Vectors and updated emphasis on statistical inference. Both syllabuses share roughly 80% of content.

How many practice papers should I do?

For Mathematics Advanced, aim for 8-10 full past papers under timed conditions before the HSC, plus targeted practice on weak topics. The marking guides published by NESA are essential reading. Most strong students do 12+ past papers in the final term.

What's the difference between differentiation and integration?

Differentiation finds the rate of change (slope) of a function. Integration is the reverse: given a rate of change, find the original function (and the area under a curve). They're inverse operations connected by the Fundamental Theorem of Calculus.

How do I approach optimisation problems?

Identify the quantity to optimise → express it as a function of one variable → take the derivative → set to zero → check it's a max/min using the second derivative or by inspecting nearby values.

When do I use the binomial distribution vs the normal distribution?

Binomial: discrete events with two outcomes and fixed N (e.g. coin flips, defective items). Normal: continuous data clustered around a mean. For large N, binomial approximates to normal.

What are the most useful trig identities to memorise?

Pythagorean (sin²θ + cos²θ = 1), double-angle, sum/difference, and tan = sin/cos. Most exam problems reduce to one of these four families.

How do I sketch a curve from its equation?

Find intercepts, then the derivative for stationary points, then the second derivative for concavity. Plot, then check behaviour as x → ±∞.