New HSC Mathematics Advanced syllabus (from the 2027 HSC): what's changed

NSW has a new Mathematics Advanced syllabus, the Mathematics Advanced 11-12 Syllabus (2024). It replaces the Mathematics Advanced Stage 6 Syllabus (2017), and the 2027 HSC is the first exam on it. If you are starting Year 12 in Term 4 2026, this is your syllabus for the whole of Year 12, and you already studied its Year 11 course this year.

This page sets out what actually changed, checked line by line against NESA's two syllabus documents and its published assessment pages. Where NESA has not said something, we say so.

Who is on which syllabus

So the Class of 2027 is on the new syllabus from start to finish. Anything below marked "Year 11" is content you should already have met; the HSC exam focuses on the Year 12 outcomes, but NESA states that the Year 11 course is assumed knowledge and may be examined.

The new course structure

NESA now organises Mathematics Advanced into seven areas of study, split into focus areas.

Every outcome now sits under a single "Working mathematically" outcome, and technology (graphing applications, spreadsheets, online computational tools) is written into the content points. That changes how topics are taught, but the HSC exam is still a pen-and-paper paper with a NESA-approved calculator.

What's new, moved or gone

The table below comes from reading the 2017 and 2024 content side by side. "Moved" means the same idea now appears in a different year or course.

New to Mathematics Advanced

• Exponential growth and decay as a differential equation (Year 12, Applications of calculus): $\frac{dQ}{dt} = kQ$, verifying that $Q = Ae^{kt}$ solves it, and modelling growth and decay with it. In the 2017 syllabuses this model was Year 11 Extension 1 content. Our page on exponential growth and decay already works through it.
• Derivatives of $\operatorname{cosec} x$, $\sec x$ and $\cot x$ (Year 12, Differential calculus). The 2017 Advanced course only defined these functions; it did not differentiate them. See our new page on derivatives of the reciprocal trigonometric functions.
• Areas bounded by a curve and the $y$-axis (Year 12, Integral calculus), including using the fact that $y = a^x$ and $y = \log_a x$ are reflections in $y = x$ to find areas. The 2017 course defined area only against the $x$-axis. See our new page on areas between a curve and the $y$-axis.
• Summation (sigma) notation $\sum_{k=i}^{j} a_k$ for sequences and series (Year 12, Sequences and series).
• A short Sets and set notation section (sets, subsets, union, intersection, complement and $|A \cup B| = |A| + |B| - |A \cap B|$) at the start of Year 11 Probability and data.

Moved between Year 11 and Year 12

• Graph transformations (translations, reflections and dilations of functions, and circles $(x-a)^2 + (y-b)^2 = r^2$) are now Year 11. Transformations of the trigonometric functions stay in Year 12.
• Discrete random variables (expected value and variance) moved from Year 11 to Year 12 Random variables, alongside continuous random variables and the normal distribution.
• Acceleration of a particle moved to Year 12. Year 11 now stops at velocity from displacement.
• Logarithmic scales (decibels, earthquake magnitude scales, star magnitudes, pH) moved from Year 11 to Year 12 (Further graph transformations and modelling).
• Sequences and series are now a Year 12 focus area of their own instead of sitting inside Financial mathematics. The content (arithmetic and geometric sequences, partial sums, limiting sums) is essentially the same.

Moved out of Advanced into Extension 1

• Trigonometry in three dimensions is now in Extension 1 Year 11 (Further trigonometry). Advanced keeps right-angled and non-right-angled trigonometry in two dimensions.
• Area between two curves is now in Extension 1 Year 12 (Further applications of calculus). Advanced keeps areas between a curve and an axis.

No longer in Mathematics Advanced

• Bivariate data analysis (scatterplots, Pearson's correlation coefficient, least-squares regression) and most descriptive statistics from the 2017 Year 12 course. These were the content shared with Mathematics Standard 2. What remains is a short Year 11 Data section: random variables (discrete versus continuous), frequency, relative frequency and cumulative frequency tables, histograms and polygons, reading the mode and median from them, and relative frequency as an estimate of probability.
• Annuity calculations using tables of interest factors. The new course models the future value of an annuity with the geometric series formula; reducing balance loans stay.

Unchanged in substance

Differentiation rules and first principles, curve sketching with first and second derivatives, optimisation, motion in a straight line, integration of $x^n$, exponential, logarithmic and trigonometric functions, the Fundamental Theorem of Calculus, the trapezoidal rule, trigonometric identities and equations, radians, exponential and logarithmic laws and graphs, continuous random variables (PDFs and CDFs), the normal distribution and $z$-scores, and reducing balance loans. The syllabus wording is clearer and more explicit, but the mathematics is the same.

School-based assessment

• Components are renamed: "Knowledge and understanding of course content" 50% and "Skills in Working mathematically" 50% (they were "Understanding, fluency and communication" and "Problem solving, reasoning and justification" in the 2017 course).
• Year 11 is reported as a grade (A to E) using the Common Grade Scale. NESA's sample program is 3 tasks, including a formal written examination, each weighted 20% to 40%.
• Year 12: NESA's sample program is 4 tasks, including a formal written examination, each weighted 10% to 40%. Formal assessment should focus on Year 12 outcomes; Year 11 is assumed knowledge and may be assessed. Unlike the 2017 sample, it no longer lists an assignment or investigation-style task.
• Take-home tasks are capped. From Term 4 2026, NESA's updated ACE Rules allow no more than one take-home assessment task per HSC course, worth at most 15% (Preliminary courses follow from Term 1 2027). Mathematics Advanced is not one of the exempt courses. Many schools used a take-home investigation in maths, so expect more of your marks to come from in-class and exam-style tasks. The same notice requires tasks to be designed so that marks reflect your own work, not generative AI.

Schools still decide the number, type and weighting of tasks, so your school's assessment schedule is what counts. Check it as soon as it is published.

The HSC exam

NESA's examination specification for the new course:

• one written paper worth 100 marks, 3 hours plus 10 minutes reading time
• Section I: 10 marks of objective-response (multiple-choice) questions
• Section II: 90 marks, 37 to 42 items, questions may contain parts, at least two items worth 4 or 5 marks
• a reference sheet is provided and NESA-approved calculators may be used

That is the same shape as the 2020 to 2026 papers. Two differences matter:

1. No common questions with Mathematics Standard 2. The 2017 specification required 20 to 25 marks of items common to both papers; NESA's sample exam states that the new Advanced exam "does not include items that are common with other Mathematics HSC examinations".
2. A new, course-specific reference sheet. NESA has published a Mathematics Advanced reference sheet for the new syllabus (the 2017 papers used one combined Advanced, Extension 1 and Extension 2 sheet). Practise with the new one so you know exactly which formulas are given.

NESA has published an annotated sample HSC examination for the new course (Questions 1 to 35 with marking guidelines and syllabus mapping). It notes that past HSC questions have been used "where they are still relevant", which tells you the old papers are still useful practice.

What this means if you are starting Year 12 now

1. Your Year 12 course is Further graph transformations and modelling, Sequences and series, Differential calculus, Integral calculus, Applications of calculus, Random variables and Financial mathematics. Map your school's assessment schedule onto that list.
2. Keep using past papers, with a filter. Skip questions on bivariate data, correlation and regression, descriptive statistics, area between two curves, three-dimensional trigonometry and interest-factor tables. Everything else in the 2020 to 2025 Advanced papers is still fair practice.
3. Add practice on the new content: derivatives of reciprocal trigonometric functions, areas against the $y$-axis, $\frac{dQ}{dt} = kQ$ modelling, sigma notation, and discrete random variables (now Year 12).
4. If you also do Extension 1, area between curves and 3D trigonometry have not disappeared: they are examined in the Extension 1 paper instead. See what's changed in Extension 1.
5. Plan for in-class assessment. With at most one take-home task worth 15% or less, almost all of your school mark will come from supervised tasks.

Most of our existing Mathematics Advanced dot-point pages were written to the 2017 syllabus. Where the mathematics is unchanged (most calculus, trigonometry, exponentials and logarithms, the normal distribution) they are still the right thing to study; each hub page now carries a note saying which syllabus it follows. For choosing between courses, see HSC Maths Standard vs Advanced.