HSC Maths Advanced Syllabus: Every Topic, and What Changed

HSC Mathematics Advanced has a new syllabus. If you're starting Year 12 in Term 4 2026, you'll sit the first HSC exam under the Mathematics Advanced 11–12 Syllabus (2024), in 2027. A lot of what you'll find online was written for the old course, so this guide covers the new structure, each Year 12 topic, where students usually lose marks, and how to study.

What Maths Advanced is

Mathematics Advanced is the calculus-based 2-unit course. It's built around functions, calculus, statistics and financial maths, and it suits students who are comfortable with algebra and want maths for further study in areas like science, engineering, economics or commerce.

If you're also taking Mathematics Extension 1, the Advanced course is the foundation it builds on.

What's new for the 2027 HSC

The 2024 syllabus is taught to Year 12 from Term 4 2026 and examined for the first time in 2027. The old 2017 syllabus had its final exam in 2026. Much of the core mathematics will feel familiar, but the topics are organised differently, so not every older past paper question will match.

The best guide to the new exam is the sample HSC exam material NESA published for the new maths courses in 2025.

How the course is structured

Year 11 covers seven topics: Working with functions; Trigonometry and measure of angles; Trigonometric identities and equations; Introduction to differentiation; Exponential and logarithmic functions; Graph transformations; and Probability and data.

Year 12 covers seven more, starting in Term 4 of Year 11. Year 12 leans on Year 11 heavily, especially functions, logarithms and differentiation, so gaps from Year 11 tend to resurface.

Further graph transformations and modelling

This extends transformations to sine, cosine and tangent graphs (amplitude, period and shifts), solving trig equations on a given domain, and modelling periodic situations. It also covers logarithmic scales in contexts like decibels, pH and earthquake magnitude. In this course, periodic modelling is done without calculus.

Common mistakes: applying horizontal dilations and translations in the wrong order, and missing solutions when solving a trig equation across a domain. Always sketch and check how many solutions you expect.

Sequences and series

Arithmetic and geometric sequences and series, sigma notation, the limiting sum of a geometric series, and growth and decay applications.

Common mistakes: off-by-one errors with the number of terms, and using a limiting sum without checking the ratio condition. Write out the first few terms before reaching for a formula.

Differential calculus

Derivatives of exponential, logarithmic and trigonometric functions, combining the product, quotient and chain rules, and finding tangents and normals.

Common mistakes: chain rule slips inside trig and log functions, and forgetting that a normal's gradient is the negative reciprocal. Practise differentiating mixed functions until the rules are automatic.

Integral calculus

Finding functions from their derivatives, the definite integral and the Fundamental Theorem of Calculus, integrating exponential, log and trig functions, areas under and between curves, and the trapezoidal rule.

Common mistakes: forgetting the constant of integration, and treating areas below the axis as positive inside a single integral. Split the region where the function changes sign.

Applications of calculus

Second derivatives, concavity and points of inflection, classifying stationary points, curve sketching, optimisation, rates of change, growth and decay, and motion in a straight line.

Common mistakes: finding a maximum but not checking endpoints, and skipping the justification that a stationary point is a maximum or minimum. In optimisation, write the function you're optimising clearly before you differentiate.

Random variables

Discrete probability distributions, expected value and variance, continuous random variables with probability density and cumulative distribution functions, the uniform distribution, the normal distribution, the empirical rule and z-scores.

Common mistakes: mixing up the PDF and CDF, and not stating what a z-score means in context. Draw the distribution and shade the region you're finding.

Financial mathematics

Reducing balance loans and annuities, modelled using geometric series.

Common mistakes: losing track of when payments and interest happen in each period. Write out the first two or three periods in full, then look for the pattern before generalising.

How Maths Advanced is assessed

Your HSC mark is the average of your moderated school assessment mark and your HSC exam mark. Bands run from 1 to 6, with Band 6 from 90.

• School assessment tasks follow your school's program and usually include topic tests, an investigation or modelling task, and trial exams. Check your school's program for details.
• The HSC exam is a written paper at the end of Year 12. Questions often combine topics, such as calculus inside a financial or probability context.

Marks are given for method, so a clearly set out solution with a small slip can still earn most of the marks. A correct answer with no working may not.

How to study Maths Advanced

1. Do questions, not notes. Maths is learned by solving problems. Read worked examples, then cover them and do them yourself.
2. Keep an error log. Every time you lose marks, write down the mistake and the fix. Review it before each test.
3. Mix topics. Once you've covered a few topics, do mixed sets. The exam won't tell you which topic a question belongs to.
4. Fix Year 11 gaps early. Logs, functions and basic differentiation underpin almost everything in Year 12.
5. Practise under time. Use the new sample materials and suitable older questions, timed, then mark them honestly.
6. Show every step. Write as if someone is marking your method, because they are.

If you get stuck between lessons, an AI study coach like otto can walk through a problem step by step and check your working, not just your final answer.

The bottom line

Mathematics Advanced rewards steady, consistent practice more than last-minute cramming. For the 2027 HSC it's a new syllabus, so plan around the new topic list, use NESA's sample materials, keep an error log, and practise mixed questions with full working.