2027 HSC maths: what changes in Advanced and Extension 1

Before buying a new set of maths notes, check your child's HSC year and course. Mathematics Advanced and Mathematics Extension 1 both move to their new syllabuses for the 2027 HSC. Their new Year 11 courses began in Term 1, 2026, with Year 12 teaching starting in Term 4. Students sitting the HSC in 2026 remain on the previous syllabuses. NESA's implementation timetable

The official documents are called the Mathematics Advanced and Mathematics Extension 1 11-12 Syllabuses (2024). Check for those names when choosing resources for a child sitting the HSC in 2027.

Advanced and Extension 1 need separate checks

Mathematics Advanced covers areas including functions, calculus, statistics and financial mathematics. Extension 1 builds on Advanced, with further work on mathematical arguments, proofs and models. Its content includes combinatorics, vectors and mathematical induction. NESA Advanced overview, NESA Extension 1 course description

For a child taking both courses, check both sets of materials. A statement that a workbook is "updated for the new maths syllabus" leaves an obvious question: which course, and which year level?

Ask the teacher or tutor to show you how the resources match the topics being taught. You should be able to identify the next topic, the practice provided for it and how your child will receive feedback.

What has changed for 2027?

Both syllabuses have revised structures and assessment requirements. The Department of Education describes additions, exclusions and movement of content between and within courses, with mathematical reasoning and technology embedded throughout. Advanced changes, Extension 1 changes

Two concrete differences are worth knowing about.

For Advanced, the HSC examination will no longer include questions common to Mathematics Standard. Older advice about shared questions should therefore be checked before it becomes part of your child's exam strategy. This change alone does not tell us how difficult the 2027 paper will be. Department of Education announcement

For Extension 1, the new Year 12 outcomes include operations with both two-dimensional and three-dimensional vectors. The previous 2017 syllabus described vector representation and operations in two dimensions. An older set of vector exercises therefore needs checking for coverage. NESA Extension 1 outcomes, NESA Mathematics Extension 1 syllabus (2017)

These examples are a starting point for checking resources, rather than a complete list of content changes. Ask for a topic-by-topic comparison when a teacher or tutor recommends keeping an older textbook.

What do the HSC exams look like?

NESA has published separate examination specifications for the two courses:

Both papers provide a reference sheet and permit NESA-approved calculators. Year 11 knowledge still matters: NESA explicitly says it may be examined in each course. Advanced exam specifications, Extension 1 exam specifications

Students taking Extension 1 complete its paper plus either the Advanced or Extension 2 paper, depending on their enrolment. The Extension 1 paper does not replace the other required mathematics examination. NESA Extension 1 examination requirements

School assessments are a separate matter. For example, NESA's Advanced requirements let schools determine the number and type of tasks and their individual weightings. Its four-task Year 12 schedule is a sample. Use your child's school assessment schedules for the deadlines and tasks they actually face. NESA Advanced school-based assessment

Two small examples of understanding the working

For parents, an explanation can be easier to assess than a page of answers. The following original practice examples illustrate Year 11 foundations used in the two courses. They are not NESA exam questions or predictions of the 2027 paper.

Advanced: explain where a graph has moved

Graph transformations appear in the new Advanced Year 11 course. NESA Advanced overview

Consider the graph

$$y = (x - 2)^2 + 3$$

Where is its lowest point, and why?

The squared part cannot be negative. It equals zero when $x = 2$, which makes $y = 3$. The lowest point is therefore $(2, 3)$. Compared with $y = x^2$, the graph has moved two units right and three units up.

A student who puts the point at $(-2, 3)$ may have remembered the sign without checking the expression. Ask them to substitute $x = 2$ and $x = -2$. The resulting $y$-values are $3$ and $19$. That calculation gives them a way to check their own reasoning.

Extension 1: decide whether order matters

Permutations and combinations appear in the Extension 1 Year 11 course. NESA Extension 1 overview

Suppose six students volunteer for two different jobs: chair and secretary. How many appointments are possible if each student can hold only one job?

There are six choices for chair and five remaining choices for secretary, giving $6 \times 5 = 30$ appointments.

Now choose two representatives with identical roles from the same six students. There are $15$ possible pairs: the earlier count lists every pair twice, so divide $30$ by $2$.

$$\frac{30}{2} = 15$$

If your child gets $30$ for both questions, ask them to describe what makes one selection different from another. Swapping the chair and secretary changes the appointments. Swapping the order in which two identical-role representatives are named does not change the pair.

A practical way to use older resources

Keep older questions when a teacher or tutor has checked that they match the current course. Avoid using an old paper as your only checklist of examinable material.

Our Extension 1 past-paper guide links official papers, identifies selected older questions and provides original worked examples on induction and three-dimensional vectors.

Before Term 4, we suggest sitting down with your child and their most recent marked work. Pick one error they can explain, then find a fresh question that tests the same idea. Ask them to solve it without copying the earlier solution.

If they cannot get started, save that attempt for their teacher or tutor. It gives the next lesson a specific problem to address. Keep a short record of what went wrong, such as an algebra step, a misunderstood question or a method they could not choose.

For families considering tutoring, Plume's Maths Advanced and Maths Extension 1 pages explain the two courses. Bring recent working, including unfinished attempts, so the discussion can start with how your child approaches a problem.