New HSC Maths Extension 1 syllabus from 2027: what's changed

The Mathematics Extension 1 11-12 Syllabus (2024) replaces the 2017 Extension 1 syllabus, and the 2027 HSC is the first exam on it. If you are starting Year 12 in Term 4 2026, you studied its Year 11 course this year and will study its Year 12 course from now until the HSC.

The core of Extension 1 (polynomials, induction, inverse trigonometric functions, calculus techniques, differential equations, the binomial distribution, projectiles) is still there. What changed is which year things sit in, a handful of topics that moved between Advanced, Extension 1 and Extension 2, and two genuinely new ideas: 3D vectors and the central limit theorem. Everything below is checked against NESA's published 2017 and 2024 syllabus documents.

Timeline

Extension 1 is still studied alongside Mathematics Advanced, and the exam assumes the whole Advanced course.

The new course structure

Notice that all calculus is now Year 12, and Year 11 is functions, polynomials, trigonometry and combinatorics.

What's new

• Vectors in three dimensions (Year 12, Introduction to vectors). The 2017 Extension 1 course was two-dimensional only; 3D coordinates, $\mathbf{i}$, $\mathbf{j}$, $\mathbf{k}$ component form, magnitude and the scalar product in 3D were Extension 2. Our Extension 2 page on three-dimensional vectors and lines covers the same 3D basics.
• Motion in vector form in two dimensions: position vectors as functions of time, velocity and acceleration vectors by differentiation and integration, non-constant velocity, and relative velocity with a constant crosswind or cross-current. See motion as a vector function and our new page on relative velocity with crosswinds and currents.
• The sampling distribution of the mean and the central limit theorem (Year 12): for large samples ($n \geq 30$) the sample mean $\bar{X}$ is approximately $N\!\left(\mu, \frac{\sigma^2}{n}\right)$. NESA's sample exam includes a 3-mark question of exactly this type; see our new page on the central limit theorem and sample means.
• Derivatives of functions defined parametrically, $\frac{dy}{dx} = \frac{dy/dt}{dx/dt}$ (Year 12, Further calculus skills). See our new page on derivatives of parametric functions.
• Transformations of the inverse trigonometric functions (reflections, translations and dilations of $\sin^{-1} x$, $\cos^{-1} x$ and $\tan^{-1} x$) are now written into the content.

Moved in from Mathematics Advanced

• Trigonometry in three dimensions (Year 11, Further trigonometry).
• Area between two curves (Year 12, Further applications of calculus), now grouped with volumes of solids of revolution. Our Advanced page on areas and volumes of revolution covers it.

Moved to Year 12

• Inverse trigonometric functions (definitions, graphs, properties) were Year 11 and are now a Year 12 focus area.
• Rates of change: related rates and the modified growth and decay model $\frac{dQ}{dt} = k(Q - P)$ (Newton's law of cooling, carrying capacity) are now Year 12 Further applications of calculus. The basic model $\frac{dQ}{dt} = kQ$ is now taught in Mathematics Advanced.
• Multiplicity of zeroes using the derivative (if $\alpha$ is a zero of multiplicity $m$, it is a zero of $P'(x)$ of multiplicity $m - 1$) moved from Year 11 Polynomials to Year 12.

Going the other way, solving trigonometric equations, including the auxiliary angle form $R\cos(x \pm \alpha)$ or $R\sin(x \pm \alpha)$, is now Year 11 (it was Year 12).

No longer in Extension 1

• The t-formulae and products-to-sums identities now sit in Extension 2 (Further integration).
• The pigeonhole principle is no longer in the course.
• The normal approximation for the sample proportion $\hat{p}$ has gone; the binomial content now says "excluding the normal approximation to the binomial distribution". The central limit theorem for sample means replaces it.
• Geometric proofs using vectors (for example, the diagonals of a rhombus) are no longer listed in Extension 1; vector proofs of geometric results are in Extension 2.

School-based assessment

• Components are "Knowledge and understanding of course content" (50%) and "Skills in Working mathematically" (50%).
• NESA's sample programs: Year 11, 3 tasks including a formal written examination, weighted 20% to 40% each; Year 12, 4 tasks including a formal written examination, weighted 10% to 40% each. The 2017 samples also listed an assignment or investigation-style task; the new samples do not.
• One take-home task at most. From Term 4 2026 the ACE Rules allow no more than one take-home assessment task per HSC course, worth at most 15%. Extension 1 is not an exempt course.

The HSC exam

The specification is the same as for the 2017 course: one written paper of 70 marks, 2 hours plus 10 minutes reading time, Section I 10 marks of objective-response questions, Section II 60 marks across 23 to 28 items with at least one item worth 4 or 5 marks. A reference sheet is provided (NESA has published a new Extension 1 sheet for this syllabus) and NESA-approved calculators may be used. The Advanced course and the Extension 1 Year 11 course are assumed knowledge, and Year 11 may be examined. You also sit the Mathematics Advanced paper, or the Extension 2 paper if you are enrolled in Extension 2.

NESA's annotated sample Extension 1 exam uses past HSC questions where they are still relevant, and includes new-content items such as a central limit theorem question (Question 14(c)).

What this means if you are starting Year 12 now

1. Your Year 12 topics: induction, vectors (2D and 3D, motion, projectiles), inverse trigonometric functions, further calculus skills, further applications of calculus (including related rates, cooling and carrying capacity, area between curves, volumes and differential equations), and the binomial distribution with the central limit theorem.
2. Past papers are still valuable. Skip questions on the t-formulae, products to sums, the pigeonhole principle and sample proportions. Everything else in the 2020 to 2025 papers remains good practice.
3. Add the new material: 3D vectors, relative velocity, parametric derivatives and the central limit theorem have no past HSC questions yet, so NESA's sample exam and your school's tasks are the best guide.
4. Check the Advanced changes too, because Extension 1 assumes all of it: see what's changed in Mathematics Advanced.

Our existing Extension 1 dot-point pages were written to the 2017 syllabus. Where the mathematics is the same (induction, polynomials, inverse trigonometric functions, integration by substitution, differential equations, projectiles, the binomial distribution) they remain the right pages to study.