HSC Maths Extension 2 tutoring

NESA lists the course as number 15260, worth 1 unit and 60 indicative hours. The enrolment rules show how tightly it is stacked: the prerequisites are Year 11 Advanced (11255) and Year 11 Extension 1 (11250), and the corequisites are Year 12 Advanced (15255) and Year 12 Extension 1 (15250). There is no shortcut into Extension 2.

The "What it adds" column is our own summary, not NESA wording, and the focus area names are the ones to plan revision around. Each of the five areas is substantial on its own, which is why Extension 2 feels heavier than its one-unit size suggests.

The 2024 syllabus "is to be implemented from 2026", according to NESA, with teaching of the new course from Term 4 of 2026 and the first HSC examination on it in 2027. A student starting Year 12 in that term is in the first cohort.

Students in the changeover year sometimes find that older worked examples cover topics in a different order or under different headings. The mathematics is still valuable; the topic list to trust is the one in the 2024 course structure.

The distance from the origin never changes, and after four multiplications the point is back where it started. Each multiplication by i has moved the point a quarter turn anticlockwise about the origin: (3, 2) to (-2, 3) is exactly the rotation (x, y) to (minus y, x). That single picture explains why i to the fourth is 1.

Now multiply by 1 + i instead. (3 + 2i)(1 + i) = 3 + 3i + 2i + 2i squared = 1 + 5i. The length grows from the square root of 13 to the square root of 26, a stretch by the square root of 2, and the angle grows by 45 degrees, from about 33.7 degrees to about 78.7 degrees.

Those two facts, lengths multiply and angles add, are the heart of the complex numbers area of study. They turn a page of algebra into a sketch a student can check by eye, and they reappear when roots of complex numbers are drawn evenly around a circle.

The same idea powers graphics and games: rotating a point on screen is multiplication by a unit complex number. Students who code can test the table above in a few lines of Python, which has complex numbers built in, and see the quarter turns for themselves.