HSC Maths Extension 1 tutoring

Extension 1 is not a separate subject so much as a second storey on the Advanced building. NESA makes that explicit in the enrolment rules: the Year 11 course, number 11250, has Year 11 Advanced as a corequisite, and the Year 12 course, number 15250, needs both Year 11 courses as prerequisites and Year 12 Advanced alongside it. Each is worth 1 unit and 60 indicative hours.

In Year 11 the new material is mostly algebraic and combinatorial: polynomials and their roots, further trigonometry, and counting arrangements. Year 12 brings the topics students remember as the real Extension 1: induction, vectors, inverse trigonometric functions and harder calculus.

The 2024 syllabus follows the same timetable as Advanced. NESA says it "is to be implemented from 2026", with Year 12 teaching from Term 4 of 2026 and the first HSC examination on it in 2027. Students moving through Year 11 and 12 during the changeover should check which version their school is teaching before buying any revision book.

Vectors is the area most likely to feel new to a student who has only seen older materials, and statistics now ends at the sampling distribution of the mean. Both reward students who understand the idea behind the formula, which is the way we teach them.

The second table is the warning. The expression n squared + n + 41 gives a prime for every n from 0 to 39, forty cases in a row, and then fails at n = 40, where it equals 1681, which is 41 times 41. A student who stopped testing at 39 would have "proved" something false.

That is the whole reason induction exists, and explaining it in a sentence is worth practising. Markers look for a correct base case, a clearly stated assumption, and a step that actually uses the assumption rather than restating it.

Choosing the base case matters too. The statement 2 to the power n is greater than n squared is true for n = 1, false for n = 2, 3 and 4 (4 is not greater than 4, 8 is not greater than 9, 16 is not greater than 16), and true from n = 5 onwards. A proof must start at n = 5, and a quick table shows why.

This test-then-prove habit also carries straight into programming, where a function can pass a hundred test cases and still be wrong. Students who study both subjects find that each one makes the other easier to understand.