What is in HSC Maths Extension 2

Five focus areas, all in Year 12: the nature of proof, further work with vectors, introduction to complex numbers, further integration, and applications of calculus to mechanics. The HSC paper is based on the Year 12 course, with Mathematics Advanced and Extension 1 assumed.

Weeks before the HSC examination

Hours a week for Extension 2

The nature of proof

Further work with vectors

Introduction to complex numbers

Further integration

Applications of calculus to mechanics

NESA publishes the HSC examination timetable; count the weeks from it.

26 weeks, 104 hours in all

Start with The nature of proof

22.2 of your hours. It is 3 of the 13 units in the course, 23%.

Hours per focus area
Focus area	Your hours	Share of the course
The nature of proof	22.2	23%
Introduction to complex numbers	22.2	23%
Applications of calculus to mechanics	22.2	23%
Further work with vectors	14.8	15%
Further integration	14.8	15%

Week by week

Week 1The nature of proof
Week 2The nature of proof
Week 3The nature of proof
Week 4The nature of proof
Week 5The nature of proof
Week 6The nature of proof, Introduction to complex numbers
Week 7Introduction to complex numbers
Week 8Introduction to complex numbers
Week 9Introduction to complex numbers
Week 10Introduction to complex numbers
Week 11Introduction to complex numbers
Week 12Introduction to complex numbers, Applications of calculus to mechanics
Week 13Applications of calculus to mechanics
Week 14Applications of calculus to mechanics
Week 15Applications of calculus to mechanics
Week 16Applications of calculus to mechanics
Week 17Applications of calculus to mechanics, Further work with vectors
Week 18Further work with vectors
Week 19Further work with vectors
Week 20Further work with vectors
Week 21Further work with vectors, Further integration
Week 22Further integration
Week 23Further integration
Week 24Further integration
Week 25Timed paper 1 (a full paper, 3 hours), then review every lost mark
Week 26Timed paper 2 (a full paper, 3 hours), then review every lost mark

Check your units with the free test

The paper	One written paper, 100 marks, 3 hours plus 10 minutes reading time
Section I	Objective-response questions worth 10 marks
Section II	90 marks in 37 to 42 items; at least two items worth 4 or 5 marks
Provided	A reference sheet; NESA-approved calculators may be used

The five focus areas

The nature of proof: the language of proof, direct proof and proof by contradiction, proving inequalities, and further mathematical induction.
Further work with vectors: vector equations of lines and curves in two and three dimensions, and geometric proofs with the scalar product.
Introduction to complex numbers: Cartesian and polar form, complex equations, de Moivre's theorem and nth roots, and lines, curves and regions in the complex plane.
Further integration and mechanics: substitution, partial fractions, integration by parts and recurrence formulas; Newton's laws, simple harmonic motion, resisted motion and projectiles.

Assumed knowledge and the Extension 1 paper

Mathematics Advanced and Mathematics Extension 1 are assumed knowledge for the Extension 2 examination, and students also sit the Extension 1 paper. School-based assessment is set by your school, so this course describes it but does not practise it.

How this course maps the syllabus

The course splits the five focus areas into thirteen units and a unit on the examination, each with a lesson, Section I questions and Section II questions. Set the planner above with the weeks you have and how sure you are of each focus area, and it splits your hours.

Try 3 questions

Section I · 1 mark · Complex numbers: arithmetic and polar form
Let $z = 5 - 12 i$ . What is $\mathrm{Im}\left(\dfrac{1}{z}\right)$ ?
Answer it, every step marked
Section II · 7 marks · Complex numbers: arithmetic and polar form
Let $z = 3 + 4 i$ and $w = 1 - 2 i$ .
Answer it, every step marked
Section I · 1 mark · Complex numbers: arithmetic and polar form
What are the two square roots of $-5 + 12 i$ ?
Answer it, every step marked

Next step

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Questions people ask

Is Extension 2 a Year 11 course?

No. Mathematics Extension 2 is a Year 12 course, and the HSC paper is based on it. Mathematics Advanced and Extension 1 are assumed knowledge.

Which syllabus does the course follow?

The NESA Mathematics Extension 2 11-12 Syllabus (2024), first examined in the 2027 HSC.

Do Extension 2 students sit the Extension 1 paper?

Yes. Students also complete the Mathematics Extension 1 paper. HSC Maths Extension 1 Prep is a separate course.