Mathematics Extension 2 (4U)

Course Overview

The Year 12 HSC Mathematics Extension 2 course is the highest level of mathematics offered in the HSC. It is for highly capable students who enjoy deep, abstract mathematical thinking. Topics include complex numbers, advanced calculus, proof, and harder applications of vectors and mechanics. This course challenges students with sophisticated multi-step problems, fostering creativity, persistence, and precision in mathematical reasoning.

Key Areas of Learning

COMPLEX NUMBERS

1. INTRODUCTION TO COMPLEX NUMBERS

2. ARGAND DIAGRAMS AND POLAR FORM

3. DE MOIVRE’S THEOREM

4. ROOTS OF COMPLEX NUMBERS

5. COMPLEX NUMBERS AS VECTORS

6. MISCELLANEOUS

VECTORS

1.VECTORS IN THREE DIMENSIONS

2. THE DOT PRODUCT AND ITS APPLICATIONS

3. VECTOR PROOFS IN GEOMETRY

4. THE VECTOR EQUATION OF A LINE

FURTHER INTEGRATION

1. USING DECOMPOSITION INTO SUM OR DIFFERENCE

2. INTEGRATION BY SUBSTITUTION

3. REDUCTION TO STANDARD FORM

4. USING PARTIAL FRACTION

5. INTEGRATION BY PARTS

6. RECURRENCE FORMULAE

7. FURTHER PROPERTIES OF DEFINITE INTEGRALS

NATURE OF PROOF

1. LOGIC OF PROOF

2. METHODS OF PROOF

3. INEQUALITIES

4. MATHEMATICAL INDUCTION

MECHANICS

1. SIMPLE HARMONIC MOTION

2. MODELLING MOTION

3. RESISTED MOTION

4. PROJECTILE MOTION

Term Calendar - 2026

Day: Friday

Time: 6:15 pm to 8:15 pm

Duration: 10 weeks per school term

Plus: 3 Holiday Lessons (usually in the first week of the school break). Holiday lessons help us stay ahead of the school curriculum and allow extra time for revision and exam preparation

Fee: For enrolment details and fee, give us a call on 0431137611

Note: Holiday lessons are included as part of the term fee. If a student cannot attend, they can revisit the lesson through our class recordings and are welcome to arrange a catch-up session for homework support.

Homework Help: Monday & Tuesday – 4:30 pm to 6:30 pm,
Saturday – 11 pm to 1 pm

Our Teaching Approach

All classes are taught by Sid, ensuring consistent guidance and a deep understanding of each student’s progress. Lessons are interactive, encouraging students to actively engage and ask questions. Our program is school and exam focused, with regular mock exams and thorough revision to build confidence and mastery. Sid goes beyond simply teaching the content—he shows students how to approach and think through problems, inspiring them to develop critical thinking skills and stay motivated throughout their learning journey.