HSC Mathematics Extension 2 Year 12 Notes

These are the 20 revision notes inside the HSC Mathematics Extension 2 Mastery Pack. Open any note to see what it covers before you buy.

1. The language of proof: implication, converse, contrapositive and proof by contradiction3 · MEX-P1

   Unit 3 MEX-P1 — Proof: The Nature of Proof

2. Proving inequalities from a > b and the non-negativity of squares3 · MEX-P1

   Unit 3 MEX-P1 — Proof: The Nature of Proof

3. The triangle inequality and the AM–GM inequality for two numbers3 · MEX-P1

   Unit 3 MEX-P1 — Proof: The Nature of Proof

4. Induction for series in sigma notation and for non-standard base cases or steps3 · MEX-P2

   Unit 3 MEX-P2 — Proof: Further Mathematical Induction

5. Divisibility and inequality proofs by induction3 · MEX-P2

   Unit 3 MEX-P2 — Proof: Further Mathematical Induction

6. Induction in calculus, geometry, the binomial theorem and recursive formulae3 · MEX-P2

   Unit 3 MEX-P2 — Proof: Further Mathematical Induction

7. Vectors in three dimensions: components, magnitude, the dot product and spheres3 · MEX-V1

   Unit 3 MEX-V1 — Vectors: Further Work with Vectors

8. Vector equations of lines: r = a + λb, parallel and perpendicular lines, and points on a line3 · MEX-V1

   Unit 3 MEX-V1 — Vectors: Further Work with Vectors

9. Complex numbers in Cartesian form: arithmetic, the conjugate, square roots and the Argand plane3 · MEX-N1

   Unit 3 MEX-N1 — Complex Numbers: Introduction

10. Polar and exponential form: modulus, argument, Euler's formula and the geometry of multiplication3 · MEX-N1

    Unit 3 MEX-N1 — Complex Numbers: Introduction

11. De Moivre's theorem: induction proof, powers and trigonometric identities4 · MEX-N2

    Year 12 - Complex Numbers: Using Complex Numbers

12. Quadratics and polynomials over the complex numbers, and the conjugate root theorem4 · MEX-N2

    Year 12 - Complex Numbers: Using Complex Numbers

13. Geometry of complex arithmetic: vectors, the parallelogram law and rotation by i4 · MEX-N2

    Year 12 - Complex Numbers: Using Complex Numbers

14. nth roots of unity, nth roots of a complex number, and regions of the Argand plane4 · MEX-N2

    Year 12 - Complex Numbers: Using Complex Numbers

15. Integration by substitution and rational functions with a quadratic denominator4 · MEX-C1

    Year 12 - Calculus: Further Integration

16. Partial fractions and integrating rational functions4 · MEX-C1

    Year 12 - Calculus: Further Integration

17. Integration by parts and reduction (recurrence) formulae4 · MEX-C1

    Year 12 - Calculus: Further Integration

18. Simple harmonic motion: equations, the defining property and graphs4 · MEX-M1

    Year 12 - Mechanics: Applications of Calculus to Mechanics

19. Straight-line motion with variable acceleration and resisted motion4 · MEX-M1

    Year 12 - Mechanics: Applications of Calculus to Mechanics

20. Projectile motion: parametric equations, the Cartesian path and resisted projectiles4 · MEX-M1

    Year 12 - Mechanics: Applications of Calculus to Mechanics