Mathematics Extension 2
Year 12 · Stage 6 · NSW Mathematics syllabus
The nature of proof
Develop rigorous proof skills: understand logical implication, quantifiers and equivalence; apply proof by contradiction, existence and uniqueness proofs; prove inequalities using algebraic identities and AM-GM.
3 sub-topics
Complex numbers
Extend the number system to complex numbers: arithmetic and Cartesian form, polar and exponential form, De Moivre's theorem, roots of unity, and loci in the Argand plane.
4 sub-topics
Further integration
Extend integration techniques to include integration by parts, partial fractions (including repeated and irreducible quadratic factors), the t-substitution, trigonometric integrals, reduction formulae, and problems requiring a strategic choice of method.
2 sub-topics
Mechanics
Apply calculus to motion problems: use all forms of acceleration (, , ); analyse simple harmonic motion including derivation of displacement and velocity; solve motion problems with resistance proportional to velocity or , including terminal velocity and projectile motion with air resistance.
3 sub-topics
Further work with vectors
Extend two-dimensional vector work into three dimensions: component form using , , ; the dot product and angles in 3D; vector equations of lines and parametric form; intersection and skew lines; geometric and coordinate-geometry proofs using vectors.
3 sub-topics