HSC Mathematics Extension 2Practice Examination 8

This paper covers

• Complex numbers — Cartesian arithmetic & conjugates, roots of z⁴ = -16/16x⁴ = 1, polar/exponential conversion, |z - a| = k|z - b| circle locus, sum of roots of unity series — ~32 marks
• Further integration — quadratic-denominator (ln + arctan split), trig (sin²) substitution x = sin u, partial fractions over a difference of squares, reduction for integral cosⁿ / xⁿ e^x — ~28 marks
• Proof, vectors & mechanics — triangle/AM-GM inequality, induction (divisibility 7 | 8ⁿ - 1 type & geometric sum), 3D dot-product angle/perpendicularity, SHM v² = n²(a² - x²) energy, vertical resisted motion to terminal speed — ~40 marks

Students are permitted to bring into the examination the materials normally allowed for this subject. Answer all questions in the spaces provided.

This is an ATARMAxxing practice paper. It is not an official examination and is not affiliated with, endorsed by, or produced by the VCAA, NESA or the QCAA.