HSC Mathematics Extension 2Practice Examination 16

This paper covers

• Complex numbers (De Moivre for cos 5θ, sum of nth roots of unity, |z−a|=|z−b| perpendicular-bisector locus, complex-coefficient quadratic with a repeated root) — ~32 marks
• Proof & further integration (proof by contradiction for ∛2, induction on a first-order recurrence, secⁿ reduction by parts, partial fractions with a repeated linear factor) — ~33 marks
• Vectors & mechanics (sphere & tangent-line condition via dot product, perpendicularity, projectile clearing a wall (two angles), SHM time to a directed centre-crossing) — ~35 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.