HSC Mathematics Extension 2Practice Examination 18

This paper covers

• Complex numbers — square roots of a complex number, sum of the nth roots of unity being zero, geometry of multiplication by i (rotation), region from |z−1| ≤ |z+i| — ~27 marks
• Further integration & proof — trig substitution x = a tan θ, reduction formula for ∫cosⁿx, AM–GM applied to a minimisation, triangle inequality with geometric interpretation, induction that 2ⁿ > n² for n ≥ 5 — ~37 marks
• Vectors & mechanics — vector equation of a line & point of closest approach to a point, dot-product proof that an angle in a semicircle is 90°, resisted vertical motion upward (first power of speed), projectile in a resisting medium (full motion) — ~36 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.