HSC Mathematics Extension 2Practice Examination 17

This paper covers

• Complex numbers — De Moivre to derive a sin/cos 5θ identity, cube roots of a complex number, real-polynomial conjugate roots, square roots & quadratics — ~30 marks
• Further integration & proof — partial fractions with a repeated linear factor, ∫xⁿeˣ reduction formula, completing-the-square inverse-tan, induction for the binomial theorem, contradiction for irrationality of log₂5 — ~35 marks
• Vectors & mechanics — sphere–line intersection in 3D, vector proof that the diagonals of a rhombus are perpendicular, resisted motion on a horizontal line (v as a function of x), SHM established from x = a sin(nt+α) — ~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.