QCE Specialist MathematicsPractice Examination 1

This paper covers

• Unit 3 further complex numbers: De Moivre's theorem, roots of zⁿ, conjugate root theorem, factorisation over C
• Unit 3 mathematical induction: summation and divisibility proofs
• Unit 3 vectors in 3D: cross product, area/volume, lines and planes, point-plane distance
• Unit 3 vector calculus: differentiation/integration of vector functions, projectile motion (cricket-ball trajectory context)
• Unit 3 further matrices: Gaussian elimination and nature of solutions
• Unit 4 integration techniques: inverse-trig integrals, by parts, partial fractions
• Unit 4 applications of integration: volumes of revolution, Simpson's rule, probability density functions
• Unit 4 rates of change and DEs: separable differential equations, related rates
• Unit 4 modelling motion: simple harmonic motion and resistive (variable-force) motion
• Unit 4 statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Paper 1 technology-free fluency (Sections A/B) and Paper 2 technology-active modelling (Sections C/D)
• Cricket-ball projectile/spin trajectory stimulus threaded through vector-calculus and motion items

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.