QCE Specialist MathematicsPractice Examination 4

This paper covers

• Statistical inference: sampling distribution of the sample mean, constructing and interpreting confidence intervals for a population mean (known sigma), and required sample size — set in a respiratory-illness clinical-trial recovery-time context
• Further complex numbers: De Moivre's theorem, powers and nth roots, polynomial factorisation over C, conjugate root theorem
• Mathematical induction: summation identities and divisibility proofs
• Vectors in three dimensions: dot and cross products, angle between vectors, lines/planes, spheres, distance
• Vector calculus and modelling motion: projectile motion, SHM, variable forces
• Further calculus: inverse-trig integrals, substitution, partial fractions, integration by parts, areas between curves, volumes of revolution, Simpson's rule, probability density functions
• Rates of change and differential equations: implicit and related rates, separable DEs, slope fields
• Further matrices: Gaussian elimination for systems of linear equations
• Paper 1 technology-free fluency and Paper 2 technology-active modelling across simple familiar (~60%), complex familiar (~20%) and complex unfamiliar (~20%) cognitions

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.