QCE Specialist MathematicsPractice Examination 3

This paper covers

• Further complex numbers: De Moivre's theorem, powers/roots, conjugate root theorem, polynomial factorisation over C
• Mathematical induction: summation and divisibility proofs
• Vectors in 3D: lines, planes, cross products, distance formulae, spheres, projectile & circular motion via vector calculus
• Further matrices: Gaussian elimination for linear systems
• Integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• Applications of integration: areas, volumes of revolution, Simpson's rule, probability density functions
• Rates of change & DEs: implicit differentiation, related rates, separable DEs, slope fields
• Modelling motion: simple harmonic motion applied to tide height, variable forces, ODE kinematics
• Statistical inference: sampling distribution of the mean, confidence intervals for mu, required sample size
• Context: modelling tide height as SHM to predict safe/optimal harbour-navigation windows

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.