QCE Specialist MathematicsPractice Examination 7

This paper covers

• Unit 3 further complex numbers: De Moivre's theorem, nth roots, conjugate root theorem, polynomial factorisation over C
• Unit 3 mathematical induction: summation and divisibility proofs
• Unit 3 vectors in 3D: cross products, lines/planes, distances, line-plane intersection
• Unit 3 vector calculus: differentiation/integration of vector functions, projectile and SHM kinematics
• Unit 3 further matrices: Gaussian elimination for 3x3 linear systems
• Unit 4 integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• Unit 4 applications of integration: areas, volumes of revolution, Simpson's rule, probability density functions
• Unit 4 rates of change and differential equations: implicit differentiation, related rates, separable DEs, slope fields
• Unit 4 modelling motion: SHM and variable forces, ODE-based kinematics of a rocket with velocity-dependent thrust
• Unit 4 statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Rocket-launch stimulus: modelling vertical motion with variable thrust as a function of velocity using ODE techniques (Paper 2 Sections C and D)
• Cognitions: Select, Recall and use, Apply, Analyse and reason, Communicate across simple familiar (~60%), complex familiar (~20%) and complex unfamiliar (~20%)

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.