QCE Specialist MathematicsPractice Examination 16

This paper covers

• Vectors in 3D: cross products, moment of a force (r×F), scalar triple product, lines/planes, distance formulae, spheres
• Further complex numbers: De Moivre's theorem, nth roots, conjugate root theorem, factorisation over C
• Mathematical induction: summation and divisibility proofs
• Vector calculus: differentiation/integration of vector functions, projectile and circular motion
• 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: SHM and ODE-based kinematics
• Statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Stimulus context throughout: bridge cable tension and the moment of a force vector about a support point

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.