QCE Specialist MathematicsPractice Examination 8

This paper covers

• Unit 3 further complex numbers: factorising z⁴+4 over C, conjugate root theorem, De Moivre for powers/roots and argument calculations (cryptography framing)
• Mathematical induction: summation and divisibility proofs
• Vectors in 3D: lines, planes, cross product, distance formulae, spheres
• Vector calculus: differentiation/integration of vector functions, projectile and circular motion
• Further matrices: Gaussian elimination for 3x3 linear systems
• Unit 4 integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• Applications of integration: areas between curves, volumes of revolution, Simpson's rule, probability density functions
• Rates of change and 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

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.