QCE Specialist MathematicsPractice Examination 10

This paper covers

• Unit 3 further complex numbers: De Moivre's theorem, roots of unity, polynomial factorisation over C, conjugate root theorem
• Signal-processing thread: proving Fourier harmonic-sum trig identities via the complex geometric series z=e^{i theta} (Dirichlet kernel, odd-harmonic sum)
• Mathematical induction: summation and divisibility proofs
• Vectors in 3D: lines/planes, cross product, distance formulae, spheres
• Vector calculus: projectile and circular motion
• Further matrices: Gaussian elimination for linear systems
• Unit 4 integration techniques: inverse-trig, substitution, partial fractions, integration by parts
• Applications of integration: areas, volumes of revolution, Simpson's rule, probability density functions
• Rates of change and differential equations: implicit/related rates, separable DEs, slope fields
• Modelling motion: SHM and variable forces
• Statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Cognitions: Select, Recall and use, Apply, Analyse and reason, Communicate across simple familiar / complex familiar / complex unfamiliar

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.