QCE Specialist MathematicsPractice Examination 6

This paper covers

• Unit 3 further complex numbers: De Moivre's theorem, modulus-argument form, conjugate root theorem, factorisation over C
• Unit 3 mathematical induction: summation and divisibility proofs
• Unit 3 vectors in 3D: dot/cross products, lines and planes, distance formulae, spheres
• Unit 3 vector calculus: differentiation/integration of vector functions, projectile motion
• Unit 3 further matrices: Gaussian elimination for linear systems
• Unit 4 integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• Unit 4 applications of integration: areas between curves, volumes of revolution, Simpson's rule, probability density functions
• Unit 4 rates of change and DEs: implicit differentiation, related rates, separable differential equations, slope fields
• Unit 4 modelling motion: simple harmonic motion and variable forces
• Unit 4 statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Stimulus context: logistic population-growth model dP/dt = rP(1 - P/K) as a separable DE under resource constraints
• Cognitive spread across simple familiar (~60%), complex familiar (~20%) and complex unfamiliar (~20%) with Paper 1 technology-free and Paper 2 technology-active

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.