QCE Specialist MathematicsPractice Examination 15

This paper covers

• Continuous probability density functions modelled on an ecological fish-weight survey (normalisation constant, mean, median, mode, variance, interval probabilities)
• 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
• Unit 4 statistical inference: sampling distribution of the mean, confidence intervals for the population mean, required sample size
• Unit 4 rates of change and differential equations: separable DEs, related rates, implicit differentiation, logistic growth
• Unit 4 modelling motion: simple harmonic motion and ODE-based kinematics
• Unit 3 further complex numbers: modulus-argument form, De Moivre's theorem, conjugate root theorem, roots over C
• Unit 3 mathematical induction: summation and divisibility proofs
• Unit 3 vectors in three dimensions: dot/cross products, lines and planes, distance formulae, spheres, projectile and circular motion
• Unit 3 further matrices: Gaussian elimination for 3x3 linear systems
• QCAA cognitive spread: simple familiar (~60%), complex familiar (~20%), complex unfamiliar (~20%) across a technology-free Paper 1 and technology-active Paper 2

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.