QCE Specialist MathematicsPractice Examination 18

This paper covers

• Unit 4 integration techniques — inverse-trig integrals, substitution, partial fractions, and integration by parts (the paper's stimulus thread: present value of a continuous income stream with exponential decay, PV = ∫ R(t)e^-rt dt)
• Unit 4 applications of integral calculus — areas between curves, volumes of revolution, Simpson's rule, probability density functions
• Unit 3 further complex numbers — De Moivre's theorem, conjugate root theorem, factorisation over C
• Unit 3 mathematical induction — summation identities and divisibility proofs
• Unit 3 vectors in three dimensions and vector calculus — cross products, distance to a plane, lines/spheres, differentiation of vector functions, projectile/circular motion
• Unit 3 further matrices — Gaussian elimination for 3x3 linear systems
• Unit 4 rates of change and differential equations — implicit differentiation, related rates, separable DEs, slope fields
• Unit 4 modelling motion — simple harmonic motion and variable-force/ODE kinematics
• Unit 4 statistical inference — sampling distribution of the mean, confidence intervals for μ, and sample-size determination
• Paper 1 technology-free fluency (Sections A/B) and Paper 2 technology-active modelling (Sections C/D), spanning simple familiar ~60%, complex familiar ~20%, complex unfamiliar ~20%

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.