QCE Specialist MathematicsPractice Examination 12

This paper covers

• Rates of change & separable differential equations applied to traffic-flow (Greenshields) modelling: setting up and solving dk/dt and dq/dk
• Unit 4 integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• 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, nth roots, factorisation over C, conjugate root theorem
• Mathematical induction: summation and divisibility proofs
• Vectors in 3D and vector calculus: cross products, lines/planes, projectile and circular motion
• Further matrices: Gaussian elimination for linear systems
• Modelling motion: SHM and variable-force/ODE kinematics
• Statistical inference: sampling distribution of the mean, confidence intervals for μ, and required sample size
• Paper 1 technology-free fluency (Sections A & B) and Paper 2 technology-active modelling (Sections C & D), spanning simple familiar (~60%), complex familiar (~20%) and 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.