QCE Specialist MathematicsPractice Examination 20

This paper covers

• Rates of change and separable differential equations — Newton's law of cooling modelled as dT/dt = -k(T - Ts), solved by separation of variables
• The time constant tau = 1/k, its interpretation (excess temperature falls to 1/e of its initial value) and half-life reasoning
• Statistical inference — sampling distribution of the mean, z-based confidence intervals for a population mean mu, and minimum sample size
• Further complex numbers — De Moivre's theorem, roots over C, conjugate root theorem
• Mathematical induction — summation proofs with base case, inductive hypothesis and inductive step
• Vectors in 3D — cross product and area, distance from a point to a plane, and vector calculus (speed, projectile motion)
• Integration techniques and applications — inverse-trig integrals, partial fractions, integration by parts, areas, volumes of revolution, Simpson's rule, probability density functions
• Further matrices — Gaussian elimination for 3x3 linear systems
• Modelling motion — simple harmonic motion and ODE-based kinematics
• Paper 1 technology-free fluency (60 marks) and Paper 2 technology-active modelling (60 marks), across simple familiar (~60%), complex familiar (~20%) and complex unfamiliar (~20%) cognitions

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.