QCE Specialist MathematicsPractice Examination 19

This paper covers

• Mathematical induction (summation and divisibility proofs) framed through a sports-science cumulative fatigue index
• Further complex numbers: De Moivre's theorem, powers and roots, conjugate root theorem, factorisation over C
• Vectors in 3D: cross products, lines and planes, point-plane distance, spheres, and vector calculus (projectile/circular motion)
• Further matrices: Gaussian elimination for systems of linear equations
• Integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• Applications of integral calculus: areas, volumes of revolution, Simpson's rule, probability density functions
• Rates of change and differential equations: implicit differentiation, related rates, separable DEs, slope fields
• Modelling motion: simple harmonic motion and variable forces
• Statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Paper 1 technology-free fluency and Paper 2 technology-active modelling across simple familiar, complex familiar and complex unfamiliar 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.