QCE Specialist MathematicsPractice Examination 13

This paper covers

• Vector calculus: differentiation of vector functions, velocity/speed/acceleration, projectile and circular/elliptical motion (astronomy satellite context)
• Further complex numbers: modulus-argument form, De Moivre's theorem, roots over C, conjugate root theorem, polynomial factorisation
• Mathematical induction: summation and divisibility proofs
• Vectors in 3D: lines and planes, cross product, distance formulae, spheres
• Further matrices: Gaussian elimination for linear systems
• Integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• Applications of integration: areas between curves, volumes of revolution, Simpson's rule, probability density functions
• Rates of change and DEs: implicit differentiation, related rates, separable differential equations
• Modelling motion: simple harmonic motion, variable forces, ODE-based kinematics
• Statistical inference: sampling distribution of the mean, confidence intervals for mu, required sample size

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.