QCE Specialist MathematicsPractice Examination 5

This paper covers

• Vectors in 3D: vector/Cartesian equations of lines and planes, cross products, concurrent vs skew roof-beam intersections, shortest-distance and point-to-plane formulae, spheres
• Further complex numbers: De Moivre's theorem, powers and roots, conjugate root theorem, factorisation over C
• Mathematical induction: summation and divisibility proofs
• Further matrices: Gaussian elimination for 3x3 linear systems
• Vector calculus and modelling motion: differentiation/integration of vector functions, projectile and circular motion, SHM, variable forces
• 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 differential equations: implicit differentiation, related rates, separable DEs, slope fields
• Statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Structural-engineering context throughout: roof-beam geometry, truss force systems, beam deflection sampling

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.