QCE Specialist MathematicsPractice Examination 9

This paper covers

• Unit 3 further complex numbers: De Moivre's theorem, powers and nth roots, conjugate root theorem and factorisation over C
• Unit 3 mathematical induction: summation and divisibility proofs
• Unit 3 vectors in 3D: cross product, scalar/vector equations of lines and planes, point-to-plane distance, spheres
• Unit 3 vector calculus: differentiating/integrating vector functions, projectile and circular motion
• Unit 3 further matrices: Gaussian elimination and parameter-dependent solution sets
• Unit 4 integration techniques: inverse-trig integrals, substitution, partial fractions, integration by parts
• Unit 4 applications of integral calculus: area between curves as energy absorption of alloys, volumes of revolution, Simpson's rule, probability density functions
• Unit 4 rates of change and differential equations: implicit differentiation, related rates, separable DEs, slope fields
• Unit 4 modelling motion: simple harmonic motion, variable forces, ODE-based kinematics
• Unit 4 statistical inference: sampling distribution of the mean, confidence intervals for mu, sample-size determination
• Materials-science stimulus thread: computing the area between stress-strain curves to compare toughness/energy absorption of two alloys
• Assessment objectives: Select, Recall and use, Apply, Analyse and reason, Communicate across 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.