QCE Specialist MathematicsPractice Examination 2

This paper covers

• Unit 3 further complex numbers: De Moivre's theorem, nth roots, conjugate root theorem, polynomial factorisation over C
• Unit 3 mathematical induction: summation and divisibility proofs
• Unit 3 vectors in 3D: cross products, vector/Cartesian equations of lines and planes, distance formulae
• Unit 3 vector calculus: differentiation of vector functions, projectile and circular motion
• Unit 3 further matrices: Gaussian elimination for 3x3 linear systems
• Unit 4 integration techniques: inverse trig integrals, substitution, partial fractions, integration by parts
• Unit 4 applications of integral calculus: areas between curves, volumes of revolution, Simpson's rule, probability density functions
• Unit 4 rates of change and DEs: implicit differentiation, related rates, separable differential equations
• Unit 4 modelling motion: simple harmonic motion and variable forces
• Unit 4 statistical inference: sampling distribution of the mean, confidence intervals for mu, sample size
• Applied context throughout: designing a water reservoir dam, estimating water volume via solids of revolution and Simpson's rule

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.