QCE Specialist MathematicsPractice Examination 14

This paper covers

• Unit 4 integration techniques — partial-fraction decomposition of proper rational functions and integration to logarithmic form, anchored in a CT-dosimetry absorption-rate context
• De Moivre's theorem, conjugate root theorem and factorisation of polynomials over the complex field (Unit 3)
• Mathematical induction — summation and divisibility proofs (Unit 3)
• Vectors in three dimensions — cross products, scalar triple product, vector/Cartesian equations of lines and planes, distance formulae and spheres (Unit 3)
• Vector calculus and modelling motion — projectile motion, circular motion and simple harmonic motion (Units 3 & 4)
• Further calculus — inverse-trig integrals, substitution, integration by parts, implicit differentiation and related rates (Unit 4)
• Applications of integral calculus — areas between curves, volumes of revolution, Simpson's rule and probability density functions (Unit 4)
• Differential equations — separable DEs and slope fields (Unit 4)
• Statistical inference — sampling distribution of the mean, confidence intervals for a population mean and sample-size determination (Unit 4)
• Gaussian elimination for systems of linear equations (Unit 3)
• Paper 1 technology-free fluency and Paper 2 technology-active modelling across simple familiar (~60%), complex familiar (~20%) and complex unfamiliar (~20%) 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.