QCE Mathematical MethodsPractice Examination 8

This paper covers

• Unit 3 Further Calculus: differentiation of exponential, logarithmic and trigonometric functions via chain, product and quotient rules
• Applications of differentiation: kinematics, stationary points, nature of stationary points, points of inflection, curve sketching and optimisation
• Introduction to integration: antidifferentiation of standard forms, reverse chain rule, constant of integration from initial conditions, definite integrals and area
• Discrete random variables: Bernoulli sequences, binomial distribution, P(X=x), P(X≥x) and expected value E(X)=np
• Unit 4 integration extension: area between two curves, signed area and the trapezoidal rule for numerical integration
• 2D and 3D trigonometry: sine rule, cosine rule and bearings (navigation problems)
• Continuous random variables and the normal distribution: z-score standardisation, technology probabilities and inverse normal
• Inferential statistics: sampling distribution of the sample proportion, 95% confidence intervals, margin of error and sample size
• Complex Unfamiliar synthesis: constructing a confidence interval from survey data and evaluating a conservation agency's population claim with a written contextual conclusion
• Band A communication: correct QCAA notation, dx in integrals, absolute value in log integrals, approximately-equals for decimals, units, and explicit interpretive statements

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.