These are ATARMAxxing’s course-guide summaries. Review all required areas, including school assessments, practical work, performances or folios where applicable. Follow your course’s option rules.
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Unit 3 — Topic 3.1: Further differentiation and applications
Differentiate exponential and trigonometric functions using product, quotient and chain rules. Use first and second derivatives to analyse rates, concavity, stationary points and optimisation.
Unit 3 — Topic 3.2: Integrals
Find antiderivatives, use initial conditions, and connect definite integrals with signed area and the fundamental theorem. Apply integration to areas, accumulated change and linear motion.
Unit 3 — Topic 3.3: Discrete random variables
Represent discrete probability distributions and calculate expected value, variance and standard deviation. Model Bernoulli trials and binomial counts and examine linear transformations.
Unit 4 — Topic 4.1: The logarithmic function
Use logarithms as indices, apply logarithm laws and interpret transformed graphs and scales. Differentiate natural logarithmic functions and recognise integrals of the form f′/f.
Unit 4 — Topic 4.2: Continuous random variables and the normal distribution
Use densities and cumulative distribution functions to calculate probabilities and moments. Apply continuous and normal models, standardisation and inverse-normal calculations.
Unit 4 — Topic 4.3: Interval estimates for proportions
Examine random sampling, bias and variation in sample proportions. Construct approximate confidence intervals, interpret coverage and compare confidence, sample size and margin of error.
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