Year 12 Mathematical Methods
Choose a main topic to find your next skill.
Differential Calculus6 subtopics
Chain, product and quotient rules
Combine differentiation rules and evaluate gradients.
Exponential differentiation
Natural exponential derivatives and growth models.
Trigonometric differentiation
Mixed trigonometric and polynomial functions, exact angles, product and quotient rules, second derivatives and tangents.
Logarithmic graphs
Domains, transformations and inverse relationships.
Calculus of logarithms
Logarithmic derivatives, integrals and domain restrictions.
Topic Review
Four linked problems drawn from this topic’s subtopics. 12 parts · untimed · answers and worked solutions at the end.
Applications of Differential Calculus5 subtopics
Rates, tangents and normals
Polynomial calculus and rates in context.
Second derivatives and curve shape
Concavity, inflection and acceleration.
Constrained optimisation
Build models, test stationary points and compare feasible endpoints.
Exponential equations with logarithms
Solve growth and decay equations and interpret solutions.
Topic Review
Four linked problems drawn from this topic’s subtopics. 12 parts · untimed · answers and worked solutions at the end.
Integration4 subtopics
Antiderivatives
Reverse differentiation and initial conditions.
Estimating area
Upper and lower rectangles and numerical approximations.
Definite integrals
Fundamental theorem, signed area and integral properties.
Worked example includedTopic Review
Four linked problems drawn from this topic’s subtopics. 12 parts · untimed · answers and worked solutions at the end.
Applications of Integration3 subtopics
Motion and accumulation
Displacement, total distance and changing inflow and outflow rates.
Areas and integral models
Bounded regions, production costs and recovering model parameters.
Topic Review
Four linked problems drawn from this topic’s subtopics. 12 parts · untimed · answers and worked solutions at the end.
Discrete Random Variables4 subtopics
Discrete probability distributions
Probability tables, expectation and variance.
Bernoulli trials
Success indicators, expectation and variance.
Binomial distributions
Exact probabilities, cumulative probabilities and model assumptions.
Topic Review
Four linked problems drawn from this topic’s subtopics. 12 parts · untimed · answers and worked solutions at the end.
Continuous Random Variables3 subtopics
Continuous random variables
Density normalisation, interval probabilities and expectation.
Normal probabilities and quantiles
Standardise, find probabilities and reverse normal calculations.
Topic Review
Four linked problems drawn from this topic’s subtopics. 12 parts · untimed · answers and worked solutions at the end.
Sampling and Confidence Intervals5 subtopics
Sampling distributions
Sample means, standard errors and the central limit theorem.
Confidence intervals for a mean
Interval endpoints, sample size and interpretation.
Sample proportions
Sampling variation, standard errors and model conditions.
Confidence intervals for a proportion
Construct intervals, estimate sample size and assess claims.
Topic Review
Four linked problems drawn from this topic’s subtopics. 12 parts · untimed · answers and worked solutions at the end.
These are the practice sets currently available for this year. Coverage is still growing.
Open Year 12 practice