Limits, differentiation and integration, and the applications that make calculus a tool rather than a procedure.
These are the statements the Mathematics Advanced syllabus makes about Calculus. Dux records each one against the questions you answer, so you can see which of them you have actually been tested on and which have never been asked.
The limit as the foundation of the derivative, and the difference between a function's value and its limit.
Product, quotient and chain rules, chosen by inspecting the structure of the expression rather than by trial.
Stationary points, the first and second derivative tests, and optimisation subject to a constraint.
The reverse of differentiation, the constant of integration, and recognising when a substitution is available.
Area between curves and the definite integral, including signed area and why it differs from total area.
The derivative as an instantaneous rate, and translating a word problem's rate into a derivative before differentiating.
Numerical integration for functions without an elementary antiderivative, and how the number of subintervals controls the error.
HSC Mathematics Advanced - Trial Paper Shape is 100 marks in 180 minutes. Questions on Calculus are not one shape repeated: the command word decides what the marker is looking for, and the mark value decides how much of it. These are the ones Mathematics Advanced uses.
Dux writes practice for this module in exactly these shapes, so the drill is the same task the paper sets — not a general knowledge quiz with the module name on it.
Calculus is module 3 of 5 in Mathematics Advanced. Students routinely lose marks because a question spans two modules, so the neighbouring modules are worth reading next to this one.
Dux diagnoses Mathematics Advanced dot point by dot point, then writes questions in the shape this course marks. Written answers come back marked against the bands.