Inverse functions, parametric representation and polynomials, including the graphing skills Extension 1 assumes and extends.
These are the statements the Mathematics Extension 1 syllabus makes about Functions. 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.
Existence of an inverse, domain restrictions, and the relationship between the graphs of a function and its inverse.
Describing a curve by a parameter, converting between parametric and Cartesian form, and the tangent and normal to a parametric curve.
Roots and multiplicity, the factor and remainder theorems, and the relationship between coefficients and roots.
Sketching from a function's algebraic features, including reciprocal and absolute-value transformations and asymptotic behaviour.
Sketching transformed functions by composing shifts, scalings and reflections, and recognising the underlying graph.
HSC Mathematics Extension 1 - Trial Paper Shape is 70 marks in 120 minutes. Questions on Functions 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 Extension 1 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.
Functions opens the Mathematics Extension 1 course. Students routinely lose marks because a question spans two modules, so the neighbouring modules are worth reading next to this one.
Dux diagnoses Mathematics Extension 1 dot point by dot point, then writes questions in the shape this course marks. Written answers come back marked against the bands.