Algebraic techniques, quadratic and polynomial behaviour, inverse relationships and the graphing skills that underpin every other strand.
These are the statements the Mathematics Advanced 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.
Domain, range, notation and composition, and the difference between a relation that is a function and one that is not.
Vertex form, the discriminant and the relationship between the algebraic form and the shape of the graph.
Degree, end behaviour, multiplicity of roots, and how the factored form predicts the graph.
The inverse as a reflection in y = x, the domain restriction needed to make one exist, and what the inverse means in context.
Arithmetic and geometric sequences and series, their general terms and sums, and recognising which model a situation requires.
Translations, reflections and dilations, and reading a transformation from the equation before graphing.
The absolute value function as a piecewise definition, and solving an inequality by interpreting it as a distance.
HSC Mathematics Advanced - Trial Paper Shape is 100 marks in 180 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 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.
Functions opens the Mathematics Advanced 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 Advanced dot point by dot point, then writes questions in the shape this course marks. Written answers come back marked against the bands.