Substitution, integration by parts, partial fractions, recurrence relations and the applications of the definite integral.
These are the statements the Mathematics Extension 2 syllabus makes about Further Calculus and Integration. 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.
Choosing a substitution, including trigonometric substitutions, and converting limits for a definite integral.
The product rule reversed, choosing the part to differentiate, and repeated application where required.
Decomposing a rational function, including repeated linear and irreducible quadratic factors, before integrating.
Establishing and using reduction formulae to evaluate a family of integrals.
Areas, volumes and other accumulated quantities, with the integral set up from a description rather than a formula.
Volumes generated by rotation about an axis, including the washer method and rotation about a line other than an axis.
HSC Mathematics Extension 2 - Trial Paper Shape is 100 marks in 180 minutes. Questions on Further Calculus and Integration 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 2 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.
Further Calculus and Integration is module 5 of 6 in Mathematics Extension 2. 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 2 dot point by dot point, then writes questions in the shape this course marks. Written answers come back marked against the bands.