Rates of change, exponential and logarithmic calculus, integration techniques, and applications to the physical world.
These are the statements the Mathematics Extension 1 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.
Related rates and the chain rule applied to quantities changing with time, including setting up the relationship before differentiating.
Modelling with the exponential, including modified growth where a limiting value or an inflow changes the model.
Substitution, standard integrals including inverse trigonometric forms, and recognising which technique an integrand invites.
Motion, velocity and acceleration as derivatives, and problems where the relationship between variables must be established first.
The logarithm as an integral and as an inverse, its graph, and the derivative of a logarithm of a function.
The derivative of the exponential, the natural base, and differentiating composite exponential expressions.
Differentiation of products, quotients and composites, and applying the derivative to rates, optima and curve sketching.
Integration by substitution and by parts, and selecting the technique before starting.
HSC Mathematics Extension 1 - Trial Paper Shape is 70 marks in 120 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 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.
Calculus is module 3 of 6 in Mathematics Extension 1. 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.