Growth and decay, the logarithm as an inverse, and the calculus of both, which is where most real modelling lives.
These are the statements the Mathematics Advanced syllabus makes about Exponential and Logarithmic 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.
The exponential function and its graph, the logarithm as its inverse, and the natural base e.
Modelling growth and decay, including doubling time and half-life, and the meaning of the rate constant.
The index laws in logarithmic form, and solving an equation by taking logarithms of both sides.
Differentiating and integrating e^x and ln x, including the chain rule case that most errors occur in.
HSC Mathematics Advanced - Trial Paper Shape is 100 marks in 180 minutes. Questions on Exponential and Logarithmic 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.
Exponential and Logarithmic Functions is module 4 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.