Discrete and continuous probability distributions, and the sampling ideas that make an estimate meaningful.
These are the statements the Mathematics Extension 1 syllabus makes about Probability and Statistics. 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.
Probability distributions, expected value and variance, and the binomial distribution as the central discrete case.
Density functions, probability as area, and the normal distribution as the standard continuous model.
The sample mean as an estimate, the effect of sample size on spread, and what a confidence statement does and does not claim.
Standardising, using tables or technology, and interpreting a probability in context.
HSC Mathematics Extension 1 - Trial Paper Shape is 70 marks in 120 minutes. Questions on Probability and Statistics 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.
Probability and Statistics is module 4 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.