Support · Mathematics Extension 2 11–12 – Year 12 · The nature of proof
Support Establish and use the relationship between the arithmetic mean and geometric mean for two non-negative numbers, that is ∀a,b ≥ 0,(a + b)/2 ≥ √(ab)
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
Examine the nature of inductive proof, including the statement to be proved, the base case and the inductive step
Mathematics Extension 1 11–12 – Year 12 · Proof by mathematical induction Draft mapping
No checked resources on this prerequisite dot point yet.
Use the formulas E(X̅) = μ and Var(X̅) = σ²/n as the mean and the variance of the sampling distribution of the mean for samples of size n drawn from a population with mean μ and variance σ²
Mathematics Extension 1 11–12 – Year 12 · The binomial distribution and sampling distribution of the mean Draft mapping
No checked resources on this prerequisite dot point yet.
Use the formulae E(X) = μ = np to find the mean, and Var(X) = np(1 - p) to find the variance when X~Bin(n,p)
Mathematics Extension 1 11–12 – Year 12 · The binomial distribution and sampling distribution of the mean Draft mapping
No checked resources on this prerequisite dot point yet.