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ACMSM137

examine the concept of the sample mean X as a random variable whose value varies between samples where X is a random variable with mean μ and the standard deviation σ

ACMEM001

solve practical problems requiring basic number operations

ACMEM008

evaluate decimal fractions to the required number of decimal places

ACMEM058

complete a five number summary for different datasets

ACMEM059

construct box plots using a five number summary

ACMMM011

recognise features of the graph of the general quadratic \(y=ax^2+bx+c\)

simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate the approximate standard normality of \(\frac{\overline X-\mu}{s/\sqrt[{}]n}\) for large samples \(\left(n\geq30\right)\), where \(s\) is the …

ACMEM118

work with the concepts of angle of elevation and angle of depression

ACMEM009

round up or round down numbers to the required number of decimal places

ACMMM099

recognise that \(e\) is the unique number \(a\) for which the above limit is 1

ACMSM070

perform complex-number arithmetic: addition, subtraction, multiplication and division.

ACMMM007

recognise features of the graphs of \(y=x^2\), \(y=a{(x-b)}^2+c\), and \(y=a\left(x-b\right)\left(x-c\right)\) including their parabolic nature, turning points, axes of symmetry and intercepts

ACMGM082

apply Euler’s formula, \(v+f-e=2\), to solve problems relating to planar graphs.

ACMMM021

recognise features of the graph of \(y^2=x\) including its parabolic shape and its axis of symmetry.

ACMSM066

prove divisibility results, such as \(3^{2n+4}-2^{2n}\) is divisible by 5 for any positive integer n.

ACMSM138

simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate properties of the distribution of \(\overline X\;\) across samples of a fixed size \(n\), including its mean \(\mu\), its standard deviation …

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