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ACMSM141

examine the approximate confidence interval \(\left(\overline{\mathrm X}\;–\frac{\mathrm z\mathrm s}{\sqrt[{}]n},\;\;\overline{\mathrm X}+\frac{\mathrm z\mathrm s}{\sqrt[{}]n}\right),\), as an interval estimate for \(\mu\) ,the population mean, where …

ACMSM141 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM053

calculate the determinant and inverse of 2x2 matrices and solve matrix equations of the form AX=B , where A is a 2x2 matrix and X and B are column vectors. 

ACMSM053 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM042

find all solutions of \(\mathrm f\left(\mathrm a\left(\mathrm x-\mathrm b\right)\right)=\mathrm c\) where \(f\) is one of \(\sin\), \(\cos\) or \(\tan\)

ACMSM042 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM043

graph functions with rules of the form \(\mathrm y=\mathrm f(\mathrm a\left(\mathrm x-\mathrm b\right))\) where \(f\) is one of \(\sin\), \(\cos\) or \(\tan\)

ACMSM043 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM143

use \(\overline x\) and \(s\) to estimate \(\mu\) and \(\sigma\), to obtain approximate intervals covering desired proportions of values of a normal random variable and compare with an approximate confidence interval for \(\mu\)

ACMSM143 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum

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 …

ACMSM138 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM139

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 …

ACMSM139 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMSM086

identify subsets of the complex plane determined by relations such as \(\left|z-3i\right|\leq4\) \(\frac\pi4\leq Arg(z)\leq\frac{3\pi}4\), \(Re\left(z\right)>Im(z)\) and \(\left|z-1\right|=2\vert z-i\vert\)

ACMSM086 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum

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