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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

Isotopes are atoms of an element with the same number of protons but different numbers of neutrons; different isotopes of elements are represented using atomic symbols (for example, \({}_6^{12}C\), \({}_6^{13}C\)

ACSCH024

The relative atomic mass of an element is the ratio of the weighted average mass per atom of the naturally occurring form of the element to \(\frac1{12}\) the mass of an atom of carbon-12; relative atomic masses reflect the isotopic composition of the …

ACMMM013

recognise features of the graphs of \(y=\frac1x\) and \(y=\frac a{x-b}\), including their hyperbolic shapes, and their asymptotes.

ACMMM021

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

ACMMM026

examine dilations and the graphs of \(y=cf\left(x\right)\) and \(y=f\left(kx\right)\)

ACMMM115

use the notation \(\int f\left(x\right)dx\) for anti-derivatives or indefinite integrals

ACMMM129

understand the concept of the signed area function \(F\left(x\right)=\int_a^xf\left(t\right)dt\)

ACMMM161

establish and use the formula \(\frac d{dx}\left(\ln x\right)=\frac1x\)

ACMSM121

integrate expressions of the form \(\frac{\pm1}{\sqrt[{}]{a^2-x^2}}\) and \(\frac a{a^2+x^2}\)

ACHAH288

The contribution of new scientific methodologies, including DNA analysis, radio-carbon dating, dendrochronology, thermoluminescence, proton magnetometer, and x-rays

ACHMH086

The role and significance of individuals in the struggle for civil rights, for example Martin Luther King Jr, Rosa Parkes, and Malcolm X

ACMGM031

construct and use parallel box plots (including the use of the ‘Q1 – 1.5 x IQR’ and ‘Q3 + 1.5 x IQR’ criteria for identifying possible outliers) to compare groups in terms of location (median), spread (IQR and range) and outliers and to interpret and …

ACMSM055

define and use basic linear transformations: dilations of the form \((\mathrm x,\mathrm y)\longrightarrow({\mathrm\lambda}_1\mathrm x,{\mathrm\lambda}_2\mathrm y)\) , rotations about the origin and reflection in a line which passes through the origin, …

ACMSM130

solve simple first-order differential equations of the form \(\frac{dy}{dx}=f(x)\), differential equations of the form \(\frac{dy}{dx}=g\left(y\right)\) and, in general, differential equations of the form \(\frac{dy}{dx}=f\left(x\right)g\left(y\right)\) …

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 …

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