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ACMMM081

examine the behaviour of the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) as \(h\rightarrow0\) as an informal introduction to the concept of a limit

ACMMM095

sketch curves associated with simple polynomials; find stationary points, and local and global maxima and minima; and examine behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

convert sums \(\mathrm a\cos\mathrm x+\mathrm b\;\sin\mathrm x\) to \(\mathrm R\;\cos{(\mathrm x\pm\mathrm\alpha)}\) or \(\mathrm R\sin{(\mathrm x\pm\mathrm\alpha)}\) and apply these to sketch graphs, solve equations of the form \(\mathrm a\cos\mathrm …

ACMMM020

recognise features of the graphs of \(x^2+y^2=r^2\) and \(\left(x-a\right)^2+\left(y-b\right)^2=r^2\), including their circular shapes, their centres and their radii

ACMMM107

use the increments formula: \(\delta y\cong\frac{dy}{dx}\times\delta x\) to estimate the change in the dependent variable \(y\) resulting from changes in the independent variable \(x\)

ACMMM130

understand and use the theorem \(F'\left(x\right)=\frac d{dx}\left(\int_a^xf\left(t\right)dt\right)=f\left(x\right)\), and illustrate its proof geometrically

ACMSM049

prove and apply other trigonometric identities such as \(\cos3\mathrm x=4\;\mathrm c\mathrm o\mathrm s^{3\;}\mathrm x-3\cos\mathrm x\)

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

ACSCH021

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 …

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