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Unit 4: Revolutions in modern physics Physics

The development of quantum theory and the theory of relativity fundamentally changed our understanding of how nature operates and led to the development of a wide range of new technologies, including technologies that revolutionised the storage, processing …

Unit 4 | Physics | Science | Senior secondary curriculum

ACSES049

Most of the thermal radiation emitted from Earth’s surface passes back out into space but some is reflected or scattered by greenhouse gases back toward Earth; this additional surface warming produces a phenomenon known as the greenhouse effect

ACMMM017

recognise features of the graphs of \(y=x^3\), \(y=a{(x-b)}^3+c\) and \(y=k(x-a)(x-b)(x-c)\), including shape, intercepts and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

ACMMM106

apply the product, quotient and chain rule to differentiate functions such as \(xe^x\), \(\tan x,\), \(\frac1{x^n}\), \(x\sin x,\text{ }e^{-x}\sin x\) and \(f(ax+b)\)

Senior secondary English subjects

The senior secondary Australian Curriculum for English is presented in four subjects that share common features. These include the continuing development of students’ knowledge, understanding and skills in listening, speaking, reading, viewing and writing. …

Senior secondary English subjects | English | Senior secondary curriculum

ACMMM037

examine amplitude changes and the graphs of \(y=a\sin x\) and \(y=a\cos x\)

ACMMM036

recognise the graphs of \(y=\sin x,\;y=\cos x,\) and \(y=\tan x\) on extended domains

ACMSM098

use and apply the notation \(\left|x\right|\) for the absolute value for the real number \(x\) and the graph of \(y=\left|x\right|\)

ACMMM039

examine phase changes and the graphs of \(y=\sin{(x+c)}\), \(y=\cos{(x+c)}\) and \(y=\tan{(x+c)}\) and the relationships \(\sin\left(x+\frac\pi2\right)=\cos x\) and \(\cos\left(x-\frac\pi2\right)=\sin x\)

ACMMM065

recognise the qualitative features of the graph of \(y=a^x(a>0)\) including asymptotes, and of its translations \(y=a^x+b\) and \(y=a^{x+c}\)

ACMMM082

define the derivative \(f'\left(x\right)\) as \(\lim_{h\rightarrow0}\frac{f\left(x+h\right)-f(x)}h\)

ACMSM117

use substitution \(u = g(x)\) to integrate expressions of the form \(f\left(g\left(x\right)\right)g'\left(x\right)\)

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

ACMMM079

use the notation \(\frac{\delta y}{\delta x}\) for the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) where \(y=f(x)\)

ACMMM080

interpret the ratios \(\frac{f\left(x+h\right)-f(x)}h\) and \(\frac{\delta y}{\delta x}\) as the slope or gradient of a chord or secant of the graph of \(y=f(x)\)

ACMMM088

establish the formula \(\frac d{dx}\left(x^n\right)=nx^{n-1}\) for positive integers \(n\) by expanding \({(x+h)}^n\) or by factorising \({(x+h)}^n-x^n\)

ACMMM159

define the natural logarithm \(\ln x=\log_ex\)

ACMSM099

examine the relationship between the graph of \(y=f(x)\) and the graphs of \(y=\frac1{f(x)}\), \(y=\vert f\left(x\right)\vert\) and \(y=f(\left|x\right|)\)

ACSES105

Human activities, particularly land-clearing and fossil fuel consumption, produce gases (including carbon dioxide, methane, nitrous oxide and hydrofluorocarbons) and particulate materials that change the composition of the atmosphere and climatic conditions …

ACMMM025

examine translations and the graphs of \(y=f\left(x\right)+a\) and \(y=f(x+b)\)

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