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ACMMM014

recognise features of the graphs of \(y=x^n\) for \(n\in\boldsymbol N,\) \(n=-1\) and \(n=½\), including shape, and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

ACMMM083

use the Leibniz notation for the derivative: \(\frac{dy}{dx}=\lim_{\mathit{δx}\rightarrow0}\frac{\delta y}{\delta x}\) and the correspondence \(\frac{dy}{dx}=f'\left(x\right)\) where \(y=f(x)\)

ACMMM124

examine the area problem, and use sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\) as area under the curve \(y=f(x)\)

ACMMM125

interpret the definite integral \(\int_a^bf\left(x\right)dx\;\) as area under the curve \(y=f\left(x\right)\) if \(f\left(x\right)>0\;\)

ACMMM126

recognise the definite integral \(\int_a^bf\left(x\right)dx\;\;\) as a limit of sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\)

Keller Road Primary School is a small school set in beautiful grounds 17km north of Adelaide. The school caters for students from Foundation to Year 7 (F – 7) and is located on the traditional lands of the Kaurna Peoples. The current enrolment is 210 …

Keller Road Primary School | Illustrations of practice | Framework for Aboriginal Languages and Torres Strait Islander Languages | Resources

Elaboration (2) ACLINC018

interacting with others, such as through greeting cards and shared digital spaces, using language related to special occasions and well-wishing, for example, Selamat Hari Ulang Tahun, Selamat Hari Raya

Elaboration (3) ACLINU102

investigating the language associated with significant cultural practices such as celebrations, for example, Selamat Hari Raya, maaf lahir batin, panjang umurnya

St Joseph’s Catholic Primary School

The Mirima Dawang Woorlab-gerring Language and Culture Centre The Mirima Dawang Woorlab-gerring (MDWg) Language and Culture Centre Kununurra is situated 3,214 km from Perth in far northern Western Australia, at the eastern extremity of the Kimberley. …

St Joseph’s Catholic Primary School | Illustrations of practice | Framework for Aboriginal Languages and Torres Strait Islander Languages | Resources

ACMEM122

generate tables of values for linear functions, including for negative values of \(x\)

ACMEM123

graph linear functions for all values of \(x\) with pencil and paper and with graphing software.

ACMMM046

expand \(\left(x+y\right)^n\) for small positive integers \(n\)

ACMMM085

interpret the derivative as the slope or gradient of a tangent line of the graph of \(y=f(x)\)

ACMMM102

establish the formulas \(\frac d{dx}\left(\sin x\right)=\cos x,\;\text{ and }\frac d{dx}\left(\cos x\right)=-\sin x\) by numerical estimations of the limits and informal proofs based on geometric constructions

ACMMM117

establish and use the formula \(\int e^xdx=e^x+c\)

ACMMM127

interpret \(\int_a^bf\left(x\right)dx\;\) as a sum of signed areas

ACMMM162

establish and use the formula \(\int\frac1xdx=\ln\;x\;+c\) for \(x>0\)

ACMSM067

define the imaginary number i as a root of the equation \(x^2=-1\)

ACMMM077

interpret the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) as the average rate of change of a function \(f\)

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

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