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Hale School

The Hale School took an initiative to assist students to develop strategies to ingrain ways of thinking mathematically into their learning. They took on a focus of problem-based learning and realised, with the implementation of the Australian Curriculum: …

Hale School | Illustrations of practice | Mathematics proficiencies | Resources

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 \(y=f(\left|x\right|)\)

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

Structure

The Australian Curriculum: Technologies Foundation – Year 10 comprises two subjects: Design and Technologies Digital Technologies. The Australian Curriculum: Technologies is written on the basis that all students will study the two subjects from Foundation …

Structure | Technologies | F-10 curriculum

ACMMM025

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

ACMMM078

use the Leibniz notation \(\delta x\) and \(\delta y\) for changes or increments in the variables \(x\) and \(y\)

ACMMM100

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

ACMMM116

establish and use the formula \(\int x^ndx=\frac1{n+1}x^{n+1}+c\) for \(n\neq-1\)

ACMMM118

establish and use the formulas, \(\int\sin xdx=-\cos x+c\) and \(\int\cos xdx=\sin x+c\)

ACMMM122

determine \(f\left(x\right),\) given \(f^{'\;}(x)\;\) and an initial condition \(f\left(a\right)=b\)

ACMMM151

define logarithms as indices: \(a^x=b\) is equivalent to \(x=\log_ab\) i.e. \(a^{\log_ab}=b\)

ACMMM153

recognise the inverse relationship between logarithms and exponentials: \(y=a^x\) is equivalent to \(x=\log_ay\)

ACMMM160

recognise and use the inverse relationship of the functions \(y=e^x\) and \(y=\ln x\)

ACMSM118

establish and use the formula \(\int\frac1xdx=\ln{\;\vert x\;\vert}+c\) for x ≠ 0

Elaboration (1) ACLINU115

describing the qualities of people using adjectives of character, for example, murah hati, bertanggung-jawab

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