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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

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 …

Elaboration ACLASFU160

exploring similarities and differences in Auslan dialects through building webcam relationships with other schools or through identifying and collecting signs that differ in the northern (Qld and NSW) and southern (Vic., SA, WA and Tas.) dialects, such …

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

Context statement Vietnamese

The place of the Vietnamese language and culture in Australia and in the world Vietnamese is the official language of Vietnam. It is spoken by approximately 90 million people in Vietnam and approximately four million Vietnamese people living …

Context statement | Vietnamese | Languages | F-10 curriculum

Achievement Standard Mathematics Year 4

By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two …

Achievement Standard | Achievement Standards | Year 4 | Mathematics | F-10 curriculum

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