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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 \(x\rightarrow-\infty\)

Achievement Standard Mathematics Year 5

By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They identify …

Achievement Standard | Achievement Standards | Year 5 | Mathematics | F-10 curriculum

ACMSM048

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 …

Achievement Standard Indonesian Years 3 and 4

By the end of Year 4, students interact in classroom routines and structured interactions with teachers and peers. They reproduce the sounds of au (for example, mau) and g (for example, gemuk) and the final sound k (for example, tidak). Students follow …

Achievement Standard Indonesian Years 5 and 6

By the end of Year 6, students use Indonesian to convey information about themselves, their family and friends, and daily routines and activities. They locate specific details and use familiar words and phrases to predict meanings in texts. They respond …

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

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 …

Rationale Framework for Aboriginal Languages and Torres Strait Islander Languages

Nganki - ka Kardu thipmam - wa! I Murrinh warda ngatha. The nganthin ngumpanngerren. I ku ngakumarl, da ngarra ngugumingki wurran. The da matha nganthin ngala i da bere matha wangu ngumamath ngumpan ngarra magulkul nganki. We are black people. …

Rationale | Framework for Aboriginal Languages and Torres Strait Islander Languages | Languages | F-10 curriculum

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

Elaboration (1) ACMNA030

modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines

Elaboration (1) ACMNA055

combining knowledge of addition and subtraction facts and partitioning to aid computation (for example 57 + 19 = 57 + 20 – 1)

Elaboration (5) ACLFRU013

developing number knowledge for numbers 0–20 and ordinals (premier, deuxième)

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, \({}_6^{12}C\), \({}_6^{13}C\)

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