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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 (2) ACLJAU156

knowing that the hiragana spelling of a particular particle does not match its pronunciation, for example, ‘wa’ for は , ‘e’ for へ, ‘o/wo’ for を

ACMMM013

recognise features of the graphs of \(y=\frac1x\) and \(y=\frac a{x-b}\), including their hyperbolic shapes, and their asymptotes.

ACMMM021

recognise features of the graph of \(y^2=x\) including its parabolic shape and its axis of symmetry.

ACMMM026

examine dilations and the graphs of \(y=cf\left(x\right)\) and \(y=f\left(kx\right)\)

ACMMM115

use the notation \(\int f\left(x\right)dx\) for anti-derivatives or indefinite integrals

ACMMM129

understand the concept of the signed area function \(F\left(x\right)=\int_a^xf\left(t\right)dt\)

ACMMM161

establish and use the formula \(\frac d{dx}\left(\ln x\right)=\frac1x\)

ACMSM121

integrate expressions of the form \(\frac{\pm1}{\sqrt[{}]{a^2-x^2}}\) and \(\frac a{a^2+x^2}\)

ACHAH288

The contribution of new scientific methodologies, including DNA analysis, radio-carbon dating, dendrochronology, thermoluminescence, proton magnetometer, and x-rays

ACHMH086

The role and significance of individuals in the struggle for civil rights, for example Martin Luther King Jr, Rosa Parkes, and Malcolm X

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’ (NSW, Qld and ACT) and ‘southern’ (Vic., SA, WA, NT and Tas.) …

Elaboration ACMNA296

graphing parabolas, and circles connecting x-intercepts of a graph to a related equation

Elaboration (4) ACSSU175

investigating the effects on humans of exposure to electromagnetic radiations such as X-rays and microwaves

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

ACMGM031

construct and use parallel box plots (including the use of the ‘Q1 – 1.5 x IQR’ and ‘Q3 + 1.5 x IQR’ criteria for identifying possible outliers) to compare groups in terms of location (median), spread (IQR and range) and outliers and to interpret and …

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