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ACMSM055

define and use basic linear transformations: dilations of the form \((\mathrm x,\mathrm y)\longrightarrow({\mathrm\lambda}_1\mathrm x,{\mathrm\lambda}_2\mathrm y)\) , rotations about the origin and reflection in a line which passes through the origin, …

ACMSM130

solve simple first-order differential equations of the form \(\frac{dy}{dx}=f(x)\), differential equations of the form \(\frac{dy}{dx}=g\left(y\right)\) and, in general, differential equations of the form \(\frac{dy}{dx}=f\left(x\right)g\left(y\right)\) …

ACMSM141

examine the approximate confidence interval \(\left(\overline{\mathrm X}\;–\frac{\mathrm z\mathrm s}{\sqrt[{}]n},\;\;\overline{\mathrm X}+\frac{\mathrm z\mathrm s}{\sqrt[{}]n}\right),\), as an interval estimate for \(\mu\) ,the population mean, where …

ACMEM035

substitute numerical values into algebraic expressions; for example, substitute different values of \(x\) to evaluate the expressions \(\frac{3x}5,\;5(2x-4)\)

ACMMM047

recognise the numbers \(\begin{pmatrix}n\\r\end{pmatrix}\) as binomial coefficients, (as coefficients in the expansion of \(\left(x+y\right)^n)\)

ACMMM131

understand the formula \(\int_a^b{f\left(x\right)dx=F\left(b\right)-F(a)}\) and use it to calculate definite integrals.

ACMSM053

calculate the determinant and inverse of 2x2 matrices and solve matrix equations of the form AX=B , where A is a 2x2 matrix and X and B are column vectors.

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

ACMMM156

recognise the qualitative features of the graph of \(y=\log_ax\) \((a>1)\) including asymptotes, and of its translations \(y=\log_ax+b\) and \(y=\log_a{(x+c)}\)

ACMSM042

find all solutions of \(\mathrm f\left(\mathrm a\left(\mathrm x-\mathrm b\right)\right)=\mathrm c\) where \(f\) is one of \(\sin\), \(\cos\) or \(\tan\)

ACMSM043

graph functions with rules of the form \(\mathrm y=\mathrm f(\mathrm a\left(\mathrm x-\mathrm b\right))\) where \(f\) is one of \(\sin\), \(\cos\) or \(\tan\)

ACMSM143

use \(\overline x\) and \(s\) to estimate \(\mu\) and \(\sigma\), to obtain approximate intervals covering desired proportions of values of a normal random variable and compare with an approximate confidence interval for \(\mu\)

ACSCH130

Data from analytical techniques, including mass spectrometry, x-ray crystallography and infrared spectroscopy, can be used to determine the structure of organic molecules, often using evidence from more than one technique

QuN5

Producing number names counts to at least 20 continues a count from a number other than 1 counts forwards by tens to 100 Counting items counts groups of up to 20 items Numeral recognition and identification points to the correct …

OwP2

Find percentage as a part of a whole uses fraction benchmarks to find percentages of quantities (to find 75% of 160, I know that 50% (half) of 160 is 80, and 25% (quarter) is 40 so 75% is 120) finds a percentage of a quantity (10%, 20%, 25%, 50%, …

ACMSM138

simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate properties of the distribution of \(\overline X\;\) across samples of a fixed size \(n\), including its mean \(\mu\), its standard deviation …

QuN4

Producing number names produces the number word just after a given number word in the range 1–10 (without dropping back to count from 1) produces the number word just before a given number word in the range 1–10 (without dropping back) Counting …

QuN6

Producing number names counts to at least 30 produces the number word just after a given number in the range 1–30 (without dropping back) produces the number word just before a given number word in the range 1–30 (without dropping back) counts forwards …

AdS7

Flexible strategies with two-digit numbers applies knowledge of 10 as a unit to add and subtract 2 two-digit numbers (jump strategy, split strategy or compensation) manipulates tens and ones flexibly for addition and subtraction (to add 45 and 37, …

MuS7

Flexible number properties uses multiplication and division as inverse operations uses factors of a number to carry out multiplication and division (to multiply a number by 72, first multiply by 12 and then multiply the result by 6) uses knowledge …

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