ACMMM021
recognise features of the graph of \(y^2=x\) including its parabolic shape and its axis of symmetry.
ACMMM021 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM026
examine dilations and the graphs of \(y=cf\left(x\right)\) and \(y=f\left(kx\right)\)
ACMMM026 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM115
use the notation \(\int f\left(x\right)dx\) for anti-derivatives or indefinite integrals
ACMMM115 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM129
understand the concept of the signed area function \(F\left(x\right)=\int_a^xf\left(t\right)dt\)
ACMMM129 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM161
establish and use the formula \(\frac d{dx}\left(\ln x\right)=\frac1x\)
ACMMM161 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM121
integrate expressions of the form \(\frac{\pm1}{\sqrt[{}]{a^2-x^2}}\) and \(\frac a{a^2+x^2}\)
ACMSM121 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACHAH288
The contribution of new scientific methodologies, including DNA analysis, radio-carbon dating, dendrochronology, thermoluminescence, proton magnetometer, and x-rays
ACHAH288 | Content Descriptions | Unit 4: Reconstructing the Ancient World | Ancient History | Humanities and Social Sciences | Senior secondary curriculum
ACHMH086
The role and significance of individuals in the struggle for civil rights, for example Martin Luther King Jr, Rosa Parkes, and Malcolm X
ACHMH086 | Content Descriptions | Unit 2: Movements for Change in the 20th century | Modern History | Humanities and Social Sciences | Senior secondary 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 …
ACMGM031 | Content Descriptions | Unit 2 | General Mathematics | Mathematics | Senior secondary curriculum
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, …
ACMSM055 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
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 \(\frac{dy}{dx}=f\left(x\right)g\left(y\right)\) …
ACMSM130 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
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 …
ACMSM141 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMEM035
substitute numerical values into algebraic expressions; for example, substitute different values of \(x\) to evaluate the expressions \(\frac{3x}5,\;5(2x-4)\)
ACMEM035 | Content Descriptions | Unit 1 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMMM047
recognise the numbers \(\begin{pmatrix}n\\r\end{pmatrix}\) as binomial coefficients, (as coefficients in the expansion of \(\left(x+y\right)^n)\)
ACMMM047 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
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.
ACMMM131 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
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.
ACMSM053 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary 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 \(y=\log_a{(x+c)}\)
ACMMM156 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
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 \(\tan\)
ACMSM042 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
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 \(\tan\)
ACMSM043 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
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 \(\mu\)
ACMSM143 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum