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
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
ACSCH130 | Content Descriptions | Unit 4 | Chemistry | Science | Senior secondary curriculum
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 …
ACMSM138 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM139
simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate the approximate standard normality of \(\frac{\overline X-\mu}{s/\sqrt[{}]n}\) for large samples \(\left(n\geq30\right)\), where \(s\) is the …
ACMSM139 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMMM149
determine and use the probabilities \(\mathrm P\left(\mathrm X=\mathrm r\right)=\begin{pmatrix}\mathrm n\\\mathrm r\end{pmatrix}\mathrm p^\mathrm r{(1-\mathrm p)}^{\mathrm n-\mathrm r}\) associated with the binomial distribution with parameters \(n\) …
ACMMM149 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMNA289
Compare, order and make correspondences between collections, initially to 20, and explain reasoning
Elaborations ScOT Terms
ACMNA289 | Content Descriptions | Foundation Year | Mathematics | F-10 curriculum
ACMMG110
Compare 12- and 24-hour time systems and convert between them
Elaborations ScOT Terms
ACMMG110 | Content Descriptions | Year 5 | Mathematics | F-10 curriculum
ACMNA001
Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point
Elaborations ScOT Terms
ACMNA001 | Content Descriptions | Foundation Year | Mathematics | F-10 curriculum
ACMMG199
Solve problems involving duration, including using 12- and 24-hour time within a single time zone
Elaborations ScOT Terms
ACMMG199 | Content Descriptions | Year 8 | Mathematics | F-10 curriculum