ACMMM179
define the approximate margin of error \(E=z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\) and understand the trade-off between margin of error and level of confidence
ACMMM179 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMGM082
apply Euler’s formula, \(v+f-e=2\), to solve problems relating to planar graphs.
ACMGM082 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
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
ACMSM066
prove divisibility results, such as \(3^{2n+4}-2^{2n}\) is divisible by 5 for any positive integer n.
ACMSM066 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMMM176
simulate repeated random sampling, for a variety of values of \(p\) and a range of sample sizes, to illustrate the distribution of \(\widehat p\) and the approximate standard normality of \(\frac{\widehat p\;-p}{\sqrt[{}]{(\widehat p(1-\widehat p)/n}}\) …
ACMMM176 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM036
When a secant (meeting the circle at \(A\) and \(B\)) and a tangent (meeting the circle at \(T\)) are drawn to a circle from an external point \(M\), the square of the length of the tangent equals the product of the lengths to the circle on the secant. …
ACMSM036 | Content Descriptions | Unit 1 | 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
ACMSM086
identify subsets of the complex plane determined by relations such as \(\left|z-3i\right|\leq4\) \(\frac\pi4\leq Arg(z)\leq\frac{3\pi}4\), \(Re\left(z\right)>Im(z)\) and \(\left|z-1\right|=2\vert z-i\vert\)
ACMSM086 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM136
consider and solve problems involving motion in a straight line with both constant and non-constant acceleration, including simple harmonic motion and the use of expressions \(\frac{dv}{dt}\), \(v\frac{dv}{dx}\) and \(\frac{d(\frac12v^2)}{dx}\) for a …
ACMSM136 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSP117
Recognise that probabilities range from 0 to 1
Elaborations ScOT Terms
ACMSP117 | Content Descriptions | Year 5 | Mathematics | F-10 curriculum