ACMMM017
recognise features of the graphs of \(y=x^3\), \(y=a{(x-b)}^3+c\) and \(y=k(x-a)(x-b)(x-c)\), including shape, intercepts and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)
ACMMM017 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMEM072
convert between units for rates; for example, km/h to m/s, mL/min to L/h
ACMEM072 | Content Descriptions | Unit 2 | Essential Mathematics | 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
ACMSM049
prove and apply other trigonometric identities such as \(\cos3\mathrm x=4\;\mathrm c\mathrm o\mathrm s^{3\;}\mathrm x-3\cos\mathrm x\)
ACMSM049 | Content Descriptions | Unit 2 | Specialist Mathematics | 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