ACMSM099
examine the relationship between the graph of \(y=f(x)\) and the graphs of \(y=\frac1{f(x)}\), \(y=\vert f\left(x\right)\vert\) and \(y=f(\left|x\right|)\)
ACMSM099 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
Texts Essential English
Teachers will use an array of material in class. Texts include literary texts, fiction and non-fiction, media texts, everyday texts, and workplace texts, from increasingly complex and unfamiliar settings, ranging from the everyday language of personal …
Texts | Essential English | English | Senior secondary curriculum
ACMMM025
examine translations and the graphs of \(y=f\left(x\right)+a\) and \(y=f(x+b)\)
ACMMM025 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM078
use the Leibniz notation \(\delta x\) and \(\delta y\) for changes or increments in the variables \(x\) and \(y\)
ACMMM078 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM100
establish and use the formula \(\frac d{dx}\left(e^x\right)=e^x\)
ACMMM100 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM116
establish and use the formula \(\int x^ndx=\frac1{n+1}x^{n+1}+c\) for \(n\neq-1\)
ACMMM116 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM118
establish and use the formulas, \(\int\sin xdx=-\cos x+c\) and \(\int\cos xdx=\sin x+c\)
ACMMM118 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM122
determine \(f\left(x\right),\) given \(f^{'\;}(x)\;\) and an initial condition \(f\left(a\right)=b\)
ACMMM122 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM151
define logarithms as indices: \(a^x=b\) is equivalent to \(x=\log_ab\) i.e. \(a^{\log_ab}=b\)
ACMMM151 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM153
recognise the inverse relationship between logarithms and exponentials: \(y=a^x\) is equivalent to \(x=\log_ay\)
ACMMM153 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM160
recognise and use the inverse relationship of the functions \(y=e^x\) and \(y=\ln x\)
ACMMM160 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM118
establish and use the formula \(\int\frac1xdx=\ln{\;\vert x\;\vert}+c\) for x ≠ 0
ACMSM118 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACHAH080
The nature of the sources and sites, including Vix and Hochdorf Burial; relevant excepts from Caesar’s Gallic War VII, Dio Cassius Roman History Books 40 &43 (Vercingetorix) and Book 62 (Boudicca), Tacitus The Annals Books 14 (Boudicca), Asterix series, …
ACHAH080 | Content Descriptions | Unit 1: Investigating the Ancient World | Ancient History | Humanities and Social Sciences | Senior secondary curriculum
ACMMM014
recognise features of the graphs of \(y=x^n\) for \(n\in\boldsymbol N,\) \(n=-1\) and \(n=½\), including shape, and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)
ACMMM014 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM083
use the Leibniz notation for the derivative: \(\frac{dy}{dx}=\lim_{\mathit{δx}\rightarrow0}\frac{\delta y}{\delta x}\) and the correspondence \(\frac{dy}{dx}=f'\left(x\right)\) where \(y=f(x)\)
ACMMM083 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM124
examine the area problem, and use sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\) as area under the curve \(y=f(x)\)
ACMMM124 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM125
interpret the definite integral \(\int_a^bf\left(x\right)dx\;\) as area under the curve \(y=f\left(x\right)\) if \(f\left(x\right)>0\;\)
ACMMM125 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM126
recognise the definite integral \(\int_a^bf\left(x\right)dx\;\;\) as a limit of sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\)
ACMMM126 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMEM122
generate tables of values for linear functions, including for negative values of \(x\)
ACMEM122 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMEM123
graph linear functions for all values of \(x\) with pencil and paper and with graphing software.
ACMEM123 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum