The Pilbara Education Region
The Pilbara Education Region is one of eight regions in the Western Australian Department of Education. The headquarters of this education region, the Pilbara Education Regional Office (PERO), is located in Karratha. The PERO staff are committed to the …
The Pilbara Education Region | Illustrations of practice | Primary curriculum | Resources
Landsdale Primary School
Lansdale Primary School is situated in the north-eastern suburbs of Perth and at the time of filming had 942 K–7 students. The students come from various cultural backgrounds with 38 per cent having English as an additional language or dialect. Lansdale …
Landsdale Primary School | Illustrations of practice | Primary curriculum | Resources
ACMMM065
recognise the qualitative features of the graph of \(y=a^x(a>0)\) including asymptotes, and of its translations \(y=a^x+b\) and \(y=a^{x+c}\)
ACMMM065 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM082
define the derivative \(f'\left(x\right)\) as \(\lim_{h\rightarrow0}\frac{f\left(x+h\right)-f(x)}h\)
ACMMM082 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM117
use substitution \(u = g(x)\) to integrate expressions of the form \(f\left(g\left(x\right)\right)g'\left(x\right)\)
ACMSM117 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
Hale School
The Hale School took an initiative to assist students to develop strategies to ingrain ways of thinking mathematically into their learning. They took on a focus of problem-based learning and realised, with the implementation of the Australian Curriculum: …
Hale School | Illustrations of practice | Mathematics proficiencies | Resources
ACMMM007
recognise features of the graphs of \(y=x^2\), \(y=a{(x-b)}^2+c\), and \(y=a\left(x-b\right)\left(x-c\right)\) including their parabolic nature, turning points, axes of symmetry and intercepts
ACMMM007 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM079
use the notation \(\frac{\delta y}{\delta x}\) for the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) where \(y=f(x)\)
ACMMM079 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM080
interpret the ratios \(\frac{f\left(x+h\right)-f(x)}h\) and \(\frac{\delta y}{\delta x}\) as the slope or gradient of a chord or secant of the graph of \(y=f(x)\)
ACMMM080 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM088
establish the formula \(\frac d{dx}\left(x^n\right)=nx^{n-1}\) for positive integers \(n\) by expanding \({(x+h)}^n\) or by factorising \({(x+h)}^n-x^n\)
ACMMM088 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM159
define the natural logarithm \(\ln x=\log_ex\)
ACMMM159 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
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
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