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
Outdoor learning: Foundation Year
Students at this stage Typically, students in Foundation Year are curious about nature. They often notice things outdoors that adults miss. There is an opportunity to encourage this curiosity and develop skills and knowledge to safely enjoy the outdoors. …
Outdoor learning: Foundation Year | Year levels | Dimensions | Curriculum connections | Resources
Outdoor learning: Years 1 and 2
Students at this stage Typically, as students develop their own identities and participate more broadly in everyday life, their movement and recreation options can expand. Gaining knowledge and skills to undertake outdoor activities in more natural settings, …
Outdoor learning: Years 1 and 2 | Year levels | Dimensions | Curriculum connections | Resources
Outdoor learning: Years 3 and 4
Students at this stage Typically, as children develop confidence in outdoor places, they can explore a greater range of environments and spend longer without direct intervention from adults. They observe plants and animals in their natural habitat and …
Outdoor learning: Years 3 and 4 | Year levels | Dimensions | Curriculum connections | Resources
Outdoor learning: Years 5 and 6
Students at this stage In Year 5 – 6 students are introduced to outdoor recreation as part of an Australian way of life through stories and direct experience. They develop skills and knowledge to participate safely in outdoor recreation activity and understand …
Outdoor learning: Years 5 and 6 | Year levels | Dimensions | Curriculum connections | Resources
Outdoor learning: Years 9 and 10
Students at this stage In these years, students typically develop a deeper understanding of, and reasons for, codes of conduct in outdoor recreation activities. They explore more adventurous activities as a way of exploring self and nature, and apply …
Outdoor learning: Years 9 and 10 | Year levels | Dimensions | Curriculum connections | Resources
Consumer and financial literacy: Year 6
The diverse circumstances in which children grow up influence their needs, wants, perceptions and behaviours related to financial and consumer matters. Typically, at age 11 to 12, children can discriminate between their needs and wants and they independently …
Consumer and financial literacy: Year 6 | Year levels | Dimensions | Curriculum connections | Resources
Consumer and financial literacy: Year 7
The diverse circumstances in which children grow up influence their needs, wants, perceptions and behaviours related to financial and consumer matters. Typically, at age 12 to 13, children are given more responsibility as their roles in family and social …
Consumer and financial literacy: Year 7 | Year levels | Dimensions | Curriculum connections | Resources
ACSES105
Human activities, particularly land-clearing and fossil fuel consumption, produce gases (including carbon dioxide, methane, nitrous oxide and hydrofluorocarbons) and particulate materials that change the composition of the atmosphere and climatic conditions …
ACSES105 | Content Descriptions | Unit 4 | Earth and Environmental Science | Science | 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