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ACMSM065

prove results for sums, such as \(1+4+9\dots+n^2=\frac{n(n+1)(2n+1)}6\) for any positive integer n

ACMSM065 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum

Senior secondary English subjects

The senior secondary Australian Curriculum for English is presented in four subjects that share common features. These include the continuing development of students’ knowledge, understanding and skills in listening, speaking, reading, viewing and writing. …

Senior secondary English subjects | English | Senior secondary curriculum

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

ACMMM106

apply the product, quotient and chain rule to differentiate functions such as \(xe^x\), \(\tan x,\), \(\frac1{x^n}\), \(x\sin x,\text{ }e^{-x}\sin x\) and \(f(ax+b)\)

ACMMM106 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM037

examine amplitude changes and the graphs of \(y=a\sin x\) and \(y=a\cos x\)

ACMMM037 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM036

recognise the graphs of \(y=\sin x,\;y=\cos x,\) and \(y=\tan x\) on extended domains

ACMMM036 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMSM098

use and apply the notation \(\left|x\right|\) for the absolute value for the real number \(x\) and the graph of \(y=\left|x\right|\)

ACMSM098 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMMM039

examine phase changes and the graphs of \(y=\sin{(x+c)}\), \(y=\cos{(x+c)}\) and \(y=\tan{(x+c)}\) and the relationships \(\sin\left(x+\frac\pi2\right)=\cos x\) and \(\cos\left(x-\frac\pi2\right)=\sin x\)

ACMMM039 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

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

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

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