Links to Foundation to Year 10 Mathematical Methods
In Mathematical Methods, there is a strong emphasis on mutually reinforcing proficiencies in Understanding, Fluency, Problem solving and Reasoning. Students gain fluency in a variety of mathematical and statistical skills, including algebraic manipulations, …
Links to Foundation to Year 10 | Mathematical Methods | Mathematics | Senior secondary curriculum
Representation of General capabilities Mathematical Methods
The seven general capabilities of Literacy, Numeracy, Information and Communication technology (ICT) capability, Critical and creative thinking, Personal and social capability, Ethical understanding, and Intercultural understanding are identified where …
Representation of General capabilities | Mathematical Methods | Mathematics | 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
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
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
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