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ACMMM081

examine the behaviour of the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) as \(h\rightarrow0\) as an informal introduction to the concept of a limit

ACMMM081 | 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

ACMEM071

review identifying common usage of rates such as km/h

ACMEM071 | Content Descriptions | Unit 2 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMEM072

convert between units for rates; for example, km/h to m/s, mL/min to L/h

ACMEM072 | Content Descriptions | Unit 2 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMMM098

estimate the limit of \(\frac{a^h-1}h\) as \(h\rightarrow0\) using technology, for various values of \(a\;>0\)

ACMMM098 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM077

interpret the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) as the average rate of change of a function \(f\)

ACMMM077 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM051

use everyday occurrences to illustrate set descriptions and representations of events, and set operations.

ACMMM051 | 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

ACMEM014

identify common usage of rates; for example, km/h as a rate to describe speed, beats/minute as a rate to describe pulse

ACMEM014 | Content Descriptions | Unit 1 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMMM044

understand the notion of a combination as an unordered set of \(r\) objects taken from a set of \(n\) distinct objects

ACMMM044 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM050

use set language and notation for events, including \(\overline A\) (or \(A'\)) for the complement of an event \(A,\) \(A?B\) for the intersection of events \(A\) and \(B\), and \(A?B\) for the union, and recognise mutually exclusive events

ACMMM050 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM045

use the notation \(\begin{pmatrix}n\\r\end{pmatrix}\) and the formula \(\begin{pmatrix}n\\r\end{pmatrix}=\frac{n!}{r!\left(n-r\right)!}\) for the number of combinations of \(r\) objects taken from a set of \(n\) distinct objects

ACMMM045 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

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