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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

ACMMM082

define the derivative \(f'\left(x\right)\) as \(\lim_{h\rightarrow0}\frac{f\left(x+h\right)-f(x)}h\)

ACMEM071

review identifying common usage of rates such as km/h

ACMEM072

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

ACMMM098

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

ACELR007

approaches to characterisation, for example, the inclusion of archetypal figures, authorial intrusion, the dramatisation of a character’s inner life, and the use of interior monologue

ACSES045

Processes within and between Earth systems require energy that originates either from the sun or the interior of Earth

ACMMM077

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

Transfers and transformations of heat and gravitational energy in Earth's interior drives the movement of tectonic plates through processes including mantle convection, plume formation and slab sinking

ACMMM051

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

ACMMM079

use the notation \(\frac{\delta y}{\delta x}\) for the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) where \(y=f(x)\)

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 \(y=f(x)\)

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 \({(x+h)}^n-x^n\)

ACMEM014

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

ACHMH229

The impact of significant individuals in the period, for example Eleanor Roosevelt, H V Evatt, Dag Hammarskjold, Ralph Bunche, Lester Pearson, Gareth Evans and Kofi Annan

ACMMM044

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

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

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

ACMMG163

Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal

Elaborations ScOT Terms

ACMMG163 | Content Descriptions | Year 7 | Mathematics | F-10 curriculum

ACLASFU138

Recognise that meaning can be expressed through English words or Auslan signs and that signs have set handshapes, movements and locations, and identify and reproduce them independently[Key concepts: handshape, movement, location, iconicity; Key processes: …