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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

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

ACMMM020

recognise features of the graphs of \(x^2+y^2=r^2\) and \(\left(x-a\right)^2+\left(y-b\right)^2=r^2\), including their circular shapes, their centres and their radii

ACMSM121

integrate expressions of the form \(\frac{\pm1}{\sqrt[{}]{a^2-x^2}}\) and \(\frac a{a^2+x^2}\)

ACMSM063

prove irrationality by contradiction for numbers such as \(\sqrt[{}]2\) and \(\log_25\)

ACMMM011

recognise features of the graph of the general quadratic \(y=ax^2+bx+c\)

ACMSM067

define the imaginary number i as a root of the equation \(x^2=-1\)

ACMEM002

apply arithmetic operations according to their correct order

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

ACMSM131

examine slope (direction or gradient) fields of a first order differential equation

ACMGM082

apply Euler’s formula, \(v+f-e=2\), to solve problems relating to planar graphs.

ACMMM021

recognise features of the graph of \(y^2=x\) including its parabolic shape and its axis of symmetry.

ACMSM066

prove divisibility results, such as \(3^{2n+4}-2^{2n}\) is divisible by 5 for any positive integer n.

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

ACEEA125

using teacher editing and conferencing including editing for word order, articles, prepositions and simple tenses.

ACMGM075

use a general first-order linear recurrence relation to generate the terms of a sequence and to display it in both tabular and graphical form

ACSCH133

Designing chemical synthesis processes includes identifying reagents and reaction conditions in order to maximise yield and purity of product

ACMSM036

When a secant (meeting the circle at \(A\) and \(B\)) and a tangent (meeting the circle at \(T\)) are drawn to a circle from an external point \(M\), the square of the length of the tangent equals the product of the lengths to the circle on the secant. …

ACMGM076

recognise that a sequence generated by a first-order linear recurrence relation can have a long term increasing, decreasing or steady-state solution

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