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ACMMM011

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

ACMMM012

examine examples of inverse proportion

ACMMM013

recognise features of the graphs of \(y=\frac1x\) and \(y=\frac a{x-b}\), including their hyperbolic shapes, and their asymptotes.

ACMMM014

recognise features of the graphs of \(y=x^n\) for \(n\in\boldsymbol N,\) \(n=-1\) and \(n=½\), including shape, and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

ACMMM015

identify the coefficients and the degree of a polynomial

ACMMM016

expand quadratic and cubic polynomials from factors

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 \(x\rightarrow-\infty\)

ACMMM018

factorise cubic polynomials in cases where a linear factor is easily obtained

ACMMM019

solve cubic equations using technology, and algebraically in cases where a linear factor is easily obtained.

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

ACMMM021

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

ACMMM022

understand the concept of a function as a mapping between sets, and as a rule or a formula that defines one variable quantity in terms of another

ACMMM023

use function notation, domain and range, independent and dependent variables

ACMMM024

understand the concept of the graph of a function

ACMMM025

examine translations and the graphs of \(y=f\left(x\right)+a\) and \(y=f(x+b)\)

ACMMM026

examine dilations and the graphs of \(y=cf\left(x\right)\) and \(y=f\left(kx\right)\)

ACMMM027

recognise the distinction between functions and relations, and the vertical line test.

ACMMM028

review sine, cosine and tangent as ratios of side lengths in right-angled triangles

ACMMM029

understand the unit circle definition of \(\cos\theta,\;\sin\theta\) and \(\tan\theta\) and periodicity using degrees

ACMMM030

examine the relationship between the angle of inclination of a line and the gradient of that line

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General Capabilities

Cross Curriculum Priorities