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
ACMMM008
solve quadratic equations using the quadratic formula and by completing the square
ACMMM008 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM009
find the equation of a quadratic given sufficient information
ACMMM009 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM010
find turning points and zeros of quadratics and understand the role of the discriminant
ACMMM010 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM011
recognise features of the graph of the general quadratic \(y=ax^2+bx+c\)
ACMMM011 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM012
examine examples of inverse proportion
ACMMM012 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM013
recognise features of the graphs of \(y=\frac1x\) and \(y=\frac a{x-b}\), including their hyperbolic shapes, and their asymptotes.
ACMMM013 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
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 \(x\rightarrow-\infty\)
ACMMM014 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM015
identify the coefficients and the degree of a polynomial
ACMMM015 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM016
expand quadratic and cubic polynomials from factors
ACMMM016 | Content Descriptions | Unit 1 | 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
ACMMM018
factorise cubic polynomials in cases where a linear factor is easily obtained
ACMMM018 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM019
solve cubic equations using technology, and algebraically in cases where a linear factor is easily obtained.
ACMMM019 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
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
ACMMM020 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM021
recognise features of the graph of \(y^2=x\) including its parabolic shape and its axis of symmetry.
ACMMM021 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
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
ACMMM022 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM023
use function notation, domain and range, independent and dependent variables
ACMMM023 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM024
understand the concept of the graph of a function
ACMMM024 | Content Descriptions | Unit 1 | 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
ACMMM026
examine dilations and the graphs of \(y=cf\left(x\right)\) and \(y=f\left(kx\right)\)
ACMMM026 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum