Mathematics K–10 - Stage 5 - Non-linear relationships C (Path) | NSW Curriculum

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Non-linear relationships C (Path)

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MA5-NLI-P-01
interprets and compares non-linear relationships and their transformations, both algebraically and graphically (Path: Adv)

Non-linear relationships C (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Graph parabolas and describe their features and transformations

Use graphing applications to compare parabolas of the form $y = {k x}^{2}$ , $y = {k x}^{2} + c, y = k {(x - b)}^{2}$ and $y = k {(x - b)}^{2} + c$ , and describe their features and transformations
Find $x$ - and $y$ -intercepts algebraically, where appropriate, for the graph of $y = {a x}^{2} + b x + c$ , given $a, b$ and $c$
Determine the equation of the axis of symmetry of a parabola using either the formula $x = - \frac{b}{2 a}$ or the midpoint of the $x$ -intercepts
Find the Loading of a parabola’s Loading using a variety of methods
Graph quadratic relationships of the form $y = {a x}^{2} + b x + c$ by identifying and applying features of parabolas and their equations without graphing software

Graph exponentials and describe their features and transformations

Use graphing applications to graph exponential relationships of the form $y = k {(a)}^{x} + c$ and $y = k {(a)}^{- x} + c$ for integer values of $k$ , $a$ and $c$ (where $a > 0$ and $a \neq 1$ ), and compare and describe any relevant features

Graph hyperbolas and describe their features and transformations

Use graphing applications to graph, compare and describe hyperbolic relationships of the form $y = \frac{k}{x}$ for integer values of $k$
Use graphing applications to graph and describe a variety of hyperbolas, including where the equation is given in the form $y = \frac{k}{x} + c$ or $y = \frac{k}{x - b}$ for integer values of $k, b$ and $c$

Graph circles and describe their features and transformations

Derive the equation of a circle $x^{2} + y^{2} = r^{2}$ with centre $(0, 0)$ and radius $r$ using the distance formula
Identify and describe equations that represent circles with centre at the origin and radius of the circle $r$
Graph circles of the form $x^{2} + y^{2} = r^{2}$ , where $r$ is the radius of the circle using graphing applications
Establish the equation of the circle with centre $(a, b)$ and radius $r$ , and graph equations of the form ${(x - a)}^{2} + {(y - b)}^{2} = r^{2}$
Find the centre and radius of a circle with the equation in the form $x^{2} + y^{2} + a x + b y + c = 0$ by completing the square

Distinguish between different types of graphs by examining their algebraic and graphical representations and solve problems

Identify and describe features of different types of graphs based on their Loading
Identify a possible equation from a graph and verify using graphing applications
Find points where a Loading intersects with a Loading , Loading or Loading , both graphically and algebraically

Graph and compare polynomial curves and describe their features and transformations

Use graphing applications to graph and compare features of cubic equations of the form $y = a x^{3} + c$ , where $a$ and $c$ are integers
Use graphing applications to graph a variety of equations of the form $y = {k x}^{n}$ , where $n$ is an integer and $n \geq 2$ , and describe the effect on the shape of the curve where $n$ is an odd or an even number
Use graphing applications to graph curves of the form $y = {k x}^{n} + c$ and $y = k {(x - b)}^{n}$ where $n$ is an integer and $n \geq 2,$ and describe the transformations from $y = {k x}^{n}$

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Life Skills

K–10Mathematics K–10 Syllabus (2022)