K–10Mathematics K–10 Syllabus (2022)

Implementation from 2024

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Content

Early Stage 1

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

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Teaching advice

Examples

Polynomials (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-POL-P-01
defines, operates with and graphs polynomials and applies the factor and remainder theorems to solve problems (Path: Adv, Ext)

Polynomials (Path)

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

Define and operate with polynomials

Recognise a polynomial expression $a_{n} x^{n} + a_{n - 1} x^{n - 1} + \dots + a_{2} x^{2} + a_{1} x + a_{0}$ where $n = 0, 1, 2 \dots$ and $a_{0}, a_{1}, a_{2}, \dots, a_{n}$ are real numbers
Describe Loading using terms such as degree, leading term, Loading and leading coefficient, constant term, Loading and non-monic
Define a monic polynomial as having a leading coefficient of one
Apply the notation $P (x)$ for polynomials and $P (c)$ to indicate the value of $P (x)$ for $x = c$
Add, subtract and multiply polynomials

Divide polynomials

Identify the Loading , divisor, Loading and Loading in numerical division
Divide a polynomial by a linear polynomial to find the quotient and remainder
Express a polynomial in the form $P (x) = D (x) Q (x) + R (x)$ , where $D (x)$ is the divisor, $Q (x)$ is the quotient and $R (x)$ is the remainder

Apply the factor and remainder theorems to solve problems

Verify the remainder theorem and use it to find factors of polynomials and solve related problems
Develop and apply the Loading to Loading particular polynomials completely and solve related problems
Apply the factor theorem and division to find the zeroes of a polynomial $P (x)$ and solve $P (x) = 0$ (degree $\leq 4$ )
State the maximum number of zeroes a polynomial of degree $n$ can have

Graph polynomials

Loading polynomials in factored form
Graph quadratic, Loading and quartic polynomials by factorising and finding the zeroes
Relate the term zeroes to polynomial Loading and roots to polynomial Loading
Use graphing applications to determine the effect of single, double and triple roots of a polynomial equation $P (x) = 0$ on the shape of the graph for $y = P (x)$
Graph polynomials using the sign of the leading term and the multiplicity of roots for the equation $P (x) = 0$
Use graphing applications to compare the graphs of $y = - P (x)$ , $y = P (- x)$ , $y = P (x) + c$ and $y = k P (x)$ to the graph of $y = P (x)$

Related files

Life Skills