Mathematics K–10 - Stage 5 - Indices C (Path) | NSW Curriculum

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Indices 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-IND-P-02
describes and performs operations with surds and fractional indices (Path: Adv)

Indices C (Path)

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

Describe surds

Describe a real number as a number that can be represented by a point on the Loading
Examine the differences between Loading and Loading and recognise that all rational and irrational numbers are real
Convert between Loading and their Loading form using digital tools
Describe the term surd as referring to irrational expressions of the form $\sqrt[n]{x}$ where $x$ is a rational number and $n$ is an integer such that $n \geq 2$ , and $x > 0$ when $n$ is even
Recognise that a Loading is an exact value that can be Loading by a Loading Loading
Demonstrate that $\sqrt{x}$ is undefined for $x < 0$ and that $\sqrt{x} = 0$ when $x = 0$ using digital tools
Describe $\sqrt{x}$ as the positive square root of $x$ for $x > 0$ and $\sqrt{0} = 0$

Apply knowledge of surds to solve problems

Establish and apply the following results for $x > 0$ and $y > 0$ : ${(\sqrt{x})}^{2} = x = \sqrt{x^{2}}$ , $\sqrt{x y} = \sqrt{x} \times \sqrt{y}$ and $\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}$
Apply the 4 Loading to simplify Loading involving surds
Expand and simplify expressions involving surds
Rationalise the denominators of surds of the form $\frac{a \sqrt{b}}{c \sqrt{d}}$

Describe and use fractional indices

Apply index laws to describe fractional indices as: $a^{\frac{1}{n}} = \sqrt[n]{a}$ and $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = {(\sqrt[n]{a})}^{m}$
Translate expressions in surd form to expressions in Loading form and vice versa
Evaluate numerical expressions involving fractional Loading including using digital tools

Related files

Life Skills

K–10Mathematics K–10 Syllabus (2022)