Indices C

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Indices C (Path) | NSW Curriculum Website

• MA5-IND-P-02 describes and performs operations with surds and fractional indices

📖 Prior Knowledge

Content	Prerequisite relationships
Fractions Decimals Percentages	- Use recurring decimal notation → Convert recurring decimals to fractions - Identify and define irrational numbers → Describe real numbers - Locate irrational numbers on a number line → Describe real numbers
Indices	- Express a number as a product of prime factors → Simplify powers using a common prime base - Use square roots and cube roots → Define and identify surds - Verify $\sqrt{ab}=\sqrt{a}\times \sqrt{b}$ → Apply the basic surd results
Algebraic Techniques A	- Expand binomial products → Expand and simplify expressions involving surds
Indices A	- Raise a product or quotient to a power → Simplify powers using a common prime base
Indices B	- Apply index laws with negative-integer indices → Describe and use fractional indices

Describe surds.pdf

• Describe a real number as a number that can be represented by a point on the number line
• Examine the differences between rational and irrational numbers and recognise that all rational and irrational numbers are real
• Convert between recurring decimals and their fractional 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 $n$≥2, and $x$>0 when $n$ is even
• Recognise that a surd is an exact value that can be approximated by a rounded decimal
• 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.pdf

• Establish and apply the following results for $x>0$ and $y>0$: ${\sqrt{x}}^2=x=\sqrt{x^2}$, $\sqrt{xy}=\sqrt{x}\times \sqrt{y}$ and $\sqrt{\frac{x}{y}}=\frac{\sqrt{x}}{\sqrt{y}}$
• Apply the 4 operations to simplify expressions 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.pdf

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