Indices C

Indices C (Path) | NSW Curriculum Website

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

📖 Prior Knowledge

Content	Prior knowledge	Used for
Fractions Decimals Percentages	- rational and irrational numbers	- identifying surds as irrational numbers
Indices	- square roots and cube roots	- simplifying surds
Algebraic Techniques B	- algebraic fractions	- rationalising the denominator
Indices B	- negative indices	- fractional indices

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 $n x$ 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 $x$ is undefined for $x$ <0 and that $x$ =0 when $x$ =0 using digital tools
Describe $x$ as the positive square root of $x$ for $x$ >0 and $0$ =0

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

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