Content:
MA4-IND-C-01
Apply index notation to represent whole numbers as products of powers of prime numbers
- Describe numbers written in index form using terms such as base, power, index and exponent
- Represent numbers in index notation limited to positive powers
- Represent in expanded form and evaluate numbers expressed in index notation, including powers of 10
- Apply the order of operations to evaluate expressions involving indices
- Determine and apply tests for divisibility for 2, 3, 4, 5, 6 and 10
- Represent a whole number greater than one as a product of its prime factors, using index notation where appropriate
Examine cube roots and square roots
- Use the notations for square root (\( \sqrt{} \)) and cube root (\( \sqrt[3]{} \))
- Recognise and describe the relationship between squares and square roots, and cubes and cube roots for positive numbers
- Verify, through numerical examples, that \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \)
- Estimate the square root of any non-square whole number and the cube root of any non-cube whole number, then check using a calculator
- Identify and describe exact and approximate solutions in the context of square roots and cube roots
- Apply the order of operations to evaluate expressions involving square roots, cube roots, square numbers and cube numbers
Use index notation to establish the index laws with positive-integer indices and the zero index
- Establish the multiplication, division and the power of a power index laws, by expressing each number in expanded form with numerical bases and positive-integer indices
- Verify through numerical examples that \( (ab)^2=a^2b^2 \)
- Establish the meaning of the zero index
- Apply index laws to simplify and evaluate expressions with numerical bases
