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NSW Syllabuses

Mathematics K–10 - Stage 5.2 - Number and Algebra Indices

Outcomes

A student:

  • MA5.2-1WM

    selects appropriate notations and conventions to communicate mathematical ideas and solutions

  • MA5.2-3WM

    constructs arguments to prove and justify results

  • MA5.2-7NA

    applies index laws to operate with algebraic expressions involving integer indices

Content

  • use index notation and the index laws to establish that \( a^{-1} = \dfrac{1}{a}, \,\, a^{-2} = \dfrac{1}{a^2}, \,\, a^{-3} = \dfrac{1}{a^3}, \,\, \ldots \) CCT
  • explain the difference between pairs of algebraic expressions that appear similar,
    eg 'Are \( x^{-2} \) and \( -\!2x \) equivalent expressions? Why or why not?' (Communicating) CCT
  • write expressions involving negative indices as expressions involving positive indices, and vice versa
  • apply the index laws to simplify algebraic products and quotients involving negative indices,
    eg  \( \, 4b^{-5} \times 8b^{-3}, \, \)  \( 9x^{-4} \div 3x^3 \)
  • explain why given statements of equality are true or false and give reasons, eg explain why each of the following is true or false: \( \, 5x^0 = 1, \, \)  \(9x^5 \div 3x^5 = 3x, \, \)  \(a^5 \div a^7 = a^2, \, \)  \(2c^{-4} = \dfrac{1}{2c^4} \) (Communicating, Reasoning) CCT
  • verify whether a given expression represents a correct simplification of another algebraic expression by substituting numbers for pronumerals (Communicating, Reasoning) CCT
  • write the numerical value of a given numerical fraction raised to the power of –1, leading to \( \, \left( \! \dfrac{a}{b} \! \right) ^{\!-1} = \dfrac{b}{a} \,\) (Communicating, Reasoning) CCT