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Achievement objective M7-6

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • manipulate rational, exponential, and logarithmic algebraic expressions.


  • Makes links between the concepts, properties, and manipulation of exponents and logarithms.
  • Solves problems that involve manipulating rational, exponential, and logarithmic algebraic expressions. Methods that could be used in solving problems include:
    • simplifying algebraic expressions including rational expressions
    • expanding and factorising
    • manipulating expressions with exponents including fractional and negative exponents
    • manipulating logarithms in order to solve exponential equations.
  • Makes links with solving equations M7-7 and graphing functions M7-2.
  • See key mathematical ideas on NZmaths.


M7-6 links from NA6-2, NA6-6 and to M8-6, M8-9.

What is new/changed?

  • Only the power rule for logs is at level 7, manipulating log of a product or quotient has moved to level 8.

Possible context elaborations

  • Amplitude of a pendulum that is attaining a height of 2/3 the previous height.
  • Compound interest: given $100 invested at 5% how long will it take to double your investment?
  • Activity: Cool coffee
  • Activity: Skid marks

Assessment for qualifications

NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The following achievement standard(s) could assess learning outcomes from this AO:

  • AS91261 Mathematics and statistics 2.6 Apply algebraic methods in solving problems

Refer to the mathematics and statistics matrix.

Last updated September 26, 2013