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Achievement objective M8-4

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:

  • use curve fitting, log modelling, and linear programming techniques.


  • Solves problems using curve fitting and log modelling.
  • Solves problems using linear programming techniques:
    • determining the variables of interest
    • translating word problems into mathematical expressions or equations
    • manipulating linear inequalities
    • graphically representing linear systems in two variables that include inequalities
    • solving simultaneous linear, and non-linear equations
    • identifying feasible regions
    • optimising a function subject to the constraints of a system
    • interpreting solutions of linear systems in context, including situations with multiple solutions.


M8-4 links from NA6-4, NA6-5, GM6-1, GM6-2, GM6-4, M7-8.

Possible context elaborations

  • Investigate the relationship between:
    • the length of a pendulum and its period
    • the length of a weighted ruler and its deflection distance
    • temperature and time as liquid cools.
  • Use statistical data to investigate change, such as the price of tomatoes over time.
  • Use log modelling to make predictions about population growth.
  • Use linear programming to maximise profit under certain production constraints.
  • Activity: 28 Days later – Zombies
  • Ball bouncing: Modelling the height that a ball bounces to when dropped.
  • Modelling the population: Modelling the population of New Zealand or other subgroups within.

Assessment for qualifications

NCEA achievement standards at levels 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 NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.

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

Last updated September 14, 2018