Te Kete Ipurangi Navigation:

Te Kete Ipurangi

Te Kete Ipurangi user options:

Senior Secondary navigation


Achievement objective M8-12

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:

  • form differential equations and interpret the solutions.


  • Uses knowledge of anti-differentiation to form and solve differential equations of the type:
    • with the rate of change directly or inversely proportional to the variable of interest
    • first and second order with variables easily separated for functions including those listed in M8-11.
  • Applies boundary or initial conditions to solutions of differential equations.
  • Distinguishes between families of solutions and exact solutions using given boundary or initial conditions and interprets these solutions.
  • Links families of solutions to the gradient field of the differential equation.
  • See key mathematical ideas on NZmaths.


M8-12 links from M7-10.

Possible context elaborations

  •   dy by dx equals y times sin x.
  •   d squared y by d x squared equals “polynomial”
  •   dy by dx equals e to the power of x.
  •   dy by dx equals one divided by x.

Situations which students will be expected to form a model for, and solve, include:

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