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Achievement objective M8-1

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:

  • apply the geometry of conic sections.


  • Demonstrates understanding of conic sections, including circles, ellipses, parabolas, hyperbolas, including links to transformations and definitions of loci.
  • Connects equations in parametric and Cartesian form with the graphs of conic sections, including understanding the standard equation of each type of conic section.
  • Identifies and uses key features of conic sections, such as vertices, foci, asymptotes, intercepts and eccentricity.
  • Makes links with solving equations M8-7 and implicit and parametric differentiation M8-11.
  • See key mathematical ideas on NZmaths.


M8-1 links from M7-1.

Possible context elaborations

  • Use properties of conic sections to solve problems, for example, the maximum height of parabolic bridge, or the width of skateboarding ramp that can be modelled by part of an ellipse, the focal length of a parabolic satellite dish.
  • Find the gradient at a point on a conic.
  • Find the equation of tangents and/or normals at a point on a conic.
  • Find the equation of a tangent and/or normal to the conic from an external point.
  • Investigate intersections between a line and a conic section.
  • Use loci to solve problems, for example, path of a satellite, body moving with fixed sum of distance from two points.
  • Find lengths of major and minor axes.
  • Activity: Big Bang Theory - The sweet spot and conics
  • Goat on a loop: Starter activity for conics
  • Ice cream cones: Starter activity for conics
  • Investigating conic sections
  • Find foci of an elliptical orbit.

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 11, 2018