Level 3


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91573: Apply the geometry of conic sections in solving problems

Updated September 2015. This document has been updated in its entirety to address new issues that have arisen from moderation.

Solving problems

The problem needs to provide sufficient scope for students to demonstrate and develop their own thinking. If there are parts to the problem all of the parts need to contribute to the solution. A task with a number of discrete skills based questions is not appropriate for students to demonstrate evidence of the required levels of thinking.

Students need to make their own decisions about what to do and how to solve problems so an instruction like ‘Sketch the conic y2 = 4(x-2)’ is inappropriate. Where an assessment task has a series of instructions that lead students through a sequence of steps towards the solution, it is likely that the opportunity for students to demonstrate all levels of thinking will be compromised.

Expected evidence for Achieved

For Achieved, the requirements include selecting and using methods. To be used as evidence a method must be relevant to the solution of the problem. The methods also need to be at curriculum level 8. Parabolas need to be related to the form y2 = 4ax.  Further information can be found in the Mathematics and Statistics teaching and learning guide on TKI.

Explanatory Note 4

Properties of conic sections are the attributes which apply to all the conic sections in a group. For example, hyperbolae consist of two branches and have two asymptotes.

Communicating solutions

At all grades there is a requirement relating to the communication of the solutions. For example, students need to identify the properties of the conic section that they have used to form the equation.

At Achieved, students need to indicate what the answer represents.

At Merit, students need to clearly indicate what they are finding and their solutions need to be linked to the context.

At Excellence, students need to explain any decisions they make in the solution of the problem.

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