Achievement objective M7-8
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 and use pairs of simultaneous equations, one of which may be non-linear.
Indicators
- Solves problems that can be modelled by pairs of simultaneous equations where one is linear and the other equation can be:
- a quadratic, y = ax^2 + bx + c
- a hyperbola, y = a/(x+b) + c
- a circle, (x-h)^2 + (y-k)^2 = r^2
- Solves problems that can be modelled by a system of linear inequations in two variables.
- Chooses appropriate methods and uses them to solve simultaneous equations.
- Interprets the existence and type of solution(s) in the context of the situation.
- Makes links to graphs
M7-2 and manipulating expressions
M7-6.
Progression
M7-8 links from NA6-5 and to M8-4, M8-8.
Possible context elaborations
- Using discriminant or otherwise find:
- When is a line tangential to a hyperbola?
- Under what circumstances does a given line cross a parabola once or twice or not at all?
- For a given practical situation, discuss why some solutions are invalid in the context of the situation.
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Activity: Skid marks
Assessment for qualifications
NCEA achievement standards at level 1 and 2 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.
Aligned level 3 achievement standards will be registered by NZQA for use in 2013.
Full information on the level 3 draft standards and the alignment process can be found on
NCEA on TKI.
The following achievement standard(s) could assess learning outcomes from this AO.
- AS91269 Mathematics and statistics 2.14 Apply systems of equations in solving problems
Refer to the draft standards matrix.
Last updated September 26, 2012
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