Achievement objective M78
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 nonlinear.
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, (xh)^2 + (yk)^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
M72 and manipulating expressions
M76.
 See
key mathematical ideas on NZmaths.
Progression
M78 links from NA65 and to M84, M88.
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.

Activity: Skid marks
Assessment for qualifications
NCEA achievement standards at level 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 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
mathematics and statistics matrix.
Last updated September 26, 2013
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