Achievement objective M8-8
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 systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context.
- Translates contextual problems into systems of linear equations.
- Solves problems that can be modelled by systems of three linear equations with up to three unknowns.
- Chooses appropriate methods and uses them to solve simultaneous equations.
- Understands the process of solving systems of equations algebraically.
- Manipulates equations.
- Interprets solution(s) of a linear system in context.
- Identifies solutions that may be unique, infinite or non-existent.
- Explains the nature of solution(s) including consistency and uniqueness and interprets this in context, including 3D.
- Makes links to graphs
M7-2 and manipulating expressions
M8-8 links from M7-8.
Possible context elaborations
- Given total prices for three selected goods over three shopping sessions, calculate prices for individual goods.
- Given a table of vitamin content in three types of energy drink and the total vitamins required, find how many cans of each kind of drink would fulfil the vitamin requirement.
- Given a system of three equations, with parameters for coefficients, find values of parameters to satisfy particular solution situations, for example, a unique solution.
- Given a contextual problem and a variety of systems of equations, select the equations that match the problem.
- Given a variety of systems of three equations, select those that involve parallel planes.
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
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.
Note: Aligned and registered level 3 achievement standards will not be on the NZQA website until December 2012.
- School planning draft level 3 achievement standards are on
NCEA on TKI.
- Final draft level 3 achievement standards will be on
NCEA on TKI from end of September.
- Aligned level 3 achievement standards will be registered and published by NZQA for use in 2013 in December.
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:
- AS91587 Mathematics and statistics 3.15 Apply systems of simultaneous equations in solving problems; Internal, 3 credits.
Refer to the draft standards matrix.
Last updated September 26, 2012