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Mathematics and Statistics 3.15

3.15

• Apply systems of simultaneous equations in solving problems

• Level 3• Credits 2• Assessment Internal

Methods include a selection from those related to:

• forming systems of simultaneous equations• solving systems of simultaneous equations• the nature of solutions to systems.

Achievement Objective

• form and use systems of simultaneous equations, including three linear equations and three variables,

• and interpret the solutions in context.

Indicators

• 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.

Indicators

• 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.

Achieved

• Apply systems of simultaneous equations in solving problems

• selecting and using methods• demonstrating knowledge of concepts and

terms• communicating using appropriate

representations.

Merit

• Apply systems of simultaneous equations, using relational thinking, in solving problems.

• carrying out a logical sequence of steps• connecting different concepts or representations • demonstrating understanding of concepts • forming and using a model• and also relating findings to a context or

communicating thinking using appropriate mathematical statements.

Excellence

• Apply systems of simultaneous equations, using extended abstract thinking, in solving problems.

• devising a strategy to investigate a situation• identifying relevant concepts in context • developing a chain of logical reasoning, or proof• forming a generalisation • and also using correct mathematical statements,

or communicating mathematical insight.