91587 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.