Level 2

Mathematics and Statistics clarifications

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91269: Apply systems of equations in solving problems

Updated December 2017. This document has been updated in its entirety to address issues that have arisen from moderation.

Solving problems

For the award of the standard students must apply systems of equations in solving problems. The problem can be set in a real life or a mathematical context.

The problem needs to provide sufficient scope for students to demonstrate and develop their own thinking. If there are parts to the problem, all the parts need to contribute to the solution.

A task with a number of discrete questions based on skills and straightforward calculations is not appropriate for students to demonstrate evidence of the required levels of thinking.

Students need to make their own decisions about what to do and how to solve problems. Where an assessment task has a series of instructions that lead students through a step or a sequence of steps towards the solution, it is likely the opportunity for students to demonstrate all levels of thinking will be compromised.

Expected evidence for Achieved

For Achieved, the requirements include selecting and using methods. Relevant methods are listed in Explanatory Note 4.

To be used as evidence, a ‘method’ must be relevant to the solution of the problem.

The ‘methods’ also need to be at the appropriate curriculum level for the standard. For forming a system of equations to provide evidence of a method, one of the equations must be non-linear.

Correctly solving a pair of given simultaneous equations does not provide evidence for the standard. Forming and using a pair of simultaneous equations or interpreting the solution of a pair of simultaneous equations in context would provide evidence.

Communicating solutions

At all levels, there is a requirement relating to the communication of the solutions.

At Achieved, students need to indicate what the calculated answer represents.

At Merit, students need to clearly indicate what they are calculating and their solutions need to be linked to the context.

At Excellence, the response needs to be clearly communicated with correct mathematical statements, and students need to explain any decisions they make in the solution of the problem.


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