# Level 1

## 91029: Apply linear algebra in solving problems

Updated May 2019. A word that was missing in the last sentence for Achieved in the section ‘Communicating Solutions’ has been inserted.

### Solving problems

For the award of the standard, students must apply linear algebra in solving problems. The problem needs to be a real life situation that can be modelled by linear equations and graphs.

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 the award of Achieved, the requirements include selecting and using a range of methods.

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 the award of Merit there needs to be an understanding that the model(s) could be used to give information relating to a range of x values in addition to specific x values.

### Communicating Solutions

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

At Achieved, the result of a numerical calculation only is insufficient. Working is expected, and students need to indicate what the calculated answer represents. If a graph of a linear model has been used to find a value this needs to be communicated, for example by a vertical and horizontal line drawn to the graph.

At Merit, students need to clearly indicate what they are finding, 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. In most cases, correct mathematical statements will include equations of the models and intersection points.