# Level 2

## 91258: Apply sequences and series in solving problems

Updated July 2019. The section dealing with ‘Solving problems’ has been updated. The sections headed ‘Expected evidence for Achieved’, ‘Expected evidence for Merit’ and ‘Expected evidence for Excellence’ have been incorporated into new sections headed ‘Expected evidence’ and ‘Communicating solutions’.

### Solving problems

Students need to investigate a situation that can be modelled by sequences and series to solve a problem. It is not appropriate to specify the type of sequence that models the situation. 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 several 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.

### Expected evidence

For Achieved, the requirements include selecting and using methods. To be used as evidence, a ‘method’ needs to be relevant to the solution of the problem and at the appropriate curriculum level for the standard.

A table of values, on its own, for an arithmetic or geometric sequence does not provide sufficient evidence for the standard. Students need to demonstrate knowledge of concepts and terms and communicate using appropriate representations. These aspects are likely to be evidenced by the use of appropriate formulae.

The use of iterative formulae such as tn+1 = tn + d and tn+1 = rtn could provide evidence for the standard.

For Merit, students are likely to demonstrate relational thinking when forming and using tn and Sn as part of their solution of the overall problem.

For Excellence, students are likely to demonstrate extended abstract thinking when making a generalisation or devising a strategy which considers different options in context.

### Communicating solutions

At all grades 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.

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.