# Mathematics and Statistics - annotated exemplars level 2 AS91258

## Apply sequences and series in solving problems (2.3)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 378KB)

This annotated exemplar is intended for teacher use only. The student work shown does not always represent a complete sample of what is required. Selected extracts are used, focused on the grade boundaries, in order to assist assessors to make judgements at the national standard.

Last updated July 2019.

Minor revisions have been made to improve quality. The main content of this exemplar has not changed.

### Low Excellence

Commentary
Student work extract

Student 1 (PDF, 83KB)

For Excellence, the student needs to apply sequences and series, using extended abstract thinking, in solving problems.

This involves one or more of: devising a strategy to investigate a situation, identifying relevant concepts in context, developing a chain of logical reasoning, or proof, or forming a generalisation, and also using correct mathematical statements, or communicating mathematical insight.

This student’s evidence is in response to the TKI task ‘Property Development’.

The student has devised a strategy to investigate and find the total weekly rent for the buildings with 15 floors in both areas (1) (2). The student has found a solution for the number of floors required in each building in order for the income difference to be less than \$1000 (3).

For a more secure Excellence, the student needs to improve the communication by clearly indicating what it is they are calculating and the decisions that they made when selecting and using formulae. The student should also use correct mathematical statements throughout the response.

### High Merit

Commentary
Student work extract

Student 2 (PDF, 67KB)

For Merit, the student needs to apply sequences and series, using relational thinking, in solving problems.

This involves one or more of: selecting and 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.

This student’s evidence is in response to the TKI task ‘Property Development’.

The student has formed and used a model to find the total weekly rent for an industrial area building (1) and a business area building (2). The student has used appropriate mathematical statements.

To reach Excellence, the student could improve the communication. This could be done by explaining why floors 17 and 19 were chosen, and by confirming that the difference is less than \$1000.

### Low Merit

Commentary
Student work extract

Student 3 (PDF, 125KB)

For Merit, the student needs to apply sequences and series, using relational thinking, in solving problems.

This involves one or more of: selecting and 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.

This student’s evidence is in response to the TKI task ‘Property Development’.

The student has formed and used models to investigate the total weekly rent for the business area (1) and industrial area buildings (2).

For a more secure Merit, the student needs to use eight inside offices rather than six, and for the solution, the difference in rents needs to be less than \$1000. The student should also use appropriate mathematical statements throughout the response.

### High Achieved

Commentary
Student work extract

Student 4 (PDF, 68KB)

For Achieved, the student needs to apply sequences and series in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is in response to the TKI task ‘Property Development’.

The student has selected and used a partial sum of an arithmetic sequence in correctly finding the total weekly rent for a 15 floor building in the industrial area (1), and a partial sum of a geometric sequence in finding the total weekly rent for a 15 floor building in the business area (2).

To reach Merit, the student needs to start to investigate different building sizes. The student would also need to more clearly communicate what they are calculating.

### Low Achieved

Commentary
Student work extract

Student 5 (PDF, 68KB)

For Achieved, the student needs to apply sequences and series in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is in response to the TKI task ‘Property Development’.

The student has selected and used the general term of a geometric sequence in correctly finding the total rent of the 15th and 23rd floor of the business area high rise building (1), and a partial sum of a geometric sequence in finding the total rent for a 15 floor building in the business area (2).

For a more secure Achieved, the student, when finding the total floor cost for the industrial area, could use the correct common difference in calculations that involve finding the cost of the outside offices.

### High Not Achieved

Commentary
Student work extract

Student 6 (PDF, 55KB)

For Achieved, the student needs to apply sequences and series in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is in response to the TKI task ‘Property Development’.

The student has selected and used a partial sum of an arithmetic sequence in correctly finding the total costs of renting one outside office for 15 floors and for 32 floors in the industrial area high rise building (1).

To reach Achieved, the student needs to select and use one further method, for example by finding the sum of all the offices on the floor, or by correctly using the 5% extra for a business area office.

The student should also give their answers in context, for example, by including the \$ sign when finding cost.