




Massachusetts Comprehensive Assessment System
2017, Grade 10 Mathematics
Question 36: OpenResponse 

Reporting Category: Algebra and Functions Standard: 10.P.1  Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships. (AI.P.1)
Standard: CCSS.Math.Content.HSFBF.A.2  Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*

Livy and Zack are writing arithmetic sequences. The first three terms of Livy's sequence are shown below.
4, 7, 10, . . .  What is the common difference for Livy's sequence? Show or explain how you got your answer.
 Write an expression that can be used to find the nth term of Livy's sequence.
The nth term of Zack's sequence is three times the nth term of Livy's sequence.
 What is the 5th term of Zack's sequence? Show or explain how you got your answer.
 Write an expression that represents the difference of the nth term of Zack's sequence and the nth term of Livy's sequence.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Algebra and Functions concepts involved in writing arithmetic sequences with an explicit formula. The student writes an expression that represents the difference of the nth terms of two sequences. 
4 
3 
The student response demonstrates a good understanding of the Algebra and Functions concepts involved in writing arithmetic sequences with an explicit formula. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points. 
2 
The student response demonstrates a fair understanding of the Algebra and Functions concepts involved in writing arithmetic sequences with an explicit formula. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates a minimal understanding of the Algebra and Functions concepts involved in writing arithmetic sequences with an explicit formula. 
0 
The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in writing arithmetic sequences with an explicit formula to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Geometry
 Question 20: Number and Quantity
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2017 Student Work Directory
Last Updated: March 1, 2019


