




Massachusetts Comprehensive Assessment System
2011, Grade 10 Mathematics
Question 21: OpenResponse 

Reporting Category: Patterns, Relations, and Algebra Standard: 10.P.7  Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. (AI.P.11)

A person’s score on a timed keyboarding test varies directly with the number of words the person types correctly. Each keyboarding test lasts the same amount of time. On her first test, Catherine earned a score of 75 when she typed 200 words correctly. What is the ratio of Catherine’s score to the number of words she typed correctly?
 Use your ratio from part (a) to write an equation that can be used to find y, the score for x words typed correctly.
On her second test, Catherine typed 240 words correctly.  Use the equation you wrote in part (b) to find the score Catherine earned on her second test. Show or explain how you got your answer.
Catherine wants to earn a score of at least 96 on her third test.  What is the least number of words Catherine must type correctly to earn a score of 96? Show or explain how you got your answer.

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 Patterns, Relations, and Algebra concepts involved in solving everyday problems that can be modeled using linear functions. The student uses direct variation to write an algebraic equation and uses the equation in an everyday situation. 
4 
3 
The student response demonstrates a good understanding of the Patterns, Relations, and Algebra concepts involved in solving everyday problems that can be modeled using linear functions. 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 fair understanding of the Patterns, Relations, and Algebra concepts involved in solving everyday problems that can be modeled using linear functions. 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 only minimal understanding of the Patterns, Relations, and Algebra concepts involved in solving everyday problems that can be modeled using linear functions. 
0 
The student response contains insufficient evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in solving everyday problems that can be modeled using linear functions to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Number Sense and Operations
 Question 20: Geometry
 Question 21: Patterns, Relations, and Algebra
 Question 31: Patterns, Relations, and Algebra
 Question 41: Data Analysis, Statistics, and Probability
 Question 42: Measurement
Return to the MCAS 2011 Student Work Directory
Last Updated: January 24, 2017


