




Massachusetts Comprehensive Assessment System
2014, Grade 10 Mathematics
Question 42: OpenResponse 

Reporting Category: Algebra and Functions 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)
Standard: Mathematics.F.IF.2.04  For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

The graph below represents y, the height in feet of a ball, x seconds after the ball was thrown upward from a bridge that crosses a river.  What is the yintercept of the graph? Show or explain how you got your answer.
 What does the yintercept represent in the context of this situation?
 After how many seconds did the ball reach its maximum height? Show or explain how you got your answer.
 What is the maximum height, in feet, the ball reached? Show or explain how you got your answer.
 After how many seconds did the ball reach the surface of the river? 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 Algebra and Functions concepts involved in interpreting key features of graphs in terms of the quantities for a function that models a relationship between two quantities. The student understands a quadratic function and demonstrates an understanding of the meaning of the characteristics of the function within the context of the problem. 
4 
3 
The student response demonstrates a good understanding of the Algebra and Functions concepts involved in interpreting key features of graphs in terms of the quantities for a function that models a relationship between two quantities. 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 interpreting key features of graphs in terms of the quantities for a function that models a relationship between two quantities. 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 interpreting key features of graphs in terms of the quantities for a function that models a relationship between two quantities. 
0 
The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in interpreting key features of graphs in terms of the quantities for a function that models a relationship between two quantities to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Number and Quantity
 Question 20: Geometry
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2014 Student Work Directory
Last Updated: October 1, 2018


