Mass.gov
Massachusetts Department of Elementary and Secondary Education
Go to Selected Program Area
Massachusetts State Seal
Students & Families Educators & Administrators Teaching, Learning & Testing Data & Accountability Finance & Funding About the Department Education Board  
>
>
>
 
 
 
 
 
 
 
 
 
 
>
>
>
>
>
>
>
>

Massachusetts Comprehensive Assessment System

2014, Grade 10 Mathematics

  Question 42: Open-Response calculator allowed
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.
A graph titled Height of Ball over Time. The x-axis is titled Time, in seconds. The x-axis goes from 0 to 6 in intervals of 1. The y-axis is titled Height, in feet. The y-axis goes from 0 to 160 in increments of 16. The graph shows part of a concave down parabola that passes through 0, 80 and 5, 0 with its max value at 2, 144.
  1. What is the y-intercept of the graph? Show or explain how you got your answer.
  2. What does the y-intercept represent in the context of this situation?
  3. After how many seconds did the ball reach its maximum height? Show or explain how you got your answer.
  4. What is the maximum height, in feet, the ball reached? Show or explain how you got your answer.
  5. 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.

ScoreDescription
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: July 5, 2013
E-mail this page| Print View| Print Pdf  
Massachusetts Department of Elementary and Secondary Education Search·Public Records Requests · A-Z Site Index · Policies · Site Info · Contact ESE