Mass.gov
Massachusetts Department of Elementary and Secondary Education
Go to Selected Program Area
 Massachusetts State Seal
 News  School/District Profiles  School/District Administration  Educator Services  Assessment/Accountability  Family & Community  
 Student Assessment  Accountability, Partnership, & Assistance  Compliance/Monitoring >  
>
>
>
 
 
 
 
 
 
 
 
 
 
 
>
>
>
>
>
>
>
>
>
>
>

Massachusetts Comprehensive Assessment System

2013, Grade 10 Mathematics

  Question 41: Open-Response calculator allowed
A flower bed in the shape of a right triangle has a circular fountain in it. The flower bed and some of its measurements are shown in the diagram below.
A diagram of a flower bed in the shape of a right triangle which contains a fountain in the shape of a circle. The sides of the triangle are labeled 16 feet, x feet, and 20 feet.
The perimeter of the flower bed is 48 feet.
  1. What is x, the length in feet of the third side of the flower bed? Show or explain how you got your answer.
  2. What is the area, in square feet, of the flower bed, including the fountain? Show or explain how you got your answer.
The circumference of the fountain is 8π feet.
  1. What is the radius, in feet, of the fountain? Show or explain how you got your answer.
  2. What is the area, in square feet, of the flower bed, not including the fountain? 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 Geometry concepts involved in knowing the formulas for the area and circumference of a circle and solving problems. The student determines the area of a triangle and circle and uses the solutions to solve a real-world problem.
4
3 The student response demonstrates a good understanding of the Geometry concepts involved in knowing the formulas for the area and circumference of a circle and solving problems. 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 Geometry concepts involved in knowing the formulas for the area and circumference of a circle and solving problems. The mixed evidence provided by the student merits 2 points.
1 The student response demonstrates only minimal understanding of the Geometry concepts involved in knowing the formulas for the area and circumference of a circle and solving problems.
0 The student response contains insufficient evidence of an understanding of the Geometry concepts involved in knowing the formulas for the area and circumference of a circle and solving problems to merit any points.

Note: There are 2 sample student responses for Score Point 4.

Grade 10 Mathematics

Question 17: Statistics and Probability
Question 20: Number and Quantity
Question 21: Algebra and Functions
Question 31: Algebra and Functions
Question 41: Geometry
Question 42: Geometry

Return to the MCAS 2013 Student Work Directory



Last Updated: November 1, 2001
E-mail this page| Print View| Print Pdf  
Massachusetts Department of Elementary and Secondary Education Search · Site Index · Policies · Site Info · Contact ESE