




Massachusetts Comprehensive Assessment System
2013, Grade 10 Mathematics
Question 41: OpenResponse 

Reporting Category: Geometry Standard: 10.M.1  Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles. Standard: Mathematics.7.G.2.04  Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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. The perimeter of the flower bed is 48 feet. What is x, the length in feet of the third side of the flower bed? Show or explain how you got your answer.
 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. What is the radius, in feet, of the fountain? Show or explain how you got your answer.
 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.
Score  Description 
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 realworld 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: October 17, 2016


