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# Massachusetts Comprehensive Assessment System

 Question 31: Open-Response Reporting Category: Algebra and FunctionsStandard: 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.A.CED.1.02 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* Katya wants to earn \$1500 this summer by doing yard work. She plans on working 125 hours over the summer.Based on her plan, what is the rate, in dollars per hour, that Katya must charge customers for doing yard work to earn \$1500 over the summer? Show or explain how you got your answer.Katya also wants to enroll in a summer class at a local college. As a result, she will have to work 50 hours less than the total number of hours she had originally planned.What is the rate, in dollars per hour, that Katya must charge customers for doing yard work to still earn \$1500? Show or explain how you got your answer.Write an equation that represents the relationship between x, the number of hours Katya will have to work, and y, the rate she must charge customers to earn \$1500.Explain how a change in x, the number of hours Katya will have to work, affects y, the rate she will have to charge customers to earn \$1500, in your equation from part (c).

### Scoring Guide and Sample Student WorkSelect 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 creating equations in two or more variables to represent relationships between quantities. The student calculates unknowns in a reciprocal relationship, writes an equation, and explains in words the reciprocal relationship.
4
3 The student response demonstrates a good understanding of the Algebra and Functions concepts involved in creating equations in two or more variables to represent relationships between 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 creating equations in two or more variables to represent relationships between 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 only minimal understanding of the Algebra and Functions concepts involved in creating equations in two or more variables to represent relationships between quantities.
0 The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in creating equations in two or more variables to represent relationships between quantities to merit any points.

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

Question 17:
Question 20:
Question 21:
Question 31:
Question 41:
Question 42: