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Massachusetts Comprehensive Assessment System
2015, Grade 10 Mathematics
 Question 41: Open-Response |
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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.A.CED.1.01 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* |
The expression below can be used to calculate the balance in a savings account for which an initial deposit of P dollars has been compounded each year for t years at interest rate r. P(1 + r)t Elaine opened a savings account with a deposit of $1000. The interest on her account is compounded each year at a rate of 2%. Elaine will not make any additional deposits to or withdrawals from her account. - What will be the balance in Elaine’s account at the end of 1 year? Show or explain how you got your answer.
- What will be the balance in Elaine’s account at the end of 3 years? Show or explain how you got your answer.
Pavel opened a savings account with a deposit of $800. The interest on his account is compounded each year at a rate of 2.5%. Pavel will not make any additional deposits to or withdrawals from his account. - Whose account, Elaine’s or Pavel’s, will have earned more interest at the end of 3 years? Show or explain how you got your answer.
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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 creating equations in one variable and using them to solve problems, including equations arising from simple exponential functions. The student compares values of exponential expressions with different initial values and growth factors. |
| 4 |
| 3 |
The student response demonstrates a good understanding of the Algebra and Functions concepts involved in creating equations in one variable and using them to solve problems, including equations arising from simple exponential functions. 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 one variable and using them to solve problems, including equations arising from simple exponential functions. 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 creating equations in one variable and using them to solve problems, including equations arising from simple exponential functions. |
| 0 |
The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in creating equations in one variable and using them to solve problems, including equations arising from simple exponential functions 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: Algebra and Functions
- Question 36: Statistics and Probability
- Question 41: Algebra and Functions
- Question 42: Geometry
Return to the MCAS 2015 Student Work Directory
Last Updated: July 24, 2017
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