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Massachusetts Comprehensive Assessment System

2013, Grade 10 Mathematics

  Question 21: Open-Response no calculator allowed
A company packages barbeque sauce in two different-sized bottles, small and large. Although the label on each small bottle states that the bottle contains 18 ounces of sauce, the company allows a tolerance of plus or minus 0.25 ounce for the amount of sauce in each small bottle. In manufacturing, tolerance is the amount of error that is allowed in packaging a product.
  1. What is the maximum amount of sauce, in ounces, the company allows in each small bottle? Show or explain how you got your answer.
In the absolute-value inequality below, x represents the amount of sauce, in ounces, the company allows in each small bottle.
open absolute value x minus eighteen close absolute value is less than or equal to zero point two five
  1. Solve the absolute-value inequality. Show or explain how you got your answer.
The company also makes a large bottle of barbeque sauce.
  • The label on the large bottle states that each bottle contains 24 ounces of sauce.
  • The minimum amount of sauce allowed in each large bottle is 23.55 ounces.
  • The maximum amount of sauce allowed in each large bottle is 24.45 ounces.
  1. What is the tolerance, in ounces, the company allows for the large bottle? Show or explain how you got your answer.
  2. Write an absolute-value inequality that represents y, the amount of sauce, in ounces, the company allows in the large bottle.

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 solving linear equations and inequalities in one variable involving absolute value. The student solves an absolute-value inequality and then writes a different absolute-value inequality in the context of manufacturing.
4
3 The student response demonstrates a good understanding of the Algebra and Functions concepts involved in solving linear equations and inequalities in one variable involving absolute value. 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 solving linear equations and inequalities in one variable involving absolute value. 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 solving linear equations and inequalities in one variable involving absolute value.
0 The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in solving linear equations and inequalities in one variable involving absolute value 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: September 16, 2015
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