School Improvement in Maryland

Public Release Item: Public Release items have appeared on HSA forms and then are released for public viewing and use. Releasing items is one step to ensuring that schools, districts, and other stakeholders understand how the core learning goals are assessed on the HSA.

Goal 1 Functions and Algebra

Expectation 1.2 The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

Indicator 1.2.2 The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.

Assessment Limits:

  • Inequalities will have no more than two variables with rational coefficients.
  • Acceptable forms of the problem or solution are the following:
    Ax + By < C, Ax + By < C, Ax + By > C, Ax + By > C, Ax + By + C < 0, Ax + By + C < 0, Ax + By + C > 0, Ax + By + C > 0, y < mx + b, y < mx + b, y > mx + b, y > mx + b, y < b, y < b, y > b, y > b, x < b, x < b, x > b, x > b, a < x < b, a < x < b, a < x < b, a < x < b, a < x + c < b, a < x + c < b, a < x + c < b, a < x + c < b.
  • The majority of these items should be in real-world context.
  • Systems of linear inequalities will not be included.
  • Compound inequalities will be included.
  • Disjoint inequalities will not be included.
  • Absolute value inequalities will not be included.

Selected Response Item - Released in 2004

Bruce bought 4 candy bars and 3 decks of cards. The candy bars cost $1.35 each. Bruce spent no more than $12.00. Which of these inequalities best represents the cost (c) for one deck of cards?

  1. c $2.20
  2. c $2.20
  3. c $3.55
  4. c $3.55
/share/clg/xml/public_release/mathematics/2004_122_alg08.xml

Correct Answer:
A

Selected Response Item - Released in 2004

Look at the graph below.

Which of these inequalities best describes this graph?

  1. y x -1
  2. y x -1
  3. y x -1
  4. y x -1
/share/clg/xml/public_release/mathematics/2004_122_alg10.xml

Correct Answer:
B

Extended Constructed Response (ECR) Item - Released in 2004

Elizabeth joins a CD buyer's club. She receives 10 free CDs when she joins this club. She must buy 3 CDs each month.

Complete the following in the Answer Book:

  • Write an equation that represents the number of CDs (y) Elizabeth will receive from the CD buyer's club after x months.
  • What is the y-intercept of your equation? What does the y-intercept mean in the context of this problem?
  • Elizabeth wants to receive no more than 55 CDs from this club. What is the maximum number of months Elizabeth will remain in the CD buyer's club? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

/share/clg/xml/public_release/mathematics/2004_122_alg19.xml

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Selected Response Item - Released in 2001

Manuel has budgeted $80 a day to rent a truck. The rental company charges $35 a day plus $0.25 per mile. Which of these inequalities represents the number of miles (m) Manuel can drive in one day and stay within his budget?

  1. m ≤ 180
  2. m ≥ 180
  3. m ≤ 460
  4. m ≥ 460
/share/clg/xml/public_release/mathematics/2001_122_alg24.xml

Correct Answer:
A

Selected Response Item - Released in 2001

Margaret is recording songs from CDs onto a cassette tape. She has already recorded 21 minutes onto her 60-minute tape. How many complete 5-minute songs will fit on the unrecorded part of the tape?

  1. 4
  2. 7
  3. 8
  4. 16
/share/clg/xml/public_release/mathematics/2001_122_alg02.xml

Correct Answer:
B

Selected Response Item - Released in 2003

A week long soccer camp needs at least $72,000 in order to pay expenses. The camp receives $250 per person for day campers and $400 for full-time campers. Which of these combinations would be enough to pay expenses?

  1. 78 day campers and 152 full-time campers
  2. 104 day campers and 114 full-time campers
  3. 117 day campers and 79 full-time campers
  4. 200 day campers and 29 full-time campers
/share/clg/xml/public_release/mathematics/2003_122_alg04.xml

Correct Answer:
A

Selected Response Item - Released in 2003

A company makes a standard model flashlight (s) and a deluxe model flashlight (d). The company makes a $3 profit on each standard model and a $4 profit on each deluxe model. The company wants to make a profit of at least $320. Which of these inequalities represents this situation?

  1. 3s + 4d ≤ 320
  2. 3s + 4d ≥ 320
  3. 4s + 3d ≤ 320
  4. 4s + 3d ≥ 320
/share/clg/xml/public_release/mathematics/2003_122_alg07.xml

Correct Answer:
B

Selected Response Item - Released in 2001

David sells both daylight and underwater cameras. For each daylight camera he sells, he makes $2, and for each underwater camera he sells, he loses $1. Let d represent the number of daylight cameras and u represent the number of underwater cameras sold. Which of these inequalities must be true for David to make money selling these cameras?

  1. 2d + u < 0
  2. 2d + u > 0
  3. 2du < 0
  4. 2du > 0
/share/clg/xml/public_release/mathematics/2001_122_alg42.xml

Correct Answer:
D

Selected Response Item - Released in 2002

Look at the graph below.

Which of these inequalities has the solution set that is shown in the graph?

  1. -2 ≤ x ≤ 3
  2. -2 < x < 3
  3. -2 ≤ x < 3
  4. -2 < x ≤ 3
/share/clg/xml/public_release/mathematics/2002_122_alg08.xml

Correct Answer:
D

Selected Response Item - Released in 2002

When a snack bar opens,the cash register contains at least 50 dollars in $1 and $5 bills. Which of these inequalities represents this situation, where x is the number of $1 bills and y is the number of $5 bills?

  1. x - 5y > 50
  2. x - 5y < 50
  3. x + 5y ≥ 50
  4. x + 5y ≤ 50
/share/clg/xml/public_release/mathematics/2002_122_alg09.xml

Correct Answer:
C

Selected Response Item - Released in 2005

Which of these graphs represents the solution set of the inequality y ≤ -2x + 4?





/share/clg/xml/public_release/mathematics/2005_122_alg08.xml

Correct Answer:
A

Selected Response Item - Released in 2005

A school store sells pens for $1.29 each and notebooks for $2.25 each. Paul bought p pens and n notebooks. He spent less than $10. Which of these inequalities represents this situation?

  1. 2.25p - 1.29n < 10
  2. 1.29p - 2.25n < 10
  3. 2.25p + 1.29n < 10
  4. 1.29p + 2.25n < 10
/share/clg/xml/public_release/mathematics/2005_122_alg26.xml

Correct Answer:
D

Extended Constructed Response (ECR) Item - Released in 2005

Sue has $75 to spend on shirts and shorts. The shirts are on sale for $10 each, including tax, and the shorts are on sale for $15 each, including tax.

Complete the following in the Answer Book:

  • Write an inequality that represents the situation above, where x represents the number of shirts and y represents the number of shorts.
  • What is the maximum number of shorts Sue can buy if she buys 2 shirts? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. (If you need to draw a graph for your solution, use the grid provided in the Answer Book.)
  • List all the number combinations of shirts and shorts Sue can buy to spend exactly $75. Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2005_122_alg21.xml

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Selected Response Item - Released in 2006

Look at the inequality below.

12-4x≤20

Which of these shows the solution to this inequality?

/share/clg/xml/public_release/mathematics/2006_122_alg04.xml

Correct Answer:
B

Selected Response Item - Released in 2007

Look at the inequality below.

−2x ≤ 6

Which of these best describes the solution of this inequality?

  1. x ≥ −3
  2. x ≤ −3
  3. x ≥ 3
  4. x ≤ 3
/share/clg/xml/public_release/mathematics/2007_122_alg08.xml

Correct Answer:
A

Selected Response Item - Released in 2007

A group of friends has $18 to spend on ice cream. A small cone costs $2 and a large cone costs $3.

Which of these graphs represents all the different combinations the group could buy?





/share/clg/xml/public_release/mathematics/2007_122_alg17.xml

Correct Answer:
C

Selected Response Item - Released in 2008

Kaila and Joey are starting a lawn mowing company. They have to buy a lawn mower for $250. They will charge $15 per lawn. Which of these inequalities represents the number of lawns (l) that they need to mow to earn at least $800 after they pay for the lawn mower?

  1. l ≤ 54
  2. l ≥ 54
  3. l ≤ 70
  4. l ≥ 70
/share/clg/xml/public_release/mathematics/2008_122_alg06.xml

Correct Answer:
D

Extended Constructed Response (ECR) Item - Released in 2008

Ichiro plans to spend no more than a total of $60 for both lunch and dinner each day during his vacation.

Complete the following in the Answer Book:

  • Write an inequality that models this relationship. Let x represent the amount, in dollars, that Ichiro spends on lunch. Let y represent the amount, in dollars, that Ichiro spends on dinner.
  • Graph the inequality on the grid provided in the Answer Book.
  • On Thursday, Ichiro spent exactly $60 on lunch and dinner. He spent three times as much on dinner as he spent on lunch. How much did Ichiro spend on lunch? How much did Ichiro spend on dinner? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanations.

/share/clg/xml/public_release/mathematics/2008_122_alg08.xml

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Selected Response Item - Released in 2008

The yearbook club washes cars to raise at least $600. The club charges $3 for each car (c) that they wash. Which of these inequalities models this situation?

  1. 3c ≤ 600
  2. 3c < 600
  3. 3c ≥ 600
  4. 3c > 600
/share/clg/xml/public_release/mathematics/2008_122_alg35.xml

Correct Answer:
C

Selected Response Item - Released in 2009

Patrick washes cars and motorcycles. He charges $6 per car and $3 per motorcycle. He earns no more than $24 a week. Which of these graphs best models this situation?





/share/clg/xml/public_release/mathematics/2009_122_alg10.xml

Correct Answer:
A

Selected Response Item - Released in 2009

Steve bought 3 hot dogs and 1 large soda using the menu shown below.

The total cost of Steve’s purchase was less than $6.75. Which of these inequalities best represents the cost (c) of each hot dog?

  1. c < $1.75
  2. c > $1.75
  3. c < $2.75
  4. c > $2.75
/share/clg/xml/public_release/mathematics/2009_122_alg11.xml

Correct Answer:
A

Selected Response Item - Released in 2009

The sign below shows the admission prices for an amusement park.

The Gomez family has 2 adults and 3 children. They want to determine how many times the whole family can visit the amusement park before the Summer Family Pass is cheaper than the Daily Admission price for the whole family. Let x represent the number of times the whole family can visit the amusement park. Which of these inequalities represents this situation?

  1. 5x ≤ 210
  2. 35x ≤ 210
  3. 85x ≤ 210
  4. 90x ≤ 210
/share/clg/xml/public_release/mathematics/2009_122_alg17.xml

Correct Answer:
C

Resources for 1.2.2:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |