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 1.2.3 The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

Assessment Limits:

  • Functions will be of the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
  • All coefficients will be rational.
  • Vertical lines will be included.
  • Systems of linear functions will include coincident, parallel, or intersecting lines.
  • The majority of these items should be in real-world context.

Student Produced Response (SPR) Item - Released in 2004

Use the answer box below to complete the following.

Martin and Anna buy books at a sale. Martin buys 3 hardcover books and 4 paperback books for $6.50. Anna buys 2 hardcover books and 6 paperback books for $6.00. What is the cost, in dollars, of each hardcover book?

/share/clg/xml/public_release/mathematics/2004_123_alg14.xml

Correct Answer:
1.5

Selected Response Item - Released in 2004

Sam needs to rent a van for a school field trip. Van Company A charges a one-time fee of $250 plus $10 for each mile driven. Van Company B charges a one-time fee of $150 plus $12 for each mile driven. Let x represent the number of miles driven. Let y represent the total cost, in dollars, to rent the van. Which system of equations models this situation?

  1. y = 250 - 10x
    y = 150 - 12x
  2. y = 10x - 250
    y = 12x - 150
  3. y = 250x + 10
    y = 150x + 12
  4. y = 10x + 250
    y = 12x + 150
/share/clg/xml/public_release/mathematics/2004_123_alg32.xml

Correct Answer:
D

Student Produced Response (SPR) Item - Released in 2003

Use the answer box below to complete the following.

The graph below compares the income and expenses involved in the production and sales of tennis shoes at a shoe factory.

How many pairs of tennis shoes must be sold for income and expenses to be equal?

/share/clg/xml/public_release/mathematics/2003_123_alg15.xml

Correct Answer:
800

Selected Response Item - Released in 2003

The graph below shows the amount of money Diana and Melinda each saved during their summer vacation.

Which of these statements can be concluded from the graph?

  1. Diana will always have more money than Melinda.
  2. Diana will never have more money than Melinda.
  3. The amount of Melinda’s savings becomes greater than Diana’s after 12 weeks.
  4. The amount of Diana’s savings becomes greater than Melinda’s after 12 weeks.
/share/clg/xml/public_release/mathematics/2003_123_alg35.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2003

At a baseball game Sam bought 2 hamburgers and 1 order of French fries for a total of $3.75. Erica bought 1 hamburger and 2 orders of French fries for a total of $3.00.

Complete the following in the answer box below:

  • Write an equation that represents Sam’s total cost. Write an equation that represents Erica’s total cost.
     
  • What is the cost of one hamburger? What is the cost of one order of French fries? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanations. (If you choose to draw a graph, use the grid provided in the Answer Book to add to your written response.)
     
  • Use mathematics to justify your answers for the cost of one hamburger and the cost of one order of French fries.
     

/share/clg/xml/public_release/mathematics/2003_123_alg36.xml

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Brief Constructed Response (BCR) Item - Released in 2001

A telephone company offers customers two payment plans for monthly service.
Plan A costs $5 per month plus $0.10 per minute for calls.
Plan B costs $8 per month plus $0.07 per minute for calls.
Complete the following in the answer box below:
  • How many minutes of calls would it take for Plan A and Plan B to cost the same? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. (You may wish to solve the problem graphically, using additional paper for your response.)

/share/clg/xml/public_release/mathematics/2001_123_alg09.xml

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Selected Response Item - Released in 2001

The graph below shows the amounts of money that Lisa and Dan saved during the summer.
How much money did they each have when their savings were equal?

  1. $200
  2. $300
  3. $500
  4. $600
/share/clg/xml/public_release/mathematics/2001_123_alg03.xml

Correct Answer:
B

Selected Response Item - Released in 2001

The Sanchez family is planning a trip to an amusement park. The park has two ticket plans.
Plan A offers a weekend pass for $12 plus $0.50 per ride.
Plan B is $1.25 for each ride.
Let x represent the number of rides each person will ride and y represent the cost per person, in dollars. Which of these systems of equations could be used to choose a ticket plan?

  1. y = 0.50x + 12
    y = 1.25x
  2. y = 12x + 0.50
    y = x + 1.25
  3. y = 0.50x
    y = 1.25x
  4. y = x + 12
    y = x + 1.25
/share/clg/xml/public_release/mathematics/2001_123_alg35.xml

Correct Answer:
A

Student Produced Response (SPR) Item - Released in 2001

Use the answer box below to complete the following:

Kareem is going to Florida. The cost for two different vacation packages is shown below.
How many nights would Kareem need to stay in a hotel to pay the same amount for either vacation package?

/share/clg/xml/public_release/mathematics/2001_123_alg38.xml

Correct Answer:
4

Selected Response Item - Released in 2002

Mary graphed the system of equations below.

Which of these best describes the relationship between the two lines?

  1. They have no point in common.
  2. They have one point in common.
  3. They have two points in common.
  4. They have infinite points in common.
/share/clg/xml/public_release/mathematics/2002_123_alg03.xml

Correct Answer:
B

Selected Response Item - Released in 2002

Look at the system of equations below.

Which of these graphs represents this system of equations?





/share/clg/xml/public_release/mathematics/2002_123_alg04.xml

Correct Answer:
A

Extended Constructed Response (ECR) Item - Released in 2002

Terry is going to the county fair. She has two choices for purchasing tickets, as shown in the table below.

Complete the following in the answer box below:
  • Write an equation for Terry's total cost (y) for ticket Choice A. Write an equation for Terry's total cost (y) for ticket Choice B. Let x represent the number of rides she plans to go on.
  • How many rides would Terry have to go on for the total cost of ticket A and ticket B to be equal? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. (If you choose to draw a graph, you should do so on a separate sheet of graph paper.)
  • Terry plans to go on 14 rides. To spend the least amount of money, which ticket choice should Terry choose? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2002_123_alg17.xml

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Selected Response Item - Released in 2005

Look at the system of equations below.

y = 3x - 2
2y = 6x - 4

Which of these describes this system?

  1. two parallel lines
  2. two equations of the same line
  3. two lines that intersect only at (1, 1)
  4. two lines that intersect only at (-1, -1)
/share/clg/xml/public_release/mathematics/2005_123_alg07.xml

Correct Answer:
B

Selected Response Item - Released in 2005

The graph below shows the cost of video rentals for members and non-members of a video club.

According to the graph, which of these statements is true?

  1. members pay less for 4 movies
  2. non-members pay less for 5 movies
  3. non-members pay less for 6 movies
  4. members pay less for 8 movies
/share/clg/xml/public_release/mathematics/2005_123_alg25.xml

Correct Answer:
D

Student Produced Response (SPR) Item - Released in 2005

Use the Response Grids in the Answer Book to complete the following.

Monique bought 2 hot dogs and 1 large soda. She spent $7. Scott bought 4 hot dogs and 1 large soda. He spent a total of $12. What is the cost of each hot dog?

/share/clg/xml/public_release/mathematics/2005_123_alg37.xml

Correct Answer:
2.5

Student Produced Response (SPR) Item - Released in 2002

Use the answer box below to complete the following.

There are 26 students in an algebra class. The number of girls in the class is one less than twice the number of boys. How many boys are in the class?

/share/clg/xml/public_release/mathematics/2002_123_alg14.xml

Correct Answer:
9

Selected Response Item - Released in 2003

Look at the system of equations below.

Which of these statements is correct?

  1. The system has no solution.
  2. The solution of the system is (-3, 8).
  3. The solution of the system is (6, -6).
  4. The system has an infinite number of solutions.
/share/clg/xml/public_release/mathematics/2003_123_alg09.xml

Correct Answer:
A

Selected Response Item - Released in 2004

A park ranger spent $208 to buy 12 trees. Redwood trees cost $24 each and spruce trees cost $16 each. How many of each tree did the park ranger buy?

  1. 10 redwoods and 2 spruce
  2. 9 redwoods and 3 spruce
  3. 3 redwoods and 9 spruce
  4. 2 redwoods and 10 spruce
/share/clg/xml/public_release/mathematics/2004_123_alg02.xml

Correct Answer:
D

Student Produced Response (SPR) Item - Released in 2006

Use the Response Grids in the Answer Book to complete the following.

Information about fees for two health clubs is shown in the table below.

For what number of months is the total cost the same for both health clubs?

/share/clg/xml/public_release/mathematics/2006_123_alg15.xml

Correct Answer:
5

Selected Response Item - Released in 2006

Look at the graph below.

Which of these statements describes the relationship between the two lines?

  1. They intersect at the point (2, 1).
  2. They intersect at the point (1, 2).
  3. They intersect at the point (1, 0).
  4. They intersect at the point (0, 3).
/share/clg/xml/public_release/mathematics/2006_123_alg20.xml

Correct Answer:
A

Selected Response Item - Released in 2006

Russ worked a total of 135 hours during the month of July. He earned $3,600. Russ earned $25 per hour each weekday that he worked. He earned $40 per hour each Saturday that he worked. Let x represent the number of weekday hours worked and y represent the number of Saturday hours worked. Which system of equations represents this situation?

  1. x + y = 135
    25x + 40y = 3,600
  2. x + y = 135
    40x + 25y = 3,600
  3. x + y = 3,600
    25x + 40y = 135
  4. x + y = 3,600
    40x + 25y = 135
/share/clg/xml/public_release/mathematics/2006_123_alg29.xml

Correct Answer:
A

Selected Response Item - Released in 2007

Mary is considering two job offers. Job A pays $8.00 an hour and offers a one-time $100 bonus. Job B pays $8.50 an hour and offers a one-time $80 bonus. How many hours would Mary have to work to earn the same amount of money at Job B as at Job A?

  1. 40
  2. 41
  3. 420
  4. 428
/share/clg/xml/public_release/mathematics/2007_123_alg11.xml

Correct Answer:
A

Student Produced Response (SPR) Item - Released in 2007

The graph below shows the cost (c), in dollars, to rent a boat for h hours at two different boat companies.

At what number of hours will the cost to rent a boat be the same at both companies?

/share/clg/xml/public_release/mathematics/2007_123_alg14.xml

Correct Answer:
range: 3.9-4.1

Selected Response Item - Released in 2007

Two lines are parallel. The equation of the first line is y = 2x + 3. Which of these could be the equation of the other line?

  1. y = −2x
  2. y = negative one halfx
  3. y = one halfx
  4. y = 2x
/share/clg/xml/public_release/mathematics/2007_123_alg20.xml

Correct Answer:
D

Extended Constructed Response (ECR) Item - Released in 2007

At the beginning of the summer, Sarah has $250. She takes a summer job and saves $150 per week. Felicia has $1,650 at the beginning of the summer. She travels during the summer and spends $200 per week.

Complete the following in the Answer Book:

  • Write an equation that represents the amount of money Sarah has at the end of each week.
  • Write an equation that represents the amount of money Felicia has at the end of each week.
  • Graph the two equations on the grid provided in the Answer Book. (Suggested graphing window: 0 ≤ weeks ≤ 10; 0 ≤ amount ≤ 2000.)
  • At the end of which week do Sarah and Felicia have the same amount of money? How much money do they have? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2007_123_alg22.xml

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Resources for 1.2.3:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |