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 1.2.1 The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

Assessment Limits:

  • Functions are to have no more than two variables with rational coefficients.
  • Linear equations will be given in the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
  • Vertical lines are included.
  • The majority of these items should be in real-world context.

Selected Response Item - Released in 2004

The rental rates at Snappy Car Rental are $30 per day plus $0.25 per mile for each mile driven. Joe rented a car for one day and drove 300 miles. What is the total amount Joe paid to rent the car?

  1. $30
  2. $75
  3. $105
  4. $300
/share/clg/xml/public_release/mathematics/2004_121_alg23.xml

Correct Answer:
C

Selected Response Item - Released in 2004

Which of these equations represents a line with an x-intercept of -3 and a y-intercept of 4?





/share/clg/xml/public_release/mathematics/2004_121_alg29.xml

Correct Answer:
D

Student Produced Response (SPR) Item - Released in 2004

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

Dominic rents a car for a trip. He pays $300 plus $0.20 per mile. Dominic has $750 to spend on the car rental. What is the maximum number of miles Dominic can drive?

/share/clg/xml/public_release/mathematics/2004_121_alg34.xml

Correct Answer:
2250

Extended Constructed Response (ECR) Item - Released in 2000

Two bicycle shops build custom-made bicycles. Bicycle City charges $160 plus $80 for each day that it takes to build the bicycle. Bike Town charges $120 for each day that it takes to build the bicycle. Complete the following in the answer box below:
  • Write an equation for each store that describes the charge (C) to build a custom-made bicycle in x days.
     
  • For what number of days will the charge be the same at each store? What will be the charge for that number of days? Use mathematics to justify your answer. (If you solve the problem graphically, use the grid provided in the Answer Book to add to your written response.)
     
  • When is it less expensive to use Bicycle City to build a custom-made bicycle than Bike Town? When is it more expensive? Use mathematics to justify your answer.
     

/share/clg/xml/public_release/mathematics/2000_121_alg18.xml

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Student Produced Response (SPR) Item - Released in 2002

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

The sign shown below is posted at a parking garage.

What is the cost, in dollars, for parking 7 hours?

/share/clg/xml/public_release/mathematics/2002_121_alg37.xml

Correct Answer:
12

Student Produced Response (SPR) Item - Released in 2001

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

Debi and some students from her geometry class went outside to measure their shadows. Debi measured Sean's and Karyn's shadows and recorded the information in the table below.

Debi plotted this data on a coordinate grid. What is the slope of the line containing these two points?

/share/clg/xml/public_release/mathematics/2001_121_alg07.xml

Correct Answer:
0.75

Selected Response Item - Released in 2003

Tees for Teens is a store that sells shirts. The graph below represents the total cost per shirt based on the number of colors in the design.

Which of these equations represents the relationship between the cost per shirt (s) and the number of colors (c)?

  1. s = 0.75c + 5
  2. s = 1.5c + 5
  3. s = 5c + 0.75
  4. s = 5c + 3
/share/clg/xml/public_release/mathematics/2003_121_alg31.xml

Correct Answer:
A

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 Book:

  • 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_121_alg36.xml

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Selected Response Item - Released in 2002

Lydia has $200 in her bank account at the beginning of the year. Each month, she deposits $40 into her account. She does not withdraw any money from her account, and the account pays no interest. Which of these equations could Lydia use to find the total amount (T) in her bank account at the end of m months?

  1. T = 40m
  2. T = 240m
  3. T = 200m + 40
  4. T = 40m + 200
/share/clg/xml/public_release/mathematics/2002_121_alg05.xml

Correct Answer:
D

Student Produced Response (SPR) Item - Released in 2002

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

The graph below shows a linear model of the number of people in the United States who have private or government health insurance.

What is the slope, in millions of people per year, of this linear model?

/share/clg/xml/public_release/mathematics/2002_121_alg13.xml

Correct Answer:
2

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 Book:

  • 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, use the grid provided in the Answer Book to add to your written response.)
  • 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_121_alg17.xml

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Student Produced Response (SPR) Item - Released in 2005

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

Denise has 24 baseball cards in her collection. She collects 9 baseball cards per month. In how many months will she have a total of 150 baseball cards in her collection?

/share/clg/xml/public_release/mathematics/2005_121_alg14.xml

Correct Answer:
14

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_121_alg21.xml

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Selected Response Item - Released in 2005

Carlos uses the formula below to change Celsius temperatures (C) into Fahrenheit temperatures (F).

F = nine fifthsC + 32

Which of these graphs represents this formula?





/share/clg/xml/public_release/mathematics/2005_121_alg23.xml

Correct Answer:
B

Selected Response Item - Released in 2005

The number of people (n) who will attend a dance depends on the admission price (p), in dollars. This relationship is represented by the equation shown below.

n = 800 - 50p

Which of these is a correct interpretation of the slope of this equation?

  1. 50 people will attend if the admission price is free
  2. 50 fewer people will attend for every dollar the admission price increases
  3. 800 people will attend if the admission price is free
  4. 800 fewer people will attend for every dollar the admission price increases
/share/clg/xml/public_release/mathematics/2005_121_alg33.xml

Correct Answer:
B

Selected Response Item - Released in 2001

The total bill for repairing Steve's television was $125. The repair shop charged $25 an hour for labor plus $19 for parts. How many hours of labor did it take to repair Steve's television? Round the answer to the nearest tenth of an hour.

  1. 4.2 hours
  2. 5.0 hours
  3. 5.3 hours
  4. 7.9 hours
/share/clg/xml/public_release/mathematics/2001_121_alg20.xml

Correct Answer:
A

Selected Response Item - Released in 2001

Courtney wants to run a total of 5 miles around a one-quarter-mile track. Which of these graphs represents the relationship between laps completed (l) and miles remaining (m)?

  1. Graph F
  2. Graph G
  3. Graph H
  4. Graph J
/share/clg/xml/public_release/mathematics/2001_121_alg34.xml

Correct Answer:
B

Selected Response Item - Released in 2001

A parachutist is 500 feet above the ground. After she opens her parachute, she falls at a constant rate of 5 feet per second. Which of these equations gives her height (h) above the ground in terms of seconds (t)?

  1. h = 5 – 500t
  2. h = 500 – 5t
  3. h = 500 + 5t
  4. h = 5 + 500t
/share/clg/xml/public_release/mathematics/2001_121_alg45.xml

Correct Answer:
B

Selected Response Item - Released in 2002

The water level in a storage tank is 14 feet. Water is released at a constant rate until the tank is empty. The graph below shows the water level (y) in the tank, as a function of time (x).

Which of these equations represents the relationship between time and the water level?

  1. y = -2x + 14
  2. y = -2x - 14
  3. y = 2x + 14
  4. y = 2x - 14
/share/clg/xml/public_release/mathematics/2002_121_alg18.xml

Correct Answer:
A

Student Produced Response (SPR) Item - Released in 2006

Use the Response Grids in the Answer Book to complete Numbers 13 through 15.

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

Julie is a member of a swim club. The swim club charges a monthly fee of $15 plus $0.50 per hour to use the pool. Julie spent $35 in August to use the pool. How many hours did Julie use the pool in August?

/share/clg/xml/public_release/mathematics/2006_121_alg13.xml

Correct Answer:
40

Selected Response Item - Released in 2006

Look at the graph below.

What is the slope of the line?

  1. −2
  2. negative one half
  3. one half
  4. 2
/share/clg/xml/public_release/mathematics/2006_121_alg17.xml

Correct Answer:
D

Student Produced Response (SPR) Item - Released in 2003

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

Alexis has $345 in her savings account and will deposit $15 each week. Alexis will not withdraw any money from her savings account. After how many weeks will she have $1,035?

/share/clg/xml/public_release/mathematics/2003_121_alg14.xml

Correct Answer:
46

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_121_alg19.xml

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Selected Response Item - Released in 2006

Art's swimming pool contains 20,000 gallons of water. He drains the pool at a rate of 5 gallons per minute. Which of these equations represents the number of gallons of water (g) remaining in the pool after m minutes?

  1. g = 20,000 - 5m
  2. g = 20,000 + 5m
  3. g = 20,000 / 5m
  4. g = 5m / 20,000
/share/clg/xml/public_release/mathematics/2006_121_alg21.xml

Correct Answer:
A

Selected Response Item - Released in 2007

A laundry service charges $10.00 plus an additional $1.25 per pound of laundry to be washed. Which of these graphs represents the relationship between the number of pounds of laundry washed (x) and the total cost (y)?





/share/clg/xml/public_release/mathematics/2007_121_alg07.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_121_alg22.xml

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Selected Response Item - Released in 2007

A group of students began a camping trip with 252 pounds of food. They plan to eat 12 pounds of food a day. At the end of what day will they have 84 pounds of food left?

  1. 7th day
  2. 14th day
  3. 21st day
  4. 28th day
/share/clg/xml/public_release/mathematics/2007_121_alg25.xml

Correct Answer:
B

Student Produced Response (SPR) Item - Released in 2007

Amy has a checking account at a bank. The graph below shows the relationship between the number of checks she writes and her monthly bank fees.

If she writes 16 checks, what will be her monthly bank fee, in dollars?

/share/clg/xml/public_release/mathematics/2007_121_alg31.xml

Correct Answer:
19

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_121_alg08.xml

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Student Produced Response (SPR) Item - Released in 2008

A car rental company has 2 rental plans. Plan A charges $49.00 per day. Plan B charges $25.00 per day, plus $0.10 per mile. How many miles must Teri drive in one day for Plan A to cost the same as Plan B?

/share/clg/xml/public_release/mathematics/2008_121_alg11.xml

Correct Answer:
240

Selected Response Item - Released in 2008

Sean’s movie rental company charges a monthly fee of $5.00 plus an additional cost of $1.25 per movie rental. Which of these equations represents the total monthly cost (c) of renting x movies?

  1. c = 1.25x+5.00
  2. c = 3.75x+5.00
  3. c = 5.00x+1.25
  4. c = 5.00x+3.75
/share/clg/xml/public_release/mathematics/2008_121_alg21.xml

Correct Answer:
A

Selected Response Item - Released in 2008

Look at the function that is graphed below.

Which of these equations represents this function?

  1. y = one halfx−4
  2. y = one halfx+2
  3. y = 2x−2
  4. y = 2x+4
/share/clg/xml/public_release/mathematics/2008_121_alg34.xml

Correct Answer:
D

Resources for 1.2.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |