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This page shows questions in the Algebra I Modeling public release module at MSDE. Algebra 1
"Algebra I Modeling"

Select from the list to explore. Read any associated passages and then interact with the questions here.

Expand All Official Practice Test

This is a multiple choice question that allows you to select only one option.

An office manager is ordering this year’s supply of pencils and pens for the office. Each pencil costs $0.10, each pen costs $0.75, and the manager will spend a total of $235 on pencils and pens.

Which additional piece of information is sufficient to determine the number of pencils and the number of pens that the manager will order?

  1. A.
    The number of pencils purchased last year will be equal to the number of pens purchased this year.
  2. B.
    The number of pens purchased this year will be three times the number of pencils purchased this year.
  3. C.
    The total cost of the pens purchased this year will be greater than the total cost of the pencils purchased this year.
  4. D.
    The total cost of the pencils and pens purchased last year will be three times the total cost of the pencils and pens purchased this year.
i2

Correcti1

Insufficient informationi3 i4

Insufficient information

This is a multiple choice question that allows you to select several options.

The table shows the distance, in miles, that an athlete will run each week for 6 weeks to prepare for a half marathon.

Distance to Run Each Week
Week Distance (miles)
1 13
2 15.5
3 15.5
4 22.5
5 23
6 30

The equation y=3.25x+8.5 models the distance, y, in miles, that the athlete will run in week x.

For which weeks is the number of miles given by the equation greater than the actual number of miles the athlete will run?

Select all that apply.

  1. A.
    week 1
  2. B.
    week 2
  3. C.
    week 3
  4. D.
    week 4
  5. E.
    week 5
  6. F.
    week 6
i3

Correct i5

Correct i1

Chooses a week when the actual number of miles is greater than the number given by the equation i2

Chooses a week when the actual number of miles is greater than the number given by the equation i4

Chooses a week when the actual number of miles is greater than the number given by the equation i6

Chooses a week when the actual number of miles is greater than the number given by the equation

This is a test question that allows you to enter extended text in your response.

The owner of a company bought 150 tickets for a circus performance. The owner paid $10 for each adult ticket and $6 for each child ticket.

Write an equation to represent y, the total amount, in dollars, the owner paid for the tickets in terms of x, the number of adult tickets the owner bought.

Enter your equation in the space provided. Enter only your equation.

This is a question with 2 parts, including a test question that allows you to enter extended text in your response.

For each one-year period after a car was purchased, its value at the end of the year was 15% less than its value at the beginning of the year.

Part A

State whether the value of the car as a function of time after it was purchased is best modeled with a linear function, a quadratic function, or an exponential function, and explain why.

Enter your answer and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Part B

If the value of the car 2 years after it was purchased is $17,918 , what was the value of the car when it was purchased? Show your work or explain your answer.

Enter your answer and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

There is no alt-text. (39 files were searched.)

Holistic Rubric for 4-Point Modeling Constructed Response Items

Sample Top Score Response

Part A

The situation is best modeled with an exponential function, because the resale value is decreasing at a constant percent rate of 15 % per year.

Part B

The situation can be modeled by the function v ( t ) = p ( 0.85 ) t , where p is the value of the car when it was purchased, t is the number of years since it was purchased, and v is the current value of the car. We can use the fact that the value of the car 2 years after it was purchased was $ 17 ,918 to find the value of the car when it was purchased by substituting into the function and solving for p .

17 ,918 = p ( 0.85 ) 2 17 ,918 = 0.7225 p p = 24 ,800 000001

This means that the value of the car when it was purchased was $ 24 ,800.

Points

Sample Characteristics

4 Points

A four-point response provides full and complete evidence of the modeling process used to solve a real-world problem.

The response may:

  • identify the problem that needs to be solved.
  • determine information that is needed to solve the problem.
  • communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and essentially precise representations.
  • contain minor flaws that do not detract from correct modeling or demonstration of a thorough understanding.
  • evaluate or validate a partial or complete solution and show how to improve or refine the solution.

3 Points

A three-point response provides evidence of the modeling process used to solve a real-world problem.

The response may:

  • identify most of the problem that needs to be solved.
  • determine most of the information that is needed to solve the problem.
  • communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and precise representations with minor flaws.
  • evaluate or validate a partial or complete solution and show how to improve or refine the solution, but the improvement or refinement may include minor flaws.

2 Points

A two-point response provides partial evidence of the modeling process used to solve a real-world problem.

The response may:

  • partially identify the problem that needs to be solved.
  • determine some of the information that is needed to solve the problem.
  • include a partial solution path that may be incomplete.
  • contain some errors in identifying the mathematics that is needed to solve the problem.
  • evaluate or validate a partial or complete solution and attempt to improve or refine the solution.

1 Point

A one-point response provides limited evidence of the modeling process used to solve a real-world problem.

The response may:

  • partially or incorrectly identify the problem that needs to be solved.
  • determine a minimal amount of the information that is needed to solve the problem.
  • include an incomplete or unorganized solution path.
  • contain errors in identifying the mathematics that is needed to solve the problem.
  • contain the correct solution, but work is limited or missing.
  • evaluate or validate a partial or complete solution but does not show how to improve or refine the solution.

0 Point

A zero-point response is completely incorrect, incoherent or irrelevant.

This is a multiple choice question that allows you to select only one option.

An object is dropped off the roof of a building. The function h(x)=−16x2+64 models the height, hx, in feet, of the object above the ground x seconds after it is dropped.

What is the best description of the meaning of h(2)=0 in terms of the context ?

  1. A.
    The object is dropped from an initial height of 2 feet.
  2. B.
    The object hits the ground 2 seconds after it is dropped.
  3. C.
    The object travels at a speed of 2 feet per second after it is dropped.
  4. D.
    The speed of the object increases at a rate of 2 feet per second each second after it is dropped.
i2

Correcti1

Reverses the meaning of x and f(x) i3

Thinks the value of 2 represents the object’s speedi4

Thinks the value of 2 represents the object’s acceleration

This is a test question that allows you to enter extended text in your response.

A nursing student works at a doctor’s office for $15 per hour and tutors other students for $25 per hour.

The student cannot work more than 20 hours each week.

The student wants to earn at least $375 each week.

  • Define two variables and write a system of inequalities that represents the given constraints.
  • Suppose the student wants to work at the doctor’s office for as many hours as possible for the experience, and suppose the student can only work a whole number of hours at the doctor’s office. How many hours should the student work at the doctor’s office each week? Show your work or explain how you found your answer.

Enter your answers and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

There is no alt-text. (39 files were searched.)

Holistic Rubric for 4-Point Modeling Constructed Response Items

Sample Top Score Response

Let x represent the number of hours in one week that the student works at the doctor’s office, and let y represent the number of hours the student tutors.

The system of inequalities is { x + y ≤ 20 15 x + 25 y ≥ 375

Solving for the intersection of the lines:

x + y = 20 → y = 20 − x 15 x + 25 ( 20 − x ) = 375 0 15 x + 500 + 25 x = 375 01 − 10 x = − 125 000000000 x = 12.5 0000000000000 y = 20 − 12.5 = 7.5 0000

Since the student only works a whole number of hours, the student should work at the office 12 hours each week since 15 ( 12 ) + 25 ( 8 ) = 380 and if the student worked at the office for 13 hours or more, the student would earn less than $ 375 .

Points

Sample Characteristics

4 Points

A four-point response provides full and complete evidence of the modeling process used to solve a real-world problem.

The response may:

  • identify the problem that needs to be solved.
  • determine information that is needed to solve the problem.
  • communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and essentially precise representations.
  • contain minor flaws that do not detract from correct modeling or demonstration of a thorough understanding.
  • evaluate or validate a partial or complete solution and show how to improve or refine the solution.

3 Points

A three-point response provides evidence of the modeling process used to solve a real-world problem.

The response may:

  • identify most of the problem that needs to be solved.
  • determine most of the information that is needed to solve the problem.
  • communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and precise representations with minor flaws.
  • evaluate or validate a partial or complete solution and show how to improve or refine the solution, but the improvement or refinement may include minor flaws.

2 Points

A two-point response provides partial evidence of the modeling process used to solve a real-world problem.

The response may:

  • partially identify the problem that needs to be solved.
  • determine some of the information that is needed to solve the problem.
  • include a partial solution path that may be incomplete.
  • contain some errors in identifying the mathematics that is needed to solve the problem.
  • evaluate or validate a partial or complete solution and attempt to improve or refine the solution.

1 Point

A one-point response provides limited evidence of the modeling process used to solve a real-world problem.

The response may:

  • partially or incorrectly identify the problem that needs to be solved.
  • determine a minimal amount of the information that is needed to solve the problem.
  • include an incomplete or unorganized solution path.
  • contain errors in identifying the mathematics that is needed to solve the problem.
  • contain the correct solution, but work is limited or missing.
  • evaluate or validate a partial or complete solution but does not show how to improve or refine the solution.

0 Point

A zero-point response is completely incorrect, incoherent or irrelevant.