This page shows questions in the Algebra I Year 1 public release module at MSDE. Algebra 1
"Algebra I Year 1"
Select from the list to explore. Read any associated passages and then interact with the questions here.
This is a multiple choice question that allows you to select only one option.
The table shown gives values of the function y equals g of x for selected values of x.
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| g of x | 3 | 6 | 12 | 24 |
Which represents g of x?
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This is a multiple choice question that allows you to select only one option.
The drawing shows the plan for a rectangular courtyard with a square garden at its center.
The expression two thousand seven hundred minus x squared gives the area of the courtyard, in square feet, not including the garden.
Which expression represents the area of the courtyard if the length of each side of the square garden is increased by n feet?
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This is a test question that allows you to enter extended text in your response.
A rectangular box has a width equal to twice the height. The formula V equals 2 h squred l can be used to find the volume, V, of the box if the height, h, and length, l, are known.
What is an equation for the height of the box in terms of the volume and length?
Enter your answer in the space provided. Enter only your answer.
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This is a question with 2 parts, including a multiple choice question that allows you to select only one option.
f of x equals x squared for all real numbers x.
g of x equals open parenthesis x minus 1 close parenthesis squared plus 2 for all real numbers x.
Part A
Which statement is true about f and g?
Part B
The graph of the function h of x is the result of reflecting the graph of f of x over the x-axis and then translating 1 unit up. Which equation defines h of x?
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This is a question with 4 parts, including a fill in the blank question that allows you to enter only numbers, and, a multiple choice question that allows you to select only one option, and, a multiple choice question that allows you to select several options.
Melissa will participate in a charity walkathon. Her mother will donate $10 for Melissa's participation plus an additional $2 for each mile that Melissa walks.
Part A
If Melissa walks 15 miles, what will be the amount of her mother's donation?
Enter your answer in the box.
$
Part B
Which equation expresses P, the amount, in dollars, of Melissa's mother's donation as a function of M, the number of miles Melissa walks?
Part C
If the donation is $44, how many miles did Melissa walk?
Part D
Melissa wants her mother to donate at least $65. Which of the listed numbers of miles would make the donation at least $65?
Select all that apply.
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This is a test question that allows you to enter extended text in your response.
A university organizes an event in which all tenth-grade students from three school districts are invited to visit the university campus. Each school district serves students from kindergarten through twelfth grade.
This table shows information about the districts from which students will be invited.
| Number of Students in a District | |
| District Name | Number of Students in the District |
|---|---|
| Allegany County | 9,022 |
| Anne Arundel County | 75,481 |
| Baltimore City | 83,799 |
The organizers expect 10% of the invited students to attend.
- Write an equation that can be used to predict the total number of tenth-grade students expected to attend.
- Describe the assumptiuons you used to determine your equation.
- Estimate the total number of tenth-grade students expected to visit the university.
Enter your equation and your work in the space provided.
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This is a question with 2 parts, including a fill in the blank question that allows you to enter only numbers.
The staff at an advertising company took a survey of 350 people, each of whom had visited one of two branches, East and West, of a store. Each person surveyed was asked whether he or she had purchased a certain product within the past month. The results of the survey, by location, are shown in the table.
| East | West | Total | |
|---|---|---|---|
| Had purchased the product | 49 | 70 | 119 |
| Had not purchased the product | 133 | 98 | 231 |
| Total | 182 | 168 | 350 |
Of the people who visited the West branch of the store, what fraction indicated that they had not purchased the product?
Give your answer as a fraction. Enter your answer in the space provided.
fraction bar
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This is a multiple choice question that allows you to select only one option.
Line k contains the points coordinates negative 9, 4 and coordinates 9, negative 8 in the xy-coordinate plane. What are two other points that lie on line k?
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This is a question with 2 parts, including a multiple choice question that allows you to select only one option, and, a test question that allows you to enter extended text in your response.
While Sam was at work, his house lost electrical power. By the time the electrical power came back on, the temperature inside the house was 88°F. The air conditioner immediately started to cool the house.
Let f of x represent the temperature, in degrees Fahrenheit, of Sam's house x minutes after the air conditioner started to cool the house.
Part A
What is the meaning of the statement f of 30 equals 76?
Part B
Use function notation to represent the temperature of the house when the air conditioner started to cool the house.
Enter your answer in the space provided. Enter only your answer.
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This is a multiple choice question that allows you to select only one option.
The function h of t equals negative 16 t squared plus 48 t plus 1 hundred 60 can be used to model the height, in feet, of an object t seconds after it is launched from the top of a building that is 160 feet tall.
Two other forms of the function are
h of t equals negative 16 open parenthesis t minus 5 close parenthesis open parenthesis t plus 2 close parenthesis
h of t equals negative 16 open parenthesis t minus 1 point 5 close parenthesis squared plus 1 hundred 96
Which value of the function represents the maximum height of the object?
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This is a multiple choice question that allows you to select only one option.
Which expression is equivalent to 3 plus 2 open parenthesis x plus 4 close parenthesis open parenthesis x minus 4 close parenthesis?
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This is test content.
Solve the inequality 5 x minus 3 is less than 2 x and graph the solution on the number line.
Select a solution set indicator. Drag the points on the indicator to the appropriate locations on the number line.
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This is a multiple choice question that allows you to select only one option.
An object is launched upward from a platform that is 10 meters above ground level. It reaches a maximum height of 88.4 meters above ground level in 4 seconds. The object hits the ground after a total of 8.25 seconds.
Let the function h of t represent the height, in meters, of the object above ground level t seconds after launch. Which inequality describes the domain of this relationship?
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This is a question with 2 parts, including a multiple choice question that allows you to select several options.
Adam ran for 30 minutes. He kept a record of his running speed, in miles per hour (mph), for each 5-minute interval. The table shows the changes in the running speed for different time intervals.
| Interval of Time | Running Speed |
|---|---|
| First 5 minutes | Went from 0 mph to 7 mph |
| 5 minutes to 15 minutes | Remained at 7 mph |
| 15 minutes to 20 minutes | Went from 7 mph to 4 mph |
| 20 minutes to 25 minutes | Went from 4 mph to 6 mph |
| 25 minutes to 30 minutes | Went from 6 mph to 0 mph |
Consider a graph in the xy-coordinate plane of Adam's running speeds as a function of time, in minutes. Assume that the increases and decreases in the running speed were constant.
Part A
In which time interval is the graph of the function increasing?
Select all that apply.
Part B
In which time interval is the graph of the function decreasing?
Select all that apply.
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This is a multiple choice question that allows you to select only one option.
Today (Week 0), a certain flower is 0.75 foot tall. Each week, the flower will grow 25% taller than it was the week before. In the function below, t is the number of weeks from today and h(t) is the predicted height after t weeks.
h of t equals three fourths times 1 point 2 5 raised to the power of t.
What will the average rate of change be from Week 0 to Week 5?
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This is a question with 2 parts, including a test question that allows you to enter extended text in your response.
Consider the function f of x equals x squared.
Functions g and h are defined asg of x equals f of open parenthesis x plus k close parenthesis
h of x equals f of x plus kwhere k is a nonzero real number.
Part A
Show algebraically that g of x and h of x are different functions.
Enter your work in the space provided.
Part B
Explain the graphical difference between g of x and h of x.
Enter your explanation in the space provided.
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This is a multiple choice question that allows you to select only one option.
The number of bacteria initially present in a culture was 1,000. Each hour, the number of bacteria in the culture was eight times the number that was present at the start of the preceding hour, as shown in the table.
| Time (hours) | Number of Bacteria in the Culture |
|---|---|
| 0 | 1,000 |
| 1 | 8,000 |
| 2 | 64,000 |
| 3 | 512,000 |
Which equation could be used to determine n, the number of bacteria in the culture at hour t?
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