Quiz about Algebra 1 Review 2025

Question 1

A water tank has a capacity of 1,000 gallons. To fill the tank, Don uses a bucket that holds 2 gallons. It takes him 3 minutes to fill the bucket with water and pour it into the tank. Which expression represents how much time it takes to fill the tank?

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 2

A swimming pool can hold 5,000 liters of water. If a hose fills the pool at a rate of 50 liters per minute, how long will it take to fill the pool completely?

Accepted Answer

100 minutes

Answer

200 minutes

Answer

300 minutes

Answer

400 minutes

Question 3

Sarah has a 1,500 ml bottle. She uses a cup that holds 150 ml to fill the bottle. If it takes her 2 minutes to fill the cup and pour it into the bottle, how much time will it take to fill the bottle completely?

Accepted Answer

20 minutes

Answer

25 minutes

Answer

15 minutes

Answer

10 minutes

Question 4

Mary has a gift card to download songs. The expression $$50-1.29s$$ represents the balance of the gift cards.

Which statement are true?

Select two answer choices.

Accepted Answer

The value 1.29 represents the cost to download a song.

Accepted Answer

The value 50 represents the initial value of the gift card.

Answer

The value 1.29 represents the initial value of the gift card.

Answer

The value 50 represents the cost to download a song.

Answer

The value 50 represents the number of songs that can be downloaded.

Question 5

Which expressions are equivalent to $$x^2+6x-27$$ ? Select two answer choices.

Accepted Answer

$$\left(x-3\right)\left(x+9\right)$$

Accepted Answer

$$\left(x+3\right)^2-36$$

Answer

$$\left(x+3\right)\left(x+9\right)$$

Answer

$$\left(x+6\right)\left(x-27\right)$$

Answer

$$\left(x+3\right)^2+36$$

Question 6

Which expressions are equivalent to $$x^2+8x+15$$ ? Select two answer choices.

Accepted Answer

$$\left(x+3\right)\left(x+5\right)$$

Accepted Answer

$$\left(x+5\right)\left(x+3\right)$$

Answer

$$\left(x+8\right)+15$$

Answer

$$\left(x+1\right)\left(x+15\right)$$

Answer

$$x^2+10x+15$$

Question 7

What are the zeros of the function $$f(x)=9x^2-36$$ ?

Accepted Answer

-2

Accepted Answer

2

Answer

-4

Answer

0

Answer

4

Question 8

Team A won the first game of the season against Team B by 5 points. The two teams together scored a total of 13 points in the game. Let x represent the points scored by Team A and let y represent the points scored by Team B.

Which system of linear equations models the points scored by both Team A and Team B? $$y=x+5$$

Accepted Answer

$$x=y+5$$

$$x+y=13$$

Answer

$$y=x+5$$

$$x+y=15$$

Answer

$$x=y-5$$

$$y=13-x$$

Answer

$$y=x-5$$

$$x-y=13$$

Question 9

The Wildcats beat the Tigers by 7 points in their first basketball game. Together, the two teams scored a total of 29 points. Let x represent the points scored by the Wildcats (winning team), and y represent the points scored by the Tigers.

Which system of linear equations models the points scored by both teams?

Accepted Answer

$$x=y+7$$

$$x+y=29$$

Answer

$$y=x+7$$

$$x+y=29$$

Answer

$$x=y-7$$

$$x+y=29$$

Answer

$$y=x-7$$

$$x+y=29$$

Question 10

A ring is a shape called an annulus. A formula for the area of an annulus is $$A=\pi\sqrt[]{x^2-y^2}$$ , where is the radius of the larger circle and is the radius of the smaller circle.

Which equation is solved for the larger radius of an annulus?

Accepted Answer

$$x=\sqrt[]{\frac{A}{\pi}+y^2}$$

Answer

$$x=\sqrt[]{A\pi+y^2}$$

Answer

$$x=\sqrt[]{\frac{A}{\pi}-y^2}$$

Answer

$$x=\sqrt[]{\frac{A+y^2}{\pi}}$$

Question 11

A ring is a shape called an annulus. A formula for the area of an annulus is $$A=\pi\left(x^2+y^2\right)$$ , where x is the radius of the larger circle and is the radius of the smaller circle. Which equation is solved for the larger radius of an annulus?

Accepted Answer

$$x=\sqrt[]{\frac{A}{\pi}+y^2}$$

Answer

$$x=\sqrt[]{A\pi+y^2}$$

Answer

$$x=\sqrt[]{\frac{A}{\pi}-y^2}$$

Answer

$$x=\sqrt[]{\frac{A+y^2}{\pi}}$$

Question 12

A washer is a flat ring-shaped object, and its area can be found using the formula: $$A=\pi\left(x^2-y^2\right)$$ , where A is the area; x is the outer radius, and y is the inner radius. Which equation below is correctly solved for the inner radius y?

Accepted Answer

$$y=\sqrt[]{x^2+\frac{A}{\pi}}$$

Answer

$$y=\sqrt[]{\frac{A}{\pi}+x^2}$$

Answer

$$y=\frac{A-\pi x^2}{\pi}$$

Answer

$$y=\sqrt[]{\frac{\pi x^2-A}{\pi}}$$

Question 13

Select the boxes that identify the property used in each step involved in solving the equation $$4x-5x=\frac{1}{2}\left(4x+8\right)$$ .

Next Step

$$-x=\frac{1}{2}\left(4x+8\right)$$

Accepted Answer

Combine like terms

Answer

Distributive Property

Answer

Commutative Property

Answer

Subtraction Property of Equality

Answer

Division Property of Equality

Question 14

Select the boxes that identify the property used in each step involved in solving the equation $$4x-5x=\frac{1}{2}\left(4x+8\right)$$ .

$$-x=\frac{1}{2}\left(4x+8\right)$$

Next Step

$$-x=2x+4$$

Accepted Answer

Distributive Property

Answer

Commutative Property

Answer

Subtraction Property of Equality

Answer

Division Property of Equality

Answer

Combine like terms

Question 15

Select the boxes that identify the property used in each step involved in solving the equation $$4x-5x=\frac{1}{2}\left(4x+8\right)$$ .

$$-x=\frac{1}{2}\left(4x+8\right)$$

$$-x=2x+4$$

Next Step

$$-3x=4$$

Accepted Answer

Subtraction Property of Equality

Answer

Distributive Property

Answer

Commutative Property

Answer

Division Property of Equality

Answer

Combine like terms

Question 16

Select the boxes that identify the property used in each step involved in solving the equation $$4x-5x=\frac{1}{2}\left(4x+8\right)$$ .

$$-x=\frac{1}{2}\left(4x+8\right)$$

$$-x=2x+4$$

$$-3x=4$$

Next Step

$$x=-\frac{4}{3}$$

Accepted Answer

Division Property of Equality

Answer

Distributive Property

Answer

Commutative Property

Answer

Subtraction Property of Equality

Answer

Combine like terms

Question 17

The graph of the equation $$y=\frac{-9.8x^2}{2}$$ represents the position of a falling object concerning time. Let represent the position of the object, measured in meters, and represent time, measured in seconds.

Which ordered pairs represent points that are on the graph? Select two answer choices.

Accepted Answer

(0,0)

Accepted Answer

(3,-44.1)

Answer

(1,-4.4)

Answer

(2,-9.8)

Answer

(4,-39.05)

Question 18

The arithmetic sequence 2, 8, 14, 20......can be represented by the equation. $$a_n=6n-4$$ .
What is the domain of this arithmetic sequence?

Accepted Answer

integers greater than or equal to 1

Answer

All real numbers

Answer

all positive real numbers

Answer

integers greater than or equal to 20

Question 19

The function $$f\left(t\right)=-\frac{1}{10}t+10$$ represents the height of a candle as it burns for minutes. The function is modeled by the graph.

Which statement describes the domain of the function?

Accepted Answer

The domain of the function includes all real numbers where $$0\le t\le100$$

Answer

The domain of the function includes all real numbers.

Answer

The domain of the function includes all numbers where $$t\ge0$$ .

Answer

D The domain of the function includes all whole numbers where $$0\le t\le100$$

Question 20

For which time interval did Mack have the fastest average rate of change?

Accepted Answer

between 1 hour and 2 hours

Answer

between 1 hour and 3 hours

Answer

between 2 hours and 4 hours

Answer

between 2 hours and 5 hours

Question 21

Given the function $$f\left(x\right)=\left(x-4\right)\left(x+2\right)$$

Which form reveals the zeros of $$f\left(x\right)$$ ?

Accepted Answer

Factored Form: $$f\left(x\right)=\left(x-4\right)\left(x+2\right)$$

Answer

Standard Form: $$f\left(x\right)=x^2-2x-8$$

Answer

Vertex Form: $$f\left(x\right)=\left(x-1\right)^2-9$$

Answer

Fraction Form: $$f\left(x\right)=\frac{\left(-4\right)\left(x+2\right)}{1}$$

Question 22

Given the function $$f\left(x\right)=-x^2+2x+3$$

Which form reveals the zeros of $$f\left(x\right)$$ ?

Accepted Answer

$$f\left(x\right)=-\left(x+1\right)\left(x-3\right)$$

Answer

$$f\left(x\right)=\left(x-1\right)\left(x+3\right)$$

Answer

$$f\left(x\right)=\left(x-1\right)^2+4$$

Answer

$$f\left(x\right)=\left(x-1\right)^2+4$$

Question 23

Which term describes the function $$f\left(x\right)=\left(x+4\right)^3-2$$ ?

Accepted Answer

Neither

Answer

Odd

Answer

Even

Question 24

Which term describes the function $$f\left(x\right)=\frac{1}{x}$$ ?

Accepted Answer

Odd

Answer

Even

Answer

Neither

Question 25

Which term describes the function $$f\left(x\right)=-3\left|x\right|+5$$ ?

Accepted Answer

Even

Answer

Odd

Answer

Neither

Question 26

If Dave can run 3 miles in 26 minutes, how long will it take him to run 5.5 miles? (assume he can keep running at the same rate)

Accepted Answer

47 2/3 minutes

Answer

50 minutes

Answer

45 minutes

Answer

43 2/3 minutes

Question 27

The table shows the height of a flower for five consecutive weeks after it was planted.

Accepted Answer

the linear function $$y=\frac{1}{2}x+3$$ because the function grows by equal differences

Answer

the exponential function $$y=\left(\frac{1}{2}\right)^x+3$$ because the function grows by equal factors

Answer

the linear function $$y=\frac{1}{2}x+3$$ because the function grows by equal factors

Answer

the exponential function $$y=\left(\frac{1}{2}\right)^x+3$$ because the function grows by equal differences

Question 28

A large lake was stocked with trout ten years ago. The change in the trout population each year is modeled by the $$P(x)=8,500(0.88)^x$$ function . Which statement describes 0.88 in the function?

Accepted Answer

A The amount of fish will decrease exponentially over time by 12% each year.

Answer

A The amount of fish will increase exponentially over time by 12% each year.

Answer

The amount of fish will increase exponentially over time by 88% each year

Answer

The amount of fish will decrease exponentially over time by 88% each year

Question 29

The results of a student survey on the favorite milkshake flavor are shown.

What is the approximate percentage of female students who chose chocolate as their favorite milkshake flavor?

Accepted Answer

52%

Answer

27%

Answer

50%

Answer

66%

Question 30

Devon is training for a marathon. His training schedule for the number of miles he wants to run each week, , is represented by the function $$y=\frac{11}{6}x+\frac{8}{3}$$ , where represents the number of weeks. The table shows the number of miles that Devon ran each week for the first ten weeks

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 31

The table shows the height, , in inches, of nine people and the corresponding length, , in inches, from hip to knee for each individual.

Which statements are true for the set of data?

Select two answer choices.

Accepted Answer

The data shows a strong correlation.

Accepted Answer

The correlation coefficient is approximately 0.85.

Answer

The data shows a weak correlation.

Answer

The data represents a negative correlation.

Answer

The correlation coefficient is approximately -0.25

Question 32

What is the value of $$x$$ in the equation $$2x + 3 = 11$$ ?

Accepted Answer

4

Answer

7

Answer

6

Answer

5

Question 33

If a car travels at a constant speed of 60 miles per hour, how long will it take to travel 180 miles?

Accepted Answer

3 hours

Answer

2 hours

Answer

4 hours

Answer

5 hours

Question 34

Which property is used in the equation $$3(x + 4) = 3x + 12$$ ?

Accepted Answer

Distributive Property

Answer

Commutative Property

Answer

Associative Property

Answer

Identity Property

Question 35

Given the function $$f\left(x\right)=x^2-4x+4$$

Which form reveals the zeros of $$f\left(x\right)$$ ?

Accepted Answer

Factored Form: $$f\left(x\right)=\left(x-2\right)^2$$

Answer

Fraction Form: $$f\left(x\right)=\frac{\left(x-2\right)^2}{1}$$

Answer

Vertex Form: $$f\left(x\right)=\left(x-2\right)^2$$

Answer

Standard Form: $$f\left(x\right)=x^2-4x+4$$

Algebra 1 Review 2025

40 questions

A water tank has a capacity of 1,000 gallons. To fill the tank, Don uses a bucket that holds 2 gallons. It takes him 3 minutes to fill the bucket with water and pour it into the tank. Which expression represents how much time it takes to fill the tank?

A swimming pool can hold 5,000 liters of water. If a hose fills the pool at a rate of 50 liters per minute, how long will it take to fill the pool completely?

Sarah has a 1,500 ml bottle. She uses a cup that holds 150 ml to fill the bottle. If it takes her 2 minutes to fill the cup and pour it into the bottle, how much time will it take to fill the bottle completely?

Sam is moving into an apartment. He has to pay one month’s rent, a security deposit, and a one-time utility fee of $200. The security deposit is 75% of the amount of one month’s rent. Sam paid a total of $1,750 to move into the apartment. How much is his rent each month?

Taylor is moving into an apartment. He has to pay one month’s rent, a security deposit, and a one-time utility fee of $375. The security deposit is 2/3 of the amount of one month’s rent. Taylor paid a total of $2,000 to move into the apartment. How much is his rent each month?

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