Free Printable Keystone Algebra Module 1 Practice ( from Item Samplers)

1.

An expression is shown below.

$2\sqrt[\ ]{51x}$

Which value of x makes the expression equivalent to $10\sqrt[\ ]{51}$ ?

a)

5

b)

25

c)

50

d)

100

2.

Simplify.

$2\left(2\sqrt[\ ]{4}\right)^{-2}$

a)

$\frac{1}{8}$

b)

$\frac{1}{4}$

c)

16

d)

32

3.

A polynomial expression is shown below.

$\left(mx^3+3\right)\left(2x^2+5x+2\right)-\left(8x^5+20x^4\right)$

The expression is simplified to $8x^3+6x^2+15x+6$ . What is the value of m?

a)

-8

b)

-4

c)

4

d)

8

4.

Which is a factor of the trinomial $x^2-2x-15$ ?

a)

(x - 13)

b)

(x - 5)

c)

(x + 5)

d)

(x + 13)

5.

Simplify.

$\frac{x^2-3x-10}{x^2+6x+8}\ \$ $x\ne-4,\ -2$

a)

$-\frac{1}{2}x\ -\ \frac{5}{4}$

b)

$x^2-\frac{1}{2}x-\frac{5}{4}$

c)

$\frac{x-5}{x+4}$

d)

$\frac{x+5}{x-4}$

6.

Anna burned 15 calories per minute running for x minutes and 10 calories per minute hiking for y minutes. She spent a total of 60 minutes running and hiking and burned 700 calories. The system of equations shown below can be used to determine how much time Anna spent on each exercise.

$15x\ +\ 10y\ =\ 700$

$x\ +\ y\ =\ 60$

What is the value of x, the minutes Anna spent running?

a)

10

b)

20

c)

30

d)

40

7.

Samantha and Maria purchased flowers. Samantha purchased 5 roses for x dollars each and 4 daisies for y dollars each and spent $32 on the flowers. Maria purchased 1 rose for x dollars and 6 daisies for y dollars each and spent $22. The system of equations shown below represents this situation.

$5x\ +\ 4y\ =\ 32$

$x\ +\ 6y\ =\ 22$

Which statement is true?

a)

A rose costs $1 more than a daisy.

b)

Samantha spent $4 on each daisy.

c)

Samantha spent more on daisies than she did on roses.

d)

Maria spent 6 times as much on daises as she did on roses.

8.

Which is a graph of the solution of the inequality $\left|2x\ -\ 1\right|\ge5$ ?

a)

A

b)

B

c)

C

d)

D

9.

A baseball team had $1,000 to spend on supplies. The team spent $185 on a new bat. New baseballs cost $4 each.

The inequality 185 + 4b ≤ 1,000 can be used to determine the number of new baseballs (b) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true?

a)

A team can purchase 204 new baseballs.

b)

The minimum number of new baseballs that can be purchased is 185.

c)

The maximum number of new baseballs that can be purchased is 185.

d)

The team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.

10.

Tyreke always leaves a tip of between 8% and 20% for the server when he pays for his dinner. This can be represented by the system of inequalities shown below, where y is the amount of tip and x is the cost of dinner.

$y>0.08x$

$y<0.2x$

Which of the following is a true statement?

a)

When the cost of dinner, x, is $10 the amount of tip, y, must be between $2 and $8.

b)

When the cost of dinner, x, is $15 the amount of tip, y, must be between $1.20 and $3.00.

c)

When the tip, y, is $3, the cost of dinner, x, must be between $11 and $23.

d)

When the tip, y, is $2.40, the cost of dinner, x, must be between $3 and $6.

11.

Four expressions are shown. Which inequality comparing two of the expressions is true when 0.1 < x < 0.4?

a)

b)

c)

d)

12.

The greatest common factor (GCF) of x³y^k and x^2ky⁴ is x³y³. What is the value of k?

a)

1

b)

2

c)

3

d)

4

13.

Which equation correctly shows that (x²)⁴ = x⁸

a)

b)

c)

d)

14.

When factored completely, which is a factor of 6x³ - 12x² - 48x?

a)

(x + 2)

b)

(x + 4)

c)

(2x - 3)

d)

(2x - 4)

15.

Anna's Baker charges a delivery fee of $10.95 for one delivery order of cupcakes. Each cupcake in the order costs $1.15. Which equation describes the relationship between the number of cupcakes ordered (x) and the total cost (y), in dollars, of the deliver order?

a)

y = 1.15x

b)

y = 12.10x

c)

y = 1.15x + 10.95

d)

y = 10.95x + 1.15

16.

Kylie and Rhoda are solving the equation 4(x - 8) = 7(x - 4). Kylie uses a first step that results in 4x - 32 = 7x - 28. Rhoda uses a first step that results in 4x - 8 = 7x - 4. Which statement about the first steps Kylie and Rhoda use is true?

a)

Kylie uses the associative property, resulting in a correct first step.

b)

Kylie uses the distributive property, resulting in a correct first step.

c)

Rhoda uses the associative property, resulting in a correct first step.

d)

Rhoda uses the distributive property, resulting in a correct first step.

17.

Darlene is collecting prize tickets. The equation y = 2x + 1 describes the relationship between the number of days (x) since she began collecting and the number of prize tickets (y) she has collected. Which statement correctly describes a solution to the system?

a)

Darlene has collected 2 prize tickets at the end of 1 day.

b)

Darlene has collected 4 prize tickets at the end of 9 days.

c)

Darlene has collected 22 prize tickets at the end of 10 days.

d)

Darlene has collected 25 prize tickets at the end of 12 days.

18.

Mary measured the heights of two different plants every day. Plant A was 1 inch tall when Mary began her measuring, and it grew 0.5 inch per day. Plant B was 3 inches tall, and it grew 0.25 inch per day. On which day were plant A and plant B the same height?

a)

day 5

b)

day 8

c)

day 12

d)

day 16

19.

Which graph shows the solution set of the inequality |2x - 7| > 3?

a)

b)

c)

d)

20.

The solution set of an inequality is shown. Which inequality has the solution set shown in the graph?

a)

b)

c)

d)

21.

A T-shirt company has a goal to earn a monthly profit of more than $3,500. The company charges $20 per T-shirt. The company has $1,500 in monthly costs. The inequality 20x - 1,500 > 3, 500 models this situation. Which BEST describes the meaning of x in the inequality?

a)

the profit made from the sale of 20 T-shirts

b)

the profit made from 1 month of T-shirt sales

c)

the number of T-shirts that need to be sold for the company to meet its goal

d)

the number of T-shirts that need to be sold for the company to recover its monthly costs

22.

A system of inequalities is shown. Which graph represents the system?

a)

b)

c)

d)

23.

When x = 2, which expression can be completely simplified to $4\ \sqrt[]{5}$ ?

a)

b)

c)

d)

24.

The greatest common factor (GCF) of 2 monomials is 3x²y. One of the monomials is 3x⁴y. Which could be the other monomial?

a)

3xy²

b)

6x²y³

c)

9x⁶y²

d)

18x⁶y²

25.

The distance from the Sun to Mercury is 57,909,227 km. The average distance from the Sun to Saturn is 1,426,666,422 km. Light travels at a speed of about 300,000 km per second. Which amount of time is the closest estimate of the difference between the number of minutes it takes light to travel from the sun to Saturn and the number of minutes it takes light to travel from the Sun to Mercury.

a)

50 minutes

b)

80 minutes

c)

110 minutes

d)

140 minutes

26.

Simplify: (3x² + 2x - 8) - (-x² + 6x + 4)

a)

2x² + 8x - 4

b)

2x² + 8x - 12

c)

4x² + 8x - 4

d)

4x² - 4x - 12

27.

In an experiment, a plant grows 0.05 centimeter per day. The plant had a height of 2 centimeters when the experiment started. Which equation describes the relationship between the number of days (d) the experiment lasts and the height (h), in centimeters, of the plant?

a)

h = 0.05d + 2

b)

h = 0.05(2) + d

c)

h = 2d + 0.05

d)

h = 2.05d

28.

Juanita used the steps shown below to correctly solve an equation. A step is missing.

Which shows the equation that is most likely a missing step and the property that justifies the step?

a)

-3c - 6 + 4c = 10c + 9; associative property of addition

b)

-3c + 18 + 4c = 10c + 45; associative property of addition

c)

-3c - 6 + 4c = 10c + 9; distributive property

d)

-3c + 18 + 4c = 10c + 45; distributive property

29.

Syliva studied a new language. The equation describes how many word she knew (y) after studying the language for x days.

y = 5x + 18

The ordered pair (6, 48) is a solution of the equation. What does the solution represent?

a)

Sylvia knew 6 words after 6 days

b)

Sylvia knew 6 words after 48 days

c)

Sylvia knew 48 words after 6 days

d)

Sylvia knew 48 words after 48 days

30.

Christine sells a total of 50 tickets to a school play. Student tickets sell for $1.50 each, and adult tickets sell for $4.00 each. Christine made a total of $112.50 in ticket sales. Christine writes a system of equations to represent this information. Which statement BEST describes the solution to the system of equations?

a)

Christine sells 35 student tickets and 15 adult tickets.

b)

Christine would earn $200.00 by selling 50 tickets.

c)

Christine sells a pair of tickets between $3.00 and $8.00.

d)

Christine could not earn $112.50 by selling 50 student tickets.

31.

A plain pizza takes 10 minutes to bake. At least 2 minutes of baking time is required for each ounce of toppings added to the pizza. The total baking time for a specialty pizza is at least 18 minutes and at most 26 minutes. Which graph shows the possible number of ounces of all the toppings on a specialty pizza?

a)

b)

c)

d)

32.

A cleaning service offers its customers a choice between two plans. Plan A costs $3,000 and includes 1 year of an unlimited number of cleanings. Plan B costs $75 per cleaning. Henry wants to choose the less expensive plan. He uses the inequality 3,000 < 75c to decide which plan to choose based on the number of cleanings (c) he expects to need. Based on the solution of the inequality, which statement about Henry's choice of plan is true?

a)

Henry should choose Plan A only if he expects to need fewer than 40 cleanings in 1 year.

b)

Henry should choose Plan A only if he expects to need more than 40 cleanings in 1 year.

c)

Henry can choose either plan and pay the same amount if he expects to need fewer than 40 cleanings in 1 year.

d)

Henry can choose either plan and pay the same amount if he expects to need more than 40 cleanings in 1 year.

33.

a)

b)

c)

d)

34.

a)

The baker could make 100 glazed doughnuts and 110 chocolate doughnuts.

b)

The baker could ear $100 from glazed doughnuts and $110 from chocolate doughnuts.

c)

The baker can make a maximum of 100 glazed doughnuts and 110 chocolate doughnuts.

d)

The baker will spend exactly $60 making 100 glazed doughnuts and 110 chocolate doughnuts.

35.

a)

2

b)

3

c)

4

d)

5

36.

When factored complete, which is a factor of $12ax^2-3a$ ?

a)

12a

b)

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

c)

3a

d)

(4x - 1)

37.

Simplify.

$\frac{\left(x-7\right)^2}{x\left(x-4\right)-21};\$ $x\ne-3,\ 7$

a)

-14

b)

$\frac{7x+7}{2x-3}$

c)

$\frac{1}{x+3}$

d)

$\frac{x-7}{x+3}$

38.

A person’s hair is 8 centimeters long. The equation below can be used to estimate the length (L), in centimeters (cm), that the person’s hair will be after w weeks.

$L=\frac{w}{4}+8$

Based on the equation, what will be the estimated length of the person's hair after 10 weeks?

a)

4.5 cm

b)

8 cm

c)

10 cm

d)

10.5 cm

39.

Ms. Bernard monitored the growth of a fish. The fish originally weighed 27 ounces. The fish grew at a rate of 5 ounces per month. The equation below can be used to describe the weight, in ounces, of the fish.

$72=27+5x$

Ms. Bernard correctly determined that x = 9. What does the solution of the equation mean?

a)

The fish grew at a rate of 9 ounces per month for 72 months.

b)

The fish grew at a rate of 72 ounces per month for 9 months.

c)

It took 9 months for the fish to grow to a weight of 72 ounces.

d)

It took 72 months for the fish to grow to a weight of 9 ounces.

40.

A system of equations is shown below.

$2x\ +\ 2y\ =\ 10$

$5x\ -\ 2y\ =\ 4$

What is the solution of the system of equations?

a)

(-2. -7)

b)

(2, 7)

c)

(2, 3)

d)

(3, 2)

41.

Juan answered all 50 questions on a test. He earned 3 points for each question he answered correctly. He lost 1 point for each question he answered incorrectly. His final test score was 102 points. The system of equations below describes the relationship between the number of questions he answered correctly (x) and the number of questions he answered incorrectly ( y).

$x+y=50$

$3x-y=102$

Part of the solution of the system of equations is x = 38. What does this value represent?

a)

the number of questions Juan answered correctly

b)

the number of questions Juan answered incorrectly

c)

the number of points Juan lost from questions he answered incorrectly

d)

the number of points Juan earned from questions he answered correctly

42.

Jason decided that he will sell his stocks if their value per share (x) goes below $5 or above $15. Which compound inequality represents the values at which Jason will sell his stocks?

a)

x > $5 or x < $15

b)

x < $5 or x > $15

c)

x > $5 and x < $15

d)

x < $5 and x > $15

43.

An inequality is shown below.

$4x+2<2x+9$

Which graph shows the solution of the inequality?

a)

A

b)

B

c)

C

d)

D

44.

A ticket to a baseball game costs $20. Each soda sold at the game costs $5. Shawn may spend no more than $50. He buys 1 ticket and x sodas. Shawn represents this situation with the inequality below.

$5x+20\le50$

The solution of the inequality is x ≤ 6. Which statement best describes the solution of the inequality?

a)

Shawn buys 6 or fewer sodas.

b)

Shawn buys 6 or fewer tickets.

c)

Shawn buys 1 ticket and 5 sodas.

d)

Shawn has less than or equal to $6 remaining when he leaves the game.

45.

A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42. They will pay $4 for each box of candy and $7 for each bag of popcorn. The system of inequalities graphed represents this information.

Which combination of boxes of candy and bags of popcorn could the group buy?

a)

2 boxes of candy and 6 bags of popcorn

b)

3 boxes of candy and 4 bags of popcorn

c)

5 boxes of candy and 4 bags of popcorn

d)

8 boxes of candy and 1 bags of popcorn

46.

Two expression are shown below.

$\pi x\ \ \ \ \ \ \ \ \ \ x^2$

For which value of x is the value of $\pi x$ greater than the value of x²?

a)

x = -2

b)

x = 0

c)

x = 1.5

d)

x = 9

47.

a)

A

b)

B

c)

C

d)

D

48.

The list below shows the items Ethan and his friends bought for lunch.

2 sandwiches for $5.29 each

2 burgers for $6.79 each

1 bowl of soup for $3.89

5 drinks for $1.19 each

They paid 8% tax. They then paid a tip that was about twice the amount of the tax they paid. Which is the closest estimate of the total amount Ethan and his friends paid for their food, drinks, tax, and tip?

a)

$22

b)

$33

c)

$43

d)

$51

49.

The difference of two polynomial expressions is shown below.

$\left(-2x^2+wx-4\right)-\left(x^2+5x+6\right)\ =\ -3x^2-10$

What is the value of w?

a)

-8

b)

-5

c)

2

d)

5

50.

Keyshawn buys 100 baseball cards to start a collection. He purchases 25 more baseball cards each week. Which equation could be used to represent the number of baseball cards (b) in Keyshawn's collection after w weeks?

a)

w = 25b + 100

b)

w = 100b + 25

c)

b = 25w + 100

d)

b = 100w + 25

51.

One of the steps Lewis used to correctly solve an equation is shown below.

$3\left(x-7\right)+40=-5$

$3x-21+40=-5$

Which statements describe the procedure Lewis used in this step of solving the equation and identify the property that justifies the procedure?

a)

Lewis added 3 and x to eliminate the parentheses. This procedure is justified by the associative property.

b)

Lewis added 3 and x to eliminate the parentheses. This procedure is justified by the distributive property.

c)

Lewis multiplied x and 7 by 3 to eliminate the parentheses. This procedure is justified by the associative property.

d)

Lewis multiplied x and 7 by 3 to eliminate the parentheses. This procedure is justified by the distributive property.

52.

Raul has $640 saved, and Jaime has $320 saved. They each begin a new job on the same day and save all of their money. Raul earns $180 per day, and Jaime earns $200 per day. In how many days will they have an equal amount of money?

a)

8

b)

16

c)

24

d)

32

53.

A compound inequality is shown below.

$x\le3\ and\ x\ge0$

Which graph represents the solution of the inequality?

a)

A

b)

B

c)

C

d)

D

54.

Patricia keeps apples in 3 bins and 2 crates in her store. Each bin can hold no more than 200 pounds. Each crate can hold no more than 50 pounds. Which graph represents all of the possible weights, in pounds, of apples Patricia can keep in her store?

a)

A

b)

B

c)

C

d)

D

55.

Nitrogen is a gas at certain temperatures under normal conditions. These temperatures (t), in degrees Celsius (°C), are represented by the inequality t ≥ -196. Which best describes the meaning of the inequality?

a)

Nitrogen is a gas only if the temperature is below -196°C.

b)

Nitrogen is a gas only if the temperature is above -196°C.

c)

Nitrogen is a gas only if the temperature is at or below -196°C.

d)

Nitrogen is a gas only if the temperature is at or above -196°C.

56.

A band is determining how many songs to record for a new album. The band members want to record no more than 16 songs, and their album has to be shorter than 78 minutes. They can record short songs that are about 3 minutes in length or long songs that are about 5 minutes in length. Which system of inequalities best represents the number of short songs (x) and the number of long songs ( y) the band can record for the new album?

a)

$x+y<16$

$3x+5y\le78$

b)

$x+y\le16$

$3x+5y<78$

c)

$x+y\le78$

$3x+5y<16$

d)

$x+y<78$

$3x+5y\le16$

57.

Nate will buy at least 10 cans of fishing bait. Each large can costs $7, and each small can costs $3. He will spend up to $54 on bait. This system of inequalities is graphed in image shown.

Which combination of cans could Nate buy?

a)

2 large cans and 6 small cans

b)

2 large cans and 10 small cans

c)

6 large cans and 10 small cans

d)

8 large cans and 2 small cans

58.

John spends $94 to buy packages of cleaning supplies for a camp. He buys t packages of towels; each package is $6 and contains 8 towels. He also buys s packages of soap; each package is $4 and contains 10 bars of soap. John buys 20 packages of cleaning supplies altogether.

Which system of equations represents the packages of cleaning supplies John buys?

a)

$8t+10s=94$ $6t+4t=20$

b)

$8t+10s=20$ $6t+4s=94$

c)

$t+s=94$

$6t+4s=20$

d)

$t+s=20$

$6t+4s=94$

59.

John spends $94 to buy packages of cleaning supplies for a camp. He buys t packages of towels; each package is $6 and contains 8 towels. He also buys s packages of soap; each package is $4 and contains 10 bars of soap. John buys 20 packages of cleaning supplies altogether.

How many packages of towels does John buy?

(a)

60.

Which expression can be

simplified to the form
$3\sqrt{y+3}$
where y is a positive integer?

a)

$\sqrt{18}$

b)

$\sqrt{63}$

c)

$\sqrt{75}$

d)

$\sqrt{84}$

61.

a)

Since normal body temperature is from 100.25°F to 103.25°F, the dog’s body temperature is considered normal.

b)

Since normal body temperature is from 100.25°F to 103.25°F, the dog’s body temperature is not considered normal.

c)

Since normal body temperature is from 101°F to 102.5°F, the dog’s body temperature is considered normal.

d)

Since normal body temperature is from 101°F to 102.5°F, the dog’s body temperature is not considered normal.

62.

Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and 221 hot dogs for $2.35 each. Which calculation will give the closest estimate of the sales of soft drinks and hot dogs?

a)

300(2) + 200(2)

b)

400(2) + 200(2)

c)

400(2) + 200(3)

d)

400(2) + 300(3)

63.

$x^3-2x^2-15x$

When the expression is factored completely, which expression is one of the factors?

a)

x - 5

b)

x + 5

c)

$x^2-5x$

d)

$x^2-2x-15$

64.

a)

c = 5(6) + 41

b)

c = 6(41) + 5

c)

41 = 5p + 6

d)

41 = 6p + 5

65.

a)

2x – (3 + 10x) = 5(3 + x)

This step is justified by the associative property.

b)

2(x – 3) = 5(3 + x) – 10x

This step is justified by the associative property.

c)

2x – 6 + 10x = 15 + 5x

This step is justified by the distributive property.

d)

2x – 3 + 10x = 15 + x

This step is justified by the distributive property.

66.

a)

10 small pizzas, 20 large pizzas

b)

14 small pizzas, 16 large pizzas

c)

18 small pizzas, 12 large pizzas

d)

20 small pizzas, 10 large pizzas

67.

a)

The objects never travel at the same velocity

b)

The objects always travel at the same velocity

c)

The objects travel at the same velocity only after they have been traveling for 1/4 second

d)

The objects travel at the same velocity only after they have been traveling for 1/2 second

68.

a)

1 < 3x < 2

b)

1 < x + 2 < 4

c)

6 < 2x < 9

d)

6 < x + 3 < 9

69.

a)

A

b)

B

c)

C

d)

D

70.

a)

-2x + y ≤ 4

2x + 3y ≤ 6

b)

-2x + y ≥ 4

2x + 3y ≥ 6

c)

-2x + y ≤ 4

2x + 3y ≥ 6

d)

-2x + y ≥ 4

2x + 3y ≤ 6

71.

a)

There will be enough games for 30 students to play at the same time, but the total cost will be greater than the maximum amount.

b)

There will be enough games for 30 students to play at the same time, and the total cost will be less than the maximum amount.

c)

There will not be enough games for 30 students to play at the same time, and the total cost will be greater than the maximum amount.

d)

There will not be enough games for 30 students to play at the same time, but the total cost will be less than the maximum amount.

72.

A scientist records the wavelengths of six waves. The wavelengths, in nanometers, are listed below.

Which two wavelengths are equal

to one another?

a)

0.0001

b)

$\frac{5}{100}$

c)

$10^{-3}$

d)

1.0001

e)

$\frac{1}{1,000}$

73.

A scientist records the wavelengths of six waves. The wavelengths, in nanometers, are listed below.

Which wavelengths is the shortest?

a)

0.0001

b)

$\frac{5}{100}$

c)

$10^{-3}$

d)

1.0001

e)

$\frac{1}{1,000}$

74.

a)

x = -2

b)

x = 0

c)

x = 1.5

d)

x = 9

75.

a)

A

b)

B

c)

C

d)

D

76.

a)

$22

b)

$33

c)

$43

d)

$51

77.

a)

- 8

b)

- 5

c)

2

d)

5

78.

a)

w = 25b + 100

b)

w = 100b + 25

c)

b = 25w + 100

d)

b = 100w + 25

79.

a)

Lewis added 3 and x to eliminate the parentheses. This procedure is justified by the associative property.

b)

Lewis added 3 and x to eliminate the parentheses. This procedure is justified by the distributive property.

c)

Lewis multiplied x and 7 by 3 to eliminate the parentheses. This procedure is justified by the associative property.

d)

Lewis multiplied x and 7 by 3 to eliminate the parentheses. This procedure is justified by the distributive property.

80.

a)

8

b)

16

c)

24

d)

32

81.

a)

A

b)

B

c)

C

d)

D

82.

a)

A

b)

B

c)

C

d)

D

83.

a)

Nitrogen is a gas only if the temperature is below -196°C.

b)

Nitrogen is a gas only if the temperature is above -196°C.

c)

Nitrogen is a gas only if the temperature is at or below -196°C.

d)

Nitrogen is a gas only if the temperature is at or above -196°C.

84.

a)

A

b)

B

c)

C

d)

D

85.

a)

2 large cans and 6 small cans

b)

2 large cans and 10 small cans

c)

6 large cans and 10 small cans

d)

8 large cans and 2 small cans

86.

a)

$t+s=20$
$6t+4s=94$

b)

$t+s=94$
$6t+4s=20$

c)

$8t+10s=20$
$6t+4s=94$

d)

$t+s=20$
$8t+10s=94$

87.

a)

7

b)

8

c)

56

d)

13

Keystone Algebra Module 1 Practice ( from Item Samplers)

Total questions: 87

Worksheet time: 3hrs 36mins

Similar Resources on Wayground