8th grade pre-algebra

8th Grade Pre-Algebra

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Kelly is learning about rational and irrational numbers. What conclusion can she draw about the number 0.01011011101111011111...?

a. It is rational because it repeats.

b. It is rational because it terminates. c. It is irrational because it neither repeats nor terminates.

d. It is irrational because it repeats.

____ 2. What rational number has as its decimal equivalent?

a.

b.

c.

d.

____ 3. Pierre worked hours today. What is the decimal equivalent of ?

a. b. c. d.

____ 4. Which of these expressions is true?

a. c. b. d.

____ 5. In a right triangle, the length of one leg is s.

The length of the other leg is times as long as s, or . The length of the hypotenuse is twice the length of the shorter leg s, or 2s. Estimate the length of the

hypotenuse if the longer leg is 14 units long.

a. 1.7 units

b. 16 units c. 8 units

d. 3.14 units

____ 6. Which whole number is the best approximation for ? Explain.

a. 2 because is a little more than 2.

b. 7 because is between 6.5 and 7.

c. 5 because squares and square roots are inverse operations.

d. 3 because the square root of 8 is a little less than 3.

____ 7. What is the relationship between and ?

a.

b.

c.

d. The relationship cannot be determined.

____ 8. Between which pair of decimals does fall on a number line? a. Between 3.2 and 3.3

b. Between 3.4 and 3.5

c. Between 3.6 and 3.7

d. Between 3.8 and 3.9

____ 9. Describe and give the value of . a. Irrational, c. Irrational,

b. Not a real number d. Rational,

____ 10. Find a rational number between and . a. c.

b. d. 16.253

____ 11. Evaluate .

a. 2 b.

c.

d.

____ 12. Colin has a square garden with an area of 97 square feet. What is the length of each side of the garden?

a. 10 ft b. ft

c. ft d. ft

____ 13. Explain how to use the properties of exponents to write an equivalent expression for .

a. Multiply 2 powers, both with a base of 6. One has an exponent of 2, and the other y.

b. Add 2 powers, both with a base of 6. One has an exponent of 2, and the other y. c. Multiply 2 times a power with a base of 6 and exponent of y.

d. Add y to 6 squared.

____ 14. Use properties of exponents to write an equivalent expression for .

a. b. c.

d.

____ 15. What is written in scientific notation?

a. b. c. d.

____ 16. What is written in standard notation?

a.

b.

c. d.

____ 17. Which is the product of in scientific notation?

a. c. b. d.

____ 18. In 2010, the population of the Dominican Republic was about . The population of Haiti was about

. About how much more was the population of Haiti than the Dominican Republic?

a. c. b. d.

____ 19. Which is the product of in scientific notation?

a. c. b. d.

____ 20. The graph shows a proportional relationship. Use the graph to identify the unit rate.

Time (hours)

Dis

tan

ce

(k

m)

1 2 3 4 5 6 7 t

40

80

120

d

a. 30 hours per kilometer

b. 60 kilometers per hour c. 30 kilometers per hour

d. kilometers per hour

____ 21. The graph shows the proportional relationship between the cost and the length for two different brands of

coaxial cable. What is the unit rate for each brand? Which brand is more expensive?

Length (m)

Co

st

(do

lla

rs)

Brand A

Brand B

1 2 3 4 5 l

2

4

6

8

10

12C

a. Brand A: $1.75 per meter; Brand B: $2.25 per meter; Brand B b. Brand A: $2.25 per meter; Brand B: $1.50 per meter; Brand A

c. Brand A: $2.00 per meter; Brand B: $1.50 per meter; Brand A

d. Brand A: 2.25 meters per dollar; Brand B: 1.5 meters per dollar; Brand B

____ 22. The number of pages p that a laser printer prints is proportional to the printing time t, in minutes. Printer A prints 104 pages in 4 minutes. The table shows the relationship between the amount of time and the number of

pages printed for printer B. Which printer prints more slowly?

Time

(minutes)

Pages

printed

3 84

5 140

9 252

14 392

a. Printer A

b. Printer B

c. Printer A and printer B have the same unit rate. d. The relationship cannot be determined.

____ 23. The graph shows the relationship between the number of hours h Greg has been driving and the total distance

d he has traveled, in miles.

1 2 3 h

10

20

30

40

50

60

70

80

90

100

110

d

Which statement is true? a. Greg is traveling at 90 miles per hour.

b. Greg is traveling at 30 miles per hour.

c. To find Greg’s rate of speed, multiply the total number of hours driven by the total distance.

d. To find Greg’s rate of speed, divide the total number of hours driven by the total distance.

____ 24. The graph shows the relationship between the number of hours h Bree has been hiking and the total distance d

she has traveled, in kilometers.

1 2 3 h

2

4

6

8

10

12

14

16

18

20d

Which statement is true?

a. The slope of the line is 8.

b. The slope of the line is 12.

c. To find the slope of the line, you could divide the total number of hours hiked by the total

distance. d. To find the slope of the line, you could multiply the total number of hours hiked by the

total distance.

____ 25. The graph shows the proportional relationship between the cost and the length for two different brands of

coaxial cable. What is the unit rate for each brand? Which brand is more expensive?

Length (m)

Co

st

(do

lla

rs)

Brand A

Brand B

1 2 3 4 5 l

2

4

6

8

10

12C

a. Brand A: $1.75 per meter; Brand B: $2.25 per meter; Brand B

b. Brand A: $2.25 per meter; Brand B: $1.50 per meter; Brand A c. Brand A: $2.00 per meter; Brand B: $1.50 per meter; Brand A

d. Brand A: 2.25 meters per dollar; Brand B: 1.5 meters per dollar; Brand B

____ 26. The number of pages p that a laser printer prints is proportional to the printing time t, in minutes. Printer A

prints 104 pages in 4 minutes. The table shows the relationship between the amount of time and the number of pages printed for printer B. Which printer prints more slowly?

Time

(minutes)

Pages

printed

3 84

5 140

9 252

14 392

a. Printer A b. Printer B

c. Printer A and printer B have the same unit rate.

d. The relationship cannot be determined.

____ 27. The cost C, in dollars, for advertising on a social networking website is proportional to the number n of clicks on the advertisement. Suppose a business is charged $45 for 180 clicks on its advertisements. What is the

slope of the line that represents the relationship between cost and clicks?

a. 4

b. 1

c. 0.25

d. The slope cannot be determined.

____ 28. Carlita goes jogging, and her GPS collects the data for her distance over time. What would the rate of change for that data represent?

a. Carlita’s distance from home

b. Carlita’s starting point c. Carlita’s distance over time, or speed

d. Carlita’s time since she left home

____ 29. What equation could be written for this table?

a. c.

b. d.

____ 30. What is the direct variation equation for the data in the table?

a.

c.

b.

d.

____ 31. Lamar starts his own painting business. He pays for some supplies to begin, and then charges a fixed amount

per room. The graph shows a linear function that models Lamar’s profit per room.

1 2 3 4 5 6 7 8–1 x

100

200

300

400

500

600

700

y

What does the initial value represent?

a. The number of rooms he paints b. The amount he charges per room

c. The amount he spends in supplies

d. The amount of profit he makes per room

____ 32. A bathtub filled with 40 gallons of water drains at an average rate of 3 gallons per minute. What is the rate of

change and initial value of the linear function that models the amount of water in the bathtub after it starts draining?

a. The rate of change is 40 gallons per minute, and the initial value is 3 gallons.

b. The rate of change is 3 gallons per minute, and the initial value is 40 gallons.

c. The rate of change is gallons per minute, and the initial value is 40 gallons. d. The rate of change is gallons per minute, and the initial value is 3 gallons.

____ 33. The graph shows the distance d, in miles, that Joe can drive his car using gallons of gasoline. What is the

rate of change in this situation?

Dis

tan

ce

(m

ile

s)

Gasoline (gallons)

1 2 3 4 5 6 7 g

10

20

30

40

50

60

70

80

90

100 d

a. 20 miles per gallon of gasoline b. 25 miles per gallon of gasoline

c. 30 miles per gallon of gasoline

d. 35 miles per gallon of gasoline

____ 34. George is selling sandwiches at a deli. The table shows the average number s of sandwiches he sells over time

, in minutes. What linear function is represented by the table?

Time

(minutes)

Sandwiches

sold

3 19

6 25

9 31

12 37

a. b. c. d.

____ 35. You observe that the line shown below passes through the point and has a slope of . You choose

as an arbitrary point on the line other than and use the fact that the slope of a line is constant to

write which equation?

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

a.

b.

c.

d.

____ 36. Maya sketches a graph of a linear function. Which graph might she have sketched? a.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

b.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

c.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

d.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

____ 37. Which is a linear equation?

a. c.

b. d.

____ 38. Which of these functions is a linear function?

a.

c.

b. d.

____ 39. Which graph represents a linear function?

a.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

c.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

b. d.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

____ 40. Three lines are drawn to form the right triangle below. The equation for the hypotenuse is , the

equation for the longer leg is , and the equation for the shorter leg is . Which of these equations,

if any, does not represent a linear function?

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

a. The equation for the hypotenuse does not represent a linear function.

b. The equation for the longer leg does not represent a linear function. c. The equation for the shorter leg does not represent a linear function.

d. Each of the equations represents a linear function.


a. c.

b. d.

____ 42. Which equation represents the values in the table?

a. c.

b. d.

____ 43. Which equation describes w?

a. c. b. d.


a. c.

b. d.


x 0 1 2 3

y 0 1 2

a. c.

b. d.


x 0 1 2 3

y 1 4 7 10

a. c.

b. d.

____ 47. Which is the rule for the function table?

a. c.

b. d.

____ 48. Mariana is 10 years old and has grown 7 inches in 2 years. When she was 8 years old, she was 52 inches tall.

Mariana writes and graphs a function that models her height in inches over time in years. What is the initial

value for this function?

a. 59

b. 3.5 c. 7

d. 52

____ 49. Lamar starts his own painting business. He pays for some supplies to begin, and then charges a fixed amount

per room. The graph shows a linear function that models Lamar’s profit per room.

1 2 3 4 5 6 7 8–1 x

100

200

300

400

500

600

700

y

What does the initial value represent?

a. The number of rooms he paints b. The amount he charges per room

c. The amount he spends in supplies

d. The amount of profit he makes per room

____ 50. The graph shows the relationship between a candle’s height h, in centimeters, and time t, in hours, as the

candle burns. What function models this relationship?

Time (hours)

He

igh

t (c

m)

1 2 3 4 5 6 7 8 9 t

2

4

6

8

10

12

14

16

18

20 h

a. b. c. d.

____ 51. Vincent’s savings over several weeks are shown in the table. If a linear function models Vincent’s savings

over time, how much money did he initially have?

Time

(weeks)

Savings

(dollars)

2 75

4 115

6 155

8 195

10 235

a. b. c. d.

____ 52. Lynn is walking from her house to the grocery store. The table shows the distance she has left to walk. What

is the rate of change for the linear function represented by the table?

Time

(minutes) Distance

(blocks)

2 9

4 8

6 7

8 6

a. blocks per minute b. block per minute

c. block per minute

d. 2 blocks per minute

____ 53. George is selling sandwiches at a deli. The table shows the average number s of sandwiches he sells over time , in minutes. What linear function is represented by the table?

Time

(minutes)

Sandwiches

sold

3 19

6 25

9 31

12 37

a. b. c. d.

____ 54. One kilometer is equal to 0.62 miles. Which best describes the relatinship between miles and kilometers?

a. linear and proportional relationship c. non-linear relationship

b. linear, non-propotional relationship

____ 55. The formula for the area of a circle is . Which best describes the relationship between the area and radius of a circle?

a. linear and proportional relationship c. non-linear relationship b. linear, non-propotional relationship

____ 56. The graph shows the cost per hour of renting a powertool.

Hours

Co

st

3 6 9 12 15 18 21 24 27 30 x

10

20

30

40

50

60

70

80

y

Which of the following best describes the relatinship between cost and the number of hours?

a. linear and proportional relationship c. non-linear relationship b. linear, non-propotional relationship

____ 57. The graph shows the amount earned and the hours worked.

Hours Worked

Am

ou

nt

Ea

rned

($

)

1 2 3 4 5 6 7 8 9 10 x

10

20

30

40

50

60

70

80

y

Which of the following best describes the relatinship between the amount earned and the number of hours

worked? a. linear and proportional relationship c. non-linear relationship

b. linear, non-propotional relationship

____ 58. Which of the statements is true about the data displayed in the scatter plot?

a. It shows a positive correlation. c. It shows no correlation. b. It shows a negative correlation. d. As speed increases, cost decreases.

____ 59. Which statement best describes the pattern of association between the variables and shown in the scatter

plot?

1 2 3 4 5 6 7 8 9 10 11 x

1

2

3

4

5

6

7

8

9

10

11

y

a. There is a positive, linear association between the two variables.

b. There is a negative, linear association between the two variables.

c. There is a positive, nonlinear association between the two variables. d. There is no association between the two variables.

____ 60. Which statement best describes any clusters there are in the data displayed in the scatter plot shown?

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

a. The data cluster around .

b. The data cluster around .

c. The data cluster around and .

d. There are no clusters.

____ 61. Maya sketches a graph of a linear function. Which graph might she have sketched? a.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

b.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

c.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

d.

1 2 3–1–2–3 x

1

2

3

–1

–2

–3

y

____ 62. Which of the following equations is not linear?

a. b.

____ 63. Which equation does not represent a linear function? a.

b.

c.

d.

____ 64. Three lines are drawn to form the right triangle below. The equation for the hypotenuse is , the

equation for the longer leg is , and the equation for the shorter leg is . Which of these equations,

if any, does not represent a linear function?

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

a. The equation for the hypotenuse does not represent a linear function.

b. The equation for the longer leg does not represent a linear function. c. The equation for the shorter leg does not represent a linear function.

d. Each of the equations represents a linear function.


a.

c.

b. d.


a. c.

b. d.


a. c.

b. d.


a. c. b. d.

____ 69. Which equation is graphed?

a. c.

b. d.


a.

c.

b.

d.

____ 71. The graph shows the relationship between a candle’s height h, in centimeters, and time t, in hours, as the candle burns. What function models this relationship?

Time (hours)

He

igh

t (c

m)

1 2 3 4 5 6 7 8 9 t

2

4

6

8

10

12

14

16

18

20 h

a. b. c. d.



Time

(weeks)

Savings

(dollars)

2 75

4 115

6 155

8 195

10 235

a. b. c. d.

____ 73. Gloria drives her daughter to school in the morning and then comes back home. She stays home until she has to go to pick up her daughter from school, and then they both return home again. Which graph best shows the

situation?

a.

TimeDis

tan

ce f

rom

ho

me

c.

TimeDis

tan

ce f

rom

ho

me

b.

TimeDis

tan

ce f

rom

ho

me

d.

TimeDis

tan

ce f

rom

ho

me

____ 74. Which situation is best represented by the graph?

Time

Sp

eed

a. A swimmer starts at a steady pace, slows down to a stop, and then starts up swimming

again, but at a slower pace than when she first started.

b. After a ball is thrown into the air, it falls back to the ground and bounces. c. An airplane starts slowly on the runway, and then quickly takes off before finding a nice

cruising speed.

d. A car starts on flat ground and drives quickly up a hill, and then it keeps driving.

____ 75. Gloria drives her daughter to school in the morning and then comes back home. She stays home until she has

to go to pick up her daughter from school, and then they both return home again. Which graph best shows the situation?

a.

TimeDis

tan

ce f

rom

ho

me

c.

TimeDis

tan

ce f

rom

ho

me

b.

TimeDis

tan

ce f

rom

ho

me

d.

TimeDis

tan

ce f

rom

ho

me

____ 76. Which statement best tells the story of the graph?

a. A car slowed down to a stop. c. A car maintained constant speed.

b. A car started from a stop. d. A car stopped and then started.

____ 77. Which graph corresponds to the temperature in an oven that is turned on to bake a loaf of bread then turned

off when the bread is done? a.

c.

b.

d.

____ 78. Which of the following situations corresponds to this graph?

a. A car accelerates from a stop, travels at a constant speed, slows, and then travels at a

slower speed.

b. An airplane travels at a constant speed then decelerates to a slower speed.

c. An athlete warms up by walking around the track, runs, then jogs. d. A bicyclist accelerates, travels at a constant speed, then slows to a stop.

____ 79. Which of the following situations corresponds to this graph?

a. An object is lifted slowly, then lowered slowly.

b. A car accelerates from a stop, then gradually stops.

c. An object starts falling, accelerates, and then falls slowly. d. An airplane climbs to 29,000 feet, then descends.

____ 80. In the graph of the function, for what values of is increasing?

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

a. Between and

b. Between and

c. Between and d. The function is never increasing.

____ 81. What words best describe the function whose graph is shown?

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

a. Increasing and linear

b. Increasing and nonlinear

c. Decreasing and linear

d. Decreasing and nonlinear

____ 82. Which graph represents a function that is always decreasing between and ? a.

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

c.

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

b.

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

d.

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

____ 83. What segment of the graph shows the function having a constant value?

1

2

3 4

1 2 3 4 5 6 7 8 9 x

1

2

3

4

5

6

7

8

9

10 y

a. 1 b. 2

c. 3

d. 4

____ 84. Which of these functions is not a linear function?

a. c.

b. d.


a. c.

b. d.


a. c.

b. d.

____ 87. Use the graph to explain why is or is not a function of .

(2, 2)

(2, –2)

(3, 3)

(3, –3)

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

a. is a function of because both and have the same -coordinate.

b. is a function of because for each -coordinate, there is exactly one -coordinate.

c. is not a function of because both and have the same -coordinate.

d. is not a function of because for each -coordinate, there is exactly one -coordinate.

____ 88. Does the table below represent a function? Explain why or why not.

Input Output

0 0

1 1 1

4

4 2

a. Yes, because each input has exactly one output assigned to it.

b. Yes, because the inputs and outputs are integers.

c. No, because there are positive inputs that have negative outputs and there are negative inputs that have positive outputs.

d. No, because there are inputs that have more than one output assigned to them.

____ 89. Carlita goes jogging, and her GPS collects the data for her distance over time. What would the rate of change

for that data represent?

a. Carlita’s distance from home b. Carlita’s starting point

c. Carlita’s distance over time, or speed

d. Carlita’s time since she left home


a.

c.

b. d.


a. c. b. d.


a. c.

b. d.


a.

c.

b.

d.


x 0 1 2 3

y 1 4 7 10

a. c.

b. d.

____ 95. Choose the equation that is represented by the data in the table.

a. c. b. d.


Mariana writes and graphs a function that models her height in inches over time in years. What is the initial value for this function?

a. 59

b. 3.5

c. 7 d. 52



Time

(weeks) Savings

(dollars)

2 75

4 115

6 155

8 195

10 235

a. b. c. d.

____ 98. The graph shows the distance d, in miles, that Joe can drive his car using gallons of gasoline. What is the

rate of change in this situation?

Dis

tan

ce

(m

ile

s)

Gasoline (gallons)

1 2 3 4 5 6 7 g

10

20

30

40

50

60

70

80

90

100 d

a. 20 miles per gallon of gasoline

b. 25 miles per gallon of gasoline

c. 30 miles per gallon of gasoline

d. 35 miles per gallon of gasoline

____ 99. Lynn is walking from her house to the grocery store. The table shows the distance she has left to walk. What is the rate of change for the linear function represented by the table?

Time

(minutes)

Distance

(blocks)

2 9

4 8

6 7

8 6

a. blocks per minute b. block per minute

c. block per minute

d. 2 blocks per minute


Mariana writes and graphs a function that models her height in inches over time in years. What is the initial value for this function?

a. 59

b. 3.5 c. 7

d. 52

Multiple Response

Identify one or more choices that best complete the statement or answer the question.

____ 1. Which of the following rational numbers fall between and on a number line?

a.

b.

c.

d.

e.

f.

____ 2. A company can hire new employees. There are applicants. Which of the following rational numbers represent the ratio of applicants to available positions?

a. 2.45 b. c. d.

e.

f.

____ 3. Which of the following numbers fall between 4.7 and 4.8 on a number line?

a. b. c.

d. e. f.

____ 4. Suppose each irrational number below is approximated by the whole number to which it is closest. Which of

the irrational numbers have whole-number approximations that are even?

a. b. c. d. e. f.

____ 5. For which values of x is the expression irrational?

a. 1 b. 2

c. 3

d. 4

e. 5

____ 6. Which of the following expressions are equivalent to ?

a.

b.

c. d.

e.

f.

____ 7. Which of the following statements are true?

a. is times as great as . b. is times as great as .

c. is times as great as .

d. is times as great as .

e. is times as great as . f. is times as great as .

____ 8. Identify all of the following values that are equivalent to .

a. b. c. d. e. f.

____ 9. Which of the following proportional situations can be represented with this graph?

Co

st

(do

lla

rs)

Number of Items1 2 3 4 5 6 7 8 9 10 n

10

20

30

40

50

60

70

80

90

100 C

a. 2 pairs of headphones cost $12.

b. 24 carrots cost $4.

c. 3 packs of D batteries cost $18.

d. 6 bags of apples cost $36. e. 6 jigsaw puzzles cost $10.

____ 10. Which of the following sets of ordered pairs represent as a function of ?

a.

b.

c.

d.

e.

f.

Short Answer

1. Use the properties of exponents to write an expression using four 8s that equals 8.

2. Julie is making muffins for a bake sale. It takes her 30 minutes to make a dozen muffins. Tim had already

made 36 muffins, which he adds to the amount Julie makes.

a. Write a linear function that models the number m of muffins based on the time , in hours, that Julie spends baking.

b. Describe what the rate of change and initial value mean in this situation.

3. Find the slope of the line that passes through the points and .

4. Find the slope-intercept form of the line that passes through the point and has a slope of .

5. Can a function assign multiple inputs to the same output? Explain why or why not

8th grade pre-algebra

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