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Personal Math Trainer

Online Practice and Helpmy.hrw.comAssessment Readiness

MODULE 1 MIXED REVIEW

1. Look at each number. Is the number between 2π and √___

52 ?

Select Yes or No for expressions A–C.

A. 6 2 _ 3 Yes No

B. 5π __ 2 Yes No

C. 3 √__

5 Yes No

2. Consider the number - 11 __ 15 .

Choose True or False for each statement.

A. The number is rational. True FalseB. The number can be written as True False

a repeating decimal.C. The number is less than –0.8. True False

3. The volume of a cube is given by V = x3, where x is the length of an edge of the cube. A cube-shaped end table has a volume of 3 3 _ 8 cubic feet. What is the length of an edge of the end table? Explain how you solved this problem.

4. A student says that √___

83 is greater than 29 __ 3 . Is the student correct? Justify your

reasoning.

28 Unit 1

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Online Practice and Helpmy.hrw.com


Assessment Readiness

1. Consider each expression. Is the expression equivalent to 2 –4 ?

Select Yes or No for expressions A–C.

A. 2 2 - 2 6 Yes No

B. ( 2 –2 ) 2 Yes No

C. 2 3 __ 2 7 Yes No

2. The variable r represents a rational number.


A. r is a real number. True FalseB. r could be a repeating decimal. True FalseC. r could be √

_ 39 . True False

3. So far this year, a company has sold 8.28 × 1 0 5 tablet computers. How many more tablets must the company sell for its tablet sales to reach 1 million this year? Explain how you solved this problem.

4. Brazil has an area of approximately 8.51 × 10 6 square kilometers and a population of about 1.99 × 10 8 people. Portugal has an area of approximately 9.21 × 10 4 square kilometers and a population of about 1.08 × 10 7 people. On average, which country has a greater number of people per square kilometer? Explain how you know.

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1. Consider each table. Are the rates of change within each table constant?

Select Yes or No for tables A–C.

A. Time (s) 1 2 5 8

Height (m) 14 28 70 112

Yes No

B. Time (s) 1 2 3 4

Height (m) 60 30 15 7.5

Yes No

C. Time (s) 2 6 10 12

Height (m) 40 120 200 240

Yes No

2. An influenza virus has a length of 1.3 × 10 -7 meter.

Choose True or False if a virus is longer than the influenza virus.

A. a hepatitis virus with a length of 4.5 × 10 -8 m True FalseB. a measles virus with a length of 0.00000022 m True FalseC. a phage virus with a length of 2 × 10 -7 m True False

The table shows travel distance and fuel usage for a train. Use the table for items 3 and 4.

3. Write an equation for the relationship shown in the table and explain how you determined your answer.

4. The equation y = 6.5x gives the number of gallons of fuel that a second train uses to travel a distance of x miles. Which train uses fuel at a greater rate? Explain how you know.

Distance (mi), x 20 40 60 80Amount of fuel (gal), y 120 240 360 480

92 Unit 2

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O

8

16

24

2 4 6Time (h)

Earn

ings

($)

y

x



1. Consider each table. Does the table represent a proportional relationship?


A. x -4 -2 0 2 4y -10 -4 2 8 14

Yes No

B. x 4 8 12 16 20y 3 6 9 12 15

Yes No

C. x -3 -1 1 3 5y -12 -4 4 12 20

Yes No

2. The graph shows the relationship between the hours Leann works and the money she earns.


A. Slope = 8. True FalseB. Unit rate = $8/h. True FalseC. Equation is y = x _ 8 True False

3. There is an initial fee to join a gym, plus a monthly charge. The table represents the linear relationship between the total cost of joining the gym and the number of months a person is a member. What is the y-intercept of the line, and what does it represent in this situation?

4. The equation y = 35x - 5 gives y as the cost of x tickets to a theme park with a $5 coupon. After the park raises ticket prices by $3, what is the new equation? How are the graphs of the two equations different?

Time (months), x

Total Cost ($), y

1 125

2 155

3 185

124 Unit 2

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O

0.5

1

1.5

1 2 3Time (h)

Rain

fall

(in.)

y

x



1. Renting a paddle board costs $12 per hour plus a $3 charge for a life jacket.

Which model(s) below could represent this situation, where y is the cost in dollars of renting a paddle board for x hours? Select all that apply.

y = 3x + 12 a line with a slope of 12 and a y-intercept of 3

a line through the points (1, 12) and (3, 15)

x 0.5 1 1.5y 9 15 21

2. A ferry leaves a city and travels to an island. The distance the ferry has left to travel is modeled by the linear equation y = 12 - 0.2x, where y is the distance in miles and x is the time in minutes since the ferry left the city.


A. The relationship is nonproportional. True FalseB. The slope of the line is 0.2. True FalseC. The island is 12 miles from the city. True False

3. The graph shows the relationship between the time it started raining and the amount of rain that has fallen. Show that the relationship is linear, and then find the equation for the relationship.

4. Alma charges $97 for a job that takes 2 hours and $187 for a job that takes 4 hours. Write an equation in slope-intercept form that gives the charge y in dollars for a job that takes x hours. Explain how you solved this problem.

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Unit 2





1. Look at each table. Is the relationship in the table a function?


A. Input -4 8 0 6 13

Output 5 12 -3 5 18

Yes No

B. Input 26 34 28 30 34

Output 52 62 55 59 60

Yes No

C. Input 17 20 15 25 19

Output 84 75 72 72 80

Yes No

2. Michelle started with $25 and saves additional money each week to buy a video game system, as shown in the table.


A. The equation is y = 25x + 18. True FalseB. The y-intercept is 25. True FalseC. The slope is 18. True False

3. The equation y = 20 - x _ 4 gives the number of pounds of dog food y remaining in a bag x days after it is opened. Determine whether the relationship between x and y is linear. Explain your reasoning.

4. The cost y in dollars of getting cable TV from Soto Cable for x months is given by y = 42.50x + 30. The cost of getting cable TV from Lang Cable is shown in the table. Mr. Oliver needs cable TV for 6 months. Which service is cheaper for Mr. Oliver? Explain how you solved this problem.

Lang CableTime (months) Total Cost ($)

1 45.902 91.803 137.70

Time (Weeks), x 0 1 2 3

Savings ($), y 25 43 61 79

182 Unit 2

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ista

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from

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12

3

4



1. Consider each equation. Does the equation have at least one solution?

Select Yes or No for equations A-C.

A. 3(x + 2) = 2x + x + 6 Yes NoB. 2x - 7 = 2(x + 4) + 3x Yes NoC. 8 + 5x = 5(x + 2) - 1 Yes No

2. Vince left home to go on a walk. The graph shows his distance from home over time.


A. Vince walked faster during segment 3 than during segment 1.

True FalseB. In segment 2, Vince’s distance from

home increased at a constant rate. True FalseC. In segment 4, Vince returned home. True False

3. Shawn’s Rental’s charges $27.50 per hour to rent a surfboard and a wetsuit. Darla’s Surf Shop charges $23.25 per hour to rent a surfboard plus $17 extra for a wetsuit. Write and solve an equation to determine the rental period in hours for which the charges for Shawn’s Rentals will be the same as the charges for Darla’s Surf Shop. Explain the steps of your solution.

4. Beach towels are on sale for $1.50 off the regular price. Ms. Ortiz buys 4 beach towels on sale for a total of $33.96. Write and solve an equation to determine the regular price of a beach towel. Explain how you can check whether your answer is reasonable.

224 Unit 3

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1. Consider each system of equations. Does the system have at least one solution? Select Yes or No for systems A–C.

A. { 3x - 2y = 4 -6x + 4y = -8

Yes No

B. { -4x + y = 1 12x - 3y = 3 Yes No

C. { 2x + y = 0 4x - y = -6 Yes No

2. Ruby ran 5 laps on the inside lane around a track. Dana ran 3 laps around the same lane on the same track, and then she ran 0.5 mile to her house. Both girls ran the same number of miles in all. The equation 5d = 3d + 0.5 models this situation.


A. The variable d represents the distance around the track in miles. True False

B. The expression 5d represents the time it took Ruby to run 5 laps. True False

C. The expression 3d + 0.5 represents the distance in miles Dana ran. True False

3. Daisies cost $0.99 each and tulips cost $1.15 each. Maria bought a bouquet of daisies and tulips. It contained 12 flowers and cost $12.52. Solve the

system { x + y = 12 0.99x + 1.15y = 12.52

to find the number of daisies x and the number of tulips y in Maria’s bouquet. State the method you used to solve the system and why you chose that method.

4. Kylie bought 4 daily bus passes and 2 weekly bus passes for $29.00. Luis bought 7 daily bus passes and 2 weekly bus passes for $36.50. Write and solve a system of equations to find the cost of a daily pass and the cost of a weekly pass. Explain how you can check your answer.

268 Unit 3

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-2

O

4

2

x

y

-4 -2 42

-4

D

F E

-2

O

4

2

x

y

-4 -2 42

-4

D

A

B



1. Consider each rational number. Is the number greater than −2 1 _ 3 but less than − 4 _ 5 ?

Select Yes or No for A–C.

A. −0.4 Yes NoB. − 9 _ 7 Yes NoC. −0.9 Yes No

2. Triangle DEF is rotated 90° clockwise about the origin.


A. E′F′ = 3 True FalseB. m∠F′ = 90° True FalseC.

_ D′F′ is vertical. True False

3. A graphic artist is working on a logo for a car company. The artist draws parallelogram LMNP with vertices L(1, 0), M(2, 2), N(5, 3), and P(4, 1). The artist then reflects the parallelogram across the x-axis. Find the coordinates of the vertices of parallelogram L′M′N′P′, and describe the algebraic rule you used to find the coordinates.

4. The map shows two of a farmer’s fields. Is field A congruent to field B? Use a sequence of transformations to explain your reasoning.

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Unit 4




A

B

C

y

xO 42 6

6

2

4

-2-2

O

4

x

y

6

-2

2

2

-4

BA(4, 1.5)

(4, -1.5)


1. Triangle ABC is dilated by a scale factor of 2 with the origin as its center and then reflected across the y-axis. Look at each ordered pair. Is the ordered pair a vertex of the image?

Select Yes or No for ordered pairs A–C.

A. (-4, 10) Yes NoB. (-2, 4) Yes NoC. (10, -6) Yes No

2. Choose True or False for each statement.

A. No integers are irrational numbers. True FalseB. No real numbers are rational numbers. True FalseC. All integers are whole numbers. True FalseD. All whole numbers are integers. True False

3. In a video game, a rectangular map has vertices M(10, 10), N(10, 20), P(40, 20), and Q(40, 10). When a player clicks the map, it is enlarged by a scale factor of 4.5 with the origin as the center of dilation. What are the coordinates of the vertices of the enlarged map? Describe the algebraic rule you used to find the coordinates.

4. An engineer is working on the design of a bridge. He draws the two triangles shown. Is triangle A similar to triangle B? Use a sequence of transformations to explain how you know.


336 Unit 4

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1 23

4 5 6

p q

a

b

J

K

L

N M

C

A B D120°

2x°

x°



1. In the diagram, lines a and b are parallel and lines p and q are parallel. Look at each pair of angles. Are the angles congruent?


A. ∠1 and ∠2 Yes NoB. ∠3 and ∠4 Yes NoC. ∠5 and ∠6 Yes No

2. The variables x and y are related proportionally, and when x = 18, y = 12.


A. When x = 3, y = 5. True FalseB. When x = 27, y = 18. True FalseC. When x = 63, y = 42. True False

3. An artist is designing a triangular pane of glass for a stained glass window, as shown in the diagram. Given that ∠ABC is an exterior angle, what is the measure of each interior angle of the triangle? Explain your reasoning.

4. The diagram shows several of the boards that form part of the frame of a roof. Is △JKN similar to △JLM? Explain how you know.

372 Unit 5

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Entrance

?

Nest

2.6 mi

3.2 mi

Ox

y

-2-2

2

2



1. Look at each set of side lengths. Is a triangle with the given side lengths a right triangle? Select Yes or No for A–C.

A. 2.8 m, 4.5 m, 5.3 m Yes NoB. 15 in., 17 in., 32 in. Yes NoC. 21 ft, 28 ft, 35 ft Yes No

2. Consider the set of numbers 29 __ 6 , 4.9, and √

_ 24 .


A. 4.9 is to the right of 29 __ 6 on a number line. True False

B. 29 __ 6 is to the left of √

_ 24 on a number line. True False

C. √_

24 is to the right of 4.9 on a number line. True False

3. A bald eagle’s nest is located 3.2 miles west and 2.6 miles north of the entrance to a national forest. A biologist plans to hike directly from the forest entrance to the nest. Will the biologist hike more than 5 miles to reach the nest? Explain how you know.

4. Three of the paths in a city park form a right triangle, as shown on the map. Each unit on the map represents 10 meters. The city plans to plant trees along these paths. To the nearest meter, what is the perimeter of the triangle? Explain how you solved this problem.

396 Unit 5

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14.0 cm

3.2 cm

Ox

y

-2-2

-4

2

2K

JL



1. Triangle JKL is dilated by a scale factor of 1.5 with the origin as the center of dilation. Look at each ordered pair. Does the ordered pair represent a vertex of the image?


A. (–3, –4.5) Yes No

B. (1.5, –6) Yes No

C. (3, 0) Yes No

2. A sphere has a radius of 4 inches.


A. A sphere with half the radius has 1 _ 8 of the volume. True False

B. A sphere with twice the radius has6 times the volume. True False

C. A sphere with 3 times the radius has27 times the volume. True False

3. A pile of sand is shaped like a cone with a height of 4 feet and a base diameter of 13 feet. Each cubic foot of sand weighs 90 pounds. Does the pile of sand weigh more than a ton (2000 pounds)? Explain how you know.

4. A cylindrical drinking glass has a base radius of 3.2 centimeters and a height of 14.0 centimeters. Given that 1 cubic centimeter is equivalent to 1 milliliter, how many milliliters of water does the glass hold when it is 3 _ 4 full? Round to the nearest milliliter.



420 Unit 5

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