ssessmet 1 - Mrs. Cao's Math Classes€¦ · Fill in the cost in dollars to manufacture different numbers of game consoles. Number of Game Consoles, x Cost (in dollars), y 0 50 100

Assessment 1

©Curriculum Associates, LLC Copying is not permitted.

Assessment 1 1

Go On

Section 1 (Calculator-Inactive)

Answer questions 1–19. Answer questions outlined in green in your test book. Answer all other questions on the Answer Form. You may NOT use a calculator.

1 Which numbers are irrational? Mark all that apply.

A 24

B 5 }} 19

C 0.5 ··· 73

D 7 } 3

E p

F Ï··· 11

2 Consider the equation below.

3 } 4 (24 2 16x) 5 2 2 }

3 (18x 2 27)

How many solutions does the equation have?

A one, x 5 0

B one, x 5 2 27 }} 8

C no solutions

D infinitely many solutions


Assessment 12

3 Consider the numbers 1.4 3 103 and 5.6 3 102.

Part A

What is the sum of the numbers, written in scientific notation?

A 1.96 3 2

B 1.96 3 103

C 1.96 3 4

D 1.969 3 5

Part B

What is the product of the two numbers, written in scientific notation?

A 0.784 3 106

B 7.84 3 105

C 7.84 3 106

D 78.4 3 105

Go On


Assessment 1 3

4 In the diagram below, m/ACB 5 m/DCE.

A B

ED

C

( )°45

110k – k

( )°12 k + 1

What is the value of k?

Show your work.

Answer


Assessment 14

5 The equation y 5 20x 1 500 models the relationship between the number of game consoles, x, a company manufactures and the cost in dollars, y, of manufacturing the consoles.

Part A

Fill in the cost in dollars to manufacture different numbers of game consoles.

Number of Game Consoles, x Cost (in dollars), y

0

50

100

150

200

Part B

Plot the points on the coordinate grid.

50 100 150 250200x

2,000

3,000

4,000

5,000

1,000

y

0Number of Game Consoles

Co

st in

Do

llars

GAME CONSOLE COSTS

Go On


Assessment 1 5

Part C

Does the equation y 5 20x 1 500 represent a linear function? Explain your answer.

Part D

The equation P 5 100x 2 (20x 1 500) represents the profit, P, earned by making and selling x game consoles. Is the profit a linear function of the number of game consoles? Explain your reasoning.


Assessment 16

6 A plane leaves the gate and moves onto the runway. Then, the plane ascends to its flying altitude. The plane stays at this altitude for some time. Then, the plane descends to the runway. The plane lands and moves to the gate. Which graph shows the relationship between the plane’s altitude and time?

y

xTime

Alt

itu

de

y

xTime

Alt

itu

de

A C

y

xTime

Alt

itu

de

y

xTime

Alt

itu

de

B D

Go On


Assessment 1 7

7 Which sequence of transformations is performed on Figure 1 to form congruent Figure 2?

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 2 3 4 5 6 7 8 9 100

10

9

8

7

6

5

4

3

2

1

y

x

B

C

A

D

B’

C’

A’

D’

1

Figure2

Figure1

A Figure 1 is translated 3 units up and 5 units to the left.

B Figure 1 is translated 5 units down and 7 units to the right.

C Figure 1 is translated 4 units down and 5 units to the right.

D Figure 1 is translated 4 units up and 5 units to the left.


Assessment 18

8 Which is true? Mark all that apply.

A 4 , Ï··· 21 , 5

B 4 , Ï··· 21 , 4.5

C 4.5 , Ï··· 21 , 5

D 10 , Ï··· 21 , 11

E 10 , Ï··· 21 , 10.5

F 10.5 , Ï··· 21 , 11

9 The function C 5 2pr gives the circumference of a circle related to its radius, while the function A 5 pr 2 gives the area of a circle related to its radius.

Which statement is correct?

A Both C 5 2pr and A 5 pr 2 are linear functions, because they both include the variable r.

B Only C 5 2pr is a linear function, because its graph is a line with a slope of 2p.

C Only A 5 pr 2 is a linear function, because its graph is a line with a slope of p.

D Neither C 5 2pr nor A 5 pr 2 are linear functions, because they both include the irrational number p.

Go On


Assessment 1 9

10 A snowstorm began on Monday evening. It snowed steadily until 6:00 am on Tuesday morning when the snow was 12 inches deep.

Kevin wrote the equation y 5 3t 2 6 to model the depth, y, in inches, of the snow on Tuesday morning, t hours after midnight.

Part A

Does Kevin’s equation correctly predict the total snowfall of 12 inches at 6:00 am on Tuesday morning? Explain.

Part B

What is the y-intercept of Kevin’s equation? Is his equation reasonable? Explain.


Assessment 110

Part C

The actual depth of the snow is shown in the graph below.

10

12

1 2 3 4 5 6

y

t

Hours after Midnight

TUESDAYSNOWFALL

Dep

th o

f Sn

ow

(in

ches

)

0

8

6

4

2

Write an equation to model the depth, y, in inches, of the snow on Tuesday morning, t hours after midnight. Explain your reasoning.

Equation

Part D

What does the y-intercept of the line from the graph represent?

Go On


Assessment 1 11

Part E

What does the slope of the line from the graph represent?

Part F

If there was no snow on the ground before this snowstorm began, and the snow fell at the same rate throughout the entire storm, what time on Monday did the snow begin to fall? Explain your reasoning.

11 Grant translated figure A 2 inches to the right to create figure B.

A B

Which comparision is true of figure A and figure B?

A The side lengths of figure A are 2 inches less than the side lengths of figure B.

B The side lengths of figure B are 2 times the side lengths of figure A.

C The angles of figure B are congruent to the corresponding angles in figure A.

D The angle measures of figure A are 2 times the angle measures of figure B.


Assessment 112

12 Which equation has infinitely many solutions?

A 2(3x 2 4) 5 6x 2 4

B 3(4x 2 2) 5 12x 1 6

C 2(4x 2 3) 5 3(4x 2 3)

D 3(2x 2 4) 5 2(3x 2 6)

13 Which expressions are equivalent to 26 3 224

}}}} 27 ? Mark all that apply.

A 1 }} 32

B 1 }} 16

C 1 1 } 2 2

4

D 1 1 } 2 2

5

E 22 }}

27

F 23 }}

27

14 Nadia was considering two different vacation packages. For each, she wrote a linear equation to model the cost of airfare and n nights in a hotel. She graphed the corresponding lines and found the two packages cost the same only when the vacation includes 5 nights in a hotel.

Which statement about Nadia’s graph must be true?

A The lines are parallel.

B The lines are not parallel.

C The x-intercepts are the same.

D The y-intercepts are the same.

Go On


Assessment 1 13

15 The students at Mercer Middle School can choose to use either a laptop or a tablet for in-class work. A survey was conducted to an equal number of seventh and eighth graders about their technology preferences.

Part A

Of the 20 seventh graders who were surveyed, 25% prefer tablets. How many seventh graders prefer tablets?

Show your work.

Answer seventh graders

Part B

The 20 eighth grade students in the survey prefer tablets to laptops in a ratio of 3:2. How many eighth graders prefer tablets?

Show your work.

Answer eighth graders


Assessment 114

Part C

Use the information in Parts A and B to complete the table.

Technology Preference

7th Grade 8th Grade

Laptop

Tablet

Part D

What percent of students who prefer laptops are in seventh grade? Round your answer to the nearest percent. Explain your reasoning.

Go On


Assessment 1 15

16 Consider the equations y 5 3x 1 5 and y 5 8 } x 2 2.

Part A

Which statement correctly describes y 5 3x 1 5?

A It is not a function.

B Its graph is not a straight line.

C It is a nonlinear function.

D It is a linear function.

Part B

Which statement correctly describes y 5 8 } x 2 2?

A It is a combination of two functions.

B It is a nonlinear function.

C Its graph is a straight line.

D It is not a function.

17 Which describes a relationship that is not a function?

A Each output of the relationship has a unique input.

B Each output of the relationship has the same input.

C Each input of the relationship has the same output.

D Each input of the relationship has a unique output.


Assessment 116

18 Stan and Olivia are learning about proportions among different body parts. They study the relationship between the length of a person’s head and that person’s height. They each collect measurement data and plot points on a scatter plot. Then they determine the equation for the best-fit line. The table shows the equations of the lines based on their data. Let h equal a person’s height, in inches, and l equal head length, in inches.

Student Equation of best-fit line

Stan h 5 7.5l 1 1.5

Olivia h 5 8.2l 2 2.2

Based on the equations above, which statements are true? Mark all that apply.

A Stan’s equation suggests that a person’s height is approximately 7.5 times his or her head length.

B Olivia’s equation suggests that a person’s height is approximately 2.2 times his or her head length.

C Olivia’s equation indicates that a person with a head length of 8 inches would likely be about 63.4 inches tall.

D Stan’s equation indicates that a person 69 inches tall would likely have a head length of about 9 inches.

E The y-intercept in Stan’s equation indicates that a person with a head length of 0 would likely be about 7.5 inches tall.


Assessment 1 17

19 The scatter plot below shows the balance of a savings account each month for 1 year.

Tara thinks a best fit line is given by the equation y 5 25x 1 300.

Vicky thinks a best fit line is given by the equation y 5 50x 1 100.

900

1000

1 2 3 4 5 6 7 8 9 11 1210

y

x

Month

SAVINGS ACCOUNT

Acc

ou

nt

Bal

ance

(d

olla

rs)

0

800

700

600

500

400

300

200

100

Which statement best describes Tara and Vicky’s lines?

A Tara’s line is most likely to be the line of best fit, because it passes through more of the data points.

B Vicky’s line is most likely to be the line of best fit, because all the data points are within $100 of the balance it predicts.

C Neither line is likely to be the line of best fit. The best fit line should pass through the points (0, 0) and (12, 800).

D Neither line is likely to be the line of best fit. The data contains the origin, so the equation should be proportional.

STOP


Assessment 118

Section 2 (Calculator-Active)

Answer questions 20–38. Answer questions outlined in green in your test book. Answer all other questions on the Answer Form. You may use a calculator.

20 Consider the graph below and the function y 5 2x 2 10.

6

8

10

4

21

3

5

7

9

0 1 2 3 4 5 6 7 8 9 10

y

x

Part A

How do the rates of change of the two functions compare?

A For the graph, the rate of change is 22 and for the equation, it is 2.

B For the graph, the rate of change is 2 and for the equation, it is 22.

C For both the graph and the equation, the rate of change is 22.

D For both the graph and the equation, the rate of change is 2.

Part B

How do the y-intercepts of the two functions compare?

A For the graph, the y-intercept is 210, and for the equation, it is 10.

B For the graph, the y-intercept is 10, and for the equation, it is 210.

C For both the graph and the equation, the y-intercept is 210.

D For both the graph and the equation, the y-intercept is 10.

Go On


Assessment 1 19

21 Consider the equations shown in each part.

Part A

How many solutions does each equation have? Fill in the blanks in the statements.

Answer The equation x 2 5 55 has solution(s).

Answer The equation y 3 5 90 has solution(s).

Part B

Give the solutions to the equations.

Answer Solution(s) to the equation x 2 5 49:

Answer Solution(s) to the equation y 3 5 64:

Part C

A calculator returns an error if you try to find the square root of 216 but returns a number for the cube root of 216. Why is this?


Assessment 120

Part D

If you use the square root button on a calculator to solve x 2 5 25, it will not give you all the

solutions. However, if you use the cube root button, it will give you all the solutions for

y 3 5 8. Explain why one button gives all the solutions but the other does not. How can you

use a calculator even when it doesn’t give all the solutions?

Go On


Assessment 1 21

22 Jeffrey and Frank walk at different speeds. Frank’s walking speed can be represented by the equation y 5 85x, where x is the time in minutes and y is the distance in meters. The distance Jeffrey walked over time is shown in the graph below.

1000

900

800

700

600

500

400

300

200

100

1 2 3 4 5 6 7 8 9 100

y

x

Time (in minutes)

JEFFREY’S DISTANCE WALKED OVER TIME

Dis

tan

ce (

in m

eter

s) (10, 800)

(5, 400)

Part A

Which of the following can be used to find Jeffrey’s walking speed?

A the slope of the line

B the y-intercept of the line

C the distance between the two points plotted on the line

D It is impossible to find Jeffrey’s walking speed based on the graph.

Part B

How many meters per minute does Frank walk?

A 75

B 80

C 85

D 90


Assessment 122

Part C

How many meters per minute does Jeffrey walk?

A 80

B 85

C 125

D 200

Part D

How many minutes does it take Jeffrey to walk the same distance that Frank can walk in 16 minutes?

A 14

B 15

C 17

D 18

Go On


Assessment 1 23

23 A cylindrical bucket has a radius of 6 inches and a height of 18 inches.

18 inches

Bucket Storage Tank

15 inches

[not drawn to scale]

6 inches

What is the minimum number of buckets of water needed to completely fill a spherical storage tank that has a radius of 15 inches? Shade the buckets to show your answer.

BUCKETS OF WATER


Assessment 124

24 The graph below shows the number of hours Dario worked and the amount of money he earned.

100

90

80

70

60

50

40

30

20

10

1 2 3 4 5 6 7 8 9 100

y

x

Time (in hours)

DARIO’S EARNINGS

Earn

ing

s (i

n d

olla

rs)

(8, 96)

(2, 24)

(5, 60)

What was Dario’s hourly wage?

A $10

B $11

C $12

D $22

Go On


Assessment 1 25

25 Rafael is using this diagram as part of a proof of the Pythagorean Theorem. A right triangle with side lengths a, b, and c is divided into two smaller, similar triangles.

ec

fda

b

For one of the steps in his proof, Rafael needs to find a ratio equivalent to a } c .

Which of these ratios could he use?

A e } a

B e } d

C f } b

D d } f

26 Moira said, “If a right triangle has one side with a length of 3 units and one side with a length of 4 units, then the third side has a length of 5 units.”

Moira’s claim is not true. Give an example of a right triangle with sides of length 3, 4, and a number other than 5. Explain your reasoning.


Assessment 126

27 An archeologist is examining an image of a bone fragment on her computer screen, which has a coordinate grid behind it. The bone fragment is shown below.

0-1

-2

-3

-4

-5

-6

1 2 3 4 5 6 -6 -5 -4 -3 -2 -1

6

5

4

3

2

1

y

x

C

A B

D

BoneFragment

Part A

The archeologist turns the fragment over, reflecting it over the y-axis. What are the new coordinates of the vertices? Write the coordinates for each vertex.

Answer A:

Answer B:

Answer C:

Answer D:

Go On


Assessment 1 27

Part B

The archeologist then rotates the fragment 180 degrees about the origin to see it from a different angle. What are the new coordinates of the vertices? Write the coordinates for each vertex.

Answer A:

Answer B:

Answer C:

Answer D:

Part C

Next, the archeologist moves the bone fragment back to its original position. Then she dilates the image of the bone fragment using a scale factor of 1.5 and a center of dilation at the origin. What are the new coordinates of the vertices? Write the coordinates for each vertex.

Answer A:

Answer B:

Answer C:

Answer D:

Part D

Compare the original and dilated images. Then complete each statement.

The perimeter of the original image is multiplied by a factor of for the dilated image.

The area of the original image is multiplied by a scale factor of for the dilated image.


Assessment 128

Part E

Explain why the area and the perimeter are not both multiplied by the same factor.

Go On


Assessment 1 29

28 A scientist has 23 beakers. There are 223 grams of calcium in each beaker. When empty, a single beaker has a mass of 27 grams.

Part A

What is the total mass of all the empty beakers?

Show your work.

Answer g

Part B

What is the total mass of the calcium in all of the beakers?

Show your work.

Answer g

Part C

What is the total mass of all the beakers and the calcium?

Show your work.

Answer g


Assessment 130

29 Consider the coordinate grid below.

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 100

10

9

8

7

6

5

4

3

2

1

y

x

B’ C’

A’ D’

B CFigure A

Figure A’

A D

Alec incorrectly said that the figures are similar because Figure A’ is the result of dilating

Figure A about the origin with a scale factor of 1 } 2 and then reflecting it over the y-axis.

Which corrects Alec’s error?

A The image was instead a dilation about the origin with a scale factor of 2.

B Instead of being reflected, the image was translated 4 units to the left and 2 units up.

C The image was instead a dilation about the origin with a scale factor of 2, and then it was translated 4 units to the left and 2 units up.

D Instead of being reflected over the y-axis, the image was reflected over the line y 5 x.

Go On


Assessment 1 31

30 In the graph below, triangle ABC is similar to triangle DEC.

x

y

10

2

3

5

6

-1

-2

-3

-4

-5

-6

-1-2-3-4-5-6 2 3 5 6

1

4

4A B

C

DE

Which statement is true?

A slope of ··· EC 5 slope of ··· CB

B slope of ··· DE 5 slope of ··· AC

C slope of ··· CB is twice the value of ··· DE

D slope of ··· CB is three times the value of ··· DE


Assessment 132

31 Antonio purchased this composting bin.

[not drawn to scale]

36 in.

21 in.

In terms of p, what is the volume of the bin? Use the formula below.

V 5 pr2h

A 378p in3

B 756p in3

C 3,969p in3

D 15,876p in3

Go On


Assessment 1 33

32 The gate shown below is made of two horizontal parallel boards and several vertical boards attached at right angles. The measure of /3 is 248.

1

3

2

4

Which explanation could be used to find the measure of /1?

A Since angles 1, 2, and 4 form a triangle, m/1 5 1808 2 90° 2 24°.

B Since m/4 is 90°, m/1 5 908 2 24°.

C Since angles 1, 3, and 4 form a triangle, m/1 5 1808 2 90° 2 24°.

D Since /1 and /2 form a right angle, m/1 5 90° 2 24°.

Go On


Assessment 134

33 Consider the figure below.

-1

-2

-3

-4

-5

-6

-6 -5 -4 -3 -2 -1 1 2 3 4 5 60

6

5

4

3

2

1

y

x

P

Q

R

Part A

What is the length of segment ··· PQ ?

A Ï··· 10 units

B 68 units

C Ï··· 68 units

D 10 units

Part B

What is the length of segment ··· PR ?

A Ï·· 5 units

B 4 units

C 5 units

D Ï··· 34 units


Assessment 1 35

34 An athletic department sold 454 tickets to a sporting event. Adults paid $3.50 per ticket, and students paid $1.00. The total ticket sales were $1,154. If 20 more adult tickets and 20 fewer student tickets had been sold, which statements would be correct? Mark all that apply.

A $154 would have been collected for student tickets.

B $980 would have been collected for adult tickets.

C $1,050 would have been collected for adult tickets.

D $134 would have been collected for student tickets.

E The total ticket sales would have been $1,114.

35 Lines l and m are parallel and are intersected by transversals t and s as shown in the figure below.

Z

C

B AX

Y

I m

tW

s

Part A

Find the sum m/A 1 m/B 1 m/C .

A 90°

B 180°

C 270°

D 360°

Go On


Assessment 136

Part B

Find each of the following sums:

m/A 1 m/X 1 m/W

m/B 1 m/Y

m/C 1 m/Z

Which statement is true?

A Each of the sums is 90°.

B Each of the sums is 180°.

C Each of the sums is 270°.

D Each of the sums is 360°.

Part C

Find the sum m/A 1 m/B 1 m/C 1 m/W 1 m/X 1 m/Y 1 m/Z .

A 180°

B 360°

C 450°

D 540°

Part D

Find the sum m/W 1 m/X 1 m/Y 1 m/Z .

A 180°

B 360°

C 450°

D 540°

Go On


Assessment 1 37

36 Consider the scatter plot below.

10

5 10

y

x0

5

Which of the following describe the relationship between the variables x and y? Mark all that apply.

A no association

B positive association

C negative association

D linear relationship

E nonlinear relationship

F proportional relationship


Assessment 138

37 On Monday, Kendra walked 3 miles and ran 2 miles in 78 minutes on a treadmill. On Tuesday, she walked 2 miles and ran 3 miles in 72 minutes using the same speed settings for the treadmill as she did on Monday. Let w and r represent the rates, in minutes per mile, that Kendra walked and ran on the treadmill, respectively.

Part A

Write an equation to represent the total number of minutes Kendra walked and ran on Monday.

Equation

Part B

Write an equation to represent the total number of minutes Kendra walked and ran on Tuesday.

Equation

Part C

Solve the system of equations from Part A and Part B.

Show your work.

Answer ________________

Part D

What does the point of intersection represent in the context of the problem?

Go On


Assessment 1 39

38 The average height of male children in the United States increases from 34 inches at 2 years old to 59 inches at 12 years old, and follows a linear relationship over this time period.

Part A

Write a linear equation to model the relationship between the average height, y, of a boy who is x years old. Explain your reasoning.

Equation

Part B

Using this equation, what would be the average height of a male, in inches, at age 24?

Answer

Part C

Is the result of Part B reasonable? Explain your reasoning.


Assessment 140

39 Consider the system of equations below:

x 1 2y 5 3

3x 1 6y 5 b

For what value(s) of b does the system have infinitely many solutions?

Answer

STOP

Cut

alo

ng th

e do

tted

line

.

79

Ready® SBAC Mathematics Assessments, Level 8

Name

Teacher Grade

Assessment 1

Section 1

1. ABCDEF

2. ABCD

3A. ABCD

3B. ABCD

4. See page 3.

5. See page 4.

6. ABCD

7. ABCD

8. ABCDEF

9. ABCD

10. See page 9.

11. ABCD

12. ABCD

13. ABCDEF

14. ABCD

15. See page 13.

16A. ABCD

16B. ABCD

17. ABCD

18. ABCDE

19. ABCD

Section 2

20A. ABCD

20B. ABCD

21. See page 19.

22A. ABCD

22B. ABCD

22C. ABCD

22D. ABCD

23. See page 23.

24. ABCD

25. ABCD

26. See page 25.

27. See page 26.

28. See page 29.

29. ABCD

30. ABCD

31. ABCD

32. ABCD

33A. ABCD

33B. ABCD

34. ABCDE

35A. ABCD

35B. ABCD

35C. ABCD

35D. ABCD

36. ABCDEF

37. See page 38.

38. See page 39.

39. See page 40.

TEACHER USE ONLY

4. 01

5. 01234

10. 012345

15. 01234

21. 01234

23. 01

26. 01

27. 0123456

28. 0123

37. 01234

38. 0123

39. 01

Documents

ssessmet 1 - Mrs. Cao's Math Classes€¦ · Fill in the cost in dollars to manufacture different numbers of game consoles. Number of Game Consoles, x Cost (in dollars), y 0 50 100