End-of-Grade Mathematics

Name

RELEASED FORM

R

Grade 8

SE D

Form R

EA

North Carolina

End-of-Grade Tests—Grade 8

R EL

Mathematics–Calculator Active

Public Schools of North Carolina

www.ncpublicschools.org State Board of Education Department of Public Instruction Office of Accountability Division of Accountability and Services/North Technology Services Carolina Testing Program Division North Raleigh, of Accountability Carolina 27699-6314 Services/North Carolina Testing Program Raleigh, North Carolina 27699-6314 © 2007 © 2009 2004 All All rights rights reserved. reserved. This This document document may may not not be be reproduced reproduced by by any any means, means, in in whole whole or or in in part, part, without without prior prior written permission from the North Carolina Department of Public Instruction, Raleigh, North written permission from the North Carolina Department of Public Instruction, Raleigh, North Carolina. Carolina.

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6 2

B

4 3

C

3 5

D

2 10

A 70-foot tree has a 35-foot shadow. If the building next to the tree has an 80-foot shadow, how tall is the building? A

What is the approximate length of the diagonal of a square if the perimeter of the square is 12 ft? A

1.7 ft

B

3.5 ft

C

4.2 ft

D

12.7 ft

160 feet

5.

B

120 feet

C

115 feet

D

40 feet

Ralph’s garden is in the shape of a square. How does the area of the garden change if he doubles the length of each side of the garden? A

The area is halved.

B

The area is doubled.

C

The area is tripled.

D

The area is quadrupled.

Which set of real numbers contains only rational numbers? A

{

B

{ 144,

13 5 , 3, 2

C

{ 169,

5 , 2

}

R EL

3.

A

4.

SE D

2.

Which is the largest value?

EA

1.

North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 2009

D

Page 1

121,

{ 169,

196,

24, 12

10

}

121, 14 4

58 13 , , 3 2

}

31

}

6.

Constance bought a box to hold her jelly beans. The dimensions of the box are 6 inches by 2 inches by 1 inch. The jelly beans weigh a total of 36 ounces. If each cubic inch inside the box can hold two ounces, how many ounces of jelly beans will have to be left out of the box? A

24

B

18

C

12

D

6

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7.


In the figure shown below, ABC.

+

+ A′B′C′ is the image produced by applying a dilation to y +8 +7

A

SE D

+6 +5 +4 +3

A’

+2

C

C’

+1

—8 —7 —6 —5 —4 —3 —2 —1 0 —1 —2 —3 —4 —5

+ 1 + 2 + 3 + 4 +5 + 6 + 7 + 8

x

B’

B

—6 —7 —8

1 3

B

2 5

C

1 2

D

5 2

R EL

A

EA

What is the scale factor for this dilation?

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Which scatterplot shows a positive correlation between the variables?

A

x

D

y

x

x

y

0

x

R EL

0

y

0

EA

0

C

B

y

SE D

8.


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The direct route from Marta’s apartment to work is a road that is a straight line. The road is closed for repairs. Marta had to drive 8 miles west and then 6 miles south to get to work. She returned home by the same route. How many miles would she have saved round-trip if she had taken the direct route? A

2

B

8

C

10

Harold took a survey on America’s favorite movies by asking 50 students at his school to complete the survey. Which is the best reason why his survey may be flawed? A

The students were not old enough to take a survey.

B

Some students are not American citizens.

C

The students may include people who do not go to the movies.

D

Harold is not getting a diverse representation from the American population.

24

R EL

EA

D

10.

SE D

9.


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11.


The data displayed represent what type of correlation? y

SE D

30

25

20

15

5

0

EA

10

0

10

15

20

25

30

35

a positive correlation where the y values are exactly predicted by the line of best fit

R EL

A

5

x

B

a negative correlation where the y values are exactly predicted by the line of best fit

C

a positive correlation where the y values are approximately predicted by the line of best fit

D

a negative correlation where the y values are approximately predicted by the line of best fit

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12.

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The Smiths made a scatterplot comparing their daily electricity costs to the outside temperature.

Smith Family Electricity Costs

SE D

y

80 70 60 50 40 30

EA

20

0

x

50° 60° 70° 80° 90° 100° Daily High Temperature (°F)

If the high temperature on a day is 95°, about how much will their cost for electricity be on that day? $0.95

R EL

A B

$0.70

C

$0.67

D

$0.64

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Which data will most likely show a negative correlation when graphed on a scatterplot? A B

C

D

15.

Solve for b: 3b3 = 81

the outside temperature and the number of people wearing gloves

A

9

B

6.2

SE D

13.


the distance a student lives from school and the amount of time it takes to get to school the number of visitors at an amusement park and the length of the lines for the rides a student’s height and grade point average

16.

C

3

D

1.4

Which statement best describes the

similarities of the graphs 2 y = 5 x + 6 and 2 y = 3 x + 6 ?

7

7

A

78

B

79

C

83

D

95

B

The slopes are the same.

C

The x-intercepts are the same.

D

The graphs are identical.

EA

Hector’s math test grades for the final quarter are 89, 93, 100, 98, and 95. He has one more test to take this quarter. All tests count equally. What is the minimum grade Hector must make on the last test in order to obtain an average of at least 93?

The y-intercepts are the same.

R EL

14.

A

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17.


What is the slope of the line graphed below?

y +6 +5

SE D

+4 +3 +2

+1

—6 —5 —4 — 3 —2 —1 0 —1

+1 +2 +3 +4 +5 +6

x

—2

—3

—4 —5

A B

—

2

−1 2

1

D

2

R EL

C

EA

—6

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18.


The equation for a balanced seesaw is w1d1 = w2d2 . As shown in the figure below, w1 and w2 are weights, and d2 and d1 are distances from the balance point.

19.

y-intercept of

w2

If w1 = 50 pounds , d1 = 5 feet , and w2 = 100 pounds , what value of

d2 would balance the seesaw? 2.5 feet

B

5.0 feet

C

7.5 feet

D

10.0 feet

10. Which is an

2 x − 3 y = — 30

B

2 x − 3 y = —10

C

2 x + 3 y = 10

D

2 x + 3 y = — 30

R EL

EA

A

and a

SE D

w1

d2

—

3

equation of the line?

A

d1

—2

A line has a slope of

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20. Which is the correct graph for 3 y = 2 x − 3 ? y +6

+6

+5

+5

+4

+4 +3

+3 +2

+2

+1

+1 —6

—5

—4

—3

—2

y

B

SE D

A

—1 0 —1

+ 1 +2 +3 +4 +5 +6

—2

x

—6

—5

—4

—3

—2

—4

—5

—5

—6

EA

—6

y

—4

—3

—2

y

D

+6

+6

+5

+5

+4

+4

+3

+3

+2

+2

+1

+1

R EL Page 10

—5

—1 0 —1

x

—3

—4

—6

+ 1 +2 +3 +4 +5 +6

—2

—3

C

—1 0 —1

+ 1 +2 +3 +4 +5 +6

x

—6

—5

—4

—3

—2

—1 0 —1

—2

—2

—3

—3

—4

—4

—5

—5

—6

—6

+ 1 +2 +3 +4 +5 +6

x

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22.

Mary’s fish tank can hold 11 2 gallons of water. Which is the greatest number of gallons of water it can hold without overflowing? A

22

B

15

C

9

D

5

The two legs of a right triangle have lengths 5 and 7. Which term best describes the length of the hypotenuse? A

Which choice lists the lengths in order from least to greatest? A

23.

1 ft, 0.25 ft, 2 ft, 3

8 ft

an irrational number less than 9

SE D

21.


24.

B

an irrational number greater than 9

C

a rational number less than 9

D

a rational number greater than 9

If three is added to both the length and width of the rectangle, what will happen to the area?

B

C

0.25 ft, 1 ft,

8 ft, 2 ft

3

0.25 ft, 1 ft, 2 ft, 3

2 ft, 0.25 ft, 1 ft, 3

Page 11

2 in.

8 ft

A

The area will be four times the original area.

B

The area will be three times the original area.

C

The area will be 12 sq in. more than the original area.

D

The area will be 4 sq in. more than the original area.

8 ft

R EL

D

EA

5 in.

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Joe wanted to know the distance across a river. He made a drawing with two similar triangles, as shown below.

2.0 cm

SE D

25.


5.0 5.0cm m

6.4 cm

x

What is the distance across the river, x? 1.6 m

B

9.4 m

C

16.0 m

D

25.6 m

R EL

EA

A

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A square tile has an area of 110 square centimeters. Which is the best estimate of the length of one side? 10.0 centimeters

B

10.5 centimeters

C

11.0 centimeters

D

11.5 centimeters

The vertices of a rectangle are

( 0, 0 ) , ( 0, 4 ) , ( 2, 4 ) , ( 2, 0 ) .

Which

of the following points is a vertex for the image produced by a dilation with a scale factor of 12 ?

SE D

A

27.

A

( 0, 3 )

B

( 0, 2 )

C

( 0, 1)

D

( 2, 1)

R EL

EA

26.


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28.


Kendra has a rectangular poster board with dimensions of 10 ft by 4 ft. She would like to cut this poster board into 6 pieces, so she can construct a box. 10 ft

SE D

4 ft

If she uses the indicated cutting guides, what will be the dimensions of her box? 2 ft × 2 ft × 4 ft

B

4 ft × 4 ft × 2 ft

C

5 ft × 2 ft × 1 ft

D

10 ft × 4 ft × 1 ft

R EL

EA

A

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29. Which scatterplot displays a negative correlation?

32 31.5 31 30.5 30 29.5 29 28.5

B

28 27.5 1985 1990 1995 2000 2005

2002 2000 1998 1996 1994 1992

28 27.5 1985 1990 1995 2000 2005

D

1.4 1.2 1.0 0.8 0.6 0.4

EA

C

32 31.5 31 30.5 30 29.5 29 28.5

SE D

A

28

29

30

31

32

0.2 0 1985 1990 1995 2000 2005

R EL

1990 1988 27

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30.


Which suggestion would result in an unbiased sample that would best represent the favorite books of the whole eighth-grade class?

31.

This scatterplot could show the relationship between which two variables?

y Ask five randomly chosen students from each class in the eighth grade.

B

Ask eighth-grade girls.

C

Ask randomly chosen eighth-grade students who play sports.

Ask students in the library after school.

x

A

speed of an airplane (x) vs. distance traveled in one hour (y)

B

outside air temperature (x) vs. air conditioning costs (y)

C

age of an adult (x) vs. height of an adult (y)

D

distance traveled (x) vs. gas remaining in the tank (y)

R EL

EA

D

SE D

A

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32.

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According to the pattern established in the scatterplot, what y-value would correspond to an x-value of 11?

y 20 16 14 12 10 8 6 4 2

32

B

25

C

15

D

8

x

R EL

A

5 10 15 20 25 30 35 40

EA

0

SE D

18

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33.

1 0

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Bill collected and plotted data concerning gestation and longevity for a science project. Animal Gestation vs. Longevity 35

25 20 15 10 5 0 0

SE D

30

100 200 300 Gestation (in Days)

400

EA

Based on the line of best fit shown, about how long would an animal be expected to live if its gestation period is 300 days? 10 years

B

12 years

C

20 years

D

22 years

R EL

A

34.

A rental company charges a flat fee of $50 to rent a jet ski. In addition, renters must pay $17.50 per hour of ski use. Which equation correctly represents the total cost, c, to rent a jet ski for h hours? A

c = 50.00h + 17.50

B

c = 17.50h + 50.00

C

c = 32.5 h

D

c = 67.5 h

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35. Heather recorded the 7 a.m. temperature at her house the first five days of four different months. Which data are nonlinear?

January

1

C

°F —

1

2

4

3

9

4

14

5

19

March Day

°F

1

41

2 3 4

Day

°F

1

31

2

29

3

27

4

25

5

23

April

D

Day

°F

1

53

51

2

57

46

3

61

51

4

65

53

5

69

R EL

5

February

SE D

Day

B

EA

A

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Which line has a slope of

A

1 2

and passes through the point ( 2, 3 ) ?

B

y +6

+6

+5

+5 +4

+4 +3

+3

+2

+2

+1 —6 —5 —4 — 3 —2 —1 0 —1

+1

+1 +2 +3 +4 +5 +6

—2

x

x

—4

—5

—5

—6

EA

—6

D

y

y

+6

+6

+5

+5

+4

+4

+3

+3

+2

+2

+1

+1

R EL

—6 —5 —4 — 3 — 2 — 1 0 —1

+1 +2 +3 +4 +5 +6

—3

—4

Page 20

— 6 —5 —4 — 3 — 2 — 1 0 —1 —2

—3

C

y

SE D

36.


+1 +2 +3 +4 +5 +6

x

— 6 —5 —4 — 3 — 2 — 1 0 —1

—2

—2

—3

—3

—4

—4

—5

—5

—6

—6

+1 +2 +3 +4 +5 +6

x

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What is the equation of the line

( )

that contains the point 1 , —3 2

—

and has a slope of 3? A

y = —3 x − 3

B

y = —3 x − 17

2

2

C

y = —3 x + 3

D

y = —3 x + 17

2

A cube has a volume of 24 cubic units. What is the approximate length of each side of the cube? A

8 units

B

4.9 units

C

2.9 units

D

2 units

R EL

EA

2

38.

SE D

37.


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39.


The equation y = 9 x + 32 can be used to find Fahrenheit temperature (y) when given 5

Celsius temperature (x). If this equation were graphed in a coordinate plane, what would be the x- and y-intercepts?

)

B

x-intercept = ( 0, 32 ) ; y-intercept =

C

− x-intercept = 0, 160 ; y-intercept = ( 32, 0 ) 9

D

x-intercept =

(

− 160 9

)

(

9

− 160 9

,0

)

, 0 ; y-intercept = ( 0, 32 )

EA

(

)

SE D

− x-intercept = ( 32, 0 ) ; y-intercept = 0, 160

A truck rental company charges $20 plus 9 cents per mile. Joe’s friend offers to rent Joe his truck for $35 and won’t charge him mileage. What is the minimum number of miles Joe has to drive to save money using his friend’s truck? A

17

B

55

R EL

40.

(

A

C

121

D

167

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What is the order of the numbers from least to greatest? 3

2,

A

B

1.6,

2,

3

16, 15 , 1.6 7

16, 15 7

2, 1.6, 15 ,

3

7

C

1.6,

D

2,

2, 15 , 7

3

43.

3

16

16

16, 15 , 1.6 7

The solution to an inequality is x ≥ 5. Which number is included in that solution? A

10

B

30

C

2 5

D

3 2

SE D

41.


44.

What is the perimeter of a triangle whose dimensions are three times the size of PQR ?

+

42.

EA

R

The formula s = 20 273 + T gives an estimate for the speed (s) of sound in meters per second when the air temperature is T°C. About how fast is the speed of sound when the temperature is —5°C ? 268 m/s

R EL

A

7 ft 4.1 ft

P

10 ft

A

23 ft

B

278 m/s

B

27.1 ft

C

327 m/s

C

69 ft

D

333 m/s

D

81.3 ft

Page 23

6 ft

Q

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45.


A tree has a shadow 12 feet long. At the same time, John, who is five feet tall, has a shadow 4 feet long. If Sherry wants to find the height of the tree, which proportion should she use?

47.

The diagonal of a square television screen measures 27 inches. What is the approximate length of the screen?

A

B

x 8 = 5 4

C

D

x 5 = 8 4 x 5 = 12 4

13 in.

SE D

A x 5 = 4 12

48.

B

15 in.

C

19 in.

D

21 in.

The coffee can below is 43 full.

Triangle ABC has vertices at A (2, 2), B (2, 7), and C (6, 3). This triangle is dilated by a scale factor of 3. What is the location of point C ′ ? A

(2, 1)

B

(6, 6)

R EL

46.

EA

3 in.

C

(6, 21)

D

(18, 9)

Page 24

8 in.

Coffee

How much coffee is in the can? A

about 57 in.3

B

about 130 in.3

C

about 170 in.3

D

about 226 in.3

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49.


Each point on the graph represents the relationship between the number of pencils in a package and how much the package costs.

SE D

4

3

W

Z

2

Y

1

EA

X

0

16 8 24 32 40 48 Number of Pencils per Package

Which package has the highest cost for each pencil? A

W X

C

Y

D

Z

R EL B

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50.


Charles researched the price of video games over the last decade.

Video Game Prices

SE D

30 25 20 15 10 5

1997

1999 Year

2001

2003

2005

EA

1995

Based on the data shown, what would be the projected price of a video game in 2005? $9.50

B

$15.50

C

$18.00

D

$19.50

R EL

A

51.

Mr. Larson’s first math test resulted in the following grades: 21, 23, 35, 43, 46, 50, 53, 59, 62, 66, 66, 66, 67, 75, 89, 95

A passing grade is anything above a 60. Mr. Larson says the central tendency for the class was to fail the test. Which statistical measure supports his claim? A

mode

B

median

C

upper quartile

D

mean

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52.


Kevin made a scatterplot of noon temperatures for a two-week period.

Noon Temperatures

76° 74° 72° 70° 68° 66° 64° 62° 60°

SE D

78°

2

4

6

8 10 12 14 16 18

EA

Day

Which statement about the data is most accurate?

The temperature had a slight increase each day.

B

The temperature had a slight decrease each day.

C

There was a trend for the temperature to increase during the second week.

R EL

A

D

Page 27

There was a trend for the temperature to increase during the first week.

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54.

A scatterplot is shown to have a negative relationship between the two variables. Which line of best fit could represent that scatterplot? A

y = —2 x + 4

B

y = —1

C

y = x−5

D

y = 3x + 4

56.

The cost of attending the state fair is a $5.00 admission charge and $1.50 per ride. Elizabeth’s mother gave her d dollars to spend at the state fair. Which equation could be used to determine the maximum number of rides, r, Elizabeth can go on?

SE D

53.


A

r = 1.50d + 5.00

B

r = ( d + 5.00 ) ÷ 1.50

C

r = ( d − 5.00 ) ÷ 1.50

D

r = 1.50d − 5.00

Which would be an appropriate first step to solve y = 5x + 3 for x ?

57.

subtract 3 from both sides

B

add 3 to both sides

C

subtract 5 from both sides

D

add 5 to both sides

The equation d = 65h describes the distance (d) a vehicle travels in

EA

A

h hours. Based on this formula, how long will it take a car to travel

Brittany programs the treadmill so that she will burn 3.2 calories per minute as she works out. What is the equation relating walking time (x) in minutes to total calories burned (y)?

R EL

55.

90 miles?

A

y = 3.2x

B

y = 3.2 + x

C

y = 3.2

D

y= x 3.2

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x

58.

A

98 minutes

B

83 minutes

C

43 minutes

D

25 minutes

Which equation is nonlinear?

A

2x − y = 9

B

y = x2 + 3

C

y = 2x − 3

D

x= y

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NCDPI

59.


What is the slope of the line that

(

)

( 4,2 ) ? A

5 3

B

3 5

C

D

What is the equation of the line with a slope of 2 and a y-intercept of 4 ? 3

A

2 x + 3 y = 12

B

2x + 3 y = 4

C

3x − 2 y = —4

D

2 x − 3 y = —12

SE D

passes through the points 1, — 3 and

60.

—3 5

—5 3

EA

STOP

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End of Mathematics– Calculator Active

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North Carolina Test of Mathematics Grade 8 Form R RELEASED Fall 2009 Answer Key EOG

CALCULATOR ACTIVE

R 31 July 2009

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Goal 1 – Number and Operations 1 – Number and Operations 1 – Number and Operations 2 – Measurement 2 – Measurement 3 – Geometry 3 – Geometry 4 – Data Analysis and Probability 3 – Geometry 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 1 – Number and Operations 1 – Number and Operations 1 – Number and Operations 2 – Measurement 2 – Measurement 3 – Geometry 3 – Geometry 3 – Geometry 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra

EA SE D

Correct Answer A C C A D C C A B D C C A C C A D A D B B C A A C B B A B A D D C B C B A C D

EL

Item Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

7

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North Carolina Test of Mathematics Grade 8 Form R RELEASED Fall 2009 Answer Key 5 – Algebra 1 – Number and Operations 1 – Number and Operations 1 – Number and Operations 2 – Measurement 2 – Measurement 3 – Geometry 3 – Geometry 3 – Geometry 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 4 – Data Analysis and Probability 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra 5 – Algebra

EA SE D

D B C B C D D C C A B D D A A A C B B A D

R

EL

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

31 July 2009

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Scale Score 332 333 333 334 334 335 335 336 337 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 357 358 359 360 360 361 361 362 363 363 364 364

R

EL

EA SE

Raw Score 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

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North Carolina Test of Mathematics Grade 8 Form R RELEASED Fall 2009 Raw to Scale Score Conversion

10 August 2009

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365 366 366 367 367 368 369 369 370 371 372 372 373 374 375 377 378 381 383

R

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EA SE

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

D

North Carolina Test of Mathematics Grade 8 Form R RELEASED Fall 2009 Raw to Scale Score Conversion

10 August 2009

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