NAEP NQT v3.0 -- Print Output

Additional Materials (1)

Additional Materials (2)

Additional Materials (3)

Additional Materials (4)

Additional Material (1)

Question 1 refers to Additional Materials (1)

The following question refers to the following information. Each of the 12 sides of the figure above has the same length.
1.	Which of the following angles has a measure of 90° ?

	A)	Angle ABI
	B)	Angle ACG
	C)	Angle ADF
	D)	Angle ADJ
	E)	Angle AEH

Question 2 refers to Additional Materials (1)

The following question refers to the following information. Each of the 12 sides of the figure above has the same length.
2.	Use your ruler to help answer this question. Of the following, which is closest to the perimeter, in inches, of quadrilateral LJFD ?

	A)
	B)
	C)
	D)	7
	E)

Question 3 refers to Additional Materials (1)


3.	Use your centimeter ruler to help answer this question. Of the following, which is closest to the area of parallelogram ABCD above?

	A)	20 square centimeters
	B)	30 square centimeters
	C)	40 square centimeters
	D)	50 square centimeters
	E)	52 square centimeters

Question 4 refers to Additional Materials (1)


4.	In Δ ABC shown above, what is the measure of

	A)	30°
	B)	40°
	C)	50°
	D)	60°
	E)	70°

5.	If a 2 by 18 rectangle has the same area as a square, what is the length of a side of the square?

	A)	4
	B)	6
	C)	8
	D)	10
	E)	12

Question 6 refers to Additional Materials (2)

The following question refers to the following diagram.
6.	Use the ruler provided to find, in terms of inches and feet, what scale has been used to construct the diagram.

7.	A scale drawing of a rectangular room is 5 inches by 3 inches. If 1 inch on this scale drawing represents 3 feet, what are the dimensions of the room?

	A)	5 feet by 3 feet
	B)	5 feet by 9 feet
	C)	15 feet by 3 feet
	D)	15 feet by 5 feet
	E)	15 feet by 9 feet

Did you use the calculator on this question?

8.	A cat lies crouched on level ground 50 feet away from the base of a tree. The cat can see a bird's nest directly above the base of the tree. The angle of elevation from the cat to the bird's nest is 40°. To the nearest foot, how far above the base of the tree is the bird's nest?

	A)	32
	B)	38
	C)	42
	D)	60
	E)	65

Did you use the calculator on this question?

A rectangle is twice as long as it is wide.

(a) If x represents the width of the rectangle, what represents the length?

Answer: ________

(b) What is the area of the rectangle in terms of x ?

Answer: ________

(c) The radius of a sphere is 2 inches. What is the surface area of this sphere, in square inches? Round your answer to the nearest tenth. (Surface area of sphere = 4πr².)

Answer: ________

(d) If the area of the rectangle from part (b) is equal to the surface area of the sphere from part (c), what would be the dimensions of the rectangle? Round your answers to the nearest inch.

Answer: ________ inches by ________ inches

Did you use the calculator on this question?

Question 10 refers to Additional Material (1)

10.	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.
	Who was correct?____________________ Use words or pictures (or both) to explain why.

Question 11 refers to Additional Material (1)

11.	Which of the shapes N, P, and Q has the longest perimeter (distance around)?
	Shape with longest perimeter:____________________ Use words or pictures (or both) to explain why.

12.	Of the following, which is the best unit to use when measuring the growth of a plant every other day during a 2-week period?

	A)	Centimeter
	B)	Meter
	C)	Kilometer
	D)	Foot
	E)	Yard

Did you use the calculator on this question?

13.	A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is )
	Answer:____________________cubic inches

Did you use the calculator on this question?


14.	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)
	Answer:____________________centimeters

15.

On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.

Stimulus Image


16.	In the figure above, the measure of angle ABC is

	A)	55°
	B)	60°
	C)	65°
	D)	125°
	E)	135°

17.

1 gallon = 4 quarts

1 quart = 2 pints

The number of pints in 10 gallons could be determined by performing which of the following operations?

Multiplying 10 by 2

Dividing 10 by 6

Multiplying 10 by 6

Dividing 40 by 2

Multiplying 40 by 2

18.	Which of the following is closest to the height of the door to your classroom?

	A)	1 meter
	B)	2 meters
	C)	4 meters
	D)	7 meters

19.

In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of

POQ changes.

Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.

x-coordinate of P	Area of POQ
4
3
2
1
0


20.	The volume V of a right circular cylinder like the one in the figure above is given by the formula . In terms of , what is the volume of a cylinder with radius r = 4 and height h = 10 ?

	A)
	B)
	C)
	D)
	E)

21.	A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0.40 cubic foot per minute. At this rate, how many hours will it take for the water level to drop 1 foot?

	A)	4
	B)	8
	C)	12
	D)	16
	E)	32


22.	The graph above best conveys information about which of the following situations over a 40-minute period of time?

	A)	Oven temperature while a cake is being baked
	B)	Temperature of water that is heated on a stove, then removed and allowed to cool
	C)	Ocean temperature in February along the coast of Maine
	D)	Body temperature of a person with a cold
	E)	Temperature on a July day in Chicago

Did you use the calculator on this question?

23.	It takes 64 identical cubes to half fill a rectangular box. If each cube has a volume of 8 cubic centimeters, what is the volume of the box in cubic centimeters?

	A)	1,024
	B)	512
	C)	128
	D)	16
	E)	8

Did you use the calculator on this question?


24.	To the nearest whole number, what is the area of the parallelogram above?
	Answer:____________________

Did you use the calculator on this question?


25.	The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?
	Answer:____________________

Did you use the calculator on this question?


26.	In the figure above, a circle with center O and radius of length 3 is inscribed in a square. What is the area of the shaded region?

	A)	3.86
	B)	7.73
	C)	28.27
	D)	32.86
	E)	36.00

Did you use the calculator on this question?


27.	Chris wishes to carpet the rectangular room shown above. To the nearest square yard, how many square yards of carpet are needed to carpet the floor of the room if the closet floor will not be carpeted? (1 square yard = 9 square feet)

	A)	8
	B)	10
	C)	11
	D)	19
	E)	22

Did you use the calculator on this question?


28.	In the figures above, the radius and height of each right circular cylinder are given. If w, x, and y represent the respective volumes of the cylinders, which of the following statements is true?

	A)	y = w = x
	B)	y< x< w
	C)	y< w< x
	D)	w< y< x
	E)	w< x< y

29.

How many hours are equal to 150 minutes?

1	1
	2

2	1
	4

2	1
	3

2	1
	2

2	5
	6


30.	In the figure above, the tube was filled to the 0 mark at the start. How much liquid has been let out?

	A)	10 milliliters
	B)	15 milliliters
	C)	25 milliliters
	D)	40 milliliters
	E)	50 milliliters

31.	If a measurement of a rectangular box is given as 48 cubic inches, then the measurement represents the

	A)	distance around the top of the box
	B)	length of an edge of the box
	C)	surface area of the box
	D)	volume of the box

32.	A circle with diameter 10 centimeters is to be cut from a square of paper 10 centimeters on a side. Of the following, which is closest to the amount of paper left over after the circle is cut out?

	A)	9 square centimeters
	B)	21 square centimeters
	C)	24 square centimeters
	D)	69 square centimeters
	E)	84 square centimeters

Did you use the calculator on this question?


33.	Semicircles are constructed on the sides of an equilateral triangle, as shown in the figure above. Of the following, which best approximates the sum of the lengths of the three darkened arcs?

	A)	4.4258
	B)	4.7124
	C)	6.0000
	D)	6.7124
	E)	9.4258

Did you use the calculator on this question?

Question 1

Key


1.	Which of the following angles has a measure of 90° ?

	A)	Angle ABI
	B)	Angle ACG
	C)	Angle ADF
	D)	Angle ADJ
	E)	Angle AEH

Question 2

Key


2.	Use your ruler to help answer this question. Of the following, which is closest to the perimeter, in inches, of quadrilateral LJFD ?

	A)
	B)
	C)
	D)	7
	E)

Question 3

Key


3.	Use your centimeter ruler to help answer this question. Of the following, which is closest to the area of parallelogram ABCD above?

	A)	20 square centimeters
	B)	30 square centimeters
	C)	40 square centimeters
	D)	50 square centimeters
	E)	52 square centimeters

Question 4

Key


4.	In Δ ABC shown above, what is the measure of

	A)	30°
	B)	40°
	C)	50°
	D)	60°
	E)	70°

Question 5

Key


5.	If a 2 by 18 rectangle has the same area as a square, what is the length of a side of the square?

	A)	4
	B)	6
	C)	8
	D)	10
	E)	12

Question 6

Scoring Guide

Solution:
1 inch = 12 feet

Score & Description

	Correct
	Correct response – may not include more than one incorrect measurement on the diagram (i.e., 30 feet = 3 inches).

Partial

Unreduced form of answer; e.g., 3 inches = 36 feet or , may include additional incorrect information.

Only measures sides. All 6 sides measured must be correct and must include units (inches or feet). All sides must be measured.

Gives scale for more than 1 side and does not indicate 1 inch = 12 feet as the answer.

	Incorrect
	Any incorrect response.

Correct - Student Response

6	Use the ruler provided to find, in terms of inches and feet, what scale has been used to construct the diagram.

	Scorer Comments: This response received full credit because the student correctly determined the scale used in the drawing and gave the answer in reduced form.

Partial - Student Response

6	Use the ruler provided to find, in terms of inches and feet, what scale has been used to construct the diagram.

	Scorer Comments: This response received partial credit because the student did not reduce the answer.

Incorrect - Student Response

6	Use the ruler provided to find, in terms of inches and feet, what scale has been used to construct the diagram.

	Scorer Comments: This response received no credit because the answer given was incorrect.

Question 7

Key


7.	A scale drawing of a rectangular room is 5 inches by 3 inches. If 1 inch on this scale drawing represents 3 feet, what are the dimensions of the room?

	A)	5 feet by 3 feet
	B)	5 feet by 9 feet
	C)	15 feet by 3 feet
	D)	15 feet by 5 feet
	E)	15 feet by 9 feet

Question 8

Key


8.	A cat lies crouched on level ground 50 feet away from the base of a tree. The cat can see a bird's nest directly above the base of the tree. The angle of elevation from the cat to the bird's nest is 40°. To the nearest foot, how far above the base of the tree is the bird's nest?

	A)	32
	B)	38
	C)	42
	D)	60
	E)	65

Question 9

Scoring Guide

Solution:

Part (a) 2x

Part (b) 2x² or x(2x) or (2x)x or x · 2x or 2x · x

Part (c) 4πr² = 4π(2)² = 16π

16(3.14) gives 50.2 or 16π gives 50.3

Score as correct 16π or any value in the range 50.2 to 50.3, inclusive.

Part (d) 2x² = 50.2 2x² = 50.3

x² = 25.1 x² = 25.15

x ≈ 5.01 x ≈ 5.01

So the rounded dimensions are 5 inches by 10 inches.

Score & Description

	Extended
	Correct response.

	Satisfactory
	Three parts correct.

	Partial
	Two parts correct.

	Minimal
	One part correct.

	Incorrect
	Incorrect response.

Extended - Student Response

9	A rectangle is twice as long as it is wide.

	Scorer Comments: This response received full credit because the student correctly answered all four parts of the problem.

Satisfactory - Student Response

9	A rectangle is twice as long as it is wide.

	Scorer Comments: This response received a satisfactory score because the student correctly answered parts a, c, and d.

Partial - Student Response

9	A rectangle is twice as long as it is wide.

	Scorer Comments: This response received partial credit because the student correctly answered parts a and c.

Minimal - Student Response

9	A rectangle is twice as long as it is wide.

	Scorer Comments: This response received minimal credit because the student correctly answered part c only.

Incorrect - Student Response

9	A rectangle is twice as long as it is wide.

	Scorer Comments: This response received no credit because all four parts of the problem were answered incorrectly.

Question 10

Scoring Guide

Solution:
An adequate explanation with or without Bob.
May say "neither" or "both".
Parts of P overlaps N, and part sticks out. The sticking out part is equal to the left out part of N.

OR
Two P's match two N's therefore they have the same area. (Therefore, one N has the same area as one P.)

OR
Areas are equal because height of P is the same as the height of N, and the base of P is twice the base of N.

OR
Either of these two figures alone are acceptable.

Scoring Guide

In this question, a student has to compare two given shapes with respect to their area. A student needed to realize that area meant the amount of surface a shape covers. They also needed to know how to compare the areas of the shapes. Using pictures and words to make the comparison between the areas of N and P, a student could have given a variety of explanations such as two shape P’s match with two shape N’s; therefore, one N has the same area as one P. They also could have used the geometric shapes placed one on top of the other to see how their areas compared.

Score & Description

	Correct
	Correct response

	Incorrect #2
	Bob was correct, but explanation not given or inadequate

	Incorrect #1
	Any response that answers Carmen or Tyler to "Who was correct?" OR omits the name and gives no satisfactory explanation

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit.

Correct - Student Response

10	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.


10	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.

Incorrect #2 - Student Response

10	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.


10	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.

Incorrect #1 - Student Response

10	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.


10	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.

Question 11

Scoring Guide

Solution:
P has the longest perimeter.

Adequate explanation

e.g. hold pieces up to each other, moving edges around to match up.
see which piece has some edge left over.

Copy the sides of each piece, in a line as shown below, and compare lengths

Scoring Guide

In this question, a student has to estimate the perimeter of each shape and then compare perimeters to see which shape has the longest perimeter. This question requires a student to come up with some method to determine the perimeter of the shapes without the use of a ruler and to explain why he or she selected the shape.

Score & Description

	Correct
	Correct response

	Incorrect #2
	P has the longest perimeter but explanation not given or inadequate

	Incorrect #1
	Any response that gives Q or N the longest perimeter OR Does not indicate that P has the longest perimeter

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit.

Correct - Student Response

11	Which of the shapes N, P, and Q has the longest perimeter (distance around)?


11	Which of the shapes N, P, and Q has the longest perimeter (distance around)?

Incorrect #2 - Student Response

11	Which of the shapes N, P, and Q has the longest perimeter (distance around)?


11	Which of the shapes N, P, and Q has the longest perimeter (distance around)?

Incorrect #1 - Student Response

11	Which of the shapes N, P, and Q has the longest perimeter (distance around)?


11	Which of the shapes N, P, and Q has the longest perimeter (distance around)?

Question 12

Key


12.	Of the following, which is the best unit to use when measuring the growth of a plant every other day during a 2-week period?

	A)	Centimeter
	B)	Meter
	C)	Kilometer
	D)	Foot
	E)	Yard

Question 13

Scoring Guide

Solution:

Score & Description

	Correct
	Correct response, 283, with correct accompanying work OR 283 with no work.

	Partial
	Response shows correct substitutions into the formula but does not round answer correctly to get 283 OR 282.74334 with no work (uses key) OR 282.6 with no work (uses 3.14) OR 282.8571 with no work (uses 22/7)

	Incorrect
	Incorrect response

Correct - Student Response

13	A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is )

Partial - Student Response

13	A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is )


13	A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is )

Incorrect - Student Response

13	A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is )

Question 14

Scoring Guide

Solution:
Since the diameter is 5 centimeters, 5 × 3.14 = 15.70 centimeters

Scoring Guide

In this question, a student has to use the centimeter ruler that was provided to measure either the diameter or radius of the circle. Once the student knows the measurement of either the diameter or radius, the circumference of the circle can be determined using the formula Πd or 2Πr.

Score & Description

	Correct #1
	Correct response

	Correct #2
	Responses that are between 15.0 and 16.4 centimeters

	Incorrect #2
	Any response in inches

	Incorrect #1
	Any incorrect response other than as described above

* The use of more than one correct category in this question enabled NAEP to gather data on different ways in which students responded correctly to this question. Any response that fell into one of these correct categories earned full credit.

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit.

Correct #1 - Student Response

14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)


14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)

Correct #2 - Student Response

14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)


14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)

Incorrect #2 - Student Response

14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)


14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)

Incorrect #1 - Student Response

14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)


14	Using the centimeter ruler provided, find the circumference of the circle with center C above. (Use = 3.14.)

Question 15

Scoring Guide

Solution:

Either one of the darkened arcs AB illustrated in the circles below is a correct answer.

Scoring Guide

In this question, a student has to use a protractor (that was provided at the assessment administration) to draw a 235Â° arc on a circle and then label the endpoint of that arc. Full credit is earned if a student correctly darkens the arc (within a certain range of tolerance) and labels the missing endpoint, B, of the arc correctly.

Score & Description

	Correct #1
	Correct response 235° (±2° tolerance)

	Correct #2
	An arc length that is not 235° but within ±5° of 235° and point B is placed on the circle

	Incorrect #3
	A sector or an arc of 235° (±5°) which does not have an endpoint at point A

	Incorrect #2
	Point B placed correctly on the circle (within ±5° of the correct location) but the arc is not clearly indicated

	Incorrect #1
	Any incorrect response other than as described above

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit.

Correct #1 - Student Response

15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.


15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.

Correct #2 - Student Response

15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.

Incorrect #3 - Student Response

15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.

Incorrect #2 - Student Response

15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.


15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.

Incorrect #1 - Student Response

15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.


15	On the circle with center C shown below, use the protractor to locate and label a point B that creates an arc AB with measure 235°. Darken this arc.

Question 16

Key


16.	In the figure above, the measure of angle ABC is

	A)	55°
	B)	60°
	C)	65°
	D)	125°
	E)	135°

Question 17

Key

17.

1 gallon = 4 quarts

1 quart = 2 pints

The number of pints in 10 gallons could be determined by performing which of the following operations?

Multiplying 10 by 2

Dividing 10 by 6

Multiplying 10 by 6

Dividing 40 by 2

Multiplying 40 by 2

Question 18

Key


18.	Which of the following is closest to the height of the door to your classroom?

	A)	1 meter
	B)	2 meters
	C)	4 meters
	D)	7 meters

Question 19

Scoring Guide

Score & Description

Correct #1

All 5 correct entries.

x-coordinate of P	Area of POQ
4	12
3	9
2	6
1	3
0	0

	Correct #2
	4 correct entries

	Incorrect #2
	1 or 2 or 3 correct entries

	Incorrect #1
	No correct entries in the table.

*The use of more than one correct category in this question enabled NAEP to gather data on different ways students responded correctly to this question. Any one of these responses that fell into one of these correct categories earned full credit.

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit.

Correct #1 - Student Response

19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.


19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.

Correct #2 - Student Response

19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.


19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.

Incorrect #2 - Student Response

19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.


19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.

Incorrect #1 - Student Response

19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.


19	In the figure above, point Q is fixed and point P starts at 4 and moves left along the x-axis. As P moves left along the x-axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.

Question 20

Key


20.	The volume V of a right circular cylinder like the one in the figure above is given by the formula . In terms of , what is the volume of a cylinder with radius r = 4 and height h = 10 ?

	A)
	B)
	C)
	D)
	E)

Question 21

Key


21.	A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0.40 cubic foot per minute. At this rate, how many hours will it take for the water level to drop 1 foot?

	A)	4
	B)	8
	C)	12
	D)	16
	E)	32

Question 22

Key


22.	The graph above best conveys information about which of the following situations over a 40-minute period of time?

	A)	Oven temperature while a cake is being baked
	B)	Temperature of water that is heated on a stove, then removed and allowed to cool
	C)	Ocean temperature in February along the coast of Maine
	D)	Body temperature of a person with a cold
	E)	Temperature on a July day in Chicago

Question 23

Key


23.	It takes 64 identical cubes to half fill a rectangular box. If each cube has a volume of 8 cubic centimeters, what is the volume of the box in cubic centimeters?

	A)	1,024
	B)	512
	C)	128
	D)	16
	E)	8

Question 24

Scoring Guide

Score & Description

Correct #1

188

A = ( + 7) x 13

A = 188.28308

A = 188

Correct #2

189

B= + 7 =
B=7.5+7
B=14.5

A = (14.5)(13) = 188.5 = 189

	Incorrect #3
	182

	Incorrect #2
	91

	Incorrect #1
	Any incorrect response other than those described in Incorrect #2, Incorrect #3.

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit.

Correct #1 - Student Response

24	To the nearest whole number, what is the area of the parallelogram above?


24	To the nearest whole number, what is the area of the parallelogram above?

Correct #2 - Student Response

24	To the nearest whole number, what is the area of the parallelogram above?

Incorrect #3 - Student Response

24	To the nearest whole number, what is the area of the parallelogram above?

Incorrect #2 - Student Response

24	To the nearest whole number, what is the area of the parallelogram above?

Incorrect #1 - Student Response

24	To the nearest whole number, what is the area of the parallelogram above?


24	To the nearest whole number, what is the area of the parallelogram above?

Question 25

Scoring Guide

Score & Description

Correct

BE==4, and Area =½×4×10=20 so,

60+20=80

	Incorrect
	Any incorrect response.

Correct - Student Response

25	The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?


25	The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?

Incorrect - Student Response

25	The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?


25	The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?

Question 26

Key


26.	In the figure above, a circle with center O and radius of length 3 is inscribed in a square. What is the area of the shaded region?

	A)	3.86
	B)	7.73
	C)	28.27
	D)	32.86
	E)	36.00

Question 27

Key


27.	Chris wishes to carpet the rectangular room shown above. To the nearest square yard, how many square yards of carpet are needed to carpet the floor of the room if the closet floor will not be carpeted? (1 square yard = 9 square feet)

	A)	8
	B)	10
	C)	11
	D)	19
	E)	22

Question 28

Key


28.	In the figures above, the radius and height of each right circular cylinder are given. If w, x, and y represent the respective volumes of the cylinders, which of the following statements is true?

	A)	y = w = x
	B)	y< x< w
	C)	y< w< x
	D)	w< y< x
	E)	w< x< y

Question 29

Key

29.

How many hours are equal to 150 minutes?

1	1
	2

2	1
	4

2	1
	3

2	1
	2

2	5
	6

Question 30

Key


30.	In the figure above, the tube was filled to the 0 mark at the start. How much liquid has been let out?

	A)	10 milliliters
	B)	15 milliliters
	C)	25 milliliters
	D)	40 milliliters
	E)	50 milliliters

Question 31

Key


31.	If a measurement of a rectangular box is given as 48 cubic inches, then the measurement represents the

	A)	distance around the top of the box
	B)	length of an edge of the box
	C)	surface area of the box
	D)	volume of the box

Question 32

Key


32.	A circle with diameter 10 centimeters is to be cut from a square of paper 10 centimeters on a side. Of the following, which is closest to the amount of paper left over after the circle is cut out?

	A)	9 square centimeters
	B)	21 square centimeters
	C)	24 square centimeters
	D)	69 square centimeters
	E)	84 square centimeters

Question 33

Key


33.	Semicircles are constructed on the sides of an equilateral triangle, as shown in the figure above. Of the following, which best approximates the sum of the lengths of the three darkened arcs?

	A)	4.4258
	B)	4.7124
	C)	6.0000
	D)	6.7124
	E)	9.4258