
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  



12. 
Of the following, which is the best unit to use when measuring the growth of a plant every other day during a 2week period?  
A)  Centimeter  
B)  Meter  
C)  Kilometer  
D)  Foot  
E)  Yard  
Did you use the calculator on this question? 



17. 
The number of pints in 10 gallons could be determined by performing which of the following operations?  
A)  Multiplying 10 by 2  
B)  Dividing 10 by 6  
C)  Multiplying 10 by 6  
D)  Dividing 40 by 2  
E)  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  

 
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 40minute 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? 


 
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  
 
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? 




Scoring Guide 
Solution: 1 inch = 12 feet 
Score & Description  
 
 

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. 



Scoring Guide 
Solution: Part (a) 2x Part (b) 2x^{2} or x(2x) or (2x)x or x · 2x or 2x · x Part (c) 4πr^{2} = 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) 2x^{2} = 50.2 2x^{2} = 50.3 x^{2} = 25.1 x^{2} = 25.15 x ≈ 5.01 x ≈ 5.01 So the rounded dimensions are 5 inches by 10 inches. 
Score & Description  
 
 
 
 


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. 

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  
 
 

* 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. 
Scoring Guide 
Solution: P has the longest perimeter. Adequate explanation e.g. hold pieces up to each other, moving edges around to match
up. OR 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  
 
 

* 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)? 

Scoring Guide 
Solution: 
Score & Description  
 
 

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 ) 
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  
 
 
 

* 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.) 
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  
 
 
 
 

* 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 
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. 


Scoring Guide 
Score & Description  
 
 
 

*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 xaxis. As P
moves left along the xaxis 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 xaxis. As P
moves left along the xaxis 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 xaxis. As P
moves left along the xaxis 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 xaxis. As P
moves left along the xaxis 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 xaxis. As P
moves left along the xaxis 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 xaxis. As P
moves left along the xaxis 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 xaxis. As P
moves left along the xaxis 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 xaxis. As P
moves left along the xaxis 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. 




Scoring Guide 
Score & Description  
 
 
 
 

*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 
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? 
Scoring Guide 
Score & Description  
 

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? 






