 
3. 
On the curve above, what is the best estimate of the value of x when y = 0?  
A)  
B) 
1.1  
C) 
1.4  
D) 
1.7  
E) 
1.9  
 
4. 
According to the pattern suggested by the four examples above, how many consecutive odd integers are required to give a sum of 144 ?  
A) 
9  
B) 
12  
C) 
15  
D) 
36  
E) 
72  


1, 9, 25, 49, 81, ...
 
12. 
The same rule is applied to each number in the pattern above. What is the 6th number in the pattern?  
A)  40  
B)  100  
C)  121  
D)  144  
E)  169  
 
13. 
The map above shows eight of the counties in a state. The largest city in the state can be found at location B3. In which county could this city lie?  
A)  Adams or Carlton  
B)  Adams or Smith  
C)  Carlton or Elm  
D)  Dade or Polk  
E)  Polk or Smith  
 
14. 
Which of the following equations represents the relationship between x and y shown in the table above?  
A)  y = x^{2} + 1  
B)  y = x + 1  
C)  y = 3x  1  
D)  y = x^{2}  3  
E)  y = 3x^{2}  1  

 
16. 
The objects on the scale above make it balance exactly. According to this scale, if balances , then balances which of the following?  
A)  
B)  
C)  
D)  
17. 
What are all the whole numbers that make 8  > 3 true?  
A)  0, 1, 2, 3, 4, 5  
B)  0, 1, 2, 3, 4  
C)  0, 1, 2  
D)  5  

 
19. 
In the figure above, if ABCD is a square, then the coordinates of vertex C are  
A)  (4,5)  
B)  (3,4)  
C)  (3,2)  
D)  (5,4)  
E)  (5,2)  
20. 
Which of the following equations is true for the three pairs of x and y values in the table above?  
A)  3x + 2 = y  
B)  3x  2 = y  
C)  2x + 3 = y  
D)  2x  3 = y  
E)  x  3 = y  
 
21. 
If the list of fractions above continues in the same pattern, which term will be equal to 0.95?  
A)  The 100th  
B)  The 95th  
C)  The 20th  
D)  The 19th  
E)  The 15th  
Did you use the calculator on this question? 
22. 
Tetsu rides his bicycle x miles the first day, y miles the second day, and z miles the third day. Which of the following expressions represents the average number of miles per day that Tetsu travels?  
A)  x + y + z  
B)  xyz  
C)  3(x + y + z)  
D)  3(xyz)  
E)  (x + y + z)/3  
Did you use the calculator on this question? 
23. 
If 3 + w = b, then w =  
A)  b/3  
B)  b× 3  
C)  b + 3  
D)  3  b  
E)  b  3  
Did you use the calculator on this question? 

25. 
If the value of the expression x + 2 is less than 12, which of the following could be a value of x?  
A)  16  
B)  14  
C)  12  
D)  10  
E)  8  
26. 
In a coordinate plane, the points (2,4) and (3,1) are on a line. Which of the following must be true?  
A)  The line crosses the xaxis.  
B)  The line passes through (0,0).  
C)  The line stays above the xaxis at all times.  
D)  The line rises from the lower left to the upper right.  
E)  The line is parallel to the yaxis.  


30. 
If n represents an even number greater than 2, what is the next larger even number?  
A)  n + 1  
B)  2n + 1  
C)  2n  
D)  n + 2  
E)  n^{2}  
 
31. 
Allen, Bridgitte, Chaz, and
Diann each live in a different house on the same side of a street. The
houses and their numbers are shown above.
 
A)  Allen only  
B)  Chaz only  
C)  Diann only  
D)  Chaz or Diann  
E)  Any of these four people could live in house number 2.  
32. 
Which of the following ordered pairs (x, y) is a solution to the equation 2x  3y = 6?  
A)  (6, 3)  
B)  (3, 0)  
C)  (3, 2)  
D)  (2, 3)  
E)  (0, 3)  
33. 
A plumber charges customers $48 for each hour worked plus an additional $9 for travel. If h represents the number of hours worked, which of the following expressions could be used to calculate the plumber's total charge in dollars?  
A)  48 + 9 + h  
B)  48 x 9 x h  
C)  48 + (9 x h)  
D)  (48 x 9) + h  
E)  (48 x h) + 9  


37. 
If represents the number of newspapers that Lee delivers each day, which of the following represents the total number of newspapers that Lee delivers in 5 days?  
A)  
B)  
C)  
D)  
 
38. 
John records the weight of his puppy every month in a chart like the one shown above. If the pattern of the puppy's weight gain continues, how many pounds will the puppy weigh at 5 months?  
A)  30  
B)  27  
C)  25  
D)  24  
 
39. 
Children's pictures are to be hung in a line as shown in the figure above. Pictures that are hung next to each other share a tack. How many tacks are needed to hang 28 pictures in this way?  
A)  27  
B)  28  
C)  29  
D)  56  

41. 
If k can be replaced by any number, how many different values can the expression k + 6 have?  
A)  None  
B)  One  
C)  Six  
D)  Seven  
E)  Infinitely many  
Did you use the calculator on this question? 

43. 
3^{3} + 4(8  5) ÷ 6 =  
A)  6.5  
B)  11  
C)  27.5  
D)  29  
E)  34.16  
Did you use the calculator on this question? 

 
45. 
If the pattern shown in the table were continued, what number would appear in the box at the bottom of column B next to 14?  
A)  19  
B)  21  
C)  23  
D)  25  
E)  29  
46. 
Harriet, Jim, Roberto,
Maria, and Willie are in the same eighthgrade class. One of them is this
year's class president. Based on the following information, who is the
class president?
 
A)  Harriet  
B)  Jim  
C)  Roberto  
D)  Maria  
E)  Willie  
48. 
The length of a rectangle is 3 more than its width. If L represents the length, what is an expression for the width?  
A)  3 ÷ L  
B)  L÷ 3  
C)  L× 3  
D)  L + 3  
E)  L– 3  
The following question refers to the following
pattern of dotfigures.  
49. 
If this pattern of dotfigures is continued, how many dots will be in the 100th figure?  
A)  100  
B)  101  
C)  199  
D)  200  
E)  201  

51. 
If n + n + n = 60, what is the value of n ?  
A)  6  
B)  10  
C)  15  
D)  20  
E)  30  
Did you use the calculator on this question? 
52. 
3 × ( + 5) = 30
The number in the box should be  
A)  2  
B)  5  
C)  10  
D)  95  
Did you use the calculator on this question? 
53. 
Which of the following describes what to do to the first number in each ordered pair shown above to obtain the corresponding second number?  
A)  Add 3  
B)  Subtract 3  
C)  Multiply by 2  
D)  Multiply by 2 and subtract 1  
E)  Multiply by 2 and add 1  
Did you use the calculator on this question? 







Scoring Guide 
Solution: 
Score & Description  
 
 

Correct  Student Response 
7 
From the starting point on the grid below, a beetle moved in the following way. It moved 1 block up and then 2 blocks over, and then continued to repeat this pattern. Draw lines to show the path the beetle took to reach the right side of the grid.  
Scorer Comments: This response received full credit because the student correctly drew the beetle's path to the right side of the grid. 

Partial  Student Response 
7 
From the starting point on the grid below, a beetle moved in the following way. It moved 1 block up and then 2 blocks over, and then continued to repeat this pattern. Draw lines to show the path the beetle took to reach the right side of the grid.  
Scorer Comments: This response received partial credit because the first iteration of the path was performed incorrectly; however, all subsequent moves were performed correctly. 

Incorrect  Student Response 
7 
From the starting point on the grid below, a beetle moved in the following way. It moved 1 block up and then 2 blocks over, and then continued to repeat this pattern. Draw lines to show the path the beetle took to reach the right side of the grid.  
Scorer Comments: This response received no credit because the pattern that was followed was not the one specified in the problem. 

Scoring Guide 
Solution: The beetle moves up 1 and 2 to the right each time. The ratio is 1 up and 2 to the right. 75 up and 100 to the right would NOT be on the path since 1/2 is not equal to 75/100. OR If the beetle moves 1 up and 2 to the right each time, then it should move 50 up (not 75 up) and 100 to the right. It is not necessary to include both the 50 and 75 in a response, but the response should clearly indicate that 75 will not work with 100, and relate it to 1/2 or that 50 will work with 100 and relate it to 1/2 or that 75 will work with 150 and relate it to 1/2. 
Score & Description  
 
 

Correct  Student Response 
8 
If the grid in Question 10 were large enough and the beetle continued to move in the same pattern, would the point that is 75 blocks up and 100 blocks over from the starting point be on the beetle’s path?  
Scorer Comments: This response received full credit. The student correctly explained that the point 75 blocks up and 100 blocks over would not be in the beetle's path given the way that it makes each move. 

Partial  Student Response 
8 
If the grid in Question 10 were large enough and the beetle continued to move in the same pattern, would the point that is 75 blocks up and 100 blocks over from the starting point be on the beetle’s path?  
Scorer Comments: This response received partial credit because the student gave some correct information. The student recognized that the beetle could be at the point 75 blocks up, but then they failed to consider that it could not be 100 blocks over given the way that it makes each move. 

Incorrect  Student Response 
8 
If the grid in Question 10 were large enough and the beetle continued to move in the same pattern, would the point that is 75 blocks up and 100 blocks over from the starting point be on the beetle’s path?  
Scorer Comments: This response received no credit because the explanation the student gave does not answer the question. 

Scoring Guide 
Solution: The response is made of five attributes: one for part a, one for part b, and three for part c. For part c, the first attribute is for drawing any line that starts at (1, 0.05), the second attribute is awarded if the drawn line is correct but solid instead of dotted, and the third attribute is awarded for drawing a correct dotted line. a. 40 cents b. 10 cents per minute c. Points should fall on the line through ( 1, 0.05 ) and ( 5, 0.25 ). (Note: line contains the points (1, 0.05), (2, 0.10), (3, 0.15), (4, 0.20), and (5, 0.25) NOTE: An alternate partially correct approach to part c would involve listing the amounts saved (5, 10, 15, 20, and 25 cents), but not graphing the points.This would earn one attribute for part c. 
Score & Description  
 
 
 
 


Extended  Student Response 
9 
The graph below shows the cost that two longdistance telephone companies each charge for calls of various lengths (in minutes).  
Scorer Comments: This response received full credit because all attributes were earned. The student correctly answered parts a, b, and c. 

Satisfactory  Student Response 
9 
The graph below shows the cost that two longdistance telephone companies each charge for calls of various lengths (in minutes).  
Scorer Comments: This response received a satisfactory score. The student got four of the five possible attributes. They correctly answered parts a and b, but in part c their line was solid instead of dashed. 

Partial  Student Response 
9 
The graph below shows the cost that two longdistance telephone companies each charge for calls of various lengths (in minutes).  
Scorer Comments: This response received partial credit. The student got two of the five possible attributes. They correctly answered parts a and b, but their answer to part c is incorrect. 

Minimal  Student Response 
9 
The graph below shows the cost that two longdistance telephone companies each charge for calls of various lengths (in minutes).  
Scorer Comments: This response received minimal credit. The student got one of the five possible attributes. The student correctly answered part a, but incorrectly answered parts b and c. 

Incorrect  Student Response 
9 
The graph below shows the cost that two longdistance telephone companies each charge for calls of various lengths (in minutes).  
Scorer Comments: This response received no credit. No attributes were awarded because all three parts were answered incorrectly. 




Scoring Guide 
Solution: 
Score & Description  
 

In this question the student needed to fill in missing entries in a pattern of the letters "A" and "B." The student was told that the pattern repeats in groups of 3, and enough information was given for the student to find the one correct sequence. 
Correct  Student Response 
15 
Peter wrote down a pattern of A's and B's that repeats in groups of 3. Here is the beginning of his pattern with some of the letters erased. Fill in the missing letters. 
Incorrect  Student Response 
15 
Peter wrote down a pattern of A's and B's that repeats in groups of 3. Here is the beginning of his pattern with some of the letters erased. Fill in the missing letters. 


Scoring Guide 
Solution: 
Score & Description  
 
 

In this question the student needed to demonstrate an
understanding of the ordering of real numbers by graphing an interval—not
individual points—on the number line.
*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  Student Response 
18 
On the number line below, shade the part of the line that shows the set of all numbers greater than or equal to 1 and less than or equal to 3. 
Incorrect #2  Student Response 
18 
On the number line below, shade the part of the line that shows the set of all numbers greater than or equal to 1 and less than or equal to 3. 
Incorrect #1  Student Response 
18 
On the number line below, shade the part of the line that shows the set of all numbers greater than or equal to 1 and less than or equal to 3. 




Scoring Guide 
Solution: 8 letters .20(6) + .33(8) = $3.84 Students may use a variety of strategies to solve this, including guess and check, formal algebra, or others. For example,
OR x + y = 14 therefore, 
Score & Description  
 
 
 
 

This question was a word problem that asked the student to consider two values—the number of letters and the number of postcards—even though the student was only asked for the number of letters. This question could be solved in several ways. A student could reason numerically to find the number of letters and the number of postcards, possibly by using a guessandcheck strategy or by creating a table. Another possibility was to set up and solve a system of two linear equations in two unknowns. To earn full credit, students needed to show how they obtained the answer. Students were permitted to use a calculator. 
Extended  Student Response 
24 
While she was on vacation, Tara sent 14 friends either a
letter or a postcard. She spent $3.84 on postage. If it costs $0.20 to
mail a postcard and $0.33 to mail a letter, how many letters did Tara
send?
Show what you did to get your answer. 
Satisfactory  Student Response 
24 
While she was on vacation, Tara sent 14 friends either a
letter or a postcard. She spent $3.84 on postage. If it costs $0.20 to
mail a postcard and $0.33 to mail a letter, how many letters did Tara
send?
Show what you did to get your answer. 
Partial  Student Response 
24 
While she was on vacation, Tara sent 14 friends either a
letter or a postcard. She spent $3.84 on postage. If it costs $0.20 to
mail a postcard and $0.33 to mail a letter, how many letters did Tara
send?
Show what you did to get your answer. 
Minimal  Student Response 
24 
While she was on vacation, Tara sent 14 friends either a
letter or a postcard. She spent $3.84 on postage. If it costs $0.20 to
mail a postcard and $0.33 to mail a letter, how many letters did Tara
send?
Show what you did to get your answer. 
Incorrect  Student Response 
24 
While she was on vacation, Tara sent 14 friends either a
letter or a postcard. She spent $3.84 on postage. If it costs $0.20 to
mail a postcard and $0.33 to mail a letter, how many letters did Tara
send?
Show what you did to get your answer. 


Scoring Guide 
Solution: 8 hours. Graphical Solution: Extend both lines to the right until they intersect. Then read the horizontal coordinate of the point of intersection. Note: If lines are extended correctly until they intersect, this will serve as sufficient justification. No words are required in this situation. Algebraic Solution: 
Score & Description  
 
 

This question could be solved using either a numerical, graphical, or algebraic approach. Whatever solution path was selected required the student to recognize that the water in tank T is decreasing at a rate of 50 gallons per hour and the water in tank W is increasing at a rate of 25 gallons per hour. These rates could be used to determine when there are equal amounts of water in the two tanks by using any one of several methods, for example, by numerically comparing values for the amount of water in the tanks at different times, by extending the given graphs until they intersect, or by setting up and solving an equation. 
Correct  Student Response 
28 
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional water starts flowing into W. The graph below shows the amount of water in each tank over a period of hours. 
Partial  Student Response 
28 
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional water starts flowing into W. The graph below shows the amount of water in each tank over a period of hours. 
Incorrect  Student Response 
28 
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional water starts flowing into W. The graph below shows the amount of water in each tank over a period of hours. 
Scoring Guide 
Solution: 6 miles east and 5 miles north of the tree 
Score & Description  
 
 

In this question, presented in context, the student
needed to determine the effect of horizontal and vertical translations on
a point in a coordinate plane.
*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. 
Correct #1  Student Response 
29 
What is the position of the treasure chest with respect to the tree? 
Correct #2  Student Response 
29 
What is the position of the treasure chest with respect to the tree? 
Incorrect  Student Response 
29 
What is the position of the treasure chest with respect to the tree? 




Scoring Guide 
Solution: 17 Scoring Guide In this question a student needed to demonstrate an understanding of diagonals of polygons. A diagonal of a polygon is a segment that joins two nonadjacent vertices.(A vertex is a common endpoint of two sides of the polygon). To answer the question it was expected that a student would observe that the number of diagonals from any vertex is 3 less than the number of sides. That is, from any vertex of a convex polygon a diagonal can be drawn to any of the other vertices of that polygon except the two adjacent vertices. For a 20sided polygon, the answer is 20  3 = 17. 
Score & Description  
 

Correct  Student Response 
34 
How many diagonals can be drawn from any vertex of a 20sided polygon? 
Incorrect  Student Response 
34 
How many diagonals can be drawn from any vertex of a 20sided polygon? 
Scoring Guide 
Solution: 1571 Scoring Guide In this question, a student needed to interpret that the lowest point of the St. Lawrence River is a negative number and the highest point of Mt. Jacques Cartier is a positive number (both with respect to sea level). To find the difference between the highest point and the lowest point and to earn full credit, a student needed to subtract the two numbers. To earn partial credit, a student would have had to show the correct procedure using positive and negative numbers, but made a computation error. 
Score & Description  
 
 

Correct  Student Response 
35 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
35 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
Partial  Student Response 
35 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
35 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
Incorrect  Student Response 
35 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
35 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 



Scoring Guide 
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 the incorrect categories earned no credit. 
Correct  Student Response 
40 

40 

Incorrect #3  Student Response 
40 

Incorrect #2  Student Response 
40 

40 

Incorrect #1  Student Response 
40 

40 


Scoring Guide 
Solution: Explanation should include one of the following ideas with no false statements. a. For each successive step, the number of rows and the number of columns is increasing by 1, forming a pattern. For example, the first step forms 1 by 2 rows and columns, the next step 2 by 3, the third step 3 × 4, and so on. Continuing this pattern would mean that the 20th step has 20 × 21 or 420 dots. b. Look at successive differences between consecutive steps. The differences 4, 6, 8, 10, . . . form a pattern. There are 19 differences forming the pattern 4, 6, 8, 10, . . . , 38, 40 and this sum is (9 x 44) + 22 or 418. However, 2 must be added for the 1st step, yielding a response of 420. 
Score & Description  
 
 
 
 

Extended  Student Response 
42 
A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. 
42 
A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. 
Satisfactory  Student Response 
42 
A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. 
Partial  Student Response 
42 
A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. 
Minimal  Student Response 
42 
A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. 
42 
A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. 
Incorrect/Off Task  Student Response 
42 
A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. 
Scoring Guide 
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 the incorrect categories earned no credit. 
Correct  Student Response 
44 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
44 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
Incorrect #2  Student Response 
44 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
Incorrect #1  Student Response 
44 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
44 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 




Scoring Guide 
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 the incorrect categories earned no credit. 
Correct  Student Response 
50 
Explain how you found your answer to question 16. 
Incorrect #1 & 2  Student Response 
50 
Explain how you found your answer to question 16. 
50 
Explain how you found your answer to question 16. 

Scoring Guide 
Score & Description  
 

Correct  Student Response 
54 
The cost to rent a motorbike is given by the following
formula:
Fill in the table below. 
54 
The cost to rent a motorbike is given by the following
formula:
Fill in the table below. 
Incorrect  Student Response 
54 
The cost to rent a motorbike is given by the following
formula:
Fill in the table below. 
Scoring Guide 
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 the incorrect categories earned no credit. 