

3. 
Each of the 6 faces of a certain cube is labeled either R or S. When the cube is tossed, the probability of the cube landing with an R face up is . How many faces are labeled R ?  
A)  Five  
B)  Four  
C)  Three  
D)  Two  
E)  One  
4. 
The prices of gasoline in a certain region are $1.41, $1.36, $1.57, and $1.45 per gallon. What is the median price per gallon for gasoline in this region?  
A)  $1.41  
B)  $1.43  
C)  $1.44  
D)  $1.45  
E)  $1.47  

 
6. 
According to the graph above, which element forms the second greatest portion of the earth's crust?  
 
A)  Oxygen  
B)  Silicon  
C)  Aluminum  
D)  Iron  
E)  Calcium  
 
7. 
The pie chart above shows the portion of time Pat spent on homework in each subject last week. If Pat spent 2 hours on mathematics, about how many hours did Pat spend on homework altogether?  
A)  4  
B)  8  
C)  12  
D)  16  


 
11. 
According to the graph above, how many times did the yearly increase of the price of a hamburger exceed 10 cents?  
A)  None  
B)  One  
C)  Two  
D)  Three  
E)  Four  
Did you use the calculator on this question? 

 
13. 
There are 1,200 students enrolled in Adams Middle School. According to the graph above, how many of these students participate in sports?  
A)  380  
B)  456  
C)  760  
D)  820  
E)  1,162  
Did you use the calculator on this question? 

POPULATION
 
15. 
A pictogram of the data above is to be drawn using as the symbol that represents 500 people. How many would it take to represent the population of Rancho Santa Fe?  
A)  1  
B)  4  
C)  8  
D)  80  
E)  4,000  
16. 
Gloria's diving scores from
a recent competition are represented in the stemandleaf plot shown
below. In this plot, 3  4 would be read as 3.4.
What was her lowest score for this competition?  
A)  0.02  
B)  1.0  
C)  2.5  
D)  5.2  
E)  8.0  


19. 
A poll is being taken at Baker Junior High School to determine whether to change the school mascot. Which of the following would be the best place to find a sample of students to interview that would be most representative of the entire student body?  
A)  An algebra class  
B)  The cafeteria  
C)  The guidance office  
D)  A French class  
E)  The faculty room  


22. 
In a bag of marbles, 1/2 are red, 1/4 are blue, 1/6 are green, and 1/12 are yellow. If a marble is taken from the bag without looking, it is most likely to be  
A)  red  
B)  blue  
C)  green  
D)  yellow  
23. 
From a shipment of 500 batteries, a sample of 25 was selected at random and tested. If 2 batteries in the sample were found to be dead, how many dead batteries would be expected in the entire shipment?  
A)  10  
B)  20  
C)  30  
D)  40  
E)  50  
 
24. 
The total distances covered by two runners during the first 28 minutes of a race are shown in the graph above. How long after the start of the race did one runner pass the other?  
A)  3 minutes  
B)  8 minutes  
C)  12 minutes  
D)  14 minutes  
E)  28 minutes  
 
25. 
The graph above shows how many of the 32 children in Mr. Rivera's class are 8, 9, 10, and 11 years old. Which of the following is true?  
A)  Most are younger than 9.  
B)  Most are younger than 10.  
C)  Most are 9 or older.  
D)  None of the above is true.  


 
28. 
The entire circle shown above represents a total of 2,675 radios sold. Of the following, which is the best approximation of the number of radios represented by the shaded sector of the circle?  
A)  70  
B)  275  
C)  985  
D)  25,880  
E)  98,420  
Did you use the calculator on this question? 
 
29. 
In the graph above, each dot shows the number of situps and the corresponding age for one of 13 people. According to this graph, what is the median number of situps for these 13 people?  
A)  15  
B)  20  
C)  45  
D)  50  
E)  55  
Did you use the calculator on this question? 
31. 
The average weight of 50 prizewinning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?  
A)  0.0472  
B)  11.8  
C)  52.36  
D)  59  
E)  118  
 
32. 
The nine chips shown above are placed in a sack and then mixed up. Madeline draws one chip from this sack. What is the probability that Madeline draws a chip with an even number?  
A) 
 
B) 
 
C) 
 
D) 
 
E) 
 
33. 
There are 15 girls and 11 boys in a mathematics class. If a student is selected at random to run an errand, what is the probability that a boy will be selected?  
A) 
 
B) 
 
C) 
 
D) 
 
E) 
 

Scoring Guide 
Solution: All categories correct. In order for a category to be counted as correct, it must have the correct number of faces (but the eyes and mouth do not have to be drawn). The use of numbers rather than faces is an incorrect response.

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 
1 
The results of a class survey on whether students liked a new television show are as follows. 25 students liked the new show. 15 students disliked the new show. 5 students had no opinion on the new show. On the graph below, each represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.  
Scorer Comments: This response was scored as correct because the student drew the correct number of faces for each category. 

Incorrect #3  Student Response 
1 
The results of a class survey on whether students liked a new television show are as follows. 25 students liked the new show. 15 students disliked the new show. 5 students had no opinion on the new show. On the graph below, each represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.  
Scorer Comments: In this paper, the student drew a face for every person. This particular response was coded to gather data on common student errors, but the paper received no credit. 

Incorrect #2  Student Response 
1 
The results of a class survey on whether students liked a new television show are as follows. 25 students liked the new show. 15 students disliked the new show. 5 students had no opinion on the new show. On the graph below, each represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.  
Scorer Comments: In this paper, the student had two of the three categories correct. This particular response was coded to gather data on common student errors, but the paper received no credit. 

Incorrect #1  Student Response 
1 
The results of a class survey on whether students liked a new television show are as follows. 25 students liked the new show. 15 students disliked the new show. 5 students had no opinion on the new show. On the graph below, each represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.  
Scorer Comments: Papers scored as incorrect #1 received no credit and represent incorrect responses different than those described under incorrect #3 and incorrect #2. 

Scoring Guide 
Solution: Both dog and hamsters correct. Any type of shading bars is acceptable. (no shading is also acceptable.) Top edge of hamsters should fall between 2 and 4 (anywhere) but not 2 or 4. Note: Vertical lines that are the same length as the appropriate bars are acceptable. 
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 
2 
Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is onehalf the number of cats.  
Scorer Comments: This paper was scored as correct because the student correctly added the bars for the number of dogs and hamsters. 

Incorrect #3  Student Response 
2 
Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is onehalf the number of cats.  
Scorer Comments: In this paper, the student correctly added the bar for the number of hamsters, but the bar for the number of dogs is not correct. This particular response was coded to gather data on common student errors, but the paper received no credit. 

Incorrect #2  Student Response 
2 
Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is onehalf the number of cats.  
Scorer Comments: In this paper, the student correctly added the bar for the number of dogs, but the bar for the number of hamsters is not correct. This particular response was coded to gather data on common student errors, but the paper received no credit. 

Incorrect #1  Student Response 
2 
Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is onehalf the number of cats.  
Scorer Comments: Papers scored as incorrect #3 received no credit and represent incorrect responses different than those described under incorrect #1 and incorrect #2. 



Scoring Guide 
Solution: He is incorrect. Two of the candies that Bill ate were blue, which leaves only 8 blue candies. A total of 28 candies remain, which gives a probability of , (, ) or 0.29. 
Score & Description  
 
 


Correct  Student Response 
5 
A package of candies contained only 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the package, opened it, and started taking out one candy at a time and eating it. The first 2 candies he took out and ate were blue. Bill thinks the probability of getting a blue candy on his third try is or . Is Bill correct or incorrect?  
Scorer Comments: This response received full credit because the student correctly explained that the probability of getting a blue candy will not be the same on the third try and that it will go down since there will be less blue candies each time. 

Partial  Student Response 
5 
A package of candies contained only 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the package, opened it, and started taking out one candy at a time and eating it. The first 2 candies he took out and ate were blue. Bill thinks the probability of getting a blue candy on his third try is or . Is Bill correct or incorrect?  
Scorer Comments: This response received partial credit because the student showed some understanding of sampling without replacement since they recognized that the number of blue candies was decreasing, but they did not take into account that the total number of candies in the bag was also decreasing each time. 

Incorrect  Student Response 
5 
A package of candies contained only 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the package, opened it, and started taking out one candy at a time and eating it. The first 2 candies he took out and ate were blue. Bill thinks the probability of getting a blue candy on his third try is or . Is Bill correct or incorrect?  
Scorer Comments: This response received no credit. The student answered that the probability would still be 10 out of 30, which is incorrect because the candies are not being replaced. 



Scoring Guide 
Solution: Both bars drawn correctly. ("Line" bars are acceptable.)

Score & Description  
 

In this question the student needed to read information presented in a table and complete a bar graph representing the given information. The student was first required to select the appropriate values from the table. Finally, the student needed to determine the correct height for the bars representing scores of 90 and 95 and draw the bars on the graph. 
Correct  Student Response 
8 
Use the information in the table above to complete the bar graph below. 
Incorrect  Student Response 
8 
Use the information in the table above to complete the bar graph below. 
Scoring Guide 
Solution: A correct pair may be repeated as long as all 9 correct pairs are present and no incorrect pairs are included.

Score & Description  
 
 
 
 
 

In this question the student needed to list all 9
possible combinations of drawing 3 chips from a box with replacement.
Determining a sample space is a prerequisite skill for the study of
probability.
*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 
9 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #5  Student Response 
9 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #4  Student Response 
9 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #3  Student Response 
9 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #2  Student Response 
9 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #1  Student Response 
9 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 

Scoring Guide 
Solution: 69 
Score & Description  
 
 
 

In this question the student needed to find the average
of 11 test scores. Since only 5 different scores were given, the student
needed either to find a weighted average or include each score an
appropriate number of times in the computation. Students were permitted to
use a calculator.
*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 
12 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 
Incorrect #3  Student Response 
12 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 
Incorrect #2  Student Response 
12 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 
Incorrect #1  Student Response 
12 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 

Scoring Guide 
Solution: No. The opinions would likely be biased in favor of those who like baseball. NOTE: Answer may or may not have a reason for the bias, but it must, in some way, indicate that a bias could exist. 
Score & Description  
 
 

This question required the student to demonstrate an
understanding of sampling bias in the design of a survey.
*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 
14 
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a baseball game be a good way to collect this data? Explain your answer. 
Incorrect #2  Student Response 
14 
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a baseball game be a good way to collect this data? Explain your answer. 
Incorrect #1  Student Response 
14 
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a baseball game be a good way to collect this data? Explain your answer. 


Scoring Guide 
Solution: During the first 20 minutes, Marisa increased her speed from 0 mph to 6 mph. From 20 to 60 minutes, she remained at 6 mph. From 60 to 80 minutes, she decreased her speed from 6 mph to 0 mph and stopped. (Must have both decrease and stop for this interval.) Summary of rate changes: speed up, maintains constant speed, slow down, stop. Notes:

Score & Description  
 
 
 
 

In this question the student was asked to translate across representations by interpreting information presented graphically and giving a verbal description (story) of Marisa's bicycle trip. The given graph presented Marisa's speed on the trip as a function of time. To earn full credit, the student needed to give both quantitative and qualitative information about the situation, including the observation that Marisa was at a stop during the last time interval. 
Extended  Student Response 
17 
The graph above represents Marisa's riding speed throughout her 80minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip. 
Satisfactory  Student Response 
17 
The graph above represents Marisa's riding speed throughout her 80minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip. 
Partial  Student Response 
17 
The graph above represents Marisa's riding speed throughout her 80minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip. 
Minimal  Student Response 
17 
The graph above represents Marisa's riding speed throughout her 80minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip. 
Incorrect  Student Response 
17 
The graph above represents Marisa's riding speed throughout her 80minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip. 
Scoring Guide 
Solution: Note: This question is listed as a short constructedresponse question. It should be considered a multiplechoice question with multiple parts. A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
Score & Description  
 
 
 
 

4 Right  Student Response 
18 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
3 Right  Student Response 
18 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
2 Right  Student Response 
18 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
1 Right  Student Response 
18 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
0 Right  Student Response 
18 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 

Scoring Guide 
Solution: N, because more students chose it. OR N, because it was first choice in one class and second choice in the other classes. "Majority" is acceptable (taken to mean most.) If student says the most classes, do not accept. Scoring Guide In this question, a student has to read and interpret information from a chart. A student then has to make a decision on which of the shapes should be the choice for the class. To earn full credit the student has to tell which of the three pieces should be the choice for the class and then explain why he or she chose that 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 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #3  Student Response 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #2  Student Response 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #1  Student Response 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
20 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Scoring Guide 
Solution: Graph B. It appears to show a large increase from October to March. It is misleading because it exaggerates a relatively small increase (misuse of scale). Scoring Guide In this question, a student needed to recognize how given graphs can be both consistent and inconsistent with stated claims. To earn full credit, a student needed to give the correct answer B with a complete explanation that would include both the large October to March increase and how the use of scale could be used to support or refute a claim. Levels of decreasing partial credit could be earned by a student if he or she just answers by giving the correct graph with an incomplete explanation or a missing explanation. 
Score & Description  
 
 
 

Correct  Student Response 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 
Partial  Student Response 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 
Minimal  Student Response 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 
Incorrect  Student Response 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 
21 
Which graph would be best to help convince others that the
Metro Rail Company made a lot more money from ticket sales in March than
in October?
Explain your reason for making this selection. 




Scoring Guide 
Score & Description  
 
 
 

Note: Any pairs that give a sum other than 2, e.g., (2,2) receive a score of Incorrect #1. Also (0,1) and (1,0) receive a score of Incorrect #1. *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 
26 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Incorrect #3  Student Response 
26 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Incorrect #2  Student Response 
26 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Incorrect #1  Student Response 
26 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Scoring Guide 
Solution: Note: This question is listed as a short constructedresponse question. It should be considered a multiplechoice question with multiple parts. 
Score & Description  
 
 
 
 

4 Right  Student Response 
27 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
3 Right  Student Response 
27 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
2 Right  Student Response 
27 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
1 Right  Student Response 
27 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
0 Right  Student Response 
27 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 


Scoring Guide 
Score & Description  
 

Note: 1980 can is really 4 times as big or holds 4 times
as much trash is incorrect. The student must either be inexact, such as "more than twice as much," or must mention "8 times as much." 
Correct  Student Response 
30 
The pictograph shown above is misleading. Explain why. 
Incorrect  Student Response 
30 
The pictograph shown above is misleading. Explain why. 
30 
The pictograph shown above is misleading. Explain why. 



Scoring Guide 
Score & Description  
 

Correct  Student Response 
34 
The table above shows the results of a survey of hair color. On the circle below, make a circle graph to illustrate the data in the table. Label each part of the circle graph with the correct hair color. 
Incorrect  Student Response 
34 
The table above shows the results of a survey of hair color. On the circle below, make a circle graph to illustrate the data in the table. Label each part of the circle graph with the correct hair color. 
34 
The table above shows the results of a survey of hair color. On the circle below, make a circle graph to illustrate the data in the table. Label each part of the circle graph with the correct hair color. 