6.	What number if placed in each box above would make both equations true?
	A)	0
	B)	1
	C)	2
	D)	3
	E)	4

9.	Which of the following could be the graph of a function?
	A)
	B)
	C)
	D)
	E)

11.	If triangles ADE and ABC shown in the figure above are similar, what is the value of x?
	A)	4
	B)	5
	C)	6
	D)	8
	E)	10

15.  In 1980, the populations of Town A and Town B were 5,000 and 6,000, respectively. The 1990 populations of Town A and Town B were 8,000 and 9,000, respectively.     Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim.

16.  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

19.  The two fair spinners shown above are part of a carnival game. A player wins a prize only when both arrows land on black after each spinner has been spun once. James thinks he has a 50-50 chance of winning. Do you agree?         Justify your answer.

21.	According to the graph above, the temperature at 10 a.m. is approximately how many degrees greater than the temperature at 8 a.m.?
	A)	1
	B)	1.5
	C)	2
	D)	2.5
	E)	3

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

26.  Four people - A, X, Y, and Z - go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below.

27.  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.

28.  In the figure below, use the protractor to draw a line m through point P perpendicular to segment AP. In the answer space provided, give the measure of the smaller angle formed by lines and m.         Answer:____________________

This question requires you to show your work and explain your reasoning. You may use drawings, words, and numbers in your explanation. Your answer should be clear enough so that another person could read it and understand your thinking. It is important that you show all your work.   29.  The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.         Describe the 20th figure in this pattern, including the total number of tiles it contains and how they are arranged. Then explain the reasoning that you used to determine this information. Write a description that could be used to define any figure in the pattern.

30.	If the string does not cost anything, how much does the necklace above cost?
	A)	10¢
	B)	24¢
	C)	28¢
	D)	34¢

31.	Carol wanted to estimate the distance from A to D along the path shown on the map above. She correctly rounded each of the given distances to the nearest mile and then added them. Which of the following sums could be hers?
	A)	4 + 6 + 5 = 15
	B)	5 + 6 + 5 = 16
	C)	5 + 6 + 6 = 17
	D)	5 + 7 + 6 = 18

32.  Divide:         Answer:____________________

33.	In the figure above, the measure of angle ABC is
	A)	55°
	B)	60°
	C)	65°
	D)	125°
	E)	135°

37.	What is the slope of the line shown in the graph above?
	A)	1/3
	B)	2/3
	C)	1
	D)	3/2
	E)	3

40.  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

41.	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)

45.	In ABC shown above, AC = 12. What is the length of segment BD?
	A)
	B)
	C)
	D)
	E)

48.	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

49.	If f(x) = and g(x) = 2x2 + 2, then f(g(2)) =
	A)	3
	B)	5
	C)	7
	D)	7 5/9
	E)	16 2/3

51.	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

52.  The piece of fudge shown above is in the shape of a rectangular solid. If a knife makes one straight cut through the fudge, which of the following can be the piece cut off? Fill in the oval to indicate YES or NO for each shape.

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

61.  The pulse rate for a group of 100 people is shown in the graph above. What is the average pulse rate per minute for these 100 people? (Note: Use the midpoint of each interval to represent the pulse rate for the entire interval. For example, 55 would be used for the pulse rate of the 15 people in the 50-60 group.)     Answer:____________________

66.	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

68.  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:____________________

69.  In the equation above, what is the value of N, rounded to the nearest tenth?     Answer:____________________

70.  The base of the pyramid shown above is a regular hexagon with side of length 12. If point O is the center of the base and the length of OB is 15, what is the degree measure of angle OAB to the nearest whole number?     Answer:____________________

74.	In the graph above, each dot shows the number of sit-ups and the corresponding age for one of 13 people. According to this graph, what is the median number of sit-ups for these 13 people?
	A)	15
	B)	20
	C)	45
	D)	50
	E)	55

76.	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

78.	The sum of the measures of angles 1 and 2 in the figure above is 90°. What is the measure of the angle formed by the bisectors of these two angles?
	A)	60°
	B)	45°
	C)	30°
	D)	20°
	E)	15°

79.	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

80.  In the figure above, the two triangles are similar. What is the value of x ?     Answer:____________________

83.	The length of a side of the square above is 6. What is the length of the radius of the circle?
	A)	2
	B)	3
	C)	4
	D)	6
	E)	8

84.  On the number line below, place a dot at the point that could represent 1.75.

85.  The figure above shows the construction of the angle bisector of AOB using a compass. Which of the following statements must always be true in the construction of the angle bisector? Fill in one oval to indicate YES or NO for each statement.

87.	In the five quadrilaterals shown above, the midpoints of the sides have been joined by broken line segments. Which best describes the five dotted figures formed?
	A)	All are parallelograms.
	B)	All are rectangles.
	C)	All are squares.
	D)	All are rhombuses.
	E)	No generalization can be made.

89.	The figure above shows the graph of y = f (x). Which of the following could be the graph of y = |f (x)|?
	A)
	B)
	C)
	D)
	E)

90.	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

91.	In right triangle ABC above, cos A =
	A)	3/5
	B)	3/4
	C)	4/5
	D)	4/3
	E)	5/3

This question requires you to show your work and explain your reasoning. You may use drawings, words, and numbers in your explanation. Your answer should be clear enough so that another person could read it and understand your thinking. It is important that you show all your work.       92.  The darkened segments in the figure above show the path of an object that starts at point A and moves to point C at a constant rate of 1 unit per second. The object's distance from point A (or from point C) is the shortest distance between the object and the point. In the space below, complete the following steps. a) Sketch the graph of the distance of the object from point A over the 7-second period. b) Then sketch the graph of the distance of the object from point C over the same period.         c) On your graph, label point P at the point where the distance of the object from point A is equal to the distance of the object from point C. d) Between which two consecutive seconds is the object equidistant from points A and C?

95.	A straight line segment could NOT be drawn on the surface of which of the following solids?
	A)
	B)
	C)
	D)
	E)

96.	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

98.	Which of the following figures best illustrates the statement 5 × (6 + 2) = (5 × 6) + (5 × 2)?
	A)
	B)
	C)
	D)
	E)

100.	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)	1 9
	B)	2 9
	C)	4 9
	D)	1 2
	E)	4 5

102.	Which of the following shows the result of flipping the above triangle over the line ?
	A)
	B)
	C)
	D)
	E)

103.	What is the distance between the midpoint of MN and the midpoint of PQ shown above?
	A)	18 cm
	B)	24 cm
	C)	26 cm
	D)	28 cm
	E)	30 cm

105.	What is the diagonal measurement of the TV screen shown in the figure above?
	A)	25 inches
	B)	35 inches
	C)	50 inches
	D)	70 inches
	E)	1,200 inches

106.	Which of the following figures contains line segments that are perpendicular?
	A)
	B)
	C)
	D)

The following question refers to the following pattern of dot-figures.
108.	If this pattern of dot-figures is continued, how many dots will be in the 100th figure?
	A)	100
	B)	101
	C)	199
	D)	200
	E)	201

The following question refers to the following pattern of dot-figures.       109.  Explain how you found your answer to question 16.     Answer:

The following question refers to the graph shown below.
110.	What is the value of g(1)?
	A)	2
	B)	4
	C)	5
	D)	6
	E)	8

The following question refers to the graph shown below.
111.	What is the value of f(g(1))?
	A)	2
	B)	4
	C)	5
	D)	6
	E)	8

115.	In the division problem above, what number does represent?
	A)	116
	B)	120
	C)	124
	D)	160
	E)	480

116.	The figure above shows the display on a scientific calculator. The value of the displayed number is between which of the following pairs of numbers?
	A)	0.04 and 0.05
	B)	0.4 and 0.5
	C)	4.0 and 5.0
	D)	40.0 and 50.0
	E)	400.0 and 500.0

FAVORITE WINTER SPORTS OF EIGHTH GRADE STUDENTS Figure Skating    Ice Hockey    Skiing     Sledding        Speed Skating   Legend: = 4 students
119.	According to the graph above, about how many students chose skiing as their favorite winter sport?
	A)	3½
	B)	4
	C)	12½
	D)	14
	E)	16

122.  In the figure above, ABDG is a parallelogram and CDEF is a rectangle. If EF = 9 and CG = 10, what is AB to the nearest hundredth?     Answer:  ____________________

124.	In the figure above, points A, E, and H are on a plane that intersects a right prism. What is the intersection of the plane with the right prism?
	A)	A line
	B)	A triangle
	C)	A quadrilateral
	D)	A pentagon
	E)	A hexagon

125.	If d = 110 and a = 20 in the formula d = (2t  -  1), then t =
	A)	15 22
	B)	15 8
	C)	5
	D)	111 20
	E)	6

127.	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

129.	How many integers are there between and
	A)	Three
	B)	Four
	C)	Five
	D)	Six
	E)	Seven

131.  In right triangle ABC shown above, AB = 14. What is BC to the nearest hundredth?     Answer:  ____________________

132.	The graphs of y = f(x) and y = g(x) for 0 x 10 are shown in the figure above. For how many values of x is the product f (x) g( x) = 0 for 0 x 10?
	A)	Two
	B)	Four
	C)	Five
	D)	Six
	E)	Seven

133.	Suppose that a1 , a2 , a3 , . . . is the sequence of numbers such that a1 = 3, a2 = + 1, a3 = + 1, and, in general, an+1 = + 1 for all n 1. To the nearest hundredth, the value of a5 is
	A)	1.63
	B)	2.62
	C)	2.73
	D)	3.24
	E)	5.73

Score & Description

Correct   Correct response

Incorrect #2   Response refers to the letters (N, P, or Q), rather than to the geometric shape.

Incorrect #1   Any incorrect response other than as described above. Not acceptable: N is bigger or N is prettier

* 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.

2.

Scoring Guide

Solution: Examples of Correct Response #1 (see note below score & description) Examples for a Correct Response #2 (see note below score & description) Space between pieces is acceptable. Freehand drawings are acceptable. Scoring Guide In this question, a student needed to take 2 isosceles triangles and construct a 4-sided figure that was not a square or a rhombus. A student had to manipulate 2 figures, form a shape other than a square or rhombus, and draw a line of separation in order to earn a score of correct #1. To earn a correct #2, a student had to manipulate 2 figures with some overlapping possible, form a shape that was not a square or rhombus, but did not have to drawn a line of separation.

Score & Description

Correct #1   Correct response (The figure may be tilted. Pieces may or may not be labeled. Line of separation must be shown.)

Correct #2   A correct shape without the line of separation shown (Figure is not a rhombus.) OR A 4-sided shape (that is not a square) that results when part of two Q shapes overlap.

Incorrect   Any incorrect response

* 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.

3.

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.

4.

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. 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

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.

5.

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

Correct   Correct response

Incorrect #3   Piece Q chosen, with an explanation that refers to a number of votes

Incorrect #2   Piece N chosen, but explanation not given or is inadequate with incorrect computation

Incorrect #1   Any incorrect response other than those 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.

6.

Key      What number if placed in each box above would make both equations true?       A)  0    B)  1   C)  2   D)  3   E)  4

7.

Scoring Guide

Solution: odd, even, odd Scoring Guide In this question, a student needed to use elementary number theory to determine whether the value of an algebraic expression was even or odd. A student could also have made numeric substitutions into the given algebraic expression in order to get the correct answer. To earn full credit a student needed to answer all three parts correctly.

Score & Description

Correct   Correct response

Incorrect #2   1 or 2 entries correct

Incorrect #1   Incorrect response

* 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.

8.

Key      cos2(3x) + sin2(3x) =         A)  0  B)  1   C)  3   D)  6   E)  9

9.

Key      Which of the following could be the graph of a function?         A)    B)    C)    D)  E)

10.

Scoring Guide

Solution: Four possible correct responses are listed below: Fold the disk in half two different ways. The intersection of the fold lines is the center of the circle. Folding the disk into semicircles causes the folds to be diameters. Since both diameters have to contain the center, the point they have in common is the center. Fold the disk to form a diameter and then locate the midpoint of the diameter by folding it to bisect the diameter. The midpoint of the diameter is the center of the circle. Fold a chord and then fold the chord in half. Repeat with another chord. The second fold is the perpendicular bisector of the chord and passes through the center. The point where the perpendicular bisectors of the 2 chords intersect is the center. A description of a ruler and compass construction similar to c above, i.e., the perpendicular bisector of 2 chords. Scoring Guide In this question, a student has to describe a geometric process for finding the center of a circle. The student is given a circular disk to use as an aid in answering the question.Geometric properties, definitions, and principles are to be used in describing the process for finding the center of a circle. Full credit is earned when a complete process is described. Varying levels of partial credit are earned depending on how much of the process the student is able to correctly communicate.

Score & Description

Extended   Locates the center by folding or compass and straight edge construction and explains clearly and completely what geometric properties lead to the decisions involved in the method chosen.

Satisfactory   Locates the center by folding or by compass and straight edge construction and gives an explanation that describes the procedure but does not include formal geometric principles or does not use appropriate terminology

Partial   Locates the center by folding or describes a compass and straight edge construction of the perpendicular bisectors of 2 non-parallel chords; explanation may be incomplete or incorrect OR Explains a drawing of 2 diameters or the perpendicular bisector of 2 non-parallel chords; explanation must be complete and correct

Minimal   A response that shows a line that appears to include the center of the circle; e.g., a diameter or the perpendicular bisector of a chord. No explanation required

Incorrect   Incorrect response

11.

Key      If triangles ADE and ABC shown in the figure above are similar, what is the value of x?       A)  4   B)  5   C)  6   D)  8   E)  10

12.

Scoring Guide

Solution: Average hourly wage for Thursday - $5.75 Hourly wage rate changes at 5pm Hourly wage from 9am - 5pm - $5.50/hr Hourly wage from 5pm - 10pm - $6.00/hr Scoring Guide In this question, a student needed to read and compute with data from a table. This problem could be solved in many different ways. One way is to use the total earnings from the five days ($153.50) to find the total daily earnings on Thursday ($34.50). The average hourly wage for Thursday can be found by dividing $34.50 by 6 (number of hours worked). To answer the second part of the question, a student should have looked at the data in the table to reason at what time the hourly wage rate changes. To earn full credit, a student has to give the correct average hourly wage for Thursday as well as give the time when the hourly wage rate changes. Partial credit could be earned if a student gives one correct answer, either the correct hourly average rate for Thursday or the correct time the wage rate changes.

Score & Description

Correct   Correct average hourly rate for Thursday and the correct time of 5 pm when the wage rate changes

Partial   Either correct average hourly rate for Thursday OR correct time the wage rate changes

Incorrect   Incorrect response

13.

Key      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

14.

Key      If each of the counting numbers from 1 through 10 is multiplied by 13, how many of the resulting numbers will be even?         A)  One   B)  Four C)  Five   D)  Six   E)  Ten

15.

Scoring Guide

Solution:

Score & Description

Correct   Correct response

Partial   Gives correct reason for Brian or Darlene but not both. (Reason must include mathematics illustrated in above solution or an appropriate reason using proportion.) OR uses 1000 or 3000 (without additional mathematics) for Brian's claim and uses 60% and 50% (or their equivalents) without additional mathematics for Darlene's claim

Incorrect   Incorrect response

Note: If a response is correct except that numbers used are 3, 5, 6, 8, and 9 instead of 3,000, 5,000, etc., it should be scored a 3.

16.

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

17.

Key      The population of the United States is approximately 250 million, and the national debt is approximately 4 trillion dollars. If this debt were divided equally among the population, what would be the debt, in dollars, per person?         A)  16   B)  1,600 C)  16,000   D)  1,600,000   E)  16,000,000

18.

Scoring Guide

Solution: Martin's drink has the stronger cherry flavor. 6÷59 < 5÷47 0.1017 < 0.1064 OR 6÷53 < 5÷42 0.1132 < 0.1190 OR Luis: 1 part CS to 8.8 parts water < Martin: 1 part CS to 8.4 parts water Scoring Guide In this question, a student has to use ratios to describe a situation and make a comparison of whether Luis or Martin makes the drink with the stronger cherry flavor. There are various combinations of ratios that could be correctly used in this question. Setting up the ratios correctly, performing the division correctly (students had a calculator available in this question) and answering that Martin's drink has the stronger cherry flavor would earn a student full credit. Partial credit could be earned if a student compares a pair of correct ratios but does not draw a conclusion on whose drink has the stronger cherry flavor.

Score & Description

Correct   Correct response

Partial   Compares a pair of correct ratios for both Luis and Martin but does not give the correct answer

Incorrect   Incorrect response

19.

Scoring Guide

Solution: Possible outcomes are BB, BW, WB, and WW. Only BB will win. The actual chance of a win is 1 in 4, or 25% Scoring Guide In this question, a student has to determine the probability of a simple event. A student could have listed a sample space and used the information to describe and make a prediction about the expected outcome. Full credit was earned for a response that included the correct answer of 1 in 4, or 25%, with a complete justification (i.e., a list of the possible outcomes). Partial credit could have been earned if a student listed the sample space but the explanation was either incomplete or missing.

Score & Description

Correct   Correct response

Partial   Lists sample space correctly with less than a complete explanation OR draws a correct tree diagram with less than a complete explanation OR just states 1 in 4 chance

Incorrect   Incorrect response

20.

Scoring Guide

Solution: Selects and provides appropriate explanation for why the mean is a better measure for the typical attendance for Theater B and the median is the better measure for Theater A. An explanation for Theater A should include the idea that the attendance on day 4 is much different than the attendance numbers for any other days for Theater A. An appropriate explanation for Theater B should include the following ideas There are two clusters of data The median is representative of only one of the clusters while the mean is representative of both OR a justification that conveys the idea that 82 is a better indicator of where the "center" of the 5 data points is located Scoring Guide In this question, a student has to look at the data and determine which measure, the median or the mean, would best describe the typical daily attendance at each Theater. A student has to have an understanding of the meaning of mean and median in order to provide a correct answer and explanation. For full credit a student has to answer the median for part a and include an explanation that would include that day 4's attendance is significantly different than the rest of the days and the mean for part b with an explanation that shows an understanding that the mean is a better indicator because all of the attendance numbers for Theater B are clustered. Varying levels of partial credit (satisfactory, partial, and minimal) could be earned depending on how well the student reasons and communicates the correct answer.

Score & Description

Extended   Indicates the better measure for each theater and gives a complete explanation for each measure

Satisfactory   Indicates the better measure for each theater and gives a complete explanation for one measure

Partial   Indicates mean for Theater B and median for Theater A with either no explanation or an incomplete explanation OR selects the better measure for one theater and gives an appropriate explanation

Minimal   Indicates the mean for Theater B with no explanation or an incomplete explanation OR indicates the median for Theater A with no explanation or an incomplete explanation

Incorrect   Incorrect response

21.

Key      According to the graph above, the temperature at 10 a.m. is approximately how many degrees greater than the temperature at 8 a.m.?         A)  1   B)  1.5   C)  2   D)  2.5 E)  3

22.

Scoring Guide

Solution: Scoring Guide In this question, a student has to realize that the only parallelograms with diagonals that form a 90-degree angle at the point of intersection are a rhombus and a square. The student needed to show the diagonals in the sketch.

Score & Description

Correct #1   Correct response - rhombus with diagonals drawn

Correct #2   Correct response - square with diagonals drawn

Incorrect #2   Quadrilateral, with or without diagonals, that appears to be a parallelogram

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.

23.

Key      A certain machine produces 300 nails per minute. At this rate, how long will it take the machine to produce enough nails to fill 5 boxes of nails if each box will contain 250 nails?         A)  4 min   B)  4 min 6 sec C)  4 min 10 sec   D)  4 min 50 sec   E)  5 min

24.

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.

25.

Key      Which of the following pieces of information would NOT be useful in deciding what type of car is the most economical to drive?       A)  Median income of drivers   B)  Range of insurance costs   C)  Average miles per gallon   D)  Typical cost of repairs per year   E)  Cost of routine maintenance

26.

Scoring Guide

Solution: All 5 of these horizontal arrangements listed in any order Scoring Guide In this question, a student had to list all the 5 possibilities for how an event could occur given that A sat in the aisle seat. Different levels of incorrect could be earned depending on the number of possibilities that the student had listed.

Score & Description

Correct   Correct response

Incorrect #3   3 or 4 correct arrangements other than XYZ

Incorrect #2   1 or 2 correct arrangements other than XYZ

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.

27.

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 235° 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.