NAEP NQT v3.0 -- Print Output

Additional Materials (1)

Additional Materials (2)

Additional Materials (3)

Additional Materials (4)

Additional Materials (5)

1.	Ravi has more tapes than magazines. He has fewer tapes than books. Which of the following lists these items from the greatest in number to the least in number?

	A)	Books, magazines, tapes
	B)	Books, tapes, magazines
	C)	Magazines, books, tapes
	D)	Tapes, magazines, books

2.	In the equation y = 4x, if the value of x is increased by 2, what is the effect on the value of y ?

	A)	It is 8 more than the original amount.
	B)	It is 6 more than the original amount.
	C)	It is 2 more than the original amount.
	D)	It is 16 times the original amount.
	E)	It is 8 times the original amount.


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


5.	If the points Q, R, and S shown above are three of the vertices of rectangle QRST, which of the following are the coordinates of T (not shown) ?

	A)	(4, -3)
	B)	(3, -2)
	C)	(-3, 4)
	D)	(-3, -2)
	E)	(-2, -3)

Question 6 refers to Additional Materials (5)


6.	Which of the figures below should be the fourth figure in the pattern shown above?

	A)
	B)
	C)
	D)

Question 7 refers to Additional Materials (5)

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.

Question 8 refers to Additional Materials (5)

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?



	Yes No

	Give a reason for your answer.

Question 9 refers to Additional Materials (5)

9.	The graph below shows the cost that two long-distance telephone companies each charge for calls of various lengths (in minutes).

	a. What is the cost of a 4-minute call using Company B ? __________________________

	b. What is the cost per minute for a call using Company B ? __________________________

	c. Determine the amounts of money saved (in cents) by using Company B instead of Company A when calls of 1, 2, 3, 4, and 5 minutes are made. Then graph the five points that represent the savings on the grid below and connect the points with a dotted line.

10.	Which of the following is equal to 6(x + 6) ?

	A)
	B)
	C)
	D)
	E)

11.	Which of the graphs below is the set of all whole numbers less than 5?

	A)
	B)
	C)
	D)
	E)

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 B-3. 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

x	y
0	-1
1	2
2	5
3	8
10	29

14.

Which of the following equations represents the relationship between x and y shown in the table above?

y = x² + 1

y = x + 1

y = 3x - 1

y = x² - 3

y = 3x² - 1

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.


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

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.


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.

x	y
0	-3
1	-1
2	1

Which of the following equations is true for the three pairs of x and y values in the table above?

3x + 2 = y

3x - 2 = y

2x + 3 = y

2x - 3 = y

x - 3 = y

Term	1	2	3	4
Fraction	1/2	2/3	3/4	4/5

21.

If the list of fractions above continues in the same pattern, which term will be equal to 0.95?

The 100th

The 95th

The 20th

The 19th

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?

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.

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 x-axis.
	B)	The line passes through (0,0).
	C)	The line stays above the x-axis at all times.
	D)	The line rises from the lower left to the upper right.
	E)	The line is parallel to the y-axis.

27.	3 + 15 ÷ 3 - 4 × 2 =

	A)	-9
	B)	-2
	C)	0
	D)	4
	E)	5

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.

Assume that the rates of water loss and water gain continue as shown. At what number of hours will the amount of water in T be equal to the amount of water in W ?

Show or explain how you found your answer.

On the map below, the rock is located 2 miles west and 1 mile north of the tree. A treasure chest (not shown) is located 8 miles east and 4 miles north of the rock. Mark the location of the treasure chest on the map with an X.
29.	What is the position of the treasure chest with respect to the tree?
	Answer: _____ miles east and _____ miles north of the tree

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)	n²


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. Only one of the other three people lives next to Bridgitte. Chaz lives next to Bridgitte and next to Diann. Which person could live in house number 2?

	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

From any vertex of a 4-sided polygon, 1 diagonal can be drawn. From any vertex of a 5-sided polygon, 2 diagonals can be drawn. From any vertex of a 6-sided polygon, 3 diagonals can be drawn. From any vertex of a 7-sided polygon, 4 diagonals can be drawn.
34.	How many diagonals can be drawn from any vertex of a 20-sided polygon?
	Answer:____________________

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.

Did you use the calculator on this question?


36.	In the pattern above, which figure would be next?

	A)
	B)
	C)
	D)

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)

Puppy's Age	Puppy's Weight
1 month	10 lbs.
2 months	15 lbs.
3 months	19 lbs.
4 months	22 lbs.
5 months	?

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?


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

40.	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.
	Answer:____________________ ____________________

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?

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.
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.
	Marcy has to determine the number of dots in the 20th step, but she does not want to draw all 20 pictures and then count the dots. Explain or show how she could do this and give the answer that Marcy should get for the number of dots.

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43.	3³ + 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?

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.


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 eighth-grade class. One of them is this year's class president. Based on the following information, who is the class president? The class president was last year's class vice president and lives on Vine Street. Willie is this year's class vice president. Jim and Maria live on Cypress Street. Roberto was not last year's class vice president.

	A)	Harriet
	B)	Jim
	C)	Roberto
	D)	Maria
	E)	Willie

47.	What is the least whole number x for which 2x > 11?

	A)	5
	B)	6
	C)	9
	D)	22
	E)	23

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 dot-figures.
49.	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.
50.	Explain how you found your answer to question 16.
	Answer:

51.	If n + n + n = 60, what is the value of n ?

	A)	6
	B)	10
	C)	15
	D)	20
	E)	30

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52.	3 × ( $\'box\'$ + 5) = 30 The number in the box should be

	A)	2
	B)	5
	C)	10
	D)	95

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53.	(2, 5), (4, 9), (6, 13) 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

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54.

The cost to rent a motorbike is given by the following formula:

Cost = ($3 × number of hours) + $2

Fill in the table below.

Time in Hours	Cost in Dollars
1	5
4
	17

Did you use the calculator on this question?

55.	Plot the point (5, 2) on the grid shown below.


Did you use the calculator on this question?

Question 1

Key


1.	Ravi has more tapes than magazines. He has fewer tapes than books. Which of the following lists these items from the greatest in number to the least in number?

	A)	Books, magazines, tapes
	B)	Books, tapes, magazines
	C)	Magazines, books, tapes
	D)	Tapes, magazines, books

Question 2

Key


2.	In the equation y = 4x, if the value of x is increased by 2, what is the effect on the value of y ?

	A)	It is 8 more than the original amount.
	B)	It is 6 more than the original amount.
	C)	It is 2 more than the original amount.
	D)	It is 16 times the original amount.
	E)	It is 8 times the original amount.

Question 3

Key


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

Question 4

Key


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

Question 5

Key


5.	If the points Q, R, and S shown above are three of the vertices of rectangle QRST, which of the following are the coordinates of T (not shown) ?

	A)	(4, -3)
	B)	(3, -2)
	C)	(-3, 4)
	D)	(-3, -2)
	E)	(-2, -3)

Question 6

Key


6.	Which of the figures below should be the fourth figure in the pattern shown above?

	A)
	B)
	C)
	D)

Question 7

Scoring Guide

Solution:

path of the beetle on grid

Score & Description

	Correct
	Correct response (Note: may continue pattern beyond endpoint. i.e., )

	Partial
	After an incorrect start, drawing picks up and completes the correct pattern. A minimum of three consecutive correct iterations must be shown.

	Incorrect
	Incorrect response

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.

Question 8

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.

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
	Correct response

Partial

Response indicates that there is a pattern, but the pattern may not be the correct 1 up and 2 to the right. Any “2” response should clearly mention or allude to some number up and some number to the right, but the numbers do not necessarily have to be 1 and 2.

The “2” category will also include incomplete explanations with some correct information (that indicates that a pattern exists).

	Incorrect
	Incorrect response – includes all responses that just repeat information in the prompt and those that indicate that “the pattern is up and to the right”, as well as all other incorrect responses.

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.

Question 9

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
	Correct response (all five attributes)

	Satisfactory
	Three or four attributes

	Partial
	Two attributes

	Minimal
	One attribute

	Incorrect
	Incorrect response

Extended - Student Response

9	The graph below shows the cost that two long-distance 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 long-distance 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 long-distance 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 long-distance 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 long-distance 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.

Question 10

Key


10.	Which of the following is equal to 6(x + 6) ?

	A)
	B)
	C)
	D)
	E)

Question 11

Key


11.	Which of the graphs below is the set of all whole numbers less than 5?

	A)
	B)
	C)
	D)
	E)

Question 12

Key


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

Question 13

Key


13.	The map above shows eight of the counties in a state. The largest city in the state can be found at location B-3. 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

Question 14

Key


14.	Which of the following equations represents the relationship between x and y shown in the table above?

	A)	y = x² + 1
	B)	y = x + 1
	C)	y = 3x - 1
	D)	y = x² - 3
	E)	y = 3x² - 1

Question 15

Scoring Guide

Solution:

Score & Description

	Correct
	Correct response

	Incorrect
	Any incorrect response

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.

Question 16

Key


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)

Question 17

Key


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

Question 18

Scoring Guide

Solution:

Score & Description

	Correct
	Correct response

	Incorrect #2
	Any of the following:

	Incorrect #1
	Any incorrect response other than those shown above

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.

Question 19

Key


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)

Question 20

Key

20.

x	y
0	-3
1	-1
2	1

Which of the following equations is true for the three pairs of x and y values in the table above?

3x + 2 = y

3x - 2 = y

2x + 3 = y

2x - 3 = y

x - 3 = y

Question 21

Key


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

Question 22

Key


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

Question 23

Key


23.	If 3 + w = b, then w =

	A)	b/3
	B)	b× 3
	C)	b + 3
	D)	3 - b
	E)	b - 3

Question 24

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,

# postcards # letters total cost

1 13 4.49

2 12 4.36

3 11 4.23

4 10 4.10

5 9 3.97

6 8 3.84

7 7 3.71

8 6 3.58

x + y = 14
.20x + .33y = 3.84

therefore,
.20x + .33(14 - x) = 3.84
so x = 6 and y = 8

Score & Description

	Extended
	Correct response

	Satisfactory
	Correct, complete process is indicated, but answer is not 8 and only has a minor computational error OR Shows correct, complete process but does not indicate answer

	Partial
	Correct, complete process is indicated, but answer is not 8 and there are several computational errors (Process must clearly illustrate a correct strategy, such as a table or equations.) OR Correct response of 8 but shows no work or incomplete work

	Minimal
	Process is incorrect because it ignores one or more pieces of given information OR Process is correct but incomplete (process may be guess and check or another process which may lead to correct answer i.e., chart but no equation, but goal is not clearly defined) and answer is not 8

	Incorrect
	Incorrect response

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 guess-and-check 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.

Question 25

Key


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

Question 26

Key


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 x-axis.
	B)	The line passes through (0,0).
	C)	The line stays above the x-axis at all times.
	D)	The line rises from the lower left to the upper right.
	E)	The line is parallel to the y-axis.

Question 27

Key


27.	3 + 15 ÷ 3 - 4 × 2 =

	A)	-9
	B)	-2
	C)	0
	D)	4
	E)	5

Question 28

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:
Equation of lines:
T y = -50x + 900
W y = 25x + 300
Point of intersection (8hrs, 500 gal)

Score & Description

	Correct
	Correct response

	Partial
	Number of hours is incorrect, but falls between 6 1/2 and 8 1/2 and a correct procedure is demonstrated. OR Number of hours is correct, but accompanying justification is insufficient or missing

	Incorrect
	Incorrect response

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.

Question 29

Scoring Guide

Solution:

6 miles east and 5 miles north of the tree

Score & Description

	Correct #1
	Treasure marked "X" at (6,5) on map (any X within the small squares that surround (6,5)) and fill-ins are correct

	Correct #2
	Treasure located incorrectly but both fill-ins are correct

	Incorrect
	Any incorrect response

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?

Question 30

Key


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)	n²

Question 31

Key


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. Only one of the other three people lives next to Bridgitte. Chaz lives next to Bridgitte and next to Diann. Which person could live in house number 2?

	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.

Question 32

Key


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)

Question 33

Key


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

Question 34

Scoring Guide

Solution:

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 20-sided polygon, the answer is 20 - 3 = 17.

Score & Description

	Correct
	Correct response

	Incorrect
	Any incorrect response

Correct - Student Response

34	How many diagonals can be drawn from any vertex of a 20-sided polygon?

Incorrect - Student Response

34	How many diagonals can be drawn from any vertex of a 20-sided polygon?

Question 35

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
	Correct response

	Partial
	Shows correct procedure (addition) but does not answer 1571. Correct procedure means either 1277-(-294) or 1277 + 294, but not 1277 - 294.

	Incorrect
	Incorrect response

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.

Question 36

Key


36.	In the pattern above, which figure would be next?

	A)
	B)
	C)
	D)

Question 37

Key


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)

Question 38

Key


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

Question 39

Key


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

Question 40

Scoring Guide

Score & Description

Correct

Any two different numbers greater than 18.

A general statement such as "Any number greater than 18."

	Incorrect #3
	Only one correct response and the other response is "18".

	Incorrect #2
	Only one correct response and the other response is *not* "18" or is missing.

	Incorrect #1
	Both responses are incorrect.

*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	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.


40	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.

Incorrect #3 - Student Response

40	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.

Incorrect #2 - Student Response

40	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.


40	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.

Incorrect #1 - Student Response

40	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.


40	54 < 3 × Write two numbers that could be put in the to make the number sentence above true.

Question 41

Key


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

Question 42

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
	Correct answer. (Must state 420; must tie step 20 back to beginning of pattern in some specific form of generalization.)

	Satisfactory
	Correct explanation of pattern but does not include or omits the correct number of dots (420).

	Partial
	A partial (incomplete) correct explanation, i.e., does not tie together well.

	Minimal
	An attempt to generalize OR to draw all 20 pictures in the pattern (with a clear understanding of the pattern).

	Incorrect/Off Task
	The work is completely incorrect, irrelevant, or off task.

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.

Question 43

Key


43.	3³ + 4(8 - 5) ÷ 6 =

	A)	6.5
	B)	11
	C)	27.5
	D)	29
	E)	34.16

Question 44

Scoring Guide

Score & Description

Correct

Any two (or more) of the correct dots should be circled, and no others.

Correct solution

This kind of circling is acceptable.

	Incorrect #2
	One correct dot circled and no incorrect dots circled.

	Incorrect #1
	Any incorrect response other than as described in Incorrect #2.

*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.

Question 45

Key


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

Question 46

Key


46.	Harriet, Jim, Roberto, Maria, and Willie are in the same eighth-grade class. One of them is this year's class president. Based on the following information, who is the class president? The class president was last year's class vice president and lives on Vine Street. Willie is this year's class vice president. Jim and Maria live on Cypress Street. Roberto was not last year's class vice president.

	A)	Harriet
	B)	Jim
	C)	Roberto
	D)	Maria
	E)	Willie

Question 47

Key


47.	What is the least whole number x for which 2x > 11?

	A)	5
	B)	6
	C)	9
	D)	22
	E)	23

Question 48

Key


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

Question 49

Key


49.	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

Question 50

Scoring Guide

Score & Description

	Correct
	An explanation that leads to 201, such as: Multiply the position of the figure by 2, then add 1 to that answer. It is the 101st odd number. 2x 100 + 1 Any statements equivalent to the previous ones. Extended the pattern and counted the dots.

Incorrect #1 & 2

Incorrect #1
Incorrect answer to #16 and an explanation given.

Incorrect #2
Correct answer to #16 but incorrect explanation given.

Includes: I guessed.

*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.

Question 51

Key


51.	If n + n + n = 60, what is the value of n ?

	A)	6
	B)	10
	C)	15
	D)	20
	E)	30

Question 52

Key


52.	3 × ( $\'box\'$ + 5) = 30 The number in the box should be

	A)	2
	B)	5
	C)	10
	D)	95

Question 53

Key


53.	(2, 5), (4, 9), (6, 13) 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

Question 54

Scoring Guide

Score & Description

Correct

Correct Answer:

Time in Hours	Cost in Dollars
1	5
4	14
5	17

	Incorrect
	Incorrect Answer Includes: one correct entry (either 5 or 14)

Correct - Student Response

54	The cost to rent a motorbike is given by the following formula: Cost = ($3 × number of hours) + $2 Fill in the table below.


54	The cost to rent a motorbike is given by the following formula: Cost = ($3 × number of hours) + $2 Fill in the table below.

Incorrect - Student Response

54	The cost to rent a motorbike is given by the following formula: Cost = ($3 × number of hours) + $2 Fill in the table below.

Question 55

Scoring Guide

Score & Description

	Correct
	Correct answer (with or without label): Label can be P or P(5,2) or (5,2)

	Incorrect #1
	Incorrect answer other than (2,5)

	Incorrect #2
	(2,5)

*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

55	Plot the point (5, 2) on the grid shown below.

Incorrect #1 - Student Response

55	Plot the point (5, 2) on the grid shown below.

Incorrect #2 - Student Response

55	Plot the point (5, 2) on the grid shown below.