NAEP NQT v3.0 -- Print Output

Additional Materials (1)

Additional Materials (2)

Additional Materials (3)

Additional Materials (4)

Additional Material (1)

Exercise Time
(minutes)

Total
Calories
Burned

Which of the following graphs best illustrates the relationship between exercise time and total calories burned, as shown in the table above?


2.	The graphs of the two equations shown above intersect at the point (x, y) What is the value of x at the point of intersection?

	A)
	B)	5
	C)	7
	D)	10
	E)	20


3.	Which of the following is the graph of \|2x - 5\| ≥ 3 ?

	A)
	B)
	C)
	D)
	E)

4.	If ƒ(x) = x² + x and g(x) = 2x + 7, what is an expression for ƒ(g(x)) ?

Sequence I: 3, 5, 9, 17, 33, . . .

Sequence I, shown above, is an increasing sequence. Each term in the sequence is greater than the previous term.

a.
Make a list of numbers that consists of the positive differences between each pair of adjacent terms in Sequence I. Label the list Sequence II.

b.
If this same pattern of differences continues for the terms in Sequence I, what are the next two terms after 33 in Sequence I ?

6th term ______________________

7th term ______________________

c. Write an algebraic expression (rule) that can be used to determine the nth term of Sequence II, which is the difference between the (n + 1)st term and the nth term of Sequence I.


6.	The graph of ƒ(x) = 2x³ is shown above. Which of the following is the graph of -ƒ(x) ?

	A)
	B)
	C)
	D)
	E)


7.	In the solution of the system of equations above, what is the value of x ?

	A)	- 1
	B)	2
	C)	3
	D)	4
	E)	5

8.	What are all values of x such that x² + 7x + 6 ≥ 0 ?

	A)	-6 ≤ x ≤ -1
	B)	-6 ≤ x ≤ 1
	C)	1 ≤ x ≤ 6
	D)	x ≤ -6 or x ≥ -1
	E)	x ≤ 1 or x ≥ 6


9.	The graph of ƒ(x) = sin x is shown above. Which of the following is the x coordinate of point P ?

	A)
	B)
	C)
	D)
	E)

10.	The first term in a sequence of numbers is . Each term after the first term is 1 more than twice its previous term. What is the 4th term?

	A)	2
	B)	4
	C)	5
	D)	11
	E)	23

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11.	Rosa is twice as old as Byron. Fred is one year older than Byron. If Fred's age is represented by F, which of the following represents the ages of Rosa and Byron, respectively?

	A)	½ (F - 1) and F - 1
	B)	½ (F + 1) and F + 1
	C)	2 (F - 1) and F - 1
	D)	2 (F + 1) and F + 1
	E)	2F and F - 1

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12.	Which of the following best illustrates a geometric representation of (x + 2) (x + 4) ?

	A)
	B)
	C)
	D)
	E)

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13.	A car costs $20,000. It decreases in value at the rate of 20 percent each year, based on the value at the beginning of that year. At the end of how many years will the value of the car first be less than half the cost?

	Answer: ________ years Justify your answer.

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14.	The number of bacteria present in a laboratory sample after t days can be represented by 500(2^t). What is the initial number of bacteria present in this sample?

	A)	250
	B)	500
	C)	750
	D)	1,000
	E)	2,000

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15.	Yvonne has studied the cost of tickets over time for her favorite sports team. She has created a model to predict the cost of a ticket in the future. Let C represent the cost of a ticket in dollars and y represent the number of years in the future. Her model is as follows. C = 2.50y + 13 Based on this model, how much will the cost of a ticket increase in two years?

	A)	$5
	B)	$8
	C)	$13
	D)	$18
	E)	$26

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Question 16 refers to Additional Material (1)


16.	What number if placed in each box above would make both equations true?

	A)	0
	B)	1
	C)	2
	D)	3
	E)	4

Question 17 refers to Additional Material (1)

17.	cos²(3x) + sin²(3x) =

	A)	0
	B)	1
	C)	3
	D)	6
	E)	9

Question 18 refers to Additional Material (1)

18.	Which of the following could be the graph of a function?

	A)
	B)
	C)
	D)
	E)

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.
19.	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.

20.

6 x 10³	=
3 x 10⁵

0.5 × 10²

2 × 10²

2 × 10^0.6

0.5 × 10^-2

2 × 10^-2

21.	If x = -4, the value of -4x is

	A)	-16
	B)	-8
	C)	8
	D)	16


22.	In ABC shown above, AC = 12. What is the length of segment BD?

	A)
	B)
	C)
	D)
	E)

23.	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

24.	If n × n = 729, what does n equal?
	Answer:____________________

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25.	For what value of x is 8¹² = 16^x?

	A)	3
	B)	4
	C)	8
	D)	9
	E)	12

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26.	If f(x) = 4x² - 7x + 5.7, what is the value of f(3.5)?
	Answer:____________________

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27.	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

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

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29.	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:____________________

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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.
30.	One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.

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31.	3³ + 4(8-5) ÷ 6 =

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

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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.

32.

15²	=	225
25²	=	625
35²	=	1225

The examples above suggest the following statement.

When a positive integer that ends in the digit 5 is squared, the resulting integer ends in 25.

Explain why this statement is always true.
(Hint: (10n + 5)²= ? )

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33.	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)


34.	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.
35.	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?

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

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

37.	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.
38.	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.
39.	Explain how you found your answer to question 16.
	Answer:

The following question refers to the graph shown below.
40.	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.
41.	What is the value of f(g(1))?

	A)	2
	B)	4
	C)	5
	D)	6
	E)	8

42.	What are the roots of 2x² + 5x + 1 = 0?
	Answer: ____________________

43.

If d = 110 and a = 20 in the formula d =

(2t - 1), then t =

111

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44.	How many integers are there between and ?

	A)	Three
	B)	Four
	C)	Five
	D)	Six
	E)	Seven

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

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46.	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

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47.	Suppose that a₁ , a₂ , a₃ , . . . is the sequence of numbers such that a₁ = 3, a₂ = + 1, a₃ = + 1, and, in general, a_n+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

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Question 1

Key


1.	Which of the following graphs best illustrates the relationship between exercise time and total calories burned, as shown in the table above?

	A)
	B)
	C)
	D)
	E)

Question 2

Key


2.	The graphs of the two equations shown above intersect at the point (x, y) What is the value of x at the point of intersection?

	A)
	B)	5
	C)	7
	D)	10
	E)	20

Question 3

Key


3.	Which of the following is the graph of \|2x - 5\| ≥ 3 ?

	A)
	B)
	C)
	D)
	E)

Question 4

Scoring Guide

Solution:

ƒ(g(x))= (2x+7)² + (2x+7)

= 4x² + 28x + 49 + 2x + 7 Any one of these is a correct response

= 4x² + 30x + 56

= 2(2x² + 15x + 28)

= (2x + 7)(2x + 8)

= 2(x + 4)(2x + 7)

Score & Description

	Correct
	Correct response. If student finds ƒ(g(x)) correctly, ignore attempts to simplify or solve the equation ƒ(g(x)) = 4x² + 30x + 56 = 0.

	Partial
	Finds g(f(x)) = 2(x² + x) + 7 or makes an error in simplification of ƒ(g(x)) i.e., (2x + 7)² + (2x + 7) = 4x² + 49 + 2x + 7 = 4x² + 2x + 56.

	Incorrect
	Incorrect response.

Correct - Student Response

4	If ƒ(x) = x² + x and g(x) = 2x + 7, what is an expression for ƒ(g(x)) ?

	Scorer Comments: This response received full credit because the student correctly performed the composition of the two given functions.

Partial - Student Response

4	If ƒ(x) = x² + x and g(x) = 2x + 7, what is an expression for ƒ(g(x)) ?

	Scorer Comments: Even though the student has written “f(g(x)),” the student actually found g(f(x)). This response was given partial credit.

Incorrect - Student Response

4	If ƒ(x) = x² + x and g(x) = 2x + 7, what is an expression for ƒ(g(x)) ?

	Scorer Comments: This response received no credit because the answer given is not the correct composition of the two functions.

Question 5

Scoring Guide

Solution:

a. 2, 4, 8, 16

b. 6th term = 65

7th term = 129

c. Difference between nth and (n + 1)st term is 2ⁿ

Value points:

a. 1 point

b. 2 points - 1 point for correct 6th term (65)

1 point for correct 7th term (129)

1 point if arithmetic error made when adding 32 to get 6th term or 64 to get 7th term (work must be shown for both terms)

c. 1 point for correct expression 2ⁿ or 2^x

Score & Description

	Correct
	4 value points

	Partial
	2 - 3 value points

	Minimal
	1 value point

	Incorrect
	0 value points

Correct - Student Response

5	Sequence I, shown above, is an increasing sequence. Each term in the sequence is greater than the previous term.

	Scorer Comments: This response received full credit because the student correctly answered all three parts of the problem.

Partial - Student Response

5	Sequence I, shown above, is an increasing sequence. Each term in the sequence is greater than the previous term.

	Scorer Comments: This response received partial credit because the student correctly answered parts a and b of the problem.

Minimal - Student Response

5	Sequence I, shown above, is an increasing sequence. Each term in the sequence is greater than the previous term.

	Scorer Comments: This response received minimal credit because the student correctly answered part a of the problem only.

Incorrect - Student Response

5	Sequence I, shown above, is an increasing sequence. Each term in the sequence is greater than the previous term.

	Scorer Comments: This response received no credit because all three parts were answered incorrectly.

Question 6

Key


6.	The graph of ƒ(x) = 2x³ is shown above. Which of the following is the graph of -ƒ(x) ?

	A)
	B)
	C)
	D)
	E)

Question 7

Key


7.	In the solution of the system of equations above, what is the value of x ?

	A)	- 1
	B)	2
	C)	3
	D)	4
	E)	5

Question 8

Key


8.	What are all values of x such that x² + 7x + 6 ≥ 0 ?

	A)	-6 ≤ x ≤ -1
	B)	-6 ≤ x ≤ 1
	C)	1 ≤ x ≤ 6
	D)	x ≤ -6 or x ≥ -1
	E)	x ≤ 1 or x ≥ 6

Question 9

Key


9.	The graph of ƒ(x) = sin x is shown above. Which of the following is the x coordinate of point P ?

	A)
	B)
	C)
	D)
	E)

Question 10

Key


10.	The first term in a sequence of numbers is . Each term after the first term is 1 more than twice its previous term. What is the 4th term?

	A)	2
	B)	4
	C)	5
	D)	11
	E)	23

Question 11

Key


11.	Rosa is twice as old as Byron. Fred is one year older than Byron. If Fred's age is represented by F, which of the following represents the ages of Rosa and Byron, respectively?

	A)	½ (F - 1) and F - 1
	B)	½ (F + 1) and F + 1
	C)	2 (F - 1) and F - 1
	D)	2 (F + 1) and F + 1
	E)	2F and F - 1

Question 12

Key


12.	Which of the following best illustrates a geometric representation of (x + 2) (x + 4) ?

	A)
	B)
	C)
	D)
	E)

Question 13

Scoring Guide

Solution:

Solution 1 - Take 80% of the cost at the beginning of each year.

Value of car at the end of year 1: $16,000 (20,000 x .8)

Value of car at the end of year 2: $12,800 (16,000 x .8)

Value of car at the end of year 3: $10,240 (12,800 x .8)

Value of car at the end of year 4: $8,192 (10,240 x .8)

$8,192 < $10,000 so at the end of 4 years.

Solution 2 - Take 20% of the cost at the beginning of each year and subtract that from the cost at the beginning of each year.

20,000 x .2 = 4,000 20,000 - 4,000 = $16,000 End of 1st year

16,000 x .2 = 3,200 16,000 - 3,200 = $12,800 End of 2nd year

12,800 x .2 = 2,560 12,800 - 2,560 = $10,240 End of 3rd year

10,240 x .2 = 2,048 10,240 - 2,048 = $8,192 End of 4th year

$8,192 < $10,000 so at the end of 4 years.

Solution 3 - Use depreciation formula.

So at the end of 4 years the car will be worth less than half of its original cost.

Solution 4 - Use depreciation formula with base e.

20,000e^k·1 = 16,000

k = -0.223

20,000e^-0.223t= 10,000

t = 3.1062...

So at the end of 4 years the car will be worth less than half of its original cost.

Score & Description

Correct

Correct response.

4 years with correct work shown or explanation given.

An answer of 3.1063 (or some rounded value of that to the nearest tenth or smaller) with correct work is acceptable. The correct work could show a sequence of correct computations and/or the results of those computations. For example, since a calculator is available for this question, the student may just show the amounts $16,000; $12,800; $10,240; and $8,192 at the ends of the first 4 years, respectively.

Partial

Partially correct response.

A correct number of years with no work or partially correct or partially complete supporting work.

For example, partially correct work might show understanding of iteration, that the solution involves or exponential depreciation.

Minimal

Partially correct response .

An incorrect number of years with work that demonstrates a correct process.

Correct process may be demonstrated by a partially correct sequence of computations, although the results of one or more of those computations may be incorrect.

	Incorrect
	Incorrect response.

Correct - Student Response

13	A car costs $20,000. It decreases in value at the rate of 20 percent each year, based on the value at the beginning of that year. At the end of how many years will the value of the car first be less than half the cost?

	Scorer Comments: This response received full credit because the student specified the correct number of years and has shown work to support the answer.

Partial - Student Response

13	A car costs $20,000. It decreases in value at the rate of 20 percent each year, based on the value at the beginning of that year. At the end of how many years will the value of the car first be less than half the cost?

	Scorer Comments: This response received partial credit because the student gave the correct number of years, but provided incomplete work.

Minimal - Student Response

13	A car costs $20,000. It decreases in value at the rate of 20 percent each year, based on the value at the beginning of that year. At the end of how many years will the value of the car first be less than half the cost?

	Scorer Comments: This response received minimal credit because the student has an incorrect number of years, but followed the correct process.

Incorrect - Student Response

13	A car costs $20,000. It decreases in value at the rate of 20 percent each year, based on the value at the beginning of that year. At the end of how many years will the value of the car first be less than half the cost?

	Scorer Comments: This response received no credit because the answer given is incorrect and there is no work to support the answer.

Question 14

Key


14.	The number of bacteria present in a laboratory sample after t days can be represented by 500(2^t). What is the initial number of bacteria present in this sample?

	A)	250
	B)	500
	C)	750
	D)	1,000
	E)	2,000

Question 15

Key


15.	Yvonne has studied the cost of tickets over time for her favorite sports team. She has created a model to predict the cost of a ticket in the future. Let C represent the cost of a ticket in dollars and y represent the number of years in the future. Her model is as follows. C = 2.50y + 13 Based on this model, how much will the cost of a ticket increase in two years?

	A)	$5
	B)	$8
	C)	$13
	D)	$18
	E)	$26

Question 16

Key


16.	What number if placed in each box above would make both equations true?

	A)	0
	B)	1
	C)	2
	D)	3
	E)	4

Question 17

Key


17.	cos²(3x) + sin²(3x) =

	A)	0
	B)	1
	C)	3
	D)	6
	E)	9

Question 18

Key


18.	Which of the following could be the graph of a function?

	A)
	B)
	C)
	D)
	E)

Question 19

Scoring Guide

Solution:

The explanation should indicate there are 442 tiles in the 20th figure.
Descriptions will vary
A correct one should suggest a row of 21 tiles across the top, a row of 21 across the bottom, and a 20 x 20 square between these rows. The top row extends one tile to the right of the square and the bottom row one tile to the left.
A diagram such as this might illustrate the student's counting methods

Counting methods are supported by generalizations (verbal or symbolic) that are based on the students' observations about the pattern.

Scoring Guide

In this question, a student had to use reasoning skills as well as problem solving skills to describe the number of tiles that would be in the 20th figure. A student needed to recognize the pattern that was given and be able to generalize it in some correct way. In addition, the student had to write a description that could be used to describe any figure in the pattern. Different levels of partial credit (satisfactory, partial, and minimal) were earned by a student depending on his or her reasoning skills and the description of the 20th figure.

Score & Description

	Extended
	The 20th figure is described correctly, including the fact that there are 442 tiles with a clear, accurate explanation.

	Satisfactory
	The 20th figure is described and the number of tiles is given. Some evidence of reasoning must be present. Reasoning is sound but there may be a computation error.

	Partial
	Illustrates or describes at least one additional figure in the pattern correctly or states there are 442 tiles in the 20th figure

	Minimal
	Attempts to draw or describe the given pattern or an additional figure in the pattern

	Incorrect
	Incorrect response

Extended - Student Response

19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.

Satisfactory - Student Response

19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.


19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.

Partial - Student Response

19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.


19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.

Minimal - Student Response

19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.


19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.

Incorrect - Student Response

19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.


19	The first 3 figures in a pattern of tiles are shown below. The pattern of tiles contains 50 figures.

Question 20

Key

20.

6 x 10³	=
3 x 10⁵

0.5 × 10²

2 × 10²

2 × 10^0.6

0.5 × 10^-2

2 × 10^-2

Question 21

Key


21.	If x = -4, the value of -4x is

	A)	-16
	B)	-8
	C)	8
	D)	16

Question 22

Key


22.	In ABC shown above, AC = 12. What is the length of segment BD?

	A)
	B)
	C)
	D)
	E)

Question 23

Key


23.	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

Question 24

Scoring Guide

Score & Description

	Correct
	27

	Incorrect
	Any incorrect response.

Correct - Student Response

24	If n × n = 729, what does n equal?


24	If n × n = 729, what does n equal?

Incorrect - Student Response

24	If n × n = 729, what does n equal?


24	If n × n = 729, what does n equal?

Question 25

Key


25.	For what value of x is 8¹² = 16^x?

	A)	3
	B)	4
	C)	8
	D)	9
	E)	12

Question 26

Scoring Guide

Score & Description

	Correct
	f(3.5) = 4(3.5)² - 7(3.5) + 5.7 = 30.2

	Incorrect
	Any incorrect response.

Correct - Student Response

26	If f(x) = 4x² - 7x + 5.7, what is the value of f(3.5)?


26	If f(x) = 4x² - 7x + 5.7, what is the value of f(3.5)?

Incorrect - Student Response

26	If f(x) = 4x² - 7x + 5.7, what is the value of f(3.5)?


26	If f(x) = 4x² - 7x + 5.7, what is the value of f(3.5)?

Question 27

Key


27.	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 28

Scoring Guide

Score & Description

	Correct #1
	85.9 or 85.90

	Correct #2
	85.8 to 85.913474, not including 85.9 or 85.90

	Incorrect #2
	687.3

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

*The use of more than one correct category in this question enabled NAEP to gather data on different ways students responded correctly to this question. Any one of these responses that fell into one of these correct categories earned full credit.

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit.

Correct #1 - Student Response

28	In the equation above, what is the value of N, rounded to the nearest tenth?


28	In the equation above, what is the value of N, rounded to the nearest tenth?

Correct #2 - Student Response

28	In the equation above, what is the value of N, rounded to the nearest tenth?


28	In the equation above, what is the value of N, rounded to the nearest tenth?

Incorrect #2 - Student Response

28	In the equation above, what is the value of N, rounded to the nearest tenth?

Incorrect #1 - Student Response

28	In the equation above, what is the value of N, rounded to the nearest tenth?


28	In the equation above, what is the value of N, rounded to the nearest tenth?

Question 29

Scoring Guide

Score & Description

	Correct #1
	51° tan OAB = 15/12, OAB = 51°

	Correct #2
	51.340192°

	Incorrect #2
	1 Radian or .8960554

	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 #1 - Student Response

29	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?

Correct #2 - Student Response

29	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?

Incorrect #2 - Student Response

29	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?

Incorrect #1 - Student Response

29	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?

Question 30

Scoring Guide

Solution:

Yes, it can be 5%:
Let x = income
.05x = .06(x-10,000)
.05x = .06x-600
600 = .01x
60,000 = x
If the income is $60,000 then the effective tax rate is 5%.

No, it can not be 6%:
Let x = income
.06x = .06(x-10,000)
0 = 60,000 FALSE
OR
Income of $x > 10,000
Tax = .06(x-$10,000)
Effective tax rate = = .06 -
As x becomes large, effective tax rate approaches 6% but theoretically never gets to 6% exactly.
OR
is always a positive number, so
.06 - is always less than .06.

Examples: (optional)
Income of $50,000:
tax = .06(50,000 - 10,000)
= $2,400
effective tax rate = = 4.8%
Income of $100,000:
tax = .06(100,000-10,000)
= $5,400
effective tax rate = = 5.4%

Score & Description

	Extended
	Complete, correct algebraic solution and explanation is given for both 5% and 6%.

	Satisfactory
	Student correctly shows that the rate can be 5%, or shows that 6% is not possible, but not both.

	Partial
	There is a relevant correct equation or example related to the effective tax rate.

	Minimal
	Student shows some evidence of trying to work with 5% or 6% and the $10,000 appropriately.

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

Extended - Student Response

30	One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.

Satisfactory - Student Response

30	One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.

Partial - Student Response

30	One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.

Minimal - Student Response

30	One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.


30	One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.

Incorrect/Off Task - Student Response

30	One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.

Question 31

Key


31.	3³ + 4(8-5) ÷ 6 =

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

Question 32

Scoring Guide

Solution:
(10n + 5)² = 100n² + 100n + 25
= 100(n² + n) + 25

Since n is an integer, n² is an integer; n² + n is also an integer and 100(n² + n) is a multiple of 100 that ends in 00. When 25 is added to that integer, the sum ends in 25.

Note: If (10n + 5) is squared incorrectly, the other work must be checked. The student can earn a Minimal of Partial depending on the correctness of the work.

Score & Description

	Extended
	Student provides a complete, correct solution. (The student need not show 100 (n² + n) if the explanation is clear and must demonstrate that (10n + 5) has been squared correctly; e.g., "When 10n + 5 is squared, two of the terms will be multiples of 100 and the other will be 25."

	Satisfactory
	States (10n + 5)² = 100n² + 100n + 25 and ties 25 to a multiple of 100. Explanation is incomplete or not clear.

	Partial
	States (10n + 5)² = 100n² + 25, and explains using multiples of 100; e.g., "An integer multiplied by 100 will always end in 2 zeros. Therefore, when you add 25, the number will always end in 25." OR Just ties 25 to a multiple of 100.

	Minimal
	Student provides numerical examples other than 5×5 = 25 or the ones provided in the question, e.g., 45×45 = 2025. OR States (10n + 5)² = 100n² + 25 only. OR Student states (10n + 5)² = 100n² + 100n + 25, but does not mention zero(s).

Incorrect/Off Task

The work is completely incorrect, irrelevant, or off task.

Only repeats given information.

Extended - Student Response

15²	=	225
25²	=	625
35²	=	1225

The examples above suggest the following statement.

When a positive integer that ends in the digit 5 is squared, the resulting integer ends in 25.

Explain why this statement is always true.
(Hint: (10n + 5)²= ? )

Satisfactory - Student Response

15²	=	225
25²	=	625
35²	=	1225

The examples above suggest the following statement.

When a positive integer that ends in the digit 5 is squared, the resulting integer ends in 25.

Explain why this statement is always true.
(Hint: (10n + 5)²= ? )

15²	=	225
25²	=	625
35²	=	1225

The examples above suggest the following statement.

When a positive integer that ends in the digit 5 is squared, the resulting integer ends in 25.

Explain why this statement is always true.
(Hint: (10n + 5)²= ? )

Partial - Student Response

15²	=	225
25²	=	625
35²	=	1225

The examples above suggest the following statement.

When a positive integer that ends in the digit 5 is squared, the resulting integer ends in 25.

Explain why this statement is always true.
(Hint: (10n + 5)²= ? )

Minimal - Student Response

15²	=	225
25²	=	625
35²	=	1225

The examples above suggest the following statement.

When a positive integer that ends in the digit 5 is squared, the resulting integer ends in 25.

Explain why this statement is always true.
(Hint: (10n + 5)²= ? )

Incorrect/Off Task - Student Response

15²	=	225
25²	=	625
35²	=	1225

The examples above suggest the following statement.

When a positive integer that ends in the digit 5 is squared, the resulting integer ends in 25.

Explain why this statement is always true.
(Hint: (10n + 5)²= ? )

Question 33

Key


33.	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)

Question 34

Key


34.	In right triangle ABC above, cos A =

	A)	3/5
	B)	3/4
	C)	4/5
	D)	4/3
	E)	5/3

Question 35

Scoring Guide

Solution:
a) and b)

d) Between 3 and 4 seconds.

Score & Description

	Extended
	Complete, correct answer, (must show change in slope exactly at (4,4) and (4,3)).

	Satisfactory
	Both graphs are correct, (Change in slope need not occur exactly as (4,4) and (4,3)). P is located correctly or the time of equidistance is correct.

	Partial
	At least one graph is correct (must show change in slope, but curve is not required). P is not located or is located incorrectly and the time of equidistance is incorrect or missing OR One or both graphs incorrect, but P is located correctly for their graph.

	Minimal
	At least 2 points are plotted correctly on at least one graph that is not just a reiteration of the position graph; i.e., a plot of distance versus time.

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

Extended - Student Response

35	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.

Satisfactory - Student Response

35	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.


35	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.

Partial - Student Response

35	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.


35	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.

Minimal - Student Response

35	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.

Incorrect/Off Task - Student Response

35	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.

Question 36

Key


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

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

Question 37

Key


37.	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 38

Key


38.	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 39

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

39	Explain how you found your answer to question 16.

Incorrect #1 & 2 - Student Response

39	Explain how you found your answer to question 16.


39	Explain how you found your answer to question 16.

Question 40

Key


40.	What is the value of g(1)?

	A)	2
	B)	4
	C)	5
	D)	6
	E)	8

Question 41

Key


41.	What is the value of f(g(1))?

	A)	2
	B)	4
	C)	5
	D)	6
	E)	8

Question 42

Scoring Guide

Score & Description

	Correct
	Correct answer:

Incorrect

Incorrect answer

Includes only one correct root

Correct - Student Response

42	What are the roots of 2x² + 5x + 1 = 0?


42	What are the roots of 2x² + 5x + 1 = 0?

Incorrect - Student Response

42	What are the roots of 2x² + 5x + 1 = 0?


42	What are the roots of 2x² + 5x + 1 = 0?

Question 43

Key

43.

If d = 110 and a = 20 in the formula d =

(2t - 1), then t =

111

Question 44

Key


44.	How many integers are there between and ?

	A)	Three
	B)	Four
	C)	Five
	D)	Six
	E)	Seven

Question 45

Scoring Guide

Score & Description

Correct

5.47

Solution:

sin 23° = (correct equation)

BC = 14 sin 23° (correct equation)

BC = 5.47

	Incorrect #1
	Incorrect equation and incorrect answer other than 5.4 or 5.5

	Incorrect #2
	A correct equation and an incorrect answer other than 5.4 or 5.5

	Incorrect #3
	5.4 or 5.5

*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

45	In right triangle ABC shown above, AB = 14. What is BC to the nearest hundredth?

Incorrect #1 - Student Response

45	In right triangle ABC shown above, AB = 14. What is BC to the nearest hundredth?

Incorrect #2 - Student Response

45	In right triangle ABC shown above, AB = 14. What is BC to the nearest hundredth?

Incorrect #3 - Student Response

45	In right triangle ABC shown above, AB = 14. What is BC to the nearest hundredth?

Question 46

Key


46.	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

Question 47

Key


47.	Suppose that a₁ , a₂ , a₃ , . . . is the sequence of numbers such that a₁ = 3, a₂ = + 1, a₃ = + 1, and, in general, a_n+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