NAEP NQT v3.0 -- Print Output

Additional Materials (1)

Additional Materials (2)

Additional Materials (3)

Additional Materials (4)

Additional Material (1)

Question 1 refers to Additional Materials (1)

1.	A triangle has two sides, each of length 8 centimeters, and the angle formed by these two sides measures 40°.

	a. Use your protractor and ruler to accurately draw the triangle.

	b. What is the measure of one of the other two angles of the triangle?

/STRONG> refers to the following diagram. The diagram is part of a scale drawing of a house.
2.	What is the length, in feet, of the side whose dimension is not given in the diagram?

	A)	12
	B)	24
	C)	30
	D)	36
	E)	40

3.	In which of the following figures is the dashed line NOT a line of symmetry?

	A)
	B)
	C)
	D)
	E)


4.	If the figure above is folded on the dotted lines so that all the points labeled P touch each other, what three-dimensional figure will result?

	Answer: _________________________

5.	Which of the right triangles below could NOT be a 30° - 60° - 90° triangle?

	A)
	B)
	C)
	D)
	E)

6.	Which of the following pairs of geometric figures must be similar to each other?

	A)	Two equilateral triangles
	B)	Two isosceles triangles
	C)	Two right triangles
	D)	Two rectangles
	E)	Two parallelograms

Did you use the calculator on this question?


7.	In the figure above, Elm Street is to be constructed parallel to Main Street. What is the value of x ?

	A)	70
	B)	110
	C)	120
	D)	130
	E)	140

Did you use the calculator on this question?


8.	The figure above will be rotated clockwise 180° about point P. Which of the following will be its position after the rotation?

	A)
	B)
	C)
	D)
	E)

Did you use the calculator on this question?

Question 9 refers to Additional Material (1)

With this test booklet, you will receive a packet of 6 pieces: 2 each of shape N, shape P, and shape Q. You will use these pieces in answering some of the questions. You can turn the pieces in any way or flip them over. You may use drawings to help explain your answers.
9.	Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q.
	Answer:

Question 10 refers to Additional Material (1)

10.	Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet.

Question 11 refers to Additional Material (1)

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.
11.	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.


12.	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

Did you use the calculator on this question?

13.	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.

14.	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:____________________

15.	Which of the following is NOT a property of every rectangle?

	A)	The opposite sides are equal in length.
	B)	The opposite sides are parallel.
	C)	All angles are equal in measure.
	D)	All sides are equal in length.
	E)	The diagonals are equal in length.


16.	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


17.	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.


Did you use the calculator on this question?

18.	What is the distance between the points (2,10) and (-4,2) in the xy-plane?

	A)	6
	B)	8
	C)	10
	D)	14
	E)	18

Did you use the calculator on this question?

19.	In the xy-plane, a line parallel to the x-axis intersects the y-axis at the point (0, 4). This line also intersects a circle in two points. The circle has a radius of 5 and its center is at the origin. What are the coordinates of the two points of intersection?

	A)	(1, 2) and (2, 1)
	B)	(2, 1) and (2, -1)
	C)	(3, 4) and (3, -4)
	D)	(3, 4) and (-3, 4)
	E)	(5, 0) and (-5, 0)

Did you use the calculator on this question?


20.	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°

Did you use the calculator on this question?


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

Did you use the calculator on this question?


22.	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


23.	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.


24.	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.

25.	A straight line segment could NOT be drawn on the surface of which of the following solids?

	A)
	B)
	C)
	D)
	E)


26.	Which of the following shows the result of flipping the above triangle over the line ?

	A)
	B)
	C)
	D)
	E)


27.	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


28.	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

29.	Which of the following figures contains line segments that are perpendicular?

	A)
	B)
	C)
	D)

30.	What is the greatest number of squares with 9-inch sides that can be cut from a rectangular piece of cloth 18 inches by 36 inches?
	Answer: ____________________

31.	If the diameter of a circle is 30 centimeters, what is the radius of the circle?

	A)	10 cm
	B)	15 cm
	C)	60 cm
	D)	90 cm
	E)	180 cm

Did you use the calculator on this question?


32.	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: ____________________

Did you use the calculator on this question?


33.	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

Did you use the calculator on this question?

Question 1

Scoring Guide

Solution:

triangle

b) Other angles measure 70°

Score & Description

	Correct
	Correct response - draws correct triangle and finds measure of other angle to be 70° . Sides must be 8 cm. , angle must be 40° .

Partial

Any three of the following four are correct:

one 8 cm. side is drawn
the other 8 cm. side is drawn
the 40-degree angle is drawn (within 1 degree)
part b response

If the two 8 cm. segments are NOT connected by a third segment to form a triangle, the score should be reduced by 1, but not below a final score of 1.

	Incorrect
	Incorrect response.

Correct - Student Response

1	A triangle has two sides, each of length 8 centimeters, and the angle formed by these two sides measures 40°.

	Scorer Comments: This response received full credit because the student correctly drew the triangle and found the measure of the other angles.

Partial - Student Response

1	A triangle has two sides, each of length 8 centimeters, and the angle formed by these two sides measures 40°.

	Scorer Comments: This response received partial credit because the student drew a triangle with two of the sides measuring eight centimeters and correctly answered part b; however, the angle enclosed by the two sides does not measure 40 degrees.

Incorrect - Student Response

1	A triangle has two sides, each of length 8 centimeters, and the angle formed by these two sides measures 40°.

	Scorer Comments: This response received no credit because the triangle is not drawn correctly and the answer given for part b is incorrect.

Question 2

Key


2.	What is the length, in feet, of the side whose dimension is not given in the diagram?

	A)	12
	B)	24
	C)	30
	D)	36
	E)	40

Question 3

Key


3.	In which of the following figures is the dashed line NOT a line of symmetry?

	A)
	B)
	C)
	D)
	E)

Question 4

Scoring Guide

Solution:

A pyramid

Any of the following are also acceptable:

a square-based pyramid
a pyramid with a square base
a square pyramid
a regular square pyramid
a rectangle pyramid

Score & Description

	Correct
	Correct response.

	Incorrect #2
	Triangle

	Incorrect #1
	Any incorrect response other than as described in 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

4	If the figure above is folded on the dotted lines so that all the points labeled P touch each other, what three-dimensional figure will result?

	Scorer Comments: This response received full credit because the student correctly determined the shape of the figure to be a pyramid when folded.

Incorrect #2 - Student Response

4	If the figure above is folded on the dotted lines so that all the points labeled P touch each other, what three-dimensional figure will result?

	Scorer Comments: In this paper, the student put triangle for an answer instead of pyramid. This particular response was coded to gather data on common student errors, but the paper received no credit.

Incorrect #1 - Student Response

4	If the figure above is folded on the dotted lines so that all the points labeled P touch each other, what three-dimensional figure will result?

	Scorer Comments: Papers scored as incorrect #1 received no credit and represent incorrect responses different than the one described in incorrect #2.

Question 5

Key


5.	Which of the right triangles below could NOT be a 30° - 60° - 90° triangle?

	A)
	B)
	C)
	D)
	E)

Question 6

Key


6.	Which of the following pairs of geometric figures must be similar to each other?

	A)	Two equilateral triangles
	B)	Two isosceles triangles
	C)	Two right triangles
	D)	Two rectangles
	E)	Two parallelograms

Question 7

Key


7.	In the figure above, Elm Street is to be constructed parallel to Main Street. What is the value of x ?

	A)	70
	B)	110
	C)	120
	D)	130
	E)	140

Question 8

Key


8.	The figure above will be rotated clockwise 180° about point P. Which of the following will be its position after the rotation?

	A)
	B)
	C)
	D)
	E)

Question 9

Scoring Guide

Solution:
N is a square (but P and Q are triangles.)
OR
N has four sides, (or vertices or points or angles), (but P and Q each have 3).
OR
All the sides of N are equal (but not so with P and Q).
OR
All the angles of N are equal (or, all right angles), (not so with P and Q.)

Scoring Guide

In this question, a student needed to compare the shapes with respect to a common attribute such as number of sides or angles or vertices. The student could choose which attribute he or she wished to use.

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.

Correct - Student Response

9	Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q.


9	Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q.

Incorrect #2 - Student Response

9	Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q.


9	Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q.

Incorrect #1 - Student Response

9	Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q.


9	Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q.

Question 10

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.

Correct #1 - Student Response

10	Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet.


10	Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet.

Correct #2 - Student Response

10	Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet.


10	Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet.

Incorrect - Student Response

10	Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet.


10	Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet.

Question 11

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

Extended - Student Response

11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.

Satisfactory - Student Response

11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.


11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.

Partial - Student Response

11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.


11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.

Minimal - Student Response

11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.


11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.

Incorrect - Student Response

11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.


11	Describe a procedure for locating the point that is the center of a circular paper disk. Use geometric definitions, properties, or principles to explain why your procedure is correct. Use the disk provided to help you formulate your procedure. You may write on it or fold it in any way that you find helpful, but it will not be collected.

Question 12

Key


12.	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

Question 13

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 incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit.

Correct #1 - Student Response

13	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.

Correct #2 - Student Response

13	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.


13	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.

Incorrect #2 - Student Response

13	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.


13	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.

Incorrect #1 - Student Response

13	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.


13	In the space below, use your ruler to draw a parallelogram that has perpendicular diagonals. Show the diagonals in your sketch.

Question 14

Scoring Guide

Solution:
A correct line m and a correct answer of 50° or angle between 46° and 54°, inclusive, are given.

Scoring Guide

In this question, a student had to use a protractor (that was provided at the assessment administration) to draw a line through a given point and perpendicular to a given line segment. The student had to know the meaning of perpendicular in order to correctly answer the question and the student had to give the angle measurement of the smaller angle formed by the intersection of the two lines.

Score & Description

	Correct
	Correct response

	Incorrect #3
	A correct angle response between 46° and 54° and an incorrect line m drawn

	Incorrect #2
	A correct line m and an incorrect angle answer not between 46° and 54°

	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.

Correct - Student Response

14	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.


14	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.

Incorrect #3 - Student Response

14	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.

Incorrect #2 - Student Response

14	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.


14	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.

Incorrect #1 - Student Response

14	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.


14	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.

Question 15

Key


15.	Which of the following is NOT a property of every rectangle?

	A)	The opposite sides are equal in length.
	B)	The opposite sides are parallel.
	C)	All angles are equal in measure.
	D)	All sides are equal in length.
	E)	The diagonals are equal in length.

Question 16

Key


16.	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

Question 17

Scoring Guide

Solution:
Note: This question is listed as a short constructed-response question. It should be considered a multiple-choice question with multiple parts.

Score & Description

	4 Right

	3 Right

	2 Right

	1 Right

	0 Right

4 Right - Student Response

17	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.


17	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.

3 Right - Student Response

17	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.


17	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.

2 Right - Student Response

17	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.


17	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.

1 Right - Student Response

17	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.


17	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.

0 Right - Student Response

17	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.


17	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.

Question 18

Key


18.	What is the distance between the points (2,10) and (-4,2) in the xy-plane?

	A)	6
	B)	8
	C)	10
	D)	14
	E)	18

Question 19

Key


19.	In the xy-plane, a line parallel to the x-axis intersects the y-axis at the point (0, 4). This line also intersects a circle in two points. The circle has a radius of 5 and its center is at the origin. What are the coordinates of the two points of intersection?

	A)	(1, 2) and (2, 1)
	B)	(2, 1) and (2, -1)
	C)	(3, 4) and (3, -4)
	D)	(3, 4) and (-3, 4)
	E)	(5, 0) and (-5, 0)

Question 20

Key


20.	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°

Question 21

Scoring Guide

Score & Description

Correct

9.6

	Incorrect #3
	8

	Incorrect #2
	6.66.... OR 6.7

	Incorrect #1
	Any incorrect response other than those described in Incorrect #2, Incorrect #3.

*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

21	In the figure above, the two triangles are similar. What is the value of x ?

Incorrect #3 - Student Response

21	In the figure above, the two triangles are similar. What is the value of x ?

Incorrect #2 - Student Response

21	In the figure above, the two triangles are similar. What is the value of x ?

Incorrect #1 - Student Response

21	In the figure above, the two triangles are similar. What is the value of x ?

Question 22

Key


22.	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

Question 23

Scoring Guide

Solution:
Note: This question is listed as a short constructed-response question. It should be considered a multiple-choice question with multiple parts.

Score & Description

	4 Right

	3 Right

	2 Right

	1 Right

	0 Right

4 Right - Student Response

23	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.

3 Right - Student Response

23	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.

2 Right - Student Response

23	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.

1 Right - Student Response

23	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.

0 Right - Student Response

23	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.

Question 24

Key


24.	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.

Question 25

Key


25.	A straight line segment could NOT be drawn on the surface of which of the following solids?

	A)
	B)
	C)
	D)
	E)

Question 26

Key


26.	Which of the following shows the result of flipping the above triangle over the line ?

	A)
	B)
	C)
	D)
	E)

Question 27

Key


27.	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

Question 28

Key


28.	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

Question 29

Key


29.	Which of the following figures contains line segments that are perpendicular?

	A)
	B)
	C)
	D)

Question 30

Scoring Guide

Score & Description

	Correct
	8

	Incorrect #1
	Incorrect answer other than 2 or 4

	Incorrect #2
	Either 2 or 4

*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

30	What is the greatest number of squares with 9-inch sides that can be cut from a rectangular piece of cloth 18 inches by 36 inches?

Incorrect #1 - Student Response

30	What is the greatest number of squares with 9-inch sides that can be cut from a rectangular piece of cloth 18 inches by 36 inches?

Incorrect #2 - Student Response

30	What is the greatest number of squares with 9-inch sides that can be cut from a rectangular piece of cloth 18 inches by 36 inches?

Question 31

Key


31.	If the diameter of a circle is 30 centimeters, what is the radius of the circle?

	A)	10 cm
	B)	15 cm
	C)	60 cm
	D)	90 cm
	E)	180 cm

Question 32

Scoring Guide

Score & Description

Correct

13.45

Solution:

FE = CD = 9

AB = DG =

= 13.45

	Incorrect #1
	Incorrect Answer other than

	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

32	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?

Incorrect #1 - Student Response

32	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?

Incorrect #2 - Student Response

32	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?

Question 33

Key


33.	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