
/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  

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? 



 
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? 


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.  

18. 
What is the distance between the points (2,10) and (4,2) in the xyplane?  
A)  6  
B)  8  
C)  10  
D)  14  
E)  18  
Did you use the calculator on this question? 
19. 
In the xyplane, a line parallel to the xaxis intersects the yaxis 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? 

 
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  

 
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  

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? 

 
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? 
Scoring Guide 
Solution: a) b) Other angles measure 70° 
Score & Description  
 
 

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. 


Scoring Guide 
Solution: A pyramid Any of the following are also acceptable:

Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
4 
If the figure above is folded on the dotted lines so that all the points labeled P touch each other, what threedimensional 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 threedimensional 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 threedimensional 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. 




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  
 
 

* 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. 
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. Scoring Guide In this question, a student needed to take 2 isosceles triangles and construct a 4sided 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  
 
 

* 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 4sided 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 4sided 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 4sided 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 4sided 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 4sided 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 4sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet. 
Scoring Guide 
Solution: Four possible correct responses are listed below:
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  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. 

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

* The use of more than one correct category in this question enabled NAEP to gather data on different ways in which students responded correctly to this question. Any response that fell into one of these correct categories earned full credit. * The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
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. 
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  
 
 
 

* 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. 

Scoring Guide 
Solution: Note: This question is listed as a short constructedresponse question. It should be considered a multiplechoice question with multiple parts. 
Score & Description  
 
 
 
 

4 Right  Student Response 
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. 



Scoring Guide 
Score & Description  
 
 
 

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

Scoring Guide 
Solution: Note: This question is listed as a short constructedresponse question. It should be considered a multiplechoice question with multiple parts. 
Score & Description  
 
 
 
 

4 Right  Student Response 
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. 





Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
30 
What is the greatest number of squares with 9inch 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 9inch 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 9inch sides that can be cut from a rectangular piece of cloth 18 inches by 36 inches? 

Scoring Guide 
Score & Description  
 
 

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