Document Sample

```					                    Grade 12 Geometry

This booklet contains sample items from the National Assessment of Educational Progress (NAEP).
Additional items can be accessed at www.nces.ed.gov/nationsreportcard/itmrls.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics
(NCES), National Assessment of Educational Progress (NAEP)
2
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Contents
Introduction ................................................................................................................................................................4
Question 1 - Find the missing dimension of a room ..................................................................................................5
Question 2 - Find the measure of angle between streets ..........................................................................................6
Question 3 - Find length of side in a 30-60-90 triangle ..............................................................................................7
Question 4 - Analyze properties of quadrilateral inscribed in circle ..........................................................................8
Question 5 - Determine which triangle is not a 30-60-90 right traingle ....................................................................9
Question 6 - Identify the 3-D figure resulting from folding paper .......................................................................... 10
Question 7 - Prove that given figure is a prallelogram ............................................................................................ 12
Question 8 - Perform multiple transformations of segment in xy-plane ................................................................ 15

3
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Introduction

This practice Geometry test includes a sample of publicly released items from NAEP. Included with
each item are the correct answer (indicated by an asterisk) and the distracters; the percentage of
Florida’s responses to each of the possible answers; and the Description, Difficulty, and Complexity of
each item.

Additional publicly released items and item data may be accessed through the NAEP Questions Tool
(NQT) at http://nces.ed.gov/nationsreportcard/itmrlsx/default.aspx. The NQT is an interactive tool
that provides access to over 2000 released questions from NAEP assessments in all NAEP subject areas.
It is also used to access NAEP assessment items, their correct answers and distracters, and their scoring
results by subject, grade, item type, difficulty, content classification, frameworks, year, and key words.

http://nces.ed.gov/nationsreportcard/naepdata/. The NDE is an interactive tool that provides access
to a wide variety of data about what students know and can do, as well as demographic and contextual
factors that may affect their performance. The NDE produces charts, customized tables, and graphics
based on NAEP results by year and jurisdiction; significance between jurisdictions, within variables, and
across years; and gap analyses between jurisdictions or across years and between groups, between
years, and between groups and years.

Additional information about the knowledge and skills the mathematics assessment is designed to
measure can be found in the 2011 Mathematics Framework,
http://www.nagb.org/publications/frameworks/math-2011-framework.pdf. The current NAEP
Mathematics Framework guided the development of all Mathematics assessments since 2005. The
previous NAEP Mathematics Framework guided the development of the mathematics assessments
between 1990 and 2003.

4
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment

Question 1
The diagram below is part of a scale drawing of a house.

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

National Data

Description: Find the missing dimension of a room
Difficulty: Easy
5
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Complexity: Low

Question 2
In the figure below, 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

National Results

Description: Find the measure of angle between streets
Difficulty: Easy

6
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Complexity: Low

Question 3
What is the value of h in the figure below?

a.

b.

c.

d.

e.

Answers            Percent chosen by Florida’s participating students
*C                 43%
A                  13%
B                  26%
D                  10%
E                  5%
Omitted            3%

Description: Find length of side in a 30-60-90 triangle
Difficulty: Medium
Complexity: Low

7
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 4
Quadrilateral ABCD is inscribed in circle O, and  is a right angle, as shown below. Segment AB is not
parallel to segment DC. Which of the following statements must be true?

Which of the following angles has a measure of 90˚?

a.
b.

c.        is a right angle

d.       is a diameter of circle O

e.        is a diameter of circle O .

Answers            Percent chosen by Florida’s participating students
*E                 61%
A                  12%
B                  11%
C                  9%
D                  7%
Omitted            1%

Description: Analyze properties of quadrilateral inscribed in circle
Difficulty: Medium
Complexity: Moderate

8
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 5
Which of the right triangles below could NOT be a 30° - 60° - 90°triangle?

a.

b.

c.

d.

e.

National Results

Description: Determine which triangle is not a 30-60-90 right angle
9
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Difficulty: Hard
Complexity: Low

Question 6
The figure below is folded on the dotted lines so that all the points labeled P touch each other, what
three-dimensional figure will result?

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.

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NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 6, continued

National Data

Description: Identify the 3-D figure resulting from folding paper
Difficulty: Easy
Complexity: Low

11
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 7
In the figure below, the vertices of ABCD are A(—4, —4), B(—2,2) C(8, 4) and D(6, —2).

Give a mathematical justification that ABCD is a parallelogram.

Solution:
Justification:

12
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 7, continued

Alternate Justifications:
Four other approaches to show that a quadrilateral is a parallelogram follow.

13
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 7, continued

NOTES:
 To be acceptable, a justification must include a complete statement or numerical
demonstration of the criteria.
 A partially correct justification shows a complete and correct process but has an arithmetic
error OR shows only that one set of lines are parallel or congruent, or that one set of angles
are congruent, etc.

Score & Description
Correct
Complete justification
Partial
Partially correct justification
Incorrect
Incorrect response

Scores                                 Percent chosen by Florida’s participating students
Complete                               3%
Partial                                2%
Unsatisfactory/Incorrect 70%
Omitted                                22%

Description: Prove that given figure is a parallelogram
Difficulty: Hard
Complexity: Moderate

14
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 8
Perform the following two transformations on the graph below. After each transformation, draw the
resulting image of segment PQ.

1. Rotate the segment 90˚ counterclockwise          about point P. Label the resulting segment
with a 1.
2. Reflect the segment you drew in part (1) across the x – axis. Label the resulting segment with
a 2.

15
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 8, continued

Solution:

Notes:
 After performing the first transformation correctly, segment PQ will have coordinates
and          . The coordinates are not required in the response.
 After performing the second transformation correctly, segment PQ will have coordinates
and                   . The coordinates are not required in the response.
 If the response includes dots in the figures, then the dots must contain the points listed above.

Score & Description

Correct
Both transformations performed correctly
Partial 1
First transformation performed correctly only
Partial 2
Second transformation performed correctly based on incorrect first transformation
Incorrect
Incorrect response

16
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment
Question 8, continued

Scores                                 Percent chosen by Florida’s participating students
Incorrect                              56%
Partial 2                              22%
Partial 1                              6%
Correct                                14%

Description: Perform multiple transformations of segment in xy-plane
Difficulty: Hard
Complexity: Low

17
NAEP Grade 12 Geometry Practice Test
Florida Department of Education
Division of Accountability, Research, and Measurement
Office of Assessment

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