Item Specifications: Algebra 1
WASHINGTON COMPREHENSIVE ASSESSMENT PROGRAM
Sample Items for
End-of-Course
Assessments
Geometry
2011-2012
OFFICE
OF THE SUPERINTENDENT OF PUBLIC INSTRUCTION
Sample Items for End-of-Course Exams: Geometry
The purpose of this document is to identify sample items and previously released items that
align to the 2008 Mathematics Standards assessed on the End-of-Course Exams.
The performance expectations (PEs) in this document are identical to those in the Washington
State Test and Item Specifications. Performance expectations that will be assessed at the state
level appear in bold text. The remaining performance expectations, which appear in italicized
text, should be taught and assessed at the classroom level.
The information in the columns to the right of each performance expectation shows alignment
of each PE to other courses and item development parameters:




Integrated sequence shows the alignment of this PE to other courses. PEs that are
common to Algebra 1/Integrated Math 1 or Geometry/Integrated Math 2 are
labeled in green; PEs that align to other courses are labeled in yellow.
Cognitive complexity (C.C.) as Level 1, Level 2, Level 3, or Level 4 as defined by
Norman Webb.
Format may be Multiple-Choice (MC), Completion (CP), Short-Answer (SA), or not
assessed at the state level (NA).
Contextual Situation (Ctxt) may be required (Y), item dependent (I), or not allowed
(N).
Restrictions to cognitive complexity, item format and context are necessary to construct a valid
and reliable on-demand assessment; these restrictions are not necessary in classroom based
assessments. For more information regarding test organization, the types of items on the
exams, and considerations and procedures involved in item development, please refer to the
Test and Item Specifications.
Below each performance expectation, you will find links to two types of items:


OSPI practice items – These are items written by OSPI staff and aligned to Washington
State performance expectations.
Tasks located at Illustrative Mathematics Project – These tasks were written to address
the Common Core State Standards and are either partially or fully aligned to each
Washington State Performance Expectation.
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Sample Items for End-of-Course Exams: Geometry
G.1 Core Content: Logical arguments and proofs
(Logic)
Items may ask students to:
Integrated
Sequence
M1.4.A
G.1.A Distinguish between inductive and deductive
reasoning.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 29
C.C.
Format Ctxt
2
MC
I
G.1.D Write the converse, inverse, and contrapositive of a
M2.3.C 2,3
MC,SA
valid proposition and determine their validity.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 29 and 40
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 19 and 29
Y
G.1.E Identify errors or gaps in a mathematical argument
M2.3.B 2,3
and develop counterexamples to refute invalid
statements about geometric relationships.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 30
MC
I
G.1.F Distinguish between definitions and undefined
geometric terms and explain the role of definitions,
undefined terms, postulates (axioms), and theorems.
MC
N
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M2.3.D 1
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Sample Items for End-of-Course Exams: Geometry
G.2 Core Content: Lines and angles
(Geometry/Measurement)
Items may ask students to:
Integrated
Sequence
G.2.A Know, prove, and apply theorems about parallel and M1.4.E
perpendicular lines.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 31
C.C.
Format Ctxt
2,3
MC,CP
I
G.2.B Know, prove, and apply theorems about angles,
M1.4.F
including angles that arise from parallel lines
intersected by a transversal.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 35
2,3
MC,CP
I
G.2.C Explain and perform basic compass and straightedge M1.4.G
1,2 MC
N
constructions related to parallel and perpendicular
lines.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 20
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 18
The following items are aligned to Common Core State Standards and are at least partially aligned to
this Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/31
http://illustrativemathematics.org/illustrations/508
http://illustrativemathematics.org/illustrations/507
G.2.D Describe the intersections of lines in the plane and
in space, of lines and planes, and of planes in space.
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M3.5.A
1
MC
OSPI, Page 4
N
Sample Items for End-of-Course Exams: Geometry
G.3 Core Content: Two- and three-dimensional figures
Items may ask students to:
Integrated
Sequence
M2.3.E
C.C. Format Ctxt
G.3.A Know, explain, and apply basic postulates and
2
MC,SA N
theorems about triangles and the special lines, line
segments, and rays associated with a triangle.
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 11
http://www.k12.wa.us/assessment/StateTesting/TestQuestions/WASLPractice-ParentStudent.aspx,
item 20
http://www.k12.wa.us/Mathematics/pubdocs/QuickGuide_YR2.pdf, 2007 item 5
G.3.B Determine and prove triangle congruence, triangle
M1.4.D M2.3.F 2,3 MC,SA N
similarity, and other properties of triangles.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 31 and pg 43
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 26-28
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 7
The following items are aligned to Common Core State Standards and are at least partially aligned to
this Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/33
http://illustrativemathematics.org/illustrations/340
http://illustrativemathematics.org/illustrations/339
http://illustrativemathematics.org/illustrations/109
http://illustrativemathematics.org/illustrations/110
http://illustrativemathematics.org/illustrations/603
G.3.C Use the properties of special right triangles (30°–
M2.3.I
60°–90° and 45°–45°–90°) to solve problems.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 36
1,2
MC,CP
I
G.3.D Know, prove, and apply the Pythagorean Theorem
M2.3.G 1,2 MC,CP I
and its converse.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 36
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 22
The following items are aligned to Common Core State Standards and are at least partially aligned to
this Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/594
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Sample Items for End-of-Course Exams: Geometry
G.3.E Solve problems involving the basic trigonometric
M2.3.H 1,2 MC,SA I
ratios of sine, cosine, and tangent.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 45
The following items are aligned to Common Core State Standards and are at least partially aligned to
this Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/607
http://illustrativemathematics.org/illustrations/397
http://illustrativemathematics.org/illustrations/416
G.3.F Know, prove, and apply basic theorems about
M2.3.J 2,3 MC,CP I
parallelograms.
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 3
http://www.k12.wa.us/assessment/StateTesting/TestQuestions/WASLPractice-ParentStudent.aspx,
item 23
The following item is aligned to Common Core State Standards and is at least partially aligned to this
Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/35
G.3.G Know, prove, and apply theorems about properties
M2.3.K 2,3 MC,CP I
of quadrilaterals and other polygons.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 33 and 37
The following item is aligned to Common Core State Standards and is at least partially aligned to this
Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/605
G.3.H Know, prove, and apply basic theorems relating
M3.7.A
circles to tangents, chords, radii, secants, and
inscribed angles.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 37
2,3
MC,CP
G.3.I
I
Explain and perform constructions related to the
M3.7.C
1,2 MC
circle.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 20
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 9
N
G.3.J Describe prisms, pyramids, parallelepipeds,
tetrahedra, and regular polyhedra in terms of their
faces, edges, vertices, and properties.
N
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M3.5.B
1
MC
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Sample Items for End-of-Course Exams: Geometry
G.3.K Analyze cross-sections of cubes, prisms, pyramids,
M3.5.C
1,2 MC
N
and spheres and identify the resulting shapes.
The following item is aligned to Common Core State Standards and is at least partially aligned to this
Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/512
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Sample Items for End-of-Course Exams: Geometry
G.4 Core Content: Geometry in the coordinate plane
(Geometry/Measurement, Algebra)
Items may ask students to:
Integrated
Sequence
M1.3.H
G.4.A Determine the equation of a line in the coordinate
plane that is described geometrically, including a
line through two given points, a line through a
given point parallel to a given line, and a line
through a given point perpendicular to a given line.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 38
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 23
C.C. Format Ctxt
1,2
MC,CP
G.4.B Determine the coordinates of a point that is
M2.3.L 1,2 MC,CP
described geometrically.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 38
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 24, 41
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 15
G.4.C Verify and apply properties of triangles and
quadrilaterals in the coordinate plane.
M2.3.M 1,2
N
I
MC, SA I
G.4.D Determine the equation of a circle that is described M3.7.B
1,2 MC,CP N
geometrically in the coordinate plane and, given
equations for a circle and a line, determine the
coordinates of their intersection(s).
The following item is aligned to Common Core State Standards and is at least partially aligned to this
Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/223
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Sample Items for End-of-Course Exams: Geometry
G.5 Core Content: Geometric transformations
(Geometry/Measurement)
Items may ask students to:
Integrated
Sequence
M3.2.A
C.C.
G.5.A Sketch results of transformations and
2
compositions of transformations for a given twodimensional figure on the coordinate plane, and
describe the rule(s) for performing translations or
for performing reflections about the coordinate
axes or the line y = x.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 34
Format Ctxt
MC
I
G.5.B Determine and apply properties of
M3.2.B
2
MC
N
transformations.
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 13
http://www.k12.wa.us/Mathematics/pubdocs/QuickGuide_YR2.pdf, 2007 item 6
The following item is aligned to Common Core State Standards and is at least partially aligned to this
Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/602
G.5.C Given two congruent or similar figures in a
M3.2.C
2
coordinate plane, describe a composition of
translations, reflections, rotations, and dilations
that superimposes one figure on the other.
http://www.k12.wa.us/Mathematics/pubdocs/QuickGuide_YR2.pdf, 2007 item 16
MC
N
G.5.D Describe the symmetries of two-dimensional
figures and describe transformations, including
reflections across a line and rotations about a
point.
MC,CP
I
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M3.2.D
2
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Sample Items for End-of-Course Exams: Geometry
G.6 Additional Key Content
(Measurement)
Items may ask students to:
Integrated
Sequence
M3.7.D
C.C. Format Ctxt
G.6.A Derive and apply formulas for arc length and area of
1,2 MC
I
a sector of a circle.
The following items are aligned to Common Core State Standards and are at least partially aligned to
this Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/621
http://illustrativemathematics.org/illustrations/607
G.6.C Apply formulas for surface area and volume of
M3.5.D
1,2 MC,CP I
three-dimensional figures to solve problems.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 39
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 2
http://www.k12.wa.us/assessment/StateTesting/TestQuestions/WASLPractice-ParentStudent.aspx,
item 9
http://www.k12.wa.us/Mathematics/pubdocs/QuickGuide_YR2.pdf, 2007 item 12
The following items are aligned to Common Core State Standards and are at least partially aligned to
this Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/514
http://illustrativemathematics.org/illustrations/527
http://illustrativemathematics.org/illustrations/40
http://illustrativemathematics.org/illustrations/414
G.6.D Predict and verify the effect that changing one, two, M3.5.E
2
MC,CP I
or three linear dimensions has on perimeter, area,
volume, or surface area of two- and threedimensional figures.
http://www.k12.wa.us/assessment/StateTesting/TestQuestions/WASLPractice-ParentStudent.aspx,
item 24
G.6.E Use different degrees of precision in measurement,
M2.5.B 2
MC,SA I
explain the reason for using a certain degree of
precision, and apply estimation strategies to obtain
reasonable measurements with appropriate
precision for a given purpose.
The following items are aligned to Common Core State Standards and are at least partially aligned to
this Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/84
http://illustrativemathematics.org/illustrations/80
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Sample Items for End-of-Course Exams: Geometry
G.6.F Solve problems involving measurement conversions
M2.5.C 2
MC,CP I
within and between systems, including those
involving derived units, and analyze solutions in
terms of reasonableness of solutions and
appropriate units.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 21, 24-25 and 42
The following item is aligned to Common Core State Standards and is at least partially aligned to this
Washington State Performance Expectation:
http://illustrativemathematics.org/illustrations/473
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Sample Items for End-of-Course Exams: Geometry
G.7 Core Processes: Reasoning, problem solving, and communication
Items assessing G.7 Core Processes will use Core Content or Additional Key Content performance
expectations from Geometry, which are identified below for each sample item.
Items may ask students to:
Integrated
Sequence
C.C.
Format Ctxt
G.7.A Analyze a problem situation and represent it
mathematically.
G.7.B Select and apply strategies to solve problems.
M2.6.
3
MC,SA
G.7.C Evaluate a solution for reasonableness, verify its
A-C
accuracy, and interpret the solution in the context
of the original problem.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 32 (G.3.C,E)
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 41 (G.3.A)
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 44 (G.3.D)
G.7.E Read and interpret diagrams, graphs, and text
containing the symbols, language, and conventions
of mathematics.
M2.6.E
G.7.G Synthesize information to draw conclusions and
evaluate the arguments and conclusions of others.
M2.6.G 3
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2,3
I
SA
I
MC,SA
I
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Sample Items for End-of-Course Exams: Geometry
Other EOC Resources:
Many teachers and districts in Washington State have created resources to help prepare their
students for EOC Exams and EOC Makeup Exams. Other states and agencies have also created
and released resources aligned to their own state standards for mathematics or to the Common
Core State Standards. The resources below have not been thoroughly reviewed by OSPI staff,
but instead are the responsibility of the reader to analyze resources and determine if they suit
the needs of their own students.
Mukilteo School District EOC Makeup Review for Geometry:
http://www.bsd405.org/portals/0/curriculum/MSPMath/Geometry%20End%20of%20Course%
20Packet%203-16-11.pdf
Snohomish School District Review packet for Geometry:
http://www.sno.wednet.edu/index.php/download_file/-/view/2430/
ESD123 Math Initiative Regional Mathematics Bank: http://www.esd123.org/mathitem
Database of Teacher-Created Resources on the EOC Supports Moodle:
http://moodle.ospi.k12.wa.us/course/view.php?id=18
Resources compiled by Bellevue School District:
http://www.bsd405.org/portals/0/curriculum/MSPMath/
Interactive Quizzes for Algebra and Geometry Review: http://www.iq.poquoson.org/math.htm
National Center for Education Statistics NAEP Questions Tool:
http://nces.ed.gov/nationsreportcard/itmrlsx/search.aspx?subject=mathematics
Released items by Science & Mathematics Achievement Required for Tomorrow (SMART):
http://www.smartconsortium.org/index.php?id=122
Wisconsin Released Item Book for Grade 10 Mathematics:
http://dpi.wi.gov/oea/pdf/mathrelease10.pdf
TIMSS Released Set of 8th Grade Mathematics Items:
http://timss.bc.edu/PDF/T03_RELEASED_M8.pdf
Interactive Web Sample Items by North Carolina State University:
http://cuacs8.mck.ncsu.edu/mathsampleitems/main.html
Tennessee EOC Item Samplers and Practice Tests:
http://tennessee.gov/education/assessment/sec_samplers.shtml
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Sample Items for End-of-Course Exams: Geometry
Virginia Department of Education:
EOC Practice Items:
http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml
Released Exams:
http://www.doe.virginia.gov/testing/sol/released_tests/index.shtml
Georgia Geometry EOC Released Test Booklet, Spring 2004:
http://archives.gadoe.org/DMGetDocument.aspx/Released%20Geometry.pdf?p=4BE1EECF99C
D364EA5554055463F1FBBF5D074D5FB1F2CAEB3B63B3ECB220CDD26C2114F3C57D8D230D42
0D1DC7E9679&Type=D
Florida EOC Practice Tests:
http://www.pearsonaccess.com/cs/Satellite?c=Page&childpagename=Florida/flPALPLayout&ci
d=1205461226846&pagename=flPALPWrapper
CCSS Resources:
The Common Core State Standards of Mathematics define the knowledge and skills students
should have within their K-12 education careers so that they will graduate high school able to
succeed in entry-level, credit-bearing academic college courses and in workforce training
programs.
Common Core State Standards: http://www.k12.wa.us/corestandards/
The Illustrative Mathematics Project: http://www.k12.wa.us/corestandards/
SMARTER Balanced Assessment Consortium: http://www.smarterbalanced.org/
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