SAMPLE TEST ITEMS Geometry

SAMPLE TEST ITEMS Geometry

CONTENTS INTRODUCTION

Purpose

MULTIPLE-CHOICE ITEMS GM: G-CO.D.12 Constructing a Perpendicular Bisector GM: G-CO.C.11 Opposite Sides of Parallelogram Proof GM: G-SRT.A.1a Line Dilation Centered at (0, 7) GM: G-SRT.B.5 Prove Triangles Similar GM: G-GPE.A.1 Determine Center and Radius of a Circle GM: G-GMD.A.3 Volume of a Pentagonal Pyramid GM: G-MG.A.2 Aviary Population Density GM: G-MG.A.3 Length of Fence for Maximum Area GM: G-CO.D.13 Square Inscribed in a Circle GM: G-SRT.A.3 Proving Angles Congruent for AA Similarity GM: G-SRT.B.4 Corresponding Angle Bisectors GM: G-SRT.C.6 Triangle Sides Given Tangent Value GM: G-SRT.C.7 cos ? = sin(90 - )? GM: G-C.A.1 Why are All Circles Similar? GM: G-GPE.B.6 Partition Segment 5 to 1 GM: G-GMD.A.1 Deriving Pyramid Volume Formula GM: G-MG.A.1 Hemisphere to Model Shape of a Pond

CONSTRUCTED-RESPONSE ITEMS GM: G-MG.A.3 Soybean Yield Sample Student Responses GM: G-SRT.C.8 Building a Wheelchair Ramp Sample Student Responses GM: G-MG.A.2 Determining Population Density

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INTRODUCTION Louisiana Believes embraces the principle that all children can achieve at high levels and promotes the idea that Louisiana's educators should be empowered to make decisions to support the success of their students. In keeping with these values, the Louisiana Department of Education (LDOE) created this document with released and sample test items to help prepare teachers and students for the End-of-Course (EOC) assessments. These items reflect the LDOE's commitment to deliver consistent and rigorous assessments and provide educators and families with clear information about expectations for student performance. Purpose of This Document Teachers are encouraged to use the released and sample test items to gauge student learning, guide instruction, and develop classroom assessments and tasks. The document includes multiple-choice and constructed-response items that exemplify how the Louisiana Student Standards for Mathematics will be assessed on the Geometry EOC test. A discussion of each item highlights the knowledge and skills the item is intended to measure. It is important to remember that these sample items represent only a portion of the knowledge and skills measured by the Geometry EOC test. The items assembled in this document have been previously available in separate documents released in 2013-2014 and 2014-2015. Additionally, these items have been reviewed by the LDOE to confirm alignment to the newly adopted content standards. MULTIPLE-CHOICE ITEMS This section presents a sampling of multiple-choice items selected to illustrate the types of skills and knowledge students need in order to demonstrate understanding of the Louisiana Student Standards and Standards for Mathematical Practices in the Geometry course. Information shown for each item includes the following: ? item data--conceptual category, domain, cluster, standard, Mathematical Practice(s) (MP), calculator designation

(allowed or not allowed), correct answer ? commentary--on the skills and knowledge associated with the standard measured by the item, on the MP(s) linked

with the item, on why the correct answer is correct (including how the answer is achieved), and on rationales for each incorrect answer option

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GM: G-CO.D.12 Constructing a Perpendicular Bisector Make formal geometric constructions with a variety of tools and methods, e.g., compass and straightedge, string, reflective devices, paper folding, or dynamic geometric software. Examples: copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Calculator Neutral Melanie wants to construct the perpendicular bisector of line segment AB using a compass and straightedge.

Which diagram shows the first step(s) of the construction?

A.

B.

C.

D.

This item requires students to identify the initial steps of constructing a perpendicular bisector. Constructions are typically difficult to assess in a multiple-choice format. However, asking students to analyze which figure will result in the given construction assesses reasoning about constructions without the need for providing geometric tools during testing or having to manually score each response. Mathematical Practice(s) MP 5 Students must recognize how to effectively use a compass to begin constructing a perpendicular bisector of a

line segment. MP 6 Students must recognize that only one method shown guarantees a precise construction. MP 7 Students must use the structure of the two congruent circles and recognize that the circles intersect at points

that are equidistant from the endpoints of the given line segment. These points may be connected to construct a perpendicular bisector.

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Correct Answer D.

Incorrect Options A.

B.

C.

Explanation The figure shows two circles that appear to be congruent centered at the endpoints of the given line segment. Connecting the intersection points of these two circles guarantees the bisecting line created is perpendicular (at a 90 degree angle) to segment AB.

Rationales for Incorrect Options This option has two circles that appear to be congruent and intersect at what appears to be the midpoint of segment AB; however, the figure does not show how a perpendicular bisector could be constructed, as it does not guarantee that a line drawn would intersect at a 90 degree angle.

This option has one circle that appears to be centered at the midpoint of segment AB. The midpoint is where a bisector will intersect, but this figure does not show how to ensure the bisector will be perpendicular.

This option has two circles with different radii centered at the endpoints of the given line segment. Connecting the intersection points of these two circles will result in a line perpendicular to segment AB that does not bisect it.

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