geometry pre assessment school year 2013-2014

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Geometry Pre Assessment – School year 2013-2014

Directions, Answer Key, and Scoring Rubrics

Before the Test

Students need: A copy of the examination

Scoring sheet (for teacher use only)

Calculator

Writing utensil

Scrap paper (if necessary)

During the Test: Students should have 80 minutes to complete Section 1 and 30

minutes to complete Section 2 of the test. At the teacher’s

discretion, the test may be administered in one or two sessions.

After the Test: Record each point value earned for every question on the scoring

sheet that should be attached to each exam. Student scores should

be calculated as follows:

Short Constructed Response:

Number of items correct 2 pt

Items 1 – 15

[30 possible SCR points]

= SCR

Multiple Choice:

Number of items correct 1 pt

Items 16 – 25


= MC

Extended Constructed Response:

Add scores on items 26 – 29

(based on rubrics)


= ECR

Student score (52 possible points - Add lines mc, scr, and ecr)

=

Assign grades according to district grading policy.

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Answer Key for Geometry Pre Test – Section 1

Answers for Short Constructed Response Items 1 – 15:

Item # Answer CCSS

1.

(1 point each)

Part A: (5, -5)

Part B: (-5, -5)

8.G.1

Description Find new coordinates of a line that has been reflected over y-axis and origin

2.

8.G.3

Description Drawing the image of a parallelogram that has been rotated

3.

8.G.3

Description Drawing the image of a triangle that has been dilated

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4.

(1 point each)

Part A:

Part B: Quadrilateral ABCD is similar to quadrilateral WXYZ

8.G.4

Description Labeling coordinates of a new shape that has been dilated and rotated; determining if the

shapes are congruent or similar

5.

12

8.G.7

Description Using Pythagorean’s Theorem to find the diagonal of a rectangle

6.

200 feet

8.G.7

Description Applying Pythagorean’s Theorem in a context and multi-step problem

7.

√ or 12.2 feet

8.G.7

Description Applying Pythagorean’s Theorem in a context

8.

√ or 17 feet

8.G.7

Description Applying Pythagorean’s Theorem in a context

9.

√ or 6.7 units

8.G.8

Description Using the distance formula to find the distance between two given coordinates

10.

13 units

8.G.8

Description Using the distance formula to find the distance between two coordinates in a plane

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11.

22 units

8.G.8

Description Finding the perimeter of a parallelogram in a coordinate plane

12.

6 centimeters

8.G.9

Description Finding the volume of a cone

13.

or 524 cubic inches

8.G.9

Description Applying volume formulas to find the volume of a basketball

14.

No, because parallel lines are still parallel after they are translated, and lines

t and u are not parallel

8.G.1

Description Applying transformations to determine if two lines are parallel

15.

Triangle ABC was reflected over the line y = 3 and then translated 9 units to

the right to make triangle XYZ (Answers may vary)

8.G.2

Description Applying transformations to justify that two shapes are congruent

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Questions 16 – 25: Multiple Choice (1 point each)

Item # Answer CCSS Description

16. A 8.G.1 Applying transformations to coordinates in a coordinate plane

17. D 8.G.2 Applying transformations to a triangle in a coordinate plane

18. C 8.G.2 Applying transformations to a rectangle in a coordinate plane

19. D 8.G.3 Analyzing the transformation of a triangle in a coordinate plane

20. C 8.G.3 Analyzing the dilation of a circle in a coordinate plane

21. C 8.G.3 Determining the scale factor of a shape in a coordinate plane

22. A 8.G.3 Analyzing the dilation of a shape in a coordinate plane

23. D 8.G.4 Analyzing the transformation of a triangle in a coordinate plane

24. D 8.G.8 Using distance formula to find distance between coordinate

points

25. B 8.G.9 Applying formula for volume

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Answers for Extended Constructed Response Items 26 – 29:

SPECIFIC SCORING RUBRIC FOR QUESTION 26

SAMPLE ANSWER:

Yes, because if ABC is dilated with a scale factor of 2 with center at the origin and then

the image is translated down 2 and right 2, the final image is ,XYZ so it is similar to

.ABC

OR

Yes, because if ABC is dilated with a scale factor of 2 with center at 2, 2 , the image

is ,XYZ so it is similar to .ABC

SCORE POINT = 3:

The student answers yes and provides a complete and correct justification, including the

center of the dilation and scale factor.

SCORE POINT = 2:

The student answers yes and provides a correct but either omits the scale factor or the

center of dilation

SCORE POINT = 1:

The student may respond that they are similar due to a dilation but fails to provide the

scale factor and the center of dilation.

SCORE POINT = 0:

The student fails to provide an answer, provides an incorrect answer, or states they are

similar but does not provide any justification.

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SAMPLE ANSWER:

Yes. Since corresponding angles are congruent, the lines are parallel.

No. We are not told that they are parallel, and we do not know if 110.x

No. We do not know if line t is parallel to line u.

No. We do not know if 110.x

SCORE POINT = 3:

The student provides the correct answer and a complete and correct explanation for each

statement. Student must state that corresponding angles are congruent.

SCORE POINT = 2:

The student provides the correct answer to the first statement accompanied by a complete

and correct explanation, but assumes that lines t and u are parallel based on the diagram

and answers the other statements accordingly, providing appropriate justifications.

SCORE POINT = 1:

The student provides the correct answer to the first statement accompanied by a complete

and correct explanation. Student answers the rest of the statements incorrectly or does not

provide a logical justification or explanation.

OR

The student answers the first statement correctly but provides an incomplete or inaccurate

explanation and answers the other statements correctly, providing complete and correct

explanations.

SCORE POINT = 0:

The student fails to provide an answer, or answers the first statement incorrectly by

saying that they are not parallel.

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SAMPLE ANSWER:

Yes, 120.a The sum of the measures of the two given angles of the triangle is 120 .

Since the sum of the measures of the angles of a triangle is 180 , the measure of the third

angle is 60 . The value of a is supplementary to the third angle, so the value of a is

120.

SCORE POINT = 3:

The student provides the correct answer with a correct explanation. The student must

reference the fact that all angles in a triangle sum to 180° and that the third angle of the

triangle is supplementary to a, and supplementary angles sum to 180°.

SCORE POINT = 2:

The student provides the correct answer with a correct but slightly incomplete

explanation. For example, the student may state that the third angle is 60° but does not

explain why OR the student may state that the third angle and angle a must sum to 180°

but does not explain why.

SCORE POINT = 1:

The student provides the correct answer with a correct but incomplete explanation. The

student may omit the fact that angles of a triangle sum to 180° or that angle a and the

third angle must sum to 180°.

SCORE POINT = 0:

The student fails to provide an answer, provides an incorrect answer, or states that angle

a does equal 120° but fails to provide any justification.

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SAMPLE ANSWER:

Part A: Jared’s drawing cannot be used to prove the Pythagorean Theorem because it

shows an isosceles right triangle. The figure does not show that the theorem holds in

general for any right triangle.

Part B: a2 + a

2 = c

2 or 2a

2 = c

2

SCORE POINT = 3:

The student provides a correct and complete explanation for Part A and B. Student must

reference isosceles triangles in Part A.

SCORE POINT = 2:

The student provides a logical explanation in Part A but does not reference isosceles

triangles. Student must also answer Part B correctly.

SCORE POINT = 1:

The student incorrectly answers Part B and provides a logical explanation in Part A but

does not reference isosceles triangles.

OR

The student incorrectly answers Part A but correctly answers Part B.

SCORE POINT = 0:

The student fails to provide an answer, or both Part A and B are answered incorrectly.

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Answer Key for Geometry Pre Test – Section 2

Part A:

Score out of 5 points using the PLD Rubric

If lines CH and DG are parallel, then Angles ABC and BED are corresponding angles

and corresponding angles are congruent. This makes angle BED also equal to 2x + 16.

Angles BEG and BED are supplementary angles, which sum to 180°. Therefore:

7x – 43 + 2x + 16 = 180

9x – 27 = 180

9x = 207

x = 23

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Part B:


Reason

2) The Pythagorean theorem.

3) Substitution.

4) Simplification.

5) Since both triangles have the same side lengths, the triangles are congruent.

6) Corresponing parts of congruent triangles are congruent.

7) Angles Q and T have the same measure and the measure of angle T is 90 degrees.

8) Since triangle PQR has a right angle (angle Q), it is a right triangle.

Note: The student does not need to identify postulates by name (such as SSS), as long as

he or she describes the reason correctly.

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Part C:


When a polygon is reflected over the y-axis, each vertex of the reflected polygon will end

up on the opposite side of the y-axis but the same distance from the y-axis. So, the x-

coordinates of the vertices will change from positive to negative or negative to positive,

but the absolute value of the number will stay the same, so the x-coordinates of the

corresponding vertices of the polygon and its image are opposites. Since the polygon is

being reflected over the y-axis, the image is in a different place horizontally, but it does

not move up or down, which means the y-coordinates of the vertices of the image will be

the same as the y-coordinates of the corresponding vertices of the original polygon. As an

example, look at the graph below and notice that the x-coordinates of the corresponding

vertices of the polygon and its image are opposites, but the y-coordinates are the same.

This means the conjecture is correct.

geometry pre assessment school year 2013-2014

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