GEOMETRY (Common Core) - JMAP

GEOMETRY (COMMON CORE)

The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY (Common Core)

Wednesday, August 12, 2015 -- 8:30 to 11:30 a.m., only

Student Name:_________________________________________________________

School Name: _______________________________________________________________

The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you.

Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet. This examination has four parts, with a total of 36 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work should be written in pen, except for graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. The formulas that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration.

Notice... A graphing calculator, a straightedge (ruler), and a compass must be available for you to use while taking this examination.

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

GEOMETRY (COMMON CORE)

Part I

Answer all 24 questions in this part. Each correct answer will receive 2 credits. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. [48]

1 A parallelogram must be a rectangle when its (1) diagonals are perpendicular (2) diagonals are congruent (3) opposite sides are parallel (4) opposite sides are congruent

Use this space for computations.

2 If ABC is the image of ABC, under which transformation will the triangles not be congruent?

(1) reflection over the x-axis (2) translation to the left 5 and down 4 (3) dilation centered at the origin with scale factor 2 (4) rotation of 270? counterclockwise about the origin

3 If the rectangle below is continuously rotated about side w, which solid figure is formed?

w

(1) pyramid (2) rectangular prism

(3) cone (4) cylinder

4 Which expression is always equivalent to sin x when 0? x 90??

(1) cos (90? x) (2) cos (45? x)

(3) cos (2x) (4) cos x

Geometry (Common Core) ? Aug. '15

[2]

5 In the diagram below, a square is graphed in the coordinate plane. y

Use this space for computations.

x

A reflection over which line does not carry the square onto itself?

(1) x 5

(3) y x

(2) y 2

(4) x y 4

6 The image of ABC after a dilation of scale factor k centered at point A is ADE, as shown in the diagram below.

A

B

C

D

E

Which statement is always true?

(1) 2AB AD (2) A??D? D??E?

(3) AC CE (4) B??C? || D??E?

Geometry (Common Core) ? Aug. '15

[3]

[OVER]

7 A sequence of transformations maps rectangle ABCD onto rectangle ABCD, as shown in the diagram below.

y

Use this space for computations.

A

B

D

C

x C B

D

C

A

B

D A

Which sequence of transformations maps ABCD onto ABCD and then maps ABCD onto ABCD?

(1) a reflection followed by a rotation (2) a reflection followed by a translation (3) a translation followed by a rotation (4) a translation followed by a reflection

8 In the diagram of parallelogram FRED shown below, E??D? is extended to A, and A??F? is drawn such that ?A?F? D??F?.

F

R

A

D

E

If mR 124?, what is mAFD?

(1) 124?

(3) 68?

(2) 112?

(4) 56?

Geometry (Common Core) ? Aug. '15

[4]

9 If x2 4x y2 6y 12 0 is the equation of a circle, the length of the radius is

(1) 25

(3) 5

(2) 16

(4) 4

Use this space for computations.

10 Given M??N? shown below, with M(6,1) and N(3,5), what is an equation of the line that passes through point P(6,1) and is parallel to M??N?? y

M

P

x

N

(1)

y

2 3

x

5

(2)

y

2 3

x

3

(3)

y

3 2

x

7

(4)

y

3 2

x

8

11 Linda is designing a circular piece of stained glass with a diameter of 7 inches. She is going to sketch a square inside the circular region.

To the nearest tenth of an inch, the largest possible length of a side of the square is

(1) 3.5 (2) 4.9

(3) 5.0 (4) 6.9

Geometry (Common Core) ? Aug. '15

[5]

[OVER]

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