GEOMETRY (Common Core) - Regents Examinations

1 The University of the State of New YorkREGENTS HIGH SCHOOL EXAMINATIONGEOMETRY ( common Core) Thursday,January 28, 2016 9:15 to 12:15 , onlyStudent Name:_____School Name:_____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 theinstructions from the proctor for completing the student information on your examination has four parts, with a total of 36 questions. You must answerall questions in this examination . Record your answers to the Part I multiple-choicequestions on the separate answer sheet. Write your answers to the questions inParts 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 indicatethe necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine youranswer.

2 Note that diagrams are not necessarily drawn to formulas that you may need to answer some questions in this examinationare found at the end of the examination . This sheet is perforated so you mayremove it from this booklet. Scrap paper is not permitted for any part of this examination , but you may usethe blank spaces in this booklet as scrap paper. A perforated sheet of scrap graphpaper is provided at the end of this booklet for any question for which graphingmay be helpful but is not required. You may remove this sheet from this work done on this sheet of scrap graph paper will notbe you have completed the examination , you must sign the statement printedat the end of the answer sheet, indicating that you had no unlawful knowledge ofthe questions or answers prior to the examination and that you have neither givennor received assistance in answering any of the questions during the answer sheet cannot be accepted if you fail to sign this ( common Core) DO NOT OPEN THIS examination BOOKLET UNTIL THE SIGNAL IS graphing calculator, a straightedge (ruler), and a compass must be available for you to use while taking this ( common Core) The possession or use of any communications device is strictly prohibited when taking this examination .

3 If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for ( common core ) Jan. 16[2]Part IAnswer all 24 questions in this part. Each correct answer will receive 2 credits. Utilize theinformation 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]Use this space is drawing pictures of cross sections of the right circular drawing can notbe a cross section of a cone?2An equation of a line perpendicular to the line represented by the equation y 1__2x 5 and passing through (6, 4) is(1)y 1__2x 4(3)y 2x 14(2)y 1__2x 1(4)y 2x 16(2)(1)(3)(4)Part IAnswer all 24 questions in this part. Each correct answer will receive 2 credits. Utilize theinformation provided for each question to determine your answer.

4 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] GEOMETRY ( common core ) Jan. 16[3][OVER]3In parallelogram QRST shown below, diagonal TR___is drawn,Uand Vare points on TS___and QR___, respectively, and UV___intersects TR___at m S 60 , m SRT 83 , and m TWU 35 , what is m WVQ?(1) 37 (3) 72 (2) 60 (4) 83 4A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank contains 1680 cubicinches of water. What percent of the fish tank is empty?(1) 10(3) 50(2) 25(4) 755 Which transformation would result in the perimeter of a trianglebeing different from the perimeter of its image?(1) (x,y) (y,x)(3)(x,y) (4x,4y)(2) (x,y) (x, y)(4)(x,y) (x 2,y 5) Use this space ( common core ) Jan. 16[4]6In the diagram below,FE ___ bisectsAC___at B, andGE ___ bisectsBD___at C.

5 Which statement is always true?(1)AB___ DC___(3)BD ___ bisects GE___at C.(2)FB___ EB___(4)AC ___ bisects FE___at shown in the diagram below, a regular pyramid has a square basewhose side measures 6 the altitude of the pyramid measures 12 inches, its volume, incubic inches, is(1) 72(3) 288(2) 144(4) 432 ABC DFGE6 inUse this space ( common core ) Jan. 16[5][OVER]8 Triangle ABCand triangle DEFare graphed on the set of axes sequence of transformations maps triangle ABConto triangle DEF?(1) a reflection over the x-axis followed by a reflection over the y-axis(2) a 180 rotation about the origin followed by a reflection over theline y x(3) a 90 clockwise rotation about the origin followed by a reflectionover the y-axis(4) a translation 8 units to the right and 1 unit up followed by a 90 counterclockwise rotation about the originyxACBFEDUse this space ( common core ) Jan. 16[6]9In ABC, the complement of Bis A. Which statement is alwaystrue?

6 (1) tan A tan B(3) cos A tan B(2) sin A sin B(4) sin A cos B10A line that passes through the points whose coordinates are (1,1) and(5,7) is dilated by a scale factor of 3 and centered at the origin. The image of the line(1) is perpendicular to the original line(2) is parallel to the original line(3) passes through the origin(4) is the original line11 Quadrilateral ABCDis graphed on the set of axes ABCDis rotated 90 in a counterclockwise direction aboutthe origin, its image is quadrilateral A B C D . Is distance preservedunder this rotation, and which coordinates are correct for the givenvertex?(1) no and C (1,2)(3) yes and A (6,2)(2) no and D (2,4)(4) yes and B ( 3,4)xyBACDUse this space ( common core ) Jan. 16[7][OVER]12In the diagram below of circle O, the area of the shaded sector LOMis 2 the length of NL___is 6 cm, what is m N?(1) 10 (3) 40 (2) 20 (4) 80 13In the diagram below, ABC AB 6 and AC 8, which statement will justify similarity by SAS?

7 (1)DE 9, DF 12, and A D(2)DE 8, DF 10, and A D(3)DE 36, DF 64, and C F(4)DE 15, DF 20, and C F14 The diameter of a basketball is approximately inches and the diameter of a tennis ball is approximately inches. The volumeof the basketball is about how many times greater than the volumeof the tennis ball?(1) 3591(3) 55(2) 65(4) 4 MOLN Use this space ( common core ) Jan. 16[8]15 The endpoints of one side of a regular pentagon are ( 1,4) and (2,3).What is the perimeter of the pentagon?(1) 10(3) 5 2(2) 5 10(4) 25 216In the diagram of right triangle ABCshown below, AB 14 and AC is the measure of A, to the nearest degree?(1) 33(3) 50(2) 40(4) 5717 What are the coordinates of the center and length of the radius ofthe circle whose equation is x2 6x y2 4y 23?(1) (3, 2) and 36(3) ( 3,2) and 36(2) (3, 2) and 6(4) ( 3,2) and 618 The coordinates of the vertices of RSTare R( 2, 3), S(8,2), andT(4,5). Which type of triangle is RST?(1) right(3) obtuse(2) acute(4) equiangular Use this space ( common core ) Jan.

8 16[9][OVER]Use this space wishes to make a lawn ornament in the form of a solid clay being used to make the sphere weighs .075 pound per cubicinch. If the sphere s radius is 4 inches, what is the weight of thesphere, to the nearest pound?(1) 34(3) 15(2) 20(4) 420 The ratio of similarity of BOYto GRLis 1:2. If BO x 3 and GR 3x 1, then the length of GR___is(1) 5(3) 10(2) 7(4) 2021In the diagram below, DC___,AC___,DOB____,CB___, and AB___are chords ofcircle O, FDE ____ is tangent at point D, and radius AO___is drawn. Samdecides to apply this theorem to the diagram: An angle inscribed ina semi-circle is a right angle. Which angle is Sam referring to?(1) AOB(3) DCB(2) BAC(4) FDBABCDEOFG eometry ( common core ) Jan. 16[10]Use this space the diagram below, CD___is the altitude drawn to the hypotenuse AB___of right triangle lengths would notproduce an altitude that measures 6 2?(1)AD 2 and DB 36(3)AD 6 and DB 12(2)AD 3 and AB 24(4)AD 8 and AB 1723A designer needs to create perfectly circular necklaces.

9 The necklaceseach need to have a radius of 10 cm. What is the largest number ofnecklaces that can be made from 1000 cm of wire?(1) 15(3) 31(2) 16(4) 3224In SCUshown below, pointsTand Oare on SU___and CU___, respectively. Segment OTis drawn so that C TU 4, OU 5, and OC 7, what is the length of ST___ ?(1) (3) 11(2) (4) 15 SCOUTABDC25 Triangle ABCis graphed on the set of axes below. Graph and label A B C , the image of ABCafter a reflection over the line x ( common core ) Jan. 16[11][OVER]Part IIAnswer all 7 questions in this part. Each correct answer will receive 2 credits. 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. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit.

10 All answers should be written in pen, except for graphs and drawings, which should be done in pencil.[14]26In the diagram below of circle Owith diameter BC___and radius OA___, chord DC___is parallel to chord m BCD 30 , determine and state m ( common core ) Jan. 16[12]27 Directed line segment PThas endpoints whose coordinates are P( 2,1) and T(4,7).Determine the coordinates of point Jthat divides the segment in the ratio 2 to 1.[The use of the set of axes below is optional.]yxGeometry ( common core ) Jan. 16[13][OVER]28As graphed on the set of axes below, A B C is the image of ABCafter a sequence of A B C congruent to ABC? Use the properties of rigid motion to explain your C B CBGeometry ( common core ) Jan. 16[14]29A carpenter leans an extension ladder against a house to reach the bottom of a window 30 feetabove the ground. As shown in the diagram below, the ladder makes a 70 angle with the the nearest foot, determine and state the length of the ft70 GEOMETRY ( common core ) Jan.