Trending ▼   ResFinder  

New York Regents Geometry (Common Core) June 2015 Exam

41 pages, 36 questions, 0 questions with responses, 0 total responses,    0    0
New York State Regents Exams
   		+Fave Message
ProfileTimelineUploadsQ & A
 Home > regents >

Formatting page ...

GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.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 Which object is formed ___ when right triangle RST shown below is rotated around leg RS ? R S T (1) a pyramid with a square base (3) a right triangle (2) an isosceles triangle (4) a cone 2 The vertices of JKL have coordinates J(5,1), K( 2, 3), and L( 4,1). Under which transformation is the image J K L not congruent to JKL? (1) a translation of two units to the right and two units down (2) a counterclockwise rotation of 180 degrees around the origin (3) a reflection over the x-axis (4) a dilation with a scale factor of 2 and centered at the origin 3 The center of circle Q has coordinates (3, 2). If circle Q passes through R(7,1), what is the length of its diameter? (1) 50 (3) 10 (2) 25 (4) 5 Geometry (Common Core) June 15 [2] Use this space for computations. 4 In the diagram below, congruent figures 1, 2, and 3 are drawn. y F A F A B 1 E B 2 E C Use this space for computations. C D D x E D F A 3 C B Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3? (1) a reflection followed by a translation (2) a rotation followed by a translation (3) a translation followed by a reflection (4) a translation followed by a rotation 5 As shown in the diagram below, the angle of elevation from a point on the ground to the top of the tree is 34 . If the point is 20 feet from the base of the tree, what is the height of the tree, to the nearest tenth of a foot? (1) 29.7 (3) 13.5 (2) 16.6 (4) 11.2 Geometry (Common Core) June 15 [3] [OVER] 6 Which figure can have the same cross section as a sphere? (1) (3) (2) (4) 7 A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pound per cubic foot. What is the weight, in pounds, of the contents in the container? (1) 1,632 (3) 102 (2) 408 (4) 92 Geometry (Common Core) June 15 [4] Use this space for computations. ___ ___ 8 In the diagram of ___ circle A ___ shown below, chords CD and EF intersect at G, and chords CE and FD are drawn. Use this space for computations. F C G D A E Which statement is not always true? ___ ___ FD CE (1) CG FG (3) EG (2) CEG FDG (4) DG CEG ~ FDG 9 Which equation represents a line that is perpendicular to the line represented by 2x y 7? 1 (1) y __ x 6 (3) y 2x 6 1 (2) y __ x 6 (4) y 2x 6 2 2 Geometry (Common Core) June 15 [5] [OVER] 10 Which regular polygon has a minimum rotation of 45 to carry the polygon onto itself? (1) octagon (3) hexagon (2) decagon (4) pentagon 11 In the diagram of AB 9.2. ___ ADC below, EB ___ || DC , AE 9, ED 5, and A 9 E 9.2 B 5 D C ___ What is the length of AC , to the nearest tenth? (1) 5.1 (3) 14.3 (2) 5.2 (4) 14.4 Geometry (Common Core) June 15 [6] Use this space for computations. 12 In scalene triangle ABC shown in the diagram below, m C 90 . Use this space for computations. A C B Which equation is always true? (1) sin A sin B (3) cos A sin C (2) cos A cos B (4) sin A cos B ___ ___ 13 Quadrilateral ABCD has diagonals AC and BD. Which information is not sufficient to prove ABCD is a parallelogram? ___ ___ (1) AC and BD bisect each other. ___ ___ ___ ___ (2) AB CD and BC AD ___ ___ ___ ___ (3) AB CD and AB || CD ___ ___ ___ ___ (4) AB CD and BC || AD 14 The equation of a circle is x2 y2 6y 7. What are the coordinates of the center and the length of the radius of the circle? (1) center (0,3) and radius 4 (2) center (0, 3) and radius 4 (3) center (0,3) and radius 16 (4) center (0, 3) and radius 16 Geometry (Common Core) June 15 [7] [OVER] Use this space for computations. 15 Triangles ABC and DEF are drawn below. C E A D F B If AB 9, BC 15, DE 6, EF 10, and B E, which statement is true? (1) CAB DEF (3) (2) AB FE CB DE (4) AB FE DE CB ABC ~ DEF 16 If ABC is dilated by a scale factor of 3, which statement is true of the image A B C ? (1) 3A B AB (3) m A 3(m A) (2) B C 3BC (4) 3(m C ) m C Geometry (Common Core) June 15 [8] 17 Steve drew line segments ABCD, EFG, BF, and CF as shown in the diagram below. Scalene BFC is formed. A B E C F Use this space for computations. D G Which statement will allow Steve to prove ABCD || EFG ? (1) CFG FCB (3) EFB CFB (2) ABF BFC (4) CBF GFC ___ ___ 18 In the diagram below, CD is the image of AB after a dilation of scale factor k with center E. y E C D A x B Which ratio is equal to the scale factor k of the dilation? (1) EC (3) EA (2) BA (4) EA EA EA Geometry (Common Core) June 15 BA EC [9] [OVER] 19 A gallon of paint will cover approximately 450 square feet. An artist wants to paint all the outside surfaces of a cube measuring 12 feet on each edge. What is the least number of gallons of paint he must buy to paint the cube? (1) 1 (3) 3 (2) 2 (4) 4 ___ ___ 20 In circle O shown below, diameter AC is perpendicular to CD at ___ ___ ___ ___ point C, and chords AB, BC, AE , and CE are drawn. B D A O E C Which statement is not always true? (1) ACB BCD (3) BAC DCB (2) ABC ACD (4) CBA AEC 21 In the diagram below, ABC ~ DEC. A D B E C If AC 12, DC 7, DE 5, and the perimeter of what is the perimeter of DEC? (1) 12.5 (3) 14.8 (2) 14.0 (4) 17.5 Geometry (Common Core) June 15 [10] ABC is 30, Use this space for computations. 22 The line 3y 2x 8 is transformed by a dilation centered at the origin. Which linear equation could be its image? (1) 2x 3y 5 (3) 3x 2y 5 (2) 2x 3y 5 Use this space for computations. (4) 3x 2y 5 23 A circle with a radius of 5 was divided into 24 congruent sectors. The sectors were then rearranged, as shown in the diagram below. x To the nearest integer, the value of x is (1) 31 (3) 12 (2) 16 (4) 10 24 Which statement is sufficient evidence that ABC? DEF is congruent to B E D C A F (1) AB DE and BC EF (2) D A, B E, C F ___ ___ ___ (3) There is a sequence of rigid motions that maps AB onto DE , BC ___ ___ ___ onto EF , and AC onto DF. (4) There is ___ a sequence ___ of rigid motions that maps point A onto point D, AB onto DE , and B onto E. Geometry (Common Core) June 15 [11] [OVER] Part II Answer 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 correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [14] 25 Use a compass and straightedge to construct an inscribed square in circle T shown below. [Leave all construction marks.] T Geometry (Common Core) June 15 [12] ___ 26 The diagram below shows parallelogram LMNO with diagonal LN , m M 118 , and m LNO 22 . L M O N Explain why m NLO is 40 degrees. Geometry (Common Core) June 15 [13] [OVER] ___ ___ 27 The coordinates of the endpoints of AB are A( 6, 5) and B(4,0). Point P is on AB. Determine and state the coordinates of point P, such that AP:PB is 2:3. [The use of the set of axes below is optional.] y x Geometry (Common Core) June 15 [14] 28 The diagram below shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures 11.75 feet from the ground to the top of the loading platform. Ramp 11.7 5 ft 4.5 ft Determine and state, to the nearest degree, the angle of elevation formed by the ramp and the ground. Geometry (Common Core) June 15 [15] [OVER] 29 ___ In the diagram below of circle O, the area of the shaded sector AOC is 12 in2 and the length of OA is 6 inches. Determine and state m AOC. A 6 in O C Geometry (Common Core) June 15 [16] 30 After a reflection over a line, congruent to triangle A B C . Geometry (Common Core) June 15 A B C is the image of [17] ABC. Explain why triangle ABC is [OVER] 31 A flagpole casts a shadow 16.60 meters long. Tim stands at a distance of 12.45 meters from the base of the flagpole, such that the end of Tim s shadow meets the end of the flagpole s shadow. If Tim is 1.65 meters tall, determine and state the height of the flagpole to the nearest tenth of a meter. Geometry (Common Core) June 15 [18] Part III Answer all 3 questions in this part. Each correct answer will receive 4 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 correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12] ___ ___ ___ ___ 32 In the diagram below, EF intersects AB and CD at G and H, respectively, and GI is drawn such ___ ___ that GH IH . E G A C H B I D F ___ If m EGB 50 and m DIG 115 , explain why AB Geometry (Common Core) June 15 [19] ___ || CD. [OVER] ___ ___ 33 Given: Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E B A E C D Prove: AED CEB Describe a single rigid motion that maps Geometry (Common Core) June 15 AED onto [20] CEB. 34 In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F. The campground is 0.25 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular. P 0.55 mi Lake F L 0.25 mi C If the path from the park ranger station to the campground is 0.55 mile, determine and state, to the nearest hundredth of a mile, the distance between the park ranger station and the lifeguard chair. Gerald believes the distance from the first aid station to the campground is at least 1.5 miles. Is Gerald correct? Justify your answer. Geometry (Common Core) June 15 [21] [OVER] Part IV Answer the 2 questions in this part. Each correct answer will receive 6 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 correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12] 35 The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower is composed of a hemisphere, a cylinder, and a cone. Let C be the center of the hemisphere and let D be the center of the base of the cone. E F G D 25 ft B C K 8.5 ft A Source: http://en.wikipedia.org Question 35 is continued on the next page. Geometry (Common Core) June 15 [22] Question 35 continued If AC 8.5 feet, BF 25 feet, and m EFD 47 , determine and state, to the nearest cubic foot, the volume of the water tower. The water tower was constructed to hold a maximum of 400,000 pounds of water. If water weighs 62.4 pounds per cubic foot, can the water tower be filled to 85% of its volume and not exceed the weight limit? Justify your answer. Geometry (Common Core) June 15 [23] [OVER] 36 In the coordinate plane, the vertices of RST are R(6, 1), S(1, 4), and T( 5,6). Prove that RST is a right triangle. [The use of the set of axes on the next page is optional.] State the coordinates of point P such that quadrilateral RSTP is a rectangle. Question 36 is continued on the next page. Geometry (Common Core) June 15 [24] Question 36 continued Prove that your quadrilateral RSTP is a rectangle. [The use of the set of axes below is optional.] y x Geometry (Common Core) June 15 [25] FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (COMMON CORE) Tuesday, June 2, 2015 1:15 to 4:15 p.m., only SCORING KEY AND RATING GUIDE Mechanics of Rating The following procedures are to be followed for scoring student answer papers for the Regents Examination in Geometry (Common Core). More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examination in Geometry (Common Core). Do not attempt to correct the student s work by making insertions or changes of any kind. In scoring the open-ended questions, use check marks to indicate student errors. Unless otherwise specified, mathematically correct variations in the answers will be allowed. Units need not be given when the wording of the questions allows such omissions. Each student s answer paper is to be scored by a minimum of three mathematics teachers. No one teacher is to score more than approximately one-third of the open-ended questions on a student s paper. Teachers may not score their own students answer papers. On the student s separate answer sheet, for each question, record the number of credits earned and the teacher s assigned rater/scorer letter. Schools are not permitted to rescore any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam score. Schools are required to ensure that the raw scores have been added correctly and that the resulting scale score has been determined accurately. Raters should record the student s scores for all questions and the total raw score on the student s separate answer sheet. Then the student s total raw score should be converted to a scale score by using the conversion chart that will be posted on the Department s web site at: http://www.p12.nysed.gov/assessment/ no later than Thursday, June 25, 2015. Because scale scores corresponding to raw scores in the conversion chart may change from one administration to another, it is crucial that, for each administration, the conversion chart provided for that administration be used to determine the student s final score. The student s scale score should be entered in the box provided on the student s separate answer sheet. The scale score is the student s final examination score. If the student s responses for the multiple-choice questions are being hand scored prior to being scanned, the scorer must be careful not to make any marks on the answer sheet except to record the scores in the designated score boxes. Marks elsewhere on the answer sheet will interfere with the accuracy of the scanning. Part I Allow a total of 48 credits, 2 credits for each of the following. Allow credit if the student has written the correct answer instead of the numeral 1, 2, 3, or 4. (1) . . . . . 4 . . . . . (9) . . . . . 1 . . . . . (17) . . . . . 1 . . . . . (2) . . . . . 4 . . . . . (10) . . . . . 1 . . . . . (18) . . . . . 1 . . . . . (3) . . . . . 3 . . . . . (11) . . . . . 3 . . . . . (19) . . . . . 2 . . . . . (4) . . . . . 4 . . . . . (12) . . . . . 4 . . . . . (20) . . . . . 1 . . . . . (5) . . . . . 3 . . . . . (13) . . . . . 4 . . . . . (21) . . . . . 4 . . . . . (6) . . . . . 2 . . . . . (14) . . . . . 2 . . . . . (22) . . . . . 1 . . . . . (7) . . . . . 3 . . . . . (15) . . . . . 3 . . . . . (23) . . . . . 2 . . . . . (8) . . . . . 1 . . . . . (16) . . . . . 2 . . . . . (24) . . . . . 3 . . . . . Updated information regarding the rating of this examination may be posted on the New York State Education Department s web site during the rating period. Check this web site at: http://www.p12.nysed.gov/assessment/ and select the link Scoring Information for any recently posted information regarding this examination. This site should be checked before the rating process for this examination begins and several times throughout the Regents Examination period. Beginning in June 2015, the Department is providing supplemental scoring guidance, the Model Response Set, for the Regents Examination in Geometry (Common Core). This guidance is intended to be part of the scorer training. Schools should use the Model Response Set along with the rubrics in the Scoring Key and Rating Guide to help guide scoring of student work. While not reflective of all scenarios, the Model Response Set illustrates how less common student responses to constructed-response questions may be scored. The Model Response Set will be available on the Department s web site at: http://www.nysedregents.org/Geometrycc/. Geometry (Common Core) Rating Guide June 15 [2] Question 25 25 Use a compass and straightedge to construct an inscribed square in circle T shown below. [Leave all construction marks.] Score 2: The student drew a correct construction showing all appropriate construction marks and the square was drawn. Geometry (Common Core) June 15 [2] Question 26 ___ 26 The diagram below shows parallelogram LMNO with diagonal LN , m M 118 , and m LNO 22 . L M O N Explain why m NLO is 40 degrees. Score 2: The student has a complete and correct response. Geometry (Common Core) June 15 [8] Question 27 ___ ___ 27 The coordinates of the endpoints of AB are A( 6, 5) and B(4,0). Point P is on AB. Determine and state the coordinates of point P, such that AP:PB is 2:3. [The use of the set of axes below is optional.] Score 2: The student has a complete and correct response. The student showed correct work that was not necessary. Geometry (Common Core) June 15 [15] Question 28 28 The diagram below shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures 11.75 feet from the ground to the top of the loading platform. Ramp 11.7 5 ft 4.5 ft Determine and state, to the nearest degree, the angle of elevation formed by the ramp and the ground. Score 2: The student has a complete and correct response. Geometry (Common Core) June 15 [22] Question 29 29 ___ In the diagram below of circle O, the area of the shaded sector AOC is 12 in2 and the length of OA is 6 inches. Determine and state m AOC. A 6 in O C Score 2: The student has a complete and correct response. Geometry (Common Core) June 15 [27] Question 30 30 After a reflection over a line, congruent to triangle A B C . Score 2: A B C is the image of The student has a complete and correct response. Geometry (Common Core) June 15 [33] ABC. Explain why triangle ABC is Question 31 31 A flagpole casts a shadow 16.60 meters long. Tim stands at a distance of 12.45 meters from the base of the flagpole, such that the end of Tim s shadow meets the end of the flagpole s shadow. If Tim is 1.65 meters tall, determine and state the height of the flagpole to the nearest tenth of a meter. Score 2: The student has a complete and correct response. Geometry (Common Core) June 15 [37] Question 32 ___ ___ ___ ___ 32 In the diagram below, EF intersects AB and CD at G and H, respectively, and GI is drawn such ___ ___ that GH IH . E G A B C D I H F ___ If m EGB 50 and m DIG 115 , explain why AB Score 4: The student has a complete and correct response. Geometry (Common Core) June 15 [46] ___ || CD. Question 33 ___ ___ 33 Given: Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E B A E C D Prove: AED CEB Describe a single rigid motion that maps Score 4: AED onto CEB. The student has a complete and correct proof, and a correct rigid motion is stated. Geometry (Common Core) June 15 [54] Question 34 34 In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F. The campground is 0.25 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular. P 0.55 mi Lake F L 0.25 mi C If the path from the park ranger station to the campground is 0.55 mile, determine and state, to the nearest hundredth of a mile, the distance between the park ranger station and the lifeguard chair. Gerald believes the distance from the first aid station to the campground is at least 1.5 miles. Is Gerald correct? Justify your answer. Score 4: The student has a complete and correct response. Geometry (Common Core) June 15 [61] Question 35 35 The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower is composed of a hemisphere, a cylinder, and a cone. Let C be the center of the hemisphere and let D be the center of the base of the cone. E F G D 25 ft B C K 8.5 ft A Source: http://en.wikipedia.org Question 35 is continued on the next page. Geometry (Common Core) June 15 [67] Question 35 continued If AC 8.5 feet, BF 25 feet, and m EFD 47 , determine and state, to the nearest cubic foot, the volume of the water tower. The water tower was constructed to hold a maximum of 400,000 pounds of water. If water weighs 62.4 pounds per cubic foot, can the water tower be filled to 85% of its volume and not exceed the weight limit? Justify your answer. Score 6: The student had a complete and correct response. Geometry (Common Core) June 15 [68] Question 36 36 In the coordinate plane, the vertices of RST are R(6, 1), S(1, 4), and T( 5,6). Prove that RST is a right triangle. [The use of the set of axes on the next page is optional.] State the coordinates of point P such that quadrilateral RSTP is a rectangle. Question 36 is continued on the next page. Geometry (Common Core) June 15 [85] Question 36 continued Prove that your quadrilateral RSTP is a rectangle. [The use of the set of axes below is optional.] Score 6: The student has a complete and correct response. Geometry (Common Core) June 15 [86]

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

 

  Print intermediate debugging step

Show debugging info


 


Tags : New York State, High School Regents, Examinations, Past exams, solvedTest Papers, Education, Assessment and Testing.  


© 2010 - 2025 ResPaper. Terms of ServiceContact Us Advertise with us

 

regents chat