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New York Regents Geometry (Common Core) January 2016 Exam

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GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Thursday, January 28, 2016 9:15 a.m. to 12:15 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 William is drawing pictures of cross sections of the right circular cone below. Which drawing can not be a cross section of a cone? (1) (3) (2) (4) 2 An equation of a line perpendicular to the line represented by the 1 equation y __ x 5 and passing through (6, 4) is 2 1 __ (1) y x 4 2 1 (2) y __ x 1 2 Geometry (Common Core) Jan. 16 (3) y 2x 14 (4) y 2x 16 [2] Use this space for computations. ___ 3 In parallelogram QRST shown below, diagonal TR U and V ___ ___ ___ is drawn, ___ are points on TS and QR, respectively, and UV intersects TR at W. T U Use this space for computations. S W Q V R If m S 60 , m SRT 83 , and m TWU 35 , what is m WVQ? (1) 37 (3) 72 (2) 60 (4) 83 4 A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank contains 1680 cubic inches of water. What percent of the fish tank is empty? (1) 10 (3) 50 (2) 25 (4) 75 5 Which transformation would result in the perimeter of a triangle being 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) Geometry (Common Core) Jan. 16 [3] [OVER] ___ ___ ___ ___ 6 In the diagram below, FE bisects AC at B, and GE bisects BD at C. E A B C F D G Which statement is always true? ___ ___ (1) AB DC (3) ___ ___ (2) FB EB (4) ___ ___ BD bisects GE at C. ___ ___ AC bisects FE at B. 7 As shown in the diagram below, a regular pyramid has a square base whose side measures 6 inches. 6 in If the altitude of the pyramid measures 12 inches, its volume, in cubic inches, is (1) 72 (3) 288 (2) 144 (4) 432 Geometry (Common Core) Jan. 16 [4] Use this space for computations. 8 Triangle ABC and triangle DEF are graphed on the set of axes below. Use this space for computations. y F E D x A B C Which sequence of transformations maps triangle ABC onto 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 the line y x (3) a 90 clockwise rotation about the origin followed by a reflection over the y-axis (4) a translation 8 units to the right and 1 unit up followed by a 90 counterclockwise rotation about the origin Geometry (Common Core) Jan. 16 [5] [OVER] 9 In ABC, the complement of B is A. Which statement is always true? (1) tan A tan B (3) cos A tan B (2) sin A sin B (4) sin A cos B 10 A 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 line 11 Quadrilateral ABCD is graphed on the set of axes below. y A B D x C When ABCD is rotated 90 in a counterclockwise direction about the origin, its image is quadrilateral A B C D . Is distance preserved under this rotation, and which coordinates are correct for the given vertex? (1) no and C (1,2) (3) yes and A (6,2) (2) no and D (2,4) (4) yes and B ( 3,4) Geometry (Common Core) Jan. 16 [6] Use this space for computations. 12 In the diagram below of circle O, the area of the shaded sector LOM is 2 cm2. M Use this space for computations. N O L ___ If the length of NL is 6 cm, what is m N? (1) 10 (3) 40 (2) 20 (4) 80 13 In the diagram below, ABC DEF. E B 6 A 8 C D F If AB 6 and AC 8, which statement will justify similarity by SAS? (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 F 14 The diameter of a basketball is approximately 9.5 inches and the diameter of a tennis ball is approximately 2.5 inches. The volume of the basketball is about how many times greater than the volume of the tennis ball? (1) 3591 (3) 55 (2) 65 (4) 4 Geometry (Common Core) Jan. 16 [7] [OVER] 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 (2) 5 10 (3) 5 2 (4) 25 2 16 In the diagram of right triangle ABC shown below, AB 14 and AC 9. A 9 14 C B What is the measure of A, to the nearest degree? (1) 33 (3) 50 (2) 40 (4) 57 17 What are the coordinates of the center and length of the radius of the 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 6 18 The coordinates of the vertices of RST are R( 2, 3), S(8,2), and T(4,5). Which type of triangle is RST? (1) right (3) obtuse (2) acute (4) equiangular Geometry (Common Core) Jan. 16 [8] Use this space for computations. 19 Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used to make the sphere weighs .075 pound per cubic inch. If the sphere s radius is 4 inches, what is the weight of the sphere, to the nearest pound? (1) 34 (3) 15 (2) 20 Use this space for computations. (4) 4 20 The ratio of similarity of BOY to ___ GRL is 1:2. If BO x 3 and GR 3x 1, then the length of GR is (1) 5 (3) 10 (2) 7 (4) 20 ___ ___ ____ ___ ___ 21 In the diagram below, DC , AC , DOB , CB , and AB ___ are chords of ____ circle O, FDE is tangent at point D, and radius AO is drawn. Sam decides to apply this theorem to the diagram: An angle inscribed in a semi-circle is a right angle. E C D O F B A Which angle is Sam referring to? (1) AOB (3) DCB (2) BAC (4) FDB Geometry (Common Core) Jan. 16 [9] [OVER] ___ ___ 22 In the diagram below, CD is the altitude drawn to the hypotenuse AB of right triangle ABC. C A D B Which lengths would not produce 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 17 23 A designer needs to create perfectly circular necklaces. The necklaces each need to have a radius of 10 cm. What is the largest number of necklaces that can be made from 1000 cm of wire? (1) 15 (3) 31 (2) 16 (4) 32 ___ ___ 24 In SCU shown below, points T and O are on SU and CU, respectively. Segment OT is drawn so that C OTU. S T C O U ___ If TU 4, OU 5, and OC 7, what is the length of ST ? (1) 5.6 (3) 11 (2) 8.75 (4) 15 Geometry (Common Core) Jan. 16 [10] Use this space for computations. 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 Triangle ABC is graphed on the set of axes below. Graph and label after a reflection over the line x 1. A B C , the image of ABC y B A Geometry (Common Core) Jan. 16 C [11] x [OVER] ___ ___ ___ 26 In the ___ diagram below of circle O with diameter BC and radius OA , chord DC is parallel to chord BA. B D O A C If m BCD 30 , determine and state m AOB. Geometry (Common Core) Jan. 16 [12] 27 Directed line segment PT has endpoints whose coordinates are P( 2,1) and T(4,7). Determine the coordinates of point J that divides the segment in the ratio 2 to 1. [The use of the set of axes below is optional.] y x Geometry (Common Core) Jan. 16 [13] [OVER] 28 As graphed on the set of axes below, transformations. A B C is the image of ABC after a sequence of y A B A x B C C Is A B C congruent to Geometry (Common Core) Jan. 16 ABC? Use the properties of rigid motion to explain your answer. [14] 29 A carpenter leans an extension ladder against a house to reach the bottom of a window 30 feet above the ground. As shown in the diagram below, the ladder makes a 70 angle with the ground. To the nearest foot, determine and state the length of the ladder. 30 ft 70 Geometry (Common Core) Jan. 16 [15] [OVER] 30 During an experiment, the same type of bacteria is grown in two petri dishes. Petri dish A has a diameter of 51 mm and has approximately 40,000 bacteria after 1 hour. Petri dish B has a diameter of 75 mm and has approximately 72,000 bacteria after 1 hour. B A 72,000 40,000 51 mm 75 mm Determine and state which petri dish has the greater population density of bacteria at the end of the first hour. Geometry (Common Core) Jan. 16 [16] 31 Line is mapped onto line m by a dilation centered at the origin with a scale factor of 2. The equation of line is 3x y 4. Determine and state an equation for line m. Geometry (Common Core) Jan. 16 [17] [OVER] 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 The aspect ratio (the ratio of screen width to height) of a rectangular flat-screen television is 16:9. The length of the diagonal of the screen is the television s screen size. Determine and state, to the nearest inch, the screen size (diagonal) of this flat-screen television with a screen height of 20.6 inches. Geometry (Common Core) Jan. 16 [18] 33 Given the theorem, The sum of the measures of the interior angles of a triangle is 180 , complete the proof for this theorem. C D E 2 1 3 A Given: B ABC Prove: m 1 m 2 m 3 180 Fill in the missing reasons below. Statements (1) ABC ____ Reasons (1) Given (2) Through point C, draw DCE parallel ___ to AB. (2) (3) m 1 m ACD, m 3 m BCE (3) (4) m ACD m 2 m BCE 180 (4) (5) m 1 m 2 m 3 180 (5) Geometry (Common Core) Jan. 16 [19] [OVER] 34 Triangle XYZ is shown below. Using a compass and straightedge, on the line below, construct and label ABC, such that ABC XYZ. [Leave all construction marks.] Based on your construction, state the theorem that justifies why ABC is congruent to Z X Geometry (Common Core) Jan. 16 [20] Y XYZ. 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 Given: Parallelogram ANDR with AW and DE bisecting NWD and REA at points W and E, respectively A N E W D R Prove that ANW DRE. Prove that quadrilateral AWDE is a parallelogram. Geometry (Common Core) Jan. 16 [21] [OVER] 36 Cathy wants to determine the height of the flagpole shown in the diagram below. She uses a survey instrument to measure the angle of elevation to the top of the flagpole, and determines it to be 34.9 . She walks 8 meters closer and determines the new measure of the angle of elevation to be 52.8 . At each measurement, the survey instrument is 1.7 meters above the ground. 52.8 34.9 1.7 m 8m Determine and state, to the nearest tenth of a meter, the height of the flagpole. Geometry (Common Core) Jan. 16 [22] Tear Here High School Math Reference Sheet 1 inch 2.54 centimeters 1 meter 39.37 inches 1 mile 5280 feet 1 mile 1760 yards 1 mile 1.609 kilometers 1 kilometer 0.62 mile 1 pound 16 ounces 1 pound 0.454 kilogram 1 kilogram 2.2 pounds 1 ton 2000 pounds 1 cup 8 fluid ounces 1 pint 2 cups 1 quart 2 pints 1 gallon 4 quarts 1 gallon 3.785 liters 1 liter 0.264 gallon 1 liter 1000 cubic centimeters Pythagorean Theorem a2 b2 c2 A bh Quadratic Formula x Circle A r 2 Arithmetic Sequence an a1 (n 1)d Circle C d or C 2 r Geometric Sequence a n a 1r n 1 General Prisms V Bh Geometric Series Sn Cylinder V r 2h Radians 1 radian 180 degrees Sphere V 4 3 r 3 Degrees 1 degree radians 180 Cone V 1 2 r h 3 Exponential Growth/Decay A A0ek(t t0) B0 Pyramid V 1 Bh 3 A Parallelogram Tear Here Triangle Geometry (Common Core) Jan. 16 1 bh 2 b b2 4ac 2a a1 a1r n 1 r where r 1 Tear Here Tear Here Tear Here Tear Here Scrap Graph Paper This sheet will not be scored. Scrap Graph Paper This sheet will not be scored. Tear Here Tear Here GEOMETRY (COMMON CORE) Printed on Recycled Paper GEOMETRY (COMMON CORE) FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Thursday, January 28, 2016 9:15 a.m. to 12:15 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/ on Thursday, January 28, 2016. 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) . . . . . 1 . . . . . (9) . . . . . 4 . . . . . (17) . . . . . 4 . . . . . (2) . . . . . 4 . . . . . (10) . . . . . 2 . . . . . (18) . . . . . 1 . . . . . (3) . . . . . 3 . . . . . (11) . . . . . 4 . . . . . (19) . . . . . 2 . . . . . (4) . . . . . 2 . . . . . (12) . . . . . 3 . . . . . (20) . . . . . 4 . . . . . (5) . . . . . 3 . . . . . (13) . . . . . 1 . . . . . (21) . . . . . 3 . . . . . (6) . . . . . 1 . . . . . (14) . . . . . 3 . . . . . (22) . . . . . 2 . . . . . (7) . . . . . 2 . . . . . (15) . . . . . 2 . . . . . (23) . . . . . 1 . . . . . (8) . . . . . 1 . . . . . (16) . . . . . 3 . . . . . (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. 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 Jan. 16 [2] General Rules for Applying Mathematics Rubrics I. General Principles for Rating The rubrics for the constructed-response questions on the Regents Examination in Geometry (Common Core) are designed to provide a systematic, consistent method for awarding credit. The rubrics are not to be considered all-inclusive; it is impossible to anticipate all the different methods that students might use to solve a given problem. Each response must be rated carefully using the teacher s professional judgment and knowledge of mathematics; all calculations must be checked. The specific rubrics for each question must be applied consistently to all responses. In cases that are not specifically addressed in the rubrics, raters must follow the general rating guidelines in the publication Information Booklet for Scoring the Regents Examination in Geometry (Common Core), use their own professional judgment, confer with other mathematics teachers, and/or contact the State Education Department for guidance. During each Regents Examination administration period, rating questions may be referred directly to the Education Department. The contact numbers are sent to all schools before each administration period. II. Full-Credit Responses A full-credit response provides a complete and correct answer to all parts of the question. Sufficient work is shown to enable the rater to determine how the student arrived at the correct answer. When the rubric for the full-credit response includes one or more examples of an acceptable method for solving the question (usually introduced by the phrase such as ), it does not mean that there are no additional acceptable methods of arriving at the correct answer. Unless otherwise specified, mathematically correct alternative solutions should be awarded credit. The only exceptions are those questions that specify the type of solution that must be used; e.g., an algebraic solution or a graphic solution. A correct solution using a method other than the one specified is awarded half the credit of a correct solution using the specified method. III. Appropriate Work Full-Credit Responses: The directions in the examination booklet for all the constructed-response questions state: Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. The student has the responsibility of providing the correct answer and showing how that answer was obtained. The student must construct the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used. Responses With Errors: Rubrics that state Appropriate work is shown, but are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errors, whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equation is written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses. IV. Multiple Errors Computational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1-credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No more than 2 credits should be deducted for such mechanical errors in a 4-credit question and no more than 3 credits should be deducted in a 6-credit question. The teacher must carefully review the student s work to determine what errors were made and what type of errors they were. Conceptual Errors: A conceptual error involves a more serious lack of knowledge or procedure. Examples of conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrect trigonometric function, or multiplying the exponents instead of adding them when multiplying terms with exponents. If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the same conceptual error is repeated in responses to other questions, credit should be deducted in each response. For 4- and 6-credit questions, if a response shows one conceptual error and one computational, graphing, or rounding error, the teacher must award credit that takes into account both errors. Refer to the rubric for specific scoring guidelines. Geometry (Common Core) Rating Guide Jan. 16 [3] Part II For each question, use the specific criteria to award a maximum of 2 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (25) [2] Triangle A B C is graphed and labeled correctly. [1] One graphing error is made, but appropriate vertices are graphed and labeled. or [1] One conceptual error is made, such as reflecting ABC over the line y 1, but appropriate vertices are graphed and labeled. or [1] The image of incorrectly. ABC is graphed correctly, but is not labeled or is labeled [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (26) [2] 120 or an equivalent radian measure is found, and appropriate work is shown, such as a labeled diagram. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] mDB 60 , mAC 60 , and mAB 120 , but no further correct work is shown. or [1] m ABO and m BAO 30 , but no further correct work is shown. or [1] m AOB 120 , but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [4] (27) [2] (2,5), and correct work is shown. [1] Appropriate work is shown, but one computational error is made. Appropriate coordinates are stated. or [1] Appropriate work is shown, but one conceptual error is made. Appropriate coordinates are stated. or [1] Appropriate work is shown to find 2 and 5, but the answer is not written as coordinates. or [1] Point J is graphed correctly, but the coordinates are not stated or are stated incorrectly. or [1] (2,5), but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (28) [2] Yes, and a correct explanation is written. [1] Yes, and an incomplete explanation is stated. or [1] Yes, and a correct sequence of transformations is written. or [1] Yes, and a statement other than properties of rigid motions is used. [0] Yes or an equivalent statement is stated, but no explanation is written. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [5] (29) [2] 32, and correct work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] Appropriate work is shown, but one conceptual error is made. or 30 30 __ [1] Sin 70 __ x or cos 20 x is written, but no further correct work is shown. or [1] 32, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (30) [2] A, and correct work is shown. [1] Appropriate work is shown, but one computational error is made. An appropriate petri dish is stated. or [1] Appropriate work is shown, but one conceptual error is made. An appropriate petri dish is stated. or [1] Appropriate work is shown to find the population density of each petri dish, but no petri dish or an incorrect petri dish is stated. [0] A, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [6] (31) [2] y 3x 8 or an equivalent equation is written, and correct work is shown. [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] y 3x 8, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [7] Part III For each question, use the specific criteria to award a maximum of 4 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (32) [4] 42, and correct work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. An appropriate screen size is found, to the nearest inch. or [3] Correct work is shown to find the width. The diagonal 42 is stated, but no work is shown. or [3] Correct work is shown to find the diagonal for 16 by 9 dimensions. The diagonal 42 is stated, but no work is shown. [2] Appropriate work is shown, but two or more computational or rounding errors are made. An appropriate screen size is found, to the nearest inch. or [2] Appropriate work is shown, but one conceptual error is made. An appropriate screen size is found, to the nearest inch. or [2] Correct work is shown to find the width, but no further correct work is shown. or [2] Using the aspect ratio 16:9 (w:h), correct work is shown to find the diagonal for 16 by 9 dimensions. No further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. An appropriate screen size is found, to the nearest inch. or [1] 42, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [8] (33) [4] All four reasons are correct. [3] Three reasons are correct. [2] Two reasons are correct. [1] One reason is correct. [0] No reasons are correct. (34) [4] A correct construction of ABC XYZ is drawn showing all construction arcs. A correct theorem is stated to justify why the triangles are congruent. [3] An appropriate construction of the congruent triangle is drawn, but one construction error is made. A correct theorem is stated to justify why the triangles are congruent. or [3] A correct construction of ABC XYZ is drawn. No theorem is stated or an incorrect theorem, based upon the construction, is stated. or [3] An appropriate construction of a congruent triangle is drawn, but the triangle is not labeled or is labeled incorrectly. A correct theorem is stated to justify why the triangles are congruent. [2] An appropriate construction of a congruent triangle is drawn, but one construction error is made. No theorem is stated or an incorrect theorem, based upon the construction, is stated. or [2] An appropriate construction of a congruent triangle is drawn. The triangle is not labeled or is labeled incorrectly. No theorem is stated or an incorrect theorem, based upon the construction, is stated. [1] All appropriate construction arcs are drawn, but the triangle is not drawn. No further correct work is shown. or [1] An appropriate congruency theorem is stated, but a drawing that is not an appropriate construction is shown. [0] A triangle congruency theorem is stated, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [9] Part IV For each question, use the specific criteria to award a maximum of 6 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (35) [6] A complete and correct proof that includes concluding statements is written. [5] A proof is written that demonstrates a thorough understanding of the method of proof and contains no conceptual errors, but one statement and/or reason is missing or incorrect. [4] A proof is written that demonstrates a good understanding of the method of proof and contains no conceptual errors, but two statements and/or reasons are missing or incorrect. [3] A proof is written that demonstrates a good understanding of the method of proof and contains no conceptual errors, but three statements and/or reasons are missing or incorrect. or [3] A proof is written that demonstrates a good understanding of the method of proof, but one conceptual error is made. or [3] A proof is written that shows is shown. ANW DRE, but no further correct work or [3] A proof is written that shows AWDE is a parallelogram, but no further correct work is shown. [2] A proof is written that demonstrates a good understanding of the method of proof and contains no conceptual errors, but four statements and/or reasons are missing or incorrect. [1] One correct relevant statement and reason about the proof are written. [0] The given and/or the prove statements are written, but no further correct relevant statements are written. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [10] (36) [6] 13.6, and correct work is shown. [5] Appropriate work is shown, but one computational or rounding error is made. or [5] Correct work is shown, but the height of the survey instrument is not added to the flagpole height. [4] Appropriate work is shown, but two computational or rounding errors are made. or [4] Correct work is shown to find the distance between the second sighting and the flagpole. No further correct work is shown. [3] Appropriate work is shown, but three or more computational or rounding errors are made. or [3] Appropriate work is shown, but one conceptual error is made. or [3] The equation (x 8)(tan 34.9) x(tan 52.8) or an equivalent equation is written. No further correct work is shown. [2] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or h h _____ [2] Equations tan 52.8 __ x and tan 34.9 x 8 are written. No further correct work is shown. h h _____ [1] The equation tan 52.8 __ x or tan 34.9 x 8 is written. No further correct work is shown. or [1] 13.6, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry (Common Core) Rating Guide Jan. 16 [11] Map to the Common Core Learning Standards Geometry (Common Core) January 2016 Question Type Credits Cluster 1 Multiple Choice 2 G-GMD.B 2 Multiple Choice 2 G-GPE.B 3 Multiple Choice 2 G-CO.C 4 Multiple Choice 2 G-GMD.A 5 Multiple Choice 2 G-CO.B 6 Multiple Choice 2 G-CO.C 7 Multiple Choice 2 G-GMD.A 8 Multiple Choice 2 G-CO.A 9 Multiple Choice 2 G-SRT.C 10 Multiple Choice 2 G-SRT.A 11 Multiple Choice 2 G-CO.A 12 Multiple Choice 2 G-C.B 13 Multiple Choice 2 G-SRT.B 14 Multiple Choice 2 G-MG.A 15 Multiple Choice 2 G-GPE.B 16 Multiple Choice 2 G-SRT.C 17 Multiple Choice 2 G-GPE.A 18 Multiple Choice 2 G-GPE.B 19 Multiple Choice 2 G-MG.A 20 Multiple Choice 2 G-SRT.B 21 Multiple Choice 2 G-C.A 22 Multiple Choice 2 G-SRT.B 23 Multiple Choice 2 G-MG.A 24 Multiple Choice 2 G-SRT.B 25 Constructed Response 2 G-CO.B 26 Constructed Response 2 G-C.A 27 Constructed Response 2 G-GPE.B 28 Constructed Response 2 G-CO.B 29 Constructed Response 2 G-SRT.C 30 Constructed Response 2 G-MG.A 31 Constructed Response 2 G-SRT.A 32 Constructed Response 4 G-SRT.C 33 Constructed Response 4 G-CO.C 34 Constructed Response 4 G-CO.D 35 Constructed Response 6 G-CO.C 36 Constructed Response 6 G-SRT.C Geometry (Common Core) Rating Guide Jan. 16 [12] Regents Examination in Geometry (Common Core) January 2016 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the January 2016 Regents Examination in Geometry (Common Core) will be posted on the Department s web site at: http://www.p12.nysed.gov/assessment/ on Thursday, January 28, 2016. Conversion charts provided for previous administrations of the Regents Examination in Geometry (Common Core) must NOT be used to determine students final scores for this administration. Online Submission of Teacher Evaluations of the Test to the Department Suggestions and feedback from teachers provide an important contribution to the test development process. The Department provides an online evaluation form for State assessments. It contains spaces for teachers to respond to several specific questions and to make suggestions. Instructions for completing the evaluation form are as follows: 1. Go to http://www.forms2.nysed.gov/emsc/osa/exameval/reexameval.cfm. 2. Select the test title. 3. Complete the required demographic fields. 4. Complete each evaluation question and provide comments in the space provided. 5. Click the SUBMIT button at the bottom of the page to submit the completed form. Geometry (Common Core) Rating Guide Jan. 16 [13] Question 25 25 Triangle ABC is graphed on the set of axes below. Graph and label after a reflection over the line x 1. A B C , the image of y B A Score 2: C The student has a complete and correct response. Geometry (Common Core) Jan. 16 [2] x ABC Question 26 ___ ___ ___ 26 In the ___ diagram below of circle O with diameter BC and radius OA , chord DC is parallel to chord BA. B D O A C If m BCD 30 , determine and state m AOB. Score 2: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [8] Question 27 27 Directed line segment PT has endpoints whose coordinates are P( 2,1) and T(4,7). Determine the coordinates of point J that divides the segment in the ratio 2 to 1. [The use of the set of axes below is optional.] y x Score 2: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [15] Question 28 28 As graphed on the set of axes below, transformations. A B C is the image of ABC after a sequence of y A B A x B C C Is A B C congruent to Score 2: ABC? Use the properties of rigid motion to explain your answer. The student has a complete and correct response. Geometry (Common Core) Jan. 16 [21] Question 29 29 A carpenter leans an extension ladder against a house to reach the bottom of a window 30 feet above the ground. As shown in the diagram below, the ladder makes a 70 angle with the ground. To the nearest foot, determine and state the length of the ladder. 30 ft 70 Score 2: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [26] Question 30 30 During an experiment, the same type of bacteria is grown in two petri dishes. Petri dish A has a diameter of 51 mm and has approximately 40,000 bacteria after 1 hour. Petri dish B has a diameter of 75 mm and has approximately 72,000 bacteria after 1 hour. B A 72,000 40,000 51 mm 75 mm Determine and state which petri dish has the greater population density of bacteria at the end of the first hour. Score 2: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [31] Question 31 31 Line is mapped onto line m by a dilation centered at the origin with a scale factor of 2. The equation of line is 3x y 4. Determine and state an equation for line m. Score 2: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [34] Question 32 32 The aspect ratio (the ratio of screen width to height) of a rectangular flat-screen television is 16:9. The length of the diagonal of the screen is the television s screen size. Determine and state, to the nearest inch, the screen size (diagonal) of this flat-screen television with a screen height of 20.6 inches. Score 4: The student has complete and correct work. Geometry (Common Core) Jan. 16 [39] Question 33 33 Given the theorem, The sum of the measures of the interior angles of a triangle is 180 , complete the proof for this theorem. D C E 2 1 3 A Given: B ABC Prove: m 1 m 2 m 3 180 Fill in the missing reasons below. Statements (1) ABC ____ (2) Through point C, draw DCE parallel ___ to AB. Reasons (1) Given (2) (3) m 1 m ACD, m 3 m BCE (3) (4) m ACD m 2 m BCE 180 (4) (5) m 1 m 2 m 3 180 (5) Score 4: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [48] Question 34 34 Triangle XYZ is shown below. Using a compass and straightedge, on the line below, construct and label ABC, such that ABC XYZ. [Leave all construction marks.] Based on your construction, state the theorem that justifies why Score 4: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [55] ABC is congruent to XYZ. Question 35 ___ ___ _____ ____ 35 Given: Parallelogram ANDR with AW and DE bisecting NWD and REA at points W and E, respectively A N E W D R Prove that ANW DRE. Prove that quadrilateral AWDE is a parallelogram. Score 6: The student has a complete and correct proof. Geometry (Common Core) Jan. 16 [62] Question 36 36 Cathy wants to determine the height of the flagpole shown in the diagram below. She uses a survey instrument to measure the angle of elevation to the top of the flagpole, and determines it to be 34.9 . She walks 8 meters closer and determines the new measure of the angle of elevation to be 52.8 . At each measurement, the survey instrument is 1.7 meters above the ground. 52.8 34.9 1.7 m 8m Determine and state, to the nearest tenth of a meter, the height of the flagpole. Score 6: The student has a complete and correct response. Geometry (Common Core) Jan. 16 [72]

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