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New York Regents Geometry January 2012

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GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: _________________________________________________________ School Name: _______________________________________________________________ Print your name and the name of your school on the lines above. Then turn to the last page of this booklet, which is the answer sheet for Part I. Fold the last page along the perforations and, slowly and carefully, tear off the answer sheet. Then fill in the heading of your answer sheet. This examination has four parts, with a total of 38 questions. You must answer all questions in this examination. Write 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. 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. The use of any communications device is strictly prohibited when taking this examination. If you use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. GEOMETRY Part I Answer all 28 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. [56] 1 Line n intersects lines l and m, forming the angles shown in the diagram below. n l (6x + 42) (18x 12) m Which value of x would prove l || m? (1) 2.5 (3) 6.25 (2) 4.5 (4) 8.75 2 In a given triangle, the point of intersection of the three medians is the same as the point of intersection of the three altitudes. Which classification of the triangle is correct? (1) scalene triangle (3) equilateral triangle (2) isosceles triangle (4) right isosceles triangle 3 A circle has the equation (x 2)2 (y 3)2 36. What are the coordinates of its center and the length of its radius? (1) ( 2,3) and 6 (3) ( 2,3) and 36 (2) (2, 3) and 6 (4) (2, 3) and 36 Geometry January 12 [2] Use this space for computations. ___ 4 In the diagram below, MATH is a rhombus with diagonals AH ___ and MT. Use this space for computations. A 12 M T H If m HAM 12, what is m AMT? (1) 12 (3) 84 (2) 78 (4) 156 5 A line segment has endpoints (4,7) and (1,11). What is the length of the segment? (1) 5 (3) 16 (2) 7 (4) 25 42 and an exterior angle at vertex H has a 6 In FGH, m F measure of 104. What is m G? (1) 34 (3) 76 (2) 62 (4) 146 Geometry January 12 [3] [OVER] 7 Which diagram represents a correct construction of equilateral ___ ABC, given side AB? C C A A B B (1) (3) C C A A B B (2) (4) 8 In the diagram below, ABC is circumscribed about circle O and the sides of ABC are tangent to the circle at points D, E, and F. B F E O A If AB 20, AE C D 12, and CF ___ 15, what is the length of AC? (1) 8 (3) 23 (2) 15 (4) 27 Geometry January 12 [4] Use this space for computations. 9 In ABC and would prove AC CB DEF, ___ ___ . Which additional information FE DF ABC DEF? (1) AC DF (3) ACB DFE (2) CB FE (4) BAC Use this space for computations. EDF 10 The angles of triangle ABC are in the ratio of 8:3:4. What is the measure of the smallest angle? (1) 12 (3) 36 (2) 24 (4) 72 11 When a quadrilateral is reflected over the line y relationship is not preserved? x, which geometric (1) congruence (3) parallelism (2) orientation (4) perpendicularity 12 Which equation represents circle O with center (2, 8) and radius 9? (1) (x 2)2 (y 8)2 9 (2) (x 2)2 (y 8)2 9 (3) (x 2)2 (y 8)2 81 (4) (x 2)2 (y 8)2 81 Geometry January 12 [5] [OVER] 13 Which statement is the negation of Two is a prime number and what is the truth value of the negation? (1) Two is not a prime number; false (2) Two is not a prime number; true (3) A prime number is two; false (4) A prime number is two; true ___ ___ 14 In the diagram below of circle O, chords AB and CD intersect at E. C 50 A If m AEC 34 and m AC B 34 E O D 50, what is m DB? (1) 16 (3) 68 (2) 18 (4) 118 15 The volume of a rectangular prism is 144 cubic inches. The height of the prism is 8 inches. Which measurements, in inches, could be the dimensions of the base? (1) 3.3 by 5.5 (3) 12 by 8 (2) 2.5 by 7.2 (4) 9 by 9 Geometry January 12 [6] Use this space for computations. 16 The diagram below shows a pair of congruent triangles, with ADB CDB and ABD CBD. Use this space for computations. B A C D Which statement must be true? (1) ADB CBD (2) ABC ADC __ _ (3) AB ___ (4) AD ___ CD ___ CD 17 What is an equation of the line that is perpendicular to the line whose 3 equation is y __ x 2 and that passes through the point (3, 6)? 5 (1) y (2) y 5 __ 3 x 11 5 __ x 3 11 5 __ x 3 (3) y (4) y 5 __ 3 x 1 1 18 Point A lies in plane B. How many lines can be drawn perpendicular to plane B through point A? (1) one (3) zero (2) two (4) infinite Geometry January 12 [7] [OVER] 19 In the diagram below of isosceles trapezoid ABCD, AB AD 26, and BC 12. B CD C 12 25 A D 26 What is the length of an altitude of the trapezoid? (1) 7 (3) 19 (2) 14 (4) 24 20 What is an equation of circle O shown in the graph below? y O ( 2,2) x (1) (x 2)2 (y 2)2 9 (2) (x 2)2 (y 2)2 3 (3) (x 2)2 (y 2)2 9 (4) (x 2)2 (y 2)2 3 Geometry January 12 [8] 25, Use this space for computations. 21 The diagram below represents a rectangular solid. E A D F H B Use this space for computations. C G Which statement must be true? ___ ___ (1) EH and BC are coplanar. ___ ___ (2) FG and AB are coplanar. ___ ___ (3) EH and AD are skew. ___ ___ (4) FG and CG are skew. 22 In RST, m R 58 and m S 73. Which inequality is true? (1) RT TS RS (3) RT RS TS (2) RS RT TS (4) RS TS RT 23 The number of degrees in the sum of the interior angles of a pentagon is (1) 72 (3) 540 (2) 360 (4) 720 24 What is the equation of a line passing through (2, 1) and parallel to the line represented by the equation y 2x 1? (1) y 1 __ x 2 (2) y 1 __ x 2 Geometry January 12 (3) y 1 2x 5 (4) y 2x 1 [9] [OVER] ___ 25 The coordinates of the endpoints of AB are A(0,0) and B(0,6). The ___ equation of the perpendicular bisector of AB is (1) x 0 (3) y 0 (2) x 3 (4) y 3 26 In the diagram below, point P is the centroid of ABC. B N A If PM 2x L P C M 5 and BP 7x ___ 4, what is the length of PM ? (1) 9 (3) 18 (2) 2 (4) 27 ___ PQR, PRQ is a right angle and RT is drawn perpendicular to ___ hypotenuse PQ. If PT x, RT 6, and TQ 4x, what is the length ___ of PQ? 27 In (1) 9 (3) 3 (2) 12 (4) 15 28 In ABC, AB 5 feet and BC 3 f___ Which inequality represents eet. all possible values for the length of AC, in feet? (1) 2 AC 8 (3) 3 AC 7 (2) 2 AC 8 (4) 3 AC 7 Geometry January 12 [10] Use this space for computations. Part II Answer all 6 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. 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] 29 In the diagram below, two parallel lines intersect circle O at points A, B, C, and D, with m AB x 20 and m DC 2x 20. Find m AB . A (x + 20) D B (2x 20) C Geometry January 12 O [11] [OVER] _ 30 In the diagram below, point M is located on AB. _ Sketch the locus of points that are 1 unit from AB and the locus of points 2 units from point M. Label with an X all points that satisfy both conditions. A Geometry January 12 M [12] B 31 Determine whether the two lines represented by the equations y parallel, perpendicular, or neither. 2x 3 and 2y x 6 are Justify your response. Geometry January 12 [13] [OVER] 32 The coordinates of the vertices of RST are R( 2,3), S(4,4), and T(2, 2). Triangle R S T is the image of RST after a rotation of 90 about the origin. State the coordinates of the vertices of RST. [The use of the set of axes below is optional.] y x Geometry January 12 [14] 33 On the diagram below, use a compass and straightedge to construct the bisector of XYZ. [Leave all construction marks.] Y Z X Geometry January 12 [15] [OVER] ___ ___ 34 In the diagram below of circle O, diameter AB is perpendicular to chord CD at E. ___ If AO 10 and BE 4, find the length of CE. B C E D O A Geometry January 12 [16] 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. 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 Triangle ABC has coordinates A(2, 2), B(2,1), and C(4, 2). Triangle A B C is the image of ABC under T5, 2. On the set of axes below, graph and label ABC and its image, Determine the relationship between the area of ABC. ABC and the area of ABC. Justify your response. y x Geometry January 12 [17] [OVER] 36 A paint can is in the shape of a right circular cylinder. The volume of the paint can is 600 cubic inches and its altitude is 12 inches. Find the radius, in inches, of the base of the paint can. Express the answer in simplest radical form. Find, to the nearest tenth of a square inch, the lateral area of the paint can. Geometry January 12 [18] ___ 37 Triangle HKL has vertices H( 7,2), K(3, 4), and L(5,4). The midpoint of HL is M and the ___ midpoint of LK is N. Determine and state the coordinates of points M and N. ___ ___ Justify the statement: MN is parallel to HK. [The use of the set of axes below is optional.] y x Geometry January 12 [19] [OVER] Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. [6] ___ 38 In the diagram below of quadrilateral ABCD, AD ___ BC and DAE Line segments AC, DB, and FG intersect at E. Prove: AEF CEG D C E G F A Geometry January 12 B [20] BCE. Tear Here Reference Sheet V Cylinder Bh where B is the area of the base Pyramid 1 Bh 3 where B is the area of the base Right Circular Cone 1 Bh 3 where B is the area of the base Sphere V 4 r3 3 Right Circular Cylinder L 2 rh L rl V Volume V Lateral Area (L) Right Circular Cone Tear Here Surface Area Geometry January 12 Sphere where l is the slant height SA 4 r2 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 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tear Here Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only ANSWER SHEET Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: Male Female Grade . . . . . . Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Your answers to Part I should be recorded on this answer sheet. Part I Answer all 28 questions in this part. 1 ................ 8 ................ 15 . . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . . . . . 2 ................ 9 ................ 16 . . . . . . . . . . . . . . . . 23 . . . . . . . . . . . . . . . . 3 ................ 10 . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . 4 ................ 11 . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . 25 . . . . . . . . . . . . . . . . 5 ................ 12 . . . . . . . . . . . . . . . . 19 . . . . . . . . . . . . . . . . 26 . . . . . . . . . . . . . . . . 6 ................ 13 . . . . . . . . . . . . . . . . 20 . . . . . . . . . . . . . . . . 27 . . . . . . . . . . . . . . . . 7 ................ 14 . . . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . . . 28 . . . . . . . . . . . . . . . . Your answers for Parts II, III, and IV should be written in the test booklet. The declaration below must be signed when you have completed the examination. Tear Here I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior to the examination and that I have neither given nor received assistance in answering any of the questions during the examination. Signature Geometry January 12 GEOMETRY Rater s/Scorer s Name (minimum of three) Question Maximum Credit Part I 1 28 56 Part II 29 2 30 2 31 2 32 2 33 2 34 2 35 4 36 4 37 4 38 6 Maximum Total 86 Part IV Rater s/Scorer s Initials Total Raw Score Part III Credits Earned Checked by Tear Here GEOMETRY Scale Score (from conversion chart) Tear Here Printed on Recycled Paper GEOMETRY Geometry January 12 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 26, 2012 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. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examinations in Mathematics. Do not attempt to correct the student s work by making insertions or changes of any kind. In rating the open-ended questions, you may make check marks in the exam booklet to indicate student errors. If the students were given scannable answer sheets for the multiplechoice questions, be careful not to make any stray marks on the answer sheet that might later interfere with the accuracy of the scanning. 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. On the back of the student s detachable answer sheet, raters must enter their initials in the boxes next to the questions they have scored and also write their name in the box under the heading Rater s/Scorer s Name. 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. R aters should record the student s scores for all questions and the total raw score on the student s detachable 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/apda/ o n Thursday, January 26, 2012. 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 detachable answer sheet. The scale score is the student s final examination score. Part I Allow a total of 56 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) . . . . . 2 . . . . . (8) . . . . . 4 . . . . . (15) . . . . . 2 . . . . . (22) . . . . . 4 . . . . . (2) . . . . . 3 . . . . . (9) . . . . . 3 . . . . . (16) . . . . . 4 . . . . . (23) . . . . . 3 . . . . . (3) . . . . . 2 . . . . . (10) . . . . . 3 . . . . . (17) . . . . . 3 . . . . . (24) . . . . . 3 . . . . . (4) . . . . . 2 . . . . . (11) . . . . . 2 . . . . . (18) . . . . . 1 . . . . . (25) . . . . . 4 . . . . . (5) . . . . . 1 . . . . . (12) . . . . . 4 . . . . . (19) . . . . . 4 . . . . . (26) . . . . . 1 . . . . . (6) . . . . . 2 . . . . . (13) . . . . . 1 . . . . . (20) . . . . . 1 . . . . . (27) . . . . . 4 . . . . . (7) . . . . . 1 . . . . . (14) . . . . . 2 . . . . . (21) . . . . . 1 . . . . . (28) . . . . . 2 . . . . . Geometry Rating Guide January 12 [2] 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/apda/ 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. General Rules for Applying Mathematics Rubrics I. General Principles for Rating The rubrics for the constructed-response questions on the Regents Examination in Geometry 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 Examinations in Mathematics, 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 State 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 any response. 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. A response with one conceptual error can receive no more than half credit. 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. If a response shows two (or more) different major conceptual errors, it should be considered completely incorrect and receive no credit. 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; i.e., awarding half credit for the conceptual error and deducting 1 credit for each mechanical error (maximum of two deductions for mechanical errors). Geometry Rating Guide January 12 [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. (29) [2] 60, and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made, but an appropriate measure for AB is found. or [1] Appropriate work is shown, but one conceptual error is made, but an appropriate measure for AB is found. or [1] Appropriate work is shown to find x shown. 40, but no further correct work is or [1] 60, 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] Both loci are sketched correctly, and four points of intersection are labeled with an X. [1] Both loci are sketched correctly, but the points of intersection are not labeled or are labeled incorrectly. or [1] Appropriate work is shown, but one conceptual error is made, but appropriate points of intersection are labeled with an X. or [1] One locus is sketched correctly, but no further correct 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 Rating Guide January 12 [4] (31) [2] Perpendicular, and appropriate work is shown, and an appropriate justification is given. [1] Appropriate work is shown, but one computational error is made, but an appropriate determination is made, and an appropriate justification is given. or [1] Appropriate work is shown, but one conceptual error is made, but an appropriate determination is made, and an appropriate justification is given. or [1] Appropriate work is shown to find 2 and 1 , the slopes of the given 2 equations, but no further correct work is shown. [0] Perpendicular, but no work is shown and no justification is given. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (32) [2] R ( 3, 2), S ( 4,4), and T (2,2). [1] One graphing error is made, but appropriate coordinates are stated and labeled. or [1] One conceptual error is made, but appropriate coordinates are stated and labeled. or [1] ( 3, 2), ( 4,4), and (2,2) are stated, but the coordinates are not labeled or are labeled incorrectly. or [1] Two of the three points are stated and labeled correctly, but no further correct work is shown. or [1] R S T is graphed and labeled correctly, but coordinates are not stated or are stated incorrectly. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. Geometry Rating Guide January 12 [5] (33) [2] A correct construction is drawn showing all appropriate arcs, and the angle bisector is drawn. [1] All appropriate arcs are drawn, but the angle bisector is not drawn. or [1] Appropriate work is shown, but one construction error is made. [0] A drawing that is not an appropriate construction 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. (34) [2] 8, and appropriate 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] 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 Rating Guide January 12 [6] 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. (35) [4 ] ABC and its image A B C are graphed and labeled correctly, and the areas are equal or the area remains the same is stated, and an appropriate justification is written, such as finding the areas of both triangles or stating that distance is preserved under a translation. [3] Appropriate work is shown, but one computational, graphing, or labeling error is made, but an appropriate relationship is determined, and an appropriate justification is written. or [3] ABC and A B C are graphed and labeled correctly, and the areas are equal is stated, but no justification is written. or [3] ABC is either not graphed or is graphed incorrectly, but an appropriate image is graphed and labeled, and the areas are equal is stated, and an appropriate justification is written. or [3] The areas are equal is stated and an appropriate justification is written, and A (7, 4), B (7, 1), and C (9, 4) are stated and labeled, but neither triangle is graphed. [2] Appropriate work is shown, but two or more computational, graphing, or labeling errors are made, but an appropriate relationship is determined, and an appropriate justification is written. or [2] Appropriate work is shown, but one conceptual error is made, such as performing an incorrect transformation, but both triangles are graphed and labeled, and an appropriate relationship is determined, and a justification is written. or [2] The areas are equal is stated, and an appropriate justification is written, but neither ABC nor A B C is graphed. or [2] Both ABC and A B C are graphed and labeled correctly, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational, graphing, or labeling error are made, but an appropriate relationship is determined, and an appropriate justification is written. Geometry Rating Guide January 12 [7] or [1] Appropriate work is shown to find the areas of further correct work is shown. ABC and A B C , but no [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. (36) [4] 5 2 and 533.1, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made, but appropriate solutions are found. or [3] Appropriate work is shown to find work is shown. 50 and 533.1, but no further correct [2] Appropriate work is shown, but two or more computational, rounding, or simplification errors are made, but appropriate solutions are found. or [2] Appropriate work is shown, but one conceptual error is made, but appropriate solutions are found. or [2] Appropriate work is shown to find 5 2 , but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational, rounding, or simplification error are made, but appropriate solutions are found. or [1] Appropriate work is shown to find 50 , but no further correct work is shown. or [1] 5 2 and 533.1, 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 Rating Guide January 12 [8] (37) [4] M( 1,3) and N(4,0), and appropriate work is shown, and an appropriate justification is given. [3] Appropriate work is shown, but one computational or graphing error is made, but appropriate coordinates for M and N are stated, and an appropriate justification is given. or [3] Midpoints M and N are graphed correctly, but the coordinates are not stated, but a correct justification is given. or [3] Appropriate work is shown to find M( 1,3) and N(4,0) and the slopes of 3 3 MN 5 and HL 5 , but no justification is given. [2] Appropriate work is shown, but two or more computational or graphing errors are made, but appropriate coordinates for M and N are stated, and an appropriate justification is given. or [2] Appropriate work is shown, but one conceptual error is made, but appropriate coordinates for M and N are stated, and an appropriate justification is given. or [2] An appropriate justification using the midsegment theorem is given, but the coordinates of M and N are not stated, and no further correct work is shown. or [2] Appropriate work is shown to find both midpoints, but no justification or an incorrect justification is given. [1] Appropriate work is shown, but one conceptual error and one computational or graphing error are made, but appropriate coordinates for M and N are stated, and an appropriate justification is given. or [1] Appropriate work is shown to find one of the midpoints, but no further correct 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 Rating Guide January 12 [9] Part IV For this question, use the specific criteria to award a maximum of 6 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (38) [6] A complete and correct proof that includes a conclusion 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 or reason is missing or is incorrect, or the concluding statement is missing. [4] A proof is written that demonstrates a good understanding of the method of proof and contains no conceptual errors, but two statements or reasons are missing or are incorrect. [3] A proof is written that demonstrates a good understanding of the method of proof, but one conceptual error is made. [2] A proof is written that demonstrates a method of proof, but one conceptual error is made, and one statement or reason is missing or is incorrect. or [2] Some correct relevant statements about the proof are made, but three or four statements or reasons are missing or are incorrect. [1] Only one correct statement and reason 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 Rating Guide January 12 [10] Map to Core Curriculum Content Band Item Numbers Geometric Relationships 15, 18, 21, 36 Constructions 7, 33 Locus Transformational Geometry 2, 30 1, 4, 6, 8, 9, 10, 13, 14, 16, 19, 22, 23, 26, 27, 28, 29, 34, 38 11, 32, 35 Coordinate Geometry 3, 5, 12, 17, 20, 24, 25, 31, 37 Informal and Formal Proofs Regents Examination in Geometry January 2012 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the January 2012 Regents Examination in Geometry will be posted on the Department s web site at: http://www.p12.nysed.gov/apda/ on Thursday, January 26, 2012. Conversion charts provided for previous administrations of the Geometry examination 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 Rating Guide January 12 [11]

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