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New York Regents Geometry August 2011

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GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.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 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 The statement x is a multiple of 3, and x is an even integer is true when x is equal to (1) 9 (3) 3 (2) 8 (4) 6 2 In the diagram below, ABC XYZ. C Y X Z A B Which statement must be true? _ _ _ _ (1) C Y (3) AC YZ (2) A X (4) CB XZ Geometry August 11 [2] Use this space for computations. _ _ 3 In the diagram below of ABC, TV BC, AT = 5, TB = 7, and AV = 10. Use this space for computations. A T V C B _ What is the length of VC ? 1 (1) 3 __ (3) 14 1 (2) 7 __ (4) 24 2 7 _ _ 4 Pentagon PQRST has PQ parallel to TS. After a translation _ of T2, 5 , which line segment is parallel to P Q ? _ _ (1) R Q _ (3) T S _ (2) R S (4) T P Geometry August 11 [3] [OVER] _ 5 In the diagram below of PAO, AP is tangent to circle O at point A, OB = 7, and BP = 18. O 7 B 18 P A _ What is the length of AP ? (1) 10 (3) 17 (2) 12 (4) 24 6 A straightedge and compass were used to create the construction below. Arc EF was drawn from point B, and arcs with equal radii were drawn from E and F. A D E C F B Which statement is false? (1) m ABD = m DBC 1 (2) __ (m ABC) = m ABD 2 (3) 2(m DBC) = m ABC (4) 2(m ABC) = m CBD Geometry August 11 [4] Use this space for computations. 7 What is the length of the line segment whose endpoints are (1, 4) and (9,2)? (1) 5 ___ (2) 2 17 (3) 10 Use this space for computations. ___ (4) 2 26 8 What is the image of the point (2, 3) after the transformation ry-axis ? (1) (2,3) (3) ( 2,3) (2) ( 2, 3) (4) ( 3,2) Geometry August 11 [5] [OVER] 9 In the diagram below, lines n and m are cut by transversals p and q. 80 n 30 x m q p Which value of x would make lines n and m parallel? (1) 110 (3) 70 (2) 80 (4) 50 10 What is an equation of the circle with a radius of 5 and center at (1, 4)? (1) (x + 1)2 + (y 4)2 = 5 (2) (x 1)2 + (y + 4)2 = 5 (3) (x + 1)2 + (y 4)2 = 25 (4) (x 1)2 + (y + 4)2 = 25 Geometry August 11 [6] Use this space for computations. _ 11 In the diagram below of BCD, side DB is extended to point A. Use this space for computations. C A B D Which statement must be true? (1) m C > m D (3) m ABC > m C (2) m ABC < m D (4) m ABC > m C + m D 12 Which equation represents the line parallel to the line whose equation is 4 x + 2y = 14 and passing through the point (2,2)? (1) y = 2 x 1 (3) y = __ x (2) y = 2 x + 6 1 (4) y = __ x + 1 2 2 13 The coordinates of point A are ( 3 a,4 b). If point A is the image of point A reflected over the line y = x, the coordinates of A are (1) (4 b, 3 a) (3) ( 3 a, 4 b) (2) (3 a,4 b) (4) ( 4 b, 3 a) Geometry August 11 [7] [OVER] _ 14 As shown in the diagram below, AC bisects BAD and B D. B D C A Which method could be used to prove ABC ADC? (1) SSS (3) SAS (2) AAA (4) AAS 15 Segment AB is the diameter of circle M. The coordinates of A are ( 4,3). The coordinates of M are (1,5). What are the coordinates of B? (1) (6,7) (3) ( 3,8) (2) (5,8) (4) ( 5,2) Geometry August 11 [8] Use this space for computations. _ 16 In the diagram below, AB is perpendicular to plane AEFG. G A Use this space for computations. F E H D B C Which plane must be perpendicular to plane AEFG? (1) ABCE (3) CDFE (2) BCDH (4) HDFG 17 How many points are both 4 units from the origin and also 2 units from the line y = 4? (1) 1 (3) 3 (2) 2 (4) 4 Geometry August 11 [9] [OVER] 18 When solved graphically, what is the solution to the following system of equations? y = x 2 4 x+ 6 y=x+2 (1) (1,4) (3) (1,3) and (4,6) (2) (4,6) (4) (3,1) and (6,4) 19 Triangle PQR has angles in the ratio of 2:3:5. Which type of triangle is PQR? (1) acute (3) obtuse (2) isosceles (4) right Geometry August 11 [10] Use this space for computations. 20 Plane A is parallel to plane B. Plane C intersects plane A in line m and intersects plane B in line n. Lines m and n are (1) intersecting (3) perpendicular (2) parallel Use this space for computations. (4) skew 21 The diagonals of a quadrilateral are congruent but do not bisect each other. This quadrilateral is (1) an isosceles trapezoid (3) a rectangle (2) a parallelogram (4) a rhombus 22 What is the slope of a line perpendicular to the line represented by the equation x + 2 y = 3? (1) 2 1 (3) __ 2 (2) 2 1 (4) __ Geometry August 11 2 [11] [OVER] 23 A packing carton in the shape of a triangular prism is shown in the diagram below. What is the volume, in cubic inches, of this carton? (1) 20 (3) 120 (2) 60 (4) 240 _ 24 In the _ diagram below of circle O, diameter AOB is perpendicular to chord CD at point E, OA = 6, and OE = 2. C A O E B D _ What is the length of CE ? __ __ (1) 4 3 (3) 8 2 (2) 2 3 (4) 4 2 __ Geometry August 11 __ [12] Use this space for computations. 25 What is the measure of each interior angle of a regular hexagon? (1) 60 (3) 135 (2) 120 Use this space for computations. (4) 270 _ 26 Which equation represents the perpendicular bisector of AB whose endpoints are A(8,2) and B(0,6)? (1) y = 2x 4 1 (3) y = __ x + 6 1 (2) y = __ x + 2 (4) y = 2x 12 2 2 27 As shown in the diagram below, a kite needs a vertical and a horizontal support bar attached at opposite corners. The upper edges of the kite are 7 inches, the side edges are x inches, and the vertical support bar is (x + 1) inches. hes hes x inc (x + 1) inches 7 inc What is the measure, in inches, of the vertical support bar? (1) 23 (3) 25 (2) 24 (4) 26 Geometry August 11 [13] [OVER] 28 Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have perpendicular diagonals? (1) the rhombus, only (2) the rectangle and the square (3) the rhombus and the square (4) the rectangle, the rhombus, and the square Geometry August 11 [14] 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, trapezoid ABCD, with bases AB and DC, is inscribed in circle O, with _ diameter DC. If m AB = 80, find mBC. 80 A D Geometry August 11 B O [15] C [OVER] 30 On the diagram of ABC_ shown below, use a compass and straightedge to construct the perpendicular bisector of AC . [Leave all construction marks.] B A C Geometry August 11 [16] 31 A sphere has a diameter of 18 meters. Find the volume of the sphere, in cubic meters, in terms of . Geometry August 11 [17] [OVER] 32 Write an equation of the circle graphed in the diagram below. y x Geometry August 11 [18] _ _ 33 The diagram below shows ABC, with AEB , ADC , and ACB AED. Prove that ABC is similar to ADE. A E D B Geometry August 11 C [19] [OVER] 34 Triangle ABC has vertices A(3,3), B(7,9), and C(11,3). Determine the point of intersection of the medians, and state its coordinates. [The use of the set of axes below is optional.] y x Geometry August 11 [20] 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 In the diagram below of GJK, H is a point on GJ, HJ JK , m G = 28, and m GJK = 70. Determine whether GHK is an isosceles triangle and justify your answer. K 28 G Geometry August 11 70 H [21] J [OVER] 36 As shown on the set of axes below, GHS has vertices G (3,1), H (5,3), and S (1,4). Graph and state the coordinates of G H S , the image of GHS after the transformation T 3,1 D2. y S H G Geometry August 11 [22] x 37 In the diagram below, ABC DEF, DE = 4, AB = x, AC = x + 2, and DF = x + 6. _ Determine the length of AB. [Only an algebraic solution can receive full credit.] D A x+2 4 x x+6 B E C F Geometry August 11 [23] [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 Given: ABC with vertices A( 6, 2), B(2,8), and C(6, 2) _ _ _ AB has midpoint D, BC has midpoint E, and AC has midpoint F Prove: ADEF is a parallelogram ADEF is not a rhombus [The use of the grid below is optional.] Geometry August 11 [24] Tear Here Reference Sheet V Cylinder Pyramid Bh where B is the area of the base 1 Bh 3 where B is the area of the base V Volume Right Circular Cone 1 Bh 3 where B is the area of the base V Sphere V 4 r3 3 Right Circular Cylinder L 2 rh L rl Lateral Area (L) Right Circular Cone Tear Here Surface Area Geometry August 11 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 Tear Here GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only ANSWER SHEET Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: Male Female Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grade . . . . . . 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. Tear Here The declaration below must be signed when you have completed the examination. 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 August 11 GEOMETRY Rater s/Scorer s Name (minimum of three) GEOMETRY 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 Question Scale Score (from conversion chart) Tear Here Printed on Recycled Paper GEOMETRY Geometry August 11 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.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 Wednesday, August 17, 2011. 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) 4 (8) 2 (15) 1 (22) 2 (2) 2 (9) 3 (16) 1 (23) 3 (3) 3 (10) 4 (17) 2 (24) 4 (4) 3 (11) 3 (18) 3 (25) 2 (5) 4 (12) 2 (19) 4 (26) 1 (6) 4 (13) 1 (20) 2 (27) 3 (7) 3 (14) 4 (21) 1 (28) 3 Geometry Rating Guide August 11 [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 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 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). I. Geometry Rating Guide August 11 [3] Part II For each question, use the specific criteria to award a maximum of two credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (29) [2] 50, 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] 2x + 80 = 180 or an equivalent equation is written, but no further correct work is shown. or [1] 50, 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 correct construction is drawn showing all appropriate arcs, and the perpendicular bisector is correctly drawn. [1] A correct construction is drawn showing all appropriate arcs, but the perpendicular bisector of AB or BC is drawn. or [1] A correct construction is drawn showing all appropriate arcs, but the perpendicular bisector is not drawn. [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. Geometry Rating Guide August 11 [4] (31) [2] 972 , and appropriate work is shown. [1] Appropriate work is shown, but one computational error is made, but an appropriate answer is written in terms of . or [1] Appropriate work is shown, but one conceptual error is made, but an appropriate answer is written in terms of . or [1] Appropriate work is shown, but the answer is not written in terms of . or [1] 972 , 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. (32) [2] (x 5)2 + ( y + 4)2 = 36. [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] Center of (5, 4) and radius of 6 are stated, 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 August 11 [5] (33) [2] A complete and correct proof that includes a conclusion is written. [1] Only one correct statement and reason are written. or [1] One conceptual error is made. [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. (34) [2] (7,5), and appropriate work is shown, such as locating the centroid on the vertical median or graphing at least two medians. [1] Appropriate work is shown, but one computational or graphing error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] One or two medians are graphed correctly and the median is located, but the coordinates are not stated or are stated incorrectly. or [1] (7,5), 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. Geometry Rating Guide August 11 [6] Part III For each question, use the specific criteria to award a maximum of four credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (35) [4] The triangle is not isosceles, and an appropriate justification is given, such as a correctly labeled diagram. [3] Appropriate work is shown, but one computational error is made, but an appropriate determination is made, and an appropriate justification is given. [2] Appropriate work is shown, but two or more computational errors are made, but an appropriate determination is made, and an appropriate justification is given. or [2] Appropriate work is shown, but one conceptual error is made, but an appropriate determination is made, and an appropriate justification is given. or [2] The correct measures of JHK or no determination is made. JKH and GKH or GHK are found, but [1] Appropriate work is shown, but one conceptual error and one computational error are made, but an appropriate determination is made, and an appropriate justification is given. or [1] Appropriate work is shown to find the correct measure of no further correct work is shown. JHK or JKH, but [0] Indicates the triangle is not isosceles, 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 Rating Guide August 11 [7] (36) [4] G (3,3), H (7,7), and S ( 1,9) are graphed, stated, and labeled correctly, and appropriate work is shown. [3] Appropriate work is shown, but one computational, graphing, or labeling error is made, but appropriate coordinates are graphed, stated, and labeled. or [3] Appropriate work is shown to find G (3,3), H (7,7), and S ( 1,9), but no graph is drawn. or [3] G H S is graphed and labeled correctly, but the coordinates are not stated or are stated incorrectly. [2] Appropriate work is shown, but two or more computational, graphing, or labeling errors are made, but appropriate coordinates are graphed, stated, and labeled. or [2] Appropriate work is shown, but one conceptual error is made, such as performing the translation before the dilation, but appropriate coordinates are graphed, stated, and labeled. or [2] The dilation is performed correctly, the image is graphed and labeled correctly, and the coordinates are labeled and stated 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 appropriate coordinates are graphed, stated, and labeled. or [1] Appropriate work is shown to find (3,3), (7,7), and ( 1,9), but the points are not labeled, and no graph is drawn. or [1] Appropriate work is shown to find G (6,2), H (10,6), and S (2,8), but no further correct work is shown. or [1] The dilation is graphed and labeled correctly, but no further correct work is shown. or [1] G (3,3), H (7,7), and S ( 1,9), but no work is shown, and no graph is drawn. [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 August 11 [8] (37) [4] 2, and appropriate algebraic work is shown. [3] Appropriate work is shown, but one computational or factoring error is made. or [3] Appropriate work is shown, but the negative root is included in the solution. [2] Appropriate work is shown, but two or more computational or factoring errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] A correct quadratic equation in standard form (set equal to zero) is written, but no further correct work is shown. or [2] Work is shown to find 2, but a method other than algebraic is used. [1] Appropriate work is shown, but one conceptual error and one computational or factoring error are made. or [1] A correct proportion is written, but no further correct work is shown. or [1] 2, 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 August 11 [9] Part IV For this question, use the specific criteria to award a maximum of six credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (38) [6] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, and an appropriate concluding statement is made. [5] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, but one computational or graphing error is made. or [5] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, but the concluding statement is missing or is incorrect. [4] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, but two or more computational or graphing errors are made. or [4] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, but one conceptual error is made. [3] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, but two or more computational or graphing errors are made, and the concluding statement is missing or is incorrect. or [3] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, but one conceptual error and one computational or graphing error are made. or [3] Appropriate work is shown to prove ADEF is a parallelogram, but no further correct work is shown. or [3] Appropriate work is shown to prove ADEF is not a rhombus, but no further correct work is shown. [2] Appropriate work is shown to prove ADEF is a parallelogram and not a rhombus, but two conceptual errors are made. or [2] Appropriate work is shown to prove DE || AF and AD || FE , but no further correct work is shown. or Geometry Rating Guide August 11 [10] [2] Appropriate work is shown to prove that DF and AE bisect each other, but no further correct work is shown. or [2] Appropriate work is shown to prove that DF is not perpendicular to AE , but no further correct work is shown. or [2] Appropriate work is shown to find the lengths of all four sides, but no further correct work is shown. or [2] Appropriate work is shown to prove one pair of opposite sides are both congruent and parallel, but no further correct work is shown. [1] Appropriate work is shown to find the midpoints of DF and AE , but no further correct work is shown. or [1] Appropriate work is shown to find all four slopes, but no further correct work is shown. or [1] Midpoints D, E, and F are found, 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 August 11 [11] Map to Core Curriculum Content Band Item Numbers Geometric Relationships 16, 20, 23, 31 Constructions 6, 30 Locus 17, 34 Informal and Formal Proofs 1, 2, 3, 5, 9, 11, 14, 19, 21, 24, 25, 27, 28, 29, 33, 35, 37 Transformational Geometry 4, 8, 13, 36 Coordinate Geometry 7, 10, 12, 15, 18, 22, 26, 32, 38 Regents Examination in Geometry August 2011 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores) The Chart for Determining the Final Examination Score for the August 2011 Regents Examination in Geometry will be posted on the Department s web site at: http://www.p12.nysed.gov/apda/ on Wednesday, August 17, 2011. 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 August 11 [12]

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Additional Info : Scoring key: page 29
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