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New York Regents Mathematics B June 2009

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MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Tuesday, June 23, 2009 1:15 to 4:15 p.m., only Print Your Name: Print Your School s Name: Print your name and the name of your school in the boxes 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. 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. Write all your work in pen, except graphs and drawings, which should be done in pencil. The formulas that you may need to answer some questions in this examination are found on page 23. This sheet is perforated so you may remove it from this booklet. This examination has four parts, with a total of 34 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. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. 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. MATHEMATICS B Part I Answer all 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. [40] 1 The number of degrees equal to (1) 45 (2) 90 5 9 Use this space for computations. radians is (3) 100 (4) 900 2 The accompanying graph shows the curves of best fit for data points comparing temperature to altitude in four different regions, represented by the relations A, B, C, and D . A 6 B C Altitude (km) 5 D 4 3 2 1 50 40 30 20 10 0 10 20 30 40 Which relation is not a function? (1) A (2) B (3) C (4) D 3 3 What is the value of (2 k)2 ? k =1 (1) 1 (2) 2 Math. B June 09 (3) 3 (4) 0 [2] 50 4 If sin x = 1 , a 0 , which statement must be true? a (1) csc x = a (2) csc x = (3) sec x = a (2) 16 + 5 7 16 16 + 5 7 9 1 (4) sec x = a 1 a 5 The expression (1) Use this space for computations. 5+ 7 5 7 is equivalent to (3) (4) 16 5 7 16 16 5 7 9 6 When the sum of 4 + 8i and 2 9i is graphed, in which quadrant does it lie? (1) I (2) II (3) III (4) IV 7 What is the solution of the inequality |2x 5|<1? (1) x < 3 (2) 2 < x < 3 (3) x > 3 (4) x 2 or x 3 8 Point A(1,0) is a point on the graph of the equation y = x2 4x + 3. When point A is reflected across the axis of symmetry, what are the coordinates of its image, point A ? (1) ( 1,2) (2) (0,3) Math. B June 09 (3) (2, 1) (4) (3,0) [3] [OVER] 9 The accompanying diagram represents the biological process of cell division. t=0 t=1 t=2 t=3 If this process continues, which expression best represents the number of cells at any time, t? (1) t + 2 (2) 2t (3) t2 (4) 2t 10 The roots of the equation x2 5x + 1 = 0 are (1) (2) (3) (4) real, rational, and unequal real, rational, and equal real, irrational, and unequal imaginary 11 Using a drawing program, a computer graphics designer constructs a circle on a coordinate plane on her computer screen. She determines that the equation of the circle s graph is (x 3)2 + (y + 2)2 = 36. She then dilates the circle with the transformation D3. After this transformation, what is the center of the new circle? (1) (6, 5) (2) ( 6,5) (3) (9, 6) (4) ( 9,6) 1 1 12 Which expression is equivalent to a2 b 2 ? (1) a 2 1 b2 (3) 1 (2) ab 4 Math. B June 09 (4) ab2 1 1 ab 4 [4] Use this space for computations. Readership (in thousands) 13 The accompanying graph shows the average daily readership, in thousands, of the newspaper El Diario La Prensa. Use this space for computations. 300 250 Fall Spr 01 02 Fall Spr Fall Spr 02 03 03 04 Time of Year Which type of function best represents this graph? (1) exponential (2) logarithmic 14 The expression (1) cos A (2) tan A (3) trigonometric (4) quadratic sin 2 A is equivalent to 2 cos A (3) sin A (4) 1 sin A 2 15 What is the solution set of the equation y = 2 + (1) { } (2) {2} y2 12 ? (3) { 4,4} (4) {4} 16 What is the third term in the expansion of (2x 3)5? (1) 1080x2 (2) 720x3 Math. B June 09 (3) 720x3 (4) 1080x3 [5] [OVER] 17 The accompanying table shows the scores on a classroom test. xi fi 100 7 90 10 80 4 70 4 What is the population standard deviation for this set of scores? (1) 10.2 (2) 10.4 (3) 25 (4) 88 18 The manager of Stuart Siding Company found that the number of workers used to side a house varies inversely with the number of hours needed to finish the job. If four workers can side the house in 48 hours, how many hours will it take six workers working at the same speed to do the same job? (1) 32 (2) 36 (3) 42 (4) 72 x x y is equivalent to 1 x y 1 19 The expression (1) 1 x (2) x y Math. B June 09 (3) y (4) y [6] Use this space for computations. 20 The Sea Dragon, a pendulum ride at an amusement park, moves from Use this space for computations. its central position at rest according to the trigonometric function P(t) = 10 sin t , where t represents time, in seconds. How many 3 seconds does it take the pendulum to complete one full cycle? (1) 5 (3) 3 (2) 6 (4) 10 Math. B June 09 [7] [OVER] Part II Answer all 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. [12] 21 If f(x) = x2 + 4 and g(x) = 2x + 3, find f(g( 2)). Math. B June 09 [8] 22 In A BC, sin A = 0.6, a = 10, and b = 7. Find sin B. 23 Solve algebraically for x: 93x = 33x + 1 Math. B June 09 [9] [OVER] 24 The accompanying diagram shows two lengths of wire attached to a wheel, so that AB and AC are tangent to the wheel. If the major arc BC has a measure of 220 , find the number of degrees in m A. B A C Math. B June 09 [10] 25 Solve for x: log8 (x + 1) = Math. B June 09 2 3 [11] [OVER] 26 The accompanying graph shows the relationship between the cooling time of magma and the size of the crystals produced after a volcanic eruption. On the same graph, sketch the inverse of this function. y Size of Crystals (mm) 5 4 f 3 2 1 0 Math. B June 09 1 2 3 4 Cooling Time of Magma (hr) [12] 5 x Part III Answer all 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. [24] 27 The number of newly reported crime cases in a county in New York State is shown in the accompanying table. Write the linear regression equation that represents this set of data. (Let x = 0 represent 1999.) Using this equation, find the projected number of new cases for 2009, rounded to the nearest whole number. Year (x) New Cases (y) 1999 2000 457 2001 369 2002 Math. B June 09 440 351 [13] [OVER] 28 On the accompanying grid, graph and label ABC with vertices A(3,1), B(0,4), and C( 5,3). On the same grid, graph and label A B C , the image of ABC after the transformation rx-axis ry = x . Math. B June 09 [14] 29 Express in simplest form: Math. B June 09 3x + 9 2x 6 6 2x [15] [OVER] 3 30 Dave does not tell the truth 4 of the time. Find the probability that he will tell the truth at most twice out of the next five times. Math. B June 09 [16] 31 In the accompanying diagram, CD is an altitude of m A = 45, and m B = 30, find the perimeter of radical form. ABC. If CD = 8, ABC in simplest C 8 A Math. B June 09 D B [17] [OVER] 32 Solve the equation cos = 2 + 3 cos 2 f or all values of , t o the nearest tenth of a degree, in the interval 0 < 360 . Math. B June 09 [18] Part IV Answer all questions in this part. Each correct answer will receive 6 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. [12] 33 The accompanying diagram shows a triangular plot of land located in Moira s garden. 12 ft 160 5f t B A 135 f t C Find the area of the plot of land, and round your answer to the nearest hundred square feet. Math. B June 09 [19] [OVER] 34 In the accompanying diagram of circle O, AD is a diameter with AD parallel to chord BC , chords AB and CD are drawn, and chords BD and AC intersect at E. Prove: BE CE B C E A Math. B June 09 O D [20] Tear Here Formulas Law of Cosines Area of Triangle K= 1 ab 2 a2 = b2 + c2 2bc cos A sin C Functions of the Sum of Two Angles Functions of the Double Angle sin (A + B) = sin A cos B + cos A sin B cos (A + B) = cos A cos B sin A sin B sin 2A = 2 sin A cos A cos 2A = cos2 A sin2 A cos 2A = 2 cos2 A 1 cos 2A = 1 2 sin2 A Functions of the Difference of Two Angles sin (A B) = sin A cos B cos A sin B cos (A B) = cos A cos B + sin A sin B Functions of the Half Angle Law of Sines sin a=b=c sin A sin B sin C 1 2 A = 1 cos A 2 cos 1 A = 1 + cos A 2 2 Normal Curve Standard Deviation 19.1% 19.1% 15.0% 15.0% Tear Here 9.2% 0.1% 0.5% 3 Math. B June 09 9.2% 4.4% 1.7% 2.5 2 1.5 4.4% 1 0.5 0 [23] 0.5 1 1.5 0.5% 1.7% 2 2.5 3 0.1% Tear Here Tear Here [24] 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 MATHEMATICS B Tuesday, June 23, 2009 1:15 to 4:15 p.m., only ANSWER SHEET I Male I Female Grade . . . . . . . . . . . Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Your answers to Part I should be recorded on this answer sheet. Part I Answer all 20 questions in this part. 1 .................... 6 ..................... 11 . . . . . . . . . . . . . . . . . . . . 16 . . . . . . . . . . . . . . . . . . . . 2 .................... 7 ..................... 12 . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . . . . . . . . . 3 .................... 8 ..................... 13 . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . . . . . . 4 .................... 9 ..................... 14 . . . . . . . . . . . . . . . . . . . . 19 . . . . . . . . . . . . . . . . . . . . 5 .................... 10 . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . . . . . . . . . . . 20 . . . . . . . . . . . . . . . . . . . . Your answers for Parts II, III, and IV should be written in the test booklet. The declaration below should 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 Math. B June 09 [27] MATHEMATICS B MATHEMATICS B Part I 1 20 40 Part II 21 2 22 2 23 2 24 2 25 2 26 2 27 4 28 4 29 4 30 4 31 4 32 4 33 6 34 6 Part III Part IV Maximum Total Credits Earned Rater s/Scorer s Initials Rater s/Scorer s Name (minimum of three) Tear Here Question Maximum Credit 88 Total Raw Score Checked by Scaled Score (from conversion chart) Tear Here [28] MATHEMATICS B Math. B June 09 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Tuesday, June 23, 2009 1:15 to 4:15 p.m., only SCORING KEY Mechanics of Rating The following procedures are to be followed for scoring student answer papers for the Mathematics B examination. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examination in Mathematics B. Use only red ink or red pencil in rating Regents papers. Do not attempt to correct the student s work by making insertions or changes of any kind. 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. 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. Raters 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 scaled score by using the conversion chart that will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Tuesday, June 23, 2009. The student s scaled score should be entered in the box provided on the student s detachable answer sheet. The scaled score is the student s final examination score. Part I Allow a total of 40 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) 3 (6) 3 (11) 3 (16) 3 (2) 1 (7) 2 (12) 4 (17) 1 (3) 2 (8) 4 (13) 3 (18) 1 (4) 1 (9) 4 (14) 3 (19) 4 (5) 2 (10) 3 (15) 4 (20) 2 MATHEMATICS B continued 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.emsc.nysed.gov/osa/ and select the link Examination 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 Mathematics B 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 Mathematics B, use their own professional judgment, confer with other mathematics teachers, and/or contact the consultants at 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, 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). [2] MATHEMATICS B continued 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. (21) [2] 5, 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, such as finding g ( f(-2)) . or [1] 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. (22) [2] 0.42, 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] A correct equation is written, but sin B is not found. or [1] 0.42, 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. [3] [OVER] MATHEMATICS B continued (23) [2] 1 3 , and appropriate algebraic 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] The equation (32)3x = 33x+1 or an equivalent equation is written, but no further correct work is shown. or [1] 1 3 [1] 1 3 , but a method other than algebraic is used. or , 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. (24) [2] 40, 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] 40, 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. [4] MATHEMATICS B continued (25) [2] 3, 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. [1] 2 83 or = x + 1 , but no further correct work is shown. or [1] 3, 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. (26) [2] The inverse function is graphed correctly. [1] One graphing error is made. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [5] [OVER] MATHEMATICS B continued 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. (27) [4] y = 35.5x + 457.5 and 103, and appropriate work is shown, such as substituting 10 into the regression equation. [3] Appropriate work is shown, but one computational, rounding, or substitution error is made. or [3] The expression 35.5x + 457.5 is written and 103, and appropriate substitution is shown, but no equation is written. or [3] y = 35.5x + 457.5 and 103, but no substitution is shown. [2] Appropriate work is shown, but two or more computational, rounding, or substitution errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] An incorrect linear regression equation is written, but an appropriate number of new cases is found. or [2] y = 35.5x + 457.5, but no further correct work is shown. or [2] The expression 35.5x + 457.5 is written and 103, but no substitution is shown. [1] Appropriate work is shown, but one conceptual error and one computational, rounding, or substitution error are made. or [1] The expression 35.5x + 457.5 is written or 103, but no substitution 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. [6] MATHEMATICS B continued (28) [4] Both ABC and A B C are graphed and labeled correctly. [3] Appropriate work is shown, but one graphing or labeling error is made. or [3] Appropriate work is shown, but only A B C is graphed and labeled correctly. [2] Appropriate work is shown, but two or more graphing or labeling errors are made. or [2] Appropriate work is shown, but one conceptual error is made, such as reflecting over the x-axis before reflecting over the line y = x. [1] Appropriate work is shown, but one conceptual error and one graphing or labeling error are made. or [1] A (1, 3), B (4,0), and C (3,5) are stated, but no work is shown. or [1] ABC is graphed and labeled correctly, but only ry correctly. =x or rx-axis is graphed [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [7] [OVER] MATHEMATICS B continued (29) [4] 3 2 , and appropriate work is shown. [3] Appropriate work is shown, but one computational, factoring, or simplification error is made. [2] Appropriate work is shown, but two or more computational, factoring, or simplification errors are made. or [2] Appropriate work is shown, but one conceptual error is made, such as not factoring out 1. or 3x 9 [2] Appropriate work is shown, but the answer is left as or as an 2(x 3) equivalent expression. [1] Appropriate work is shown, but one conceptual error and one computational, factoring, or simplification error are made. or [1] Appropriate work is shown, but the answer is left as 3x 9 + . 2(x 3) 2(3 x) or [1] 3 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. [8] MATHEMATICS B continued (30) [4] 918 1024 or an equivalent answer, and appropriate work is shown, such as 0 5 1 4 2 3 C0 1 3 + 5C1 1 3 + 5C2 1 3 . 5 4 4 4 4 4 4 [3] Appropriate work is shown, but one computational or rounding error is made. or 0 5 1 4 2 3 [3] 5C0 1 3 , 5C1 1 3 , and 5C2 1 3 are evaluated, but the values 4 4 4 4 4 4 are not added. [2] Appropriate work is shown, but two or more computational or rounding errors are made. or [2] Appropriate work is shown, but one conceptual error is made, such as finding the probability of not telling the truth at most twice or the probability of telling the truth at least twice. or 0 5 1 4 2 3 [2] 5C0 1 3 + 5C1 1 3 + 5C2 1 3 , but no further correct work 4 4 4 4 4 4 is shown. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] Appropriate work is shown to find 270 1024 , the probability of telling the truth exactly twice out of five times. or [1] 918 1024 or an equivalent answer, 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. [9] [OVER] MATHEMATICS B continued (31) [4] 24 + 8 2 + 8 3 , and appropriate work is shown, such as labeling the diagram using special right triangle rules or right triangle trigonometry. [3] Appropriate work is shown, but one computational error is made or the answer is not in simplest radical form. or [3] The measures of the four segments are found correctly, but the perimeter is not found or is found incorrectly. [2] Appropriate work is shown, but two or more computational errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] The measures of three segments are found correctly, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] The measures of two segments are found correctly, but no further correct work is shown. or [1] 24 + 8 2 + 8 3 , 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. [10] MATHEMATICS B continued (32) [4] 60, 109.5, 250.5, 300, and appropriate work is shown algebraically or graphically. [3] Appropriate work is shown, but one computational, factoring, graphing, or rounding error is made. or [3] Appropriate work is shown, but only three correct values of are found. [2] Appropriate work is shown, but two or more computational, factoring, graphing, or rounding errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] Appropriate work is shown, but only two correct values of are found. [1] Appropriate work is shown, but one conceptual error and one computational, factoring, graphing, or rounding error are made. or [1] Appropriate substitutions are made and the equation is written in standard form, but no further correct work is shown. or [1] 60, 109.5, 250.5, 300, but no work is shown. [0] 60 or 109.5 or 250.5 or 300, 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. [11] [OVER] MATHEMATICS B continued Part IV For each question, use the specific criteria to award a maximum of six credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (33) [6] 8,200, and appropriate work is shown, such as using the Law of Cosines or Hero(n) s formula. [5] Appropriate work is shown, but one computational or rounding error is made. [4] Appropriate work is shown, but two or more computational or rounding errors are made. [3] Appropriate work is shown, but one conceptual error is made. or [3] The Law of Cosines is used to find an angle, but no further correct work is shown. [2] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. [1] A correct substitution is made into the Law of Cosines, but no further correct work is shown. or [1] 8,200, 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. [12] MATHEMATICS B continued (34) [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 and/or reason is missing or is incorrect. or [5] BEA = CED is proven or correct work is shown. BEC is proven to be isosceles, but no further [4] A proof is written that demonstrates a good understanding of the method of proof, but two statements and/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] Some correct relevant statements about the proof are made, but three or four statements and/or reasons are missing or are incorrect. or [2] A proof is written that demonstrates understanding of the method of proof, but one conceptual error is made, and one statement or reason is missing or is incorrect. [1] Only one correct relevant statement and reason are written. [0] The given and/or the prove statements are rewritten in the style of a formal proof, 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. [13] [OVER] MATHEMATICS B concluded Map to Learning Standards Key Ideas Item Numbers Mathematical Reasoning 34 Number and Numeration 5, 10, 19 Operations 28, 29 Modeling/Multiple Representation 6, 8, 9, 11, 12, 13, 18, 20, 25 Measurement 1, 4, 22, 24, 31, 33 Uncertainty 3, 16, 27, 30 Patterns/Functions 2, 7, 14, 15, 17, 21, 23, 26, 32 Regents Examination in Mathematics B June 2009 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the June 2009 Regents Examination in Mathematics B will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Tuesday, June 23, 2009. Conversion charts provided for the previous administrations of the Regents Examination in Mathematics B 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.emsc.nysed.gov/osa/exameval. 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. As a reminder . . . Regents examinations based on the Mathematics B syllabus will not be offered after June 2010. [14] [16]

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Additional Info : Refer : Formulas (page 23) and Scoring Key (page 29)
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