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New York Regents Mathematics B June 2008

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MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, June 19, 2008 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 For which value of x is f (x) = (1) 1 (2) 0 Use this space for computations. 1 undefined? 27 3 x (3) 3 (4) 3 2 In the accompanying diagram of circle O, AB and BC are chords and m AOC = 96. What is m ABC? A C O B (1) 32 (2) 48 (3) 96 (4) 192 3 Kathy deposits $25 into an investment account with an annual rate of 5%, compounded annually. The amount in her account can be determined by the formula A = P(1 + R)t, where P is the amount deposited, R is the annual interest rate, and t is the number of years the money is invested. If she makes no other deposits or withdrawals, how much money will be in her account at the end of 15 years? (1) $25.75 (3) $51.97 (2) $43.75 (4) $393.97 Math. B June 08 [2] 4 The accompanying graph shows the elevation of a certain region in New York State as a hiker travels along a trail. Use this space for computations. Elevation (ft) y 1600 1500 1400 1300 1200 1100 1000 900 x 0 5 10 Distance Hiker Travels (mi) What is the domain of this function? (1) 1,000 x 1,500 (3) 0 x 12 (2) 1,000 y 1,500 (4) 0 y 12 5 Which relation is a function? (1) x2 + y2 = 16 (3) y2 = x2 + 3x 4 (2) 2x2 + 6y2 = 1 (4) y = x2 + 3x 4 6 If f(x) = x2 + 4 and g(x) = (1) 2 i 3 (2) 2 Math. B June 08 1 x , what is the value of f(g( 3))? (3) 8 (4) 13 [3] [OVER] 7 Which expression represents the sum of the sequence 3, 5, 7, 9, 11? 5 5 (1) (2 n + 1) (3) n=1 n=0 5 (2) 3n n=1 (3 n + 1) 5 (4) (2 n + 1) n=1 8 Which value of a does not satisfy the inequality |a| > 2a 3? (1) 1 (3) 3 (2) 0 (4) 5 9 If point (5,2) is rotated counterclockwise 90 about the origin, its image will be point (1) (2,5) (3) ( 2,5) (2) (2, 5) (4) ( 5, 2) 10 What is the sum of 5 3i and the conjugate of 3 + 2i? (1) 2 + 5i (3) 8 + 5i (2) 2 5i (4) 8 5i Math. B June 08 [4] Use this space for computations. 11 In the accompanying diagram of circle O, AB CD . Use this space for computations. B A O D C Which statement is true? (1) AB CD (3) AB | | CD (2) AC BD (4) ABC BCD 12 The expression cos2 4 + sin2 4 is equivalent to (1) 1 (3) cos (2) 2 (4) cos 8 13 The value of (1) 5 (2) 0 x 2 9 is a real and irrational number when x is equal to (3) 3 (4) 4 14 If 24x+1 = 8x+a, which expression is equivalent to x? (1) a 1 (2) 3a 1 Math. B June 08 a 1 15 a 1 (4) 3 (3) [5] [OVER] 15 In 1995, the federal government paid off one-third of its debt. If the original amount of the debt was $4,920,000,000,000, which expression represents the amount that was not paid off? (1) 1.64 104 (3) 3.28 108 (2) 1.64 1012 (4) 3.28 1012 2 5 is equivalent to sin x sin x 1 3 3 sin x 2 (1) (3) sin x(sin x 1) sin x(sin x 1) 16 The expression (2) 3 sin x 1 (4) 3 sin x 2 sin x 1 17 Al is standing 50 yards from a maple tree and 30 yards from an oak tree in the park. His position is shown in the accompanying diagram. If he is looking at the maple tree, he needs to turn his head 120 to look at the oak tree. 50 yd Maple tree Al s 120 location 30 y d Oak tree How many yards apart are the two trees? (1) 58.3 (3) 70 (2) 65.2 (4) 75 Math. B June 08 [6] Use this space for computations. 18 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet. Use this space for computations. 20 ft A B C What is the length of arc AC, in feet? (1) 63 (3) 20 (2) 31 (4) 10 19 The expression i100 + i101 + i102 equals (1) 1 (3) i (2) 1 (4) i 20 Which equation has roots whose sum is 3 and whose product is 4? (3) x2 + 4x 3 = 0 (1) x2 + 3x 4 = 0 (2) x2 3x 4 = 0 (4) x2 4x + 3 = 0 Math. B June 08 [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 The entire graph of f(x) is symmetric with respect to the origin. If the accompanying graph represents f(x) for x 0, sketch, on the same set of axes, the graph of f(x) for x 0. y x Math. B June 08 [8] 22 A laundry owner s estimate of her weekly profits, p, in dollars, is given by the equation p = 4 w2 + 160 w, where w represents the number of workers she hires. What is the number of workers she should hire in order to earn the greatest profit? [The use of the accompanying grid is optional.] Math. B June 08 [9] [OVER] 23 Simplify: Math. B June 08 x 3 x 3 x 3 x [10] 24 The coordinates of quadrilateral PRAT are P(a,b), R(a,b + 3), A(a + 3, b + 4), and T(a + 6, b + 2). Prove that RA is parallel to PT . Math. B June 08 [11] [OVER] fe e .4 et fe 20 .4 20 t 25 The accompanying diagram shows the peak of a roof that is in the shape of an isosceles triangle. A base angle of the triangle is 50 and each side of the roof is 20.4 feet. Determine, to the nearest tenth of a square foot, the area of this triangular region. 50 Math. B June 08 [12] 26 The weights of the boxes of animal crackers coming off an assembly line differ slightly and form a normal distribution whose mean is 9.8 ounces and whose standard deviation is 0.6 ounce. Determine the number of boxes of animal crackers in a shipment of 5,000 boxes that are expected to weigh more than 11 ounces. Math. B June 08 [13] [OVER] 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 accompanying table shows the amount of water vapor, y, that will saturate 1 cubic meter of air at different temperatures, x. Amount of Water Vapor That Will Saturate 1 Cubic Meter of Air at Different Temperatures Air Water Vapor (y) Temperature (x) (g) ( C) 20 1 10 2 0 5 10 9 20 17 30 29 40 50 Write an exponential regression equation for this set of data, rounding all values to the nearest thousandth. Using this equation, predict the amount of water vapor that will saturate 1 cubic meter of air at a temperature of 50 C, and round your answer to the nearest tenth of a gram. Math. B June 08 [14] 28 Four streets in a town are illustrated in the accompanying diagram. If the distance on Poplar Street from F to P is 12 miles and the distance on Maple Street from E to M is 10 miles, find the distance on Maple Street, in miles, from M to P. E Math. B June 08 M Maple ar pl Po m El Fern F P [15] [OVER] 29 Find all values of in the interval 0 < 360 that satisfy the equation 3 cos 2 + 2 sin + 1 = 0, and round all answers to the nearest hundredth of a degree. [Only an algebraic solution can receive full credit.] Math. B June 08 [16] 30 The probability of rain on the last day of July is 90%. If the probability remains constant for the first seven days of August, what is the probability that it will rain at least six of those seven days in August? Math. B June 08 [17] [OVER] 31 The engineering office in the village of Whitesboro has a map of the village that is laid out on a rectangular coordinate system. A traffic circle located on the map is represented by the equation (x + 4)2 + (y 2)2 = 81. The village planning commission asks that the transformation D2 be applied to produce a new traffic circle, where the center of dilation is at the origin. Find the coordinates of the center of the new traffic circle. Find the length of the radius of the new traffic circle. Math. B June 08 [18] 32 A radio wave has an amplitude of 3 and a wavelength (period) of meters. On the accompanying grid, using the interval 0 to 2 , draw a possible sine curve for this wave that passes through the origin. Math. B June 08 [19] [OVER] 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 Solve for x: log3 (x2 4) log3 (x + 2) = 2 Math. B June 08 [20] 34 Gerardo and Bennie are pushing a box. Gerardo pushes with a force of 50 pounds in an easterly direction, and Bennie pushes with a force of 39 pounds in a northeasterly direction. The resultant force forms an angle of 32 with the 39-pound force. Find the angle between the 50-pound force and the 39-pound force, to the nearest tenth of a degree. Find the magnitude of the resultant force, to the nearest pound. Math. B June 08 [21] 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 08 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 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 Thursday, June 19, 2008 1:15 to 4:15 p.m., only ANSWER SHEET Male 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 08 [27] MATHEMATICS B MATHEMATICS B Question Maximum Credits Rater s/Scorer s Credit Earned Initials 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 Tear Here Part I 1 20 6 Part III Part IV Maximum Total Rater s/Scorer s Name (minimum of three) 88 Total Raw Score Checked by Scaled Score (from conversion chart) Tear Here [28] MATHEMATICS B Math. B June 08 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, June 19, 2008 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 Examinations in Mathematics A and 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 Thursday, June 19, 2008. 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) 1 (16) 3 (2) 2 (7) 4 (12) 1 (17) 3 (3) 3 (8) 3 (13) 4 (18) 3 (4) 3 (9) 3 (14) 2 (19) 4 (5) 4 (10) 4 (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 Examinations in Mathematics A and 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 Examinations in Mathematics A and 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] A correct graph of f(x) for x < 0 is drawn. [1] One conceptual error is made, such as reflecting f(x) over an axis. [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] 20, and appropriate work is shown, such as finding the turning point or sketching the graph of the equation. [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] The graph of the equation is sketched correctly, but no further correct work is shown. or [1] (20,1600) is identified as the turning point, but the number of workers is not stated. or [1] 20, 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] x + 3 , and appropriate work is shown. 3 [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] x + 3 , but no work is shown. 3 [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] The slopes of RA and PT are calculated correctly, and appropriate work is shown, and the statement is made that since their slopes are equal, the lines are parallel. [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] Appropriate work is shown, and the slopes are shown to be equal, but no concluding statement is written. [0] A statement is written that lines with equal slopes are parallel, 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. [4] MATHEMATICS B continued (25) [2] 204.9, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 204.9, 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] 115, 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] 115, 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. [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 = 4.194(1.068)x and 112.5, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. or x [3] y = 4.194(1.068) and 112.5, but no substitution is shown. or [3] The expression 4.194(1.068)x is written and 112.5, and appropriate substitution is shown. [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. or [2] y = 4.194(1.068)x, but no further correct work is shown. or [2] An incorrect regression equation of equal difficulty is solved appropriately. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] An incorrect regression equation of a lesser degree of difficulty is solved appropriately. or x [1] The expression 4.194(1.068) is written and 112.5, but no work is shown. or [1] 112.5, 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. [6] MATHEMATICS B continued (28) [4] 8, and appropriate work is shown, such as solving the proportion 10 + x = 12 . 12 x [3] Appropriate work is shown, but one computational error is made. [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 10 + x = 12 [2] The proportion is written, but no further correct work is shown. 12 x [1] Appropriate work is shown, but one conceptual error and one computational error are 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. [7] [OVER] MATHEMATICS B continued (29) [4] 90, 221.81, and 318.19, and appropriate work is shown, such as solving the equation 3 sin2 sin 2 = 0. [3] Appropriate work is shown, but one computational or rounding error is made. or [3] The equation is solved correctly for , but only one or two of the solutions are found. [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. or [2] 90, 221.81, and 318.19, and appropriate work is shown, but a graphic method is used. or [2] Appropriate work is shown to find the values of sin , but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] A correct quadratic equation in standard form is written, but no further correct work is shown. or [1] 90, 221.81, and 318.19, 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] .8503056 or an equivalent answer, and appropriate work is shown, such as 6 1 7 0 7 C6(.9) (.1) + 7 C7(.9) (.1) . [3] Appropriate work is shown, but one computational or rounding error is made. or [3] The two individual probabilities are calculated correctly, but they 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 at most 6 days. or [2] The expression 7 C6(.9)6(.1)1 + 7 C7(.9)7(.1)0 is written, but no further correct work 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 .3720087, the probability of exactly 6 days, but no further correct work is shown. or [1] .8503056 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] ( 8,4) and 18, and appropriate work is shown. [3] Appropriate work is shown, but one computational error is made. [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, such as using an incorrect dilation. or [2] The center and radius are found appropriately for an incorrect center and radius of the original equation. or [2] ( 8,4), and appropriate work is shown, but no further correct work is shown. [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] 18, and appropriate work is shown, but no further correct work is shown. or [1] ( 8,4) and 18, but no work is shown. [0] ( 8,4) or 18, 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. [10] MATHEMATICS B continued (32) [4] The graph of y = 3 sin 2x or the graph of y = 3 sin 2x is drawn. [3] Appropriate work is shown, but one graphing error is made, such as not drawing the graph over the entire interval. [2] Appropriate work is shown, but two or more graphing errors are made. or [2] Appropriate work is shown, but one conceptual error is made, such as graphing y = sin 2x or y = 3 sin x. [1] Appropriate work is shown, but one conceptual error and one graphing error are made. or [1] The equation y = 3 sin 2x or y = 3 sin 2x is written, but 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. [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] 11, and appropriate work is shown. [5] Appropriate work is shown, but one computational error is made. or [5] The given equation is solved correctly for x, but the extraneous root is not rejected. [4] Appropriate work is shown, but two or more computational errors are made. [3] Appropriate work is shown, but one conceptual error is made. or [3] The equation x2 9x 22 = 0 is written, but no further correct work is shown. [2] Appropriate work is shown, but one conceptual error and one computational error are made. 2 or [2] The equation x 4 = 9 is written, but no further correct work is shown. x+2 [1] The equation log 3 (x 2) = 2 is written, but no further correct work is shown. or [1] 11, 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] 56.4 and 79, and appropriate work is shown, such as using the Law of Sines and then the Law of Cosines or the Law of Sines. [5] Appropriate work is shown, but one computational or rounding error is made. or [5] Appropriate work is shown, and the angle between the resultant and the 50-pound force is found to be 24.4 and the force is found to be 79, but the angle between the original forces is not stated. [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] Appropriate work is shown to find 56.4, but no further correct work is shown. [2] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [2] Appropriate work is shown to find 24.4, but no further correct work is shown. or [2] 56.4 and 79, but no work is shown. [1] A complete and correctly labeled diagram is drawn to illustrate the problem, but no further correct work is shown. or [1] 56.4 or 79, 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. [13] [OVER] MATHEMATICS B concluded Map to Learning Standards Key Ideas Item Numbers Mathematical Reasoning 11, 24 Number and Numeration 13, 19, 20, 23 Operations 9, 10, 16, 21 Modeling/Multiple Representation 3, 5, 14, 15, 22, 32, 34 Measurement 2, 17, 18, 25, 26, 28 Uncertainty 4, 7, 27, 30 Patterns/Functions 1, 6, 8, 12, 29, 31, 33 Regents Examination in Mathematics B June 2008 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the June 2008 Regents Examination in Mathematics B will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Thursday, June 19, 2008. 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. Submitting 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. [14]

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