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New York Regents Mathematics B June 2004

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MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Tuesday, June 22, 2004 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. 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. 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. The formulas that you may need to answer some questions in this examination are found on page 19. 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 your use while taking this examination. 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 What is the sum of 2 (1) 1 + 2i (2) 1 + i 20 4 and 3 + 16 expressed in a + bi form? (3) 1 + 12i (4) 14 + i 2 The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 0.7. Which expression can be used to find the probability that it will rain on exactly three of the seven days they are there? (1) 7C3(0.7)3(0.3)4 (3) 4C3(0.7)3(0.7)4 (2) 7C3(0.3)3(0.7)4 (4) 4C3(0.4)4(0.3)3 3 What is the amplitude of the function y = 2 sin 4x? 3 (1) 2 (3) 3 (2) 2 (4) 4 3 4 Which quadratic function is shown in the accompanying graph? y (2,8) 5 ( 1,2) x 5 5 (1) y = 2 x2 (3) y = 1 x2 2 (2) y = 2 x2 (4) y = Math. B June 04 12 x 2 [2] Use this space for computations. 5 In the accompanying graph, the shaded region represents set A of all points (x,y) such that x2 + y2 1. The transformation T maps point (x,y) to point (2 x,4y). Use this space for computations. y 2 1 x 2 1 1 1 2 2 Which graph shows the mapping of set A by the transformation T? y 4 y 2 2 1 x 2 1 1 1 x 4 2 2 2 4 2 2 4 (1) (3) y 4 y 2 2 1 x x 2 1 1 2 1 2 4 2 2 4 2 4 (2) Math. B June 04 (4) [3] [OVER] 6 If f(x) = 4x0 + (4x) 1, what is the value of f(4)? 1 (1) 12 (3) 1 16 Use this space for computations. 1 (4) 4 16 (2) 0 2 2 7 What is the domain of the function f(x) = 2 x ? x 9 (1) all real numbers except 0 (2) all real numbers except 3 (3) all real numbers except 3 and 3 (4) all real numbers Stream Velocity Stream Velocity 8 Which graph represents an inverse variation between stream velocity and the distance from the center of the stream? (1) (3) Stream Velocity Distance Stream Velocity Distance Distance Distance (2) (4) 9 If log b x = y, then x equals (3) yb (1) y b y (2) (4) by b 10 The expression i0 i1 i2 i3 i4 is equal to (1) 1 (3) i (2) 1 (4) i Math. B June 04 [4] 11 Which equation models the data in the accompanying table? Time in hours, x 0 1 2 3 4 5 6 Population, y 5 10 20 40 80 160 Use this space for computations. 320 (1) y = 2x + 5 (2) y = 2 x (3) y = 2x (4) y = 5(2x) 12 The amount of juice dispensed from a machine is normally distributed with a mean of 10.50 ounces and a standard deviation of 0.75 ounce. Which interval represents the amount of juice dispensed about 68.2% of the time? (1) 9.00 12.00 (3) 9.75 11.25 (2) 9.75 10.50 (4) 10.50 11.25 13 If is an acute angle such that sin = (1) (2) 12 13 10 26 (3) (4) 5 13 , what is the value of sin 2 ? 60 169 120 169 14 Which function is symmetrical with respect to the origin? (1) y = x+ 5 (2) y = 5 x 15 The expression xy (1) y x xy (2) x y Math. B June 04 (3) y = 5 x x (4) y = 5 1+1 x y is equivalent to 1_1 x2 y2 (3) y x xy (4) y x [5] [OVER] 16 Sam is designing a triangular piece for a metal sculpture. He tells Martha that two of the sides of the piece are 40 inches and 15 inches, and the angle opposite the 40-inch side measures 120 . Martha decides to sketch the piece that Sam described. How many different triangles can she sketch that match Sam s description? (1) 1 (3) 3 (2) 2 (4) 0 17 If f(x) = x + 1 and g(x) = x2 1, the expression (g f)(x) equals 0 when x is equal to (1) 1 and 1 (3) 2, only (2) 0, only (4) 0 and 2 18 If is a positive acute angle and sin = a, which expression represents cos in terms of a? 1 (1) a (3) a (2) 1 1 a2 (4) 1 a2 19 The expression (1) 2a2b 4 16 a 6 b4 is equivalent to (3) 4a2b 3 2 3 (2) 2a b (4) 4a 2 b 20 In the accompanying diagram, HK bisects IL and H K. K I J H L What is the most direct method of proof that could be used to prove HIJ KLJ? (1) HL HL (3) AAS AAS (2) SAS SAS (4) ASA ASA Math. B June 04 [6] Use this space for computations. 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 projected total annual profits, in dollars, for the Nutyme Clothing Company from 2002 to 2004 can be approximated by the model 2 (13,567n + 294), where n is the year and n = 0 represents 2002. Use n=0 this model to find the company s projected total annual profits, in dollars, for the period 2002 to 2004. Math. B June 04 [7] [OVER] 22 Solve algebraically for x: 272 x+1 = 94 x 23 Find all values of k such that the equation 3x2 2x + k = 0 has imaginary roots. Math. B June 04 [8] 24 In the accompanying diagram of square ABCD, F is the midpoint of AB, G is the midpoint of BC, H is the midpoint of CD, and E is the midpoint of DA . D H C O E A G B F Find the image of EOA after it is reflected in line . Is this isometry direct or opposite? Explain your answer. Math. B June 04 [9] [OVER] 25 Given: ABT, CBTD, and AB CD A C B T D Write an indirect proof to show that AT is not perpendicular to CD. Math. B June 04 [10] 26 The equation V = 20 C + 273 relates speed of sound, V, in meters per second, to air temperature, C, in degrees Celsius. What is the temperature, in degrees Celsius, when the speed of sound is 320 meters per second? [The use of the accompanying grid is optional.] Math. B June 04 [11] [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 Navigators aboard ships and airplanes use nautical miles to measure distance. The length of a nautical mile varies with latitude. The length of a nautical mile, L, in feet, on the latitude line is given by the formula L = 6,077 31 cos 2 . Find, to the nearest degree, the angle , 0 90 , at which the length of a nautical mile is approximately 6,076 feet. Math. B June 04 [12] 28 Two equal forces act on a body at an angle of 80 . If the resultant force is 100 newtons, find the value of one of the two equal forces, to the nearest hundredth of a newton. 29 Solve for x and express your answer in simplest radical form: 3 4 =7 x x+1 Math. B June 04 [13] [OVER] 30 A baseball player throws a ball from the outfield toward home plate. The ball s height above the ground is modeled by the equation y = 16 x2 + 48x + 6, where y represents height, in feet, and x represents time, in seconds. The ball is initially thrown from a height of 6 feet. How many seconds after the ball is thrown will it again be 6 feet above the ground? What is the maximum height, in feet, that the ball reaches? [The use of the accompanying grid is optional.] Math. B June 04 [14] 31 An archaeologist can determine the approximate age of certain ancient specimens by measuring the amount of carbon-14, a radioactive substance, contained in the specimen. The formula used to determine the t age of a specimen is A = A0 2 5760 , where A is the amount of carbon-14 that a specimen contains, A0 is the original amount of carbon-14, t is time, in years, and 5760 is the half-life of carbon-14. A specimen that originally contained 120 milligrams of carbon-14 now contains 100 milligrams of this substance. What is the age of the specimen, to the nearest hundred years? Math. B June 04 [15] [OVER] 32 Mrs. Ram rez is a real estate broker. Last month, the sale prices of homes in her area approximated a normal distribution with a mean of $150,000 and a standard deviation of $25,000. A house had a sale price of $175,000. What is the percentile rank of its sale price, to the nearest whole number? Explain what that percentile means. Mrs. Ram rez told a customer that most of the houses sold last month had selling prices between $125,000 and $175,000. Explain why she is correct. Math. B June 04 [16] 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 circular machine part that has rods PT and PAR attached at points T, A, and R, which are located on the circle; mTA:m AR:m RT = 1:3:5; RA = 12 centimeters; and PA = 5 centimeters. T P A O R Find the measure of P, in degrees, and find the length of rod PT, to the nearest tenth of a centimeter. Math. B June 04 [17] [OVER] 34 A surveyor is mapping a triangular plot of land. He measures two of the sides and the angle formed by these two sides and finds that the lengths are 400 yards and 200 yards and the included angle is 50 . What is the measure of the third side of the plot of land, to the nearest yard? What is the area of this plot of land, to the nearest square yard? Math. B June 04 [18] 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% 9.2% 0.1% 0.5% 3 Math. B June 04 9.2% 4.4% 1.7% 2.5 2 1.5 4.4% 1 0.5 0 [19] 0.5 1 1.5 0.5% 1.7% 2 2.5 3 0.1% 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 22, 2004 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 04 [23] MATHEMATICS B MATHEMATICS B Maximum Credit 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 88 Total Raw Score Checked by Scaled Score Notes to raters. . . Each paper should be scored by a minimum of three raters. The table for converting the total raw score to the scaled score is provided in the scoring key for this examination. The scaled score is the student s final examination score. Tear Here [24] MATHEMATICS B Math. B June 04 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Tuesday, June 22, 2004 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 Administering and 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 checkmarks 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 22, 2004. 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) 1 (6) 4 (11) 4 (16) 1 (2) 1 (7) 3 (12) 3 (17) 4 (3) 2 (8) 1 (13) 4 (18) 2 (4) 2 (9) 4 (14) 3 (19) 2 (5) 3 (10) 2 (15) 1 (20) 3 [1] 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. Visit the site http://www.emsc.nysed.gov/osa/ and select the link Latest Information for any recently posted information regarding this examination. This site should be checked before the rating process for this examination begins and at least one more time before the final scores for the examination are recorded. I. General Rules for Applying Mathematics Rubrics 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 Administering and Scoring 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] 41,583, and appropriate work is shown. [1] Appropriate work is shown, but one conceptual error or one computational error is made. or [1] 41,583, 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] 3, 2 and appropriate work is shown. [1] Appropriate work is shown, but one conceptual error or one computational error is made. or [1] 3, 2 but a graphic solution is provided. 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. (23) 1 [2] k > 3 , and appropriate work is shown, such as the solution of 4 4(3)(k) < 0. [1] Appropriate work is shown, but one conceptual error or one computational error is made. or 1 [1] Appropriate work is shown, but the answer is written as k < 3 . or [1] k > 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. [3] [OVER] MATHEMATICS B continued (24) [2] HOC and opposite, and an appropriate explanation is written. [1] The image of EOA is identified incorrectly, but the type of isometry is appropriate, and an appropriate explanation is written. or [1] The difference between a direct and opposite isometry is explained correctly, but no further correct work is shown. or [1] HOC, but no explanation or an incorrect explanation is written. [0] Opposite, but no further correct 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. (25) [2] A correct indirect proof is written with appropriate statements and reasons. [1] The assumption that AT is perpendicular to CD is written, but no further correct work is shown. or [1] A method other than an indirect proof is used to show that AT is not perpendicular to CD. [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] 17, and appropriate work is shown. [1] Appropriate work is shown, but one conceptual error or one computational or graphing error is made. or [1] 17, 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 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] 44, and appropriate work is shown, such as solving the equation 6,076 = 6,077 31 cos 2 . [3] Appropriate work is shown, but one computational or rounding error is made. [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] An incorrect equation of equal difficulty is solved appropriately. [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] 44, 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 (28) x 100 [4] 65.27, and appropriate work is shown, such as sin 100 = sin 40 . [3] Appropriate work is shown, but one computational or rounding error is made. or [3] Appropriate work is shown, but calculations are performed in radians, resulting in an answer of 147.15. [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 the use of an incorrect trigonometric function. or [2] An incorrect diagram is drawn, but appropriate work is shown, and an appropriate answer is found. [1] A correctly labeled diagram is drawn, but no further correct work is shown. or [1] 65.27, 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 (29) [4] 3 37 7 or an equivalent answer, and appropriate work is shown. [3] A correct quadratic equation is written and appropriate work is shown, but one computational or simplification error is made. or [3] An incorrect quadratic equation of equal difficulty is solved appropriately. [2] A correct quadratic equation is written and appropriate work is shown, but two or more computational or simplification errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] A correct quadratic equation is written in standard form, but no further correct work is shown. [1] An incorrect equation of a lesser degree of difficulty is solved appropriately. or [1] 3 37 7 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. [7] [OVER] MATHEMATICS B continued (30) [4] 3 and 42, and appropriate work is shown, such as a graph, substitution, or a table of values. [3] Appropriate work is shown, but one computational or graphing error is made. [2] Appropriate work is shown, but two or more computational or graphing errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] The number of seconds is found correctly, and appropriate work is shown, but the height is not found or is found incorrectly. or [2] The height is found correctly, and appropriate work is shown, but the number of seconds is not found or is found incorrectly. [1] 3 and 42, but no work is shown. [0] 3 or 42, 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. [8] MATHEMATICS B continued (31) [4] 1,500, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. [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. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] A correct equation is written, but no further correct work is shown. or [1] 1,500, 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) [4] 84, and appropriate work is shown, and correct explanations are written. [3] Appropriate work is shown, but one computational or rounding error is made, but both explanations are correct. or [3] 84, but only one of the explanations is correct. [2] 84, but both explanations are only partially correct. [1] 84, but both explanations are missing or are incorrect. or [1] One correct explanation is written, 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. [9] [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] 80 and 9.2, and appropriate work is shown. [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. or [4] Appropriate work is shown, but one conceptual error is made in solving for one of the values. or [4] 80, and appropriate work is shown, but the length of PT is not found or is found incorrectly. or [4] The measure of all three arcs and the length of PT are found correctly, but the measure of P is not found or is found incorrectly. [3] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. [2] Appropriate work is shown, but one conceptual error is made in solving for each value. or [2] 80 and 9.2, but no work is shown. or [2] 9.2, and appropriate work is shown, but no further correct work is shown. or [2] The measures of all three arcs are found correctly, but no further correct work is shown. [1] 80 or 9.2, 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. [10] The University of the State of New York THE STATE EDUCATION DEPARTMENT Office of State Assessment Albany, New York 12234 IMPORTANT NOTICE Notice to Teachers Mathematics B Scoring Key Tuesday, June 22, 2004 1:15 p.m. ___________________________ Please refer to the following additional guidance when rating Question 33: 1. Students who assumed that m RT referred to the minor arc should be awarded 2 credits for writing the equation x + 3x = 5x. 2. You may accept multiple solutions when students solve for PT. Students who use a mean proportion to solve for PT will find the answer 9.2, as specified in the rubric. Example of response using a mean proportion: 17 x = x 5 x 2 = 85 x = 9.2 Students who use the Law of Sines or the Law of Cosines will find different measures for PT , based on whether TRP or TAP is constructed. Example of response using Law of Cosines and TRP : x2 = 172 + 172 2(17)(17) cos 20 x2 = 289 + 289 543.1423348 x2 = 34.85766519 x = 5.9 Example of response using Law of Sines and TAP : sin 20 sin 80 = x 5 x = 14.4 Apply the rubric as written to the student s method of response, whether it is a method described here or another mathematically appropriate method. MATHEMATICS B continued (34) [6] 312 and 30,642, and appropriate work is shown, such as using the Law of Cosines and the area 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. or [4] Appropriate work is shown, but one conceptual error is made. or [4] Appropriate work is shown, but the square root is not computed to find the length of the third side, but an appropriate area is found. or [4] The length of the third side is found correctly, but no further correct work is shown. [3] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. [2] The area of the triangle is found correctly, but no further correct work is shown. or [2] 312 and 30,642, but no work is shown. [1] Appropriate work is shown to find the area of the triangle, but one computational or rounding error is made, and no further correct work is shown. or [1] 312 or 30,642, 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. [11] [OVER] MATHEMATICS B concluded Map to Learning Standards Key Ideas Item Numbers Mathematical Reasoning 20, 25 Number and Numeration 1, 15, 23 Operations 4, 10, 14, 19 Modeling/Multiple Representation 6, 8, 9, 11, 28, 30, 31 Measurement 3, 12, 16, 33, 34 Uncertainty 2, 7, 21, 32 Patterns/Functions 5, 13, 17, 18, 22, 24, 26, 27, 29 Regents Examination in Mathematics B June 2004 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the June 2004 Regents Examination in Mathematics B, normally located on this page, will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Tuesday, June 22, 2004. Conversion charts provided for previous administrations of the Mathematics B examination must NOT be used to determine students final scores for this administration. [12]

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Additional Info : Refer : Formulas (page 23) and Scoring Key (page 25)
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