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New York Regents Mathematics B June 2006

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MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, June 15, 2006 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 19. 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] Pressure Pressure 1 Each graph below represents a possible relationship between temperature and pressure. Which graph does not represent a function? Pressure Temperature (3) Pressure Temperature (1) Temperature (2) 3 Temperature (4) 1 2 If f(x) = x 2 , then f ( 4 ) is equal to 1 8 (1) 8 (3) (2) 2 (4) 4 Math. B June 06 [2] Use this space for computations. 3 In the accompanying diagram of circle O, chord AY is parallel to diameter DOE, AD is drawn, and m AD = 40. A Y D What is m DAY? (1) 90 (2) 110 Use this space for computations. E O (3) 130 (4) 150 4 If x is a positive acute angle and sin x = (1) 1 2 (3) (2) 1 2 (4) 1 2, what is sin 2 x? 3 2 3 2 5 The temperature generated by an electrical circuit is represented by t = f(m) = 0.3m2, where m is the number of moving parts. The resistance of the same circuit is represented by r = g(t) = 150 + 5t, where t is the temperature. What is the resistance in a circuit that has four moving parts? (1) 51 (3) 174 (2) 156 (4) 8,670 6 If the equation x2 kx 36 = 0 has x = 12 as one root, what is the value of k? (1) 9 (3) 3 (2) 9 (4) 3 Math. B June 06 [3] [OVER] 7 The height, f(x), of a bouncing ball after x bounces is represented by f(x) = 80(0.5)x. How many times higher is the first bounce than the fourth bounce? (1) 8 (3) 16 (2) 2 (4) 4 8 A radio transmitter sends a radio wave from the top of a 50-foot tower. The wave is represented by the accompanying graph. y 1.5 2 2 x What is the equation of this radio wave? (1) y = sin x (3) y = sin 1.5x (2) y = 1.5 sin x (4) y = 2 sin x 9 If tan = 2.7 and csc < 0, in which quadrant does lie? (1) I (3) III (2) II (4) IV 2 10 The expression 1 cos x is equivalent to sin2 x (1) 1 (3) sin x (2) 1 (4) cos x 11 The graph of y = (x 3)2 is shifted left 4 units and down 2 units. What is the axis of symmetry of the transformed graph? (1) x = 2 (3) x = 1 (2) x = 1 (4) x = 7 Math. B June 06 [4] Use this space for computations. 2 Use this space for computations. 12 The solution set of 2x +2 x = 2 1 is (1) {1} (3) { 1,1} (2) { 1} (4) { } 13 Which transformation best describes the relationship between the functions f(x) = 2x and g(x) =(1 )x? 2 (1) (2) (3) (4) reflection in the line y = x reflection in the origin reflection in the x-axis reflection in the y-axis 14 What is the multiplicative inverse of 3i? (1) 3i (3) 1 3 i (2) 3 (4) 3 15 Mrs. Donahue made up a game to help her class learn about imaginary numbers. The winner will be the student whose expression is equivalent to i. Which expression will win the game? (1) i46 (3) i48 (2) i47 (4) i49 16 Which equation represents a hyperbola? (1) y2 = 16 x2 (3) y = 16x2 (2) y = 16 x2 6 (4) y = 1x Math. B June 06 [5] [OVER] 17 The solution set of which inequality is represented by the accompanying graph? 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 (1) x 2 > 7 (2) x 2 < 7 (3) 2 x > 7 (4) 2 x < 7 18 According to Boyle s Law, the pressure, p, of a compressed gas is inversely proportional to the volume, v. If a pressure of 20 pounds per square inch exists when the volume of the gas is 500 cubic inches, what is the pressure when the gas is compressed to 400 cubic inches? (1) 16 lb/in2 (2) 25 lb/in2 (3) 40 lb/in2 (4) 50 lb/in2 19 What is the fourth term in the expansion of (y 1)7? (1) 35y4 (2) 35y3 (3) 35y4 (4) 35y3 20 Sam needs to cut a triangle out of a sheet of paper. The only requirements that Sam must follow are that one of the angles must be 60 , the side opposite the 60 angle must be 40 centimeters, and one of the other sides must be 15 centimeters. How many different triangles can Sam make? (1) 1 (3) 3 (2) 2 (4) 0 Math. B June 06 [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 Find the sum of 2 + 3i and 1 2i. Graph the resultant on the accompanying set of axes. Imaginary Real Math. B June 06 [7] [OVER] 22 In L ABC, m A = 53, m B = 14, and a = 10. Find b to the nearest integer. 23 Solve for x: log 2 (x + 1) = 3 Math. B June 06 [8] 2 24 Evaluate: ( 1)k 1 (2 k 1)! k =1 25 Ginger and Mary Anne are planning a vacation trip to the island of Capri, where the probability of rain on any day is 0.3. What is the probability that during their five days on the island, they have no rain on exactly three of the five days? Math. B June 06 [9] [OVER] 26 The pendulum of a clock swings through an angle of 2.5 radians as its tip travels through an arc of 50 centimeters. Find the length of the pendulum, in centimeters. Math. B June 06 [10] 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 Solve the following system of equations algebraically: 9x2 + y2 = 9 3x y = 3 Math. B June 06 [11] [OVER] 28 Simplify for all values of a for which the expression is defined: 29 Solve algebraically for x: Math. B June 06 3x + 1 + 1 = x [12] 1 2 a 4 1 a2 30 The number of children of each of the first 41 United States presidents is given in the accompanying table. For this population, determine the mean and the standard deviation to the nearest tenth. How many of these presidents fall within one standard deviation of the mean? Number of Children (xi ) 0 1 2 3 4 5 6 7 8 10 15 Math. B June 06 Number of Presidents (fi ) 6 2 8 6 7 3 5 1 1 1 1 [13] [OVER] 31 A factory is producing and stockpiling metal sheets to be shipped to an automobile manufacturing plant. The factory ships only when there is a minimum of 2,050 sheets in stock. The accompanying table shows the day, x, and the number of sheets in stock, f(x). Day (x ) Sheets in Stock (f(x )) 1 860 2 930 3 1000 4 1150 5 1200 6 1360 Write the linear regression equation for this set of data, rounding the coefficients to four decimal places. Use this equation to determine the day the sheets will be shipped. Math. B June 06 [14] 32 A small rocket is launched from a height of 72 feet. The height of the rocket in feet, h, is represented by the equation h(t) = 16 t2 + 64 t + 72, where t = time, in seconds. Graph this equation on the accompanying grid. Use your graph to determine the number of seconds that the rocket will remain at or above 100 feet from the ground. [Only a graphic solution can receive full credit.] Math. B June 06 [15] [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 Given: A( 2,2), B(6,5), C(4,0), D( 4, 3) Prove: ABCD is a parallelogram but not a rectangle. [The use of the grid on the next page is optional.] Math. B June 06 [16] Question 33 continued Math. B June 06 [17] [OVER] 34 A triangular plot of land has sides that measure 5 meters, 7 meters, and 10 meters. What is the area of this plot of land, to the nearest tenth of a square meter? Math. B June 06 [18] 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 06 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 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 15, 2006 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 06 [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 (from conversion chart) Tear Here [24] MATHEMATICS B Math. B June 06 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, June 15, 2006 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 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 Thursday, June 15, 2006. 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) 1 (11) 2 (16) 4 (2) 1 (7) 1 (12) 2 (17) 1 (3) 2 (8) 2 (13) 4 (18) 2 (4) 4 (9) 3 (14) 4 (19) 3 (5) 3 (10) 1 (15) 2 (20) 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. 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] 3 + i, and an appropriate graph is drawn. [1] The sum is found incorrectly, but an appropriate graph is drawn. or [1] 3 + i, but no graph or an incorrect 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. (22) 10 b [2] 3, and appropriate work is shown, such as sin 53 = sin 14 . [1] Appropriate work is shown, but one computational or rounding error is made. or [1] The proportion 10 = b is written, but no further correct work is shown. sin 53 sin 14 or [1] An incorrect proportion of equal difficulty is solved appropriately. 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. [3] [OVER] MATHEMATICS B continued (23) [2] 7, and appropriate work is shown, such as 23 = x + 1. [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] 23 = x + 1 is written, but no further correct work is shown. or [1] 7, 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] 5 6 or 0.83, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made, 5 such as representing 6 as a terminating decimal. or [1] Appropriate work is shown, but one conceptual error is made. or [1] 5 6 or 0.83, 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. (25) [2] .3087 or an equivalent answer, 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 evaluating 5C3(0.3)3(0.7)2. or [1] .3087 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. [4] MATHEMATICS B continued (26) [2] 20, and appropriate work is shown, such as using the formula S = r . [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] 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. [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] (0, 3) and (1,0) or an equivalent answer, and appropriate algebraic work is shown. [3] Appropriate work is shown, but one computational error is made. or [3] Appropriate work is shown, but only one correct solution is found or only the x- or the y-values are found correctly. [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] (0, 3) and (1,0), but a method other than an algebraic solution is used. or [2] A correct quadratic equation is written in standard form, such as 18x2 18x = 0, but no further correct work is shown. or [2] An incorrect quadratic equation of equal difficulty is solved appropriately. [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] An incorrect equation of a lesser degree of difficulty is solved appropriately. or [1] y = 3x 3 is found and substituted into the second equation, but no further correct work is shown. or [1] (0, 3) and (1,0), but no work is shown. [0] Only one correct solution is found or only the x- or the y-values are found correctly, and 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. [6] MATHEMATICS B continued (28) a a [4] 2 + a or 2 a , and appropriate work is shown. [3] Appropriate work is shown, but one computational or simplification error is made. [2] 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, such as not recognizing that 1 is a factor. [1] Appropriate work is shown, but one conceptual error and one computational or simplification error are made. or a a [1] 2 + a or 2 a , 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] 5, and appropriate algebraic work is shown. [3] Appropriate work is shown, but one computational error is made. or [3] 5 and 0, and appropriate work is shown, but the zero is not rejected. [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 squaring x 1 incorrectly. or [2] 5, but a method other than an algebraic solution is used, such as graphing or trial and error with at least three trials and appropriate checks. or [2] A correct quadratic equation is written in standard form, such as 0 = x2 5x, but no further correct work is shown. or [2] An incorrect quadratic equation of equal difficulty is solved appropriately. [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] An incorrect equation of a lesser degree of difficulty is solved appropriately. or [1] 5, but no work is shown. [0] 5 and 0, and 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 (30) [4] Mean = 3.6, standard deviation = 2.9, and 31, and appropriate work is shown, such as an explanation of how the solutions were found. [3] Appropriate work is shown, but one computational or rounding error is made. or [3] The mean and standard deviation are calculated correctly and appropriate work is shown, but the number of presidents in the specified interval is found incorrectly. [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 using the sample standard deviation. or [2] The mean and standard deviation are calculated correctly, but the number of presidents is not found. or [2] The mean and standard deviation are calculated incorrectly, but an appropriate number of presidents is found. [1] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [1] Mean = 3.6, standard deviation = 2.9, and 31, but no work is shown. [0] Mean = 3.6 or standard deviation = 2.9 or 31, 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. [9] [OVER] MATHEMATICS B continued (31) [4] f(x) = 98.8571x + 737.3333 or y = 98.8571x + 737.3333 and day 14, and appropriate substitution is made, such as 2050 = 98.8571x + 737.3333. [3] Appropriate work is shown, but one computational or rounding error is made. or [3] A correct linear regression equation is written and day 14, but no substitution is made. or [3] The expression 98.8571x + 737.3333 is written and day 14, and appropriate substitution is made, but no equation is written. [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] A correct linear regression equation is written, but no further correct work is shown. or [2] An incorrect 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] The expression 98.8571x + 737.3333 is written, but no further correct work is shown. or [1] Day 14, 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] A correct graph is drawn, and 3. [3] 3, and appropriate work is shown, but one graphing error is made. or [3] A correct graph is drawn and the points 0.5 and 3.5 are identified, but the difference is not calculated. [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. or [2] 3, but a method other than a graphic solution is used. [1] Appropriate work is shown, but one conceptual error and one graphing error are made. or [1] A correct graph is sketched with t = 0 to t = 4, but no further correct work is shown. or [1] 3, but no work is shown and no graph is drawn. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [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] Appropriate work is shown, such as using slopes to prove ABCD is a parallelogram but not a rectangle, and an appropriate concluding statement is made. [5] Appropriate work is shown, but one computational or graphing error is made. [4] Appropriate work is shown, but two or more computational or graphing errors are made. or [4] Appropriate work is shown, but one conceptual error is made, such as using an incorrect formula. or [4] A proof is written that correctly shows either ABCD is a parallelogram or it is not a rectangle, but not both. [3] Appropriate work is shown, but two or more computational or graphing errors are made, and the concluding statement is incomplete. [2] Appropriate work is shown, but one conceptual error and one computational or graphing error are made. or [2] All four slopes are found correctly or the lengths of all four sides are found correctly, and appropriate work is shown, but no further correct work is shown. [1] The slopes of all four sides are identified or the lengths of all four lines are identified, but no work is shown and no proof is written. [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] 16.2, and appropriate work is shown, such as using the Law of Cosines to find one angle, and then using K = A= 1 2 ab sin C or Hero(n) s formula, s( s a)( s b)( s c) , to find the area. [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, but an appropriate area is found. or [3] The Law of Cosines is used to find a correct measure for one of the angles of the triangle, 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] Correct substitution is made into the Law of Cosines, but no further correct work is shown. or [1] 16.2, but no work is shown. [0] Right triangle trigonometry is used inappropriately. 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 33 Number and Numeration 6, 14, 28 Operations 2, 5, 11, 15 Modeling/Multiple Representation 13, 16, 18, 21, 23, 27, 32 Measurement 3, 8, 9, 20, 22, 26, 34 Uncertainty 19, 24, 25, 31 Patterns/Functions 1, 4, 7, 10, 12, 17, 29, 30 Regents Examination in Mathematics B June 2006 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the June 2006 Regents Examination in Mathematics B will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Thursday, June 15, 2006. Conversion charts provided for previous administrations of the Mathematics B examination must NOT be used to determine students final scores for this administration. The Teacher Evaluation of State Examinations forms will also be posted on the same web site. Please select the link Teacher Evaluation Forms and then the examination title to complete the evaluation form for the June 2006 Regents Examination in Mathematics B. [14]

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Additional Info : Refer : Formulas (page 19) and Scoring Key (page 25)
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