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New York Regents Mathematics B January 2006

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MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Friday, January 27, 2006 9:15 a.m. to 12:15 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] Use this space for computations. 5 1 What is the value of ( 2n + 100) ? n=1 (1) 70 (2) 130 (3) 470 (4) 530 2 The effect of pH on the action of a certain enzyme is shown on the accompanying graph. Rate of Enzyme Action y x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 pH What is the domain of this function? (1) 4 x 13 (3) x 0 (2) 4 y 13 (4) y 0 Math. B Jan. 06 [2] Use this space for computations. Runoff Runoff 3 Which graph shows that soil permeability varies inversely to runoff? Soil Permeability (3) Runoff Runoff Soil Permeability (1) Soil Permeability (2) Soil Permeability (4) 4 On a standardized test, a score of 86 falls exactly 1.5 standard deviations below the mean. If the standard deviation for the test is 2, what is the mean score for this test? (1) 84 (2) 84.5 (3) 87.5 (4) 89 5 Which transformation of the graph of y = x2 would result in the graph of y = x2 + 2? (1) D2 (3) ry =2 (2) T0,2 (4) R0,90 6 A sound wave is modeled by the curve y = 3 sin 4x. What is the period of this curve? (1) (2) 2 Math. B Jan. 06 (3) 3 (4) 4 [3] [OVER] 7 If Use this space for computations. 2 x 1 + 2 = 5 , then x is equal to (1) 1 (2) 2 (3) 5 (4) 4 8 The expression (1 + cos x)(1 cos x) is equivalent to (3) sin2 x (4) csc2 x (1) 1 (2) sec2 x 9 If is a positive acute angle and sin 2 = (cos + sin )2 equals , then (3) 30 (1) 1 (2) 1 + 3 2 3 2 (4) 60 10 What is the solution of the inequality y + 8 > 3? (1) y > 5 or y < 11 (2) y > 5 (3) 11 < y < 5 (4) 5 < y < 11 11 The speed of sound, v, at temperature T, in degrees Kelvin, is represented by the equation v = 1087 T . Which expression is equiva273 lent to log v? (1) 1087 + (2) 1087 ( 1 2 1 2 log T log 273 log T (3) log 1087 + 1 2 1 2 ) log 273 log T 1 2 log 273 (4) log 1087 + 2 log (T + 273) Math. B Jan. 06 [4] 12 In physics class, Eva noticed the pattern shown in the accompanying diagram on an oscilloscope. Use this space for computations. y 3 2 1 0 2 3 4 x Which equation best represents the pattern shown on this oscilloscope? (1) y = sin 1 x + 1 2 (3) y = 2 sin x + 1 (2) y = sin x + 1 (4) y = 2 sin 1 x + 1 2 13 The expression 5 5 1 is equivalent to (1) 5 4 (3) 5 5 5 4 (2) 5 5+5 4 (4) 5 5 5 6 14 The roots of the equation 2 x2 5 = 0 are (1) (2) (3) (4) imaginary real, rational, and equal real, rational, and unequal real and irrational Math. B Jan. 06 [5] [OVER] 15 What is the radian measure of the angle formed by the hands of a clock at 2:00 p.m.? (1) (3) 2 4 (2) 3 (4) 6 16 If is an angle in standard position and P( 3,4) is a point on the terminal side of , what is the value of sin ? (1) 3 5 (2) (3) (4) 3 5 4 5 17 When simplified, the expression (1) (2) 3 4 m m 2 3 (3) (4) 4 5 ( )( m ) is equivalent to 3 m4 5 1 2 m 4 6 m5 18 What are the coordinates of point A , the image of point A( 4,1) after the composite transformation R90 ry=x where the origin is the center of rotation? (1) ( 1, 4) (2) ( 4, 1) Math. B Jan. 06 (3) (1,4) (4) (4,1) [6] Use this space for computations. 19 The accompanying diagram shows a 24-foot ladder leaning against a building. A steel brace extends from the ladder to the point where the building meets the ground. The brace forms a right angle with the ladder. Use this space for computations. 24 ft 10 x ft If the steel brace is connected to the ladder at a point that is 10 feet from the foot of the ladder, which equation can be used to find the length, x, of the steel brace? x 10 = (1) (3) 102 + x2 = 142 x 14 (2) x 10 = x 24 (4) 102 + x2 = 242 20 The center of a circle represented by the equation (x 2)2 + (y + 3)2 = 100 is located in Quadrant (1) I (2) II Math. B Jan. 06 (3) III (4) IV [7] [OVER] Part II Answer all questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. [12] 21 If f(x) = 5x2 1 and g(x) = 3x 1, find g(f(1)). 22 On the accompanying diagram, draw a mapping of a relation from set A to set B that is not a function. Explain why the relationship you drew is not a function. Set A Set B 1 2 b 3 Math. B Jan. 06 a c [8] 23 In the accompanying diagram, PA is tangent to circle O at A, secant PBC is drawn, PB = 4, and BC = 12. Find PA. A P B O C 24 The time it takes to travel to a location varies inversely to the speed traveled. It takes 4 hours driving at an average speed of 55 miles per hour to reach a location. To the nearest tenth of an hour, how long will it take to reach the same location driving at an average speed of 50 miles per hour? Math. B Jan. 06 [9] [OVER] 25 During a recent survey, students at Franconia College were asked if they drink coffee in the morning. The results showed that two-thirds of the students drink coffee in the morning and the remainder do not. What is the probability that of six students selected at random, exactly two of them drink coffee in the morning? Express your answer as a fraction or as a decimal rounded to four decimal places. 26 Solve algebraically for x: 82x = 46 Math. B Jan. 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 In physics class, Taras discovers that the behavior of electrical power, x, in a particular circuit can be represented by the function f(x) = x2 + 2x + 7. If f(x) = 0, solve the equation and express your answer in simplest a + bi form. Math. B Jan. 06 [11] [OVER] 28 On the accompanying grid, sketch the graphs of y = 2x and 3y = 7x + 3 over the interval 3 x 4. Identify and state the coordinates of all points of intersection. Math. B Jan. 06 [12] 29 Simplify completely: Math. B Jan. 06 1 m m 1 m m [13] [OVER] 30 An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 x , where x is expressed in radians. Solve algebraically for all values of x in the interval 0 x , where the height of the opening, f(x), is 6. Express your answer in terms of . If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel? Math. B Jan. 06 [14] 31 The Vietnam Veterans Memorial in Washington, D.C., is made up of two walls, each 246.75 feet long, that meet at an angle of 125.2 . Find, to the nearest foot, the distance between the ends of the walls that do not meet. Math. B Jan. 06 [15] [OVER] 32 The current population of Little Pond, New York, is 20,000. The population is decreasing, as represented by the formula P = A(1.3) 0.234t, where P = final population, t = time, in years, and A = initial population. What will the population be 3 years from now? Round your answer to the nearest hundred people. To the nearest tenth of a year, how many years will it take for the population to reach half the present population? [The use of the grid on the next page is optional.] Math. B Jan. 06 [16] Question 32 continued Math. B Jan. 06 [17] [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 Since 1990, fireworks usage nationwide has grown, as shown in the accompanying table, where t represents the number of years since 1990, and p represents the fireworks usage per year, in millions of pounds. Number of Years Since 1990 (t ) Fireworks Usage per Year, in Millions of Pounds (p) 0 2 4 6 7 8 9 11 67.6 88.8 119.0 120.1 132.5 118.3 159.2 161.6 Find the equation of the linear regression model for this set of data, where t is the independent variable. Round values to four decimal places. Using this equation, determine in what year fireworks usage would have reached 99 million pounds. Based on this linear model, how many millions of pounds of fireworks would be used in the year 2008? Round your answer to the nearest tenth. Math. B Jan. 06 [18] 34 Given: parallelogram FLSH, diagonal FGAS , LG FS , HA FS L S A G F Prove: Math. B Jan. 06 LGS H HAF [19] [OVER] 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% 9.2% Tear Here 0.1% 0.5% 3 Math. B Jan. 06 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 Friday, January 27, 2006 9:15 a.m. to 12:15 p.m., only ANSWER SHEET Student ........................................... Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: School Male Female Grade . . . . . . . . . ................................. 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 Jan. 06 [27] 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 table) Tear Here [28] MATHEMATICS B Math. B Jan. 06 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Friday, January 27, 2006 9:15 a.m. to 12:15 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 Friday, January 27, 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) 2 (11) 3 (16) 3 (2) 1 (7) 3 (12) 1 (17) 4 (3) 1 (8) 3 (13) 2 (18) 4 (4) 4 (9) 2 (14) 4 (19) 1 (5) 2 (10) 1 (15) 2 (20) 4 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 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] 11, and appropriate work is shown, such as f(1) = 4 and g(4) = 11. [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 solving for f(g(1)). 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. (22) [2] A mapping is drawn that maps at least one element of set A to more than one element of set B, and an appropriate explanation of the difference between functions and relations is written. [1] An appropriate mapping is drawn, but no explanation is written. or [1] An incorrect mapping is drawn, but an appropriate explanation 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. (23) [2] 8, and appropriate work is shown, such as (PA)2 = 4 16 = 64. [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 failing to reject the negative root. 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. [3] [OVER] MATHEMATICS B continued (24) [2] 4.4, 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] Only the constant of variation, 220, is found. or [1] 4.4, but no work is shown. [0] Direct variation is used. 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] 60 729 or 20 243 2 4 1 3 . or .0823, and appropriate work is shown, such as 6C2 2 3 [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] A correct expression is written, such as 6C2 work is shown. 2 4 2 1 3 3 , but no further correct or [1] 60 729 or 20 243 or .0823, 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] 2, 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] 2, but a method other than an algebraic solution is used. or [1] 2, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [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] 1 i 6 , and appropriate work is shown, such as appropriately substituting for a, b, and c in the quadratic formula, solving the equation, and simplifying the answer correctly. [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 writing the quadratic formula incorrectly. [1] Appropriate work is shown, but one conceptual error and one computational or simplification error are made. or [1] 1 i 6 , 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] (0,1) and (3,8), and both graphs are sketched correctly. [3] Appropriate work is shown, but one graphing error is made, but all appropriate points of intersection are identified. [2] Appropriate work is shown, but two or more graphing errors are made, but all appropriate points of intersection are identified. or [2] Appropriate work is shown, but one conceptual error is made, such as failing to draw the graph over the specified interval, resulting in only one point of intersection. or [2] Both graphs are sketched correctly, and the two points of intersection are indicated, but the coordinates are not stated or are stated incorrectly. [1] Only the graph of the exponential function is sketched correctly, and no further correct work is shown. or [1] (0,1) and (3,8), but no graph is sketched. [0] (0,1) or (3,8), but no graph is sketched. or [0] Only the line is graphed correctly. or [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] 1 or 1 , and appropriate work is shown. m 1 m +1 [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. [1] Appropriate work is shown, but one conceptual error and one computational or simplification error are made. or [1] 1 or 1 , but no work is shown. m 1 m +1 [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] 6 and 5 and 10, and appropriate work is shown. 6 [3] Appropriate work is shown, but one computational error is made. or [3] x = 0.52 and x = 2.62 or x = 30 and x = 150 and 10, and appropriate work is shown. or [3] 6 and 5 , and appropriate work is shown, but the maximum height is missing. 6 [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] x = 0.52 and x = 2.62 or x = 30 and x = 150 , and appropriate work is shown, but the maximum height is missing. or [2] 6 or 5 and 10, and appropriate work is shown. 6 [1] Appropriate work is shown, but one conceptual error and one computational error are made. or [1] 30 or 150 and 10, and appropriate work is shown. or [1] 6 and 5 and 10, but no work is shown. 6 [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] 438, and appropriate work is shown, such as using the Law of Cosines or the Law of Sines. [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] Correct substitution is made into the Law of Cosines or the Law of Sines, 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] 438, 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. [10] MATHEMATICS B continued (32) [4] 16,600 and 11.3, and appropriate work is shown. [3] Appropriate work is shown, but one computational, rounding, or graphing error is made. [2] Appropriate work is shown, but two or more computational, rounding, or graphing errors are made. or [2] Appropriate work is shown, but one conceptual error is made. or [2] Either 16,600 or 11.3 is found, and appropriate work is shown, but the other answer is not found. [1] Appropriate work is shown, but one conceptual error and one computational, rounding, or graphing error are made. or [1] Correct substitutions are made into both formulas, but no further correct work is shown. or [1] 16,600 and 11.3, but no work is shown. [0] 16,600 or 11.3, but no work is shown. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [11] [OVER] MATHEMATICS B continued Part IV For each question, use the specific criteria to award a maximum of six credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit. (33) [6] p = 8.1875t + 72.7860, 1993, and 220.2, and appropriate work is shown. [5] Appropriate work is shown, but one computational or rounding error is made. or [5] The expression 8.1875t + 72.7860 is written and 1993 and 220.2 are found, and appropriate work is shown. [4] Appropriate work is shown, but two or more computational or rounding errors are made. or [4] A correct equation is written, but either the year or the predicted value for 2008 is not found, but appropriate work is shown. or [4] An incorrect equation is solved appropriately. [3] Appropriate work is shown, but one conceptual error is made. or [3] p = 8.1875t + 72.7860, 1993, and 220.2, but no work is shown. or [3] The expression 8.1875t + 72.7860 is written and either 1993 or 220.2 is found, and appropriate work is shown. [2] Appropriate work is shown, but one conceptual error and one computational or rounding error are made. or [2] A correct equation is written, but no further correct work is shown. or [2] 1993 and 220.2, but no work is shown. [1] The expression 8.1875t + 72.7860 is written, but no further correct work is shown. or [1] 1993 or 220.2, 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. [12] MATHEMATICS B continued (34) [6] A complete and correct proof is written. [5] A proof is written that demonstrates a thorough understanding of the method of proof and contains no conceptual errors, but one statement or reason is missing or is incorrect, or the concluding statement is missing. [4] A proof is written that demonstrates a good understanding of the method of proof and contains no conceptual errors, but two statements or reasons are missing or are incorrect. [3] A proof is written that demonstrates a good understanding of the method of proof, but one conceptual error is made. [2] Some correct relevant statements about the proof are made, but three or four statements or reasons are missing or are incorrect. [1] Only one correct statement and reason are written. [0] The given and/or the prove statements are rewritten in the style of a formal proof, but no further correct relevant statements are written. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [13] [OVER] MATHEMATICS B concluded Map to Learning Standards Key Ideas Item Numbers Mathematical Reasoning 34 Number and Numeration 13, 14, 29 Operations 17, 21, 27 Modeling/Multiple Representation 3, 11, 16, 18, 20, 24, 28, 32 Measurement 4, 6, 9, 15, 19, 23, 31 Uncertainty 1, 2, 25, 33 Patterns/Functions 5, 7, 8, 10, 12, 22, 26, 30 Regents Examination in Mathematics B January 2006 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) The Chart for Determining the Final Examination Score for the January 2006 Regents Examination in Mathematics B will be posted on the Department s web site http://www.emsc.nysed.gov/osa/ on Friday, January 27, 2006. Conversion charts provided for previous administrations of the Mathematics B examination must NOT be used to determine students final scores for this administration. [14]

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