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New York Regents Mathematics B August 2003

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The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Wednesday, August 13, 2003 8:30 to 11:30 a.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. 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 Which graph does not represent a function of x? x Chance of Human Survival y Chance of Human Survival y Use this space for computations. x Pollution Pollution (1) (3) x Chance of Human Survival y Chance of Human Survival y x Pollution Pollution (2) (4) 2 What is the value of x in the equation 5 2 x = 3 i ? (1) 1 (3) 2 (2) 7 (4) 4 3 Which graph represents the solution set of 2 x 1 < 7? (1) (2) (3) (4) Math. B Aug. 03 5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5 [2] 4 The strength of a medication over time is represented by the equation y = 200(1.5) x, where x represents the number of hours since the medication was taken and y represents the number of micrograms per millimeter left in the blood. Which graph best represents this relationship? y Use this space for computations. y x x (1) (3) y y x x (2) (4) 5 Written in simplest form, the expression x2 y2 9 is equivalent to 3 xy (1) 1 (3) (3 + x y) 1 (2) 3 + xy (4) 3 + x y 6 Which graph represents data used in a linear regression that produces a correlation coefficient closest to 1? y y x x (1) (3) y y x (2) Math. B Aug. 03 x (4) [3] [OVER] 7 Which expression is equal to 2+ 3 2 3 Use this space for computations. ? (1) 1 4 3 7 (3) 1 4 3 (2) 7+4 3 7 (4) 7 + 4 3 8 Which transformation is not an isometry? (1) rotation (3) dilation (2) line reflection (4) translation 9 A dog has a 20-foot leash attached to the corner where a garage and a fence meet, as shown in the accompanying diagram. When the dog pulls the leash tight and walks from the fence to the garage, the arc the leash makes is 55.8 feet. ge ra Ga Fence (Not drawn to scale) What is the measure of angle between the garage and the fence, in radians? (1) 0.36 (3) 3.14 (2) 2.79 (4) 160 Math. B Aug. 03 [4] 10 In the accompanying diagram of parallelogram ABCD, DE BF. D E Use this space for computations. C G A F B Triangle EGC can be proved congruent to triangle FGA by (1) HL HL (3) AAS AAS (2) AAA AAA (4) SSA SSA 11 An architect commissions a contractor to produce a triangular window. The architect describes the window as ABC, where m A = 50, BC = 10 inches, and AB = 12 inches. How many distinct triangles can the contractor construct using these dimensions? (1) 1 (3) more than 2 (2) 2 (4) 0 12 The accompanying graph shows the relationship between a person s weight and the distance that the person must sit from the center of a seesaw to make it balanced. y Distance (feet) 12 10 8 6 4 2 0 20 40 60 80 100 120 140 160 x Weight (pounds) Which equation best represents this graph? (3) y = 2 log x (1) y = 12x2 (2) y = 120x (4) y = 120 x Math. B Aug. 03 [5] [OVER] 13 If f and g are two functions defined by f(x) = 3x + 5 and g(x) = x2 + 1, then g(f(x)) is (3) 3x2 + 8 (1) x2 + 3 x + 6 (2) 9x2 + 30 x + 26 (4) 9x2 + 26 14 What is the product of 5 + a + bi form? (1) 37 + 41i (2) 5 71i 36 and 1 49 , expressed in simplest (3) 47 + 41i (4) 47 29i 15 The expression 2 cos is equivalent to sin 2 (3) cot (1) csc (2) sec (4) sin 16 If sin x = 12 , cos y = 13 cos (x y) is (1) (2) 21 65 63 65 3 , 5 and x and y are acute angles, the value of (3) 14 65 (4) 33 65 17 The amount of ketchup dispensed from a machine at Hamburger Palace is normally distributed with a mean of 0.9 ounce and a standard deviation of 0.1 ounce. If the machine is used 500 times, approximately how many times will it be expected to dispense 1 or more ounces of ketchup? (1) 5 (3) 80 (2) 16 (4) 100 Math. B Aug. 03 [6] Use this space for computations. 18 A commercial artist plans to include an ellipse in a design and wants the length of the horizontal axis to equal 10 and the length of the vertical axis to equal 6. Which equation could represent this ellipse? (1) 9x2 + 25y2 = 225 (3) x2 + y2 = 100 2 25y2 = 225 (2) 9x (4) 3y = 20x2 19 A function is defined by the equation y = defines the inverse of this function? (1) y = 2x + 3 (3) y = 2x + 3 (2) y = 2x 3 (4) y = 2x 1 x 2 3. 2 Use this space for computations. Which equation 2 3 2 20 In the equation a x2 + 6 x 9 = 0, imaginary roots will be generated if (1) 1 < a < 1 (3) a > 1, only (2) a < 1, only (4) a < 1 Math. B Aug. 03 [7] [OVER] Part II Answer all questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. [12] 21 The height, h, in feet, a ball will reach when thrown in the air is a function of time, t, in seconds, given by the equation h(t) = 16t2 + 30t + 6. Find, to the nearest tenth, the maximum height, in feet, the ball will reach. 22 Find the value of (x + 2)0 + (x + 1) Math. B Aug. 03 2 3 when x = 7. [8] x 4 23 Express in simplest form: 4 x 1 4 x 24 The triangular top of a table has two sides of 14 inches and 16 inches, and the angle between the sides is 30 . Find the area of the tabletop, in square inches. Math. B Aug. 03 [9] [OVER] 25 Meteorologists can determine how long a storm lasts by using the 3 function t(d) = 0.07d 2 , where d is the diameter of the storm, in miles, and t is the time, in hours. If the storm lasts 4.75 hours, find its diameter, to the nearest tenth of a mile. 26 Tom scored 23 points in a basketball game. He attempted 15 field goals and 6 free throws. If each successful field goal is 2 points and each successful free throw is 1 point, is it possible he successfully made all 6 of his free throws? Justify your answer. Math. B Aug. 03 [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 On the accompanying grid, graph and label AB , where A is (0,5) and B is (2,0). Under the transformation rx-axis ry-axis( AB), A maps to A , and B maps to B . Graph and label A B . What single transformation would map AB to A B ? Math. B Aug. 03 [11] [OVER] 28 Express, in simplest a + bi form, the roots of the equation x2 + 5 = 4x. 29 A ship at sea is 70 miles from one radio transmitter and 130 miles from another. The angle between the signals sent to the ship by the transmitters is 117.4 . Find the distance between the two transmitters, to the nearest mile. Math. B Aug. 03 [12] 30 A student attaches one end of a rope to a wall at a fixed point 3 feet above the ground, as shown in the accompanying diagram, and moves the other end of the rope up and down, producing a wave described by the equation y = a sin b x + c. The range of the rope s height above the ground is between 1 and 5 feet. The period of the wave is 4 . Write the equation that represents this wave. 3 ft Math. B Aug. 03 3 ft [13] [OVER] 31 The table below shows the results of an experiment that relates the height at which a ball is dropped, x, to the height of its first bounce, y. Drop Height (x) (cm) Bounce Height (y) (cm) 100 90 80 70 60 26 23 21 18 16 Find x, the mean of the drop heights. Find y, the mean of the bounce heights. Find the linear regression equation that best fits the data. Show that (x,y) is a point on the line of regression. [The use of the grid on the next page is optional.] Math. B Aug. 03 [14] Question 31 continued Math. B Aug. 03 [15] [OVER] 32 A company calculates its profit by finding the difference between revenue and cost. The cost function of producing x hammers is C(x) = 4x + 170. If each hammer is sold for $10, the revenue function for selling x hammers is R(x) = 10 x. How many hammers must be sold to make a profit? How many hammers must be sold to make a profit of $100? Math. B Aug. 03 [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 Given circle O with diameter GOAL ; secants HUG and HTAM intersect at point H; m GM:m ML:m LT = 7:3:2; and chord GU chord UT. Find the ratio of m UGL to m H. G U O M A H T L Math. B Aug. 03 [17] [OVER] 34 When Joe bowls, he can get a strike (knock down all the pins) 60% of the time. How many times more likely is it for Joe to bowl at least three strikes out of four tries as it is for him to bowl zero strikes out of four tries? Round your answer to the nearest whole number. Math. B Aug. 03 [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 Aug. 03 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% 2 1.7% 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 Wednesday, August 13, 2003 8:30 to 11:30 a.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 Aug. 03 [23] 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 Math. B Aug. 03 [24] FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Wednesday, August 13, 2003 8:30 to 11:30 a.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 printed at the end of this key. 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) 2 (16) 2 (2) 2 (7) 4 (12) 4 (17) 3 (3) 1 (8) 3 (13) 2 (18) 1 (4) 1 (9) 2 (14) 4 (19) 1 (5) 3 (10) 3 (15) 1 (20) 4 [1] [OVER] MATHEMATICS B continued Part II For each question, use the specific criteria to award a maximum of two credits. (21) [2] 20.1, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] The time when the ball reaches its maximum height is found correctly, but no further correct work is shown. or [1] 20.1, 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] 1 1 or an equivalent answer, and appropriate work is shown. 4 [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] 1 1 or an equivalent answer, but no work is shown. 4 [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [2] MATHEMATICS B continued (23) [2] x + 4 , and appropriate work is shown. 4 [1] Appropriate work is shown, but one computational error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] x + 4 , but no work is shown. 4 [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] 56, and appropriate work is shown, such as 1 2 14 16 sin 30. [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] 56, 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] 16.6, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] Appropriate work is shown, but one conceptual error is made. or [1] A correct substitution of 4.75 for t is made, but no further correct work is shown. or [1] 16.6, 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. [3] [OVER] MATHEMATICS B continued (26) [2] No, and a correct justification is given. [1] No, but an incomplete or partially incorrect explanation is given. [0] No, but no explanation is given. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [4] MATHEMATICS B continued Part III For each question, use the specific criteria to award a maximum of four credits. (27) [4] AB and A B are graphed and labeled correctly, A (0, 5) and B ( 2,0), and a correct transformation is identified, such as R180 , R 180 , or r(0,0). [3] One error is made in graphing AB , but A B is graphed and labeled appropriately, and an appropriate transformation is identified. [2] AB is graphed and labeled correctly but one mistake is made in finding A B , but an appropriate transformation is identified. or [2] Both AB and A B are graphed and labeled correctly, but the transformation is missing or is incorrect. [1] AB is graphed and labeled correctly, but one mistake is made in finding A B , and the transformation is missing or is incorrect. or [1] One error is made in graphing AB , but A B is graphed and labeled appropriately, but the transformation is missing or is incorrect. or [1] R180 , R 180 , or r(0,0), but no graph is drawn. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [5] [OVER] MATHEMATICS B continued (28) [4] 2 i, and appropriate work is shown. [3] Appropriate work is shown, but one computational error is made, but the result is expressed as a complex number in simplest a + bi form. or [3] Appropriate work is shown, but the roots are not expressed in simplest a + bi form. or [3] Appropriate work is shown, but only one complex root, in simplest a + bi form, is found. [2] Appropriate work is shown, but one computational error is made, resulting in a solution that is not a complex number. or [2] Appropriate work is shown, but two or more computational errors are made, but the result is expressed as a complex number in simplest a + bi form. or [2] Appropriate work is shown, but one conceptual error is made. or [2] An incorrect quadratic formula is used, but the result is expressed as a complex number in simplest a + bi form. [1] Incorrect substitution is made into the quadratic formula, such as a = 1, b = 5, and c = 4, but the resulting equation is solved appropriately. or [1] 2 i, 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] 174, and appropriate work is shown, such as the use of the Law of Cosines. [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] One conceptual error is made when applying the Law of Cosines, but an appropriate answer is found. [1] Correct substitution is made into the Law of Cosines, but no further correct work is shown. or [1] 174, 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. (30) [4] y = 2 sin 1 x 2 + 3 or y = 2 sin 1 x 2 + 3, and appropriate work is shown. [3] The fact that c is equal to 3 is not recognized, resulting in an answer of y = 2 sin 1 x or y = 2 sin 1 x. 2 2 or [3] The values of a, b, and c are determined correctly, and appropriate work is shown, but the equation is not written. or [3] The value of a or c is determined incorrectly, but the value of b is determined correctly, and appropriate work is shown, and an appropriate equation is written. [2] Only the value of b is determined correctly, but appropriate work is shown, and an appropriate equation is written. or [2] Only the values of a and c are determined correctly, but appropriate work is shown, and an appropriate equation is written. [1] The value of a or c is determined incorrectly, and the value of b is not determined or is determined incorrectly, but appropriate work is shown, and an appropriate equation is written. or [1] y = 2 sin 1 x + 3 or y = 2 sin 1 x + 3, but no work is shown. 2 2 [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 (31) [4] x = 80, y = 20.8, and y = 0.25x + 0.8, and appropriate work is shown to prove that ( x, y) is a point on the line of regression. [3] Appropriate work is shown, but one computational error is made. [2] Appropriate work is shown, but two or more computational errors are made. or [2] Appropriate work is shown, but one conceptual error is made. [1] x = 80, y = 20.8, and y = 0.25x + 0.8, 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. (32) [4] 29 hammers to make a profit and 45 hammers to make a profit of $100, 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] Either the number of hammers to make a profit or the number of hammers to make a profit of $100 is determined correctly, and appropriate work is shown. [1] One conceptual and one computational error are made. or [1] The correct equation and inequality or the correct equations are written, but no further correct work is shown. or [1] 29 hammers to make a profit and 45 hammers to make a profit of $100, but no work is shown. [0] 29 and 45, but no work is shown and the answers are not labeled. 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 Part IV For each question, use the specific criteria to award a maximum of six credits. (33) [6] 2 1 or 2:1 or an equivalent ratio, and appropriate work is shown. [5] Appropriate work is shown, but one computational error is made, but an appropriate ratio is found. or [5] Appropriate work is shown, but the answer is not written as a ratio. or [5] Appropriate work is shown, but the ratio is reversed or is simplified incorrectly. [4] Appropriate work is shown, but two or more computational errors are made, but an appropriate ratio is found. or [4] Correct measures are found for all the arcs and the angles, and appropriate work is shown, but no ratio is found. or [4] Correct measures are found for all the arcs, but the measure of one angle is found incorrectly, but an appropriate ratio is found. [3] One conceptual error is made, but appropriate work is shown, and an appropriate ratio is found. or [3] Correct measures are found for all the arcs, but the measures of both angles are found incorrectly, but an appropriate ratio is found. [2] Correct measures are found for all the arcs, but no further correct work is shown. [1] Only the value of x is found correctly, and appropriate work is shown. or [1] 2 1 or 2:1 or an equivalent ratio, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [9] [OVER] MATHEMATICS B concluded (34) [6] 19, and appropriate work is shown, such as P(at least three) = 4C3(0.6)3(0.4) + 4C4(0.6)4 and P(0) = (0.4)4. [5] Appropriate work is shown, but one computational error is made. or [5] Correct probabilities are computed, but no answer or an incorrect answer is found. [4] Appropriate work is shown, but two or more computational errors are made. or [4] Only the probability for at least three strikes is found correctly, but an appropriate ratio is determined. [3] The probability for at least three strikes is found correctly, and no further correct work is shown. or [3] Only the probability for zero strikes is found correctly, but an appropriate ratio is determined. [2] Only the probability for zero strikes is found correctly, and no further correct work is shown. or [2] Only the equation for the probability for at least three strikes is written, and it is not solved. [1] Conceptual errors are made in finding the probabilities, but an appropriate ratio is determined, based on the incorrect probabilities. or [1] 19, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [10] MATHEMATICS B Map to Learning Standards Key Ideas Item Numbers Mathematical Reasoning 10, 26 Number and Numeration 5, 7, 20, 23 Operations 14, 22, 28 Modeling/Multiple Representation 4, 12, 18, 21, 25, 29, 30, 32 Measurement 6, 9, 11, 16, 17, 24, 33 Uncertainty 31, 34 Patterns/Functions 1, 2, 3, 8, 13, 15, 19, 27 Regents Examination in Mathematics B August 2003 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) Raw Score Scaled Score Raw Score Scaled Score Raw Score Scaled Score 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 100 99 99 98 97 97 96 95 95 94 93 92 92 91 90 89 88 88 87 86 85 84 83 82 81 80 79 79 78 77 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 76 75 74 73 72 70 69 68 67 66 65 64 63 62 61 59 58 57 56 55 53 52 51 50 49 47 46 45 43 42 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 41 39 38 37 35 34 33 31 30 28 27 26 24 23 21 20 18 17 15 14 12 11 9 8 6 5 3 2 0 To determine the student s final examination score, find the student s total test raw score in the column labeled Raw Score and then locate the scaled score that corresponds to that raw score. The scaled score is the student s final examination score. Enter this score in the space labeled Scaled Score on the student s answer sheet. All student answer papers that receive a scaled score of 60 through 64 must be scored a second time. For the second scoring, a different committee of teachers may score the student s paper or the original committee may score the paper, except that no teacher may score the same open-ended questions that he/she scored in the first rating of the paper. The school principal is responsible for assuring that the student s final examination score is based on a fair, accurate, and reliable scoring of the student s answer paper. Because scaled scores corresponding to raw scores in the conversion chart may change from one examination to another, it is crucial that for each administration, the conversion chart provided in the scoring key for that administration be used to determine the student s final score. The chart above is usable only for this administration of the mathematics B examination. [12]

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