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New York Regents Mathematics B June 2001

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The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Wednesday, June 20, 2001 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. Any work done on this sheet of scrap graph paper will not be scored. All work should be written 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 2. 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. 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 9.2% 4.4% 1.7% 2.5 2 1.5 4.4% 1 0.5 0 0.5 1 1.5 0.5% 1.7% 2 2.5 3 0.1% Part I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Record your answers in the spaces provided on the separate answer sheet. [40] 1 An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = 16t2 + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k? (1) 128 (3) 8 (2) 64 (4) 4 Use this space for computations. 2 The magnitude (R) of an earthquake is related to its intensity (I) by R = log I , T where T is the threshold below which the earthquake is not noticed. If the intensity is doubled, its magnitude can be represented by (1) 2(log I log T) (2) log I log T (3) 2 log I log T (4) log 2 + log I log T 3 Jacob is solving a quadratic equation. He executes a program on his graphing calculator and sees that the roots are real, rational, and unequal. This information indicates to Jacob that the discriminant is (1) zero (3) a perfect square (2) negative (4) not a perfect square 4 Camisha is paying a band $330 to play at her graduation party. The amount each member earns, d, varies inversely as the number of members who play, n. The graph of the equation that represents the relationship between d and n is an example of (1) a hyperbola (3) a parabola (2) a line (4) an ellipse 5 A modulated laser heats a diamond. Its variable temperature, in degrees Celsius, is given by f(t) = T sin at. What is the period of the curve? (1) |T| (3) 1 a 2p (2) (4) 2 ap a a Math. B June 01 [3] [OVER] 6 The circumference of a circular plot of land is increased by 10%. What is the best estimate of the total percentage that the area of the plot increased? (1) 10% (3) 25% (2) 21% (4) 31% 7 Which equation states that the temperature, t, in a room is less than 3 from 68 ? (1) |3 t| < 68 (3) |68 t| < 3 (2) |3 + t| < 68 (4) |68 + t| < 3 8 Fractal geometry uses the complex number plane to draw diagrams, such as the one shown in the accompanying graph. i -1 R 1 Which number is not included in the shaded area? (1) 0.5i (3) 0.9 (2) 0.5 0.5i (4) 0.9 0.9i Math. B June 01 [4] Use this space for computations. 9 The relationship of a woman s shoe size and length of a woman s foot, in inches, is given in the accompanying table. Woman s Shoe Size Foot Length (in) 5 6 7 8 9.00 9.25 9.50 Use this space for computations. 9.75 The linear correlation coefficient for this relationship is (1) 1 (3) 0.5 (2) 1 (4) 0 10 The center of a circular sunflower with a diameter of 4 centimeters is ( 2,1). Which equation represents the sunflower? (1) (x 2)2 + (y + 1)2 = 2 (2) (x + 2)2 + (y 1)2 = 4 (3) (x 2)2 + (y 1)2 = 4 (4) (x + 2)2 + (y 1)2 = 2 11 Melissa and Joe are playing a game with complex numbers. If Melissa has a score of 5 4i and Joe has a score of 3 + 2i, what is their total score? (1) 8 + 6i (3) 8 6i (2) 8 + 2i (4) 8 2i 12 In a science experiment, when resistor A and resistor B are connected 1 in a parallel circuit, the total resistance is 1 1 . This complex frac+ AB tion is equivalent to (1) 1 (3) A + B (2) AB (4) AB A+B Math. B June 01 [5] [OVER] 13 A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars, x > 100, at 8 a.m., what, in terms of x, is the cost of Hakeem s purchase? (1) 0.20x 15 (3) 0.85x 20 (2) 0.20x 3 (4) 0.80x 12 14 A bug travels up a tree, from the ground, over a 30-second interval. It travels fast at first and then slows down. It stops for 10 seconds, then proceeds slowly, speeding up as it goes. Which sketch best illustrates the bug s distance (d) from the ground over the 30-second interval (t)? d d t t (1) (3) d d t (2) t (4) 15 The inverse of a function is a logarithmic function in the form y = logb x. Which equation represents the original function? (3) x = by (1) y = bx (2) y = bx (4) by = x Math. B June 01 [6] Use this space for computations. 16 On her first trip, Sari biked 24 miles in T hours. The following week Sari biked 32 miles in T hours. Determine the ratio of her average speed on her second trip to her average speed on her first trip. (1) (2) 3 4 2 3 (3) (4) 3 17 What is the value of (1) 15 (2) 55 m =1 Use this space for computations. 4 3 3 2 (2m + 1)m 1? (3) 57 (4) 245 18 If is an obtuse angle and sin = b, then it can be concluded that (1) tan > b (3) cos 2 > b (2) cos > b (4) sin 2 < b 19 Main Street and Central Avenue intersect, making an angle measuring 34 . Angela lives at the intersection of the two roads, and Caitlin lives on Central Avenue 10 miles from the intersection. If Leticia lives 7 miles from Caitlin, which conclusion is valid? (1) Leticia cannot live on Main Street. (2) Leticia can live at only one location on Main Street. (3) Leticia can live at one of two locations on Main Street. (4) Leticia can live at one of three locations on Main Street. 20 Through how many radians does the minute hand of a clock turn in 24 minutes? (1) 0.2p (3) 0.6p (2) 0.4p (4) 0.8p Math. B June 01 [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 Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his garden will be 55 square yards, find, to the nearest tenth of a degree, the three angles of the triangle. 22 At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. Find, to the nearest tenth, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light. Math. B June 01 [8] 23 The cost of a long-distance telephone call is determined by a flat fee for the first 5 minutes and a fixed amount for each additional minute. If a 15-minute telephone call costs $3.25 and a 23-minute call costs $5.17, find the cost of a 30-minute call. 2 2 24 A rectangular prism has a length of 2 x + 2 x - 24 , a width of 4x + x x 2 + x - 6 , and a height of 8 x 2 + 2 x . For all values of x for which it is x2 9 x+4 defined, express, in terms of x, the volume of the prism in simplest form. Math. B June 01 [9] [OVER] 25 The scientists in a laboratory company raise amebas to sell to schools for use in biology classes. They know that one ameba divides into two amebas every hour and that the formula t = log2 N can be used to determine how long in hours, t, it takes to produce a certain number of amebas, N. Determine, to the nearest tenth of an hour, how long it takes to produce 10,000 amebas if they start with one ameba. 26 Professor Bartrich has 184 students in her mathematics class. The scores on the final examination are normally distributed and have a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 82 and 90? Math. B June 01 [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 A wooden frame is to be constructed in the form of an isosceles trapezoid, with diagonals acting as braces to strengthen the frame. The sides of the frame each measure 5.30 feet, and the longer base measures 12.70 feet. If the angles between the sides and the longer base each measure 68.4 , find the length of one brace to the nearest tenth of a foot. 28 A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeowner cannot have a deck larger than 900 square feet. If the length and the width are to be increased by the same amount, find, to the nearest tenth, the maximum number of feet that the length of the deck may be increased in size legally. Math. B June 01 [11] [OVER] 29 Two parabolic arches are to be built. The equation of the first arch can be expressed as y = x2 + 9, with a range of 0 y 9, and the second arch is created by the transformation T7,0. On the accompanying set of axes, graph the equations of the two arches. Graph the line of symmetry formed by the parabola and its transformation and label it with the proper equation. y x Math. B June 01 [12] 30 Draw f(x) = 2x2 and f 1(x) in the interval 0 x 2 on the accompanying set of axes. State the coordinates of the points of intersection. f(x) 8 7 6 5 4 3 2 1 0 Math. B June 01 1 2 3 4 [13] 5 6 7 8 x [OVER] 31 In the interval 0 A < 360 , solve for all values of A in the equation cos 2A = 3 sin A 1. 32 Point P lies outside circle O, which has a diameter of AOC . The angle formed by tangent PA and secant PBC measures 30 . Sketch the conditions given above and find the number of degrees in the measure of minor arc CB. Math. B June 01 [14] 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: chords AB and CD of circle O intersect at E, an interior point of circle O; chords AD and CB are drawn. A C O E D B Prove: (AE)(EB) = (CE)(ED) Math. B June 01 [15] [OVER] 34 The 1999 win-loss statistics for the American League East baseball teams on a particular date is shown in the accompanying chart. New York Boston Toronto Tampa Bay Baltimore W 52 49 47 39 36 L 34 39 43 49 51 Find the mean for the number of wins, W, and the mean for the number of losses, L, and determine if the point ( W, L) is a point on the line of best fit. Justify your answer. Math. B June 01 [16] 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, June 20, 2001 9:15 a.m. to 12:15 p.m., only ANSWER SHEET Pupil ............................................. 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 June 01 [19] 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 June 01 [20] FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Wednesday, June 20, 2001 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 Administering and Scoring 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) 2 (11) 4 (16) 3 (2) 4 (7) 3 (12) 2 (17) 2 (3) 3 (8) 4 (13) 4 (18) 4 (4) 1 (9) 1 (14) 3 (19) 3 (5) 2 (10) 2 (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] 49.8, 65.1, and 65.1, and the appropriate use of the area formula is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] Only one or two angles are found correctly. or [1] Cosine is used instead of sine, but appropriate work is shown. or [1] The setup is appropriate, but incorrect work is shown, such as the sine of the angle but not the angle is found. or [1] 49.8, 65.1, and 65.1, 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] 0.3 or an equivalent answer, 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 no answer is found. or [1] 0.3 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. [2] MATHEMATICS B continued (23) [2] $6.85, and appropriate work is shown. [1] The correct rate for the first 5 minutes and the correct rate for each additional minute is shown, but the cost of a 30-minute call is not found. or [1] Appropriate work is shown, but one computational error is made. or [1] $6.85, but no work is shown. [0] The student calculates either the rate for the first 5 minutes or the rate for each additional minute, but no further 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. (24) [2] 4(x 2) or 4x 8, and appropriate work is shown. [1] The problem is factored correctly but not reduced to simplest form. or [1] Only two of the expressions are factored correctly, but an appropriate answer is found. or [1] 4(x 2) or 4x 8, but no work is shown. [0] Only the formula for volume 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. [3] [OVER] MATHEMATICS B continued (25) [2] 13.3, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] The correct value is substituted for n, and the equation is converted to exponential form, but it is not solved. or [1] 13.3, 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. (26) [2] 25, and appropriate work is shown. [1] Appropriate work is shown, but one computational or rounding error is made. or [1] The solution is incomplete, such as only the correct percent is shown. or [1] 25, but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [4] MATHEMATICS B continued Part III For each question, use the specific criteria to award a maximum of four credits. (27) [4] 11.8, and an appropriate application of the Law of Cosines is shown. [3] Appropriate work is shown, but one computational or rounding error is made. or [3] The Law of Cosines is correctly applied, but the square root is not found. [2] The Law of Cosines is applied correctly, and correct substitutions are shown, but no further work is shown. or [2] Appropriate work is shown, but more than one computational error is made. [1] The diagram is set up with the correct sides and angles, and the Law of Cosines is written, but substitution is not made. or [1] The diagram is set up with the correct sides and angles, but no further work is shown. or [1] 11.8, 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. [5] [OVER] MATHEMATICS B continued (28) [4] 12.6, and appropriate work is shown. [3] Appropriate work is shown, but one computational or rounding error is made. or [3] Appropriate work is shown, but the quadratic formula is incorrect. [2] An appropriate equation is shown and put in standard form, but the quadratic formula is not used correctly. or [2] An appropriate equation is shown and put in standard form, but no further work is shown. or [2] Appropriate work is shown, but more than one computational error or one computational and one rounding error are made. [1] An appropriate equation is shown, but all other work is missing or is incorrect. or [1] 12.6, 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 (29) [4] Both parabolas are graphed correctly with the line of symmetry x = 3.5 drawn and labeled as x = 3.5. [3] y = x2 + 9 is graphed incorrectly, but an appropriate translation is drawn, and an appropriate line of symmetry is drawn and labeled correctly. or [3] y = x2 + 9 and its translation are graphed correctly, but no line of symmetry or an incorrect line of symmetry is drawn for the translation or no equation or an incorrect equation is shown for the line of symmetry. [2] y = x2 + 9 is graphed correctly, but its translation is graphed incorrectly, but an appropriate line of symmetry is drawn and labeled correctly. or [2] y = x2 + 9 is graphed incorrectly, but an appropriate translation is graphed, but an incorrect line of symmetry is drawn. [1] y = x2 + 9 and its translation are graphed incorrectly, but an appropriate line of symmetry is drawn and labeled correctly. or x2 + 9 is graphed correctly, but an incorrect translation and line of symmetry [1] y = are drawn. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [7] [OVER] MATHEMATICS B continued (30) [4] (0,0) and 1 , 1 , and both graphs are drawn correctly. 22 [3] Both graphs are drawn correctly, but one or both points of intersection are stated incorrectly. or [3] The graph of y = 2x2 is incorrect, but the inverse is appropriate or correct, and the appropriate points of intersection are stated correctly. [2] Both points of intersection are found correctly, using an algebraic solution. or [2] The graph of y = 2x2 is incorrect, but the inverse is appropriate or correct, but no further work is shown. or [2] The graph of y = 2x2 is correct, but the inverse is incorrect, but the appropriate points of intersection are stated. or [2] The graph of y = 2x2 is incorrect, but the inverse is correct, but the points of intersection are not stated or are incorrect. [1] Both graphs are incorrect, but the points of intersection are appropriate, based on the incorrect graphs. or [1] The graph of y = 2x2 is correct, but the inverse is incorrect, and the points of intersection are labeled or stated incorrectly. or [1] (0,0) and 11 , 22 , but no work is shown. [0] Straight lines are used as graphs of the functions. or [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [8] MATHEMATICS B continued (31) [4] 210 and 330 , and appropriate work is shown. [3] Correct substitution and factoring are shown, with at least the reference angle of 30 found. or [3] Correct substitution is shown, and the equation is put in standard form and factored correctly, but an incorrect reference angle is used to find appropriate answers. or [3] An incorrect quadratic equation is solved correctly, and appropriate angles are determined. [2] Correct substitution is shown, and the equation is put in standard form and factored correctly, but no angles are found. [1] Correct substitution is shown, but the equation is not factored or is factored incorrectly. or [1] 210 and 330 , but no work is shown. [0] 210 or 330 or 30 , 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. (32) [4] 60 , and an appropriate sketch is drawn, and appropriate work is shown. [3] A correct sketch is shown, and m AB is correct. or [3] A correct sketch is shown, but one computational error is made, leading to an incorrect m AB, but mCB is appropriate, based on the incorrect m AB. [2] A correct sketch is shown, but an incorrect procedure is used to find either the correct or incorrect m AB, but mCB is appropriate, based on the incorrect m AB. or [2] An incorrect sketch is shown, but an appropriate mCB is found, based on the incorrect sketch. [1] Only a correct sketch is shown. or [1] 60 , but no work is shown. [0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure. [9] [OVER] MATHEMATICS B continued Part IV For each question, use the specific criteria to award a maximum of six credits. (33) [6] A complete and correct proof is shown, such as the example below: Reasons Statements 1 Chords AB and CD of circle O intersect at E, and chords AB and CD are drawn. 1 Given 2 A @ C 2 Inscribed angles of a circle that intercept the same arc are congruent. 3 AED @ CEB 3 Vertical angles are congruent. 4 v AED ~ v CEB 4 AA @ AA 5 AE = ED CE EB 5 Corresponding sides of similar triangles are in proportion. 6 (AE)(EB) = (CE)(ED) 6 In a proportion, the product of the means equals the product of the extremes. [5] v AED and v CEB are correctly proved to be similar, and the appropriate proportion is written with justification. or [5] A correct proof is shown, but one of the justifications is missing or is incorrect. [4] v AED and v CEB are correctly proved to be similar, but no further work is shown. [3] A correct proof is shown, but more than one justification is missing or is incorrect. [2] The triangles are said to be similar, and the conclusion is written. [1] Only one correct statement and justification are given. [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 (34) [6] W = 44.6 and L = 43.2, the line of best-fit equation (y = 1.007559x + 88.137149) is shown, and an appropriate justification of point ( W, L ) fitting or not fitting, depending on the rounding of the equation, is given. [5] W or L is incorrect, but the rest of the work is appropriate. or [5] All conditions of the problem are met, except it is not stated whether ( W, L ) lies or does not lie on the line of best fit. or [5] W and L and the equation of the line of best fit are correct, but one error results in an incorrect conclusion, such as the calculation or interchanging of W and L . [4] Both W and L are incorrect, but the rest of the work is appropriate. or [4] W and L are correct, but the equation of the line of best fit is incorrect, but the justification is appropriate, based on the incorrect equation. or [4] W and L are correct, a correct scatter plot is drawn, a correct line of best fit is drawn, ( W, L ) is plotted correctly, and a statement indicating that the point does or does not fit the line is given, with an appropriate explanation, but no equation is used. or [4] All conditions of the problem are met, except for the justification of whether ( W, L ) lies on the line. [3] W and L are correct, but the equation of the line of best fit is stated incorrectly, and no further work is shown. [2] Only W and L are found correctly. [1] Only one mean is found correctly. [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] [13] [OVER] Regents Examination in Mathematics B June 2001 Chart for Converting Total Test Raw Scores to Final Examination Scores (Scaled Scores) 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 98 97 97 96 96 95 95 94 94 93 93 92 91 91 90 90 89 89 88 87 87 86 86 85 84 84 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 83 82 82 81 80 80 79 78 77 76 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 60 59 58 57 55 Raw Score 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 Scaled Score 54 53 51 50 48 47 45 44 42 40 38 37 35 33 31 29 27 25 23 21 19 17 15 12 10 8 5 3 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.

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  Print intermediate debugging step

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Additional Info : Refer : Formulas (page 2) and Scoring Key (page 21)
Tags : , papers, New York State, High School Regents, Examinations, Past exams, solvedTest Papers, Education, Assessment and Testing.  


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