The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III

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1 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Thursday, June 20, 2002 :5 to 4:5 p.m., only Notice... Scientific calculators must be available to all students taking this eamination. The formulas that you may need to answer some questions in this eamination are found on page 2. The last page of the booklet is the answer sheet. Fold the last page along the perforations and, slowly and carefully, tear off the answer sheet. Then fill in the heading of the answer sheet. When you have completed the eamination, 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 eamination and that you have neither given nor received assistance in answering any of the questions during the eamination. The answer sheet cannot be accepted if you fail to sign this declaration. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

2 Math. Course III June 02 [2]

3 Part I Answer 0 questions from this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Write your answers in the spaces provided on the separate answer sheet. Where applicable, answers may be left in terms of π or in radical form. [60] What is the amplitude of the graph of the equation y = sin 2? 2A translation maps P(4,) to P (2, ). What are the coordinates of Q, the image of Q(,) under the same translation? Epress in simplest form in terms of i: 4 If g() = ( ), find g( ). 5 Epress 45 in radian measure. 6 If log 4 = 2, find. 7 If f() = 2 + and g() = 2, find (g f)(2). 8 If is written in scientific notation as.26 0 n, find the value of n. 9 If the domain of f()= 2 + is limited to {0,,2,}, what is the maimum value of the range? 0 Epress in simplest form: In ABC, m A = 0, m B = 65, and BC = 0. Find AC to the nearest tenth. 2 Evaluate: Solve for r: k 2 k= 0 r = Solve for the negative value of : 2 + = 7 Directions (5 5): For each question chosen, write on the separate answer sheet the numeral preceding the word or epression that best completes the statement or answers the question. 5 Which epression is equivalent to cos 20? () cos 60 () sin 60 (2) cos 0 (4) sin 0 6 In the distance formula, rate varies inversely with time. If rate is doubled, time is () decreased by 2 () halved (2) increased by 2 (4) doubled 7 For which value or values of n is the epression n 2n + 4 undefined? (), only () and 2 (2) 2, only (4) 0 8 What is the reciprocal of 5? 5 4 () () (2) (4) 9 The graph of y = 6 lies in () Quadrant I, only (2) Quadrant II, only () Quadrants I and III (4) Quadrants II and IV The epression sec 2 tan 2 is equal to () () sin 2 (2) 0 (4) cos 2 Math. Course III June 02 [] [OVER]

4 2 In the accompanying diagram of circle O, chords AB and CD intersect at E and mac: mcb: mbd: mda = 4:2:6:8. 28 Which graph represents the function f() = sin in the interval π π? y y C E B O D π ( ) π π ( ) π A y y What is m DEB? () 6 () 00 (2) 90 (4) 26 π π π π 22 The roots of the equation = 0 are () imaginary (2) real and irrational () real, rational, and unequal (4) real, rational, and equal 2 In ABC, m A = 0, a = 2, and b = 0. Which type of triangle is ABC? () acute () obtuse (2) isosceles (4) right 24 What is the value of (5i )? () 25i () 5i (2) 25i (4) 5i 25 What is a value of cos (Arc tan )? () () 5 (2) (4) 26 If sin is less than 0 and sec is greater than 0, in which quadrant does the terminal side of lie? () I () III (2) II (4) IV 27 Which equation is equivalent to 6 =? t2 t () (t )(t + 2) = 0 () (2t + )(t ) = 0 (2) (t 2)(t + ) = 0 (4) (2t )(t + ) = The epression csc A sin 2A is equivalent to () 2 sin A () 2 cos A (2) 2 (4) 2 cot A 0 If a fair si-sided die is tossed five times, what is the probability of getting eactly three even numbers? 2 2 ( 2 ) () () (2) (4) 0 2 The sides of a parallelogram are 6 and 8, and the included angle is 50º. What is the area of the parallelogram? () 24 () 24 (2) 48 (4) What is the solution set of the inequality 2 0 > 0? () { 2 < < 5} () { < 5 or > 2} (2) { 5 < < 2} (4) { < 2 or > 5} What is the third term in the epansion of (2 y) 4? () 6 y () 24 2 y 2 (2) 6 y (4) 24 2 y 2 5 ( 4 ) Math. Course III June 02 [4]

5 4 In a circle, an arc of length 5 is subtended by a 5 central angle of radians. What is the radius of the circle? () 25 () 25 (2) (4) 5 5 What is the inverse of the function y = 2? () y = + 2 () y = 2 (2) y = +2 (4) y = 2 Answers to the following questions are to be written on paper provided by the school. Part II Answer four questions from this part. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Calculations that may be obtained by mental arithmetic or the calculator do not need to be shown. [40] 6 a On the same set of aes, sketch and label the graphs of the equations y = cos and y = sin 2 in the interval π π. [8] b Using the graphs sketched in part a, determine all values of in the interval π π that satisfy the equation cos = sin 2. [2] 40 In the accompanying diagram of circle O, secant PFCQ, secant PAOEB, tangent QB, and chord CEG are drawn; mbc: mcf: mfa = 7:8:; and m AEG = 95. P 7 a Solve for and epress the roots in simplest a + bi form: b Epress in simplest form: = [5] [5] F A 8 a On graph paper, sketch the graph of the equation y = in the interval 2 2. [4] C O E b On the same set of aes, reflect the graph drawn in part a in the y-ais and label it b. [4] c Write the equation of the graph drawn in part b. [2] 9 Find, to the nearest ten minutes or nearest tenth of a degree, all values of in the interval 0 < 60 that satisfy the equation 6 cos 2 5 sin 5 = 0. [0] Q Find: a mcf [2] b mag [2] c m P [2] d m FCG [2] e m FQB [2] B G Math. Course III June 02 [5] [OVER]

6 4 a Mr. Truong gave his 25 final grades according to the following chart: i f i a Two forces of 25 pounds and 8 pounds act on a body at an angle of Find, to the nearest tenth of a pound, the magnitude of the resultant force. [6] b Using the answer found in part a, find the angle between the resultant and the larger force to the nearest tenth of a degree. [4] () Find the standard deviation of this set of grades to the nearest tenth. [4] (2) What percentage of the grades fall outside one standard deviation of the mean? [2] b During the school year, Michele receives four report cards. The probability that she will get an A in mathematics on any one report card is 4. What 5 is the probability that she will get an A in mathematics on at least three of the four report cards? [4] Math. Course III June 02 [6]

7 Tear Here Tear Here The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION SEQUENTIAL MATH COURSE III Thursday, June 20, 2002 :5 to 4:5 p.m., only ANSWER SHEET Part I Score Part II Score Total Score Rater s Initials: Student Se: Male Female Grade Teacher School Your answers to Part I should be recorded on this answer sheet. Part I Answer 0 questions from this part Your answers for Part II should be placed on paper provided by the school. The declaration below should be signed when you have completed the eamination. I do hereby affirm, at the close of this eamination, that I had no unlawful knowledge of the questions or answers prior to the eamination and that I have neither given nor received assistance in answering any of the questions during the eamination. Signature Math. Course III June 02 [7]

8 Tear Here Tear Here Math. Course III June 02 [8]

9 FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Thursday, June 20, 2002 :5 to 4:5 p.m., only SCORING KEY 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. Part I Allow a total of 60 credits, 2 credits for each of 0 of the following. [If more than 0 are answered, only the first 0 answered should be considered.] Allow no partial credit. For questions 5 5, allow credit if the student has written the correct answer instead of the numeral, 2,, or 4. () () 8. (2) 2 () (2) (,) (2) (22) (2) 4 () 5i () 6 (2) () 4 5 (4) 4 (4) 6 2 (24) 2 (4) π (5) (5) 4 (25) 2 (5) 2 4 (6) 6 (6) (26) 4 (7) 25 (7) 2 (27) (8) (8) 2 (28) (9) 0 (9) 4 (29) (0) (20) (0) 2 [OVER]

10 SEQUENTIAL MATH COURSE III concluded Part II Please refer to the Department s publication Guide for Rating Regents Eaminations in Mathematics, 996 Edition. Care should be eercised in making deductions as to whether the error is purely a mechanical one or due to a violation of some principle. A mechanical error generally should receive a deduction of 0 percent, while an error due to a violation of some cardinal principle should receive a deduction ranging from 0 percent to 50 percent, depending on the relative importance of the principle in the solution of the problem. (6) b _ π, π [2] 2 2 (7) a ± 2i [5] b ( + 4) [5] (8) cy= [2] (9) 9 40', 70 20', 270 or 9.6, 70.4, 270 [0] (40) a 80 [2] b 20 [2] c 20 [2] d 75 [2] e 70 [2] (4) a () 7. [4] (2) 28 [2] b [4] (42) a 50.8 [6] b 28. [4] As a reminder... Regents eaminations based on the Sequential Mathematics, Course II, syllabus will not be offered after January 200. Regents eaminations based on the Sequential Mathematics, Course III, syllabus will not be offered after January 2004.