The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Wednesday, August 6, 000 8:0 to :0 a.m., only Notice... Scientific calculators must be available to all students taking this examination. The formulas which you may need to answer some questions in this examination are found on age. The last age of the booklet is the answer sheet. Fold the last age along the erforations and, slowly and carefully, tear off the answer sheet. Then fill in the heading of your answer sheet. When you have comleted the examination, you must sign the statement rinted at the end of the answer aer, indicating that you had no unlawful knowledge of the questions or answers rior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer aer cannot be acceted if you fail to sign this declaration. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
Math. Course III Aug. 00 []
Part I Answer 0 questions from this art. Each correct answer will receive credits. No artial credit will be allowed. Write your answers in the saces rovided on the searate answer sheet. Where alicable, answers may be left in terms of π or in radical form. [60] If f(x) = x 4 and g(x) = x, find the value of f() g(). What is the amlitude of the function y = sin x? 0 If oint A has coordinates (,4), what are the coordinates of A, the image of A under r y-axis D? Factor comletely: x 9x What is the value of sin (Arc tan )? Evaluate: Â k = 0 ( - k ) 4 In the accomanying diagram, PQ and PS are tangents drawn to circle O, and chord QS is drawn. If m P = 40, what is m PQS? Q Solve for the smallest non-negative value of : cos q + = + 4 Exress x x in simlest form. - 9 x O P 5 Circle O has its center at the origin, OB =, and BA ^ OA. If m BOA =, which line segment shown has a length equal to cos? S 5 An angle that measures radians is drawn in standard osition. In which quadrant does the terminal side of the angle lie? 5 O q B A 6 Exress 4-5 - -8 as a monomial in terms of i. 7 In ABC, a = 6, b = 0, and m C = 0. Find the area of ABC. 8 Solve for the ositive value of x: x + = 8 9 What is the solution set of the equation Ωx Ω = 5? 4 Directions (6 5): For each question chosen, write on the searate answer sheet the numeral receding the word or exression that best comletes the statement or answers the question. 6 In scientific notation, the number, 000, 000 is written as () 9.0 0 6 () 9.0 0 6 () 9.0 0 7 (4) 9.0 0 7 9 Math. Course III Aug. 00 [] [OVER]
7 For which value of is the fraction undefined? () π () 4 () (4) 0 cos q 8 What is the solution of the inequality x + x 5 < 0? () x < 5 or x > () x < or x > 5 () 5 < x < (4) < x < 5 5 In ABC, a =, b =, and m C = 0. The value of c is () () 5. () (4) 6 In the accomanying diagram, PAB and PCD are secants drawn to circle O, PA = 8, PB = 0, and PD = 6. P C D 9 The roots of the equation x + kx + = 0 are real if the value of k is () 0 () () (4) 4 0 The heights of the members of a high school class are normally distributed. If the mean height is 65 inches and a height of 7 inches reresents the 84th ercentile, what is the standard deviation for this distribution? () 7 () () (4) 7 What is the greatest ossible integral value of x for which x - 5 is an imaginary number? () 5 () () 6 (4) 4 The exression log 4x is equivalent to () log x 4 () log 4 + log x () 4 log x (4) (log 4)(log x) Which value of satisfies the equation cos cos = 0? () () 6 () (4) 0 4 4 If the robability that Mike will successfully comlete a foul shot is 4, what is the robability that 5 he will successfully comlete exactly three of his next four foul shots? 56 () 64 () 65 9 65 () (4) 65 64 5 Math. Course III Aug. 00 [4] What is PC? () 6.4 () () 0 (4) 40 7 When the grahs of the equations xy = 6 and y = x are drawn on the same set of axes, what is the total number of common oints? () () () (4) 0 8 The inverse of the function y = x 5 is () y = (x + 5) () y = x + 5 () y = (x 5) (4) y = 5 x 9 As x increases from π to π, the value of sin x () increases, only () decreases, only () increases, then decreases (4) decreases, then increases 0 If x y = x+, what is the value of y? () () () (4) A If m A =, a = 5, and b =, it is ossible to construct () an obtuse triangle () two distinct triangles () no triangles (4) a right triangle O B
The exression sin x cos x tan x is equivalent to () () cos x () sin x (4) cos x Which field roerty is not satisfied by the set of integers for addition and multilication? () identity for multilication () inverses for multilication () identity for addition (4) closure for addition 4 What is the fourth term of the exansion (x y) 7? () 6x 4 y () 560x 4 y () 5x y 4 (4) 560x y 4 5 If sec x < 0 and tan x < 0, then the terminal side of angle x is located in Quadrant () I () III () II (4) IV Answers to the following questions are to be written on aer rovided by the school. Part II Answer four questions from this art. Clearly indicate the necessary stes, including aroriate formula substitutions, diagrams, grahs, charts, etc. Calculations that may be obtained by mental arithmetic or the calculator do not need to be shown. [40] 6 In the accomanying diagram of circle O, diameters BD and AE, secants PAB and PDC, and chords BC and AD are drawn; mad = 40; and mdc = 80. P A 7 a On the same set of axes, sketch and label the grahs of the equations y = 4 sin x and y = cos x in the inverval 0 x π. [8] b Based on the grah drawn in art a, how many values in the interval 0 x π satisfy the equation 4 sin x = cos x? [] B E Find: a mab [] b m BCD [] c m BOE [] d m P [] e m PAD [] O C D 8 Given: f(x) = log x a On grah aer, sketch and label the grah of f(x) = log x. [4] b On the same set of axes, rotate the grah drawn in art a 90 counterclockwise about the origin. Sketch this rotation and label it b. [4] c Write an equation of the function grahed in art b. [] Math. Course III Aug. 00 [5] [OVER]
9 a Five marbles are in a jar. Two are red and three are white. Four marbles are selected at random with relacement. () Find the robability that at most two red marbles are selected. [4] () Find the robability that at least three red marbles are selected. [] b Find, to the nearest tenth, the standard deviation of this set of data. [4] x i f i 87 89 4 9 9 6 95 4 a The roots of a quadratic equation are r = + i and r = i. () Find the sum of the roots r and r. [] () Find the roduct of the roots r and r. [] () Write a quadratic equation that has roots r and r. [] b Solve for x: 4x - = [5] x + x 4 a Two forces of 0 and 50 ounds yield a resultant force of 70 ounds. Find, to the nearest ten minutes or nearest tenth of a degree, the angle between the original two forces. [7] b Given: z = + i and z = 5 + i. Plot z, z, and z + z on grah aer. [] 40 a In the interval 0 < 60, find all values of that satisfy the equation + sin = csc. [5] b Prove the following identity: tan q + = sec [5] cot q Math. Course III Aug. 00 [6]
Tear Here Tear Here The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION SEQUENTIAL MATH COURSE III Wednesday, August 6, 000 8:0 to :0 a.m., only ANSWER SHEET Part I Score............ Part II Score............ Total Score............ Rater s Initials:.............. Puil............................................... Sex: Male Female Grade........... Teacher............................................. School................................... Your answers to Part I should be recorded on this answer sheet. Part I Answer 0 questions from this art..................................................................................................................................................................................................................................... 4................... 4................... 4................... 4................... 5................... 5................... 5................... 5................... 6................... 6................... 6................... 7................... 7................... 7................... 8................... 8................... 8................... 9................... 9................... 9................... 0................... 0................... 0................... Your answers for Part II should be laced on aer rovided by the school. The declaration below should be signed when you have comleted the examination. I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers rior to the examination and that I have neither given nor received assistance in answering any of the questions during the examination. Signature Math. Course III Aug. 00 [7]
Tear Here Tear Here Math. Course III Aug. 00 [8]
FOR TEACHERS ONLY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Wednesday, August 6, 000 8:0 to :0 a.m., only SCORING KEY Use only red ink or red encil in rating Regents aers. Do not attemt to correct the student s work by making insertions or changes of any kind. Use checkmarks to indicate student errors. Unless otherwise secified, 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, credits for each of 0 of the following. [If more than 0 are answered, only the first 0 answered should be considered.] Allow no artial credit. For questions 6 5, allow credit if the student has written the correct answer instead of the numeral,,, or 4. () () x(x + 8) (x 8) () 4 () () () 6 () () 4 () () 0 or 0 () () (4) 70 (4) (4) (4) x (5) IV (5) OA (5) 4 (5) (6) i (6) (6) (7) 5 (7) (7) 4 (8) 8 (8) (8) (9), (9) 4 (9) 4 (0) (6,8) (0) (0) [OVER]
SEQUENTIAL MATH COURSE III concluded Part II Please refer to the Deartment s ublication Guide for Rating Regents Examinations in Mathematics, 996 Edition. Care should be exercised in making deductions as to whether the error is urely a mechanical one or due to a violation of some rincile. A mechanical error generally should receive a deduction of 0 ercent, while an error due to a violation of some cardinal rincile should receive a deduction ranging from 0 ercent to 50 ercent, deending on the relative imortance of the rincile in the solution of the roblem. (6) a 40 [] b 90 [] c 40 [] d 0 [] e 90 [] (7) b [] (8) c f(x) = x [] (40) a 0, 50, 70 [5] (4) a () 6 [] () [] () x 6x + = 0 [] b 4, 6 [5] (4) a 05.6 or 05 40' [7] (9) a () 5 65 [4] () 65 [] b.6 [4]