The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE III. Wednesday, June 21, :15 to 4:15 p.m.

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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 Wednesday, June, 000 :5 to 4:5 p.m., only Notice... Scientific calculators must be available to all students taking this eamination. The formulas which you may need to answer some questions in this eamination are found on page. 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 your answer sheet. When you have completed the eamination, you must sign the statement printed at the end of the answer paper, 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. Your answer paper 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 00 []

3 Part I Answer 30 questions from this part. Each correct answer will receive 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] In ABC, sin A = 0.3, sin B = 0.8, and b =. Find the length of side a. If f() = sin + cos, find f( ). 3 An angle inscribed in a circle measures 80 degrees. What is the number of degrees in the intercepted arc? π 4 In a circle whose radius is centimeters, a central angle intercepts an arc of 6 centimeters. What is the number of radians in the central angle? 5 Determine the maimum number of triangles possible when m A = 50, a = 4, and b = 0. 6 Solve for : = In ABC, a =.3, b =.4, and m C = 30. Find the area of ABC. 5 Solve for : 9 = If sin A < 0 and cot A > 0, in which quadrant does the terminal side of A lie? 7 A translation maps P(3, ) to P (,). Under the same translation, find the coordinates of Q, the image of Q( 3,). 8 Factor completely: Solve for all values of : + 3 = 7 0 If g() = 36, evaluate g( ). Evaluate: Epress in simplest form: 4 n n= y y y Directions (7 35): 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. 7 Which transformation is not an isometry? () dilation (3) reflection () rotation (4) translation 8 The epression sin (cot csc ) is equivalent to () cos sin (3) sin () cos (4) cos 9 Which equation is sketched in the accompanying graph? () y = cos (3) y = cos () y = cos (4) y = cos y π π 3π π 3 Epress + 8 as a monomial in terms of i. Math. Course III June 00 [3] [OVER]

4 0 As angle increases from to π, the value of sin will () increase from to 0 () increase from 0 to (3) decrease from 0 to (4) decrease from to 0 Which graph represents the solution set for the inequality 0 < 0? ( ) π 6 Which equation is not a function? () 3 + 4y = (3) y = () y = cos (4) y = log 7 When the sum of 4 + 6i and 6 8i is graphed, in which quadrant does it lie? () I (3) III () II (4) IV 8 In the accompanying diagram, point P( 0.6, 0.8) is on unit circle O. y ( ) ( 3 ) θ O ( 4 ) If the fraction 0, 000 is epressed in the form.3 0 n, the value of n is () (3) 3 () (4) 4 3 If f() = sin (Arc tan ), the value of f() is () (3) () (4) 4 A solution of the equation cos + sin = is () 40 (3) 45 () 35 (4) 30 5 In circle O, PA and PB are tangent to the circle from point P. If the ratio of the measure of major arc AB to the measure of minor arc AB is 5:, then m P is () 60 (3) 0 () 90 (4) P ( 0.6, 0.8) What is the measure of angle to the nearest degree? () 43 (3) 5 () 7 (4) 33 9 The epression log is equivalent to () log 6 + log 6 (3) log 3 log () log 3 + log (4) log 3 log 4 30 In the equation 7 + = 0, the sum of the roots eceeds the product of the roots by () 9 (3) 9 () 5 (4) 5 3 What is the third term in the epansion of (a 3b) 4? () 6a b (3) 54a b () 6a b (4) 54a b 3 The roots of the equation 4 + k = 0 are real and equal if k is equal to () (3) 4 () (4) 4 Math. Course III June 00 [4]

5 33 The epression cos (70 A) is equivalent to () cos A (3) sin A () cos A (4) sin A 34 The scores on a test approimate a normal distribution with a mean score of 7 and a standard deviation of 9. Approimately what percent of the students taking the test received a score greater than 90? () % (3) 0% () 5% (4) 6% 35 Mr. and Mrs. Douville have si children. What is the probability that there is eactly one female child? [Assume that P(male) = P(female).] 6 () (3) () (4) 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] 36 In the accompanying diagram of circle O, tangent BA, diameter AD, secant BCE, AD intersects BE at F, chords DE and DC are drawn, m AFB = 80, and mac = 00. A B E O D F C Find: a m BED [] b m BAF [] c med [] d m B [] e m EDC [] GO RIGHT ON TO THE NEXT PAGE Math. Course III June 00 [5] [OVER]

6 37 a On the same set of aes, sketch and label the graphs of the equations y = sin and y = 3 cos in the interval π π. [8] b Using the graphs drawn in part a, find the number of values of in the interval π π that satisfy the equation sin = 3 cos. [] 38 a Assume that in the United States 5 of all cars are red. Suppose you are driving down the highway and you pass 6 cars. () What is the probability that at most one of the cars you pass is red? [3] () What is the probability that at least four of the cars you pass are red? [3] b The scores on a mathematics test are 4, 5, 58, 64, 70, 76, 76, 8, 84, 88, 88, 90, 94, 94, 94, and 97. For this set of data, find the standard deviation to the nearest tenth. [4] 39 Find all values of in the interval 0 < 360 that satisfy the equation 4 cos 5 sin 5 = 0. Epress your answer to the nearest ten minutes or nearest tenth of a degree. [0] 40 a On the same set of aes, sketch and label the graphs of the equations y = 8 and = y. [6] b On the same set of aes used in part a, sketch the reflection of = y in the line y =. Label it b. [3] c Write an equation of the graph drawn in part b. [] 4 a Two forces of 50 pounds and 69 pounds act on a body to produce a resultant of 70 pounds. Find, to the nearest tenth of a degree or nearest ten minutes, the angle formed between the resultant and the smaller force. [6] b For all values of for which the epressions are defined, prove the following is an identity: (cot + csc )( cos ) = sin [4] 4 a Solve for and epress your answer in simplest a + bi form: 0 = 4 [6] b Epress in simplest form: [4] Math. Course III June 00 [6]

7 Tear Here Tear Here The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION SEQUENTIAL MATH COURSE III Wednesday, June, 000 :5 to 4:5 p.m., only ANSWER SHEET Part I Score Part II Score Total Score Rater s Initials: Pupil Se: Male Female Grade Teacher School Your answers to Part I should be recorded on this answer sheet. Part I Answer 30 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 00 [7]

8 Tear Here Tear Here Math. Course III June 00 [8]