The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE III. Friday, January 25, :15 a.m. to 12:15 p.m.

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1 The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Frida, Januar 5, 00 9:5 a.m. to :5 p.m., onl Notice... Scientific calculators must be available to all students taking this eamination. The formulas that ou ma 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, slowl and carefull, tear off the answer sheet. Then fill in the heading of the answer sheet. When ou have completed the eamination, ou must sign the statement printed at the end of the answer sheet, indicating that ou had no unlawful knowledge of the questions or answers prior to the eamination and that ou have neither given nor received assistance in answering an of the questions during the eamination. The answer sheet cannot be accepted if ou fail to sign this declaration. DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

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3 Part I Answer 0 questions from this part. Each correct answer will receive credits. No partial credit will be allowed. Write our answers in the spaces provided on the separate answer sheet. Where applicable, answers ma be left in terms of π or in radical form. [60] 0 p Epress radians in degree measure. In the accompaning diagram, BA is a diameter and m BC = 50. Find m CBA. C 50 B A 8 If varies inversel as, and = 8 when =, find the value of when = 6. 9 Epress in simplest form: 0 Evaluate: 6 Â k= k a a b If f() = + and g() =, find (f g)(). Epress in simplest form: Find the value of 7. 4 Solve for : = Directions ( 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 In ABC, m A = 5, m C = 60, and AC = meters. Find the length of BC nearest meter. to the Which graph does not represent a function? 6 In the accompaning diagram of a circle, chords AB and CD intersect at E, CE = 5, CD =, and AE = 4. Find the length of BE. C E A ( ) ( ) D B ( ) ( 4 ) 7 In a circle with a radius of 4 centimeters, what is the number of radians in a central angle that intercepts an arc of 4 centimeters? Math. Course III Jan. 0 [] [OVER]

4 4 The amplitude of the graph of the equation = sin is p () () () 6p (4) 5 If n = , what is the value of n? () () () (4) 6 The value of sin 70 cos 0 cos 70 sin 0 is () () () (4) 5 7 If sin A = and cos A > 0, angle A terminates in Quadrant () I () III () II (4) IV 8 Which epression is equivalent to? () () + + () (4) ( ) + 9 What is the best approimation for the area of a triangle with consecutive sides of 4 and 5 and an included angle of 59? () 5.0 () 0.0 () 8.6 (4) 7. 0 If A = pr, log A equals () log p + log r () log p + log r () log p + log r (4) p log r The value of tan (Arc sin ) is () () 90 () (4) undefined The solution set of the equation + = 9 is () {} () {,} () { } (4) {,} The solution set of the equationω Ω+ 4 = 8 is () {} 5 () { } () { 5, } (4) {} 4 What is the image of point (,) after a reflection in the line =? () (5,) () (,) () (,) (4) (, ) 5 For all values of for which the epression is sec q defined, is equivalent to csc q () sin () tan () cos (4) cot 6 In the accompaning diagram of a unit circle, the ordered pair (,) represents the point where the terminal side of intersects the unit circle. If = 50, what is the value of? () () (,) () (4) 7 Which equation has roots i and + i? () = 0 () = 0 () = 0 (4) = 0 Math. Course III Jan. 0 [4]

5 8 What is the domain of the function 4 f() = + 5 over the set of real numbers? () {Ω > 5} () {Ω 5} () {Ω < 5} (4) {Ω = 5} 9 What is one possible value of in the equation cot = cos? () 0 () 90 () 45 (4) 80 0 The graph of the equation 4 + = 8 forms () a straight line () a hperbola () an ellipse (4) a parabola If m A = 8 0, a = 0, and b = 5, what is the maimum number of distinct triangles that can be constructed? () () () (4) 0 The solution set for the inequalit is () 5 () 5 or () or 5 (4) 5 To the nearest degree, what is the measure of the largest angle in a triangle with sides measuring 0,, and 8 centimeters? () 09 () 7 () 8 (4) 4 The roots of the equation = 0 are () imaginar () real and irrational () real, rational, and unequal (4) real, rational, and equal 5 The epression (i )(i + ) is equivalent to () () i + () i (4) i Answers to the following questions are to be written on paper provided b the school. Part II Answer four questions from this part. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Calculations that ma be obtained b mental arithmetic or the calculator do not need to be shown. [40] 6 Find, to the nearest ten minutes or nearest tenth of a degree, all values of in the interval 0 < 60 that satisf the equation 6 sin + = csc. [0] 7 a On the same set of aes, sketch and label the graphs of the equations = cos and = tan in the interval p p. [8] b Using the graph sketched in part a, find the number of values of in the interval p p that satisf the equation cos = tan. [] 8 a On the same set of aes, sketch and label the graphs of the equations below: () = 9 in the interval 9 9 [] () = in the interval [] b On the same set of aes, sketch the reflection of = in the -ais in the interval. Label the reflection b. [] c Write an equation of the graph sketched in part b. [] Math. Course III Jan. 0 [5] [OVER]

6 9 In the accompaning diagram of circle O, tangent AB and chord BC are drawn, secant ACD intersects diameter EB at F, m BD = 60, and m BC = 80. A C Find: a m A [] b m ABE [] c m ABC [] d m EFC [] e m ACB [] E 40 a The plaground at a da-care center has a triangular-shaped sandbo. Two of the sides measure 0 feet and 4.5 feet and form an included angle of 45. Find the length of the third side of the sandbo to the nearest tenth of a foot. [6] b Given: = 4. F Find, to the nearest tenth, when = 6. [4] D O B 4 a Christina participated in 0 basketball games this season. The scorekeeper recorded the number of shots she attempted in each game. The table below shows the number of shots she attempted in the number of games she plaed. Shots Attempted Number of Games () Find the mean number of shots that Christina attempted. [] () Find the standard deviation of the shots attempted to the nearest tenth. [] () What is the total number of games in which the number of shots attempted fell outside one standard deviation of the mean? [] b The probabilit that bus A will arrive on time is 5. Yolanda takes this bus on 4 consecutive 6 das. Find the probabilit that this bus will arrive on time: () all 4 das [] () at least das [] 4 a Solve for and epress our answer in simplest a + bi form: = [5] 4 b Prove the following identit: sin q sec [5] = q sin q + cos q cot q Math. Course III Jan. 0 [6]

7 Tear Here Tear Here The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION SEQUENTIAL MATH COURSE III Frida, Januar 5, 00 9:5 a.m. to :5 p.m., onl 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 b the school. The declaration below should be signed when ou have completed the eamination. I do hereb 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 an of the questions during the eamination. Signature Math. Course III Jan. 0 [7]

8 Tear Here Tear Here Math. Course III Jan. 0 [8]