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 University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Friday, January 5, 00 9:5 a.m. to :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. 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 Jan. 0 []

3 Part I Answer 0 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] 0 p Epress radians in degree measure. In the accompanying diagram, BA is a diameter and m BC = 50. Find m CBA. C 50 B A 8 If varies inversely as y, and = 8 when y =, find the value of when y = 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? y y 6 In the accompanying 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 y ( ) ( ) y 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 y = 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 accompanying diagram of a unit circle, the ordered pair (,y) represents the point where the terminal side of intersects the unit circle. If = 50, what is the value of? () () (,y) () (4) 7 Which equation has roots i and + i? () = 0 () = 0 () = 0 (4) = 0 y 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 + y = 8 forms () a straight line () a hyperbola () 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 inequality 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 () imaginary () 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 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 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 sin + = csc. [0] 7 a On the same set of aes, sketch and label the graphs of the equations y = cos and y = 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 satisfy the equation cos = tan. [] 8 a On the same set of aes, sketch and label the graphs of the equations below: () y = 9 in the interval 9 9 [] () y = in the interval [] b On the same set of aes, sketch the reflection of y = 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 accompanying 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 playground at a day-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: y = 4. F Find, to the nearest tenth, when y = 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 played. 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 probability that bus A will arrive on time is 5. Yolanda takes this bus on 4 consecutive 6 days. Find the probability that this bus will arrive on time: () all 4 days [] () at least days [] 4 a Solve for and epress your answer in simplest a + bi form: = [5] 4 b Prove the following identity: sin q sec [5] = q sin q + cos q cot q Math. Course III Jan. 0 [6]

7 Tear Here Tear Here The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION SEQUENTIAL MATH COURSE III Friday, January 5, 00 9:5 a.m. to :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 Jan. 0 [7]

8 Tear Here Tear Here Math. Course III Jan. 0 [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 Friday, January 5, 00 9:5 a.m. to :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, 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, allow credit if the student has written the correct answer instead of the numeral,,, or 4. () 600 () () 4 () () 65 () () () () 8 () 4 () () (4) 9 (4) (4) (4) (5) 7 (5) 4 (5) (5) (6) 0 (6) (6) (7) 6 (7) 4 (7) 4 (8) 4 (8) 4 (8) (9) b (9) (9) b a (0) 86 (0) (0) 4 [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)., 57.7, 4.5, 98.5 or [0] 0', 57 40', 4 0', 98 0' (7) b [] (8) cy= [] (9) a 40 [] b 90 [] c 40 [] (40) a 4. [6] b. [4] (4) a () 8.4 [] () 6.8 [] () 6 [] b () 65, 96 [] (), 5, 96 [] (4) a ± i [5] d 0 [] e 00 [] As a reminder... Regents eaminations based on the Sequential Mathematics, Course I, syllabus will not be offered after January 00. Regents eaminations based on the Sequential Mathematics, Course II, syllabus will not be offered after January 00. Regents eaminations based on the Sequential Mathematics, Course III, syllabus will not be offered after January 004.

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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