The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Tuesday, January 22, :15 to 4:15 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 II Tuesda, Januar, 00 1:15 to 4:15 p.m., onl Notice... Scientific calculators must be available to all students taking this eamination. 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.

2 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] 1 In ABC, D is a point on AB and E is a point on AC such that DE Ω BC. If AB = 1, AC = 18, and AD = 4, find the length of AE. The operation for the set {S,M,I,L,E} is defined in the accompaning table. If S M = E, solve for. S M I L E S S M I L E M E S M I L I L E S M I L I L E S M E M I L E S What is the area of the triangle whose vertices are (,1), (7,1), and (6,4)? 4 In ABC, m B is 4 more than twice m A, and m C is 1 more than m B. What is the longest side of ABC? 5 In the accompaning diagram of RET, side RT is etended through T to C. If m ETC = , m RET = + 50, and m ERT = 4 0, find the value of. E 7 In the accompaning diagram, CAB is parallel to DOG, AO is a transversal, m CAO =, and m DOA = Find m CAO. C A () ( + 40) D O 8 What is the total number of different five-person committees that can be formed from a group of eight people? 9 What is the total number of different eight-letter arrangements that can be formed from the letters in the word TOMATOES? 10 The lengths of the bases of an isosceles trapezoid are 0 and 44, and the length of the altitude is 16. Find the length of a leg of the trapezoid. 11 Find the image of point P( 6,5) under a reflection in the origin. Directions (1 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. B G R T C 1 If is a binar operation defined b a b = a b + b a, the value of is (1) 1 () 17 () 15 (4) 15 6 Find the distance between the two points whose coordinates are ( 5, 4) and (,). Math. Course II Jan. 0 []

3 1 Which graph represents the locus of points units from the origin? 14 The coordinates of the vertices of right triangle SUE are S(6,0), U(0,8), and E(0,0). What are the coordinates of the midpoint of the hpotenuse? (1) (,4) () (0,4) () (,0) (4) (, 8 ) 15 If ( ) = 5, then is equal to (1) ± 5 () 5 ± () ± 5 (4) ± 5 16 When two parallel lines are cut b a transversal, which angles are not alwas congruent? (1) a pair of alternate interior angles () a pair of alternate eterior angles () two interior angles on the same side of the transversal (4) two corresponding angles 17 A triangle that has vertices (1,1), ( 4,1), and (,) is (1) a right triangle () an isosceles but not an equilateral triangle () an equilateral triangle (4) a scalene triangle ( 1 ) ( ) ( ) ( 4 ) 18 What is the negation of the statement Suzanne likes to rollerblade and Bran likes to work out at the gm? (1) Suzanne likes to rollerblade and Bran does not like to work out at the gm. () Suzanne does not like to rollerblade or Bran does not like to work out at the gm. () Suzanne does not like to rollerblade and Bran does not like to work out at the gm. (4) Bran likes to rollerblade and Suzanne likes to work out at the gm. 19 In right triangle DEF, m E = 90, DE = 8, EF = 15, and FD = 17. What is the value of tan F? (1) () () (4) 0 Which tpe of quadrilateral has diagonals that will alwas divide it into four congruent triangles? (1) rhombus () trapezoid () rectangle (4) isosceles trapezoid 1 Point A (1,4) is the image of point A(,1) under a dilation with respect to the origin. What is the constant of dilation? (1) 9 () 1 () (4) What is a solution for the sstem of equations = + 4 and = + 4? (1) (,8) () ( 1,) () (0,4) (4) (,8) What is + + 1, 0, epressed as a 5 single fraction? (1) + + () 8 15 () (4) If the lengths of two sides of a triangle are 6 and 7, the length of the third side ma be (1) 1 () 1 () 1 (4) 14 Math. Course II Jan. 0 [] [OVER]

4 5 Which diagram represents the graph of the equation = 1? 0 0 ( 1 ) ( ) 0 The accompaning diagram shows the graph of the parabola = a + b + c ( ) ( 4 ) What must be one root of the equation a + b + c = 0? (1) 4 () 0 () (4) 4 6 If the statements c, c Æ d, and p Æ ~d are true, which statement must also be true? (1) p () ~d () ~p (4) c Æ p 7 The graph of the equation ( ) + ( + ) = 6 is a circle. What are the radius and the center of this circle? (1) radius 6, center (,) () radius 6, center (, ) () radius 6, center (,) (4) radius 6, center (, ) 8 A base angle of an isosceles triangle measures 0, and the length of one of the legs is 1. What is the length of the altitude drawn to the base of the triangle? (1) 6 () 6 () 1 (4) 9 9 Which equation represents a line that is perpendicular to the graph of the line = ? 1 (1) = + 6 () = () = + 6 (4) = Which epression is the complete factorization of 18? (1) (16 9 ) () ( + 4)( 4) () (4 ) (4) (4 )(4 + ) What is the turning point of the parabola whose equation is = 4 +? (1) (, 1) () (, 9) () (,7) (4) (, 1) Which construction is shown in the accompaning diagram? A (1) the bisector of ACD () the midpoint of DF () the perpendicular bisector of AB (4) a perpendicular line to AB from point D D F C E B Math. Course II Jan. 0 [4]

5 4 The altitude drawn to the hpotenuse of a right triangle divides the hpotenuse into segments of lengths 4 and 1. The length of the shorter leg of the right triangle is (1) 8 () 48 () 0 (4) 19 5 If each interior angle of a regular polgon measures 170, what is the total number of sides in the polgon? (1) 10 () 18 () 17 (4) 6 Answers to the following questions are to be written on paper provided b the school. Part II Answer three 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. [0] 6 a Draw and label the graph of the equation = for all values of in the interval 4. [6] b On the same set of aes, draw the image of the graph drawn in part a after a reflection in the -ais and label it b. [] c What is the equation of the ais of smmetr of the graph drawn in part b? [] 7 a In right triangle PQR, altitude RS is drawn to hpotenuse PQ, RS = 1, and PS is 7 more than QS. Find QS. [6] b Solve for, 0 and 1: 4 + = a For all values of k for which these epressions are defined, epress the product in simplest form: k 7k k + k [5] k + 4k + 6k b Christine plans to rent si videos for the weekend. She has narrowed her selection to four comedies, eight msteries, and three musicals. What is the probabilit that she randoml selects two comedies, three msteries, and one musical? [5] [4] 9 Solve the following sstem of equations graphicall or algebraicall and check: + = 5 [8,] = 1 40 In the accompaning diagram of HMA, MT is drawn, m A = 90, m MHA = 4, m AMT = 5, and HM = 76.7 meters m 5 4 H T A a Find, to the nearest tenth of a meter, the length of (1) MA [] () HA [] b Using the results from part a, find the area of HMT to the nearest square meter. [6] M Math. Course II Jan. 0 [5] [OVER]

6 Answers to the following questions are to be written on paper provided b the school. Part III Answer one question 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. [10] 41 Given: If Ale does not score well on his final eams and Ale does not earn an academic scholarship, then he does not go to college. If Ale does not stud, then he does not score well on his final eams. If Ale gets involved in too man etracurricular activities, then Ale does not stud. Ale gets involved in too man etracurricular activities. Ale goes to college. Let C represent: Ale goes to college. Let E represent: Ale earns an academic scholarship. Let F represent: Ale scores well on his final eams. Let S represent: Ale studies. Let X represent: Ale gets involved in too man etracurricular activities. Prove: Ale earns an academic scholarship. [10] 4 The vertices of quadrilateral ABCD are A( 1,1), B(4,5), C(9,1), and D(4, ). Using coordinate geometr, prove that a ABCD is a rhombus [5] b ABCD is not a square [5] Math. Course II Jan. 0 [6]

7 Tear Here Tear Here The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION SEQUENTIAL MATH COURSE II Tuesda, Januar, 00 1:15 to 4:15 p.m., onl ANSWER SHEET Part I Score Part II Score Part III 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 and Part III 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 II Jan. 0 [7]

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