The University of the State of New York REGENTS HIGH SHOOL EXMINTION THREE-YER SEQUENE FOR HIGH SHOOL MTHEMTIS OURSE II Wednesday, June, 000 :5 to 4:5 p.m., only Notice... Scientific calculators must be available to all students taking this examination. 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 examination, 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 examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer paper cannot be accepted if you fail to sign this declaration. DO NOT OPEN THIS EXMINTION OOKLET UNTIL THE SIGNL IS GIVEN.
Part I nswer 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] The set {a,b,c,d} and the operation i are shown in the accompanying table. What is the identity element for the operation? i a b c d a d a b c b a b c d c b c d a d c d a b In the accompanying diagram of isosceles triangle SUM, SM UM and MUD is an exterior angle formed by extending SU to D. If m MUD = 4, find m M. M 8 In the accompanying diagram, is a straight line, m D = 44, and E bisects D. Find m E. D 44 9 In the accompanying diagram, parallel lines and m are cut by transversal r, m = x + 40, and m = 5x 0. Find m. r E 4 S U D m In IG, m = 5 and m G = 66. Which is the longest side of this triangle? 4 Solve for the positive value of x: x + 4 = 4 x 5 If a translation maps (,5) to (,9), what are the coordinates of, the image of (, ) under the same translation? 6 If one of the roots of the equation x + kx = 8 is 4, find the value of k. 7 What is the total number of different four-digit numerals that can be formed using the digits, 9, 9, and 9? 0 In the accompanying diagram of SRT, LM RT. If SL = 4, LR =, and RT =, find LM. R L S Lake High School has nine mathematics teachers. How many different four-teacher committees can be formed from these nine mathematics teachers? Find the distance between points (4, 4) and (,). M T Math. ourse II June 00 []
In the accompanying diagram of right triangle, a right angle is at, = 6, and m = 7. Find the length of to the nearest tenth. 7 6 Directions (4 5): For each question chosen, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. 4 The coordinates of three of the vertices of rectangle RET are R(,), E(,), and (,5). What are the coordinates of vertex T? () ( 5,) () (,) () (,5) (4) (, 5) 5 What is the negation of the statement m q? () m q () m q () m q (4) m q 6 If the statements a b, b c, and a are true, which statement must also be true? () b () c () a (4) c 7 If a conditional statement is true, what must also be true? () the negation of the statement () the converse of the statement () the inverse of the statement (4) the contrapositive of the statement 8 Which statement is true about the lines formed by the graphs of the equations y = x and x = y? () They are identical. () They intersect but are not perpendicular. () They are parallel. (4) They are perpendicular. 9 Which graph represents the equation y = x? 0 If x # y = x y + y x, what is the value of # 5? () 0 () 4 () 5 (4) 57 The image of P(6, 9) after a dilation with respect to the origin is (4, 6). What is the constant of dilation? () () () (4) y 4 ( ) x 0 ( ) 4 ( ) y 0 4 5 6 In the accompanying diagram, ED, D and E are drawn, and. x ( 4 ) Triangle D can be proved congruent to triangle E by () HL HL () S S () SS SS (4) D 0 4 E y 4 6 5 4 0 y x x Math. ourse II June 00 [] [OVER]
The sum of x 6 + x + is x () x () () x 4 (4) x 4 x x x + 6 x 9 In the accompanying diagram, RST is a right triangle, SU is the altitude to hypotenuse RT, RT = 6, and RU = 7. S 4 Which equation represents the axis of symmetry of the graph of the equation y = x 4x + 5? () x = () y = () x = (4) y = 5 If each exterior angle of a regular polygon measures 40, what is the total number of sides in the polygon? () 5 () 8 () 6 (4) 9 6 What are the coordinates of, the image of point (4, ) after a reflection in the origin? () ( 4,) () ( 4, ) () (4,) (4) (,4) 7 Points,,, and D are midpoints of the sides of square JETS. J D S If the area of JETS is 6, the area of D is () 9 () 9 () 8 (4) 8 8 If a tree casts a 90-foot shadow at the same time that a -foot pole held perpendicular to the ground casts a 5-foot shadow, what is the height of the tree, expressed in feet? () 8 () 7 () 54 (4) 50 E T R U T What is the length of ST? () 7 () 9 () 4 7 (4) 0 The midpoint of is M, the coordinates of are (a,b), and the coordinates of are (a + 4,5b). What are the coordinates of M? () (,b) () (a + 4,6b) () (a +,b) (4) ( a+ 4, 5b ) If the graphs of the equations x + y = 6 and y = 4 are drawn on the same set of axes, what is the total number of points common to both graphs? () () () (4) 0 The roots of the equation x 6x = 0 are () ± () ± 7 () ± (4) ± 7 What is the slope of a line that is perpendicular to the line whose equation is y x = 5? () () () (4) 4 What is an equation of the straight line whose slope is and that passes through point (,0)? () y = x () x = y () y = x + 6 (4) x = y + Directions (5): Leave all construction lines on the answer sheet. 5 On the answer sheet, construct the angle bisector of. Math. ourse II June 00 [4]
nswers to the following questions are to be written on paper provided by the school. Part II nswer three questions from this part. learly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. alculations that may be obtained by mental arithmetic or the calculator do not need to be shown. [0] 6 Solve the following system of equations graphically or algebraically and check. y = x + x [8,] x + y = 7 The coordinates of the vertices of are ( 4,), (4,9), and (9, ). Point M(,6) lies on. a Show by means of coordinate geometry that M. [4] b Find, to the nearest degree, the measure of angle. [6] 8 a On graph paper, draw and label the graph of circle, which is represented by the equation x + y = 9. [] b On the same set of axes, draw the image of circle after the translation (x,y) (x + 5,y ) and label it. [] c On the same set of axes, draw the image of circle after a reflection in the x-axis and label it. [] d What is the area of the triangle formed by connecting the centers of the circles drawn in parts a, b, and c? [] 9 nswer both a and b. a For all values of y for which the expressions are defined, express the quotient in simplest form: y 6y y + y [5] y 7y 4 y 6 b Lorraine won a contest and can select six compact discs (D s) from a list of D s. The list contains 5 rock, jazz, and 4 classical D s. What is the probability that a random selection includes rock, jazz, and classical D s? [5] 40 In the accompanying diagram, ~ and = 4. a If is more than, and is 6 more than, find. [Only an algebraic solution will be accepted.] [8] b Using the results from part a, determine the smallest possible integral value of. Justify your answer. [,] GO RIGHT ON TO THE NEXT PGE Math. ourse II June 00 [5] [OVER]
nswers to the following questions are to be written on paper provided by the school. Part III nswer one question from this part. learly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. alculations that may be obtained by mental arithmetic or the calculator do not need to be shown. [0] 4 Given: If Mike is the catcher, then Robin plays first base. If Uk-Hae is not in the lineup, Mike is the catcher. If Edgardo plays second base and Robin plays first base, then Luis is the centerfielder. Luis is not the centerfielder. Edgardo plays second base. 4 Given: E is the midpoint of D, D, D D,, E, and E are drawn, and. Let E represent: Edgardo plays second base. Let L represent: Luis is the centerfielder. Let M represent: Mike is the catcher. Let R represent: Robin plays first base. Let U represent: Uk-Hae is in the lineup. Prove: Uk-Hae is in the lineup. [0] E Prove: D [0] D Math. ourse II June 00 [6]
Tear Here Tear Here The University of the State of New York REGENTS HIGH SHOOL EXMINTION SEQUENTIL MTH OURSE II Wednesday, June, 000 :5 to 4:5 p.m., only NSWER SHEET Part I Score............ Part II Score............ Part III Score............ Total Score............ Rater s Initials:.............. Pupil............................................... Sex: Male Female Grade........... Teacher............................................. School................................... Your answers to Part I should be recorded on this answer sheet. Part I nswer 0 questions from this part..................................................................................................................................................................................................................................... 4................... 4................... 4................... 4................... 5................... 5................... 5................... 5 6................... 6................... 6................... 7................... 7................... 7................... 8................... 8................... 8................... 9................... 9................... 9................... 0................... 0................... 0................... nswer question 5 on the other side of this sheet. Math. ourse II June 00 [7] [OVER]
5 Tear Here Your answers for Part II and Part III should be placed on paper provided by the school. The declaration below should be signed when you have completed the examination. I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior to the examination and that I have neither given nor received assistance in answering any of the questions during the examination. Signature Tear Here Math. ourse II June 00 [8]
FOR TEHERS ONLY The University of the State of New York REGENTS HIGH SHOOL EXMINTION THREE-YER SEQUENE FOR HIGH SHOOL MTHEMTIS OURSE II Wednesday, June, 000 :5 to 4:5 p.m., only SORING 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 llow 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.] llow no partial credit. For questions 4 4, allow credit if the student has written the correct answer instead of the numeral,,, or 4. () b () 6 () () () 68 () () () () I ().8 () 4 () (4) 4 (4) (4) (4) (5) (5,) (5) (5) 4 (5) construction (6) (6) (6) (7) 4 (7) 4 (7) 4 (8) 68 (8) (8) (9) 00 (9) (9) 4 (0) (0) 4 (0) [OVER]
SEQUENTIL MTH OURSE II concluded Part II Please refer to the Department s publication Guide for Rating Regents Examinations in Mathematics, 996 Edition. are should be exercised in making deductions as to whether the error is purely a mechanical one or due to a violation of some principle. 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) (0, ), ( 4,5) [8] heck [] (7) b 58 [6] (8) d 5 [] y (9) a [5] y + b 80 [5] 94 (40) a [8] b [] triangular inequality or an equivalent answer [] s a reminder... Regents examinations based on the Sequential Mathematics, ourse II, syllabus will not be offered after January 00. Regents examinations based on the Sequential Mathematics, ourse I, syllabus will not be offered after January 00.