# TENTH YEAR MATHEMATICS

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3 17 Tangents PD and PE intersect a circle at D and E, respectively, and chord ED is drawn. If mlp = 40, what is the measure of LPED? (1) 70 (3) 40 (2) 90 (4) In a right triangle, the altitude to the hypotenuse divides the figure into two right triangles which are always (1) equal in area (2) equal in perimeter (3) similar (4) congruent 19 The total number of points in a plane that are distance d from a given straight line and are also distance r from a certain point on the line could not be (1) 0 (2) 2 (3) 3 (4) 4 24 If LABC is similar to LDEF with vertices A, B, and C corresponding to vertices D, E, and F, respectively, which statement is true? (1) AB = BC DE DF (2) AB = DE AC DF (3) AB = EF DE BC (4) AB = DF AC DE 25 In the accompanying figure, the length of a side of the square is 6. What is the area of the circle inscribed in this square? 6T 20 Two parallel lines are cut by a transversal. The bisectors of a pair of interior angles on the same side of the transversal intersect to form an angle that is (1) always acute (2) always right (3) always obtuse (4) either acute or obtuse, but never right 21 The length of a side of a regular 8-sided polygon is s and the length of its apothem is a. What is the area of the polygon? (1) 6as (2) 8as (3) 3as (4) 4as 22 In a regular polygon, the sum of the measures of the interior angles is 540. What is the total number of sides of this polygon? (1) 5 (3) 9 (2) 7 (4) The coordinates of the vertices of rectangle ABCD are A(O,O), B(O,4), C(5,4), and D(5,O). The length of a diagonal is (1) 5 (2) ffi (3) 3 (4) 4 (1) 36?r (2) 12?r (3) 9?r (4) 6?r 26 The ratio of the perimeters of two regular pentagons is 4:1. The ratio of their apothems is (1) 2:1 (3) 8:1 (2) 4:1 (4) 16:1 27 Which quadrilateral can not always be inscribed in a circle? (1) isosceles trapezoid (2) rectangle (3) rhombus (4) square 28 Which statement about a diagonal of a parallelogram is always true? (1) It bisects the other diagonal of the parallelogram. (2) It bisects an angle of the parallelogram. (3) It is congruent to the other diagonal of the parallelogram.. (4) It is perpendicular to the other diagonal of the parallelogram. Math. lo-jan. '89 [3] [OVER]

4 29 Which equation represents the locus of points equidistant from points (2,4) and (2,2)? (1) x = 3 (3) x = 2 (2) y = 2 (4) y = 3 Directions (30): Leave all construction lines on the answer sheet. 30 On the answer sheet, construct the altitude from vertex A to side BC of 6ABC. Math. lo-jan. '89 [4]

5 Answers to the following questions are to be written on paper provided by the school. Part II Answer four questions from this part. Show all work unless otherwise directed. [40] 31 Prove either a or b but not both. a The sum of the measures of the angles of a triangle is 180 degrees. [10] OR b Two right triangles are congruent if the hypotenuse and a leg of one are congruent to the corresponding parts of the other. [io] ~ - 33 Given: AB with ~1 the midpoint of AB. a Describe fully the locus of points: (1) equidistant from points A and B [:3] ~ (2) 4 units from AB [.3] (3) 4 units from point M [:3] b What is the total number of points that satisfy all three conditions described in part a? [1] 32 Given: circle 0, chord AB II chord DC, secants EAD and EBG, tangent RCF, mad = 90, and rodg = 120. E 34 Given: 6ABC, D is the midpoint of AB, F is the midpoint of AC, BEGC, BE == CG, LB == LG, and Ll is supplementary to L2. B F A F c Prove: a DE == FC [7] b DE II FC [:3] H 35 Given: circle 0, chord CE, secants ABC and ADE, and BC == DE. Find: a mae b InLD c mldgh d mle e mlabe A Prove: AB == AD [10] ~ GO RIGHT ON TO THE NEXT PAGE. Math. IO-Jan. '89 [5] [OVER1

6 36 The radius of a regular IO-sided polygon is 6. a Find the length of the apothem to the nearest tenth. [4] b Find the length of a side of the polygon to the nearest tenth. [4] c Using the results obtained in parts a and b, find the area of the polygon to the nearest integer. [2] 37 Show, by means of coordinate geometry, that the quadrilateral whose vertices are A(O,5), B(3,4), C(O,-5), and D(-3,-4) is a rectangle. State a reason for your conclusion. [10] Math. lo-jan. '89 [6]

7 THE UNIVERSITY OF THE STATE OF NEW YORK THE STATE EDUCATION DEPARTMENT DIVISION OF EDUCATIONAL TESTING Tables of Natural Trigonometric Functions (For use with 10th Year Mathematics Regents Examinations) Angle Sine Cosine Tangent Angle Sine Cosine Tangent , , Math. lo-jan. '89 [9]

8 The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION TENTH YEAR MATHEMATICS Thursday, January 26, I: 15 to 4:15 p.m., only Part I Score. Part II Score. 'rota}.... "'. ANSWER SHEET Rater's Initials:. Pupil rea{~her. School. Name and author of textbook used. Your answers to Part I should be recorded on this answer sheet. Part I Answer all questions in this part ' ~ Answer question :30 on the other side of this sheet. Math. 10-1an. '89 [11]

9 30 A B"" _~ C 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 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 Math. lo-jan. '89 {l2j

10 FOR TEACHERS ONLY 10 SCORING KEY TENTH YEAR MATHEMATICS Thursday, January 2fi, I HS~' - I:) 5 to,!:15 p.m., only USt~ nul)' red ink or red pencil in rating Ht ~t"nts papers. Do not attempt to onrcct till" pupil's work by making insertions Of changes of any kind. VS(~ eheekmarks to indieate pupil 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 omis SiOBS. Part I Allow 2 credits for each correct answer; allow no partial credit. For questions 14-29, allow credit if the pupil has written the correct answer instead of the numeral 1, 2, :3, 01'4. (1) 50 (II) 18 (21) -1 (2) 120 (12) 40 (22) 1 (3) 3 (13) 3 (23) 2 (4) (-2,1) m"). := -2 (14) 2 (24) 2!I := 1 (5) 8 (15) 4 (25) :1 (6) 13 (Hi) 4 (2ll) 2 (7) 15 (17) I (27) a (8) 15 (18) 3 (28) 1 (9) 8 (19) 3 (29) 4 (10) 6 (20) 2 (30) construction [ovu)

11 TENTH YEAR MATHEMATICS - concluded Part II Please refer to the Department publication Guide for Rating Regents Examinations in Mathematics. Care should be exercised 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 10 percent, while an error due to a violation of some cardinal principle should receive a deduction ranging from 30 percent to,so percent, depending on the relative importance of the principle in the solution of the problem. (32) a 60 b 75 c 60 d 30 e 75 (36) a,s.7 b 3.7 c 105 (33) a (1) the perpendicular bisector of AB or ~] a line perpendicular to AB through M ~ (2) 2 lines parallel to AB and 4 units ~ on either side of AB [3] (3) a circle with center M and radius 4 [3] b 2 [1] As a reminder... This is the last Regents examination based on the Tenth Year Mathematics syllabus.

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