Arkansas Council of Teachers of Mathematics Regional Exam. Geometry

Transcription

1 rkansas ouncil of Teachers of Mathematics 2014 Regional xam Geometry In each of the following please select the appropriate answer for each question and record the corresponding letter on the answer sheet. ny erasure on the answer sheet should be completely erased to avoid errors in scoring the exam. nswer each of the 25 questions prior to working on the Tie reaker questions as they will be used only to break ties for first, second and/or third place. Figures are not necessarily drawn to scale. In some of the questions you may want to draw a figure when none is given. 1. The statement Jack gets his weekly allowance if he takes the garbage out is true. Which of the following statements is also true?. Jack does not take the garbage out or he gets his weekly allowance.. Jack does not take the garbage out and he gets his weekly allowance.. Jack does not get his weekly allowance or he takes the garbage out.. Jack takes the garbage out and he does not get his weekly allowance.. None of these. 2. In the figure at the right the measure of angle() is 0 o. If the measures of = (2x 1) o, = (x + 5) o and = 3x o then the measure of is. 52 o. 56 o o o. None of these 3. What is the supplement of the angle whose complement is 38 o? 3x (x+5) (2x-1) Problem # o. 138 o. 118 o. 132 o. None of these 4. In the figure is the midpoint of. Which of the following statement(s) is/are true? P: Q: R: rea( ) = rea( ). P, Q. P, R. Q, R. P. None of these Problem #4 Page 1

2 rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest 5. In the figure m OP = (2x + ) o and m OQ = (290 3x) o. In terms of x, what is m POQ?. (-x + 120) o. (x 120) o. (-x + 300) o. (300 x) o. None of these P Q O Problem #5 6. In the quadrilateral, the diagonals bisect each other at. Which of the following statements is/are true? P. Q: R: is a parallelogram. Only P and R. Only Q, R. Only P and Q. P, Q, R. None of these Problem #6 7. Which of the following statements is/are true about a parallelogram. raw a figure. P: and are complementary angles. Q: R: bisects. P. Q. R. P, Q, R. None of these 8. In the figure and. Which of the following statements has to be true?..... None of these 9. The orthocenter of a triangle is the point of intersection of the Problem #8. medians. bisectors. altitudes. Perpendicular bisectors of the sides. None of these. In, bisects and bisects. If m = 115 o, then m =. Not enough information. 30 o. 40 o. 50 o. None of these 115 Problem # Page 2

3 rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest 11. It is given that is an exterior angle of. Which of the following has to be true? [raw a figure]. m > m. m > m. m + m = m. m + m > m. None of these 12. In the figure F bisects and F. Which of the following is/are true? P: F Q: F R: F. P, Q, R. P, Q. P, R. Q, R. None of these F Problem # triangle has an area of 20 sq ft. If the altitude is halved and the corresponding base is tripled the new triangle has an area of. 15 sq ft. 36 sq ft. 30 sq ft. 24 sq ft. None of these 14. ~ F and = 2.5. If the area of F = 325 in 2 then the area of is. 130 in in in in 2. None of these 15. In the figure = 3, = 8 and =. etermine None of these 8 3 Problem # The diagonals of a rhombus measure cm and 24 cm. The perimeter of the rhombus is [raw a figure]. Not enough information. 68 cm. 60 cm. 52 cm. None of these Page 3

4 rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest 17. The diagonal of a square is ft. The area of the square is. 25 ft 2. 0 ft ft ft 2. None of these 18. The perimeter of a rectangle is 84 cm. If the length of the rectangle is 6 more than the width, the length of the diagonal (to the nearest tenth of a centimeter) is [raw a figure] cm cm cm cm. None of these 19. The circle at the right is a unit-circle centered at the origin. If PQ at and the coordinates of are ( 3, 0), then the coordinates of P are 4. ( 3, 1 ) 4 4. (3, 7 ) (3, 7 ) 4 4. ( 3, 1 ) 4 2. None of these O Problem # In the circle at the right the chord is the perpendicular bisector of the radius OR at M. If the diameter of the circle is 12, then the length of the arc(r) is P Q. 3π. 4π. 6π. Not enough information. None of these O M R Problem # The point (a,b) is reflected in both the x-axis and the y-axis. The distance between the two images of these reflections is [raw a figure]. 2a + 2b. 2 a 2 + b 2. 2a. 2b. None of these 22. The point (4,0) is rotated 60 o in a counterclockwise direction about the origin. The coordinates of the image are [raw a figure]. (2 3, 2). (2, 2 3). ( 2, 2 3). ( 2 3, 2). None of these Page 4

5 rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest 23. onsider and F as shown. Which of the following statements is true?. The triangles are right triangles. m > m. = 21. = 21. None of these F Problem # The parallel sides of an isosceles trapezoid measure 20 and 50. The area of the trapezoid is What is the perimeter of the trapezoid to the nearest hundredth? [raw a figure] None of these 25. In the figure if, then determine the value of x = x None of these Problem #25 e sure you have answered each of the previous 25 questions before proceeding to the tie-breaker questions. The tie-breakers will only be used to break ties for 1 st, 2 nd, and/or 3 rd place. They will be used in the order given to break the ties so begin with the first tiebreaker question. Page 5

6 rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest Name Tie-reaker 1 is a square with a side of. If is the midpoint of and, and F are collinear find F. F Tie reaker #1 Page 6

7 Name rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest Tie-reaker 2 In the figure at the right determine which sign (<, =, >) replaces? in the following. Give all the necessary reasons for your conclusions.? _ Q Q S 60 Tie reaker #2 T Page 7

8 Name rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest Tie-reaker 3 Use right triangle trigonometry to determine y to the nearest hundredth. y x Tie reaker #3 Page 8

9 rkansas ouncil of Teachers of Mathematics 2014 Geometry Regional ontest Key Geometry KY Tie-reaker Questions 1. is a square with a side of. If is the midpoint of and, and F are collinear find F. ecause F ~ F, F = F+. Therefore, F =. 5 Since (F) 2 + () 2 = (F) 2, then F = = 500 So, F = 5. x Tie reaker #1 5 F 2. In the figure at the right determine which sign (<, =, >) replaces? in the following. Give all the necessary reasons for your conclusions.? _ Q ompute remaining angles in the figure. > S since S is the larger angle in its triangle. S > T since TS is the larger angle in its triangle. T > Q since TQ is the larger angle in its triangle. Therefore, > Q S Tie reaker # T 66 Q 3. Use right triangle trigonometry to determine y to the nearest hundredth. y sin 40 o = x and tan 40o = y x. = y sin 40 o tan 40 tan 40o Therefore, o. So, y =. sin 40 o So y = Thus rounding, y = Watch for premature rounding to hundredths. x Tie reaker #3 Page 9