# Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition. GEOMETRY and MEASUREMENT GRADE 7-8

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1 Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition INSTRUCTIONS GEOMETRY and MEASUREMENT GRADE 7-8 Do not open this booklet until instructed to do so. Time limit: 20 minutes Mark your answer on the answer sheet by FILLING in the oval. You may use calculators. For pi, use the key or on your calculator. You may not use rulers, protractors, or other measurement devices on this test. Letter E is None of the above or Not given. It may be the correct answer to some of the problems. The figures may not be drawn to scale. Area Formulas: Triangle Parallelogram Trapezoid Volume Formulas: Rect. Prism Cylinder A = bh/2 A = bh A = h(b1 + b2)/2 V = l*w*h V = π * r 2 * h Student Name Student Number School

2 Use the diagram dimensions of the sketch for a new sidewalk and pool to calculate questions #51-#53. Note: The sidewalk is uniform width of three feet. I I I I I I 20m I I I I I. I I I I I 50 m 51. What is the perimeter of the pool? A. 58 m B. 70 m C. 106 m D. 140 m 52. What is the area covered by the sidewalk only? A. 90m 2 B. 140m 2 C. 800 m 2 D m What is the volume of the pool if it is five feet deep? A. 400mm 3 B. 75mm 3 C. 85mm 3 D. 105mm 3 Use the right triangle for problems # 54 - # What is the area of this triangle? 13 cm A. 25 cm 2 B. 30 cm 2 C. 60 cm 2 D. 78 cm 2 12 cm 55. Which term best describes the right triangle classifying it by its sides? A. Equilateral B. Isosceles C. Scalene D. Acute 56. What is the sum of the angles in a right triangle? A. 45 o B. 60 o C. 90 o D. 180 o PAGE 1

3 Use the triangle in the coordinate plane for problems #57 - #62. On the graph Point A is the lowest point of the figure. If this was a map, A is the southern point of the triangle. 57. Classify the type of triangle in the diagram. A. Isosceles Right B. Scalene Acute C. Obtuse Isosceles D. Equilateral 58. If the figure is reflected across the x-axis, what would be the coordinates of reflection of point A? A. ( - 2, - 3) B. ( - 2, 3) C. ( 2, 3) D. ( -2, -3). 59. If the original figure is reflected over the y-axis, what would be the coordinates of A (the reflection of point A). A. ( - 2, - 3). B. (- 2, 3) C. ( 2, 3). D. ( - 2, - 3) 60. If the figure is translated < 2, - 5 >, where would A be located? A. ( -3, 3). B. (0, - 2). C. ( 4, - 2). D. ( 4, 8 ) 61. If you reflect the triangle first across the y-axis, and then across the x-axis, what would be the location of A? A. (2, 3) B. (-2, -3) C. (-2, 3) D. (2, -3) 62. If the triangle is stretched so that pt. A is placed vertically on the x-axis, what is the difference between the original area and the new area? A. 4 sq.units B. 5 sq. units C. 6 sq. units D. 8 sq. units 63. What is the circumference of a circle with diameter 10 km? Round to the nearest tenth. A km B km C km D km 64. If the area of a circle is cm 2, what is the radius? A. 9 cm. B. 8 cm C. 7 cm D. 6 cm PAGE 2

4 Use the figures below to respond to problems # A B C D E 65. Which of the above figures are quadrilaterals? A. A, B B. A, D, E C. B & E D. A, B, C, D & E 66. Which of the above figures are rectangles? A. A B. B C. C D. E 67. Which of the above figures are rhombuses? A. D & E B. B & E C. B D. E 68. Which of the above figures are parallelograms? A. A & B B. B & D C. A, B, D & E D. A, B, C & D 69. Which of the following statements is NOT true? A. A parallelogram is sometimes a rectangle, and a rectangle is always a parallelogram. B. A square is always a rectangle, but a rectangle is always a square. C. A trapezoid is always a quadrilateral, but a trapezoid is never a parallelogram. D. A rhombus is sometimes a square, but a square is always a rhombus. E. All statements are true. 70. Which term best describes figure on the right? Find the missing angle measure. Both must be true. A. Supplementary; 41 o B. Linear Pair; 51 o C. Linear Pair; 129 o D. Vertical; 129 o PAGE 3

5 Use the diagram below to answer problems # Name a line that is on Plane P and Plane R. A. AB B. FG C. CH D. IE 72. Name a point not on either Plane R or Plane P. A. C B. G C. F D. B Use the rectangular solid below to answer problems # Name a line segment that is parallel to segment XY on the rectangular solid. A. RU B. ST C. SX D. YZ 74. Name a line segment that is skew to XY A. UZ B. WX C. SX D. ST. 75. Name a line segment that is perpendicular to XY. A. YZ B. RW C. WZ D. UZ 76. Given: WZ is four less than twice ZY and ZY = UZ. If ZY = 9m, what is the volume of the rectangular solid? A. 1782m 3 B. 396m 3 C. 252m 2 D. 1134m 3 PAGE 4

6 Use the coordinate graph below for problems # What is the slope of AB? A. 1 B. 1/7 C. undefined D What is the slope of EF? A. 3/4 B. 0 C. -3/4 D. -4/3 79. Given the Pythagorean Theorem: In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse, find EF. A. 1 B. 3 C. 5 D What is the linear equation that best describes EF? A. y = -1 x B. Y = -1 x + 0 C. Y = - 1 x + 0 D. y = What is the linear equation for the line BA? A. y = 20 B. x = 15 C. x = 1 y D. y = 17x 5 PAGE 5

7 82. What is the total area in square meters of red rings on this dartboard? A. 8 π B. 10 π C. 11 π D. 16 π Note: Each band is 1 m in width. 83. How many unit squares would be in Stage 6? A. 30 B. 42 C. 56 D Provided l m, find the value of one acute angle labeled with x. A. x = 8.75 B. x = 20 C. x = 45 D. x = 70 PAGE 6

8 85. What are the measures of angle 2 in the diagram below? A. 72 o B. 82 o C. 98 o D. 108 o 86. Perimeter = 31 Find the value of x when the triangle has the following lengths for sides. x, 2x 5, 3x + 6 A. 1 B. 4 C. 5 D Find the exact circumference and the area of a circle with a radius of 5 cm. Circumference Area A. 5π cm 10π cm 2 B. 5π cm 25π cm 2 C. 10π cm 20 π cm 2 D. 10π cm 25 π cm Find the amount of tape that would wrap around this shape both directions once. A. 20 cm B. 24 cm C. 40 cm D. 48 cm PAGE 7

9 Volume Formulas: Rectangular Prism V = l * w * h Cylinder: V = π r 2 h 89. Find the volume of the T bar. A. 20 cm 3 B. 28 cm 3 C. 48 cm 3 D. 56 cm Find the volume of the cylinder post on a wind turbine with an 80 meters height and a base 50 feet in diameter. A. 80 π m 3 B. 225 π m 3 C π m 3 D π m 3 PAGE 8

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