Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition
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1 Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 6 INSTRUCTIONS 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 are not to scale. Area Formulas: Triangle Parallelogram Trapezoid Volume Formulas: Rect. Prism Cylinder A = bh 2 A = bh A = h(b 1 + b 2 ) 2 V = lwh V = πr 2 h Student Name Student Number School
2 Use the following composite shape for problems # What is the perimeter of the L shaped figure? A. 72mm B. 51mm C. 71mm D. 120mm 52. What is the area of the L shaped figure? A. 120mm 2 B. 140mm 2 C. 150mm 2 D. 170mm If a diagonal line (see dashed line above) was drawn to form 2 trapezoids, what would be the area of the trapezoid on the left? A. 41mm 2 B. 75mm 2 C. 105mm 2 D. 85mm 2 Use the triangle on the right for problems # What is the area of the right triangle? A. 13cm 2 B. 18cm 2 C. 26cm 2 D. 6.5mm 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 two acute angles in the right triangle? A. 45 o B. 60 o C. 75 o D. 180 o PAGE 1
3 Use the composite shape in the coordinate plane for problems # In which quadrant is the figure located? A A. I B. II C. IIII D. IV 58. If you reflect the figure below across the y-axis, what would be the coordinates of the A (the reflection of pt. A)? A. (-1, 4) B. (1, 4) C. (4, 1) D. (4, -1) 59. What is the area of the figure? A. 10 units B. 10 sq. units C. 5 units D. 5 sq. units Use the triangle in the coordinate plane for problems # What are the coordinates of pt. A? A. (2, 3) B. (3, 2) C. (-2, 3) D. (-2, -3) A 61. If you translate the triangle down 4 and left 1, what would be the new coordinates of A, called A? A. (1, -1) B. (2, -1) C. (3, -1) D. (2, -2) 62. What is the area of the triangle? B. 4 units B. 4 sq. units C. 8 units D. 8 sq. units km = m A. 50m B. 500m C. 5000m D. 0.5m 64. A basketball player who is 6 5 is how many inches tall? A. 65 in. B. 72 in. C. 75 in. D. 77 in. PAGE 2
4 Use the figures below to respond to problems # A B C D E 65. Which of the above figures are parallelograms? A. A B. A & C C. B & D D. A, B, C & D 66. Which of the above figures are rhombi? A. A B. B C. B & C D. E 67. Which of the above figures are rectangles? A. D B. B C. A & C D. B & D 68. Which of the above figures are quadrilaterals? A. A & C B. B & D C. A, B, C, D & E D. A, B, C & D 69. What is the supplement of the given angle? A. 51 o B. 39 o C. 129 o D. 61 o 70. What is the complement, x o, of the given angle? A. 23 o B. 27 o C. 90 o D. 63 o PAGE 3
5 Use the diagram below to answer problems # Name a line that is on with Plane P. 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 horizontal face on the rectangular solid. A. RSXW B. XYZW C. RUWZ D. TUZY 74. Name a line segment that is parallel to XY. A. YZ B. WX C. ST D. SX 75. Name a line segment that is perpendicular to XY. A. YZ B. RW C. WZ D. UZ Decide if the logic is inductive, based on patterns, or deductive, based on facts, theory, or definitions. 76. If 2x + 7 = 23, then x = 8 A. Inductive B. Deductive 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. 4/3 C. undefined D 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. 4 D What is the linear equation for the line? A. y = 1x + 3 B. y = 3x + 1 C. y = 1x + 3 D. y = 3x What is the linear equation for the line? A. y = 20 B. x = 15 C. y = 3 D. y = 17x You are buying lemonade for your classroom. There are 24 students that each will have an 8 oz. glass of lemonade. How many gallons of lemonade do you have to buy to have each student have only one glass? A. 1 gallon B. 2 gallons C. 3 gallons D. 4 gallons PAGE 5
7 83. How many unit squares would be in Stage 7? A. 30 B. 42 C. 56 D Find the value of x: A. x = 117 B. x = 20 C. x = 60 D. x = What are the measures of angles 1 and 2 in the diagram below? m 1 m 2 A. 108 o 72 o B. 72 o 108 o C. 98 o 82 o D. 82 o 98 o PAGE 6
8 86. Perimeter = 31 Find x. x 2x + 7 3x + 6 A B. 3 C. 2.5 D Find the exact circumference and the area. Circumference Area A. 6π cm 36π cm 2 B. 6π cm 12π cm 2 C. 12π cm 36π cm 2 D. 12π cm 12π cm Find the surface area. A. 56 sq. cm B. 104 sq. cm C. 112 sq. cm D. 208 sq. cm Volume Formulas: Rectangular Prism V = l x w x h Cylinder: V = π r 2 h 89. Find the volume. A. 20 cm 3 B. 28 cm 3 C. 56 cm 3 D. 48 cm Find the exact volume. A. 525 ft 3 B. 210 ft 3 C ft 3 D. 105 ft 3 PAGE 7
9 Shade the correct answer! Example: A B C D E Name School 51. A B C D E 71. A B C D E 52. A B C D E 72. A B C D E 53. A B C D E 73. A B C D E 54. A B C D E 74. A B C D E 55. A B C D E 75. A B C D E 56. A B C D E 76. A B C D E 57. A B C D E 77. A B C D E 58. A B C D E 78. A B C D E 59. A B C D E 79. A B C D E 60. A B C D E 80. A B C D E 61. A B C D E 81. A B C D E 62. A B C D E 82. A B C D E 63. A B C D E 83. A B C D E 64. A B C D E 84. A B C D E 65. A B C D E 85. A B C D E 66. A B C D E 86. A B C D E 67. A B C D E 87. A B C D E 68. A B C D E 88. A B C D E 69. A B C D E 89. A B C D E 70. A B C D E 90. A B C D E PAGE 8
10 Shade the correct answer! Example: A B C D E Name School ANSWER KEY 51. A B C D E 71. A B C D E 52. A B C D E 72. A B C D E 53. A B C D E 73. A B C D E 54. A B C D E 74. A B C D E 55. A B C D E 75. A B C D E 56. A B C D E 76. A B C D E 57. A B C D E 77. A B C D E 58. A B C D E 78. A B C D E 59. A B C D E 79. A B C D E 60. A B C D E 80. A B C D E 61. A B C D E 81. A B C D E 62. A B C D E 82. A B C D E 63. A B C D E 83. A B C D E 64. A B C D E 84. A B C D E 65. A B C D E 85. A B C D E 66. A B C D E 86. A B C D E 67. A B C D E 87. A B C D E 68. A B C D E 88. A B C D E 69. A B C D E 89. A B C D E 70. A B C D E 90. A B C D E PAGE 9
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