Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition
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1 Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 6 #51-90 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 51. Which statement is true? A. One line segment can divide a hexagon into two smaller hexagons. B. One line segment can divide a triangle into two smaller triangles. C. One line segment can divide a square into two smaller squares. D. One line segment can divide a circle into two smaller circles Which shape is possible? A. A rhombus with 4 acute angles. B. A parallelogram with 4 angles of equal measure. C. A rhombus with sides that measure 4cm, 4cm, 8 cm, and 8cm. D. A parallelogram with sides that measure 2cm, 4cm, 6cm, and 8cm Juan made cones and cylinders out of paper. He cut a total of 10 circles for the bases. Juan made 4 cones. How many cylinders did he make? A. 1 B. 2 C. 3 D. 6 E. Not given 54. The shapes below are five faces of a three-dimensional figure. What is the threedimensional figure? A. Cube B. Cone C. Prism D. Pyramid E. Not given 55. Look at figures P and Q. Which motion or motions will result in Figure P exactly covering Figure Q? A. Slides only B. Turns only C. Flips and turns only D. Flips and slides only PAGE 1
3 56. Maria drew a rectangle with the following properties: (a) the area is 32 square centimeters and (b) the length is twice the width. What is the perimeter of Maria s rectangle? A. 12cm B. 16cm C. 24cm D. 36cm E. Not given 57. Look at the picture. 1 square represents 1 square foot. What is the area of the grass around the fountain? Fountain Grass 1 square = 1 square foot A. 46 ft 2 B. 44 ft 2 C. 42 ft 2 D. 40 ft 2 E. Not given 58. Look at the solid below. What is the volume of the solid? KEY represents 5 cm 3 A. 8cm 3 B. 20cm 3 C. 40cm 3 D. 60cm 3 E. None of these 59. What is the surface area of the solid pictured in #58? A. 20cm 2 B. 24cm 2 C. 300 cm 2 D. 600cm 2 E. Not given 60. Which of the following words has line symmetry? A. MODE B. HOSE C. CONE D. NOSE E. Not given PAGE 2
4 61. Which regular polygon has 60 rotational symmetry? A. triangle B. square C. pentagon D. hexagon 62. Which of the following is true? A. All rectangles are squares. B. All rhombi are squares C. Some rhombi are rectangles. D. Some squares are rhombi. 63. What is the area of the irregular polygon pictured below? A. 12 units 2 B. 11 units 2 C. 10 units 2 D. 9 units 2 E. Not given 64. What is the surface area of the figure below? A. 15 units 2 B. 19 units 2 C. 22 units 2 D. 24 units 2 E. Not given 65. What is the volume of the figure below? A. 8 units 3 B. 7 units 3 C. 6 units 3 D. 5 units 3 E. Not given PAGE 3
5 66. What is the measure of angle e in the figure? A. 121 B. 120 C. 119 D What is the measure of angle c in the figure? A. 45 B. 61 C. 84 D Describe a transformation that would map segment ST onto segment RU. A. A reflection across a horizontal line through point M B. A translation along the height of parallelogram STRU C. A translation along segment SU D. A 180 degree rotation clockwise about point M 69. How many lines of reflection are in parallelogram STRU (the parallelogram in #68)? A. 3 B. 2 C. 1 D. 0 E. Not given 70. What is the area of the trapezoid below? 6.4 cm 4.7 cm 15.7 cm A cm 2 B cm 2 C cm 2 D cm 2 E. Not given 71. What is the perimeter of the trapezoid pictured in #70? A cm B cm 2 C cm D cm 2 E. Not given PAGE 4
6 72. What is the area of the figure below? 6 cm 12 cm 8 cm A. 72 cm 2 B. 48 cm 2 C. 36 cm 2 D. 24 cm 2 E. Not given 73. What is the perimeter of the parallelogram in #72? A. 26 cm B. 40 cm C. 46 cm D. 52 cm E. Not given 74. What is the area of the circle pictured? 12 cm A. 144π cm 2 B. 12π cm 2 C. 24π cm 2 D. 36π cm 2 E. Not given 75. What is the circumference of the circle in #74? A. 144π cm B. 12π cm C. 24π cm D. 36π cm E. Not given 76. Marcy is drawing a right triangle by placing starts on the grid below and connecting them with line segments. Which point could be the location of a third star of Marcy s right triangle? A D B C A. Point A B. Point B C. Point C D. Point D E. Not given PAGE 5
7 77. The image below shows quadrilateral ABCD and a line of reflection. Determine the coordinate of A. B A C D r A. (4, -1) B. (-1, 4) C. (-9, 4) D. (4, -9) E. Not given 78. Rotate the quadrilateral in #77 ninety degrees clockwise about point C. What is the coordinate of B? A. (5, 8) B. (2, 2) C. (2, 4) D. (4, 6) E. Not given 79. Jeff bought 6 quarts of juice for a party. One glass holds 8 fluid ounces of juice. What is the total number of glasses Jeff can fill with the juice he bought? [1 quart = 32 fluid ounces] A. 24 B. 48 C. 16 D. 12 E. Not given 80. Mr. Randall s class is making puppets. Each puppet needs 60 centimeter or string. How many puppets can Mr. Randall s class make from 12 meters of string? A. 20 B. 50 C. 200 D. 500 E. Not given 81. The endpoints of a line segment are the points with coordinates (2, 1) and (8, 9). What are the coordinates of the midpoint of this line segment? A. (2, 3.5) B. (3, 4) C. (5, 5) D. (4.5, 5.5) E. Not given 82. The complement of an angle that measures 40 must have a measure of A. 60 B. 30 C. 50 D. 40 E. Not given PAGE 6
8 83. Identify the point on the grid below that corresponds to the ordered pair (6, 4). A. Point M B. Point N C. Point O D. Point P 84. A museum has an aquarium the shape of a right rectangular prism that is 22.9 meters long, 7.5 meters wide, and 4.6 meters high. What is the volume, rounded to the nearest cubic meter, of the aquarium? A. 280 B. 623 C. 790 D. 1,288 E. Not given 85. What is the radius, in centimeters, of a circle that has a circumference of 16π centimeters? A. 8 B. 16 C. 32 D. 64 E. Not given 86. The diagram below shows three lines that intersect to form a triangle. Based on the angle measures in the diagram, what is the value of x? A. 32 B. 67 C. 81 D. 99 E. Not given 87. A circle inscribed in a square is shown below. The area of the square is 81 square centimeters. Which of the following is closes to the circumference, in centimeters, of the circle inscribed in the circle? (Use 3.14 for π) A B C D E. Not given PAGE 7
9 88. A disk in the shape of a circle has a diameter of 64 millimeters. What is the radius of the disk? A. 8 mm B. 32 mm C. 64 mm D. 128 mm E. Not given 89. Muhammed bought a circular tablecloth that has a radius of 3 feet. What is the circumference, to the nearest foot, of Linda s tablecloth? (Use 3.14 for π.) A. 6 feet B. 9 feet C. 19 feet D. 28 feet E. Not given 90. How many ½ cm cubes does it take to fill the prism pictured below? A. 3 B. 8 C. 12 D. 24 E. Not given PAGE 8
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