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OGT Math

Measurement. OGT Math. Mitchell is planting tulip bulbs in a rectangular planter with the dimensions shown.  Mitchell plans to fill 3/4 of the planter with soil. How much soil will Mitchell need? A.   1,188 cubic inches B.   1,584 cubic inches C.   2,107 cubic inches D. 11,880 cubic inches.

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OGT Math

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  1. Measurement OGT Math

  2. Mitchell is planting tulip bulbs in a rectangular planter with the dimensions shown.  Mitchell plans to fill 3/4 of the planter with soil. How much soil will Mitchell need? A.   1,188 cubic inches B.   1,584 cubic inches C.   2,107 cubic inches D. 11,880 cubic inches

  3. Points R and T are the midpoints of the sides of triangle QSU, as shown in the diagram below. What is the perimeter of ∆RST? A. 26 B. 40 C. 54 D. 80

  4. The Johnsons were going to a family wedding and drove a total of 1,244 miles to reach their cousin’s house. They spent 9 hours driving the first day at an average speed of 60 miles per hour. They reached their cousin’s house on the second day after driving 11 hours. What was their average speed on the second day? A. 60 miles per hour B. 62 miles per hour C. 64 miles per hour D. 78 miles per hour

  5. A manufacturer wants to make a rectangular storage box with volume 0.75 cubic meters, length 1.5 meters, and width 0.4 meters. What is the height of this box? A. 0.15 m B. 0.45 m C. 0.80 m D. 1.25 m

  6. The diagram shows a hexagon drawn inside a rectangle. What is the area of the hexagon? A. 21 cm² B. 24 cm² C. 30 cm² D. 54 cm²

  7. () Zack is packing for a trip to Scotland. He read that the average temperature in the summer is 18ºC during the day and 7ºC during the night. What is the difference between the high and low temperatures in degrees Fahrenheit? A. 19.8°F         B. 43.0°F C. 51.8°F D. 77.4°F

  8. Federico is paid $8.50 per hour for the first 40 hours he works each week. For each hour Federico works over 40 hours, he is paid for one-and-a-half hours. One week Federico works 48 hours. How much does Federico earn for working 48 hours in one week? A. $340 B. $408 C. $442 D. $612

  9. Tammy is roofing a house. She must buy enough shingles to cover the shaded rectangular areas on both sides of the roof, as shown in the diagram below. What is the area she must cover? A.    715 ft2 B.    835 ft2 C. 1,430 ft2 D. 6,600 ft2

  10. A compound glue comes in a cylindrical tube divided down the middle to separate the glue agent from the hardening agent as shown. What is the approximate volume of the section of the tube containing the hardening agent? A. 71 cm3 B. 141 cm3 C. 424 cm3 D. 565 cm3

  11. Madison is filling balloons with helium. When full, the balloons are nearly spherical in shape with a diameter of 12 inches. What is the approximate volume of each balloon when it is full? A. 115 cubic inches B. 450 cubic inches C. 680 cubic inches D. 900 cubic inches

  12. ED and AB are both perpendicular to BD  . In triangle ABC, the length of  AC  is 4 cm and the length of  AB  is 2 cm. • If the length of  EC  is 8 cm, what is the length of  ED ? • A.    4 cm • B.  • C.  • D. 16 cm

  13. The city flag for Celina, Ohio, is shown below. The flag has a total area of 5,472 square centimeters. In the center of the flag is a circular design. The diameter of this design is 48 centimeters. What is the approximate area of the flag that is NOT covered by the circular design? A. 1,763 cm3 B.  1,809 cm3 C.  3,663 cm3 D.  5,321 cm3

  14. In the diagram below, line segment AT is a diameter of the circle with center O. What is the area of the shaded part of the circle? A.   18.3 cm2 B.   42.3 cm2 C. 145.6 cm2 D. 194.1 cm2

  15. Janice had a 5-inch high by 3-inch wide photo enlarged to a 3.5-foot tall poster. What should be the approximate width of the poster?         A. 1.5 feet B. 2.1 feet C. 4.5 feet D. 5.8 feet

  16. Bart has a cylindrical pitcher with a radius of 6 cm and a height of 12 cm. He pours 1,300 cubic centimeters of lemonade into the pitcher. Approximately how much more lemonade will the pitcher hold? A.      36 cubic centimeters B.      57 cubic centimeters C.    622 cubic centimeters D. 1,357 cubic centimeters

  17. Enrica took two days to drive 1,020 miles. On the first day, she drove 10 hours at an average speed of 62 miles per hour. On the second day, her average speed was 57 miles per hour. Approximately how long did she drive on the second day? A.   7.0 hours B.   8.6 hours C. 10.9 hours D. 17.0 hours

  18. Marcia’s house is approximately ten miles east of the airport. A jet is flying directly over her house after taking off from the airport and flying approximately twelve miles, as shown in the diagram below. Approximately how many miles high is the jet when it flies over Marcia’s house? A.   2.0 miles B.   6.6 miles C. 12.0 miles D. 15.6 miles

  19. Artie constructed a decorative planter using ten 4-inch squares attached to a rectangular base as shown below. What is the volume of his planter? A. 160 cubic inches B. 192 cubic inches C. 256 cubic inches D. 384 cubic inches

  20. The diagram below gives the lengths of all but one side of pentagon ABCDE. What is the perimeter of pentagon ABCDE? A. 39 cm B. 42 cm C. 43 cm D. 44 cm

  21. Jennifer wants to close off a rectangular area in her lawn so that she can leave her dog outside. She buys enough fencing to close off 252 square feet of lawn. If the length of the enclosure is 21 feet, what is the width? A.  12 feet B.  14 feet C. 231 feet D. 273 feet

  22. . Jennifer is designing a quilt. The pattern for one part is shown in the rectangle. Triangles ADC and EBF are similar. . What is the length of EF? A. 5 in. B. 6 in. C. 10 in. D. 12 in.

  23. An aquarium is 60 centimeters long, 20 centimeters wide and 30 centimeters high. What volume of water, in cubic centimeters, does the aquarium contain if it is 2/3 full? A.  1,200 cm3 B. 11,000  cm3 C. 24,000  cm3 D. 36,000  cm3

  24. Dominic cuts out the largest possible circle from his 2-foot by 2-foot piece of art paper. Which is a reasonable estimate of the fraction of the art paper that is left over? A. less than 1/4 B. between  and1/4 and 1/2 C. between  and 1/2 and 3/4 D. more than  3/4

  25. Marny wants to approximate the amount of wax needed to make a crayon. The dimensions of the crayon are shown below. About how many cubic centimeters of wax are needed to make this crayon? A. 18 cm3 B. 22 cm3 C. 28 cm3 D. 88 cm3

  26. The anchoring wire of a telephone pole has snapped and needs to be replaced. The telephone pole is 30 feet tall. The anchor for the wire is 13.8 feet from the bottom of the pole. Which of these is approximately the minimum length necessary for the new wire? A. 10 ft B. 21 ft C. 35 ft D. 44 ft

  27. The area of a right triangle is 24 square feet. A second right triangle has a base that is 2 times as long as the first triangle’s base and a height that is 3 times as long as the first triangle’s height. What is the area of the second triangle? A. 48 square feet B. 72 square feet C. 144 square feet D. 864 square feet

  28. A diagram of the floor plan of a storage room as shown. If the ceiling is 12 feet above the floor, what is the capacity of the storage room, in cubic feet? A.   118 ft3 B.   600 ft3 C. 1,416 ft3 D. 1,800 ft3

  29. Lester keeps his frog in a glass container with the dimensions shown below. He pours water into the container to a height of 1.5 inches. What is the volume of water in the container? A. 135 cubic inches B. 216 cubic inches C. 1,440 cubic inches D. 2,160 cubic inches

  30. A circular pool has a diameter of 12 feet. About how much water is needed to fill the pool to a depth of 4 feet? A.      75 cubic feet B.    150 cubic feet C.    450 cubic feet D. 1,800 cubic feet

  31. A right triangle has the dimensions as shown in the diagram below. What is the area of the triangle? A.  8.0 square inches B. 11.3 square inches C. 13.9 square inches D. 16.0 square inches

  32. Identical boxes are to be stacked along the back wall of a storage room from floor to ceiling. The diagram shows the dimensions of the back wall and the dimensions of one of the boxes, which has a square base. Which of these is the best estimate of the maximum number of boxes that can be stacked against the entire back wall? A. 200 B.   70 C.   50 D.   15

  33. Alanis is moving and needs to pack two mirrors. The larger mirror fits in a box that is 18 inches wide by 20 inches long. Her smaller mirror is similar in proportion to the larger mirror. Alanis determines that the width of the smaller box needs to be at least 9 inches. What should be the minimum length of the box to hold the smaller mirror? A.   2 inches B.   6 inches C.   9 inches D. 10 inches

  34. Darius and his father are constructing a set of bunk beds as shown in the diagram below. What is the measure of angle X? A. 540º B. 390º C. 150º D. 120º

  35. Gene has a cylinder with radius 4 inches and height 2 inches. He cut the cylinder in half along the length of the diameter, as shown in the diagram below. What is the area of the shaded cross-section? A. 48π square inches B. 24π square inches C.   16 square inches D.     8 square inches

  36. Extended Response

  37. The diagram below shows the dimensions of a wall that needs to be painted.  The door represented by the shaded rectangle is not to be painted. In your Answer Document, determine the area, to the nearest square foot, of the wall that is to be painted.  Show your work or provide an explanation for your answer. (2 points)

  38. Brian and Caleb walked 5 kilometers north from their car to set up their tent. They hiked 3 kilometers east from their campsite to look for firewood. Then they walked 2 kilometers south. Caleb said that after they had walked the 2 kilometers south, they were the same distance from their car as they were from their tent. In your Answer Document, determine whether Caleb was correct by drawing a sketch of their hike and comparing the distances. Show your work. (2 points)

  39. Before her trip to Canada, Liz exchanged 300 U.S. dollars for Canadian dollars at a rate of 1 U.S. dollar to 1.35 Canadian dollars. When Liz arrived in Canada, the exchange rate was 1 Canadian dollar to 0.76 U.S. dollars. In your Answer Document: Determine the amount of money in Canadian dollars that Liz received for her 300 U.S. dollars. Determine whether Liz would have received more Canadian money for her 300 U.S. dollars if she had waited to exchange her money in Canada. Show your work or provide an explanation for your answers.

  40. The floor plan of one room in a bookstore is a square with an area of 576 square feet. Part of this room is taken up by a café. The border of the café runs from the midpoints of two adjacent walls. In your Answer Document, find the area, in square feet, of the café. Show your work or explain how you found your answer. (2 points)

  41. For lunch Fanya drank a can of cola that had a diameter of 2 inches and a height of 5 inches. After school, she drank a can of juice that measures twice the diameter and twice the height of the can of cola. In your Answer Document, find the volume of each can. Show work or provide an explanation to support your answers. Determine how many times larger the volume of the juice can is than the volume of the cola can.

  42. Helga earns $6.30 per hour working part-time at the grocery store. She records her starting and ending times each day on her time card. In your Answer Document, determine Helga’s total wages for the week. Show your work or provide an explanation for your answer. (2 points)

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