2012 Shoreline Math Olympiad Fourth Grade – Team Test 1 1. Zavox, the very naughty, can with his zap‐o‐matic transform one Gragnor into a perfect cube of material that measures 1 foot on an edge. Zavox wishes to construct a solid pyramid using these cubes that has five steps up to the summit with each step one cube deep and one cube high. The summit’s flat top will be 4 square feet in area. How many Gragnors must Zavox zap to build this pyramid? 2. In a hockey tournament, seven teams each played each other once, and then the top two teams played a final game to determine the champion. How many games were played in all? 3. 4. A square rug with an area of 121 sq. feet ties a large square room together by leaving a border in the room of exactly 2 feet around the rug uncovered. What is the area of the room that is not covered by the rug? Two clocks both correctly indicate the time is noon on Friday, April 13. From that time forward, the first clock continues to keep correct time while the second clock runs 3 minutes fast for each actual hour that passes. One hour and 45 minutes ago, the second clock stopped working altogether showing a time of 3:00 a.m. on Saturday, April 14, and making a loud “boing” sound. What is the actual day and time now? ‐ PLEASE TURN OVER ‐ 5. Old man Smith has a total of 75 wrinkles and old man Jones has twice as many as old man Smith. If old man Jenkins has one and a half times as many wrinkles as old man Jones, how many more wrinkles does old man Jenkins have than old man Smith? 6. 6 13 7 5 4
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4 3 6 7 In the large rectangle shown above, there are regions A, B, C, and D (a parallelogram) with the listed unit values showing length of line segments. List the regions in order from largest area to smallest area (note the figure is not drawn to scale). 7. A witness to a cat burglary saw the bad guy drive away from the animal shelter in a car with a Wyoming State license plate similar to the one shown here. The witness was sure that the cat burglar’s license plate had a “19” to the left of the cowboy, but as to the other four numbers could only say that at least three of them and maybe all four were the number six. Assuming that all possible numbers have been issued by the State of Wyoming, how many possible license plates could match the witness’ description? END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED 2012 Shoreline Math Olympiad Fourth Grade – Team Test 2 1. 2. Reginald has a four‐sided die (with sides numbered 1 through 4), a six‐sided die (with sides numbered 1 through 6), and a ten‐sided die (with sides numbered 1 through 10). He rolls these three dice twice each. What number do you get if you take the highest possible sum of all the numbers rolled, add it to the lowest possible sum of all the numbers rolled, and divide that number by two? In the rectangular figure ABCD below, the area for triangle CED is 90 square yards and the length of line segment BD is 10 yards, the length of line segment CF and FD are each 15 yards, and the area for triangle AEC is 75 square yards. Line segment EF forms a right angle with line segment CD. What is the area of triangle ABE? A C
3. B F
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Admiral Ackbar baked brownies in a square pan to use as bait for his mouse traps. All together the brownies weighed 732 grams which was too heavy for the Admiral to use in his traps. He fixed the problem by cutting the pan of brownies from left to right twice and from top to bottom three times making sure that all the resulting pieces were of equal size. Rounded to the nearest gram, how much would each brownie weigh? 4. On Friday night at the restaurant “Mer‐n‐Terre”, 27 diners ordered some lobster, 44 diners ordered some steak, 15 ordered both lobster and steak, and one diner just had a big salad with no lobster or steak. How many diners were there at the restaurant that night? ‐ PLEASE TURN OVER ‐ 5. 6. 7. The Umbrella Corporation had some money to invest. After one year they doubled their money, after the next year they tripled their money from the previous year, and the year after that they quadrupled their money from the previous year! The following year was bad and they lost $918,000. If they wound up with $162,000, with how much money did they start? Karlie wants her dad to make a compact disc for her containing some of her favorite zydeco songs. Each song is 4 minutes and 10 seconds long. If you need a 3 second gap between songs, what is the greatest number of complete songs that will fit on a disc that has space for 1 1/3 hours of music? Judy’s neighbor, Angry Angus, has a twenty foot tall wall that runs North to South for ten miles along the border that separates their properties. If Judy is allowed to connect her electric fence to this wall, in square feet what is the largest rectangular Velociraptor pen she can create on her property with 72 feet of electric fencing? END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED