2010_geo - GEOMETRY STATE MATHEMATICS CONTEST FINALS 1 Sara...

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GEOMETRY STATE MATHEMATICS CONTEST FINALS APRIL 29, 2010 1. Sara can go to the movies tonight provided she fnishes all her homework and fnds a way to get there. To get there she can either borrow her dad’s car or she can get a ride with her Friend Amy. IF Sara isn’t able to go to the movies, what conclusion can we draw? a. Amy couldn’t give her a ride or she couldn’t borrow her dad’s car. b. Sara didn’t fnish her homework and Amy couldn’t give her a ride c. Sara didn’t fnish her homework and she couldn’t fnd a way to get there. d. Sara didn’t fnish her homework or she could neither borrow her dad’s car nor get a ride with Amy. e. Sara couldn’t get a ride From Amy and she couldn’t borrow her dad’s car. 2. A perFectly spherical orange with radius r units is sliced into eighths by three perpendicular planes through its center so that the peel oF each piece looks like the fgure. Determine the distance around the edge oF the peel in the picture (on the right) in terms oF its radius r . r a. 3 r b. 3 πr 2 c. 3 d. 2 3 e. 2 3. It takes 20 large ants to liFt a cube oF a certain material that measures 10 inches to a side. IF all ants can liFt the same amount oF weight, how many more ants will be required to liFt a cube oF the same material that measures 11 inches to a side? a .1 b .3 c .6 d .7 e .9
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4. In the diagram, AB is a diameter of a circle and AB CD .I f AD =1and DB = a , Fnd . A B C D a. =2 a b. = 2 a c. = 1+ a d. = a 2 e. = a 5. The triangular numbers, 1 , 3 , 6 , 10 ,... , are so-named because they occur as the number of points in an equilateral triangular arrangment. Which of the following is NOT a triangular number? a. 210 b. 28 c. 465 d. 84 e. 55 6. A rectangular Feld is partitioned into four smaller rectangular Felds. The areas of three of the Felds are given. ±ind the missing area. 20 24 x 15 a. 11 b. 12 c. 25 2 d. 21 2 e. 19 2
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7. The diagram shows a regular heptagon, a regular hexagon and a regular pentagon all with equal side length. Find m 1. a. 24 7 b. 74 21 c. 70 21 d. 23 7 e. 22 7 1 8. In the fgure, the segments o± length a and b lie on perpendiculars to the diagonals o± a square o± side length 2. Find a + b .
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2010_geo - GEOMETRY STATE MATHEMATICS CONTEST FINALS 1 Sara...

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