Rocket City Math League Junior Division 2013-2014 Inter-School Test Answers must be written inside the corresponding box on the answer sheet. All answers must be written in exact, reduced, simplified, and rationalized form. No calculators, books, or other aides may be used. 1. Space Monkey Badoo was eating walnuts during his space exploration. Due to zero gravity, for every 2 walnuts he ate, one flew away without him noticing. If a total of 28 walnuts flew away, how many walnuts did he eat? (1 point) 2. Find the slope of the following line: (Assume all increments are one unit) (1 punt )(1 point) 3. Evaluate the following expression: (2 3 4) (8 4 2) . (1 point) 4.If A = 1, B = 2, C = 3,…etc., what is the smallest number divisible by G, M, and Z? (1 point) 5. Martha was doing a very difficult math problem but got distracted by Spacetube videos. She accidentally squared the correct answer, then subtracted 1, and finally added 15. The resulting answer of 39 was incorrect. What was the absolute value of the correct answer? (1 point) 6. The amount of time it takes planet Earth to make one rotation is 24 hours. The amount of time it takes for planet Earth to make one revolution around the sun is 8760 hours. How many rotations will planet Earth make if it revolves around the sun 3.5 times? (2 points) 7. Larry’s current age is equivalent to the number of prime numbers between 1 and 100. He planted a magic tree 2 feet tall on his fourth birthday that grows at a rate of z feet per year. How many feet tall is Larry’s tree now if z is the smallest of three consecutive odd integers whose sum is equals 147? (2 points) 8. Poliglots are $1.64 each and Jubalons are $1.37 each at the Zorion Market. If Kailet buys 2 Poliglots and 4 Jubilons and gives the cashier $9, then how many distinct ways can the cashier give Kailet her change using quarters, dimes, nickels, and pennies? (2 points) 9. A right triangle inscribed in a circle has legs of length of x and y. 2 2 If x = (41 39 ) and y = the smallest positive integer which is 20 neither a square number nor a prime number, then what is the area of the circle? (If a right triangle is inscribed in a circle, then the hypotenuse of the triangle is a diameter of the circle.) (2 points) 10. A meteor is plummeting towards Earth along the course described by y = 5x+2. A projectile is fired to intercept the meteor along the course described by y = 2x+8. At what point (x,y) will the projectile collide with the meteor? (3 points) 11. How many distinct ways can 6 identical chocolate candies be divided between 4 children? 2 (3 points) 3 12. If Endeavor’s age is 3 of Atlantis’s age and in 4 years Endeavor will be 4 of Atlantis’s current age, how old is Atlantis currently? (3 points) 13. If 1 + 3 + 5 + 7 + 9 + 11 +…+ 99 = x, then solve for x. (4 points) 14. A new zoo featuring out of-this-world creatures has opened up. If a family visits each of the 11 exhibits exactly once, let p be the probability that they randomly visit all 11 exhibits in alphabetical order if each exhibit begins with a different letter of the alphabet(ex. Aardvark, Baboon, Chimpanzee, etc.). If p is written as a reduced fraction m/n where m and n are positive integers, find m+n. (4 points) 15. Given that ABDE is a square, BC = 6 units, GH is a perpendicular bisector of FC , AF = EF, and FCB is a right angle, what is the volume of the resulting solid if square ABDE is rotated all the way around AD ? (5 points) The material on this page is the property of the Rocket City Math League. Reproduction other than for non-profit educational purposes is strictly prohibited without the expressed written consent of the RCML. Rocket City Math League www.rocketcitymath.org Sponsored by Mu Alpha Theta - National Math Honor Society www.mualphatheta

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# JuniorInterschool2013