Name: __________________________ Team #: ________ School: ______________________________________________ Mount Rainier Math Invitational February 17 2012 Team Test 1. Find the product of x and y if: 3x+5y= 50 11y + 8x = 117 2. What is the maximum number of circles you can have where all the circles are tangent to all the other circles? 3. It’s raining cats and dogs. For every 11 dogs that rain, 17 cats rain. How many dogs rained if 3179 cats rained? 4. Chowder runs twice as fast as Stewbeaf, Stewbeaf runs 6/5 times as fast as Porridge and Mealoats runs 10 times as fast as Stewbeaf. They are running a one-­‐mile relay. Chowder runs at 12 mph. How long, in minutes will it take their team to finish if they each run a quarter mile? 5. Evaluate 𝟗𝟗𝟗𝟗𝟗𝟗×𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏. 6. What is the area of a triangle which has vertices at (1,3) (4,5) and (7,12)? 7. Evaluate 𝟔𝟔×𝟓𝟓 𝟔𝟔
𝟔𝟔
+ 𝟏𝟏𝟏𝟏𝟐𝟐 − 𝟖𝟖! 8. What is the volume of this rectangular prism in m3? 9. What is the next number in this sequence: 1, 3, 9, 21, 41.... 10. What is the product of the mean, mode, and median of this set of numbers? 5, 7, 34, 4, 28, 12, 5, 5, 7, 3, 0 11. Gandalf the Grey can kill a mountain troll in 1 hour. Gandalf the White can kill a mountain troll in 45 minutes. How long will it take Gandalf the Grey and Gandalf the White to kill a mountain troll together, in hours? 12. What is 𝟒𝟒𝟒𝟒 + 𝟒𝟒𝟒𝟒 + 𝟒𝟒𝟒𝟒 + ⋯ + 𝟔𝟔𝟔𝟔? 13. What is the area of an equilateral triangle with side length 4? 14. What is the sum of the digits of 𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟐𝟐 ? 15. How many prime numbers are there between 20 and 60? 16. Harry, Ron, Hermione, Dumbledore, Snape, and Voldemort must be paired up so they can compete in the greatest flaming quidditch hippogriff duel of all time. How many different pairs can be formed if Harry and Voldemort cannot be paired together? 17. For 30 minutes, Tyson rode his scooter at a rate of 30 mph. He then rode his segway for 40 minutes at a rate of 45 mph. Lastly he decides to jog for 90 minutes at a rate of 8 miles an hour. What is the total distance Tyson travelled? 18. How many sides does a heptagon have? 19. Matt was born on a Wednesday in January in the year 2006. What day of the week will his birthday be on in 2011 (2008 was a leap year)? 20. James has 7 math shirts and Mr. Roths has 10. If they only have one math shirt that is the same what is the probability that they will both be wearing the same math shirt?