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MATH COUNTS

MATH COUNTS. . 2005 School Competition Countdown Round. 1. What is the positive difference between 2 5 and 5 2 ? . Answer: 7. 2. Jane turns 15 in the year 2008. In what year was she born?. Answer: 1993.

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MATH COUNTS

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  1. MATHCOUNTS  2005 School Competition Countdown Round

  2. 1. What is the positive difference between 25 and 52?

  3. Answer: 7

  4. 2. Jane turns 15 in the year 2008. In what year was she born?

  5. Answer: 1993

  6. 3. What is the sum of the nexttwo terms in the geometric sequence 1, ? Express your answer as a common fraction.

  7. Answer:

  8. 4. How many obtuse interior angles are in an obtuse triangle?

  9. Answer: 1 (angle)

  10. 5. Evaluate for x = -2.

  11. Answer: 8

  12. 6. A printer prints 17 pages per minute. How many minutes will it take to print 200 pages? Express your answer to the nearest whole number.

  13. Answer: 12 (minutes)

  14. 7. Jenna is at a fair with four friends. They all want to ride the roller coaster, but only three people can fit in a car. How many different groups of three can the five of them make?

  15. Answer: 10 (groups)

  16. 8. The length of a rectangle is three times the width. The perimeter is 96 cm. What is the length of the rectangle, in centimeters?

  17. Answer: 36 (centimeters)

  18. 9. What is the value of the following expression:100 – 99 + 98 – 97 + 96 – 95 + ….+ 4 – 3 + 2 – 1?

  19. Answer: 50

  20. 10. A five-digit integer will be chosen at random from all possible positive five-digit integers. What is the probability that the number’s units digit will be less than 5? Express your answer as a common fraction.

  21. Answer:

  22. 11. If 3x +5 = 18, what is the value of 6x ?

  23. Answer: 26

  24. 12. The equation of the line that passes through the points (-2, 0) and (0, 2) can be expressed in the form y = mx + b. What is the value of m + b ?

  25. Answer: 3

  26. 13. How many positive factors does 30 have?

  27. Answer: 8 (factors)

  28. 14. A company makes a six-sided hollow aluminum container in the shape of a rectangular prism as shown. The container is 10” by 10” by 12”. Aluminum costs $0.05 per square inch. What is the cost, in dollars, of the aluminum used to make one container? 10” 10” 12”

  29. Answer: 34 (dollars)

  30. 15. Kaya ate 60 cookies over a five-minute period. On average, how many cookies did she eat each minute?

  31. Answer: 12 (cookies)

  32. 16. What is the value of 5012 – 4992 ?

  33. Answer: 2000

  34. 17. In a 5 by 5 grid, each of the 25 small squares measures 2 cm by 2 cm and is shaded. Five unshaded circles are then placed on top of the grid as shown. The area of the visible shaded region can be written in the form A - Bp square cm. What is the value of A + B?

  35. Answer: 113

  36. 18. What is the mean of 8, 12, 16, 20 and 24?

  37. Answer: 16

  38. 19. How many edges does a hexagonal prism have?

  39. Answer: 18 (edges)

  40. 20. If two numbers are chosen from the set {0, -5, -8, 4, 7}, and one is subtracted from the other, what is the smallest possible result?

  41. Answer: -15

  42. 21. The sum of two numbers is 50 and their difference is 6. What is their product?

  43. Answer: 616

  44. 22. What is the simplified valueof 0.75 ¸ ?

  45. Answer: 3

  46. 23. The area of a circle is 49p square units. What is the radius of the circle, in units?

  47. Answer: 7 (units)

  48. 24. What is the least common multiple of 51, 68 and 85?

  49. Answer: 1020

  50. 25. The lateral surface area of a cylindrical tube with a height of 6 cm is 48p square centimeters. In cubic centimeters, what is the tube’s volume? Express your answer in terms of p.

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