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Math Challenges from 2001 National Competition

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annapowers
51 diapositives · 581 Views · Jan 06, 2020

Test your math skills with problems from the 2001 MATHCOUNTS National Competition, including geometry, probability, and algebra questions.

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  1. MATHCOUNTS 2001 National Competition Countdown Round

  2. The NASA Space Shuttle transports material to theInternational Space Station at a cost of $22,000 per kilogram. What is the number of dollars in the cost of transporting a 250g control module?

  3. Answer: 5500 (dollars)

  4. What is the value of ? Express your answer as a common fraction.

  5. Answer: 1 3

  6. Two rectangles have integer dimensions, and both have a perimeter of 144 cm. What is the greatest possible difference between the areas of two such rectangles?

  7. Answer: 1225 (square centimeters)

  8. The expression can be written as . What is the value of ? - ´ 14 1 . 25 10 + m n 1 × m n 2 5

  9. Answer: 29

  10. How many ways can change for $16.00 be made using quarters and dimes if at least one of each type of coin must be used?

  11. Answer: 31 (ways)

  12. For how many different values of does ? = + 5 4 3 x x 72 x x

  13. Answer: 3 (values)

  14. What is the sum of the odd integers between 46 and 64?

  15. Answer: 495

  16. It takes 64 identical wooden cubes to fill a cubical box. How many of these cubes does it take to make the bottom layer of the box?

  17. Answer: 16 (cubes)

  18. Find such that . × = × 5 2 2 3 n 8! n

  19. Answer: 140

  20. At Makettle's, Jim bought30 oranges at a price of threefor 59¢. At Paduka's, he then bought 20 oranges at a price of two for 41¢. What was the number of cents in the average price of an orange?

  21. Answer: 20 (cents)

  22. If each edge of a cube is increased by 50% , what is the percent increase in the surface area of the cube?

  23. Answer: 125 (percent)

  24. What is the value of ? 3 + + 5 5 5 3 3 3

  25. Answer: 9

  26. How many isosceles triangles exist which have a perimeter of 10 and integer side lengths?

  27. Answer: 2 (triangles)

  28. The prime factorization of 2160 is . How many of its positive integer factors are perfect squares? ´ ´ 4 3 2 3 5

  29. Answer: 6 (factors)

  30. If f (x) = x 4 + x 2 + 5x, evaluate f (5) - f (-5).

  31. Answer: 50

  32. A piece of lumber feet long is cut into 9 pieces. If the waste per cut is inch, how many inches of lumber are wasted? 1 5 4 1 8

  33. Answer: 1 (inch)

  34. The product of three consecutive multiples of 5 is 26,250. What is the largest of these three factors?

  35. Answer: 35

  36. What is the value of the arithmetic series 28 + 30 + 32 + ... + 86 ?

  37. Answer: 1710

  38. What is the probability that a two-digit number selected at random has a tens digit less than its units digit? Express your answer as a common fraction.

  39. Answer: 2 5

  40. What is the sum of all possible values of for which is the square of a binomial? + - + 2 k x 12 x 16 x k

  41. Answer: 24

  42. What is the maximum number of square centimeters in the area of a triangle whose perimeteris 30 cm? Express your answer in simplest radical form.

  43. Answer: 25 (square centimeters) 3

  44. How many digits are in the decimal representation of the product of and ? 7 12 5 2

  45. Answer: 9

  46. Two different integers from1 through 20 inclusive are chosen at random. What is the probability that both numbers are prime? Express your answer as a common fraction.

  47. Answer: 14 95

  48. What is the remainder when is divided by 8? 137 5

  49. Answer: 5

  50. Find the distance between the points (1, 1) and (4, 7) . Express your answer in simplest radical form.