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MATHCOUNTS 1993-1994 State Competition Countdown Round

MATHCOUNTS 1993-1994 State Competition Countdown Round. A man digs a hole 6 inches deep for a post to hold his mailbox. If the square base of the post is 4 in. x 4 in., how many cubic inches of dirt will be displaced by the post?. 96 (cubic inches). If 2 x = 8 what is 3 x ?. 27.

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MATHCOUNTS 1993-1994 State Competition Countdown Round

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  1. MATHCOUNTS1993-1994State CompetitionCountdown Round

  2. A man digs a hole 6 inches deep for a post to hold his mailbox. If the square base of the post is 4 in. x 4 in., how many cubic inches of dirt will be displaced by the post?

  3. 96 (cubic inches)

  4. If 2x = 8 what is 3x?

  5. 27

  6. At a certain intersection, 30% of the cars turn left, 40% turn right, and 30% go straight. What is the probability that the next car turns left and the following one turns right?

  7. 3 25

  8. (26 + 26+ 26+ 26) Expressin simplest form

  9. 16

  10. What is the sum of the two values that will make the following expression undefined? x – 2 x2 – 6x + 8

  11. 6

  12. Find the largest integer less than or equal to 2-3·33.

  13. 3

  14. Seven equal 10-inch-long pieces are cut from an eight-foot-long piece of lumber. If the waste per cut is 1/8 inch, how many inches long is the piece that is left over? Express your answer as a mixed number.

  15. 25 1/8 (inches)

  16. If 5 technicians can produce 64 surfboards in 4 days, how many surfboards can 8 technicians produce in 10 days?

  17. 256 (surfboards)

  18. What digit is used only once in the decimal representation of(1,111,111)2

  19. 7

  20. The school population has increased from 3,200 to 3,600 this year. If this percent rate of increase remains constant, what will be the school population be at the end of next year?

  21. 4,050 (students)

  22. In an arithmetic sequence the 113th term is 786 and the 125th term is 870. Find the 150th term

  23. 1,045

  24. A rectangle has length 15 inches and width 10 inches. If these dimensions are both increased by 20%, by how many square inches will the area of the rectangle be increased?

  25. 66 (square inches)

  26. If f(x) = 2x + 3 and g(x) = 3x – 2, find f(g(f(2))) g(f(g(2)))Express your answer in the form a .b

  27. 41 31

  28. What is the sum of the distinct prime factors of 3, 780

  29. 17

  30. Two interior angles A and B of pentagon ABCDE are 60º and 85º. Two remaining angles, C and D, are equal and the fifth angle is 15º more than twice C. Find the measure of the largest angle.

  31. 205 (degrees)

  32. Simplify the following and express the result without using negative exponents.(3a-2b3c-1)2·(√2ab-1c2)2 3

  33. 3√2b52a3

  34. Evaluate 1312 – 2(131)(31) + 312

  35. 10,000

  36. Segment AC has three semi-circles with radii 4cm, 6cm, and 10 cm. In terms of π, how many square centimeters are in the shaded area? A C

  37. 24π (sq. cm.)

  38. Find

  39. 120

  40. Find the volume, in cubic inches, of a cube whose surface area is 96 square inches.

  41. 64 (cubic inches)

  42. Given that ab = (a2 - b2), abexpress 62 as a common fraction.

  43. 8 3

  44. A candy bar weighs 4.48 oz. If a person eats half the remaining candy bar with each bite, how many bites have been taken when there is exactly 0.07 oz remaining?

  45. 6 (bites)

  46. Evaluate (35)(23) – (24)(34)

  47. 648

  48. If the sides of a right triangle are 14cm, 48 cm, and 50 cm, how many square centimeters are in its area?

  49. 336 (sq. cm.)

  50. Central angles a, b, and c separate the circle into regions which are 1/3, 1/4, and 1/6 of the area. How many degrees are there in central angle d?a b c d

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