MATH COUNTS 

1. MATHCOUNTS 1999-2000 Chapter Competition Countdown Round

2. On a recent trip, Jessica drove 35 mph to a store and 40 mph on the return. If the combined driving time was 1.5 hours, how many miles did she drive one way?

3. Answer: 28 (miles)

4. Jana gave 4 cookies to each of her classmates. She would have needed 36 more cookies to give them 7 cookies each. How many classmates were there?

5. Answer: 12 (classmates)

6. The letter A is worth 1 point, B is worth 2 points, C is worth 3 points, ..., Z is worth 26 points, and the values of letters are added to determine the point value of a word. What is the point value of the word SEVEN?

7. Answer: 65 (points)

8. Compute: 99. 3

9. Answer: 729

10. A hollow cube has a volume of 0.008 cm3. What is the number of meters in the perimeter of the figure formed by opening and flattening the cube as shown? Express your answer as a decimal to the nearest tenth.

11. Answer: 2.8 (meters)

12. Teresa has lived one-fourth of her life in England, one-fifth in Ireland, one-third in France and 13 years in Switzerland. Assuming she lived in no other countries, how many years old is she?

13. Answer: 60 (years)

14. Beginning with January 1 in a leap year, what is the calendar date of the last day of the first of the year? 1 3

15. Answer: May 1

16. The side length of a regular hexagon is 9 inches. What is the number of inches in the difference between the greatest and the least distance between two vertices of the hexagon?

17. Answer: 9 (inches)

18. A cashier changed a $10 bill into dimes, nickels and quarters. If each coin was used the same number of times, how many total coins were used?

19. Answer: 75 (coins)

20. If the present time is 9:00 on a 12-hour clock, what hour will it be 1447 hours later?

21. Answer: 4:00 (or 4 o'clock)

22. A circle is inscribed in a semicircle as shown. The diameter of the circle and the radius of the semicircle are both 12 inches. What is the number of square inches in the area of the shaded region? Express your answer in terms of p.

23. Answer: 36p (square inches)

24. 12.5% of 420 is what percent of 210?

25. Answer: 25 (percent)

26. The average of 10 numbers is 28, and the average of 8 numbers is 100. What is the average of all 18 numbers?

27. Answer: 60

28. If x, y and z are positive integers and 2x • 3y • 5z = 27,000, what is the value of x + y + z?

29. Answer: 9

30. How many of the first 10 positive integers have reciprocals that are repeating decimals?

31. Answer: 4 (integers)

32. Alex counted to 400 by 6's beginning with 6, and Matthew counted to 400 by 4's starting with 4. How many of the numbers counted by Alex were also counted by Matthew?

33. Answer: 33 (numbers)

34. What is the sum of the two prime numbers between 110 and 130?

35. Answer: 240

36. In an isosceles right triangle whose area is 15 square units, each leg is as long as the side of a certain square. What is the number of square units in the area of the square?

37. Answer: 30 (square units)

38. A line has an x-intercept of 4 and a y-intercept of -3. What is the slope of the line? Express your answer as a common fraction.

39. Answer: 3 4

40. What is the value of f (4) if f (x) = x3 + 1?

41. Answer: 65

42. The Little Pieces Tuna Company is reducing the size of the radius of its best selling can of tuna by 10%. By what percent is the volume of the can reduced?

43. Answer: 19 (percent)

44. Express as a common fraction. 3 4 2 3 7 8 4 5

45. Answer: 15 16

46. A 12-foot piece of string is cut in half, and each of the two halves is used to form an equilateral triangle. What is the sum of the number of square feet in the areas of the two triangles? Express your answer in simplest radical form.

47. Answer: 2 3 (square feet)

48. Evaluate: [4 - 3(6 - 8)-1]-1. Express your answer as a common fraction.

49. 2 11 Answer:

50. For what value of n does 218 522 = 6.25  10n?