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MATHCOUNTS® 2000 National Competition Countdown Round.

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Presentation on theme: "MATHCOUNTS® 2000 National Competition Countdown Round."— Presentation transcript:

1 MATHCOUNTS® 2000 National Competition Countdown Round

2

3 In the Village League, the team to win two of three softball games becomes the champion. If the probability of Team Alpha beating Team Beta is 60% for every game, what is the probability that Beta wins the championship? Express your answer as a common fraction.

4 44 125 Answer:

5 Circles A and B are congruent
Circles A and B are congruent. Circle A is rolled around circle B, remaining tangent at all times. Circle A rolls around circle B exactly once. How many times will circle A revolve around its own center before the radii are lined up again as shown? A B

6 Answer: 2 (times)

7 A line that passes through (-5,-8) and (-3,-4) will cross the y-axis at what y-coordinate?

8 Answer: 2

9 What is the number of inches in the radius of a circle whose area is one-half the area of a circle with radius 4 inches? Express your answer in simplest radical form.

10 Answer: (inches) 2 2

11 A unicycle has a wheel with a radius of 1 foot
A unicycle has a wheel with a radius of 1 foot. How many complete revolutions will the wheel make when the unicycle rolls 100 feet? Express your answer to the nearest whole number.

12 Answer: 16 (revolutions)

13 What is the value of - + - + - + 1 2 3 4 5 6 . . . - + - 98 99 100 ?

14 Answer: –50

15 A 3-foot high tree was planted and grows by an equal number of feet each year. At the end of the seventh year, it is 1/9 taller than at the end of the sixth year. How many feet tall will it be at the end of the 13th year?

16 Answer: 16 (feet)

17 x, y and z are positive odd integers
x, y and z are positive odd integers. What is the remainder when is divided by 4? x y z 2 +

18 Answer: 3

19 In how many consecutive zeroes does the product end?
115 116 117 201 L

20 Answer: 23 (zeroes)

21 What is the total number of different committees that can be formed by selecting one or more persons from a group of six people?

22 Answer: 63 (committees)

23 In ABC, AB = 5 cm, BC = 10 cm, and the altitude drawn to AB is 8 cm
In ABC, AB = 5 cm, BC = 10 cm, and the altitude drawn to AB is 8 cm. What is the number of centimeters in the length of the altitude to BC?

24 Answer: 4 (centimeters)

25 When four numbers are added three at a time, the four sums are 42, 43, 47 and 48. What is the sum of the four numbers?

26 Answer: 60

27 The average of 11 consecutive even integers is 24
The average of 11 consecutive even integers is 24. What is the greatest of these integers?

28 Answer: 34

29 What is the fewest possible number of units in the perimeter of a triangle with side lengths that are relatively prime integers?

30 Answer: 12 (units)

31 Four distinct digits are used to make 2 two-digit numbers
Four distinct digits are used to make 2 two-digit numbers. What is the greatest possible product of the two numbers formed?

32 Answer: 8352

33 How many whole numbers from 10 to 99 have a units digit greater than the tens digit?

34 Answer: 36 (numbers)

35 A 200% increase is the same as a 50% increase followed by what other percent increase?

36 Answer: 100 (percent)

37 What percent of the first 200 prime numbers have reciprocals less than 0.05?

38 Answer: 96 (percent)

39 What is the probability that the product of two numbers chosen randomly from the set of all positive integers is divisible by 2? Express your answer as a common fraction.

40 3 Answer: 4

41 A circle has a radius of 10 centimeters and a chord of the circle is 16 centimeters long. How many centimeters is the midpoint of the chord from the center of the circle?

42 Answer: 6 (centimeters)

43 How many miles per hour is 1298 feet per second?

44 Answer: 885 (mph)

45 The ratio of length to width to height of a rectangular prism is 3:2:1
The ratio of length to width to height of a rectangular prism is 3:2:1. If the surface area of the prism is 198 m2, how many cubic meters are in its volume?

46 Answer: 162 (cubic meters)

47 In 1984, July 4 fell on a Wednesday
In 1984, July 4 fell on a Wednesday. On what day of the week did July 4, 1990, fall?

48 Answer: Wednesday

49 1 3 4 6 : The measures of the angles of a triangle are in the ratio of What is the number of degrees in the measure of the largest angle?

50 Answer: 80 (degrees)

51 How many integers 1–9 are divisors of the five-digit number 24,516?

52 Answer: 6 (integers)


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