2006 Washington State Math Championship. Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth.

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Chastity Whitehead
6 years ago
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1 Potpourri - Grade = 2. (88,888,888, ,888 8) 8 = 3. What is the last positive integer you count if you count backwards from 1000 by 7 s? 4. How many prime numbers have a remainder of 0 when divided by 2? 5. To keep the answers safe, the words were written with a secret code. In this code, the number 26 stood for the letter A, the number 25 stood for B, and so on. In this code, the seven numbers 24, 12, 9, 9, 22, 24, 7 stand for what word? 6. If 6 widgets = 24 fidgets, then how many widgets is 16 fidgets? 7. If the pattern of the first four letters in MATHMATHMATH continues, then 8. Bob ran a 5km race where each kilometer his speed decreased 1km/hr. If he 9. How many revolutions does the second hand on a clock make in 10. What time is 1 hour and 31 minutes before 2 hours and 59

2 Potpourri - Grade 6 1. How many prime numbers have a remainder of 0 when divided by 2? 2. To keep the answers safe, the words were written with a secret code. In this code, the number 26 stood for the letter A, the number 25 stood for B, and so on. In this code, the seven numbers 24, 12, 9, 9, 22, 24, 7 stand for what word? 3. If 6 widgets = 24 fidgets, then how many widgets is 16 fidgets? 4. If the pattern of the first four letters in MATHMATHMATH continues, then 5. Bob ran a 5km race where each kilometer his speed decreased 1km/hr. If he 6. How many revolutions does the second hand on a clock make in 7. What time is 1 hour and 31 minutes before 2 hours and How many positive integers are factors of 40? 9. If today is March 15 th, then 2006 days from now what month will it be? 10. If one blue equals 3 greens, 6 reds equals 3 blues, and 3 yellows equals 9 red, then

3 Potpourri - Grade 7 1. If the pattern of the first four letters in MATHMATHMATH continues, then 2. Bob ran a 5km race where each kilometer his speed decreased 1km/hr. If he 3. How many revolutions does the second hand on a clock make in 4. What time is 1 hour and 31 minutes before 2 hours and How many positive integers are factors of 40? 6. If today is March 15 th, then 2006 days from now what month will it be? 7. If one blue equals 3 greens, 6 reds equals 3 blues, and 3 yellows equals 9 red, then 8. What is the largest power of 5 which divides evenly into the product of the first 100 positive integers: ? 9. What are the last three elements in the pattern: A, 2, B, 0, C, 2, D, 0, E, 3, F, 3, G, 2, H, 4, I, 2, J, 2, K, 4, L, 2, M, 2, N, 2, O, 0, P, 1, Q, 1, R, 2, S, 2, T, 3, U, 2, V, 2, W, 2, X, 4, Y,,, 10. Express 254(base 6) as a base 8 number.

4 Potpourri - Grade 8 1. What time is 1 hour and 31 minutes before 2 hours and How many positive integers are factors of 40? 3. If today is March 15 th, then 2006 days from now what month will it be? 4. If one blue equals 3 greens, 6 reds equals 3 blues, and 3 yellows equals 9 red, then 5. What is the largest power of 5 which divides evenly into the product of the first 100 positive integers: ? 6. What are the last three elements in the pattern: A, 2, B, 0, C, 2, D, 0, E, 3, F, 3, G, 2, H, 4, I, 2, J, 2, K, 4, L, 2, M, 2, N, 2, O, 0, P, 1, Q, 0, R, 2, S, 2, T, 3, U, 2, V, 2, W, 2, X, 4, Y,,, 7. Express 254(base 6) as a base 8 number. 8. There are seven circles of different sizes, arranged as shown, such that their centers are aligned on a straight line. The total distance they spanned from end to end is 60 centimeters. What is the exact sum of the circumferences of all the circles. 9. A large gasoline tank has three inlet pipes and one outlet pipe. One inlet pipe, colored red takes 2 hours to fill the tank. Another inlet pipe, colored blue, takes 3

5 hours to fill the tank. The third inlet pipe, colored green, takes 4 hours to fill the tank. The outlet pipe empties the whole tank in 12 hours. If the tank is initially empty, how many hours would it take to fill the tank if all the pipes are fully in operation? 10. Consider the flow chart: Start N = 1 X = 2 Y = 100 Y = Y - X N No Is N an odd number Yes Y = Y + X N N = N + 1 Is N 5 Yes No Stop What is the value of Y when you reach Stop?

Multiples and Divisibility

Multiples and Divisibility A multiple of a number is a product of that number and an integer. Divisibility: A number b is said to be divisible by another number a if b is a multiple of a. 45 is divisible