2003 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Individual Test - Grade 5 The first 10 problems are multiple choice and will count toward your team score. Answer by putting the appropriate letter in the blank on the answer sheet. 1. What is the sum of the prime numbers between 0 and 20? a. b. 100 c. 66 d. 8 e. 101 2. Three pizzas will feed 8 people. How many pizzas will it take to feed 24 people? a. 9 b. 10 c. 12 d. 1 e. 20 3. Which area is largest? a. a square with sides 5 cm b. a circle with radius 3 cm c. a rectangle with sides 4 and cm d. a rhombus with sides 5 cm e. a triangle which has each of its sides touching the circle exactly once 4. In a basketball league with 6 teams, how many games will there be if each team is to play every other team twice? a. 10 b. 24 c. 30 d. 36 e. 2 5. Which fraction is the median of this set? 3 5, 5 8, 10, 11,16 25 a. 3 5 b. 5 8 c. 10 d. 11 e. 16 25 6. Which of these numbers is not divisible by 9? a. 1802 b. 1694 c. 9594 d. 1513 e. 15984
. What is the perimeter of this polygon? [Assume all angles are right angles.] 12 4 9 10 1 a. 6 b. 110 c. 152 d. 304 e. cannot be determined 8. Which number is the median of this set? π, 22 355,3.14, 113, 10 a. π b. 22 355 c. 3.14 d. e. 10 113 9. If today is Saturday, what day of the week is it 2003 days from today? a. Friday b. Sunday c. Monday d. Tuesday e. Thursday 10. On a compact disk each bit of information is 5 10 meters long. The entire track of all these bits on the CD is 5 kilometers long. The number of bits on the entire track is closest to a. 25 b. 10 4 c. 10 10 d. 10 21 e. 10 25 Problems 11-30 will count toward your individual score but not your team score. 11. Josh bought 5 pairs of socks for $3 each and 6 t-shirts for $ each. How many dollars did he spend? 12. On the old apple tree the trunk splits into 3 limbs; the limbs each split into 5 branches; the branches split into 6 twigs; and each twig has 10 leaves. How many leaves are on the old apple tree? 13. Skip Towne s telephone rings for 2 seconds followed by 5 seconds of silence. Immediately after the sixth ring his answering machine receives the call. How many seconds does Skip have to answer the phone from the beginning of the first ring until the answering machine take over? 14. A piece of string 8 feet long is cut into 3 pieces each 28 inches long and another piece x inches long. What is the value of x? 15. Bob, Kellie, and Bill are running a race. If there are no ties, how many ways are there to award first, second, and third place?
16. Jackie is four years older than Lizzie. Lizzie is 5 years younger than Morgan. If Morgan is 15 years old, how old is Jackie? 1. If one card is drawn from a standard 52 card deck, what is the probability of not drawing a? [Answer as a reduced fraction.] 18. The fraction 13 5 is equivalent to what percent? 19. The sum of 3 consecutive numbers is 1293. What is the smallest of the three numbers? 20. Bonnie bought 3 pounds of grapes at $0.89 per pound. How much change did she receive from a five-dollar bill? 21. What is the sum of the reciprocals of 0.6 and 3 1? Express your answer as a mixed number. 5 22. Seventy percent of the salmon eggs were fertilized. Sixty percent of the fertilized eggs hatched. Ninety percent of the hatched were eaten before they reach the ocean. If 2100 salmon reached the ocean, how many eggs were there to start with? 23. A 2-inch rope is cut into 5 pieces but one piece is 4 5 are the longer pieces? of the others. How many inches long 24. What is 0.24 as a reduced common fraction? 25. In 12 minutes of swimming 80 calories are burned. At this rate how many calories are burned on a half-hour swim? 26. How many differently shaped rectangles with whole number sides could have an area of 360? 2. Coyote Car Rental charges $24 for a single day rental and $12 per day for additional days. If someone rents a car for a week, s/he gets one of the additional days free. Coyote also charges $0.05 per mile if the car is not returned in the city where it was originally rented. It is 1300 miles from Seattle to Denver. What does it cost to take one of Coyote s cars from Seattle to Denver and leave it there if the trip lasts days? 28. The area of one small square is 1, and the area of the largest square is 100. What is the area of the quadrilateral region enclosed by heavier lines?
29. The approximate radius of the meteorite that caused the extinction of the dinosaurs 65 million years ago was 3.1 miles. Assuming the meteorite was spherical, to the nearest cubic mile what was its volume? 30. A speed of 60 miles per hour is equivalent to 88 feet per second. If Boris traveled 5 miles in 3 hours and 45 minutes, to the nearest tenth what was his average speed in feet per second?
2003 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Individual Test - Grade 6 The first 10 problems are multiple choice and will count toward your team score. Answer by putting the appropriate letter in the blank on the answer sheet. 1. In a basketball league with 6 teams, how many games will there be if each team is to play every other team twice? a. 10 b. 24 c. 30 d. 36 e. 2 2. Which fraction is the median of this set? 3 5, 5 8, 10, 11,16 25 a. 3 5 b. 5 8 c. 10 d. 11 e. 16 25 3. Which of these numbers is not divisible by 9? a. 1802 b. 1694 c. 9594 d. 1513 e. 15984 4. What is the perimeter of this polygon? [Assume all angles are right angles.] 12 4 9 10 1 a. 6 b. 110 c. 152 d. 304 e. cannot be determined 5. Which number is the median of this set? π, 22 355,3.14, 113, 10 a. π b. 22 355 c. 3.14 d. e. 10 113 6. If today is Saturday, what day of the week is it 2003 days from today? a. Friday b. Sunday c. Monday d. Tuesday e. Thursday
. On a compact disk each bit of information is 5 10 meters long. The entire track of all these bits on the CD is 5 kilometers long. The number of bits on the entire track is closest to a. 25 b. 10 4 c. 10 10 d. 10 21 e. 10 25 8. Congruent copies of which of the following can not cover a flat surface without gaps or overlaps? a. rhombus b. trapezoid c. convex quadrilateral d. non-convex quadrilateral e. all can cover 9. Two dice are rolled. What is the probability that one die is less than 4 and the other is more than 4? a. 2 3 b. 1 2 c. 1 3 d. 1 4 e. 1 6 10. What is the smallest number boards 2 units 3 units 8 units that can be stacked into the shape of a cube? a. 56 b. 288 c. 48 d. 24 e. 12 Problems 11-30 will count toward your individual score but not your team score. 11. If one card is drawn from a standard 52 card deck, what is the probability of not drawing a? [Answer as a reduced fraction.] 12. The fraction 13 5 is equivalent to what percent? 13. The sum of 3 consecutive numbers is 1293. What is the smallest of the three numbers? 14. Bonnie bought 3 pounds of grapes at $0.89 per pound. How much change did she receive from a five-dollar bill? 15. What is the sum of the reciprocals of 0.6 and 3 1? Express your answer as a mixed number. 5 16. Seventy percent of the salmon eggs were fertilized. Sixty percent of the fertilized eggs hatched. Ninety percent of the hatched were eaten before they reach the ocean. If 2100 salmon reached the ocean, how many eggs were there to start with? 1. A 2-inch rope is cut into 5 pieces but one piece is 4 5 are the longer pieces? of the others. How many inches long 18. What is 0.24 as a reduced common fraction?
19. In 12 minutes of swimming 80 calories are burned. At this rate how many calories are burned on a half-hour swim? 20. How many differently shaped rectangles with whole number sides could have an area of 360? 21. Coyote Car Rental charges $24 for a single day rental and $12 per day for additional days. If someone rents a car for a week, s/he gets one of the additional days free. Coyote also charges $0.05 per mile if the car is not returned in the city where it was originally rented. It is 1300 miles from Seattle to Denver. What does it cost to take one of Coyote s cars from Seattle to Denver and leave it there if the trip lasts days? 22. The area of one small square is 1, and the area of the largest square is 100. What is the area of the quadrilateral region enclosed by heavier lines? 23. The approximate radius of the meteorite that caused the extinction of the dinosaurs 65 million years ago was 3.1 miles. Assuming the meteorite was spherical, to the nearest cubic mile what was its volume? 24. A speed of 60 miles per hour is equivalent to 88 feet per second. If Boris traveled 5 miles in 3 hours and 45 minutes, to the nearest tenth what was his average speed in feet per second? 25. Evaluate: 1 3 8 4 + 2 5 6 9 26. Three equilateral triangles are pictured. The smallest has side lengths that are 1 3 of the largest, and the other triangle has side lengths that are 2 of the largest. If the largest triangle has side 3 lengths of 12, what is the perimeter of the entire figure?
2. In the previous problem the area of the smallest triangle is 4 3. What is the area of the entire figure? 28. A badger weighs the same as 4 marmots, and 3 marmots weigh the same as 5 weasels. So that we can replace all six of the stinking badgers, how many weasels weigh the same as 6 badgers? 29. What is the area of rhombus RHOM? [Assume that each small square is one unit on a side.] R H M O 30. If RHOM is rotated 90 clockwise around point R, what will be the new coordinates of point O?
2003 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Individual Test - Grade The first 10 problems are multiple choice and will count toward your team score. Answer by putting the appropriate letter in the blank on the answer sheet. 1. What is the perimeter of this polygon? [Assume all angles are right angles.] 12 4 9 10 1 a. 6 b. 110 c. 152 d. 304 e. cannot be determined 2. Which number is the median of this set? π, 22 355,3.14, 113, 10 a. π b. 22 355 c. 3.14 d. e. 10 113 3. If today is Saturday, what day of the week is it 2003 days from today? a. Friday b. Sunday c. Monday d. Tuesday e. Thursday 4. On a compact disk each bit of information is 5 10 meters long. The entire track of all these bits on the CD is 5 kilometers long. The number of bits on the entire track is closest to a. 25 b. 10 4 c. 10 10 d. 10 21 e. 10 25 5. Congruent copies of which of the following can not cover a flat surface without gaps or overlaps? a. rhombus b. trapezoid c. convex quadrilateral d. non-convex quadrilateral e. all can cover 6. Two dice are rolled. What is the probability that one die is less than 4 and the other is more than 4? a. 2 3 b. 1 2 c. 1 3 d. 1 4 e. 1 6
. What is the smallest number boards 2 units 3 units 8 units that can be stacked into the shape of a cube? a. 56 b. 288 c. 48 d. 24 e. 12 8. Which choice is nearest to the perimeter of ΔPER? EA is an altitude of ΔPER. E 20 21 48 P A a. 100 b. 125 c. 150 d. 15 e. 200 R 9. If 2 a 3 b 5 c = 360,000, then a + b + c =? a. 12 b. 10 c. 9 d. 8 e. 12000 10. Three views are given of the same block structure. The highest part of the structure is in which corner? TOP FRONT RIGHT a. left back b. right back c. left front d. right front Problems 11-30 will count toward your individual score but not your team score. 11. A 2-inch rope is cut into 5 pieces but one piece is 4 5 are the longer pieces? of the others. How many inches long 12. What is 0.24 as a reduced common fraction? 13. In 12 minutes of swimming 80 calories are burned. At this rate how many calories are burned on a half-hour swim? 14. How many differently shaped rectangles with whole number sides could have an area of 360? 15. Coyote Car Rental charges $24 for a single day rental and $12 per day for additional days. If someone rents a car for a week, s/he gets one of the additional days free. Coyote also charges $0.05 per mile if the car is not returned in the city where it was originally rented. It is 1300 miles from Seattle to Denver. What does it cost to take one of Coyote s cars from Seattle to Denver and leave it there if the trip lasts days?
16. The area of one small square is 1, and the area of the largest square is 100. What is the area of the quadrilateral region enclosed by heavier lines? 1. The approximate radius of the meteorite that caused the extinction of the dinosaurs 65 million years ago was 3.1 miles. Assuming the meteorite was spherical, to the nearest cubic mile what was its volume? 18. A speed of 60 miles per hour is equivalent to 88 feet per second. If Boris traveled 5 miles in 3 hours and 45 minutes, to the nearest tenth what was his average speed in feet per second? 19. Evaluate: 1 3 8 4 + 2 5 6 9 20. Three equilateral triangles are pictured. The smallest has side lengths that are 1 3 of the largest, and the other triangle has side lengths that are 2 of the largest. If 3 the largest triangle has side lengths of 12, what is the perimeter of the entire figure? 21. In the previous problem the area of the smallest triangle is 4 3. What is the area of the entire figure? 22. A badger weighs the same as 4 marmots, and 3 marmots weigh the same as 5 weasels. So that we can replace all six of the stinking badgers, how many weasels weigh the same as 6 badgers? 23. What is the area of rhombus RHOM? [Assume that each small square is one unit on a side.] R H M O
24. If RHOM is rotated 90 clockwise around point R, what will be the new coordinates of point O? 25. If 52a + 68b = 156, then what does 39a + 51b equal? 26. If 5 cents added to Kamal s hourly wage increases it by 15%, what was his original hourly wage? 2. Using a standard 52 card deck, what is the probability of drawing a queen or a diamond or a club? [Answer as a reduced fraction.] 28. The combined perimeter of 2 different sized squares is 1200. If the area of the larger square is 16 times the smaller, what is the area of the smaller square? 29. If the area of the semicircle is 25π, to the nearest tenth what is the perimeter of the entire 2 figure? 30. In the first 25% of the season the Crows won 25% of their games. To the nearest tenth of a percent, what percentage of their remaining games must they win to have won at least 60% of their games by season s end.
2003 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Individual Test - Grade 8 The first 10 problems are multiple choice and will count toward your team score. Answer by putting the appropriate letter in the blank on the answer sheet. 1. On a compact disk each bit of information is 5 10 meters long. The entire track of all these bits on the CD is 5 kilometers long. The number of bits on the entire track is closest to a. 25 b. 10 4 c. 10 10 d. 10 21 e. 10 25 2. Congruent copies of which of the following can not cover a flat surface without gaps or overlaps? a. rhombus b. trapezoid c. convex quadrilateral d. non-convex quadrilateral e. all can cover 3. Two dice are rolled. What is the probability that one die is less than 4 and the other is more than 4? a. 2 3 b. 1 2 c. 1 3 d. 1 4 e. 1 6 4. What is the smallest number boards 2 units 3 units 8 units that can be stacked into the shape of a cube? a. 56 b. 288 c. 48 d. 24 e. 12 5. Which choice is nearest to the perimeter of ΔPER? EA is an altitude of ΔPER. P 21 E A 20 48 R a. 100 b. 125 c. 150 d. 15 e. 200 6. If 2 a 3 b 5 c = 360,000, then a + b + c =? a. 12 b. 10 c. 9 d. 8 e. 12000
. Three views are given of the same block structure. The highest part of the structure is in which corner? a. left back b. right back TOP FRONT RIGHT c. left front d. right front 8. Which of the following equations is not equivalent to the others? a. x 3 + 4 3 = 8 b. 0.3x 14 = 8 c. 5x 6 + 1 3 =1 d. 0.003x 0.006 = 0.054 e. x 3 + 2 3 = 4 9. Tom has grades of 88, 93, 98, and 84 on the first 4 tests. What is the minimum score he needs on the fifth test in order to have an average of at least 88? a. b. 8 c. 88 d. 90 e. 96 10. Sinbad has 5 white signal flags and 5 black signal flags. He can fly only 5 flags at a time. How many different 5-flag messages can he send? a. 5 b. 10 c. 25 d. 32 e. 50 Problems 11-30 will count toward your individual score but not your team score. 11. The approximate radius of the meteorite that caused the extinction of the dinosaurs 65 million years ago was 3.1 miles. Assuming the meteorite was spherical, to the nearest cubic mile what was its volume? 12. A speed of 60 miles per hour is equivalent to 88 feet per second. If Boris traveled 5 miles in 3 hours and 45 minutes, to the nearest tenth what was his average speed in feet per second? 13. Evaluate: 1 3 8 4 + 2 5 6 9 14. Three equilateral triangles are pictured. The smallest has side lengths that are 1 3 of the largest, and the other triangle has side lengths that are 2 of the largest. If 3 the largest triangle has side lengths of 12, what is the perimeter of the entire figure?
15. In the previous problem the area of the smallest triangle is 4 3. What is the area of the entire figure? 16. A badger weighs the same as 4 marmots, and 3 marmots weigh the same as 5 weasels. So that we can replace all six of the stinking badgers, how many weasels weigh the same as 6 badgers? 1. What is the area of rhombus RHOM? [Assume that each small square is one unit on a side.] R H M 18. If RHOM is rotated 90 clockwise around point R, what will be the new coordinates of point O? 19. If 52a + 68b = 156, then what does 39a + 51b equal? 20. If 5 cents added to Kamal s hourly wage increases it by 15%, what was his original hourly wage? 21. Using a standard 52 card deck, what is the probability of drawing a queen or a diamond or a club? [Answer as a reduced fraction.] 22. The combined perimeter of 2 different sized squares is 1200. If the area of the larger square is 16 times the smaller, what is the area of the smaller square? 23. If the area of the semicircle is 25π, to the nearest tenth what is the perimeter of the entire 2 figure? O
24. In the first 25% of the season the Crows won 25% of their games. To the nearest tenth of a percent, what percentage of their remaining games must they win to have won at least 60% of their games by season s end. 25. How many positive integers values of x are there such that 2 x 5 26. What is the perimeter of the pentagon formed by these graphs? is an integer? x = 3 y = 0 8 6 y = 3 4 x + 25 4 y = 4 3 x + 25 3 4 y = 3 4 x 2 5-2 2. Ben paid $1238.08 for his computer including.8% sales tax. To the nearest cent, what was the price of computer without tax? 28. How many 4 digit whole numbers are possible if the first digit must be odd, the second digit must be prime, the third digit must be even and prime or odd and composite, and the fourth digit even? 29. What is the area of the region bounded by these graphs? x + y = 4 2x + y = 1 x = 5 30. Two different sized cubes have a combined surface area of 50,544. If the volume of the larger cube is 125 times that of the smaller, what is the volume of the larger cube?