ROUND 1 1. TOSS-UP: What is 24% of 50? (12) (10 points) BONUS: A clothing store is having a 60% off sale on its dresses. Brandi has a coupon that lets her take 20% off of the sale price. If she pays $24 for a dress, what was the original price of the dress? ($75) (12 points) 2. TOSS-UP: A right triangle has legs of lengths 6 and 13. What is the length of the hypotenuse? (7) or (7 units) (10 points) BONUS: A triangle has two sides of lengths 6 and 8. If the length of the third side is also an integer, how many different lengths are possible for the third side? (11) (12 points) 3. TOSS-UP: How many square inches are in one square foot? (144) (10 points) BONUS: An 8-inch by 12-inch pan of brownies is cut into individual square-inch brownies. How many of the brownies border the edge of the pan? (36) (12 points) 4. TOSS-UP: If Kara is running at a speed of 10 miles per hour, how long will it take her to run a mile? (6 minutes) (10 points) BONUS: Ashley and Betsy live 10 miles apart and start running towards each other, with Ashley running one mile per hour faster than Betsy. If they meet after 40 minutes, what was Betsy s speed, in miles per hour? (7) or (7 mph) (12 points) 5. TOSS-UP: What is the mean of 2, 4, and 9? (5) (10 points) BONUS: Richard s first three test scores were 74, 83, and 67. What must he make on the fourth test to bring his average to 80? Assume that all four tests are weighted equally. (96) (12 points) 6. TOSS-UP: How many positive integers have exactly two digits? (90) (10 points) BONUS: If a two-digit positive integer is chosen at random, what is the probability that neither of its digits is a 7? Express you answer as a simplified fraction. (4/5) (12 points)
ROUND 2 1. TOSS-UP: What is the perimeter, in inches, of a square whose area is 49 square inches? (28) or (28 inches) (10 points) BONUS: A cube has a volume of x cubic centimeters and a surface area of x square centimeters, where x is a positive number. Find x. (216) (12 points) 2. TOSS-UP: Express 44% as a simplified fraction. (11/25) (10 points) BONUS: When Al got sick, his weight decreased by 20%. By what percentage would he have to increase his current weight in order to return to his previous weight? (25) or (25%) (12 points) 3. TOSS-UP: Between which two integers is the square root of 53? (7 and 8) (10 points) BONUS: A rectangular box is 6 feet long, 3 feet wide, and 2 feet high. What is the straight-line distance, in feet, from one corner of the box to the opposite corner? (7) or (7 feet) (12 points) 4. TOSS-UP: How many sides does a decagon have? (10) (10 points) BONUS: What is the measure, in degrees, of each interior angle of a regular decagon? (144) or (144 ) (12 points) 5. TOSS-UP: What is the median of 2, 0, 1, and 2? (1 ½ ) or (1.5) (10 points) BONUS: A company boasts that the average annual salary of its employees is $104,950. If the CEO of the company has an annual salary of $40,000,000, what is the average annual salary, in dollars, of the other 499 employees of the company? (25,000) or ($25,000) (12 points) 6. TOSS-UP: What is 20 divided by one-fourth? (80) (10 points) BONUS: A brownie recipe calls for two-thirds of a cup of sugar and makes 16 servings. How many cups of sugar would you need to make 78 servings? (3.25) or (3 ¼) or (13/4) (12 points)
ROUND 3 1. TOSS-UP: If a game starts at 3:45 and lasts for an hour and a half, at what time does the game finish? (5:15) (10 points) BONUS: How many minutes are there in a leap year? (527,040) (12 points) 2. TOSS-UP: What is the least common multiple of 8 and 10? (40) (10 points) BONUS: Express 5/8 9/10 + 7/12 as a simplified fraction. (37/120) (12 points) 3. TOSS-UP: What is the square root of one million? (1000) (10 points) BONUS: How many zeros are at the end of 125 28? (174) (12 points) 4. TOSS-UP: What is three-fourths of twenty? (15) (10 points) BONUS: Annie and Bobby are going to see a movie with 8 of their friends. They arrive early and find a row of 10 empty seats. If they seat themselves randomly, what is the probability that Annie and Bobby will sit next to each other? (1/5) or (0.2) or (20%) (12 points) 5. TOSS-UP: What is the mode of 2, 0, 1, and 2? (2) (10 points) BONUS: For six points each, find the exact values of the mean and the median of the set of prime numbers less than 30. (mean:12.9, median 12) (6 points each) 6. TOSS-UP: What is 49 times 51? (2,499) (10 points) BONUS: The hypotenuse of a right triangle is 2 inches longer than one of its legs. If the other leg is 12 inches long, what is the area, in square inches, of the right triangle? (210) or (210 sq. in.) (12 points)
ROUND 4 1. TOSS-UP: What is the sum of negative 4 and positive 7? (3) (10 points) BONUS: Find three consecutive integers whose product is negative 2,184? (-14, -13, -12) (in any order) (12 points) 2. TOSS-UP: Find the least common multiple of 4, 5, and 6. (60) (10 points) BONUS: Alex, Ben, and Corey share a dorm room, and they all have alarm clocks with snooze buttons. Alex sets his alarm to go off every 15 minutes; Ben s goes off every 20 minutes, and Corey s goes off every 25 minutes. If all three alarms go off at 6:30, and all three boys keep hitting the snooze button, what is the next time that all three alarms will go off? (11:30) (12 points) 3. TOSS-UP: Name two consecutive integers whose sum is 39. (19 and 20) (10 points) BONUS: Find the sum of the first 2012 positive integers. (2,025,078) (12 points) 4. TOSS-UP: What is the name of the type of triangle that has two congruent edges? (isosceles) (10 points) BONUS: The measure of the largest angle of an isosceles triangle is three times the measure of the smaller two angles. Find the measure, in degrees, of the largest angle. (108 ) (12 points) 5. TOSS-UP: What is one-half plus one-third plus one-sixth? (1) (10 points) BONUS: Swift can mow the lawn in an hour and a half. Mose can mow the same lawn in two hours. If Swift and Mose work together, how long will it take them to mow the lawn? Give the exact answer as a simplified fraction of an hour. (6/7) or (6/7 of an hour) (12 points) 6. TOSS-UP: In how many different ways can four books be arranged on a shelf? (24) (10 points) BONUS: If you toss a fair coin 8 times, what is the probability that it will come up heads exactly 4 times? Express your answer as a simplified fraction. (35/128) (12 points)
ROUND 5 1. TOSS-UP: In baseball, a hitter s batting average is computed by dividing the number of hits by the number of at-bats. If a batter has 400 at-bats over the course of a season, how many hits would he need to have a batting average of 0.300? (120) (10 points) BONUS: This year Chipper Jones retired after a career as one of baseball s best switch-hitters. In his major league career with the Atlanta Braves, he had 1,956 hits in 6,451 at-bats batting left-handed, while batting right-handed he had 770 hits in 2,533 at-bats. For 6 points each, calculate Chipper s career batting average batting left-handed, and his career batting average batting right-handed. Round each batting average to 3 decimal places. (LH: 0.303, RH: 0.304) (6 points each) 2. TOSS-UP: What is the product of the smallest two prime numbers? (6) (10 points) BONUS: Find the prime factors of 2013. (3, 11, and 61) (12 points) 3. TOSS-UP: What is the diameter, in centimeters, of a circle that has an area of 36 square centimeters? (12) or (12 cm) (10 points) BONUS: The minute hand on a clock is 12 centimeters long. Calculate the area, in square centimeters, swept out by the minute hand in one minute. Round your answer to two decimal places. (7.54) or (7.54 cm ) (12 points) 4. TOSS-UP: At the laundromat, it costs $2.50 to wash one load in the washing machine, which takes only quarters. How many quarters would you need to wash one load in this machine? (10) (10 points) BONUS: Imani has 31 coins in her purse, which are all nickels, dimes, or quarters. If there are two more dimes than quarters, and the value of the coins is $4.40, how many coins of each type does Imani have in her purse? (7 nickels, 13 dimes, and 11 quarters) (12 points) 5. TOSS-UP: Fred s microwave is so old that the buttons are broken for the numbers 0 and 1 on its numeric keypad. If Fred wants to microwave a slice of pizza for one minute and 30 seconds, what is the least amount of time greater than one minute and 30 seconds that he can punch in on his microwave? (2:22) (10 points) BONUS: Recall that the buttons are broken for the numbers 0 and 1 on Fred s microwave. If the electricity at Fred s house goes out and comes back on at a random time, what is the probability that he will be able to reset the clock on the microwave to the correct time of day, using 12-hour time, rather than 24-hour military time? Express the answer as simplified fraction. (16/45) (12 points) 6. TOSS-UP: How many edges does a cube have? (12) (10 points) BONUS: A regular dodecahedron is a three-dimensional solid with 12 pentagonal faces. For 6 points each, how many vertices and how many edges does a regular dodecahedron have? (20 vertices, 30 edges) (6 points each)
ROUND 6 1. TOSS-UP: If a quarterback passes the ball 40 times during a football game, and 80% of his passes are caught, how many of his passes are caught? (32) (10 points) BONUS: Quarterback Matt Ryan has led the Atlanta Falcons to be the only undefeated team in the National Football League so far this season. In 6 games, he has completed 160 out of 236 passes, for a completion percentage of 67.8%. What is the fewest number of additional passes Matt would need to raise his completion percentage for the season to 80%? (144) (12 points) 2. TOSS-UP: Today in Savannah, sunrise was at 7:32 a.m. Sunset will be at 6:45 p.m. How long will the sun be up today? (11 hrs, 13 min.) (10 points) BONUS: Dick said, Two days ago I was 12 years old. Later next year I will be 15 years old. For 6 points each, (a) When is Dick s birthday? (Dec. 31) (6 points) (b) On what day of the year did Dick make this statement? (Jan. 1) (6 points) 3. TOSS-UP: If you travel for two hours at a constant speed of 65 miles per hour, how many miles will you travel? (130) (10 points) BONUS: Two trains are heading towards each other on the same set of straight tracks. One train is traveling at 35 mph and the other at 45 mph. When the two trains are 100 miles apart, a bird starts flying from one train to the other at a speed of 60 mph. When the bird reaches a train, it immediately turns around and flies back in the opposite direction. How many miles does the bird fly before it is tragically crushed when the two trains collide? (75) or (75 miles) (12 points) 4. TOSS-UP: Give the value of three factorial. (6) (10 points) BONUS: How many distinct arrangements are there of the letters in the word FACTORIAL? (181,440) (12 points) 5. TOSS-UP: What is the sum, in degrees, of the measures of the interior angles in a quadrilateral? (360) or (360 ) (10 points) BONUS: A rhombus is a quadrilateral with four congruent edges. If one diagonal of a rhombus is 10 cm long, and the other diagonal is 24 cm long, what is the perimeter, in centimeters, of the rhombus? (52) or (52 cm) (12 points) 6. TOSS-UP: What is the largest two-digit prime number? (97) (10 points) BONUS: The sum of three distinct prime numbers is 40. For four points each, find these three prime numbers. (2, 7, and 31) (4 points each)
TIE-BREAKERS 1. TOSS-UP: An isosceles triangle has one angle with a measure of 100 degrees. Give o the measure of one of the other two angles. ( 40 ) (10 points) BONUS: A certain isosceles triangle has sides of length 5 cm, 5 cm, and 8 cm. Find 2 the area of the triangle, in square centimeters. (12) or (12 cm ) (12 points) 2. TOSS-UP: How many hours are there in three days? (72) (10 points) BONUS: Assume you started school on Tuesday, Sept. 4 of this year, and that you spend 8 hours each day at school. If you had no weekdays that you were out of school, on what date would you have been at school for 100 hours? (Sept. 20) (12 points) 3. TOSS-UP: When a normal die is rolled, each of the six faces, labeled 1 through 6, is equally likely to land face up. If a normal die is rolled, what is the probability that a prime number will land face up? (3/6) or (1/2) or (50%) or (0.5) (10 points) BONUS: If two normal dice are rolled, what is the probability that the sum of the numbers landing face up will be a prime number? Express your answer as a fraction in simplest form. (5/12) (12 points) 4. TOSS-UP: What is the product when you multiply ten to the fourth power by four? (forty thousand) (10 points) BONUS: An earthquake in San Francisco measured 5.6 on the Richter scale. That means that it was 10 to the 5.6 power times as intense as a standard earthquake. An earthquake that measures 8.6 on the Richter scale is how many times more intense than an earthquake that measures 5.6 on the Richter scale? 3 (1000) or ( 10 ) or (1000 times) (12 points) 5. TOSS-UP: Name a positive number that is twice as much as its square. (1/2) or (0.5) (10 points) BONUS: The number of inches in the perimeter of a certain square is twice the number of square inches in the area of the square. Find the perimeter of the square, in inches. (8) or (8 inches) (12 points) 6. TOSS-UP: What is the radius, in inches, of a circle whose area is π 64 square inches? (8) or (8 inches) (10 points) BONUS: A race track has the shape of a rectangle with semicircles at the shorter ends. The diameter of each semicircle is equal to the width of the rectangle, which is 50 yards. The length of the rectangle is 140 yards. To the nearest whole yard, what is the distance of one lap around the track? (437) or (437 yds) (12 points)