Columbus High School Middle School Math Tournament

Transcription

1 Columbus High School Middle School Math Tournament October 8, 2011 Individual Test Instructions - Do not open your test booklet until you are told to do so. - There are forty (40) multiple-choice questions on the test. Each correct answer is worth one (1) point, and there is no penalty for guessing. No calculator is allowed. - The individual test booklet is yours to keep, so you may use the margins for scratch work. Additional scratch paper will be provided; however, no answers written on the test booklet or scratch paper will be graded. All answers must be properly coded on the Scantron sheet. - Mark your answers on the Scantron sheet provided using only a #2 pencil. If you change your answer, be sure to erase completely. If you do not have a pencil, one will be provided. - You will have one (1) hour to complete this test. - If there is a tie, questions marked with an asterisk will be used as tie-breaker questions. The student who correctly answers fewer tie-breaker questions will be eliminated. If a tie still exists, the first student to miss a tie-breaker question will be eliminated CHS Middle School Math Tournament

2 1. The price of an antique chair is reduced by 20% and after a week, this price is reduced by 10%. If the original cost was $200, how much is the final price? A) $100 B) $140 $144 $160 $ Deborah is a very busy girl! If she has cross country practice for 1/12 of her 24 hour day, school for 7/24 of her day, eats for 6.25% of her day, and sleeps for 480 minutes, how many hours does she have leftover to do homework? A) 2 hours B) 3 hours 3.5 hours 4.5 hours 5.5 hours 3. What integer is closest to? A) 5 B) Solve for x: A) -8/3 B) 1/3 8/ Find the measurement of x. 6. Find the next term of the sequence: 2, 4, 7, 11, 16, A) 18 B) The sun burns approximately 4.4 tons of hydrogen per second. How much hydrogen will the sun burn in 24 hours? A) 4.4 B) There are 21 markers in a bag. Three are blue, 3 are red, 4 are green, and the rest are yellow. What is the probability that a randomly selected marker is green or yellow? A) 4/21 B) 11/21 3/7 5/ If, what does equal? A) 6 B) Simplify: A) 35 B) x Note: Figure not drawn to scale. A) B) CHS Middle School Math Tournament

3 11. If a + 3b is equal to 175 percent of 6b, what is the value of a/b? A) -6 B) -16/5 30/8 18/5 15/2 12. Corey and Aditya were once the same height. Since then, Aditya has grown 20% while Corey has grown half as many inches as Aditya. If Aditya is now 60 inches tall, how tall, in inches, is Corey? A) 48 B) How many cubic yards of concrete are needed to make a cement floor with dimensions, 9 ft. by 12 ft. by 6 in. thick? A) 2 yd³ B) 4 yd³ 18 yd³ 24 yd³ 54 yd³ 14. Sarah has $200 in her bank account. If she deposits $10 weekly, which of the following formulas will show her account balance,, at the end of weeks? A) B) 15. Zasmine is 5-feet tall and she lets go of 3 blue and 3 green helium filled balloons. If the blue balloons go up at a rate of 5 ft/sec and the green go up at a rate of 2 ft/sec, what is the elevation of each balloon after 20 seconds? A) Blue: 105 ft. ; Green: 45 ft. B) Blue: 40 ft. ; Green: 100 ft. Blue: 100 ft. ; Green: 40 ft. Blue: 45 ft. ; Green: 100 ft. Blue: 105 ft. ; Green: 40 ft. 16. Which length is greatest? A) B) The tax rate in one school district is $48 per $1000 of assessed value. What is the tax on a house assessed at $210,000? A) $100,080 B) $10,080 $1,080 $1,008 $ Find the fifth multiple of A) 25/56 B) 5/14 5/7 1 5 ( ) ( ) CHS Middle School Math Tournament 3

4 19. Solve. A) 13 B) Jacob took three tests this semester. He received 80% on a thirty question test, 90% on a fifty question test, and 93% on a 100-question test. What percent of all questions did Jacob answer correctly? A) 63% B) 75% 77% 80% 90% 21. If a b = for all positive integers a and b, what does 8 6 equal? A) -4/3 B) -3/4 3/4 4/3 None of these 22. In a class of 20 people, the average on a test for the class was 92. If 10 people got a 100 on their test, what was the average for the 10 people who did not get a 100? A) 82 B) * is the product of two consecutive integers. It is also the product of three consecutive integers. What is the sum of the 5 integers? A) 47 B) *24. If a can of beans has a volume of 96π grams, what would be the volume of a cone with congruent dimensions? A) 288π grams B) 183π grams 64π grams 32π grams 24π grams 25. Bob and Alice were both born in However, Bob was born on February 29 th, which only occurs in a leap year or once every four years. By the last day of 2012, what will be the ratio of birthdays that Bob has celebrated to the number that Alice has celebrated? A) 1:2 B) 1:3 1:4 1:5 2:3 26. Students need a 4-character password to log onto school computers. The first two characters are letters of the alphabet and may not be repeated. The last 2 are digits from 1 through 9 and can be repeated. How many different passwords are possible? A) 52,650 B) 54,756 58,500 65,000 67, CHS Middle School Math Tournament 4

5 27. Given A = {0, 1, 2, 4, 8, 9}, B = {1, 3, 6, 7, 9}, C = {0, 2, 4, 6, 10}, and D = {9}. Find the set of [(A B) C] D. A) {9} B) {0, 1, 2, 3, 4, 6, 7, 8, 9, 10} {0, 2, 4, 6, 9,10} {0, 2, 4, 6, 9} { } *28. What is the units digit for? A) 0 B) *29. In the world of Zlorg, there exist different types of robots. There are 17 that can fly, 24 that have red eyes, and 21 that are evil. Ten robots can fly and have red eyes. Five can fly and are evil. Six have red eyes and are evil. If there are exactly 4 robots that can fly, have red eyes and are evil, determine the total number of robots on planet Zlorg. A) 42 B) Given = 175, find the value of x in the key configuration below. *31. Find the sum of the marked angles x, y, and z in the figure below, given and a. A) 180 B) *32. A sphere is placed inside a cube. The diameter of the sphere equals the length of the edge of the cube. If the volume of the cube is 512 cm³, how much volume is not taken up by the sphere? ( A) B) x a *33. Spongebob has a certain number of ties. Given that and Spongebob has b red-checkered ties, how many red-checkered ties does Spongebob have? y z Note: Figure not drawn to scale. l m A) 0 B) x A) 321 B) CHS Middle School Math Tournament 5

6 *34. Harry travels into the depths of Hogwarts, led by his telepathy with the dreaded basilisk. He arrives there at exactly 12:00 AM. The number of minutes he will spend in the Chamber of Secrets is inversely proportional to the number of minutes Ginny spends in the Chamber. Say Ginny spends 20 minutes in the Chamber, then Harry would spend 30 minutes in the Chamber. If Ginny spends 15 minutes in the Chamber, what time will Harry exit the Chamber of Secrets? A) 12:40 PM B) 12:22 AM 12:40 AM 12:45 AM 1:00 AM 35. A) 1 B) *36. If A, B, and C are the vertices of a triangle. Find the slope of the altitude from B to. A) B)? *37. Write the following with no negative exponents: A) B) *38. Two lines have slopes whose sum is 5 and both go through the point (1, 1). If one line goes through (5, ) and the other line goes through (5, ), then is equal to A) 6 B) How many of the first one hundred positive integers are divisible by all of the numbers 2, 3, 4, 5? A) 4 B) A school has 1200 students. Each student takes 4 classes a day. Each teacher teaches 4 classes. Each class has 30 students and 1 teacher. How many teachers are there at this school? A) 30 B) CHS Middle School Math Tournament 6