AMC-8 2015 год. Англоязычная олимпиада, проводимая в США и Канаде. Пробуем свои силы!

Попробуйте свои силы в американской олимпиаде АМС-8! Регламент: пользоваться калькулятором нельзя, вспомогательным материалом тоже пользоваться нельзя. На 25 задач дают только 40 минут! Только несколько сотен школьников по все стране делают все задачи верно. Неправильный ответ НЕ штрафуется. Соцсети: Instagram: VK: FB: Twitch: Tiktok: @ Telegram: Тайм-коды: 0:00 Вступление 2:15 1. How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.) 3:45 2. Point O is the center of the regular octagon ABCDEF GH, and X is the midpoint of the side AB. What fraction of the area of the octagon is shaded? 5:25 3. Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of 10 miles per hour. Jack walks to the pool at a constant speed of 4 miles per hour. How many minutes before Jack does Jill arrive? 7:55 4. The Centerville Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible? 9:55 5. Billy’s basketball team scored the following points over the course of the first 11 games of the season: 42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73 If his team scores 40 in the 12th game, which of the following statistics will show an increase? 12:05 6. In △ABC, AB = BC = 29, and AC = 42. What is the area of △ABC? 14:54 7. Each of two boxes contains three chips numbered 1, 2, 3. A chip is drawnrandomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even? 17:00 8. What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19? 19:40 9. On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working 20 days? 21:30 10. How many integers between 1000 and 9999 have four distinct digits? 24:50 11. In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read ”AMC8”? 27:27 12. How many pairs of parallel edges, such as AB and GH or EH and F G, does a cube have? 29:45 13. How many subsets of two elements can be removed from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} so that the mean (average) of the remaining numbers is 6? 31:45 14. Which of the following integers cannot be written as the sum of four consecutive odd integers? 37:20 15. 40:10 16. 44:00 17. 50:05 18. 52:28 19. 56:30 20. 1:02:30 21. 1:07:50 22. 1:11:53 23. 1:20:55 24. 1:26:50 25. One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space? 1:29:57 Заключение