2015年美国“数学大联盟杯赛”(中国赛区)初赛六年级试卷.pdf

2012014 4- -2012015 5 年度美国“数学大联盟杯赛”年度美国“数学大联盟杯赛”( (中国赛区中国赛区) )初初赛赛 ( (六六年级年级) ) ( (初赛时间：初赛时间：20152015 年年 1 1 月月 3 3 日日，考试时间，考试时间 9 90 0 分钟分钟，总分，总分 200200 分分) ) 学学生诚信协议生诚信协议：：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论， 我确定以下的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚 一、选择题一、选择题( (每小题每小题 5 5 分，分，答对加答对加 5 5 分，答错不扣分，分，答错不扣分，共共 175175 分分，，请将正确答案请将正确答案 A A、、B B、、C C 或者或者 D D 写在每题后面的圆括号内写在每题后面的圆括号内) ) 正确答案填写示例如下： 20 5 2 = 2 ? ( A ) A) 5 B) 15 C) 25 D) 30 1. 2 0 + 1 4 2 0 + 1 5 = ( ) A) 0 B) 5 C) 9 D) 15 2. There are 84 beavers in a colony. Yesterday they all went out in teams of 6 to collect logs. Today they are all going out in teams of 4. There will be ? more teams today than there were yesterday. ( ) A) 2 B) 7 C) 14 D) 21 3. 12 345 + 54 321 = 11 111 ? ( ) A) 66 666 B) 666 C) 66 D) 6 4. My brother is exactly twice my age, and he is 192 months old. I am ? years old. ( ) A) 8 B) 16 C) 32 D) 96 5. Apple cost $1.25 each, or 3 for $3. If I want to buy 11 apples, I need at least how much money? ( ) A) $11.00 B) $11.50 C) $12.00 D) $13.75 6. Multiplying a number by 2 3 is the same as dividing it by ( ) A) 0.667 B) 0.75 C) 1.5 D) 1.667 7. How many prime factors of 120 are multiples of 4? ( ) A) 0 B) 6 C) 7 D) 8 8. I have test scores of 80, 84, and 94, and I want my average test score to be 86 after my next test. What score must I get on the next test? ( ) A) 0 B) 86 C) 87 D) 88 9. The lengths of the sides of a triangle are consecutive even integers. Which of the following cannot be the length of the longest side? ( ) A) 6 B) 10 C) 12 D) 16 10. Nigel has the volume set at 8, but it goes to 10. He could increase the volume by at most ? . ( ) A) 2% B) 10% C) 20% D) 25% 11. 752 25 = 252 ? ( ) A) 32 B) 52 C) 75 D) 152 12. The sum of two different primes cannot be ( ) A) odd B) even C) 123 D) a perfect square 13. The product of a circles circumference and radius divided by its area is ( ) A) 2 B) C) 2 D) 22 14. Mr. Wells is becoming invisible. Today he is 100% visible, but each morning from tomorrow on he will wake to find himself 80% as visible as he had been the day before. He will first be less than 50% visible in ? days. ( ) A) 3 B) 4 C) 5 D) 6 15. 111 111 345 ( ) A) 2 B) 3 C) 1 1 6 D) 1 1 60 16. The largest prime factor of 1 000 000 000 is ( ) A) 1 B) 2 C) 5 D) 10 17. 999 999 999 998 = 999 9992 ? ( ) A) 1 B) 999 997 C) 999 998 D) 999 999 18. The combined value of my quarters and nickels is ten times the combined value of my pennies and nickels. If I have the same number of pennies as nickels, my ratio of quarters to pennies is ( ) A) 1:1 B) 2:1 C) 10:3 D) 11:5 19. 500 is ? % greater than 200. ( ) A) 50 B) 150 C) 250 D) 300 20. Between 100 and 1000, ? numbers are squares of odd integers. ( ) A) 11 B) 16 C) 21 D) 31 21. A square of perimeter 360 consists of exactly ? squares of area 9. ( ) A) 40 B) 400 C) 900 D) 1600 22. The largest odd factor of 66 1010 is ( ) A) 65 109 B) 63 105 C) 36 510 D) 33 55 23. Greg finished senior year without learning how to type! His friend Ori charged him $4 per page the first time a page was typed, and $2 each time a page was redone. Ori typed 150 pages, then redid 30 pages, and finally redid 15 pages a 2nd time. The total cost to Greg was ( ) A) $660 B) $690 C) $720 D) $760 - 1 - - 2 - 城市城市 区区 学校学校 年级年级 性别性别 姓名（正楷）姓名（正楷） 装订线装订线 装订装订线内不答线内不答题题 0 2 1 5 A B D C P 24. What fraction of the factors of 102 are factors of 10? ( ) A) 1 10 B) 4 9 C) 5 9 D) 9 10 25. Which of the following sums is equal to a prime number? ( ) A) 292 + 662 B) 422 + 452 C) 222 + 642 D) 322 + 542 26. If the square shown is rotated 1890 counterclockwise, side ? will be at the top. ( ) A) A B) B C) C D) D 27. The least common multiple of 22, 42, 62, 82, and 102 is ( ) A) 3840 B) 14 400 C) 57 600 D) 230 400 28. A snail crawls 2400 mm per hour. It takes ? seconds to crawl 1 mm. ( ) A) 1 3 B) 2 3 C) 1.5 D) 3 29. A circle can intersect a quadrilateral at ? points. ( ) A) 0, 2 or 8 only B) 0, 2, 4, 6 or 8 only C) 1, 2, 3, 4, 6, or 8 only D) 0, 1, 2, 3, 4, 5, 6, 7, or 8 30. Carla loves shells! She collects them, labelling each with a 1-, 2-, or 3-letter code. If the same letters are used in a different order, it is a different code. She has used every such code, so she has ? shells. ( ) A) 156 B) 17 576 C) 18 278 D) 20 888 31. If the sum of 50 consecutive integers is 1525, what is the sum of the next 50 consecutive integers? ( ) A) 1575 B) 2775 C) 4025 D) 76 250 32. Of 4 pairs of twins, 3 students are chosen to do a report together. There are ? possible groups of 3 that dont include both twins from a pair. ( ) A) 16 B) 24 C) 28 D) 32 33. 八年后我的年龄是两年前我的年龄的两倍。

请问两年后我是几岁？ ( ) A) 14 B) 16 C) 18 D) 20 34. 将 0.75 转换为分数，这些分数的分子和分母都是小于 100 的正整数这样的分数共有 多少个？ ( ) A) 3 B) 24 C) 25 D) 33 35. 船长们划船 5 个小。