1、 2014-2015 年度美国“数学大联盟杯赛” (中国赛区 )初 赛 (六 年级 ) (初赛时间： 2015 年 1 月 3 日 ，考试时间 90 分钟 ，总分 200 分 ) 学 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 (每小题 5 分， 答对加 5 分，答错不扣分， 共 175 分 ， 请将正确答案 A、 B、 C或者 D 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)
2、 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 =
3、 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. Mu
4、ltiplying a number by 23 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
5、 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 ?
6、. ( ) 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 i
7、nvisible. 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. 1 1 11 1 1345 ( ) A) 2 B) 3 C) 116 D) 1160 16. The largest prime factor of 1
8、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 pen
9、nies 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) 160
10、0 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
11、finally redid 15 pages a 2nd time. The total cost to Greg was ( ) A) $660 B) $690 C) $720 D) $760 - 1 - - 2 - 城市区学校年级性别姓名（正楷）装订线装订线内不答题0 2 1 5 A B D C P 24. What fraction of the factors of 102 are factors of 10? ( ) A) 110 B) 49 C) 59 D) 910 25. Which of the following sums is equal to a prime number
12、? ( ) 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
13、 hour. It takes ? seconds to crawl 1 mm. ( ) A) 13 B) 23 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-,
14、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)
15、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
16、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 个小时。从第二个小时开始，每个小时行驶的距离比 前一个小时少了 2 千米。如果 5 个小时的平均行驶速度是 6 千米 /小时 ， 那么前 2 个小时行驶了多少千米？ ( ) A) 6 B) 12 C) 16 D) 18 二 、 填空 题 (每小题 5 分， 答对加 5 分，答错不扣分， 共 25 分 ) 36. Calculate the number of digits which are equal to 0 in the product of 82644628
17、1, 11 and 11. Answer: _. 37. In this problem as shown on the right, each square represents a digit from 0 to 9. What is the final product? Answer: _. 38. For some integer n, the sum of all of the digits of n is a multiple of 8 and the sum of all of the digits of n + 1 is also a multiple of 8. If n =
18、 2015, what is the greatest possible value of n? Answer: _. 39. In triangle ABC on the right, BD:DC = 1:2. If the area of triangle ABP is 7 and the area of triangle ACP is 5, what is the area of triangle ADP? Answer: _. 40. 地球表面由陆地和海洋构成，其中陆地面积占 29%，并且陆地的四分之三 在北半球，那么 北半球的海洋面积占所有海洋面积的 _%。 （结果四舍五入保留整数） - 3 - - 4 - 城市区学校年级性别姓名（正楷）装订线装订线内不答题
