2015年美国“数学大联盟杯赛”(中国赛区)初赛六年级试卷
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性别
Hale Waihona Puke Baidu
年级
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 ? years old.
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 × ? ( 2 2 A) 3 B) 5 ) C) 75 D) 152
( ) 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 2 6. Multiplying a number by is the same as dividing it by ( ) 3 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
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
姓名（正楷）
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) 30
12. The sum of two different primes cannot be ( ) A) odd B) even C) 123 D) a perfect square 13. The product of a circle’s circumference and radius divided by its area is B) π A) 2 C) 2π D) 2π2 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 1 1 1 15. 1 1 1 ( ) 3 4 5 1 1 C) 1 D) 1 A) 2 B) 3 60 6 16. The largest prime factor of 1 000 000 000 is A) 1 B) 2 C) 5 ( ) D) 10 D) 999 999 ( )
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 <= 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? 2 0 1 5 A P
姓名（正楷）
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. ( ) 1 2 A) B) C) 1.5 D) 3 3 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 don’t 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 826446281, 11 and 11. Answer: ___________.
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。
24. What fraction of the factors of 102 are factors of 10? ( ) 1 4 5 9 A) B) C) D) 10 9 9 10 25. Which of the following sums is equal to a prime number? ( ) 2 2 2 2 2 2 2 2 A) 29 + 66 B) 42 + 45 C) 22 + 64 D) 32 + 54 26. If the square shown is rotated 1890°counterclockwise, side ? at the top. ( ) A) A B) B C) C D) D will be
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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 ( ) 5 9 3 5 6 10 A) 6 × 10 B) 6 × 10 C) 3 × 5 D) 33 × 55
17. 999 999 × 999 998 = 999 9992 – ? ( ) A) 1 B) 999 997 C) 999 998
4. My brother is exactly twice my age, and he is 192 months old. I am
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
性别
Hale Waihona Puke Baidu
年级
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 ? years old.
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 × ? ( 2 2 A) 3 B) 5 ) C) 75 D) 152
( ) 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 2 6. Multiplying a number by is the same as dividing it by ( ) 3 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
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
姓名（正楷）
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) 30
12. The sum of two different primes cannot be ( ) A) odd B) even C) 123 D) a perfect square 13. The product of a circle’s circumference and radius divided by its area is B) π A) 2 C) 2π D) 2π2 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 1 1 1 15. 1 1 1 ( ) 3 4 5 1 1 C) 1 D) 1 A) 2 B) 3 60 6 16. The largest prime factor of 1 000 000 000 is A) 1 B) 2 C) 5 ( ) D) 10 D) 999 999 ( )
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 <= 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? 2 0 1 5 A P
姓名（正楷）
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. ( ) 1 2 A) B) C) 1.5 D) 3 3 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 don’t 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 826446281, 11 and 11. Answer: ___________.
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。
24. What fraction of the factors of 102 are factors of 10? ( ) 1 4 5 9 A) B) C) D) 10 9 9 10 25. Which of the following sums is equal to a prime number? ( ) 2 2 2 2 2 2 2 2 A) 29 + 66 B) 42 + 45 C) 22 + 64 D) 32 + 54 26. If the square shown is rotated 1890°counterclockwise, side ? at the top. ( ) A) A B) B C) C D) D will be
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„„„„„„„„„„„„„„„„„„装„„„„„„„„„„„„„„„„„订„„„„„„„„„„„„„„„„„线„„„„„„„„„„„„„„„„„„„„„„„ „„„„„„„„„„„„„„装„„„„„„„订„„„„„„„线„„„„„„„内„„„„„„„不„„„„„„„答„„„„„„„题„„„„„„„„„„„„„„„
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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 ( ) 5 9 3 5 6 10 A) 6 × 10 B) 6 × 10 C) 3 × 5 D) 33 × 55
17. 999 999 × 999 998 = 999 9992 – ? ( ) A) 1 B) 999 997 C) 999 998
4. My brother is exactly twice my age, and he is 192 months old. I am
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