2018年美国“数学大联盟杯赛”(中国赛区)初赛五年级试卷(1)
2018 年小学五年级数学竞赛试题(附答案)
9 2018 年小学五数学竞赛试题（附答案）【学生注意】请把答案写在答题纸上，只填在原题上不得分． 考试时间 70 分钟，总分 150 分一、 填空题 I （本大题共 10 小题，每题 6 分，共 60 分）1. 计算： 1 + 1 + 1 =． 2 4 82. 一项工程，甲单独做 18 天完成，乙单独做 36 天完成，那么甲乙合作 天能完成．3. 六位数1A 211B 是 72 的倍数，那么 A + B = ．4. 156 有 个约数．5. 车库中停着摩托车和小轿车，一共 39 辆，已知摩托车的数量和小轿车的数量之比是 6 : 7，那么车库 中的小轿车有 辆．6. 甲乙两个自然数，它们的最大公约数是 6，最小公倍数是 144．甲是 48，那么乙是．7. 运送一堆水泥，第一天运了这堆水泥的 2，第二天运了剩下的 3 ，还剩下 12 吨没有运，这堆水泥有二、 填空题 I I （本大题共 6 小题，每题 7 分，共 42 分）11. 20180101 ÷11的余数是 ．12. 4 + 4++4 + 4=． 3 ⨯ 7 7 ⨯1155 ⨯ 59 59 ⨯ 6313. 一个三位数，若首位数字可被 5 整除，前两位数可被 4 整除，这个三位数可被 3 整除，那么这样的 三位数有 个．14. 如图，△BCE 的面积为 16 平方厘米，高 E H = 4 厘米，延长 C B 至点 A ， A B = 2厘米，△BCE 外有 一点 D ，连接 AD 、BD ，EC 与 BD 相交于点 F ，△BEF 比△DFC 的面积大 4 平方厘米，△ABD 的面 积是平方厘米．E7 5D吨．F8. 阿呆和阿瓜绕着一个圆形操场跑步，阿呆 3 分钟跑一圈，阿瓜 5 分钟跑一圈．两人同时从同一起点出发，分钟后两人第一次同时回到起点．9. 一堆苹果不到 100 个，3 个 3 个数多 2 个，4 个 4 个数多 3 个，5 个 5 个数多 4 个，那么这堆苹果有AB H C15. 下图中有个等腰梯形．个．10. 下图中，正三角形和正六边形的周长相等，已知正三角形的面积为 6 平方厘米，那么正六边形的面 积是平方厘米．16. A 、B 两码头相距 45 千米，每天定时有甲、乙两艘船速相同的客轮分别从两码头同时出发相向而行．一天甲船从上游 A 码头出发时掉下一物，此物浮于水面顺水漂下，4 分钟后，与甲船相距 1 千米．预 计乙船出发后小时可以与此物相遇．-1--2-三、 填空题 I II （本大题共 3 小题，每题 9 分，共 27 分）17. 一个国家住着两种人，善面人和恶面人，善面人只说真话，恶面人只说假话．一天这个国家的 2018 位居民从前往后排成一列，每个人“在我后面的恶面人比在我前面的善面人”那么这 2018 个居民里一共有 个善面人．18. 三个连续自然数，从小到大排列，第一个数有 2 个约数，第二个数有 4 个约数，第三个数有 6 个约 数，那么这三个数之和最小是 ．19. 如图，在梯形 A BCD 中，E 是 A D 上最靠近 A 的三等分点，G 点是 B C 上最靠近 B 的四等分点，已知 三角形 E DG 面积为 20，三角形 C EG 面积为 24．那么梯形 A BCD 的面积是 ．四、 解答题（本大题共 1 小题，3 小问，第 1 问 6 分，第 2 问 7 分，第 3 问 8 分，共 21 分）20. 一项工程，由甲队单独承担，需工期 60 天；由乙队单独承担，需工期 l 00 天．为节省工期，实际施 工时，甲、乙两队合作若干天后，撤出乙队，由甲队继续做到工程完成时，一共用了 42 天． （1）甲队单独工作 42 天能完成全部的几分之几？（2）甲、乙两队合作了多少天？（3）如果甲队单独完成需要工程费 90 万元，乙队单独完成需要工程费 70 万元，那么甲、乙两队共 得多少工程费？ABGEFD C-3- -4-。
2018年美国“数学大联盟杯赛”(中国赛区)初赛四年级试卷(1)
2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛(四年级)(初赛时间：2017年11月26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，我确定我所填写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。
请在装订线内签名表示你同意遵守以上规定。
考前注意事项：1. 本试卷是四年级试卷，请确保和你的参赛年级一致；2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；3. 请确保你已经拿到以下材料：本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、草稿纸。
考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、及如何参加复赛的说明。
其他材料均不能带走，请留在原地。
选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。
1.Which of the following is the smallest?A) 2.018 B) 20.18 C) 0.218 D) 20182.What is the least common multiple of 20 and 18?A) 90 B) 180 C) 240 D) 3603.The sum of the degree-measures of the exterior angles of a triangle is?A) 180 B) 360 C) 540 D) 7204.In the figure on the right, please put the numbers 1 – 11 in the elevencircles so that the three numbers in every straight line add up to 18.What is the number in the middle circle? Note: There are 5 straightlines in total in this figure.A) 6 B) 7 C) 8 D) 95.I am a lovely cat. When I multiply the digits of a whole numberand the product I get is 8, I put that whole number on my list offavorite numbers. Of the whole numbers from 1000 to 9999,how many would I put on my list of favorite numbers?A) 10 B) 12 C) 16 D) 206.Two planes take off at the same time from the same point to race to apoint and back. Place A travels at 180 miles per hour on the way out and240 miles per hour on the return trip. Plane B covers the entire distance at an averagespeed of 210 miles per hour. Which plane wins the race, or is it a tie?A) plane A wins B) plane B winsC) a tie D) non-deterministic 7.52 × 88 = 44 ×?A) 102 B) 96 C) 104 D) 1248.What is the smallest whole number that leaves a remainder of 4, 5, 6 when divided byeach of 5, 6, 7?A) 29 B) 209 C) 210 D) 20099.In △ABC, m∠A + m∠C = m∠B. What is the degree measure of ∠B?A) 80 B) 90 C) 100 D) 18010.I bought a toy for $10, sold it for $20, rebought it for $30, and resold it for $40. My totalprofit on the 4 transactions was ?A) 10 B) 20 C) 30 D) 4011.What is the greatest number of integers I can choose from the first ten positive integers sothat any 3 of the chosen integers could be the lengths of the three sides of a triangle?A) 4 B) 5 C) 6 D) 712.How many whole numbers between 200 and 400 have all their digits increasing in valuewhen read from left to right?A) 30 B) 36 C) 42 D) 4813.What is the value of 1% of 10% of 100?A) 0.01 B) 0.1 C) 1 D) 1014.If three cats can eat three bowls of food in three minutes, how many minutes will it take100 cats to eat 100 bowls of food?A) 1 B) 3C) 100 D) None of the above15.There are three squares. The area of the smallest one is 2. The side-length of the secondsquare is twice the side-length of the smallest one. And the side-length of the third square is three-times the side-length of the smallest one. The total area of the three squares isA) 12 B) 28 C) 36 D) 7216.A man, who had been married for three years, spent25of his yearly income on his family,14on business, and110on personal travel. If he saved $45000 during those three years, what was his annual income?A) $45000 B) $50000C) $65000 D) None of the above17.Given four different integers, at most how many different sums can be formed bychoosing two, three, or four of them and finding each sum?A) 8 B) 9 C) 10 D) 1118. Max places 100 eggs in 10 baskets, with each basket receiving at least1 egg, but no2 baskets receiving the same number of eggs. What is the greatest number of eggs that may be placed in a basket?A) 45 B) 47 C) 55 D) 6519. 2 + 3 × 4 – 5 =A) 0 B) 6 C) 9 D) 15 20. What is the highest power of 2 that divides 2 × 4 × 6 × 8 × 10? A) 25 B) 27 C) 28 D) 215 21. Which of the following is a prime number?A) 2017B) 2018C) 2015D) 201622. What is the greatest possible number of acute angles in a figure consisting of a triangleand a line passing through two sides of the triangle?A) 5B) 6C) 7D) 823. Amy can solve 5 questions every 3 minutes. Kate can solve 3 questions every 5 minutes.How many more questions Amy can solve than Kate in one hour?A) 15B) 32C) 60D) 6424. Using 3 Ts and 2 Js, in how many different orders can the five letters be arranged? Forexample, TTTJJ and TTJJT are two such different orders.A) 2B) 10C) 20D) 6025. Coastal Coconuts can divide all their coconuts evenly among 8, 9, or10 customers, with 1 coconut left over each time. If Coastal Coconuts has more than 1 coconut, what is the least number of coconuts they could have?A) 561 B) 721C) 831 D) None of the above 26. 35 ÷ 32 =A) 3 B) 9 C) 27 D) 81 27. If the sum of three prime numbers is 30, what is the least prime number?A) 2B) 3C) 5D) 728. Juxtaposing two identical squares to form a rectangle, the perimeter of the rectangle is 12less than the sum of the perimeter of the two squares. What is the side-length of the original square?A) 3B) 6C) 9D) 1229. It takes Mike 2 hours to finish a task. It takes 4 hours for Tom to finish the same task.Mike and Tom worked together on this task for one hour before Mike had to leave. How long will it take Tom to finish the rest of the task?A) 1 B) 2 C) 3 D) 4 30. The number of triangles in the figure on the right isA) 9 B) 10 C) 11 D) 12 31. What is the thousands digit of the product 1234560 × 2345670 × 3456780?A) 8B) 6C) 5D) 032. The sum of nine consecutive positive integers is always divisible byA) 2B) 5C) 7D) 933. You can put as many as 96 books in 6 backpacks. How many backpacks are necessary for144 books?A) 7B) 8C) 9D) 1034. The number of nickels I have is twice the number of dimes I have, and together thesecoins are worth more than $1. The least number of dimes that I can have isA) 5B) 6C) 8D) 1035. The ages of four kids are four consecutive positive integers. The product of their ages is3024. How old is the oldest kid?A) 8B) 9C) 10D) 1136. In the Game of Life, you earn 3 points for flipping a coin to “heads”, and 5 points forflipping a coin to “tails”. In all, how many positive whole number scores are IMPOSSIBLE to get after flipping it one or more times?A) 4B) 5C) 7D) 1137. Four monkeys can eat four bags of peanuts in three minutes. How many monkeys will ittake to eat 100 bags of peanuts in one hour?A) 4 B) 5 C) 20 D) 100 38. The tens digit of the product of the first 100 positive integers isA) 2B) 4C) 8D) 039. Someone put three dimes into my pile of quarters. If I add up the value of these coins,including the dimes, the sum could beA) $6.25B) $7.75C) $8.05D) $9.5040. Brooke's empty tub fills in 20 minutes with the drain plugged, andher full tub drains in 10 minutes with the water off. How manyminutes would it take the full tub to drain while the water is on?A) 12B) 15 C) 20 D) 30。
2018年美国“数学大联盟杯赛”（中国赛区）初赛四年级试卷（1）
2018年美国“数学⼤联盟杯赛”（中国赛区）初赛四年级试卷（1）2017-2018年度美国“数学⼤联盟杯赛”(中国赛区)初赛(四年级)(初赛时间：2017年11⽉26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，我确定我所填写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。
请在装订线内签名表⽰你同意遵守以上规定。
考前注意事项：1. 本试卷是四年级试卷，请确保和你的参赛年级⼀致；2. 本试卷共4页(正反⾯都有试题)，请检查是否有空⽩页，页数是否齐全；3. 请确保你已经拿到以下材料：本试卷(共4页，正反⾯都有试题)、答题卡、答题卡使⽤说明、英⽂词汇⼿册、草稿纸。
考试完毕，请务必将英⽂词汇⼿册带回家，上⾯有如何查询初赛成绩、及如何参加复赛的说明。
其他材料均不能带⾛，请留在原地。
选择题：每⼩题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。
1.Which of the following is the smallest?A) 2.018 B) 20.18 C) 0.218 D) 20182.What is the least common multiple of 20 and 18?A) 90 B) 180 C) 240 D) 3603.The sum of the degree-measures of the exterior angles of a triangle is?A) 180 B) 360 C) 540 D) 7204.In the figure on the right, please put the numbers 1 – 11 in the elevencircles so that the three numbers in every straight line add up to 18.What is the number in the middle circle? Note: There are 5 straightlines in total in this figure.A) 6 B) 7 C) 8 D) 95.I am a lovely cat. When I multiply the digits of a whole numberand the product I get is 8, I put that whole number on my list offavorite numbers. Of the whole numbers from 1000 to 9999,how many would I put on my list of favorite numbers?A) 10 B) 12 C) 16 D) 206.Two planes take off at the same time from the same point to race to apoint and back. Place A travels at 180 miles per hour on the way out and240 miles per hour on the return trip. Plane B covers the entire distance at an averagespeed of 210 miles per hour. Which plane wins the race, or is it a tie?A) plane A wins B) plane B winsC) a tie D) non-deterministic 7.52 × 88 = 44 ×?A) 102 B) 96 C) 104 D) 1248.What is the smallest whole number that leaves a remainder of 4, 5, 6 when divided byeach of 5, 6, 7?A) 29 B) 209 C) 210 D) 20099.In △ABC, m∠A + m∠C = m∠B. What is the degree measure of ∠B?A) 80 B) 90 C) 100 D) 18010.I bought a toy for $10, sold it for $20, rebought it for $30, and resold it for $40. My totalprofit on the 4 transactions was ?A) 10 B) 20 C) 30 D) 4011.What is the greatest number of integers I can choose from the first ten positive integers sothat any 3 of the chosen integers could be the lengths of the three sides of a triangle?A) 4 B) 5 C) 6 D) 712.How many whole numbers between 200 and 400 have all their digits increasing in valuewhen read from left to right?A) 30 B) 36 C) 42 D) 4813.What is the value of 1% of 10% of 100?A) 0.01 B) 0.1 C) 1 D) 1014.If three cats can eat three bowls of food in three minutes, how many minutes will it take100 cats to eat 100 bowls of food?A) 1 B) 3C) 100 D) None of the above15.There are three squares. The area of the smallest one is 2. The side-length of the secondsquare is twice the side-length of the smallest one. And the side-length of the third square is three-times the side-length of the smallest one. The total area of the three squares isA) 12 B) 28 C) 36 D) 7216.A man, who had been married for three years, spent25of his yearly income on his family,14on business, and110on personal travel. If he saved $45000 during those three years, what was his annual income?A) $45000 B) $50000C) $65000 D) None of the above17.Given four different integers, at most how many different sums can be formed bychoosing two, three, or four of them and finding each sum?A) 8 B) 9 C) 10 D) 1118. Max places 100 eggs in 10 baskets, with each basket receiving at least1 egg, but no2 baskets receiving the same number of eggs. What is the greatest number of eggs that may be placed in a basket?A) 45 B) 47 C) 55 D) 6519. 2 + 3 × 4 – 5 =A) 0 B) 6 C) 9 D) 15 20. What is the highest power of 2 that divides 2 × 4 × 6 × 8 × 10? A) 25 B) 27 C) 28 D) 215 21. Which of the following is a prime number?A) 2017B) 2018C) 2015D) 201622. What is the greatest possible number of acute angles in a figure consisting of a triangleand a line passing through two sides of the triangle?A) 5B) 6C) 7D) 823. Amy can solve 5 questions every 3 minutes. Kate can solve 3 questions every 5 minutes.How many more questions Amy can solve than Kate in one hour?A) 15B) 32C) 60D) 6424. Using 3 Ts and 2 Js, in how many different orders can the five letters be arranged? Forexample, TTTJJ and TTJJT are two such different orders.A) 2B) 10C) 20D) 6025. Coastal Coconuts can divide all their coconuts evenly among 8, 9, or10 customers, with 1 coconut left over each time. If Coastal Coconuts has more than 1 coconut, what is the least number of coconuts they could have?A) 561 B) 721C) 831 D) None of the above 26. 35 ÷ 32 =A) 3 B) 9 C) 27 D) 81 27. If the sum of three prime numbers is 30, what is the least prime number?A) 2B) 3C) 5D) 728. Juxtaposing two identical squares to form a rectangle, the perimeter of the rectangle is 12less than the sum of the perimeter of the two squares. What is the side-length of the original square?A) 3B) 6C) 9D) 1229. It takes Mike 2 hours to finish a task. It takes 4 hours for Tom to finish the same task.Mike and Tom worked together on this task for one hour before Mike had to leave. How long will it take Tom to finish the rest of the task?A) 1 B) 2 C) 3 D) 4 30. The number of triangles in the figure on the right isA) 9 B) 10 C) 11 D) 12 31. What is the thousands digit of the product 1234560 × 2345670 × 3456780?A) 8B) 6C) 5D) 032. The sum of nine consecutive positive integers is always divisible byA) 2B) 5C) 7D) 933. You can put as many as 96 books in 6 backpacks. How many backpacks are necessary forA) 7B) 8C) 9D) 1034. The number of nickels I have is twice the number of dimes I have, and together thesecoins are worth more than $1. The least number of dimes that I can have isA) 5B) 6C) 8D) 1035. The ages of four kids are four consecutive positive integers. The product of their ages is3024. How old is the oldest kid?A) 8B) 9C) 10D) 1136. In the Game of Life, you earn 3 points for flipping a coin to “heads”, and 5 points forflipping a coin to “tails”. In all, how many positive whole number scores are IMPOSSIBLE to get after flipping it one or more times?A) 4B) 5C) 7D) 1137. Four monkeys can eat four bags of peanuts in three minutes. How many monkeys will ittake to eat 100 bags of peanuts in one hour?A) 4 B) 5 C) 20 D) 100 38. The tens digit of the product of the first 100 positive integers isA) 2B) 4C) 8D) 039. Someone put three dimes into my pile of quarters. If I add up the value of these coins,including the dimes, the sum could beA) $6.25B) $7.75C) $8.0540. Brooke's empty tub fills in 20 minutes with the drain plugged, and her full tub drains in 10 minutes with the water off. How many minutes would it take the full tub to drain while the water is on?A) 12B) 15 C) 20 D) 30。
2014-2015年美国“数学大联盟杯赛”(中国赛区)初赛五年级试卷
………………………………………………装……………………………………………订……………………………………………线…………………………………………………………… ……………………………………装…………………订…………………线…………………内…………………不…………………答…………………题………………………………………2014-2015 年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)(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) 25D) 301. Three cases of 24 cans each is the same number of cans as twelve boxes of ? cans each. ( )A) 6 B) 15 C) 21 D) 96 2. A trapezoid has ? sides. ( )11. Thok has a simple plan. He will spend 50% of the day in the cave, 25% of the rest of the day on the hunt, and the remainder of the day watching films outside. How many hours will Thok spend watching films? ( ) A) 3 B) 6 C) 9 D) 25 12. 2 × 3 × 6 × 36 × 2 × 3 × 6 × 36 = ( )A) 65 B) 66C) 67D) 6813. I have 5 pennies, 4 nickels, 3 quarters, 2 half-dollars, and 1 dollar. The average value of one of my coins is ( )14.Wyatt O’Vine’s sheep weighs twice as much as Wyatt, and Wyatt weights twice as much as his hat. If Wyatt, his sheep, and his hat have a combined weight of 210 kg, how much does Wyatt weigh? ( ) A) 30 kg B) 35 kg C) 60 kg D) 70 kg 15. (12 + 34) × (56 + 78) = 12 × (56 + 78) + ? × (56 + 78) ()A) 12 B) 34 C) 56 D) 78 16. If 2 flocks equal 5 flecks, then 500 flocks equal ? flecks. ( )3. Abby put an X through 7 of the 28 days in this month. Abby put anX through ? of the days. ()17.2= ( )4. 60 ÷ 4 = 3 × ? ( )A) 20 B) 12 C) 6 D) 5 5. 30 × 40 × 50 = 120 × ? ( )A) 50 B) 200 C) 500 D) 6006. If 3 out of 4 of the students in my class have brown eyes, and there are 24 students in my class, then how many have brown eyes? ( ) A) 6 B) 8 C)18 D)217. Four identical squares, each with a perimeter of 36, are put together as shown to make one big square. What is the perimeter of the big square? ()8. 80 + (160 + 240) ÷ 4 = 40 + 80 + (120 ÷ ? ) ( )A) 4 B) 2 C) 1 D) 0 9. In which of the following divisions is the remainder greatest? ()A) 1111 ÷ 8 B) 2222 ÷ 7 C) 3333 ÷ 6 D) 4444 ÷ 5 10. Of the following, which is a factor of 20 × 14 × 20 × 15? ( )A) 13 B) 11 C) 9 D) 718.If the sum of seven consecutive even numbers is 182, the smallest of the seven numbers is ( ) A) 20 B) 23 C) 26 D) 3219. While he was standing on his head, Flip decided to count backward from 777 by eights. Which of the following numbers did Flip count? ( A) 123 B) 125 C) 127 D) 129 20. The cost of five apples is the same as the cost of six pears. If one apple costs 15 cents more than one pear, then what is the total cost of 5 apples and 6 pears? ( ) A) $3 B) $6 C) $9 D) $1821. What is the difference between 27 and the product of all its whole-number factors? ( ) A) 2 B) 27 C) 2 × 27 D) 26 × 27 22. The prime factorization of a whole number less than 100 is the product of at most ? primes (not necessarily different). ( )A) 3 B) 4 C) 5 D) 6 23. A rectangle with sides of integer length is divided into a square regionand a shaded rectangular region as shown. If the area of the shaded)城市区 学校年级性别姓名（正楷）A) 3 B) 4 C) 5 D) 10 A) 0.07 B) 0.25C) 0.28D) 0.35A) 36B) 48C) 72D) 144A) $0.20 B) $0.60 C) $1.50 D) $3.00A) 200 B) 250 C) 1000 D) 1250 A) 16B) 64C) 128D) 256)2 ………………………………………………装……………………………………………订……………………………………………线…………………………………………………………… ……………………………………装…………………订…………………线…………………内…………………不…………………答…………………题………………………………………region is 8, the area of the entire figure is at most ( )A) 24 B) 64 C) 72 D) 8124. Gabriel wrote his name 100 times in the sand. What was the 100th letter hewrote? ( ) A) a B) b C) r D) i 25. I put $100 in a savings account. At the end of each year, I earned 10% interest on the balance of my account at that point. With no deposits or withdrawals, after 5 years I had ? . (Round to the nearest dollar.) ( ) A) $162 B) $161 C) $160 D) $150 26. Mrs. Andrews enjoys feeding the birds her special mix of birdseed. She mixes 1 part sunflower seed with 3 parts sesame seed to make a total of 200 6-kg bags. If sunflower seed comes in 12-kg bags, how many such bags does she need? ( ) A) 25 B) 34 C) 50 D) 6737. There are several apples in a basket. Tony removes half of the apples in the basket and then places 15 additional apples in the basket. Sophie then removes half of the apples in the basket, and then places 10 additional apples in the basket. The number of apples Tony removes from the basket is the same as the number of apples Sophie removes. How many apples are now in the basket?Answer: .38. In this problem as shown on the right, each square represents a digit from 0 to 9. What is the final product? 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. 甲、乙、丙三位同学参加运动会，他们的号码都 27. The product of 100 one hundreds is the same as the sum of ? one hundreds. ()A) 100100 B) 10099 C) 10010 D) 1002 不一样。
2018-2019年美国“大联盟”(Math League)思维探索活动第一阶段五年级试卷
act is twice as long as the 3rd, what fraction of the play is the 3rd act?
A) 1/9
B) 2/9
C) 3/9
D) 4/9
15. If I double my speed of 12 000 m/hr., my new speed will be
城市
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年级
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won every 6th game we played. If my team qualified for the finals after our
96th game, how many wins did we need?
A) 12
B) 16
C) 18
D) 90
12. What is the greatest common factor of 1 ×3 ×5 ×7 ×9 and 2 ×4 ×6 ×8 ×10?
A) 200 m/min.
B) 400 m/min.
C) 600 m/min.
D) 2400 m/min.
16. Which of the following could be the perimeter of an equilateral triangle with integral side-lengths?
2018年美国“数学大联盟杯赛”(中国赛区)初赛三年级试卷(1)
2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛(三年级)(初赛时间：2017年11月26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，我确定我所填写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。
请在装订线内签名表示你同意遵守以上规定。
考前注意事项：1. 本试卷是三年级试卷，请确保和你的参赛年级一致；2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；3. 请确保你已经拿到以下材料：本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、草稿纸。
考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、及如何参加复赛的说明。
其他材料均不能带走，请留在原地。
选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。
1. 5 + 6 + 7 + 1825 + 175 =A) 2015 B) 2016 C) 2017 D) 20182.The sum of 2018 and ? is an even number.A) 222 B) 223 C) 225 D) 2273.John and Jill have $92 in total. John has three times as much money as Jill. How muchmoney does John have?A) $60 B) $63 C) $66 D) $694.Tom is a basketball lover! On his book, he wrote the phrase “ILOVENBA” 100 times.What is the 500th letter he wrote?A) L B) B C) V D) N5.An 8 by 25 rectangle has the same area as a rectangle with dimensionsA) 4 by 50 B) 6 by 25 C) 10 by 22 D) 12 by 156.What is the positive difference between the sum of the first 100 positive integers and thesum of the next 50 positive integers?A) 1000 B) 1225 C) 2025 D) 50507.You have a ten-foot pole that needs to be cut into ten equal pieces. If it takes ten secondsto make each cut, how many seconds will the job take?A) 110 B) 100 C) 95 D) 908.Amy rounded 2018 to the nearest tens. Ben rounded 2018 to the nearest hundreds. Thesum of their two numbers isA) 4000 B) 4016 C) 4020 D) 4040 9.Which of the following pairs of numbers has the greatest least common multiple?A) 5,6 B) 6,8 C) 8,12 D) 10,2010.For every 2 pencils Dan bought, he also bought 5 pens. If he bought 10 pencils, how manypens did he buy?A) 25 B) 50 C) 10 D) 1311.Twenty days after Thursday isA) Monday B) Tuesday C) Wednesday D) Thursday12.Of the following, ? angle has the least degree-measure.A) an obtuse B) an acute C) a right D) a straight13.Every student in my class shouted out a whole number in turn. The number the firststudent shouted out was 1. Then each student after the first shouted out a number that is 3 more than the number the previous student did. Which number below is a possible number shouted out by one of the students?A) 101 B) 102 C) 103 D) 10414.A boy bought a baseball and a bat, paying $1.25 for both items. If the ball cost 25 centsmore than the bat, how much did the ball cost?A) $1.00 B) $0.75 C) $0.55 D) $0.5015.2 hours + ? minutes + 40 seconds = 7600 secondsA) 5 B) 6 C) 10 D) 3016.In the figure on the right, please put digits 1-7 in the sevencircles so that the three digits in every straight line add upto 12. What is the digit in the middle circle?A) 3 B) 4 C) 5 D) 617.If 5 adults ate 20 apples each and 3 children ate 12 apples in total, what is the averagenumber of apples that each person ate?A) 12 B) 14 C) 15 D) 1618.What is the perimeter of the figure on the right? Note: Allinterior angles in the figure are right angles or 270°.A) 100 B) 110C) 120 D) 16019.Thirty people are waiting in line to buy pizza. There are 10 peoplein front of Andy. Susan is the last person in the line. How manypeople are between Andy and Susan?A) 18 B) 19C) 20 D) 2120.Thirty-nine hours after 9:00 AM isA) 1:00 AM B) 12:00 PM C) 8:00 PM D) 12:00 AM21.200 + 400 + 600 + 800 = (1 + 2 + 3 + 4) ×?A) 2 B) 20 C) 200 D) 200022.11…11 (the number consisting of 2016 1’s) is not a mult iple ofA) 11 B) 111 C) 1111 D) 1111123.The average of two thousands and two millions isA) 10000 B) 1000000 C) 1001000 D) 111100024.A triangle has the same area as a square. If the length of a base of the triangle is the sameas the side-length of the square, and the height of the triangle to the base is 4, what is thearea of the square?A) 1/2 B) 2 C) 4 D) 825.When V olta found a field in the shape of an isosceles triangle, she was soexcited that she ran a lap around all three sides. Two sides of the field havelengths of 505 m each, and the third side has a whole-number length.What is the greatest possible distance that V olta might have run in one lap?A) 2016 B) 2017 C) 2018 D) 201926.25 ×66 = 75 ×?A) 22 B) 44 C) 16 D) 3327.The number that has an odd number of whole number divisors isA) 15 B) 16 C) 17 D) 1828.In a sequence of 8 numbers, the average of the 8 terms is 15. If the average of the firstthree terms is 16 and the average of the next two terms is 15, what is the average of thelast three terms?A) 12 B) 13 C) 14 D) 1529.All years between 2000 and 2050 that are divisible by 4 are leap years.No other years between 2000 and 2050 are leap years. How many daysare there all together in the 17 years from 2010 to 2026?A) 6029 B) 6030 C) 5018 D) 501930.The sum of the hundreds digit and the tens digit of 2357 isA) 5 B) 8 C) 10 D) 1231.Which of the expressions below has the greatest value of (quotient × remainder)?A) 27 ÷ 4 B) 47 ÷ 6C) 57 ÷ 8 D) 87 ÷ 1232.I have some dimes and nickels, and together these coins are worth $3. If I replace everynickel with a quarter, I will have $5. How many dimes do I have?A) 10 B) 15 C) 20 D) 2533.I am a lovely cat. When I multiply the digits of a whole numberand the product I get is 9, I put that whole number on my list offavorite numbers. Of the whole numbers from 1000 to 9999, howmany would I put on my list of favorite numbers?A) 5 B) 10 C) 15 D) 2034.The sum of the tens digit and the units digit of the sum 1 + 12 + 123 + 12345+ … + 123456789 isA) 4 B) 5 C) 6 D) 735.The product of all prime numbers between 1 and 10 isA) 210 B) 105C) 1890 D) none of the above36.What is the average of 12, 14, 16, and 18?A) 13 B) 14 C) 15 D) 1637.When Jon shouts out a whole number, Al shouts out the product ofits digits, Barb shouts out the product of the digits of the number Alshouted out, and Cy shouts out the product of the digits of thenumber Barb shouted out. When Cy shouts out 18, what numbermight Jon have shouted out?A) 789 B) 799 C) 899 D) 99938.Each big box contains 3 medium boxes, each medium box contains2 small boxes, and each small box contains 5 apples. How many bigboxes are necessary for 1200 apples?A) 30 B) 40 C) 50 D) 6039.Eighteen years from now, my age will be 4 more than twice my currentage. My age now isA) 12 B) 14 C) 16 D) 1840.Each time Wanda waved her wand, 4 more stars appeared on herdress (which started with no stars). After several waves, Wandamultiplied the total number of stars then on her dress by thenumber of times she had waved her wand. This product cannot beA) 144 B) 256 C) 364 D) 676。
2015年美国“数学大联盟杯赛”(中国赛区)初赛五年级试卷
2014-2015 年度美国“数学大联盟杯赛”(中国赛区)初赛
(五年级) (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。
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城市
22. The prime factorization of a whole number less than 100 is the product of at most ? primes (not necessarily different). ( ) A) 3 B) 4 C) 5 D) 6 23. A rectangle with sides of integer length is divided into a square region and a shaded rectangular region as shown. If the area of the shaded
11. Thok has a simple plan. He will spend 50% of the day in the cave, 25% of the rest of the day on the hunt, and the remainder of the day watching films outside. How many hours will Thok spend watching films? ( ) A) 3 B) 6 C) 9 D) 25 12. 2 × 3 × 6 × 36 × 2 × 3 × 6 × 36 = A) 65 B) 66 ( C) 67 ) D) 68
20162017年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级).doc
2016-2017年度美国“数学大联盟杯赛”（中国赛区）初赛（五年级）1.Which of the has the greatest value?A) 2017 B) 2017C) 20 × 17 D) 20 + 172.Which of the leaves a remainder of 2 when divided by 4?A) 2014 B) 2015 C) 2016 D) 20173.Which of the is a product of two consecutive primes?A) 30 B) 72 C) 77 D) 1874.A Bizz-Number is a integer that either contains the 3 or is a multiple of 3. What is the of the 10th Bizz-Number?A) 24 B) 27 C) 30 D) 315.The of an isosceles triangle with side-lengths 1 and 1008 isA) 1010 B) 1012 C) 2017 D) 20186.How integers less than 2017 are divisible by 16 but not by 4?A) 0 B) 126 C) 378 D) 5047.Jon has a number of pens. If he distributed them evenly among 4 students,he have 3 left. If he distributed them evenly among 5 students, he have 4 left. The minimum number of pens that Jon have isA) 14 B) 17 C) 19 D) 248.Which of the numbers is not divisible by 8?A) 123168 B) 234236 C) 345424 D) 4566249.Which of the is both a square and a cube?A) 36 × 58B) 36 × 59C) 36 × 512D) 39 × 51210.The of two prime numbers cannot beA) odd B) even C) prime D) composite11.At the end of day, the amount of water in a cup is twice what it was atthe beginning of the day. If the cup is at the end of 2017th day, then it was1/4 at the end of the ? day.A) 504th B) 505th C) 2015th D) 2016th12.The grades on an exam are 5, 4, 3, 2, or 1. In a class of 200 students, 1/10of got 5’s, 1/5 of got 4’s, 25% of got 3’s, and 15% of got 2’s. How many students got 1’s?A) 40 B) 60 C) 80 D) 10013.22000 × 52017 = 102000 × ?A) 517B) 51000C) 52000D) 5201714.1% of 1/10 of 10000 is ? percent than 10A) 0 B) 9 C) 90 D) 90015.What is the of the of Circle C to the of Square S if the of adiameter of C and a of S are equal?A) π:1 B) π:2 C) π:3 D) π:416.Which of the is not a prime?A) 2003 B) 2011 C) 2017 D) 201917.If the sum of prime numbers is 30, what is the possible value of any of the primes?A) 19 B) 23 C) 27 D) 2918.For $3 I spend on books, I spend $4 on and $5 on toys. If I spent $20 on food, how much, in dollars, did I spend in total?A) 60 B) 90 C) 120 D) 15019.How positive odd factors does 25 × 35 × 55 have?A) 25 B) 36 C) 125 D) 21620.The of scalene triangles with perimeter 15 and side-lengths isA) 3 B) 5 C) 6 D) 721.Which of the when rounding to the nearest thousands, hundreds, and tens, 3000, 3500, and 3460, respectively?A) 3210 B) 3333 C) 3456 D) 351722.Which of the below has exactly 5 positive divisors?A) 16 B) 49 C) 64 D) 10023.Each after the 1st in the sequence 1, 5, 9, … is 4 than the previousterm. The greatest in sequence that is < 1000 and that leaves a of1 when divided by 6 isA) 991 B) 995 C) 997 D) 99924.For integer from 100 to 999 I the of the integer’s digits. Howmany of the products I are prime?A) 4 B) 8 C) 12 D) 1625.If a machine paints at a of 1 m2/sec, its is alsoA) 600 cm2/min B) 6000 cm2/minC) 60000 cm2/min D) 600000 cm2/min26.The of Square A is 1. The of Square B is times ofSquare A. The of Square C is times of Square B. The of Square C is ? times of Square A.A) 3 B) 6 C) 36 D) 8127.If the 17 minutes ago was 19:43, what will be the 17 minutes from now?A) 20:00 B) 20:17 C) 20:34 D) 20:1528.Pick any greater than 100 and subtract the sum of its from theinteger. The largest that must the result isA) 1 B) 3 C) 9 D) 2729.The number of needed in a room so there are always atleast five in the room born in the same month isA) 48 B) 49 C) 60 D) 6130.If M, A, T, and H are digits such that MATH + HTAM = 12221, is the value of M + A + T + H?A) 8 B) 20 C) 22 D) 2431.If 10 forks, 20 knives, and 30 $360, and 30 forks, 20 knives, and10 $240, what is the of 5 forks, 5 knives, and 5 spoons?A) 15 B) 75 C) 150 D) 22532.Write, in reduced form, the value ofA) 0.5 B) 1 C) 1.5 D) 233.Al, Barb, Cal, Di, Ed, Fred, and participated in a chess tournament. Eachplayer play each of his six opponents exactly once. So far, Al has 1match. Barb has 2 matches. Cal has 3 matches. Di has 4matches. Ed has 5 matches, and has 6 matches. How manymatches has at this point?A) 1 B) 3 C) 5 D) 734.What is the number of different integers I can choose from the 100positive integers so that no of these integers could be the of the sides of the same triangle?A) 8 B) 9 C) 10 D) 1135.What is the value of change that you can have in US (pennies, nickels, dimes, and quarters) without being able to someone exact change for a one-dollar bill?A) $0.90 B) $0.99 C) $1.19 D) $1.2936.小罗星期一工作了2个小时。
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2017-2018年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)(初赛时间：2017年11月26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， 我确定我所填写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。
请在装订线内签名表示你同意遵守以上规定。
考前注意事项：1. 本试卷是五年级试卷，请确保和你的参赛年级一致；2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全；3. 请确保你已经拿到以下材料：本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、 草稿纸。
考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、 及如何参加复赛的说明。
其他材料均不能带走，请留在原地。
选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。
1. The smallest possible sum of two different prime numbers isA) 3B) 4C) 5D) 62. The greatest common factor of two numbers is3. The product of these two numbers mustbe divisible byA) 6 B) 9 C) 12 D) 18 3. The sum of 5 consecutive one-digit integers is at most A) 15 B) 25 C) 35 D) 45 4. How many two-digit multiples of 10 are also multiples of 12?A) 4B) 3C) 2D) 15. I have read exactly13of the total number of chapters in my 120-page book. If each chapter has the same whole number of pages, then the total number of chapters I have left could beA) 16 B) 24 C) 32 D) 50 6. What is the greatest odd factor of 44 × 55 × 66?A) 36 B) 55 C) 35 × 55 D) 36 × 55 7. What is the sum of the factors of the prime number 2017? A) 2016B) 2017C) 2018D) 20198. Lynn ran in 6 times as many races as the number of racesshe won. How many of her 126 races did Lynn not win?A) 21B) 90C) 96D) 1059. The least common multiple of 8 and 12 is the greatest common factor of 120 andA) 80B) 124C) 144D) 18010. January has the greatest possible number of Saturdays when January 1 occurs on any ofthe following days of the week exceptA) Thursday B) Friday C) Saturday D) Sunday 11. The number that is 10% of 1000 is 10 more than 10% ofA) 90B) 100C) 900D) 99012. The sum of 16 fours has the same value as the product of ? fours.A) 2 B) 3 C) 4 D) 16 13. Of the following, which is the sum of two consecutive integers?A) 111 111B) 222 222C) 444 444D) 888 88814. Abe drove for 2 hours at 30 km/hr. and for 3 hours at 50 km/hr. What was Abe’s averagespeed over the 5 hours?A) 35 km/hr.B) 40 km/hr.C) 42 km/hr.D) 45 km/hr.15. My broken watch runs twice as fast as it should. If my watch first broke at 6:15 P.M.,what time was displayed on my watch 65 minutes later?A) 7:20 P.M. B) 7:25 P.M.C) 8:20 P.M. D) 8:25 P.M.16. (2018 × 2017) + (2018 × 1) =A) 20172 B) 20182 C) 20183D) (2018 + 2017)217. A prized bird lays 2, 3, or 4 eggs each day. If the bird laid 17 eggs in 1 week,on at most how many days that week did the bird lay exactly 2 eggs?A) 2B) 3C) 4D) 518. Of the following, which could be the perimeter of a rectangle whoseside-lengths, in cm, are prime numbers?A) 10 cmB) 22 cmC) 34 cmD) 58 cm19. The average of all possible total values of a 4-coin stack of nickels and dimes (containingat least one of each coin) isA) 20¢B) 30¢C) 40¢D) 60¢20. The diameter of Ann’s drum i s 40 cm more than the radius. What is half the circumference of the drum?A) 120π cmB) 80π cmC) 60π cmD) 40π cm21. Of the following, which expression has the greatest number offactors that are multiples of 2018?A) 2018 × 12B) 20182C) 20192D) 20192019第1页，共4页 第2页，共4页22. When the sum of the factors of a prime number is divided by that prime number, theremainder isA) 0 B) 1 C) 2 D) 3 23. What is the sum of the digits of the greatest integer that has a square root less than 100? A) 18B) 36C) 99D) 10024. My favorite number has 6 different factors. If the product of all 6 factors is 123, what isthe sum of the factors of my favorite number?A) 24B) 28C) 32D) 3625. For how many different pairs of unequal positive integers less than 10 is the least commonmultiple of the numbers less than their product?A) 6B) 7C) 8D) 926. Exactly 12 of the students in my class have at least one brother, and 12 have at least onesister. If 13have no siblings, what fraction of the students in my class have at least onebrother and at least one sister?A) 16 B) 15 C) 14 D) 1327. Each day, Sal swims a lap 1 second faster than on the daybefore. If Sal swims a lap in 60 minutes on the 1st day, on what day does he swim a lap in 10% less time than the 1st day?A) 359th B) 360th C) 361st D) 362nd 28. 20172018 × 20172019 = 2017 ? × 20171009A) 1010B) 2010C) 3028D) 403829. Both arcs AB and AD are quarter circles of radius 5, figure on the right.Arc BCD is a semi-circle of radius 5. What is the area of the region ABCD ?A) 25 B) 10 + 5π C) 50D) 50 + 5π30. For every $5 I earn from my job, I save $2. For every $4 I save from my job, I am givenan additional $1 from my parents to add to my savings. How much must I earn in order to have $40 in savings?A) $160B) $120C) $100D) $8031. In the figure on the right, the side-length of the smaller squareis 4. The four arcs are four semi-circles. Each side of square ABCD is tangent to one of the semi-circles. The area of ABCD isA) 32B) 36C) 48D) 6432. A million is a large number, a “1” follo wed by 6 zeros. A googol is a large number, a “1”followed by one hundred zeros. A googolplex is a large number, a “1” followed by a googol of zeros. A googolplexian is a large number, a “1” fo llowed by a googolplex of zeros. A googolplexian isA) 10100 B) 1001010C) 100101010D) None of the above33. An integral triangle is a triangle with positive integral side-lengths and a positive area.Such a triangle can have a perimeter as small as 3. What is the next smallest possible perimeter of an integral triangle?A) 4B) 5C) 6D) 734. 2 liter of 2% fat milk + 3 liter of 3% fat milk = 5 liter of ? fat milkA) 2.5%B) 2.6%C) 5%D) 6%35. One day, a motorist came to a hill that was ten-mile drive up one side and a ten-mile drivedown the other. He drove up the hill at an average speed of 30 miles per hour. How fast will he have to drive down the other side to average 60 miles per hour for the entire 20-mile distance?A) 30 miles per hour B) 60 miles per hour C) 90 miles per hour D) None of the above 36. What is the weight of a fish if it weighs ten pounds plus half its weight?A) 10B) 15C) 20D) 2537. Without using pennies, how many different combinations of coins (nickels, dimes,quarters) will make 30 cents?A) 3B) 4C) 5D) 638. A man once bought a fine suit for which he paid $30 more than14of its price. How much did he pay for the suit? A) $30B) $35C) $40D) $4539. A father is five times as old as his son. In fifteen years he will be only twice as old. Howold is the father at present?A) 40B) 35C) 30D) 2540. It takes 30 minutes to completely fill a tank. If, however, a hole allows13of the water that is entering the tank to escape, how long will it then take to fill the tank?A) 40 B) 45 C) 60 D) 90第3页，共4页第4页，共4页。