2018-2019年美国“大联盟”(Math League)思维探索活动第一阶段四年级试卷及答案

首先感谢胡锐博士从美国引进了“数学大联盟杯赛”这么好的一个活动，它让中国的学生得以领略美国最为普及、最受欢迎的数学竞赛的原貌，同时也为数英双优的培训开辟了新的模式，尤其是目前在北京及全国都缺少这样一种培养方式。

古希腊伟大的哲学家亚里士多德曾说：“虽然数学没有明显提到善和美，但善和美也不能和数学完全分开，因为美的形式，就是‘秩序、匀称和确定性’，这些正是数学研究的原则。

”让孩子们年少时就开始接触数学，感受数学之美，从而培养他们对数学的兴趣，这在国外被称为“天才少年培养计划”。

虽然国内也很早就开始了这样的尝试，但像引进美国“数学大联盟杯赛”这种形式的活动还尚属首次。

美国“数学大联盟杯赛”至今已连续举办了35年，它不仅是美国及北美地区影响力最大的中小学数学赛事，也是一项具有世界影响力的中小学数学赛事。

杯赛每年举办一次，分为初赛(包括复赛)和决赛两个阶段。

初赛(包括复赛)试题灵活、生动，富有趣味性，同时也贴近生活。

让学生理解数学、欣赏数学，激励学生创新，更能激发学生学习数学的兴趣，培养学生主动探索的精神。

初赛的目的是普及数学。

决赛的试题由美国“数学大联盟杯赛”和斯坦福大学联合命题，具有很高的挑战性，着力培养学生创造性地解决问题和创新思维的能力(fun and creative problems that promote critical-thinking and problem-solving skills)，是数学超常少年展现才华的绝佳平台。

2012年伊始，在各方的努力之下美国“数学大联盟杯赛”得以成功登陆中国，中国赛区初赛于2012年2月25日举行，首次举办即得到广大中小学生的积极响应及踊跃参与，同时也涌现出大批数学能力与英语水平俱佳的优秀学生。

而随着2011-2012年度美国“数学大联盟杯赛”颁奖会的圆满结束，决赛的大幕正式拉起，我们也马不停蹄的投入到决赛和数学夏令营的组织工作中。

2011-2012年度美国“数学大联盟杯赛”中学组的决赛和数学夏令营是由美国“数学大联盟杯赛”和斯坦福大学联合举办，试题新颖、灵活、生动，富有趣味性和挑战性，培养学生创造性地解决问题和创新思维的能力。

2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(七年级)(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)学生诚信协议：答题期间，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. 本试卷是七年级试卷，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。

试卷、答题卡、答题卡使用说明、草稿纸均不能带走，请留在原地。

4. 本试卷题目很多也很难，期待一名学生所有题目全部答对是不现实的，能够答对一半题目的学生就应该受到表扬和鼓励。

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.(4 × 6 × 8 × 10) ÷ (6 × 8 × 10) =A) 3 B) 4 C) 12 D) 3 × 6 × 8 × 102.(2 ÷ 3) rounded to the nearest hundredth isA) 0.33 B) 0.66 C) 0.67 D) 0.703.Baby Amy is one day older than Baby Barry. The product of theirages measured in days could beA) 33 B) 132 C) 245 D) 2464.(The largest even divisor of 200) ÷ (the largest odd divisor of 200) =A) 4 B) 8 C) 20 D) 2005.An equilateral triangle with integer side-lengths has a perimeter that is numerically equalto the area of a square. Which of the following could be the length of a side of the square?A)12 B)10 C) 8 D) 46.I have only nickels, dimes, and quarters to pay for my dinner, which costs $12.60. Thesmallest number of coins I can use to pay isA) 51 B) 52 C) 54 D) 557.The smallest prime factor of 2019 isA) 1 B) 3 C) 19 D) 6738.The product of four consecutive integers must be divisible by each of the following exceptA) 4 B) 6 C) 10 D) 129.There are ? hours in 4 weeks.A) 48 B) 96 C) 336 D) 67210.If I divide my favorite number by its reciprocal, the quotient is 10 times as large as myfavorite number. My favorite number isA)110B)15C)12D) 1011.The height of the smoke from my barbecue is 100 000 cm, which is thesame as ? km.A) 1 B) 10C) 100 D) 100012.If the degree measures of the angles of a triangle are in a 4:5:6 ratio, whatis the difference between the measures of the largest and the smallest angles?A) 12°B) 24°C) 30°D) 36°13.The population of a town started at 1000, then went up 10%, then down 20%, then backup 10%. The population of the town ended atA) 968 B) 972 C) 1000 D) 102414.In my orchard, there are 60 more apples than oranges, and 5times as many apples as oranges. How many apples are there?A) 50 B) 75 C) 100 D) 12515.A polygon in which every pair of angles is supplementary must be aA) triangle B) squareC) rectangle D) hexagon16.Which of the following is smallest in value?A) 2600B) 3500C) 4400D) 530017.(2100 × 450) ÷ 2 =A) 275B) 2100C) 2149D) 219918.What is the remainder when 3333 is divided by 10?A) 1 B) 3 C) 7 D) 919.On a series of tests, Gus got 100 once, 90 twice, and 80 five times. What was his averagescore for all of the tests?A) 80 B) 85 C) 90 D) 9220.The product of the thousands and tenths digits of 1234.5678 isA) 5 B) 10 C) 35 D) 40第1页，共4页第2页，共4页21. The probability of heads then tails then heads on 3 tosses of a coin isA) 0.125B) 0.25C) 0.375D) 0.522. On January 1 last year, Rui got a jar of jellybeans. On each day he ate the same number ofjellybeans. He counted 560 on January 31 before eating any and he counted 380 on March 17 before eating any. There were ? jellybeans in the jar when Rui got it.A) 600 B) 650 C) 680D) 74023. Jake used 120 boxes of tissues in 3 days! There are 144 tissues per box. That’s ? tissues per minute!A) 2B) 3C) 4D) 524. The number 5184 has ? positive odd divisors.A) 1B) 2C) 4D) 525. The sum of 5 consecutive even integers could beA) 120B) 125C) 164D) 21226. Jacques, who paints only smiley faces, signs and numbers each of his paintings. If he started with Smiley #1 and has painted through Smiley #111, how many times has he used the digit 1 in his numbering?A) 12B) 22C) 24D) 3627. How many whole numbers have squares that are between 2 and 200?A) 12B) 13C) 24D) 2628. A baker cuts circular cookies out of a flat rectangle of cookie dough. If the rectangle is2 m by 1 m, and the cookies have radius 10 cm, at most how many cookies can the baker cut from the sheet of dough?A) 50B) 63C) 64D) 20029. 0.02% of 20% of ? = 200% of 2000A) 1000 B) 100 000 C) 1 000 000D) 100 000 00030. A miner combines 1200 kg of ore that is on average 3% gold with 2400 kg of ore that is on average 6% gold. If the 100 kg containing the most gold of the 3600 kg is 40% gold, the remaining ore will be ? gold.A) 2%B) 3%C) 4%D) 5%31. Including face diagonals, the total number of diagonals of a cube isA) 12B) 14C) 16D) 2432. How many odd 3-digit integers greater than 500 are composed of 3 different non-zero digits?A) 154B) 175C) 185D) 20033. If I square all whole-number factors of 36 and multiply the resulting numbers, the product will be equal toA) 362B) 364C) 368D) 36934. When the four members of the Beaverton family carry a log, each has a 0.02 probability of tripping, and each probability is independent of the others. What is theprobability that they will carry the log without any of them tripping?A) 1 – (0.02)4 B) (0.98)4 C) (0.02)4D) 1 – (0.98)435. What is the largest prime factor of the product of all even numbers from 2 through 200?A) 47B) 97C) 199D) 201936. What is the sum of the solutions to |10 – 4x | = 5?A) 1.25 B) 3.75C) 5 D) 1037. If 2x × 42x × 83x = 2y , then y =A) 2x 3B) 6xC) 6x 3D) 14x38. Each time Alan falls asleep, he sleeps for exactly 8m minutes and then is awake for the next 4m minutes. If he falls asleep for the 1st time at 11 P.M. and wakes from his 6th time asleep at 4:06 A.M., then m = A) 4.25 B) 4.5 C) 5.125D) 6.37539. If x is a positive integer, the remainder when 2018x is divided by 10 could NOT beA) 4B) 6C) 8D) 040. If a + b = 8 and114a b+=, then ab = A) 2 B) 6 C) 12 D) 32第3页，共4页 第4页，共4页2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(八、九年级)(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)学生诚信协议：答题期间，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。

AMC8（美国数学竞赛）历年真题、答案及中英文解析艾蕾特教育的AMC8 美国数学竞赛考试历年真题、答案及中英文解析：AMC8-2020年：真题 --- 答案---解析（英文解析+中文解析）AMC8 - 2019年：真题----答案----解析（英文解析+中文解析）AMC8 - 2018年：真题----答案----解析（英文解析+中文解析）AMC8 - 2017年：真题----答案----解析（英文解析+中文解析）AMC8 - 2016年：真题----答案----解析（英文解析+中文解析）AMC8 - 2015年：真题----答案----解析（英文解析+中文解析）AMC8 - 2014年：真题----答案----解析（英文解析+中文解析）AMC8 - 2013年：真题----答案----解析（英文解析+中文解析）AMC8 - 2012年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 2010年：真题----答案----解析（英文解析+中文解析）AMC8 - 2009年：真题----答案----解析（英文解析+中文解析）AMC8 - 2008年：真题----答案----解析（英文解析+中文解析）AMC8 - 2007年：真题----答案----解析（英文解析+中文解析）AMC8 - 2006年：真题----答案----解析（英文解析+中文解析）AMC8 - 2005年：真题----答案----解析（英文解析+中文解析）AMC8 - 2004年：真题----答案----解析（英文解析+中文解析）AMC8 - 2003年：真题----答案----解析（英文解析+中文解析）AMC8 - 2002年：真题----答案----解析（英文解析+中文解析）AMC8 - 2001年：真题----答案----解析（英文解析+中文解析）AMC8 - 2000年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 1998年：真题----答案----解析（英文解析+中文解析）AMC8 - 1997年：真题----答案----解析（英文解析+中文解析）AMC8 - 1996年：真题----答案----解析（英文解析+中文解析）AMC8 - 1995年：真题----答案----解析（英文解析+中文解析）AMC8 - 1994年：真题----答案----解析（英文解析+中文解析）AMC8 - 1993年：真题----答案----解析（英文解析+中文解析）AMC8 - 1992年：真题----答案----解析（英文解析+中文解析）AMC8 - 1991年：真题----答案----解析（英文解析+中文解析）AMC8 - 1990年：真题----答案----解析（英文解析+中文解析）AMC8 - 1989年：真题----答案----解析（英文解析+中文解析）AMC8 - 1988年：真题----答案----解析（英文解析+中文解析）析）AMC8 - 1986年：真题----答案----解析（英文解析+中文解析）AMC8 - 1985年：真题----答案----解析（英文解析+中文解析）◆AMC介绍◆AMC（American Mathematics Competitions) 由美国数学协会（MAA）组织的数学竞赛，分为 AMC8 、 AMC10、 AMC12 。

2015-2016年度美国“数学大联盟杯赛”(中国赛区)初赛(十、十一、十二年级)(初赛时间：2015年11月14日，考试时间90分钟，总分300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。

如果您同意遵守以上协议请在装订线内签名一、选择题(每小题10分，答对加10分，答错不扣分，共100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) 301.If a square has the same area as a circle whose radius is 10, then the side-length of thesquare is ( )A) B) 10πC) D) 100π2.x2–y2 + x + y = ( )A) (x + y– 1)(x–y) B) (x + y)(x–y– 1)C) (x + y + 1)(x–y) D) (x + y)(x–y + 1)3.If x + y = 25 and x2–y2 = 50. What is the value of xy? ( )A) 150.25 B) 155.25 C) 175 D) 12504.Janet picked a number from 1 to 10 and rolled a die. What is the probability that the sumof the number she picked and the outcome on the die is an even number? ( )A) 1/5 B) 1/4 C) 1/3 D) 1/25.Let r be a solution of x2– 7x + 11 = 0. What is the value of (r– 3)(r– 4) + (r– 12)(r + 5)?( )A) -71 B) -70 C) -69 D) 70st month the ratio of males to females in Miss Fox’s company was 3:4. When 9 newmales and 52 new females were employed this month, the new ratio of males to females is now 1/2. How many employees are there now in the company total? ( )A) 68 B) 120 C) 180D) 240第1页，共4页his task, he returned 40 mph from the castle to home. What is his average speed, in mph, of his quest? ( )A) 120/7 B) 240/7 C) 35 D) 70to shoot 3 apples, then when I use up the darts, I will be left with 35apples; if each dart is used to shoot 4 apples, then when I use up the apples,I will be left with 5 darts. I have ? apples at the beginning. ( )A) 51 B) 55 C) 200 D) 2409.x/2 = y/3 = z/4, what is the value of x:y:z? ( )A) 6:4:3 B) 3:4:6 C) 2:3:4 D) 4:3:210.Super Jack and Almighty Jill were doing the 100-mile walk at the same time and samestarting point, at constant speeds. Jack took a 5-minute break at the end of every 10 miles;Jill took a 10-minute break at the end of each 20 miles. Jill’s speed was 5/8 of that of Jack.They finished at the same time. How long, in minutes, does the trip take? ( )A) 53.333 B) 56.667 C) 60.333 D) 60.667二、填空题(每小题10分，答对加10分，答错不扣分，共200分。

2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(四年级)(活动日期：2018年11月25日，答题时间：90分钟，总分：200分)学生诚信协议：答题期间，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。

试卷、答题卡、答题卡使用说明、草稿纸均不能带走，请留在原地。

4. 本试卷题目很多也很难，期待一名学生所有题目全部答对是不现实的，能够答对一半题目的学生就应该受到表扬和鼓励。

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.(123 + 456) + 678 = (123 + 678) + ?A) 123 B) 456 C) 579 D) 6782.Bea sharpened 1200 pencils. Half the pencils had erasers, andhalf of all the erasers were pink. How many pencils with pinkerasers did Bea sharpen?A) 200 B) 300C) 400 D) 6003.I have a prime number of pairs of socks. The total number of socks I have could not beA) 26 B) 38 C) 46 D) 544.The product of 500 000 and 200 000 has exactly ? zeros.A) 5 B) 6 C) 10 D) 115.Divide 100 by 10, then multiply the result by 10. The final answer isA)0 B)1 C) 10 D) 1006.At most how many complete 8-minute songs can I sing in 3 hours?A) 22 B) 23 C) 24 D) 1807. 2 × (44 + 44 + 44) = 88 + 88 + ?A) 0 B) 44 C) 66 D) 888. A rectangle has sides of even lengths and perimeter 12. Its area isA) 6 B) 8 C) 9 D) 169.16 × (17 + 1) –? × (15 + 1) = 0A) 15 B) 16 C) 17 D) 1810.The crowd clapped for 840 seconds, stopping at 8:15 P.M. Theystarted clapping at ? P.M.A) 7:59 B) 8:01C) 8:08 D) 8:1411.If each digit of my 5-digit ID code is different, the sum of its digitsis at mostA) 15 B) 25 C) 35 D) 4512.At the museum, adult tickets cost $4 each and child tickets cost $3 each. With $50, I canbuy ? more child tickets than adult tickets.A) 1 B) 4 C) 12 D) 1613.Each day last week I read for a whole number of hours. I read forthe same number of hours each day except Sunday. If I read for 12hours last week, I read for ? hours on Sunday.A) 7 B) 6 C) 5 D) 414.The product 2 × 3 × 4 × 5 × 6 has the same value as the product ? × 3 × 5.A) 12 B) 36 C) 48 D) 6315.The average test grade in my class is a whole number, and the sum of the test grades is2400. Of the following, which could be the total number of test grades?A) 18 B) 21 C) 27 D) 3216.If twice a whole number is 120 less than five times the same whole number, then half thewhole number isA) 10 B) 20 C) 40 D) 6017.The number of bees I have doubles each day. If I had 1024 bees last Friday, the first daythe number of bees was more than 100 was aA) Tuesday B) WednesdayC) Thursday D) Friday18.Each of 6 dogs ate 3 treats from each of 4 bags. If each bag started with 30 treats, the 4bags together ended with ? treats.A) 36 B) 48 C) 72 D) 9619.What is the greatest possible product of two different even whole numbers whose sum is100?A) 196 B) 625 C) 2496 D) 250020. Ed built 3 times as many houses as Bob, who built half as many houses as Ally. If the 3 of them built 96 houses in all, Ed and Ally built a combined total of ? houses.A) 16 B) 32 C) 48D) 8021. How many factors of 2 × 4 × 8 × 16 are multiples of 4?A) 3B) 4C) 8D) 922. When I divide a certain number by 3 or 5, I get a remainder of 2. The sum of the digits ofthe least number for which this is true isA) 1B) 3C) 7D) 823. My 144 fish are split between 2 tanks so that 1 tank has twice as many fish as the other. How many fish must I move from one tank to the other so that both tanks have the same number of fish?A) 24 B) 48 C) 60D) 7224. A 3-digit number is the product of at most ? whole numbers greater than 1.A) 2B) 3C) 9D) 1025. Abby earns $2 for every clam she finds and $3 for every oyster. If Abby finds 5 times asmany oysters as clams, which of the following could be her total earnings?A) $150B) $160C) $170D) $18026. (The average value of the 10 smallest even whole numbers greater than 0) – (the average value of the 10 smallest odd whole numbers) =A) 0B) 1C) 10D) 1127. Ana planted seeds in rows. If the total number of rowsequaled the number of seeds in each row, the number of seeds planted could have beenA) 194B) 216C) 250D) 28928. What is the greatest possible sum of five 2-digit whole numbers if all 10 digits of the fivenumbers are different?A) 270B) 315C) 360D) 48529. I thought I wrote every whole number between 1 and 500 in order from least to greatest, but actually I skipped 3 numbers in a row. If I left out a total of 8 digits, what is the sum of the numbers I skipped?A) 100B) 150C) 300D) 39030. Written backwards, 123 becomes 321. How many whole numbers between 100 and 200 have a larger value when written backwards?A) 70B) 80C) 90D) 9831. The average of four different numbers is 18. And the least of the four numbers is 3. What is the least possible value of the biggest of the four numbers?A) 21B) 23C) 24D) 6032. 3 tigers can eat 36 Big Macs in 6 minutes. How many Big Macs can 12 tigers eat in 3 minutes?A) 18B) 36C) 72D) 28833. In the followi ng sequence, 2, 0, 1, 8, 2, 0, 1, 8, … (repeating), what is its 2018th term?A) 2B) 0C) 1D) 834. 2018a b c is a multiple of 9. What is the least possible value of abc ? (Note: abc is a three-digit number, which means a is not 0.)A) 7B) 100C) 106D) 99735. What is the least common multiple of 84 and 112?A) 28B) 196C) 336D) 940836. In triangle ABC , ∠C = 90°, ∠A = 15°, AB = 20. What is the area of this triangle?A) 20B) 50C) 100D) 20037. ABCD is a rectangle and its perimeter is 22, as shown at the right. EFGH is a square. AH = 6. CF = ?A) 4 B) 5 C) 6D) 838. How many leap years are there between 2018 and 2081?A) 16B) 17C) 18D) 1939. My class was lined up on the gym floor in 8 rows, with 2 students in each row. If our coach rearranged us so that the number of rows was the same as the number of students in each row, how many rows were there after we were rearranged? A) 4B) 6C) 10D) 1640. Of the 100 numbers from 1 to 100, how many of them don’t contain 7 as its digit?A) 65 B) 75C) 80 D) none of the above。

美国数学大联盟一等奖
美国数学大联盟一等奖
美国数学大联盟（MAA）奖项是为识别杰出的美国年轻数学家和研究者而设立
的荣誉。

MAA管理着多项奖项，其中包括一等奖。

MAA一等奖被认为是回馈美国数学界最早、最重要的奖项，旨在鼓励和奖励杰出的美国数学学者。

获得MAA一等奖的学者将获得一笔现金奖励，以及MAA一等奖证书。

获奖的个
人将被视为MAA的特殊会员，并享有参加年度MAA会议的机会，以及参与组织活动的资格。

此外，获奖者还可以获得贴近数学界的一些机会，包括参与招聘会、参加职业
发展会议、报名参加其他数学联盟的项目以及访问MAA会员学校所提供的数学研究机会，这些都将为其他有志于从事数学研究的研究者提供更多的积极机会和激励。

MAA一等奖的获得者都具有卓越的学术成就和杰出的研究能力，他们为美国数
学社区的发展做出了杰出的贡献。

获得MAA一等奖是全国范围内数学界获得荣誉的一个重要标志，被认为是改善学生对数学和科学的认识是一个终身成就。