2018-2019年美国“大联盟”(Math League)思维探索活动第一阶段三年级试卷及答案
数学思维【初中】：2018-2019年美国“大联盟”思维探索七和八、九年级试卷(2份,含参考答案)
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。
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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。
历届美国数学邀请赛试题集
历届美国数学邀请赛试题集历届美国数学邀请赛试题集是向全球数学爱好者提供的难题挑战。
参加这些比赛需要高超的数学水平和一些独特的思维技巧。
以下是一些历届数学邀请赛试题集的例子，让我们一起领略一下这些难题带来的魅力：第一份试题集：1. 计算$\frac{1}{1 \times 2 \times 3}+\frac{1}{2 \times 3 \times4}+\frac{1}{3 \times 4 \times 5}+\cdots+\frac{1}{99 \times 100 \times 101}$的值。
2. 求以 $(1, 2), (3, 5), (4, 5)$为顶点的三角形的面积。
3. $a_1=1, a_2=2, a_3=3, a_4=4$，对于 $n>4$，$a_n$ 是所有使得$a_1+a_2+\cdots+a_{n-1}+k \equiv 0 \pmod n$ 的 $k$ 的最小正整数解。
求$a_{2019}$。
4. 在平面上给定 $2n$ 点，其中没有三点共线。
证明存在一种方法将这$2n$ 点分成两组，每组包含各 $n$ 个点，并且这两组点可以每组内同时作一条直线使得这两条直线平行且距离相等。
第二份试题集：1. 已知 $\triangle ABC$ 中 $\angle A=60^\circ$，$AD$ 为 $BC$ 上的高，$M$ 是 $AB$ 上的满足 $\angle ACD = \angle AMD$ 的点。
证明：$\angle BMC = 90^\circ$。
2. 对于正整数 $n$，设 $S(n)$ 表示所有可以表示成 $a^2+b^2+c^2$，其中 $a, b, c$ 都是不同的正整数且 $a<b<c<n$ 的数的和，求 $S(17)$ 的值。
3. 设 $p$ 是一个奇素数，$b$ 是一个介于 $2$ 到 $p-2$ 之间的整数。
证明：$b^{p-1} \equiv 1 \pmod {p^2}$ 的充分必要条件是 $b \equiv \pm 1\pmod p$。
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。
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
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“数学大联盟杯赛”介绍演示文稿PPT课件
a) /education/best-highschools/national-rankings/spp+100
2. 美国“数学大联盟杯赛”第一届竞赛于1977年 举行， 至今已经连续举办了35年。
3. 每年有来自全球的超过一百万名中小学生参加。
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Math League History
Mr. Steven R. Conrad & Mr. Daniel Flegler: 美国著 名的数学教育家
students.php c) Lectures
a) Brian Conrad, /2012/finals/professor/professor1.php
b) Ravi Vakil, /2012/finals/professor/professor3.php
2. Math League in China
a) Intro of Committee Members b) Comparison c) 2012-2013 Math League in China d) Online Learning System
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Math League in North America & The World
b) /jointly/consequence.php
b) Harvard Twins Sisters
a) /jointly/consequence.php#
c) US newspaper coverage
2018-2019年美国“大联盟”(Math League)思维探索活动第一阶段六年级试卷及答案
B) Monday
C) Tuesday
D) Friday
12. Rounding a decimal to the nearest whole number yields a number that is at most ? greater than the original decimal.
A) 0.05
B) 0.1
C) 0.5
D) 0.9
13. The perimeter of a rectangle with area 2019 and integral side-lengths is greatest when its length and width diffC) 670
A) 6
B) 9
C) 12
D) 18
3. The number 36 is the product of -6 and
A) -6
B) 6
C) -30
D) 42
4. 20 ×18 = 20 ×19 + 20 × ?
A) -1
B) 0
C) 1
D) 20
5. Angel arrived 3 of an hour early for her noon appointment. At what time did Angel 10
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AMC8(美国数学竞赛)历年真题、答案及中英文解析
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 。
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
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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?
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2018-2019年度美国“大联盟”(Math League)思维探索活动第一阶段(三年级)(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。
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。
1.20 + 20 + 20 = 18 + 18 + ?A) 14 B) 18 C) 22 D) 242.It takes four Beaver Brothers to carry a sharpened stick. How many Beaver Brothers doesit take to carry eight sharpened sticks?A) 12 B) 18C) 24 D) 323.On a number line, what is the difference between the two numbers that are 20 away from30?A) 10 B) 20 C) 40 D) 504.Seven weeks = ? daysA) 14 B) 49 C) 77 D) 3435.Which of the following numbers is a multiple of both 3 and 7?A)10 B)37 C) 42 D) 736.Which of the following has the greatest remainder?A) 3 ÷ 2 B) 11 ÷ 3 C) 13 ÷ 5 D) 15 ÷ 77.20 – 18 + 16 – 14 + 12 – 10 + 8 – 6 + 4 – 2 =A) 2 × 5 B) 3 × 5 C) 4 × 5 D) 5 × 58.Which number is 10 times as large as 2018?A)2028 B)2128 C) 3018 D) 20 1809.100 × 100 + ? = 1000 × 1000A) 900 B) 9000 C) 99 900 D) 990 00010.Yogi the Yelling Bear can yell for 15 seconds, but then needs a 10-secondbreak. For at most how many seconds can he yell in two minutes?A) 60 B) 75C) 90 D) 11011.Which of the following expressions has the lowest value?A) 1 ÷ (2 ÷ 3) B) (1 ÷ 2) ÷ 3C) (3 ÷ 2) ÷ 1 D) 3 ÷ (2 ÷ 1)12.The difference between two odd numbers cannot beA) 0 B) 6 C) 9 D) 1213.I have a pizza that can be cut into either 12 equal small slices or8 equal large slices. If I’ve already cut 4 large slices from thepizza, how many small slices can I cut from what remains?A) 2 B) 4C) 6 D) 814.The sum of 4 consecutive odd numbers is 80. What is the greatest of the 4 odd numbers?A) 21 B) 23 C) 25 D) 2715.I started with $20.18, and then spent 2 quarters, 0 dimes, 1 nickel, and 8 pennies. Howmuch money do I have left?A) $19.55 B) $19.60 C) $19.65 D) $19.7516.If Cyrus can buy 5 apples for 80 cents, then at that same rate he can buy 9 apples forA) $0.64 B) $1.44 C) $1.60 D) $1.8017.It is 1:00 p.m. now. I spent 20 minutes eating and finished eating 200 minutes ago. Atwhat time did I begin eating?A) 9:20 a.m. B) 9:40 a.m.C) 10:20 a.m. D) 10:40 a.m.18.Eighteen $10 bills and eighteen $100 bills equalsA) $1818 B) $1880 C) $1918 D) $198019.My square has an area of 4 cm2. The sides of your square are three times as long as thesides of my square. Your square has areaA) 9 cm2B) 16 cm2C) 24 cm2D) 36 cm220. There was no snow on the ground on December 31. Each evening after that, 4 cm of snow fell, and no other snow fell that day. If 2 cm of snow melted each morning, ? cm were on the ground the afternoon of January 4th.A) 4B) 6C) 8D) 1221. The product of 2 ÷ (1 ÷ 4) and 4 ÷ (1 ÷ 2) isA) 1B) 4C) 8D) 6422. A carton of milk and a muffin cost $2.60, and the milk costs 40 cents more than the muffin.How much does the milk cost?A) $0.75B) $1.10C) $1.50D) $2.2023. There are 30 students in my class. Eighteen of them can juggle, ten of them can ride a unicycle, and six of them can do neither. How many can do both?A) 2 B) 4 C) 6D) 824. (24 + 18 + 12 + 6) ÷ (16 + 12 + 8 + 4) =A) 1.5B) 2C) 4D) 625. A 4 m by 5 m rectangular floor is tiled with square tiles that have sides that are 1 m long. How many of the tiles are NOT surrounded by other tiles on all four sides?A) 12B) 14C) 16D) 1826. Of the following, which has the least value?A) 5500 ones B) 7 thousands C) 60 hundredsD) 500 tens27. Colton ran 1 km on Monday last week, and on each day after that he rantwice as many km as he had the day before. Cayden runs the same whole number of km every day. For the 7 days from Monday last week to Sunda y, if Cayden ran more total km than Colton did, Cayden’s daily run must be at least ? km.A) 2B) 7C) 19D) 3328. How many 2-digit whole numbers contain neither the digit 1 nor the digit 2?A) 56B) 64C) 70D) 8029. Every time Emma, Gaby, and Rosie play a game, the winner gets a quarter. After 3 gameswith no ties, some players may have no quarters, some 1 or 2 quarters, or one may have 3 quarters. In how many ways can the 3 quarters be distributed among the three players?A) 8B) 9C) 10D) 1230. If a teacher gives each of his students 4 crayons from his box of crayons, 16 crayons remain. If instead he gives each student 6 crayons from this box, 2 crayons remain. How many students are there?A) 7B) 8C) 12D) 1431. Which of the following results in an odd number?A) even × oddB) odd × even C) odd + evenD) odd + odd32. Zach multiplied the number on his shirt by itself. What could be his result?A) 24B) 25C) 26D) 2733. Find the missing term in the following sequence: 4, 7, 10, 13, _____, 19A) 3B) 16C) 19D) 2334. Ella wears different colored sneakers each day of the week, but her sneakers fall apart after four days of wear! At least how many pairs of sneakers does she need for the month of December?A) 7B) 8C) 10D) 1235. The largest whole-number multiple of 7 less than 100 isA) 91B) 93C) 97D) 9836. How many two-digit positive integers can be written using only even numbers?A) 16B) 20C) 25D) 5037. Simona has only dimes and quarters, and has exactly one dollar. If she has at least one dime and one quarter, how many coins must she have?A) 3B) 5C) 7D) 938. How many numbers between 100 and 200 are evenly divisible by 4 and 6?A) 4B) 6C) 8D) 1039. In Olive’s kingdom, castles have 8 beds and homes have 2 beds. If there are 48 beds in total and 3 castles, how many homes are there? A) 8 B) 12C) 16D) 2440. How many additional 2 × 2 non-overlapping squares can fit into a 6 × 6 square than a4 × 4 square? A) 4 B) 5C) 6D) 8。