2016-2017六年级美国大联盟答案

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。

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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。

六年级美国大联盟第一阶段-计算专题（教师版）学生/课程年级学科授课教师日期时段核心内容美国大联盟——计算专题课型null教学目标null重、难点null导学一知识点讲解 1、四舍五入专业词汇总结：tenth：十分位 hundredth：百分位 thousandth：千分位ten 十 hundred 百千 thousand million 百万 billion 十亿round to：四舍五入到round to the nearest tenth 四舍五入到十分位round to the nearest ten 四舍五入到十位例题1. [单选题] [近似数及其求法] [难度：★★★ ] （2016 年第 2 题）To the nearest ten, 54.545=.A .50 B. 54.5 C. 54.6 D. 60【参考答案】A【题目解析】54.545保留到整十数是.2. [ 单选题 ] [ 近似数及其求法 ] [ 难度：★★★ ] (2015 年第 23 题）The number N when rounded to the nearest hundredth is 20.16. When rounded to the nearest thousandth, N is at mostA.20.159B.20.160C.20.164D.20.165【参考答案】C【题目解析】数字 N 四舍五入到百分位是20.16，当它四舍五入到千分位最大可能是我爱展示1. [单选题] [近似数及其求法] [难度：★★★ ] （2011 年第 3 题）What is 0.3456 rounded to the nearest hundredth?A.0.34B.0.35C.0.345D.0.346【参考答案】B【题目解析】0.3456四舍五入到百分位是多少？2. [单选题] [近似数及其求法] [难度：★★★ ] （2011 年第 10 题）(8.426 rounded to the nearest tenth )× （7531 rounded to the nearest hundred ）=A.6300B.63450C.63750D.64005【参考答案】A【题目解析】8.426四舍五入到十分位乘7531四舍五入到百位等于多少知识点讲解 2、分数运算专业词汇总结：reciprocal：倒数 fraction:分数 a unit fraction: 分数单位 numerator：分子denominator：分母whole number：整数eg: This must be a whole number between-120 and127. integer number:整数eg: I demand that you give me a positive integer.例题1. [单选题] [分数计算] [难度：★★★ ]A. B. C. D.【参考答案】B2. [单选题] [分数计算] [难度：★★★ ] （2016 年第18 题）The reciprocal ofplus the square of minus the cube of isA. B. C. D.【参考答案】C【题目解析】的倒数加上的平方减去的立方是3. [单选题] [分数计算] [难度：★★★ ] （2015 年第 6 题）How many numbers have their reciprocals equal to themselves?A.0B.1C.2D.3【参考答案】B【题目解析】有多少个数字的倒数等于它本身4. [单选题] [分数计算] [难度：★★★ ] （2011 年第12 题）(The reciprocal of)÷(the reciprocal of )=A.1B. C. D.【参考答案】B【题目解析】的倒数除以的倒数等于？5.[单选题] [分数计算] [难度：★★★ ] （2016 年第 29 题）A unit fraction is a fraction whose numerator is 1 and whose denominator is whole number. The number of unit fractions between and isA.18B.19C.20D.21【参考答案】A【题目解析】大小在到之间的，分子是1且分母是整数的分数有多少个？6.[分数计算] [难度：★★★★ ] （2011 年第 40 题）Find the fraction number with the smallest possible integer numerator that is between andAnswer:【参考答案】【题目解析】找出在和之间最小整数分子的分数我爱展示1. [单选题] [分数计算] [难度：★★★ ]A. B. C. D.【参考答案】B2. [单选题] [分数计算] [难度：★★★ ] （2015年第15题）B.4 D.8A. C.【参考答案】A3. [单选题] [分数计算] [难度：★★★ ] （2014 年第 15 题）A.2B.3C.D.【参考答案】A4. [单选题] [分数计算] [难度：★★★ ] （2012 年第 9 题）A. B. C. D.【参考答案】C5. [单选题] [分数计算] [难度：★★★ ] （2014 年第 6 题）Multiplying a number by is the same a s dividing it by ( )A.0.667B.0.75C.1.5D.1.667【参考答案】C【题目解析】一个数乘相当于这个数除以（）.6. [单选题] [分数计算] [难度：★★★ ] （2014 年第 34 题）将 0.75 转换为分数，这些分数的分子和分母都是＜100 的正整数。

六年级美国大联盟第一阶段-数论专题（教师版）学生/课程年级学科授课教师日期时段核心内容数论专题课型一对一/一对N 教学目标null重、难点null知识导图课首小测1. [数学竞赛] [难度：★★★ ] 专业词汇总结:prime 质数composite number 合数the square of 平方cube 立方 the sum of 和be equal to 等于odd number 奇数even number 偶数factor 因数multiple 倍数【eg：16 is a multiple of 4.(16是4的倍数)】prime factor 质因数 odd factor 奇因数even factor 偶因数odd divisor 奇因数whole- number 整数 multiple of 4 4的倍数Positive 正数 divisor 因数/除数a perfect square 一个完全平方数square of a a的平方 o di n t e g r奇数the greatest common factor 最大公因数the greatest common divisor 最大公因数the least common multiples of 最小公倍数digit 数字numerical digit 数字be divisible by3 能被3整除remainder 余数twice 2倍 is divided by13 除以13【参考答案】必备专业词汇总结【题目解析】必备专业词汇总结导学一知识点讲解一、质数与合数100 以内的25个质数（牢记）一位数：2、3、5、7两位数：以1结尾的：11、31、41、61、71以3结尾的：13、23、43、53、73、83以7结尾的：17、37、47、67、97以9结尾的：19、29、59、79、89偶数个奇数相加得偶数，奇数个奇数相加得奇数；偶数×奇数＝偶数，偶数×偶数＝偶数，奇数×奇数＝奇数。

六年级美国大联盟第一阶段-几何专题（教师版）学生/课程年级学科授课教师日期时段核心内容美国大联盟几何专题课型一对N教学目标多边形的性质、周长、面积以及内角和，正方体长方体的棱长和、表面积、体积。

重、难点几何模型的应用导学一：多边形知识点讲解 1、多边形的认识专业词汇总结：rectangle：矩形 trapezoid：梯形 rhombus：菱形 pentagon：五边形hexagon：六边形 parallelogram：平行四边形 square：正方形例题1.[单选题] [平面图形的分类及识别] [难度：★ ] （2015年第7题）Which of the following is not a parallelogram?A、rectangleB、trapezoidC、rhombusD、square【参考答案】B【题目解析】翻译：下列哪个不是平行四边形？A、矩形B、梯形C、菱形D、正方形2.[单选题] [平面图形的分类及识别] [难度：★ ] （2013年第16题）Which of the following figures has an odd number of sides?A、rhombusB、trapezoidC、pentagonD、hexagon【参考答案】C【题目解析】翻译：下列哪个图形有奇数条边？A、菱形B、梯形C、五边形D、六边形3.[单选题] [平面图形的分类及识别;2、3、5的倍数特征] [难度：★★★ ] （2016年第28题）Each side of square S, pentagon P,and hexagon H is an integer.If the perimeter of each figure is the same,the perimeter could beA、2020B、2030C、2040D、2050【参考答案】C【题目解析】翻译：正方形S、五边形P、六边形H的边长都是整体，如果它们的周长相等，那么它们的周长可能是我爱展示1.[单选题] [平面图形的分类及识别] [难度：★ ] A trapezoid has sides.A、3B、4C、5D、10【参考答案】B【题目解析】翻译：梯形有多少条边？2.[单选题] [平面图形的分类及识别] [难度：★ ] Five pentagons have sides.A、20B、25C、30D、35【参考答案】A【题目解析】翻译：五个正方形有多少条边？3.[单选题] [平面图形的分类及识别] [难度：★ ] All together, 27 trapezoids have the same number of sides astriangle.A、16B、18C、27D、36【参考答案】D【题目解析】翻译：27个梯形的边数与多少个三角形的边数相同？知识点讲解长方形与正方形的面积与周长专业词汇总结：equilateral triangle：等边三角形 perimeter：周长rectangle：长方形side-length：边长length：长area：面积width：宽例题1. [单选题] [正方形的周长;三角形的周长;长方形、正方形的面积] [难度：★★★ ] （2016 年第 9 题）A square and equilateral triangle have the same side-lengths ,and the total of their perimeters is 42. What is the area of the square?A、6B、24C、36D、42【参考答案】C【题目解析】翻译：正方形和等边三角形的边长相同，它们的边长总和为42，正方形的面积是多少？2. [单选题] [正方形的周长;长方形、正方形的面积] [难度：★★★ ] 2. （2015 年第 13 题）The quotient of the square of the perimeter of square S divided by the area of square S isA、1B、2C、4D、16【参考答案】D【题目解析】翻译：正方形周长的平方除以它的面积结果是多少？3. [单选题] [长方形的周长;正方形的周长] [难度：★★★ ] （2013 年第 8 题）Four 2 × 8 rectangles havea total area equal to that of a square of perimeterA、8B、16C、32D、64【参考答案】C【题目解析】翻译：由四个2×8的矩形组成正方体，其周长为？我爱展示1.[单选题] [正方形的周长] [难度：★★★ ] 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?A、36B、48C、72D、144【参考答案】C【题目解析】翻译：如图所示，将四个相同的正方形（每个正方形的周长为36）组合在一起，形成一个大正方形。

六年级美国大联盟第一阶段-几何专题（教师版）学生/课程年级学科授课教师日期时段核心内容美国大联盟几何专题课型一对N教学目标多边形的性质、周长、面积以及内角和，正方体长方体的棱长和、表面积、体积。

重、难点几何模型的应用导学一：多边形知识点讲解 1、多边形的认识专业词汇总结：rectangle：矩形 trapezoid：梯形 rhombus：菱形 pentagon：五边形hexagon：六边形 parallelogram：平行四边形 square：正方形例题1.[单选题] [平面图形的分类及识别] [难度：★ ] （2015年第7题）Which of the following is not a parallelogram?A、rectangleB、trapezoidC、rhombusD、square【参考答案】B【题目解析】翻译：下列哪个不是平行四边形？A、矩形B、梯形C、菱形D、正方形2.[单选题] [平面图形的分类及识别] [难度：★ ] （2013年第16题）Which of the following figures has an odd number of sides?A、rhombusB、trapezoidC、pentagonD、hexagon【参考答案】C【题目解析】翻译：下列哪个图形有奇数条边？A、菱形B、梯形C、五边形D、六边形3.[单选题] [平面图形的分类及识别;2、3、5的倍数特征] [难度：★★★ ] （2016年第28题）Each side of square S, pentagon P,and hexagon H is an integer.If the perimeter of each figure is the same,the perimeter could beA、2020B、2030C、2040D、2050【参考答案】C【题目解析】翻译：正方形S、五边形P、六边形H的边长都是整体，如果它们的周长相等，那么它们的周长可能是我爱展示1.[单选题] [平面图形的分类及识别] [难度：★ ] A trapezoid has sides.A、3B、4C、5D、10【参考答案】B【题目解析】翻译：梯形有多少条边？2.[单选题] [平面图形的分类及识别] [难度：★ ] Five pentagons have sides.A、20B、25C、30D、35【参考答案】A【题目解析】翻译：五个正方形有多少条边？3.[单选题] [平面图形的分类及识别] [难度：★ ] All together, 27 trapezoids have the same number of sides astriangle.A、16B、18C、27D、36【参考答案】D【题目解析】翻译：27个梯形的边数与多少个三角形的边数相同？知识点讲解长方形与正方形的面积与周长专业词汇总结：equilateral triangle：等边三角形 perimeter：周长rectangle：长方形side-length：边长length：长area：面积width：宽例题1. [单选题] [正方形的周长;三角形的周长;长方形、正方形的面积] [难度：★★★ ] （2016 年第 9 题）A square and equilateral triangle have the same side-lengths ,and the total of their perimeters is 42. What is the area of the square?A、6B、24C、36D、42【参考答案】C【题目解析】翻译：正方形和等边三角形的边长相同，它们的边长总和为42，正方形的面积是多少？2. [单选题] [正方形的周长;长方形、正方形的面积] [难度：★★★ ] 2. （2015 年第 13 题）The quotient of the square of the perimeter of square S divided by the area of square S isA、1B、2C、4D、16【参考答案】D【题目解析】翻译：正方形周长的平方除以它的面积结果是多少？3. [单选题] [长方形的周长;正方形的周长] [难度：★★★ ] （2013 年第 8 题）Four 2 × 8 rectangles havea total area equal to that of a square of perimeterA、8B、16C、32D、64【参考答案】C【题目解析】翻译：由四个2×8的矩形组成正方体，其周长为？我爱展示1.[单选题] [正方形的周长] [难度：★★★ ] 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?A、36B、48C、72D、144【参考答案】C【题目解析】翻译：如图所示，将四个相同的正方形（每个正方形的周长为36）组合在一起，形成一个大正方形。

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。

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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。

2022-2023年度美国Math League思维探索第一阶段活动(六年级)(答题时间：75分钟，总分：175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。

选择题：每小题5分，答对加5分，答错不扣分，共175分。

1. A farmer has 36 more pigs than sheep. If he has 10 times as many pigs as sheep,how many pigs does the farmer have?A) 40 B) 44C) 45 D) 462.If the cost of a dozen bagels increases by $1.80, the average cost of eachbagel will increase byA) 10¢B) 15¢C) 18¢D) 30¢3.The integer 2 equals ? times the reciprocal of 2.A) 2 B) 4 C) 6 D) 84.Which of the following could be the perimeter of a rectangle with both odd and even whole-numberside-lengths?A)12 B) 13 C) 14 D) 165.How many positive divisors of 122 are multiples of 12?A) 2 B) 6 C) 12 D) 246.What is the difference between 23.456 rounded to the nearest tenth and 23.456 rounded to the nearesthundredth?A) 0 B) 0.04 C) 0.05 D) 0.17.The area of a square is 36 m2. The perimeter of the square in cm isA) 900 cm B) 2400 cmC) 3600 cm D) 360 000 cm8.What is the greatest odd divisor of 2 × 4 × 6 × 8 × 10 × 12?A) 9 B) 15 C) 45 D) 1359. Roy painted 100 houses. If Roy painted 40% of the houses gray and 20% ofthe remaining houses yellow, how many houses did Roy paint yellow?A) 8B) 12C) 20D) 4010. Which of the following expressions has the greatest value?A) 221 B) 212 C) 2221 D) 221⎪⎭⎫ ⎝⎛ 11. The temperature of a pot of soup increases by 3° every 40 seconds. How much will the temperatureincrease in 30 minutes?A) 135°B) 450°C) 750°D) 1800°12. I counted from 1 to 100 out loud, skipping every multiple of 3. How many numbers did I say out loud?A) 66B) 67C) 76D) 7713. What is the difference between 2 primes whose product is 10 135?A) 2022B) 2023C) 2027D) 203214. A pile of 1003 pennies can be divided equally into exactly ? equal piles worth $4 each.A) 25B) 250C) 2500D) 25 00015. In 2022 I ran on 101 more days than the number of days I did not run. The sum of the digits of the number of days I ran in 2022 isA) 5 B) 6 C) 8 D) 1116. 2999 + 2999 =A) 21 + 999B) 21 × 999C) 22 + 999D) 22 × 99917. If 80% of Ari’s savings equals 20% of Ari’s and Bev’s savings combined, Bev must have ? times as much savings as Ari.A) 2 B) 3 C) 4 D) 6 18. What is the greatest power of 2 that is a factor of the product of the 6 smallest positive 2-digit integers?A) 23B) 24C) 26D) 2819. A square poster consists of an 8 cm-wide border around the perimeter of a square photo. If the area of the entire poster is 6400 cm 2, what is the area of the photo portion of the poster?A) 4096 cm 2B) 4608 cm 2C) 5120 cm 2D) 5184 cm 220. A triangle’s angles have measures that are consecutive multiples of 15°. What is the averag e measure of the 2 smallest angles?A) 37.5°B) 52.5°C) 67.5°D) 82.5°21. I divided a multiple of 5 by a smaller multiple of 5 and got a remainder of 15. What is the smallest possible sum of the multiples?A) 30 B) 45C) 55D) 6522. Every third gumball dispensed has cracks, but the rest do not. If I keep every 4thgumball dispensed and discard the rest, how many of the 72 gumballs I keep will have cracks?A) 6B) 12C) 18D) 2423. How many factors greater than or equal to 5 does 2 × 5101 have?A) 101B) 102C) 201D) 20224. Each of the integers from 1 through 50 was written on a separate tag, then 3 consecutively numbered tags were lost. If the sum of the integers on the 47 remaining tags is 1221, what is the sum of the digits of the integers on the lost tags?A) 13B) 17C) 27D) 3025. If the median of 6 consecutive integers is 4.5, what is the median of their reciprocals?A) 92 B) 94 C) 209 D) 40926. My ride to school takes from 10 to 18 minutes, depending on traffic. I cannot arrive before 8:10 AM or after 8:30 AM. What is the difference between the earliest and latest times I could start riding to ensure that I arrive on time?A) 8 minutes B) 12 minutes C) 20 minutes D) 28 minutes 27. What is the average of 2100 and 2101?A) 2100.5B) 2 × 299C) 2 × 2100D) 3 × 29928. If (0, 0) and (3, 4) are two vertices of a parallelogram in a coordinate plane, which of the following couldnot be another vertex of this parallelogram?A) (4, 3)B) (-1, 7)C) (-3, -4)D) (-4, 3)29. On a class test, the average score of the boys and girls combined was 88. Ifthe average score of the boys was 80, and the average score of the girls was 100, which of the following numbers could be the total number of the boys and girls combined?A) 105B) 63C) 48D) none of above30. A clock that uniformly loses 4 minutes every 24 hours was correctly set at 6 A.M. on January 1. What is the correct time when the clock reads 11:39 AM on January 6 of the same year?A) 11:54 AM, January 6 B) 12:00 PM, January 6 C) 12:30 PM, January 6D) 11:00 AM, January 731. If we get a bullseye half the time that we play darts, is it most likely that weA) miss a bullseye in any single try, B) get a bullseye at least 1 time in 2 tries, or C) get a bullseye 2 or 3 times in 3 tries?32. What is the quotient of the least common multiple of the first 40 positive integers divided by the least common multiple of the first 30 positive integers?A) 1209B) 1147C) 2294D) none of above33.How many points does one have to place on a 1 inch by 3 inches rectangle to guarantee that two of themare strictly less than 1 inch apart? (The rectangle here includes its complete interior.)A) 8 B) 10 C) 12 D) none of above34.One square has twice the area of another square. Is it possible for both squares to have side lengths thatare whole numbers?A) Yes B) No35.What is the radius of the circle inscribed in a triangle with side lengths 7, 24, and 25?Note: The figure below shows the circle inscribed in a triangle.A) 3 B) 4.5 C) 6 D) none of above。

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。