2015年美国“数学大联盟杯赛”(中国赛区)初赛五年级试卷答案

2015年.世界奥林匹克数学竞赛5年级试题.A卷第⼗三届世界奥林匹克数学竞赛（中国区）选拔赛五年级试卷⼀．知识题（每⼩题6分，共42分）1．如图所⽰，每个图中点的数量被称为“⾦字塔数”．请问从⼩到⼤第2015个“⾦字塔数”是__________．2．某⼯⼚买来0.7m和0.8m的两种钢条各若⼲根．这些钢条可以通过焊接得到许多不同长度的钢条（钢条不允许切割），那么在3.3m、3.6m、3.7m、3.8m、3.9m这些长度中，________m是不能通过焊接得到的．3．观察下图44的表格，请问表格中所有数的平均数为________．20.1220.1320.1420.1520.1320.1420.1520.1620.1420.1520.1620.1720.1520.1620.1720.184．如上图所⽰的四边形的⾯积是________．5．加拿⼤2014年的⼿机号码是7位数，⼈⼝普查结束后，议会决定在2015年统⼀将全国的⼿机号码升⾄8位数（⼿机号码第1位数字不能为0），以应对因为⼈⼝增长带来的⼿机号码将不够⽤的情况．请问2015年，加拿⼤的⼈⼝数量将突破________万．6．某⼈驾船在河流中匀速逆流⾏驶，8:00时船上的⼀个⽊箱不慎掉⼊⽔中，⼀⼩时后发现情况，马上调头以相同的速度追赶顺流⽽下的⽊箱．请问追上⽊箱的时间为________．7．歌⼿蔡国庆在⼀⾸歌中唱道“⼀年有三百六⼗五个⽇出”，歌⼿陈奕迅有⾸歌叫《⼗年》，请问⼗年可能有______________________________________天．（写出所有可能的天数）⼆．能⼒题（每⼩题6分，共36分）1．“数缺形不直观，形缺数不⼊微”，数形结合思想是数学学习中的⼀个重要的数学思想，请仔细观察下⾯⼏幅图形并回答后⾯的问题：（1.5分46?=分）图D 有问题①由图形________可知勾股定理222a b c +=成⽴；②由图形________可知平⽅差公式()()22a b a b a b -=+-；③由图形________可知完全平⽅公式()2222a b a b ab +=++成⽴；④由图形________可知公式()()224a b a b ab +--=成⽴．2．敏敏在家的后院养了⼀只⼩⽩兔，为了控制院中草的⽣长，敏敏把⼩⽩兔喂养在如下图所⽰的⼀个可移动的圈栏内．已知这个圈栏为长3⽶、宽2⽶的长⽅形．接连四天圈栏分别向东移动1⽶，向南移动2⽶，向西移动1⽶，向北移动2⽶．请问⼩⽩兔可以啃咬的草地⾯积是________平⽅⽶．3．房间⾥有3种⼩动物：⼩⽩⿏、⼩花猫、⼩黄狗，如果猫的数量不超过狗，狗就会欺负猫；如果⿏的数量不超过猫，猫就会欺负⿏；如果猫、狗数量之和不超过⿏，⿏就会偷吃东西，现在房间⾥没有发⽣任何事情，但是再进来任意⼀只，都会打破平衡．那么，原来房间⾥有________只⼩动物．4．⼀个棱长为15的正⽅体⽊块，在它的⼋个顶点处各截去⼀个棱长分别为1、2、3、4、5、6、7、8的⼩正⽅体．则这个⽊块剩下部分的表⾯积可能是________．5．飞马“帕加索斯”是古希腊神话中缪斯⼥神的坐骑，传说被其马蹄踏过的地⽅就会有灵泉涌出，诗⼈引⽤之后可获得灵感．下图展⽰了如何通过“平移”来穿创造“帕加索斯”飞马：步骤1：在正⽅形ABCD中，从点A引⼀条折线⾄点B，如图1；步骤2：把折线AB平移到DC处，如图2；步骤3：在正⽅形ABCD中，从点A引⼀条折线⾄点D，如图3；步骤4：把折线AD平移到BC处，如图4．则图4中“帕加索斯”所围成图形⾯积________正⽅形ABCD的⾯积．（填“>”“<”或“=”）6．安安买了个玩具⼩汽车，⼩汽车的底部有如上图所⽰的两个互相咬合的齿轮，安安在齿轮上各画了⼀条带箭头的直线．开始时两个箭头正好相对．然后安安将⼩轮顺时针⽅向转动，同时⼤轮被带动着逆时针⽅向转动．若⼤轮有41个齿，则⼩轮在转了________圈以后这两个箭头第⼀次重新相遇．三．过程题（每⼩题10分，共30分）1．下图是⼀⽚稻⽥，每个⼩⽅格的边长都是1⽶，其中A、B、C三个圆圈是⽔洼．⼀只⼩鸟飞来觅⾷，它最初停留在0号位，过了⼀会⼉，它跃过⽔洼，飞到关于A点对称的1号位；不久，它⼜飞到关于B点对称的2号位；接着，它飞到关于C点对称的3号位，再飞到关于A点对称的4号位，……，如此继续，⼀直A、B、C对称地飞下去，那么，2019号位和0号位之间的距离是多少⽶？并简单说明你的理由．2．某迷宫的正确路线如下图所⽰，已知迷宫中⽅格的边长都是1⽶，且每⼀段路都按照螺旋形顺次编号为1、2、3、4、…，请问：⑴编号2016的那段路有多长？（5分）⑵长为2016⽶的路段编号是多少？（5分）3．“⼟豪”⾦⽼师要在微信群⾥陆续地发⼤、中、⼩三个“红包”，但⼤伙不知道顺序如何，也不能看出“红包”⼤中⼩，但可以⽐较当前“红包”与上个“红包”的⼤⼩．且“红包”出现时，每⼈必须马上选择“抢”或者“不抢”，否则“红包”将在下个“红包”出现之前被抢完．现在规定每⼈只能抢⼀个“红包”，请问：⑴红包出现的顺序⼀共有多少种不同情况？（5分）⑵采取某种策略能最⼤可能的抢到“⼤红包”，请问这个“最⼤可能”的可能性是多少？（5分）四．⽅法题（12分）朋友租了个店⾯开起了⼿机店，⼀个季度的租⾦是8000元加上若⼲台“⽼⼈机”．他抱怨说去年“⽼⼈机”的价格为每台75元，这笔租⾦相当于每平⽅⽶700元；但是现在“⽼⼈机”的市价已经涨到了每台100元，所以这笔租⾦相当于每平⽅⽶800元．他觉得有点贵了．请问朋友所租的店⾯⾯积是多少平⽅⽶？（⼀种⽅法得4分，两种⽅法得8分，三种及三种以上⽅法得12分）。

五年级美国大联盟第一阶段-计算+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null 课型null教学目标1、掌握分数、百分数、乘方的计算。

2、掌握因数倍数、质数合数、奇数偶数、最大公因数和最小公倍数、倍数关系。

3、掌握组合图形的面积。

重、难点1、掌握分数、百分数、乘方的计算。

2、掌握因数倍数、质数合数、奇数偶数、最大公因数和最小公倍数、倍数关系。

3、掌握组合图形的面积。

导学一知识点讲解计算数的计算：整数、分数、百分数的计算与乘方例题1.[单选题] [整数的加法和减法] [难度：★★★ ] The sum of 5 consecutive one-digit integers is at most （）A、15B、25C、35D、45【参考答案】C【题目解析】5个连续的一位数的整数之和最大是（）2.[单选题] [数的运算] [难度：★★★ ] I have read 1/3 of the total 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 be （）A、16B、24C、32D、50【参考答案】A【题目解析】我已经阅读了120页的书的章节总数的1/3。

如果每一章都有相同的总页数，那么我剩下的章节总数可以是（）3.[单选题] [数的运算] [难度：★★★ ] Which of the following has the greatest value?A 、2017B、2017 C、20×17D、20+17【参考答案】B【题目解析】下面的数中，哪个数的值最大？我爱展示1. [单选题] [数的运算] [难度：★★★ ] Which of the following when rounding to the nearestthousands,hundreds, and tens, equals 3000, 3500, and 3460, respectively?A、3210B、3333C、3456D、3517【参考答案】C【题目解析】下面的数中，哪个数分别四舍五入到千位、百位、十位，结果是3000、3500、3460？2000 2017 20002. [单选题] [数的运算] [难度：★★★ ] 2 ×5= 10 ×?17 1000 2000 2017A、5B、5C、5D、5【参考答案】A3. [单选题] [数的运算] [难度：★★★ ] The number that is 10% of 1000 is 10 more than 10% of（）A、90B、100C、900D、990【参考答案】A【题目解析】1000的10%大于（）的10%的10倍。

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。

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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。

五年级美国大联盟第一阶段-应用专题（教师版）学生/课程年级学科授课教师日期时段核心内容熟悉美国大联盟常考应用题课型一对一/一对N教学目标1、理解题目中的倍数关系，解决相关应用题；2、掌握抽屉原理、容斥原理等问题；3、掌握时钟问题、行程问题；4、运用多种方法，灵活解决应用题。

重、难点重难点：4 知识导图导学一：倍数关系/量率关系知识点讲解1、简单的倍数关系（1）倍数问题小数（一倍数）×倍数＝大数大数÷倍数＝小数（一倍数）单位1×分率＝对应量对应量÷分率＝单位1（2）如何判断“一倍数”/“单位1”“的”前“比”后（3）解题方法①画图法：画线段图，用一格表示一倍数②方程法：设一倍数为X例题1.[单选题] [整数、小数复合应用题] [难度：★★★ ] Lynn ran in 6 times as many races as the number of races she won. How many of her 126 races did Lynn not win?A）21 B）90 C）96 D）105【参考答案】D【题目解析】翻译：Lynn参加的比赛是她赢的比赛的6倍，她126场比赛中有（）场没有赢。

解析：Lynn参加的比赛是她赢的比赛的6倍，题目中“小数”为“赢的比赛”，求小数用除法：126÷6=21（场），没有赢的比赛：126-21=105（场）故选D。

2.[单选题] [列方程解含有一个量的应用题] [难度：★★★ ] What is the weight of a fish if it weighs ten pounds plus half its weight?A）10 B）15 C）20 D）25【参考答案】C【题目解析】翻译：如果一条鱼的重量是十磅加上它重量的一半，那么它的重量是多少? 解析：方法一：方程法。

解：设鱼的重量为X，则：X＝10＋X÷2，解得x＝20方法二：算术法。

五年级美国大联盟计算和几何专题讲义教师版(含题目翻译答案解析)五年级美国大联盟第一阶段-计算+几何专题（教师版）学生/课程授课教师核心内容年级日期null1、掌握分数、百分数、乘方的计算。

学科时段课型null教学目标2、掌握因数倍数、质数合数、奇数偶数、最大公因数和最小公倍数、倍数关系。

3、掌握组合图形的面积。

重、难点1、掌握分数、百分数、乘方的计算。

2、掌握因数倍数、质数合数、奇数偶数、最大公因数和最小公倍数、倍数关系。

3、掌握组合图形的面积。

导学一知识点讲解计算数的计算：整数、分数、百分数的计算与乘方例题1.[单项选择题] [整数的加法和减法] [难度：★★★] Thesum of 5 consecutive one-digit integers is at most（）A、15【参考谜底】C【问题剖析】5个继续的一名数的整数之和最大是（）B、25C、35D、45A、16【参考谜底】A是（）B、24C、32D、503.[单选题] [数的运算] [难度：★★★] Which of the following has the greatest value?A、2017【参考答案】BB、2017C、20×17D、20+17【题目解析】下面的数中，哪个数的值最大？XXX我爱展示1. [单选题] [数的运算] [难度：★★★] Which of the following when rounding to the nearestthousands,hundreds, and tens, equals 3000, 3500, and 3460, respectively?A、3210【参考答案】C【题目解析】下面的数中，哪个数分别四舍五入到千位、百位、十位，结果是3000、3500、3460？B、3333C、3456D、35172.[单项选择题] [数的运算] [难度：★★★] 2×5= 10×?A、5B、5C、52017D、5【参考答案】A3. [单选题] [数的运算] [难度：★★★] The number that is 10% of 1000 is 10 more than 10% of（）A、90【参考谜底】A【题目解析】1000的10%大于（）的10%的10倍。

2014-2015年度美国“数学大联盟杯赛”（中国赛区）初赛（五年级）中文版一、选择题（每小题5分，答对加5分，答错不扣分，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）8. 80+(160+240) ÷4=40+80+(120÷____ ) （）A. 4B. 2C. 1D. 09. 下列式子中哪个式子的余数最大? （）A. 1111 ÷8B. 2222 ÷7C. 3333 ÷6D. 4444 ÷510. 下列各数中，哪个是20×14×20×15的因数? （）A. 13B. 11C. 9D. 711. Thok有一个简单的计划。

他准备花费一天中50%的时间在洞穴中，剩下的时间中的25%用来打猎，剩余的时间在外面看电影。

那么他将花费多少时间看电影呢? （）A. 3B. 6C. 9D. 2512. 2×3×6×36×2×3×6×36=（）?A. 65B. 66C. 67D. 6813. 我有5个1美分的便士，4个5美分的硬币，3个0.25的硬币，2个0.5美元的硬币和1美元。

那这些硬币的平均值是多少（）?A. 0.02美元B.0.06美元C. 1.5美元D. 3美元14. Wyatt O’Vine的羊的体重是Wyatt的两倍，Wyatt的体重是他帽子的两倍，如果Wyatt，羊，他的帽子体重在一起时210kg，那Wyatt重多少? （）A. 30kgB. 35kgC. 60kgD. 70kg15. （12+34）×（56+78）=12×（56+78）+_____×(56+78) ? （）A. 12B. 34C. 56D. 7816. 如果2个群等于5个斑点，那么500个群等于______个斑点。

（）A. 200B. 250C. 1000D. 125017.（64+64）2 =（）A. 16B. 64C. 128D. 25618. 如果7个连续的偶数和是182，那么7个数中最小的数字是（）A. 20B. 23C. 26D. 3219. 当他倒立时，Flip决定从777开始每8个数字一倒数，那以下的哪个数字他会数到? （）A. 123B. 125C. 127D. 12920. 买5个苹果和买6个梨的价格是一样的，如果一个苹果比一个梨多花15美分，那么5个苹果和6个梨在一起一共多少钱? （）A. 3美元B. 6美元C. 9美元D. 18美元21. 27和27所有因数的乘积之间相差多少? （）A. 2B. 27C. 2×27D. 26×2722. 一个小于100的最大素数分解数最多是_____个素数的乘积（不一定是不同的）? （）A. 3B. 4C. 5D. 623. 一个四边都是整数边的长方形被分成了一个正方形和一块阴影的长方形。

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。

2015美国数学竞赛AMC12试题及答案Problem1What is the value ofProblem2Two of the three sides of a triangle are20and15.Which of the following numbers is not a possible perimeter of the triangle?Problem3Mr.Patrick teaches math to15students.He was grading tests and found that when he graded everyone's test except Payton's,the average grade for the class was80.after he graded Payton's test,the class average became81.What was Payton's score on the test?Problem4The sum of two positive numbers is5times their difference.What is the ratio of the larger number to the smaller?Problem5Amelia needs to estimate the quantity,where and are large positiveintegers.She rounds each of the integers so that the calculation will be easier to do mentally.In which of these situations will her answer necessarily be greater than the exact value of?Problem6Two years ago Pete was three times as old as his cousin Claire.Two years before that, Pete was four times as old as Claire.In how many years will the ratio of their ages be ?Problem7Two right circular cylinders have the same volume.The radius of the second cylinderis more than the radius of the first.What is the relationship between the heights of the two cylinders?Problem8The ratio of the length to the width of a rectangle is:.If the rectangle hasdiagonal of length,then the area may be expressed as for some constant.What is?Problem9A box contains2red marbles,2green marbles,and2yellowmarbles.Carol takes2 marbles from the box at random;then Claudia takes2of the remaining marbles at random;and then Cheryl takes the last2marbles.What is the probability that Cheryl gets2marbles of the same color?Problem10Integers and with satisfy.What is?Problem11On a sheet of paper,Isabella draws a circle of radius,a circle of radius,and all possible lines simultaneously tangent to both circles.Isabella notices that she has drawn exactly lines.How many different values of are possible?Problem12The parabolas and intersect the coordinate axes in exactly four points,and these four points are the vertices of a kite of area.What is?Problem13A league with12teams holds a round-robin tournament,with each team playing every other team exactly once.Games either end with one team victorious or else end in a draw.A team scores2points for every game it wins and1point for every game it draws.Which of the following is NOT a true statement about the list of12scores?Problem14What is the value of for which?Problem15What is the minimum number of digits to the right of the decimal point needed toexpress the fraction as a decimal?Problem16Tetrahedron has and .What is the volume of the tetrahedron?Problem17Eight people are sitting around a circular table,each holding a fair coin.All eight people flip their coins and those who flip heads stand while those who flip tails remain seated.What is the probability that no two adjacent people will stand?Problem18The zeros of the function are integers.What is the sum of the possible values of?Problem19For some positive integers,there is a quadrilateral with positive integerside lengths,perimeter,right angles at and,,and.Howmany different values of are possible?Problem20Isosceles triangles and are not congruent but have the same area and the sameperimeter.The sides of have lengths of and,while those of have lengthsof and.Which of the following numbers is closest to?Problem21A circle of radius passes through both foci of,and exactly four points on,the ellipse with equation.The set of all possible values of is an interval. What is?Problem22For each positive integer n,let be the number of sequences of length n consisting solely of the letters and,with no more than three s in a row and nomore than three s in a row.What is the remainder when is divided by12?Problem23Let be a square of side length1.Two points are chosen independently at random onthe sides of.The probability that the straight-line distance between the points is atleast is,where and are positive integers and.Whatis?Problem24Rational numbers and are chosen at random among all rational numbers in the interval that can be written as fractions where and are integers with .What is the probability that is a real number?Problem25A collection of circles in the upper half-plane,all tangent to the-axis,is constructedin layers as yer consists of two circles of radii and that areexternally tangent.For,the circles in are ordered according to their points of tangency with the-axis.For every pair of consecutive circles in this order, a new circle is constructed externally tangent to each of the two circles in the pair.Layer consists of the circles constructed in this way.Let,andfor every circle denote by its radius.What isDIAGRAM NEEDED。

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。

2014-2015年度美国”数学大联盟杯赛“（中国赛区）初赛（十、十一、十二年级）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：=-⨯⨯20522 ？ （A ）A)5 B)15 C)25 D)301. Meg loves her megaphone! The large circular end has a circumference that is the reciprocal of its diameter. What is the area of the circle? ( )A)π14 B) π12 C) 14 D) 122. How many solutions does the equation x x +=233 have? ( )A)0 B)1 C)2 D)43. If y x =-1, which of the following is always true for any value of x ? ( )A) ()()x y -=-2211B) ()()x x y y -=-222211 C) ()()x x y y --=-222211 D) ()()()()x x y y -+=-+22221111 4. Lee the crow ate a grams of feed that was 1% seed, b grams of feed that was 2% seed, and c grams of feed that was 3% seed. If combined, all the feed he ate was 1.5% seed. What is a in terms of b and c ?( )A)b c +3B)b c +3 C)b c +23 D)b c +32 5. If <x 0 and <.x 2001, then x -1 must be ( )A)less than -10B)between-0.1 and 0 C)between 0and 0.1 D) greater than 106. At 9:00 A.M., the ratio of red to black cars in a parking lot was 1 to 5. An hour later the number of red cars had increased by 2, the number of black cars had decreased by 5, and the ratio of red to black cars was 1 to 4. How many black cars were in the lot at 10:00 A.M.? ( )A)13 B)15 C)60 D)657. If x ≠1and x ≠-1, then ()()()x x x x x --++-32241111=( ) A)x -21 B) x +21 C) x -241 D) x -341 8. The Camps are driving at a constant rate. At noon they had driven 300 km.At 3:30 P.M. they had driven 50% further than they had driven by 1:30 P.M.What is their constant rate in km/hr? ( )A)150 B)120 C)100 D)909. The letters in DIGITS can be arranged in how many orders without adjacent I ’s? ( )A)240 B)355 C)600 D)71510. Al, Bea, and Cal each paint at constant rates, and together they are painting a house. Al and Bea togethercould do the job in 12 hours; Al and Cal could to it in 15, and Bea and Cal could do it in 20. How many hours will it take all three working together to paint the house?( )A)8.5 B)9 C)10 D)10.5二、填空题（每小题10分，答对加10分，答错不扣分，共200分）11. What is the sum of the degree-measures of the angles at the outer points ,,,A B C D and E of a five-pointed star, as shown? Answer: . 12. What is the ordered pair of positive integers (,k b ), with the least value of k , which satisfiesk b ⋅⋅=34234?Answer: .13. A face-down stack of 8 playing cards consisted of 4 Aces (A ’s) and 4 Kings (K ’s).After I revealed and then removed the top card, I moved the new top card to thebottom of the stack without revealing the card. I repeated this procedure until thestack without revealing the card. I repeated this procedure until the stack was leftwith only 1 card, which I then revealed. The cards revealed were AKAKAKAK ,in that order. If my original stack of 8 cards had simply been revealed one card at atime, from top to bottom (without ever moving cards to the bottom of the stack),in what order would they have been revealed?Answer: .14. For what value of a is one root of ()x a x a -+++=222120 twice the other root?Answer: .15. Each time I withdrew $32 from my magical bank account, the account ’sremaining balance doubled. No other account activity was permitted. My fifth$32 withdrawal caused my account ’s balance to become $0. With how manydollars did I open that account?Answer: .16. In how many ways can I select six of the first 20 positive integers, disregarding the order in which these sixintegers are selected, so that no two of the selected integers are consecutive integers?Answer: .17. If, for all real ,()()xx f x f x =-21, what is the numerical value of f (3)?Answer: .18. How many pairs of positive integers (without regard to order) have a least common multiple of 540?Answer: .19. If the square of the smaller of consecutive positive integers is x , what is the square of the larger of thesetwo integers, in terms of x ?Answer: .20. A pair of salt and pepper shakers comes in two types: identical and fraternal.Identical pairs are always the same color. Fraternal pairs are the same colorhalf the time. The probability that a pair of shakers is fraternal is p andthat a pair is identical is .q p =-1 If a pair of shakers is of the same color, AE DCBword 格式-可编辑-感谢下载支持 determine, in terms of the variable q alone, the probability that the pair is identical. Answer: .21. As shown, one angle of a triangle is divided into four smaller congruentangles. If the lengths of the sides of this triangle are 84, 98, and 112, as shown,how long is the segment marked x ?Answer: .22. How long is the longer diagonal of a rhombus whose perimeter is 60, if threeof its vertices lie on a circle whose diameter is 25, as shown?Answer: .23. The 14 cabins of the Titanic Mail Boat are numbered consecutively from1 through 14, as are the 14 room keys. In how many different ways canthe 14 room keys be placed in the 14 rooms, 1 per room, so that, for everyroom, the sum of that room ’s number and the number of the key placed inthat room is a multiple of 3?Answer: .24. For some constant b , if the minimum value of ()x x b f x x x b -+=++2222is 12, what is the maximum value of ()f x ? Answer: .25. If the lengths of two sides of a triangle are 60cos A and 25sin A , what is the greatest possible integer-length of the third side?Answer: .26. {}n a is a geometric sequence in which each term is a positive number. If a a =5627, what is the value oflog log log ?a a a +++3132310Answer: . 27. What is the greatest possible value of ()=sin cos ?f x x x ++3412Answer: .28. Let C be a cube. Triangle T is formed by connecting the midpoints of three edges of cube C . What is the greatest possible measure of an angle of triangle T ?Answer: .29. Let a and b be two real numbers. ()sin f x a x b x =++34 and (lg log )f =3105. What is the value of (lg lg )f 3?Answer: .30. Mike likes to gamble. He always bets all his chips whenever the number of chips he has is <=5. He always bets n （10-）chips whenever the number of chips he has is greater than 5 and less than 10. He continues betting until either he has no chips or he has more than 9 chips. For every round, if he bets n chips. The probability that he wins or loses in each round is 50%. If Mike begins with 4 chips, what is the probability that he loses all his chips?Answer: .1129884xword格式-可编辑-感谢下载支持。

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)2017B)2017C)20×17D)20+172.Which of the leaves a remainder of2when divided by4?A)2014B)2015C)2016D)20173.Which of the is a pr oduct of two consecutive primes?A)30B)72C)77D)1874.A Bizz-Number is a integer that either contains the3or is a multiple of3.What is the of the10th Bizz-Number?A)24B)27C)30D)315.The of an isosceles triangle with side-lengths1and1008isA)1010B)1012C)2017D)20186.How integers less than2017are divisible by16bu t not by4?A)0B)126C)378D)5047.Jon has a n u mbe r of pens.If he distributed them evenly among4students, he have3left.If he distributed them evenly among5students,he have 4left.The minimum n u mbe r of pens that Jon have isA)14B)17C)19D)248.Which of the numbers is not divisible by8?A)123168B)234236C)345424D)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 at the beginning of the day.If the cup is at the end of2017th day,then it was1/4at the end of the?day.A)504th B)505th C)2015th D)2016th12.The grades on an exam are5,4,3,2,or1.In a class of200students,1/10of got5’s,1/5of got4’s,25%ofgot3’s,and15%of got2’s.How many students got1’s?A)40B)60C)80D)10013.22000×52017=102000×?A)517B)51000C)52000D)5201714.1%of1/10of10000is?percent than10A)0B)9C)90D)90015.What is the of the of Circle C t o the of Square S if the ofa diameter of C and a of S are equal?A)π:1B)π:2C)π:3D)π:416.Which of the is not a prime?A)2003B)2011C)2017D)201917.If the su m of prime numbers is30,what is the possible value of any of the primes?A)19B)23C)27D)2918.For$3I s pe n d on books,I s pe n d$4on and$5on toys.If I spent$20 on food,how much,in dollars,did I s pen d in total?A)60B)90C)120D)15019.How positive odd factors do e s25×35×55have?A)25B)36C)125D)21620.The of scalene triangles with perimeter15and side-lengths isA)3B)5C)6D)721.Which of the when rounding t o the nearest thousands,hundreds,and tens,3000,3500,and3460,respectively?A)3210B)3333C)3456D)351722.Which of the below has exactly5positive divisors?A)16B)49C)64D)10023.Each after the1st in the sequence1,5,9,…is4than the previous term.The gr eatest in sequence that is<1000and that leavesa of1when divided by6isA)991B)995C)997D)99924.For integer from100t o999I the of the integer’s digits.How many of the products I are prime?A)4B)8C)12D)1625.If a machine paints at a of1m2/sec,its is alsoA)600cm2/min B)6000cm2/minof Square C is timesC)60000cm2/min D)600000cm2/min26.The of Square A is1.The of Square B is times of Square A.The of Square B.The of Square C is?times of Square A.A)3B)6C)36D)8127.If the17minutes ago was19:43,what will be the17minutes from now?A)20:00B)20:17C)20:34D)20:1528.Pick any greater than100and subtract the su m of its from the integer.The largest that must the result isA)1B)3C)9D)2729.The n u mbe r of needed in a room so there are always at least five in the room born in the s ame month isA)48B)49C)60D)6130.If M,A,T,and H are digits such that MA TH+HT AM=12221,is the value of M+A+T+H?A)8B)20C)22D)2431.If10forks,20knives,and30$360,and30forks,20knives,and10$240,what is the of5forks,5knives,and5spoons?A)15B)75C)150D)22532.Write,in r educed form,the value ofA)0.5B)1C)1.5D)233.Al,Barb,Cal,Di,Ed,Fred,and participated in a chess tournament.Each player play each of his six o ppo n en t s exactly once.So far,Al has1 match.Barb has2matches.Cal has3matches.Di has4 matches.Ed hasmatches has5matches,andat this point?has6matches.How many A)1B)3C)5D)7of these integers could be the34. What is the n u mber of different integers I can choose from the100positive integers so that noof the sides ofthe s a me triangle? A) 8 B) 9 C) 10 D) 1135. What is thevalue of change that you can have in US(pennies,nickels, dimes, and quarters) without being able t o someone exact change for aone-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。

第十三届“走进美妙的数学花园”上海决赛小学五年级----王洪福老师第十三届“走进美妙的数学花园”青少年展示交流活动趣味数学解题技能展示大赛初赛（上海决赛）小学五年级试卷（B卷）2015年3月8日上午10:45——12:15满分150分一、填空题（每小题8分，共40分）【第1题】计算：20150308=101×(100000+24877×)考点：整数计算解析：()()20150308÷101−100000÷24877=199508−100000÷=99508÷24877=424877【第2题】将23，581523，1017，按照从小到大顺序排列。

考点：分数比较大小解析：251510（解法一）先把分数化为小数形式：≈0.666，=0.625，≈0.652，≈0.58838231710<<<2515通过比较小数的大小，从小到大顺序排列为17823 3 （解法二）比较倒数2515103823174548，，，的倒数分别为，，，，通分后为，382317251510303017>>>，倒数大的原分数反而小，所以823310<5<15<2所以105152178233，4630，5130【第3题】像2，3，5，7这样只能被1和自身整除的大于1的自然数叫做质数或素数。

将2015分拆成100个质数之和，要求其中最大的质数尽可能小，那么这个最大质数是。

考点：质数合数解析：要求最大的质数尽可能小，也就是当这100个数越接近越好。

2015÷=…1002015因此最大的质数再小也要比20大，比20大的最小的质数为23.2015=23×86+11×1+2×13（2015可以表示为86个23、1个11、13个2的和）所以这个最大质数是23.第1页共8页第十三届“走进美妙的数学花园”上海决赛小学五年级----王洪福老师【第4题】质数就好像自然数的“建筑基石”，每一个自然数都能写成若干个质数（可以有相同的）的乘积，比如4=2×2，6=2×3，8=2×2×2，9=3×3，10=2×5等，那么，5×13×31−2写成这种形式为考点：分解质因数解析：5×13×31−2=2015−2=2013=3×11×612013【第5题】“24点游戏”是很多人熟悉的数学游戏，游戏过程如下：任意从52张扑克牌（不包括大小王）中抽取4张，用这4张扑克牌上的数字（A=1，J=11，Q=12，K=13）通过加减乘除四则运算得出24，最先找到算法者获胜。

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。