2013 - 2014 4 2014-2015美国“数学大联盟杯赛”( 中国赛区) 初 赛
2013-2014年度美国“数学大联盟杯赛”(中国赛区)初赛(五、六年级)(初赛时间：2014年2月22日，考试时间60分钟，总分200分)学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定以下的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。
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5分，答对加5分，答错不扣分，共150分，答案请填涂在答题卡上)1.The band’s trombone plays 2013 note s, the trumpet plays 2014 notes,and the tuba plays 218 notes. That’s a total of? notes.A) 6245 B) 6045 C) 4245 D) 6452.The remainder when (999 999 999 + 666 666 + 333 + 1) isdivided by 3 isA) 0 B) 1 C) 2 D) 33.20 − 5 × 2 = 2 ×?A) 5 B) 15 C) 25 D) 304. 4 × 6 × 8 × 10 = 2 × 3 × 4 × 5 ×?A) 2 B) 6 C) 8 D) 165.When I split the cost of a video game equally with 4 friends, we each pay$12.00. How much more do each of us pay if I split the cost equally withonly 3 friends?A) $3.00 B) $4.00 C) $15.00 D) $16.006.At 5:00 P.M. on a Friday, Hal got locked in the vault. He was inthere for 5040 minutes before it opened. On what day did it open?A) Sunday B) MondayC) Tuesday D) Wednesday7.150% of 20 = 200% ofA) 15 B) 25 C) 30 D) 408.Four 2 × 8 rectangles have a total area equal to that of a square of perimeterA) 8 B) 16 C) 32 D) 649.I see a km marker at the end of each km I drive. The markers are numberedconsecutively from 1 through 100. How many markers are more than 30 kmfrom the marker numbered 50?A) 38 B) 39 C) 40 D) 4110.Of 60 people at a school board meeting, 24 are men. The ratio of women tomen at the meeting isA) 3:2 B) 2:3 C) 11:6 D) 6:1111.I rode my bicycle a total of 450 km in 15 hours. At this rate I would travel? km in 30 minutes.12.If the sum of 7 consecutive integers is 63, the sum of the largest and the smallestof the 7 integers isA) 18 B) 24 C) 42 D) 6413.Of the first 100 positive whole numbers, the ratio of the number of multiples of 8to the number of multiples of 4 isA) 2:1 B) 12:25 C) 13:25 D) 1:214.If two consecutive whole numbers have a different number of digits, then theirproduct must be a multiple ofA) 4 B) 11 C) 15 D) 10015.23 × 25 × 27 × 211 =A) 413B) 1626C) 21155D) 16115516.Which of the following figures has an odd number of sides?A) rhombus B) trapezoid C) pentagon D) hexagon17.For how many integers from 55 to 66 is the ones digit greater than the tens digit?A) 4 B) 5 C) 10 D) 1118.Lex buys 6 same-priced books and pays with a $50 bill. The change Lex receivesis twice the price of a book. Each book costsA) $6.25 B) $7.14 C) $8.33 D) $12.5019.In what month is the 222nd day of the year?A) May B) June C) July D) August20.The number of heart balloons that Cora has is divisible by threedifferent primes. What is the least number of heart balloons thatCora can have?A) 6 B) 10 C) 15 D) 3021.10 quarters + 30 dimes = ? nickelssA) 50 B) 60 C) 100 D) 11022.The average of 2014 sixes is equal to the average of 4028 ? .A) threes B) sixesC) nines D) twelves23.What is 0.625% of 8% of 500?A) 0.25 B) 2.5 C) 25 D) 25024.If 5 and 9 are the lengths of two sides of a triangle, ? cannot be the lengthof the 3rd side.A) 3 B) 6 C) 9 D) 1225.When I divide the number of pencils in my backpack by 6, the remainder is 4.If I had twice as many pencils and divided that number of pencils by 6, theremainder would beA) 0 B) 2 C) 4 D) 826.If15of the 200 stripes on Frank’s giant shell are blue,25of the remainingstripes are brown, and the rest are white, there are ? more white stripesthan blue.A) 0 B) 40 C) 42 D) 5627.The sum of the squares of 2 integers each greater than 0 is 172 = 289. Thesum of these 2 integers isA) 23 B) 25 C) 27 D) 2928.Bei’s and Fay’s ages average 12, and Ray’s and Clyde’s ages average 16.If Bei’s, Fay’s, and Ray’s ages average 11, how old is Clyde?A) 28 B) 23 C) 20 D) 1729.95942552-=A) 1.25 B) 591– 590C) 593– 592D) 59430.Each vertex of square S is on a different side of a square of side-length 20.The least possible area of S isA) 100 B) 160 C) 200 D) 250二、填空题(每小题5分，答对加5分，答错不扣分，共50分，答案请填涂在答题卡上)31.The sum of the digits of 2014 is 2 + 0 + 1 + 4 = 7. Let n be a natural number.m = n + 2014. The sum of the digits of m is half the sum of the digits of n.What is the minimum value of n?Answer: ______.32.The sum of 5 different prime numbers is 200. Each of the 5 primenumbers is less than 100. Four of the 5 prime numbers have thesame units digit. What is the median of the 5 prime numbers?Answer: ______.33.把三支飞镖掷向如图所示的镖盘上，然后把三支飞镖的得分相加，镖盘上的数字代表这个区域的得分，未中镖盘记0分。
那么最小的不可能得到的总分是。
34.如图，将1 ~ 6填入到图中的6个括号里，每个数恰好用一次，使得两个耳朵里填的数和为2的倍数，两个眼睛里的数和为3的倍数，鼻子和嘴巴里的数和为5的倍数，则两只眼睛里较小的数是。
2014-2015年度全美数学竞赛
双击图片，修改大小即可放大看2015 AMC美国数学竞赛试题及答案2014年度全美数学竞赛（amc10-B）1、小红现有13个硬币，面值为1分和5分，再给她1个5分的硬币，两种面值的硬币数目将相等，请问小红现有硬币的总面值是多少？评价：题目难度属弱智级。
2、求(2^3+2^3)/[2^(-3)+2^(-3)]的值。
评价：题目难度属于弱智级，简单的计算题。
3、小明驾车的前1/3路程是砂石路，接着是20英里的水泥路，剩下的1/5路程是土路。
问小明行驶的总路程是多少？评价：小学高年级难度奥数题，需要用到分数概念。
4、小丽买了3块发糕和3个香蕉，小军花了2倍钱买了2块发糕和12个香蕉。
问：1块发糕的价格是1个香蕉的几倍？评价：小学高年级难度奥数题。
5、小道做了一扇正方形的窗，这扇窗有8块同样尺寸的玻璃，如图所示。
每块玻璃的高、宽尺寸之比为5：2，玻璃四周的木料宽度为2英寸，请问这扇窗的边长多少？评价：小学高年级难度奥数题。
6、小区去商店买气球，他带了刚好够买30个气球的钱。
到商店后，小区发现气球有促销活动：按正常价格买1个气球的话，第2个气球可享受1/3的优惠。
问：小区最多可买几个气球？评价：来源于生活的题目，但难度仍然是小学难度。
7、假设A>B>0，且A是B的x%，问：x=？（用A和B来表示）评价：终于达到初中代数部分了，但是题目仍比较简单，但是有小陷阱。
8、卡车每t秒内行使b/6英尺，已知1码=3英尺，问卡车3分钟内行驶多少码？评价：初中代数，主要考单位换算吧。
9、对于实数w、z，有（1/w+1/z）/（1/w-1/z）=2014，求（w+z）/（w-z）的值。
评价：初中代数，但题目确实不难。
10、在如下加法算式中，A、B、C、D是互不相等的数字，问D最多可能有几种取值？评价：算式请见附图，数论内容，有一定难度了。
11、对于消费者来说，单一的n%折扣优于以下任何一种优惠：（1）双重15%折扣；（2）三重10%折扣；（3）5%折扣之后再折25%问n的最小整数值是多少？评价：来源于生活的题目，更像经济学题目。
美国“数学大联盟杯赛”(中国赛区)组委会竞赛总结
首先感谢胡锐博士从美国引进了“数学大联盟杯赛”这么好的一个活动，它让中国的学生得以领略美国最为普及、最受欢迎的数学竞赛的原貌，同时也为数英双优的培训开辟了新的模式，尤其是目前在北京及全国都缺少这样一种培养方式。
古希腊伟大的哲学家亚里士多德曾说：“虽然数学没有明显提到善和美，但善和美也不能和数学完全分开，因为美的形式，就是‘秩序、匀称和确定性’，这些正是数学研究的原则。
”让孩子们年少时就开始接触数学，感受数学之美，从而培养他们对数学的兴趣，这在国外被称为“天才少年培养计划”。
虽然国内也很早就开始了这样的尝试，但像引进美国“数学大联盟杯赛”这种形式的活动还尚属首次。
美国“数学大联盟杯赛”至今已连续举办了35年，它不仅是美国及北美地区影响力最大的中小学数学赛事，也是一项具有世界影响力的中小学数学赛事。
杯赛每年举办一次，分为初赛(包括复赛)和决赛两个阶段。
初赛(包括复赛)试题灵活、生动，富有趣味性，同时也贴近生活。
让学生理解数学、欣赏数学，激励学生创新，更能激发学生学习数学的兴趣，培养学生主动探索的精神。
初赛的目的是普及数学。
决赛的试题由美国“数学大联盟杯赛”和斯坦福大学联合命题，具有很高的挑战性，着力培养学生创造性地解决问题和创新思维的能力(fun and creative problems that promote critical-thinking and problem-solving skills)，是数学超常少年展现才华的绝佳平台。
2012年伊始，在各方的努力之下美国“数学大联盟杯赛”得以成功登陆中国，中国赛区初赛于2012年2月25日举行，首次举办即得到广大中小学生的积极响应及踊跃参与，同时也涌现出大批数学能力与英语水平俱佳的优秀学生。
而随着2011-2012年度美国“数学大联盟杯赛”颁奖会的圆满结束，决赛的大幕正式拉起，我们也马不停蹄的投入到决赛和数学夏令营的组织工作中。
2011-2012年度美国“数学大联盟杯赛”中学组的决赛和数学夏令营是由美国“数学大联盟杯赛”和斯坦福大学联合举办，试题新颖、灵活、生动，富有趣味性和挑战性，培养学生创造性地解决问题和创新思维的能力。
2014年美国“数学大联盟杯赛”(中国赛区)初赛五、六年级试卷
37. 将 1 ~ 9 九个数不重不漏地组成一个两位数、一个三位数、一个四位数。 这三个数均能被 9 整除，并且 7、8、9 分别在这三个数中，三个数十位 数字为三个连续的偶数，个位数字为三个连续的奇数。如果将四位数的 千位移到两位数的百位，组成新的三个三位数，新的三位数也均能被 9 整除。那么题中最初的三位数是 。 38. 如图为一个正方体有盖纸盒的示意图，在 1 ~ 30 的数中 选出 7 个，在纸盒的每个面填一个数。将盒盖的两个数 字相加后，三组相对面填的数均满足两两乘积相等。那 么 x 处的数字有 种可能。
姓名(签名)
A) 413 B) 1626 C) 21155 D) 161155 16. Which of the following figures has an odd number of sides? A) rhombus B) trapezoid C) pentagon D) hexagon 17. For how many integers from 55 to 66 is the ones digit greater than the tens digit? A) 4 B) 5 C) 10 D) 11 18. Lex buys 6 same-priced books and pays with a $50 bill. The change Lex receives is twice the price of a book. Each book costs A) $6.25 B) $7.14 C) $8.33 D) $12.50
14. If two consecutive whole numbers have a different number of digits, then their 一、选择题(每小题 5 分，答对加 5 分，答错不扣分，共 150 分，答案请填涂在答题卡上) 1. The band’s trombone plays 2013 notes, the trumpet plays 2014 notes, and the tuba plays 218 notes. That’s a total of ? notes. A) 6245 B) 6045 C) 4245 D) 645 2. The remainder when (999 999 999 + 666 666 + 333 + 1) is divided by 3 is A) 0 B) 1 C) 2 D) 3 3. 20 − 5 × 2 = 2 × ? A) 5 B) 15 C) 25 D) 30 C) 15 D) 100
华中科技大学附属中学： 用十年磨砺实现华丽“转身”
A07校园风采2014年5月2日星期五十年来：办校规模不断壮大华中科技大学附属中学系教育部直属重点大学附中，湖北省示范高中，创建于1954年，伴随着华中科技大学的创立而诞生，五十多年的风雨历程，伴随着大学的发展而进步，铸就了附中坚实的基础。
从一所面积小、师资少、各方面资质一般的传统学校发展成为一所“理念先进、管理科学、队伍优良、条件完善、质量上乘、特色鲜明”的现代化中学。
华科大附中用十年的艰苦磨砺实现了华丽“蜕变”。
2003年的附中，校园占地面积30亩、建筑面积不足一万平方米，无田径场，水泥篮球场三片；武汉市中考报名人数14.7万，高中招生学校152所，在校学生1800名，教职工150多人；仅被授予武汉市体育（排球）传统学校；10年艰辛发展，2013年的附中校园占地120亩、建筑面积37000㎡，八跑道标准塑胶运动场、天然草坪足球场、塑胶篮球场6片、塑胶排球场8片、室内羽毛球场3片、乒乓球台若干。
各类教学用实验室、图书馆、功能室齐全。
目前筹建的师生食堂、学生宿舍、外教公寓约9000多平方米。
校园环境幽雅优美，布局合理，校舍建筑错落有致，气势恢宏。
设施设备前沿先进，功能齐全；武汉市中考报名人数6.7万，高中招生学校101所，在校学生2846名，教职工207人。
十年来：教学实力显著增强除了硬件上的改观，学校也着力提高教育软实力。
2003年，学校任职教师中特级教师2人、区级以上名师2人；重点大学上线率为15%，二本上线率为30%，三本上线率为60%。
十年后，任职教师中特级6人、全国模范（优秀）教师4人，国家、省、市级骨干教师40人，6人次教师参加湖北省高考命题和武汉市中考命题，近五年有10多位青年教师获全国全省教学比武一等奖；重点大学上线率为46%，二本上线率为72%，三本上线率为95%，清华2人。
近年来，学校致力提高教学竞争力，取得的成绩喜人。
2007年获全国首届中小学外语教研示范学校（全国30所，全省唯一）称号，2009年获全国青少年科技教育先进学校（全国50所，全省两所）称号，2009年获湖北省高中课改样本学校称号，2010年评为湖北省省级示范高中，2011年评为湖北省校园文化建设示范校，2013年授牌全国中小学“书香校园”及其他湖北省、武汉市各类荣誉20余项。
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。
2021/3/12
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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
2021/3/12
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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
(参考资料)美国数学大联盟2015年复赛试题
2015-2016 Math League Contests, Grades 9 – 12Second-Round, Jan - Feb 2016Instructions:1.This second-round contest consists of two parts. Part 1 is math questions. Part 2 is essay.2.For all the questions below, login to your account at / , and enter youranswers. Answers written on this document will NOT be credited.3.In Part 1, you are asked to read one math subject, The Mathematics of Normal Distributions, and thesupplementary materials if necessary, Descriptive Statistics. Then you have 28 questions to work on.You will need to give precise, unambiguous answers to Questions 1-19 (The Mathematics of Normal Distributions), and Questions 21-26 (Descriptive Statistics).4.Question 20 (The Mathematics of Normal Distributions) and 27-28 (Descriptive Statistics) areProjects and Papers, which means you need to do your research and write a paper for each question.There is no word limit on each of your papers, but it doesn’t necessary mean the more words thebetter. The best paper is precise and succinct. Please don’t feel frustrated at all if you can’t write apaper, as the topics, Confidence Intervals (Question 20); Lies, Damn Lies, and Statistics (Question27); and Data in Your Daily Life (Question 28), are very hard for a high school student, even for anadult. Please don’t feel frustrated even if you can’t finish all of Questions 1-19, 21-26, as they are not trivial questions and it requires a lot reading and thinking. Students who can work out a few questions should be commended.5.For the subject of Normal Distributions, if you really understand what it is and how it works,then the questions are fairly easy to solve. So our recommendation is don’t rush to solve theproblems. Instead please take your time to read and understand the subject thoroughly. Once you understand how Normal Distributions works, you can solve most of the problems without much difficulty. So this is really a test of your research and analytical skill, your patience, and perseverance.6.In order to understand Normal Distributions, you need to be familiar with basic statistics termssuch as mean, median, standard deviation, percentile, quartile, and etc. It is a good idea to read the subject Descriptive Statistics, the supplementary materials, thoroughly to refresh yourmemory.7.The more questions you answered correctly, the more credit you will get. The total credit, or perfectscore, of Part 1 is 180. The total credit, or perfect score, of Part 2, is 90. The problems are ordered by content, NOT DIFFICULTY. It is to your advantage to attempt problems from throughout the test. 8.You can seek help by reading books, searching the Internet, asking an expert, and etc. But you can’tdelegate this to someone else and turn in whatever he/she wrote for you. To make it clear, the purpose of the second-round contest is to test your ability to read and research. You need to be the one who understand the topics and solve the problems. You will be caught if it is not the case during theinterview.9.For Part 1, you can write in either English or Chinese.10.In Part 2, you are asked to write an essay. You have to write in English in Part 2.11.If you have any questions regarding the contest, please contact us at once atINFO@12.This document contains 16 pages in total, including this page.13.Submission of your answers:a)For all the questions below, login to your account at / , and enter youranswers. Answers written on this document will NOT be credited.b)You need to submit your answers no later than 12:00AM, Feb 7, 2016, Beijing Time. Latersubmission will not be accepted.Part 1 – The Mathematics of Normal DistributionThe following is an excerpt from some math book.The Mathematics of Normal Distributions, (see separate document).Understanding the above Chapter on “Normal Distributions” requires familiarity with basic statistics terms such as mean, median, standard deviation, percentile, quartile, and etc. It helps to read the following Chapter on “Descriptive Statistics”, the supplementary materials, if you need to refresh your memory of these terms.Descriptive Statistics, (the supplementary materials, see separate document).For all the questions below, login to your account at / , and enter your answers. Answers written on this document will NOT be credited.Question 1: (credit: 4)Hint:1Q is the first quartile.3Q is the third quartile. For the definition of 1Q and 3Q , see Section 14.3, of Chapter 14, “Descriptive Statistics.”Question 2: (credit: 4)Estimate the value of the standard deviation (rounded to the nearest inch) of a normal distribution with 81.2μ=inch and 394.7Q =inch.Hint:3Q is the third quartile. For the definition of 3Q , see Section 14.3, of Chapter 14, “Descriptive Statistics.”Question 3: (credit: 4)Note:1Q is the first quartile.3Q is the third quartile. For the definition of 1Q and 3Q , see Section 14.3, of Chapter 14, “Descriptive Statistics.”Note: For this question, please write your answer on file “high-school-answersheet.doc ”, downloadable together with this document at , and submit file “high-school-answersheet.doc ” at after you are done.Question 4: (credit: 4)Question 5: (credit: 4)Question 6: (credit: 4): Question 7: (credit: 4)Question 8: (credit: 4)Question 9: (credit: 4)Questions 10 & 11 refer to the following:Note: For the definition of percentile, see Section 14.3, of Chapter 14, “Descriptive Statistics.”Question 10: (credit: 6)Question 11: (credit: 6)Hint:(c) Rounded to the nearest pound.Question 12: (credit: 6)Hint:(b)Rounded to nearest integer.(c)Enter your answer as a decimal between 0 and 1, rounded to the nearest hundredth. Question 13: (credit: 6)Hint:(b)Rounded to nearest thousandth.(c)Rounded to the nearest hundredth.Question 14: (credit: 4)Questions 15-18:In Questions 15-18, you should use the table above to make your estimates.Note: For the definition of percentile, s ee Section 14.3, of Chapter 14, “Descriptive Statistics.”Question 15: (credit: 4)Question 16: (credit: 4)Consider again the distribution of weights of six-month-old baby boys in Question 15.Question 17: (credit: 6)Question 18: (credit: 8)Question 19: (credit: 4)Question 20: (credit: 20, note: paper with exceptional quality can get up to 40 credits)Note: You can write in either Engish or Chinese.Note: For this question, please write your answer on file “high-school-answersheet.doc”, downloadable together with this document at , and submit file “high-school-answersheet.doc” at after you are done.Question 21: (credit: 4)Question 22: (credit: 4)The two histograms below summarize the team payrolls in Major League Baseball (2008).Using the information in the figure, where did the median payroll of 2008 baseball teams fall?(a)Somewhere between $50 million and $80 million(b)Somewhere between $70 million and $80 million(c)Somewhere between $70 million and $100 million(d)Somewhere between $80 million and $100 millionQuestion 23: (credit: 6)This question refers to histograms with unequal class intervals.Question 24: (credit: 8)Note: For (c) and (d), please write your answer on file “high-school-answersheet.doc ”, downloadable together with this document at , and submit file “high-school-answersheet.doc ” at after you are done.Question 25: (credit: 4)Let A denote the mean of data set 12{,,...,}N x x x . Let B denote the mean of dataset 12{,,...,}N x c x c x c +++.(a) Find the relationship between A and B .a) A B <b) A B c =-c) A B c =+d) Nondeterministic(b) Find the mean of 12{,,...,}N x A x A x A ---.Question 26: (credit: 4)Let 1R and 1σdenote the range and standard deviation of data set 12{,,...,}N x x x , respectively. Let 2R and 2σdenote the range and standard deviation of data set 12{,,...,}N x c x c x c +++, respectively. (a) Find the relationship between 1R and 2R .a) Nondeterministicb) 1R = 2Rc) 1R = 2R + cd) 1R = 2R - c(b) Find the relationship between 1σand 2σ.a) Nondeterministicb) 1σ = 2σc) 1σ = 2σ+ cd) 1σ = 2σ- cQuestion 27: (credit: 20, note: paper with exceptional quality can get up to 40 credits)Note: You can write in either Engish or Chinese.Note: For this question, please write your answer on fi le “high -school-answersheet .doc”, downloadable together with this document at , and submit file“high-school-answersheet.doc” at after you are done.Question 28: (credit: 20, note: paper with exceptional quality can get up to 40 credits)Note: You can write in either Engish or Chinese.Note: For this question, please write your answer on fi le “high-school-answersheet.do c”, downloadable together with this document at , and submit file “high-school-answersheet.doc” at after you are done.Part 2 Essay (Credit: 90)Pros and Cons of Math Competitionsby Richard RusczykMathematics competitions such as MATH LEAGUE, MATHCOUNTS, and the American Mathematics Competitions are probably the extracurricular math programs with the widest participation. The most immediate value of these math contests is obvious –they pique students’ interest in mathematics and encourage them to value intellectual pursuits. Kids love games, and many will turn just about any activity into a contest, or in other words, something to get good at. Math contests thus inspire them to become good at mathematics just like sports encourage physical fitness. Eventually, students put aside the games. By then, hopefully an interest in the underlying activity has developed.Beyond encouraging an interest in mathematics, contests help prepare students for competition. For better or worse, much of life is competition, be it for jobs or resources or whatever. Competition of any sort trains students to deal with success and failure, and teaches them that effective performance requires practice. Moreover, nearly every interesting and worthwhile venture in life comes with some element of pressure; competition teaches students how to handle it.Despite all the benefits of math contests, they are not an unmitigated good. First of all, not all contests are designed well. Students shouldn’t take too seriously contests that greatly emphasize speed or memorization. Curricular contests (particularly calculus contests for high school students) can also be misleading, as they deepen the misconception that there is no more to math than what is in the classroom. Such contests run the risk of encouraging students to overvalue skills that aren’t nearly as valuable as the one asset a contest should help them develop – the ability to think about and solve complex problems.A second danger of contests is extending kids beyond their ability. Students should certainly be challenged with problems they can’t do from time to time, but if this happens consistently, the experien ce goes from humbling and challenging to humiliating and discouraging.A third potential pitfall, burnout, often comes on the heels of the first two. Participants in math contests are just as much at risk of burnout as musicians or athletes. Parents, teachers, and the students themselves should be on the lookout for signs of decreased interest, and they must be willing to back off and allow the student to rediscover an interest in mathematics on his or her own. Burnout is particularly pernicious because th e end result often isn’t a backlash against competition, but against math in general. Indeed, even students not involved in contests have to watch out for burnout, though the pressure of contests tends to encourage burnout more quickly than the classroom.These possible perils are usually more than offset not only by the values we’ve already mentioned, but also by the greatest asset of math contests - cooperation. These competitions bring together students of like interests and abilities, allowing them to form their own community in which they will find friendship, inspiration, and encouragement to a far greater degree than most of these students can find in the typical classroom. Whereas a student may be one of only three or four in her school who pursues math the way others play basketball, she will not find herself so lonely at a math contest, where she’ll find many kindred spirits.In summary, math contests are a tremendous social and intellectual opportunity for students, but exposingstudents to contests must be done wisely, else they become counterproductive to the goal of encouraging a lifelong interest in mathematics and other intellectual pursuits.Direction (Note: For this question, please write your answer on fi le “high-school-answersheet.doc”, downloadable together with this document at , and submit file“high-school-answersheet.doc” at after you are done.):In his article “Pros and Cons of Math Competitions”, Richard Rusczyk lists and explains the advantages and the disadvantages of math competitions. Are math contests beneficial or harmful to students? Everything always has two sides: the good and the bad. This proverb probably also applies to math competitions. Write a response in which you discuss whether students should be encouraged to participate in math competitions. You may draw examples from your reading, studies, experience, observations, and etc.Hint: Here are some questions to think about. You do not have to answer them, but they will help you to craft your response.1. What is the purpose of math contests?2. What are the good and the bad sides of math contests?3. How should you value your scores on math contests?4. What are the most important qualities that a successful mathematician should have?5. To a student who is highly interested in mathematics, what are much more important than math contests?。
2014年美国“数学大联盟杯赛”(中国赛区)初赛七年级(初一)详解
(七年级) 一、 选择题 1. B. No even number can be written as the product of two odd integers. Since 11 is the product of 1 and 11, Skip may have run 11 kilometers. A) 10 B) 11 C) 12 D) 14
27. D. As shown, only choice D is not a product of a divisor of 24 and a divisor of 35.
A) 1 × 1 B) 6 × 7 C) 8 × 7 D) 6 × 11 28. B. The sum of the dimensions is 40 ÷2 = 20. Its dimensions are 16 × 4, and its area is 64. A) 100 B) 64 C) 40 D) 24 29. A. Her average score for 6 tests was 82. So her total was 6 × 82 = 492. Adding 2 × 98, her total for 8 tests was 688. Her average score was 86. A) 86 B) 88 C) 90 D) 94 30. D. From 1 to 99 there are 9; in every 100 #s after there are 19. Include 1000. A) 162 B) 171 C) 180 D) 181 二、填空题 31. 8. 32. 2257. 33. 21. 34. 37. 35. 120. 36. 7410. 37. 2. 38. 81. 39. 32451. 40. 671.
2014-2015美国大联盟五年级
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。
2014年美国“数学大联盟杯赛”(中国赛区)初赛三、四年级详解
2013-2014年度美国“数学大联盟杯赛”(中国赛区)初赛答案(三、四年级)一、选择题1. A.Since 0 is a factor, 2 × 0 × 1 × 4 = 0.A) 0B) 7C) 8D) 20142. B.If 2 years ago I was 3 years old, I am now 3 + 2 = 5.A) 4B) 5C) 6D) 233. D.8 + (60 ÷ 4) = 8 + (15) = 23.A) 15B) 17C) 22D) 234. B.(1 + 7) + (2 + 6) + (3 + 5) = 3 × 8 = 24 = 4 + 20.A) 4B) 20C) 24D) 285. C.The prime numbers less than 10 are 2, 3, 5, and 7.A) 2B) 3C) 4D) 56. B.Caleb the dog dreams he has 12 dozen bones. Since 12 dozen = 12 × 12 = 144, there are 144 ÷ 2 = 72 pairs. Caleb will have to dig 72 holes.A) 24B) 72C) 144D) 2887. C.From 9:45 PM to 10:45 PM is 60 mins. From 10:45 PM to 11 PM is 15 mins. From 11 PM to 11:10 PM is 10 mins. That’s (60 + 15 + 10) mins.A) 65B) 75C) 85D) 958. D.From January 1st to January 31st, there are 16 odd-numbered dates. From February 1st to February 21st, there are 11 odd-numbered dates. That’s 27 × $2 = $54.A) $48B) $50C) $52D) $549. C.9 × 9 + 9 × 8 + 9 × 7 + 9 × 6 = 9 × (9 + 8 + 7 + 6).A) 20B) 24C) 30D) 3610.D.Manny weighs three times as much as Murray. Manny also weighs 8000 kg more than Murray, so 8000 kg is twice Murray’s weight. Thus Murray weighs 4000 kg and Manny weighs 12 000 kg.D) 12 00011.B.I have twice as many shirts as hats, and four times as many hats as scarves. If I have 24 shirts, I have 24÷ 2 = 12 hats and 12 ÷ 4 = 3 scarves.A) 2B) 3C) 6D) 1212.C.My coins have a total value of $6.20. If I have 1 of each coin, I have (1 + 5 + 10 + 25)¢ = 41¢. Subtract 41¢ from $6.20 repeatedly until there is 5¢ left. After 15 subtractions, there is 5¢ left. I have 15 + 5 or20 pennies.A) 10B) 15C) 20D) 2513.D.The diagrams demonstrate choices A, B, and C.A) 14 kmB) 10 kmC) 8 kmD) 1 km14.C.(2014 −1014) + (3014 − 2014) = 1000 + 1000 = 2000.A) 0B) 1000C) 2000D) 201415.A.10 + (9 ×8) − (7 × 6) = 10 + 72 − 42 = 40.A) 40B) 110The prime factorization of 72 is 2 × 2 × 2 × 3 × 3. The largest prime is 3.A) 3B) 7C) 36D) 7217.D.6 × 4 = 24 = 96 ÷ 4.A) 6B) 12C) 24D) 9618.C.If 6 cans contain 96 teaspoons of sugar, 1 can contains 96 ÷ 6 = 16 teaspoons of sugar. Thus 15 cans contain 16 × 15 = 240 teaspoons of sugar.A) 192B) 208C) 240D) 28819.C.The largest possible such sum is 98 + 99 = 197.A) 21B) 99C) 197D) 19820.B.Ann sent Wilson hearts with odd numbers with odd tens digits. The number on each heart he received must be two digits with both digits odd. There are 5 possible tens digits and 5 possible ones digits.That’s a total of 5 × 5 = 25 hearts.A) 23B) 25C) 30D) 4521.B.Since Rich ate his favorite sandwich 8 days ago, today is the 9th day of the month. Since the shortest month has 28 days, it is at least 28 − 9 = 19 days until the last day of the month. He must wait 1 more day.A) 1922.D.The factors of 49 are 1, 7, and 49. Since 49 has 3 factors, it has a prime number of factors.A) 6B) 12C) 36D) 4923.D.Dividing a certain two-digit number by 10 leaves a remainder of 9, so it is 19, 29, 39, 49, 59, 69, 79, 89, or 99. The only number listed with remainder 8 when divided by 9 is 89, so the number is 89 and 8 + 9 = 17.A) 7B) 9C) 13D) 1724.A.The whole numbers less than 1000 that can be written as such a product are 0 × 1 × 2, 1 × 2 × 3, 2 × 3 ×4, 3 × 4 × 5, 4 × 5 × 6, 5 × 6 × 7, 6 × 7 × 8, 7 × 8 × 9, 8 × 9 × 10, and 9 × 10 ×11. In all, that’s 10.A) 10B) 11C) 15D) 2125.B.The only such numbers are 5432, 5431, 5430, 5421, 5420, 5410, 5321, 5320, 5310, and 5210. In all, there are 10 such numbers.A) 3B) 10C) 69D) 12026.C.2014 × 400 = 805 600; the hundreds digit is 6.A) 0B) 5C) 6D) 827.B.Greta was 110 cm tall 2 years ago, when she was 10 cm taller than her brother. Her brother was 100 cmB) 130C) 140D) 15028.B.The number 789 678 567 456 is added to the number 987 876 765 654. Since we carry a 1 when adding the left-most digits, the sum has 12 + 1 digits.A) 12B) 13C) 24D) 2529.D.We must find which number among the choices is two more than a multiple of 5. Divide each choice by5 (or recogniz e that any number that ends in “2”or “7” is 2 more than a multiple of 5).A) 4351B) 5215C) 5616D) 646230.C.Of every 11 people, there are 2 adults and 9 children. Since 99 ÷ 11 = 9, there are 9 groups of 11 people.Of these, 9 × 2 = 18 are adults.A) 9B) 11C) 18D) 22二、填空题31.5.32.22.33.4.34.1.35.617.36.21.37.499.38.765.39.69.40.10.。
数学思维(高中)：2015-2016年度美国“数学大联盟”思维探索十至十二年级试卷(含参考答案)
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。