美国数学大联盟杯赛五年级试卷精编版
- 1 -
2015-2016年度美国“数学大联盟杯赛”(中国赛区)初赛
(五年级)
(初赛时间：2015年11月14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
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. A 6 by 6 square has the same area as a 4 by ? rectangle.
A) 3 B) 6 C) 8 D) 9 2. Every prime has exactly ? positive divisors.
A) 1
B) 2
C) 3
D) 4 or more
3. If I answered 34 out of 40 questions on my math test correctly, I answered ? % of the questions correctly.
A) 75
B) 80 C) 85 D) 90
4. 120 ÷ 3 ÷ 4 × 12 =
A) 1 B) 10 C) 12 D) 120 5. 10 × 20 × 30 × 40 = 24 × ?
A) 1000
B) 10 000
C) 100 000
D) 1000 000
6. One of my boxes contains 1 pencil and the others each contain 5 pencils. If there are 101 pencils in my boxes, how many boxes do I have?
A) 19
B) 20
C) 21
D) 22
7. An electrical company imports 2016 light bulbs. Unfortunately, 25% of those are damaged. How many light bulbs are not damaged?
A) 25
B) 504 C) 1512 D) 2016 8. 50 × (16 + 24
) is the square of
A) -40 B) -4 C) 4 D) 80 9. Which of the following numbers has exactly 3 positive divisors?
A) 49
B) 56
C) 69
D) 100
10. Ten people stand in a line. Counting from the left, Jerry stands at the 5th position. Counting from the right, which position is he at?
A) 4 B) 5
C) 6
D) 7
11. On a teamwork project, Jack contributed 2/7 of the total amount of work, Jill contributed 1/4 of the work, Pat contributed 1/5 of the work, and Matt contributed the rest. Who contributed the most toward this project?
A) Jack B) Jill C) Pat D) Matt 12. Which of the following numbers is a factor of 2016? A) 5 B) 11 C) 48 D) 99 13. 2 × 4 × 8 × 16 × 32 × 64 =
A) 210
B) 215
C) 221
D) 2120
14. On a game show, Al won four times as much as Bob, and Bob won four times as much as Cy. If Al won $1536, how much did Al, Bob, and Cy win together?
A) $96 B) $384 C) $1920 D) $2016 15. The sum of two composites cannot be
A) odd B) even C) 11 D) 17
16. If a and b are positive integers such that a /b = 5/7, then a + b is
A) 12 B) 24 C) 36 D) not able to be determined 17. What is the greatest odd factor of the number of hours in all the days of the year 2015? A) 3
B) 365 C) 1095 D) 3285 18. If the current month is February, what month will it be 1 199 999 months from now?
A) January
B) February
C) March
D) April
19. Two angles are complementary. One of these angles is 36° less than the other. What is the measure of the larger angle?
A) 36° B) 54° C) 63° D) 72° 20. (The square root of 16) + (the cube root of 64) + (the 4th root of 256) = A) 12 B) 24 C) 32 D) 64 21. In ?ABC , m ∠A – m ∠B = m ∠B – m ∠C . What is the degree measure of ∠B ?
A) 30
B) 60
C) 90
D) 120
22. For every 3 math books I bought, I bought 2 biology books. I bought 55 books in all. How many of those are math books?
A) 11
B) 22
C) 33
D) 44
23. John wrote a number whose digits consists entirely of 1s. This number was a composite number. His number could contain exactly ? 1s.
A) 17
B) 19
C) 29
D) 32
24. Weird Town uses three types of currencies: Cons, Flegs, and Sels. If 3 Sels = 9 Cons and 2 Cons = 4 Flegs, then 5 Sels = ? Flegs.
A) 12
B) 24
C) 30
D) 36
第1页，共4页
- 2 -
25. If the length of a rectangular prism with volume V is doubled while the width and the height are halved, the volume of the new prism will be
A) 4V
B) V /2
C) V
D) 2V
26. Rick and Roy each stands at different ends of a straight road that is 64 m long. They run toward each other. Rick ’s speed is 3 m/s and Roy ’s speed is 5 m/s. They will meet in ? seconds.
A) 1
B) 2
C) 4
D) 8
27. If the area of a certain circle is 2016, its radius is
A) sqrt(2016/π) B) sqrt(4032/π) C) 2016/π
D) 1008/π
28. In a toy shop, the cost of a Teddy Bear is 200% as much as that of a toy train. The cost of a toy train is 6/5 the cost of a pack of the wooden blocks. The cost of a pack of wooden blocks is $50. What is the cost, in dollars, of the Teddy Bear?
A) 60
B) 100
C) 120
D) 200
29. In the sequence 2016, 225, 141, 66, 432, 99, 1458 …, each term after the first term is the sum of the cubes of the digits of the previous term. What is the 100th term of this sequence?
A) 153 B) 351 C) 370 D) 371 30. What is the sum of all the positive divisors of 210?
A) 210 – 1
B) 211 – 1
C) 212 – 1
D) 213 – 1
31. It takes 4 hours for Mike and Lucy to finish a task. It takes Lucy and Jerry 5 hours to
finish the same task. And it takes 6 hours for Mike and Jerry to finish the same task. Lucy and Jerry first work on the task for 1 hour and 45 minutes. Then Mike takes over the task on his own. How many more hours does it take for Mike to finish the task?
A) 3
B) 4
C) 5
D) 6
32. If you sell a cloth at its current price, you get $40 profit. The total profit you get selling 10 clothes at 70% of its current price is equal to the total profit you get selling 20 clothes at $82 per cloth. What is the current price of a cloth?
A) 80
B) 100
C) 120
D) 125
33. There are 6 identical squares in the figure on the right. The side length of each square is 1. Of all the triangles constructed by connecting three of the 18 vertices in the figure, how many of them are triangles whose area is 2 and which has at least one vertical or horizontal side?
A) 12
B) 16
C) 24
D) 28
34. Pick up N numbers from 1 to 2015 inclusively, such that the sum of any three of the N numbers is divisible by 24. What is the maximum value of N ?
A) 83
B) 84
C) 168
D) 252
35. 汤姆有一件花了64美金买来的衬衫，他打算以比原价高出25%的价格出售，他会卖出多少钱？
A) $16
B) $32
C) $48
D) $80
36. 满足以下条件的最小整数是多少：“除以3余2，除以5余4，除以7余6。” A) 59 B) 61 C) 104 D) 106 37. 飞人以每小时360千米的速度飞行，这相当于每秒多少米？
A) 10 B) 36 C) 64 D) 100
38. 设A 为一个可整除11但不可整除10的正整数，若B 为一个颠倒A 数位的整数，那么B 必须被几整除？
A) 11 B) 22
C) 33
D) A, B, C 都不选
39. 珍妮花50美金买了一条围巾。她一开始准备以60美金卖出，然后把价格增加25%，再把新的价格减少20%并且出售。在这笔交易之中，她 ? 。
A) 赚了7美金 B) 赚了10美金 C) 亏了7美金
D) 亏了10美金
40. A , B
两个袋子里分别有若干个球，A 袋球和B 袋球的数量比是4:1。从A 袋中取出若干个球放入B 袋后，A 袋球和B 袋球的数量之比变为8:3；再从B 袋中取出若干个球放入A 袋后，A 袋球和B 袋球的数量之比变为9:2。两个袋子里最少一共有几只球？ A) 11 B) 44
C) 55
D) 110
第3页，共4页
第4页，共4页
2010年美国大学生数学建模竞赛B题一等奖
Summary Faced with serial crimes,we usually estimate the possible location of next crime by narrowing search area.We build three models to determine the geographical profile of a suspected serial criminal based on the locations of the existing crimes.Model One assumes that the crime site only depends on the average distance between the anchor point and the crime site.To ground this model in reality,we incorporate the geographic features G,the decay function D and a normalization factor N.Then we can get the geographical profile by calculating the probability density.Model Two is Based on the assumption that the choice of crime site depends on ten factors which is specifically described in Table5in this paper.By using analytic hierarchy process (AHP)to generate the geographical profile.Take into account these two geographical profiles and the two most likely future crime sites.By using mathematical dynamic programming method,we further estimate the possible location of next crime to narrow the search area.To demonstrate how our model works,we apply it to Peter's case and make a prediction about some uncertainties which will affect the sensitivity of the program.Both Model One and Model Two have their own strengths and weaknesses.The former is quite rigorous while it lacks considerations of practical factors.The latter takes these into account while it is too subjective in application. Combined these two models with further analysis and actual conditions,our last method has both good precision and operability.We show that this strategy is not optimal but can be improved by finding out more links between Model One and Model Two to get a more comprehensive result with smaller deviation. Key words:geographic profiling,the probability density,anchor point, expected utility
如何准备美国大学生数学建模比赛
如何准备美赛 数学模型：数学模型的功能大致有三种：评价、优化、预测。几乎所有模型都是围绕这三种功能来做的。比如，2012年美赛A题树叶分类属于评价模型，B题漂流露营安排则属于优化模型。 对于不同功能的模型有不同的方法，例如 评价模型方法有层次分析、模糊综合评价、熵值法等； 优化模型方法有启发式算法（模拟退火、遗传算法等）、仿真方法（蒙特卡洛、元胞自动机等）； 预测模型方法有灰色预测、神经网络、马尔科夫链等。 在数学中国、数学建模网站上有许多关于这些方法的相关介绍与文献。 软件与书籍： 软件一般三款足够：Matlab、SPSS、Lingo，学好一个即可。 书籍方面，推荐三本，一本入门，一本进级，一本参考，这三本足够： 《数学模型》姜启源谢金星叶俊高等教育出版社 《数学建模方法与分析》Mark M. Meerschaert 机械工业出版社 《数学建模算法与程序》司守奎国防工业出版社 入门的《数学模型》看一遍即可，对数学模型有一个初步的认识与把握，国赛前看完这本再练习几篇文章就差不多了。另外，关于入门，韩中庚的《数学建模方法及其应用》也是不错的，两本书选一本阅读即可。如果参加美赛的话，进级的《数学建模方法与分析》要仔细研究，这本书写的非常好，可以算是所有数模书籍中最好的了，没有之一，建议大家去买一本。这本书中开篇指出的最优化模型五步方法非常不错，后面的方法介绍的动态模型与概率模型也非常到位。参考书目《数学建模算法与程序》详细的介绍了多种建模方法，适合用来理解模型思想，参考自学。 分工合作：数模团队三个人，一般是分别负责建模、编程、写作。当然编程的可以建模，建模的也可以写作。这个要视具体情况来定，但这三样必须要有人擅长，这样才能保证团队最大发挥出潜能。 这三个人中负责建模的人是核心，要起主导作用，因为建模的人决定了整篇论文的思路与结构，尤其是模型的选择直接关系到了论文的结果与质量。 对于建模的人，首先要去大量的阅读文献，要见识尽可能多的模型，这样拿到一道题就能迅速反应到是哪一方面的模型，确定题目的整体思路。 其次是接口的制作，这是体现建模人水平的地方。所谓接口的制作就是把死的方法应用到具体问题上的过程，即用怎样的表达完成程序设计来实现模型。比如说遗传算法的方法步骤大家都知道，但是应用到具体问题上，编码、交换、变异等等怎么去做就是接口的制作。往往对于一道题目大家都能想到某种方法，可就是做不出来，这其实是因为接口不对导致的。做接口的技巧只能从不断地实践中习得，所以说建模的人任重道远。 另外，在平时训练时，团队讨论可以激烈一些，甚至可以吵架，但比赛时，一定要保持心平气和，不必激烈争论，大家各让3分，用最平和的方法讨论问题，往往能取得效果并且不耽误时间。经常有队伍在比赛期间发生不愉快，导致最后的失败，这是不应该发生的，毕竟大家为了一个共同的目标而奋斗，这种经历是很难得的。所以一定要协调好队员们之间的关系，这样才能保证正常发挥，顺利进行比赛。 美赛特点：一般人都认为美赛比国赛要难，这种难在思维上，美赛题目往往很新颖，一时间想不出用什么模型来解。这些题目发散性很强，需要查找大量文献来确定题目的真正意图，美赛更为注重思想，对结果的要求却不是很严格，如果你能做出一个很优秀的模型，也许结果并不理想也可能获得高奖。另外，美赛还难在它的实现，很多东西想到了，但实现起来非常困难，这需要较高的编程水平。 除了以上的差异，在实践过程中，美赛和国赛最大的区别有两点： 第一点区别当然是美赛要用英文写作，而且要阅读很多英文文献。对于文献阅读，可以安装有道词典，
2018年美国“数学大联盟杯赛”(中国赛区)初赛三年级试卷及答案
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。 请在装订线内签名表示你同意遵守以上规定。 考前注意事项： 1. 本试卷是三年级试卷，请确保和你的参赛年级一致； 2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全； 3. 请确保你已经拿到以下材料： 本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、草稿纸。考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、及如何参加复赛的说明。其他材料均不能带走，请留在原地。 选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。 1. 5 + 6 + 7 + 1825 + 175 = A) 2015 B) 2016 C) 2017 D) 2018 2.The sum of 2018 and ? is an even number. A) 222 B) 223 C) 225 D) 227 3.John and Jill have $92 in total. John has three times as much money as Jill. How much money does John have? A) $60 B) $63 C) $66 D) $69 4.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) N 5.An 8 by 25 rectangle has the same area as a rectangle with dimensions A) 4 by 50 B) 6 by 25 C) 10 by 22 D) 12 by 15 6.What is the positive difference between the sum of the first 100 positive integers and the sum of the next 50 positive integers? A) 1000 B) 1225 C) 2025 D) 5050 7.You have a ten-foot pole that needs to be cut into ten equal pieces. If it takes ten seconds to make each cut, how many seconds will the job take? A) 110 B) 100 C) 95 D) 90 8.Amy rounded 2018 to the nearest tens. Ben rounded 2018 to the nearest hundreds. The sum of their two numbers is A) 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) 10,20 10.For every 2 pencils Dan bought, he also bought 5 pens. If he bought 10 pencils, how many pens did he buy? A) 25 B) 50 C) 10 D) 13 11.Twenty days after Thursday is A) Monday B) Tuesday C) Wednesday D) Thursday 12.Of the following, ? angle has the least degree-measure. A) an obtuse B) an acute C) a right D) a straight 13.Every student in my class shouted out a whole number in turn. The number the first student 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) 104 14.A boy bought a baseball and a bat, paying $1.25 for both items. If the ball cost 25 cents more than the bat, how much did the ball cost? A) $1.00 B) $0.75 C) $0.55 D) $0.50 15.2 hours + ? minutes + 40 seconds = 7600 seconds A) 5 B) 6 C) 10 D) 30 16.In the figure on the right, please put digits 1-7 in the seven circles so that the three digits in every straight line add up to 12. What is the digit in the middle circle? A) 3 B) 4 C) 5 D) 6 17.If 5 adults ate 20 apples each and 3 children ate 12 apples in total, what is the average number of apples that each person ate? A) 12 B) 14 C) 15 D) 16 18.What is the perimeter of the figure on the right? Note: All interior angles in the figure are right angles or 270°. A) 100 B) 110 C) 120 D) 160 19.Thirty people are waiting in line to buy pizza. There are 10 people in front of Andy. Susan is the last person in the line. How many people are between Andy and Susan? A) 18 B) 19 C) 20 D) 21
2018年美国“数学大联盟杯赛”(中国赛区)初赛五年级试卷(1)
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。 请在装订线内签名表示你同意遵守以上规定。 考前注意事项： 1. 本试卷是五年级试卷，请确保和你的参赛年级一致； 2. 本试卷共4页(正反面都有试题)，请检查是否有空白页，页数是否齐全； 3. 请确保你已经拿到以下材料： 本试卷(共4页，正反面都有试题)、答题卡、答题卡使用说明、英文词汇手册、 草稿纸。考试完毕，请务必将英文词汇手册带回家，上面有如何查询初赛成绩、 及如何参加复赛的说明。其他材料均不能带走，请留在原地。 选择题：每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答题卡上。 1. The smallest possible sum of two different prime numbers is A) 3 B) 4 C) 5 D) 6 2. The greatest common factor of two numbers is 3. The product of these two numbers must be divisible by A) 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) 4 B) 3 C) 2 D) 1 5. I have read exactly 1 3 of 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 be A) 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) 2016 B) 2017 C) 2018 D) 2019 8. 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 9. The least common multiple of 8 and 12 is the greatest common factor of 120 and A) 80 B) 124 C) 144 D) 180 10. January has the greatest possible number of Saturdays when January 1 occurs on any of the following days of the week except A) Thursday B) Friday C) Saturday D) Sunday 11. The number that is 10% of 1000 is 10 more than 10% of A) 90 B) 100 C) 900 D) 990 12. 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) 111 111 B) 222 222 C) 444 444 D) 888 888 14. Abe drove for 2 hours at 30 km/hr. and for 3 hours at 50 km/hr. What was Abe’s average speed 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) 20183 D) (2018 + 2017)2 17. 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) 2 B) 3 C) 4 D) 5 18. Of the following, which could be the perimeter of a rectangle whose side-lengths, in cm, are prime numbers? A) 10 cm B) 22 cm C) 34 cm D) 58 cm 19. The average of all possible total values of a 4-coin stack of nickels and dimes (containing at least one of each coin) is A) 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 cm B) 80π cm C) 60π cm D) 40π cm 21. Of the following, which expression has the greatest number of factors that are multiples of 2018? A) 2018 × 12 B) 20182 C) 20192 D) 20192019 第1页，共4页 第2页，共4页
美国大学生数学建模竞赛优秀论文翻译
优化和评价的收费亭的数量 景区简介 由於公路出来的第一千九百三十，至今发展十分迅速在全世界逐渐成为骨架的运输系统，以其高速度，承载能力大，运输成本低，具有吸引力的旅游方便，减少交通堵塞。以下的快速传播的公路，相应的管理收费站设置支付和公路条件的改善公路和收费广场。 然而，随着越来越多的人口密度和产业基地，公路如花园州公园大道的经验严重交通挤塞收费广场在高峰时间。事实上，这是共同经历长时间的延误甚至在非赶这两小时收费广场。 在进入收费广场的车流量，球迷的较大的收费亭的数量，而当离开收费广场，川流不息的车辆需挤缩到的车道数的数量相等的车道收费广场前。因此，当交通繁忙时，拥堵现象发生在从收费广场。当交通非常拥挤，阻塞也会在进入收费广场因为所需要的时间为每个车辆付通行费。 因此，这是可取的，以尽量减少车辆烦恼限制数额收费广场引起的交通混乱。良好的设计，这些系统可以产生重大影响的有效利用的基础设施，并有助于提高居民的生活水平。通常，一个更大的收费亭的数量提供的数量比进入收费广场的道路。 事实上，高速公路收费广场和停车场出入口广场构成了一个独特的类型的运输系统，需要具体分析时，试图了解他们的工作和他们之间的互动与其他巷道组成部分。一方面，这些设施是一个最有效的手段收集用户收费或者停车服务或对道路，桥梁，隧道。另一方面，收费广场产生不利影响的吞吐量或设施的服务能力。收费广场的不利影响是特别明显时，通常是重交通。 其目标模式是保证收费广场可以处理交通流没有任何问题。车辆安全通行费广场也是一个重要的问题，如无障碍的收费广场。封锁交通流应尽量避免。 模型的目标是确定最优的收费亭的数量的基础上进行合理的优化准则。 主要原因是拥挤的
1985~美国大学生数学建模竞赛题目集锦
1985~2015年美国大学生数学建模竞赛题目集锦 目录 1985 MCM A: Animal Populations (3) 1985 MCM B: Strategic Reserve Management (3) 1986 MCM A: Hydrographic Data (4) 1986 MCM B: Emergency-Facilities Location (4) 1987 MCM A: The Salt Storage Problem (5) 1987 MCM B: Parking Lot Design (5) 1988 MCM A: The Drug Runner Problem (5) 1988 MCM B: Packing Railroad Flatcars (6) 1989 MCM A: The Midge Classification Problem (6) 1989 MCM B: Aircraft Queueing (6) 1990 MCM A: The Brain-Drug Problem (6) 1990 MCM B: Snowplow Routing (7) 1991 MCM A: Water Tank Flow (8) 1991 MCM B: The Steiner Tree Problem (8) 1992 MCM A: Air-Traffic-Control Radar Power (8) 1992 MCM B: Emergency Power Restoration (9) 1993 MCM A: Optimal Composting (10) 1993 MCM B: Coal-Tipple Operations (11) 1994 MCM A: Concrete Slab Floors (11) 1994 MCM B: Network Design (12) 1995 MCM A: Helix Construction (13) 1995 MCM B: Faculty Compensation (13) 1996 MCM A: Submarine Tracking (13) 1996 MCM B: Paper Judging (13) 1997 MCM A: The Velociraptor Problem (14) 1997 MCM B: Mix Well for Fruitful Discussions (15) 1998 MCM A: MRI Scanners (16) 1998 MCM B: Grade Inflation (17) 1999 MCM A: Deep Impact (17) 1999 MCM B: Unlawful Assembly (18) 2000 MCM A: Air Traffic Control (18) 2000 MCM B: Radio Channel Assignments (19) 2001 MCM A: Choosing a Bicycle Wheel (20) 2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...). (21) 2002 MCM A: Wind and Waterspray (23) 2002 MCM B: Airline Overbooking (23) 2003 MCM A: The Stunt Person (24) 2003 MCM B: Gamma Knife Treatment Planning (24) 2004 MCM A: Are Fingerprints Unique? (25) 2004 MCM B: A Faster QuickPass System (25)
美国数学大联盟杯赛五年级试卷
2015-2016年度美国“数学大联盟杯赛”(中国赛区)初赛 (五年级) (初赛时间：2015年11月14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 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. A 6 by 6 square has the same area as a 4 by ? rectangle. A) 3 B) 6 C) 8 D) 9 2.Every prime has exactly ? positive divisors. A) 1 B) 2 C) 3 D) 4 or more 3.If I answered 34 out of 40 questions on my math test correctly, I answered ? % of the questions correctly. A) 75 B) 80 C) 85 D) 90 4.120 ÷ 3 ÷ 4 × 12 = A) 1 B) 10 C) 12 D) 120 5.10 × 20 × 30 × 40 = 24 ×? A) 1000 B) 10 000 C) 100 000 D) 1000 000 6.One of my boxes contains 1 pencil and the others each contain 5 pencils. If there are 101 pencils in my boxes, how many boxes do I have? A) 19 B) 20 C) 21 D) 22 7.An electrical company imports 2016 light bulbs. Unfortunately, 25% of those are damaged. How many light bulbs are not damaged? A) 25 B) 504 C) 1512 D) 2016 8.50 × (16 + 24) is the square of A) -40 B) -4 C) 4 D) 80 9.Which of the following numbers has exactly 3 positive divisors? A) 49 B) 56 C) 69 D) 100 10.Ten people stand in a line. Counting from the left, Jerry stands at the 5th position. Counting from the right, which position is he at? A) 4 B) 5 C) 6 D) 7 11.On a teamwork project, Jack contributed 2/7 of the total amount of work, Jill contributed 1/4 of the work, Pat contributed 1/5 of the work, and Matt contributed the rest. Who contributed the most toward this project? A) Jack B) Jill C) Pat D) Matt 12.Which of the following numbers is a factor of 2016? A) 5 B) 11 C) 48 D) 99 13.2 × 4 × 8 × 16 × 32 × 64 = A) 210B) 215C) 221D) 2120 14.On a game show, Al won four times as much as Bob, and Bob won four times as much as Cy. If Al won $1536, how much did Al, Bob, and Cy win together? A) $96 B) $384 C) $1920 D) $2016 15.The sum of two composites cannot be A) odd B) even C) 11 D) 17 16.If a and b are positive integers such that a/b = 5/7, then a + b is A) 12 B) 24 C) 36 D) not able to be determined 17.What is the greatest odd factor of the number of hours in all the days of the year 2015? A) 3 B) 365 C) 1095 D) 3285 18.If the current month is February, what month will it be 1 199 999 months from now? A) January B) February C) March D) April 19.Two angles are complementary. One of these angles is 36° less than the other. What is the measure of the larger angle? A) 36°B) 54°C) 63°D) 72° 20.(The square root of 16) + (the cube root of 64) + (the 4th root of 256) = A) 12 B) 24 C) 32 D) 64 21.In ?ABC, m∠A–m∠B = m∠B–m∠C. What is the degree measure of ∠B? A) 30 B) 60 C) 90 D) 120 22.For every 3 math books I bought, I bought 2 biology books. I bought 55 books in all. How many of those are math books? A) 11 B) 22 C) 33 D) 44 23.John wrote a number whose digits consists entirely of 1s. This number was a composite number. His number could contain exactly ? 1s. A) 17 B) 19 C) 29 D) 32 24.Weird Town uses three types of currencies: Cons, Flegs, and Sels. If 3 Sels = 9 Cons and 2 Cons = 4 Flegs, then 5 Sels = ? Flegs. A) 12 B) 24 C) 30 D) 36 第1页，共4页
美国大学生数学竞赛2011题目中文版
A题：滑雪场问题 请设计一个单板滑雪场（现为“半管”或“U型池”）的形状，以便能使熟练的单板滑雪选手最大限度地产生垂直腾空。“垂直腾空“是超出“半管”边缘以上的最大的垂直距离。定制形状时要优化其他可能的要求，如：在空中产生最大的身体扭曲。在制定一个“实用”的场地时哪些权衡因素可能需要？ 微分方程，确定一个形状，现在是半圆形的 B题中继站的协调 甚高频无线电频谱包含信号的发送和接收。这种限制是可以被“中继站”克服，中继站捕捉到弱信号,放大它们,再用不同的频率重新发送。这样, 低功耗的用户们/站（例如移动电话用户/站）在用户与用户（站与站）之间无法直接接触联系的情况下，通过使用中继站,就可以相互交流。然而,中继站之间会相互干扰,除非它们离的足够远或者它们通过充分分离的频率来传送。 除了地理的分离、“持续的音频编码控制系统”,有时被称为“私人专线”技术，可以用来减轻干扰问题。该系统给每一个中继站连接了一个独立的次声频音,这个次声频音由想通过中继站交流的每一个用户所发送。中继站只回应接收到的特殊的私人专线信号。通过这个系统,两个邻近的中继站可以共享相同的频率对(包括接收和发送);这样，在一个特定的区域可以容纳更多的中继站(并因此能同时容纳更多的用户)。 单纯形方法，分配问题：匈牙利方法， 问题： 1.为一个半径40英里的圆形平台区域决定最少数量的中继站，设计一个方案，要求能容纳1000个用户同时在线。假设甚高频无线电频谱范围是145兆赫~148兆赫,中继站发送的频率要么是600千赫以上，要么低于接收的频率600千赫，共有54种不同的私人专线可用。 2.如果有10,000用户同时被容纳，如何改变你的解决方案? 3. 在由于山区引起信号传播阻碍的地区，讨论这样的情形。 频率和距离 甚高频无线频谱包括视距发送和接收。这种限制可以被“中继器”所克服，中继器接收到微弱的信号，放大然后在不同的频率重传信号。所以，如果使用一个中继器，低功率用户（比如移动台）可以和另外一个不能直接建立用户至用户联系的用户进行通信。但是，如果中继器之间距离不够远或者频率相距不够大，中继器之间会产生相互的干扰。 除了空间上的远离外，“连续语音控制静噪系统”（CTCSS），有时被称为“专线”(PL)的技术可以被用来解决干扰的问题。这个系统以不同的亚音频和每个中继器联系，所有希望通过那个中继器通信的用户都发送那个亚音频。只有当以自己的专线音频接收信号时中继器才响应。有了这个系统，两个相邻的中继器可以共享同样的频率对（为了接收和发送）；所以更多地中继器（也意味着更多的用户）可以共存于一个特别的地带。 对于一个半径为40英里的圆形平坦地带，决定满足1000个同时存在的用户的最小中继器数目。假设可用频谱从145到148MHz，中继器的发送频率高于或低于接收频率600kHz，则有54个不同的亚音频可供使用。
2015 年美国大学生数学建模竞赛获奖学生名单
我校首获美国大学生数学建模竞赛特等奖提名奖 近日，从美国大学生数学建模竞赛官方网站获悉，我校在2015年美国大学生数学建模竞赛上首次获得特等奖提名奖（Finalist Winner）。特等奖提名奖是在2010年设立的介于特等奖（Outstanding Winner）与国际一等奖（Meritorious Winner）之间的一个奖项，今年该项比赛全球共评出特等奖19个，特等奖提名奖33个。这是我校自2011年在该项竞赛首次获得国际一等奖以来取得的又一重大突破。 据悉，美国大学生数学建模竞赛是一项公认的国际大学生数学建模竞赛，包括数学建模竞赛（MCM：A题和B题）和交叉学科建模竞赛（ICM：C题和D题）。竞赛以通信形式进行，由3名学生组成一队，在4天时间内针对所选赛题自由收集材料、调查研究，利用计算机、数学软件和互联网等工具，完成一篇包含模型的假设、建立和求解等方面的全英文论文。论文按时提交美国主办机构，由主办机构组织专家对全球各地提交的论文进行统一评审，奖项设置包括特等奖（Outstanding Winner）、特等奖提名奖（Finalist Winner）、国际一等奖（Meritorious Winner）、国际二等奖（Honorable Mention）、成功参赛奖（Successful Participant）、未成功参赛奖（Unsuccessful Participant）。本次比赛吸引了来自中国、美国、英国、加拿大在内的18个国家和地区的9773个队29000多名在校大学生参加。 我校2015年美国大学生数学建模竞赛获奖学生名单参赛 参赛队员（学院）获奖级别队号 41677 黄山（工程）汪海伦（工程）季忠良（工程）特等奖提名奖（Finalist Winner) 41699 吴毓龙（理学）马龙（理学）刘烈梅（经管）国际一等奖（Meritorious Winner）41702 张美男（资环）李玉珠（食品）相征（工程）国际一等奖（Meritorious Winner）41680 周宇（经管）郭强（生命）陈颖（动医）国际一等奖（Meritorious Winner）41686 潘亮（电信）张伟（工程）周璐（理学）国际一等奖（Meritorious Winner）41646 周建轩（理学）沈文斌（农学）张伟（经管）国际二等奖（Honorable Mention) 41698 徐翩翩（资环）魏雪莹（资环）石岩（生命）国际二等奖（Honorable Mention) 41695 周斌（理学）张慧林（食品）马婧（经管）国际二等奖（Honorable Mention) 41697 李治佟（电信）冯渊智（食品）杜泽坤（食品）国际二等奖（Honorable Mention) 41696 刘郝哲（电信）荆壮壮（经管）李子璇（电信）国际二等奖（Honorable Mention)
历年美国大学生数学建模竞赛试题
PROBLEM A: The Keep-Right-Except-To-Pass Rule In countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane. Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important. In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed. Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis? PROBLEM B: College Coaching Legends Sports Illustrated, a magazine for sports enthusiasts, is looking for the ―best all time college coach‖ male or female for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Present your model’s top 5 coaches in each of 3 different sports. In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will understand.