2003ICM Mathematical Contest in Modeling
大学生数学建模竞赛简介及试题分析
程以及技术含量 5）关于模型的有说服力的检验及精道的优缺点分析 6）由模型得到的关于问题有实际意义的结论 7）某个方面突出的亮点
美国（国际）大学生数学建模竞赛特点
7 是否给出了清晰的摘要。
美国大学生数学建模竞赛论文等级
不合格论文（Unsuccessful Participants）
合格论文（Successful Participants）
乙级论文（Honorablus）
（一等奖）
特级提名论文（Finalist）
赛题内容涉及经济、管理、环境、资源、生态、医学、 安全、未来科技等众多领域。
MCM/ICM 着重强调：
研究问题、解决方案的原创性，团队合作、交流以及结果的合理性。
美国大学生数学建模竞赛题目
每个团队在下列问题中选择且只能选择一个问题， 并提交解决方案。
MCM 问题A（连续） MCM 问题B（离散） MCM 问题C （对于数据的见解） ICM 问题D（运筹学或网络科学） ICM 问题E（环境科学） ICM 问题F （政策）
特级论文（优胜论文）（Outstanding Winner）
评委眼中数学建模竞赛论文 论文的评审流程
提交的论文 不合格论文 合格论文 下一轮论文
淘汰轮
乙级论文
下一轮
摘要与框架
最 评奖轮 终
评
分析与理解
奖 轮
甲级论文 下一轮
结构严谨 条理清晰 简单易读 结果以最简单最明了的方式表达
模型 方法 结果
Are Fingerprints Unique?
欧几里得滑铁卢数学竞赛_2003EuclidContest
parts are indicated like this: .Enter the answer in the appropriate box in the answer booklet.be given for a correct answer which is placed in the box. Part marks will be awarded parts are indicated like this: .Finished solutions must be written in the appropriate location in the answer booklet.Sybasei Anywhere SolutionsCanadian Instituteof ActuariesChartered Accountants Great West Lifeand London LifeNOTE: 1.Please read the instructions on the front cover of this booklet.2.Place all answers in the answer booklet provided. 3.For questions marked “”, full marks will be given for a correct answer placed in theappropriate box in the answer booklet. Marks may be given for work shown . Students are strongly encouraged to show their work.4.It is expected that all calculations and answers will be expressed as exact numbers such as4π, 27+, etc., except where otherwise indicated.1.(a)In the diagram, the parabola cuts the y -axis at the point 08,(), cuts the x -axis at the points 20,() and 40,(),and passes through the point a ,8(). What is the value of a ?(b)The quadratic equation x x k 260++= has two equal roots. What is the value of k ?(c)The line y x =+22 intersects the parabola y x x c =+23– at two points. One of these points is 14,(). Determine the coordinates of the second point of intersection.2.(a)If 090o o <<x and 3150sin cos x ()−()=o , what is the value of x to the nearest tenth of a degree?(b)In the diagram, ∆ABC is right-angled at B and AC =20. If sin C =35, what is the length ofside BC ?(c) A helicopter is flying due west over level ground at a constant altitude of 222 m and at aconstant speed. A lazy, stationary goat, which is due west of the helicopter, takes two measurements of the angle between the ground and the helicopter. The first measurement the goat makes is 6° and the second measurement, which he makes 1 minute later, is 75°. If the helicopter has not yet passed over the goat, as shown, how fast is the helicopter travelling to the nearest kilometre per hour?A B C3.(a)The function f x () has the property that f x f x 2323+()=()+ for all x .If f 06()=, what is the value of f 9()?(b)Suppose that the functions f x () and g x () satisfy the system of equations f x g x x x f x g x x ()+()=++()+()=+36242422for all x . Determine the values of x for which f x g x ()=().4.(a)In a short-track speed skating event, there are five finalists including two Canadians. Thefirst three skaters to finish the race win a medal. If all finalists have the same chance of finishing in any position, what is the probability that neither Canadian wins a medal?(b)Determine the number of positive integers less than or equal to 300 that are multiples of 3or 5, but are not multiples of 10 or 15.5.(a)In the series of odd numbers 1357911131517192123+++++––––––... the signs alternate every three terms, as shown. What is the sum of the first 300 terms of the series?(b)A two-digit number has the property that the square of its tens digit plus ten times its units digit equals the square of its units digit plus ten times its tens digit. Determine all two-digit numbers which have this property, and are prime numbers.6.(a)A lead box contains samples of two radioactive isotopes of iron. Isotope A decays so that after every 6 minutes, the number of atoms remaining is halved. Initially, there are twice as many atoms of isotope A as of isotope B, and after 24 minutes there are the same number of atoms of each isotope. How long does it take the number of atoms of isotopeB to halve?(b)Solve the system of equations:log log log log 103102102103113x y x y ()+()=()−()=7.(a) A regular hexagon is a six-sided figure which has all of its angles equal and all of its side lengths equal. Inthe diagram, ABCDEF is a regular hexagon with anarea of 36. The region common to the equilateral triangles ACE and BDF is a hexagon, which isshaded as shown. What is the area of the shadedhexagon?(b)At the Big Top Circus, H erc theHuman Cannonball is fired out of the cannon at ground level. (For the safetyof the spectators, the cannon ispartially buried in the sand floor.)Herc ’s trajectory is a parabola until he catches the vertical safety net, on his way down, at point B . Point B is 64 mdirectly above point C on the floor ofthe tent. If Herc reaches a maximumheight of 100 m, directly above a point30 m from the cannon, determine thehorizontal distance from the cannon tothe net.8.(a) A circle with its centre on the y-axis intersects the graph of y x = at the origin, O , and exactly two otherdistinct points, A and B , as shown. Prove that the ratioof the area of triangle ABO to the area of the circle isalways 1 : π.(b)In the diagram, triangle ABC has a right angle at Band M is the midpoint of BC . A circle is drawn usingBC as its diameter. P is the point of intersection of thecircle with AC . The tangent to the circle at Pcuts ABat Q . Prove that QM is parallel to AC .9.Cyclic quadrilateral ABCD has AB AD ==1, CD ABC =∠cos , and cos –∠=BAD 13. Provethat BC is a diameter of the circumscribed circle.10. A positive integer n is called “savage” if the integers 12,,...,n{} can be partitioned into three sets A, B and C such thati)the sum of the elements in each of A, B, and C is the same,ii)A contains only odd numbers,iii)B contains only even numbers, andiv)C contains every multiple of 3 (and possibly other numbers).(a)Show that 8 is a savage integer.(b)Prove that if n is an even savage integer, then n+412is an integer.(c)Determine all even savage integers less than 100.PUBLICATIONS2003 Euclid Contest(English)。
建模美赛培训-试题解析
秩 和 比 法 熵 权 法 相 关 系 数 法
评价合成
系 统 分 析 法
同 向 化
无 量 纲 化
专 家 法
河北金融学院
相 邻 指 标 比 较 法
层 次 分 析 法
算 术 平 均 法
几 何 平 均 法
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常见题目分类
预测、模拟
疾病传播趋势模拟
新闻传播特征模拟
河北金融学院 第 20 页
经典题目解析 2008年A题：洗个澡
河北金融学院
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经典题目解析 2008年A题：洗个澡
提示1：评价 寻找影响因素(或指标)，分别计算每种因素对 海平面上升的影响程度(或影响因子)，最终合成
总的影响。
提示2：预测
搜集并分析过去几年的各影响因素的相关数据
，以过去的变化趋势预测未来的变化趋势。
试题演进 你的团队最喜欢哪个题目？ 题目1：空气净化器风扇和滤芯形状对净化效率的影响 题目2：大气污染物的防治、处理最优方案分析 题目3：给N多地区的N多数据，对每个地区的污染程 度进行排序 题目4：大气污染物的扩散规律及对周边区域的影响 题目5：对某地区大气污染的严重程度进行评价，并对 居民10年后的生命健康水平进行预测
雨量变化趋势预测
海平面上升幅度预测
全球温度上升幅度预测 动植物数量变化预测 证券市场波动趋势预测 电力需求波动预测
第 15 页
河北金融学院
常见题目分类
预测、模拟
预测和模拟的目的在于认识自然和社会发展规律， 以及在不同历史条件下各种规律的相互作用，揭示 事物发展的方向和趋势，分析事物发展的途径和条 件。 作用：预测的结果可以为当前的决策提供参考。 方法：1、对过去和现在的数据进行总结，从中找出
MCM(MCM Mathematical Contest i
奖项
美国大学生数学建模竞赛共设置四个奖项，分别为 Outstanding Winner， Finalist， Meritorious Winner， Honorable Mentions， Successfully Participation。 在国内，约定俗成地将这四个奖项分别对应为特等奖、特等候选奖、一等奖、二等奖、成功参赛。
MCM（MCM Mathematical Contest i
MCM-Mathematical Contest in Modeling
01 简介
03 奖项
目录
02 历史背景 04 其他
《MCM》是MCM-Mathematical ContCM/ICM），是一项国际级的竞赛项目，为现今各类数学建模竞赛之鼻祖。
感谢观看
竞赛以三人（本科生）为一组，在四天时间内，就指定的问题完成从建立模型、求解、验证到论文撰写的全 部工作。竞赛每年都吸引大量著名高校参赛。2008年 MCM/ICM有超过 2000个队伍参加，遍及五大洲。MCM/ICM 已经成为最著名的国际大学生竞赛之一。
历史背景
1985年，在美国科学基金会的资助下，创办了一个名为“数学建模竞赛”（Mathematical Competition in Modeling后改名Mathematical Contest in Modeling，简称MCM）一年一度的大学水平的竞赛，MCM的宗旨是鼓 励大学师生对范围并不固定的各种实际问题予以阐明、分析并提出解法，通过这样一种结构鼓励师生积极参与并 强调实现完整的模型构造的过程。它是一种彻底公开的竞赛，每年只有若干个来自不受限制的任何领域的实际问 题，学生以三人组成一队的形式参赛，在三天（72小时）（近年改为四天，即96小时）内任选一题，完成该实际 问题的数学建模的全过程，并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解（及软件）、 检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出论文。由专家组成的评阅组进行评阅，评 出优秀论文，并给予某种奖励，它只有唯一的禁律，就是在竞赛期间不得与队外任何人（包括指导教师）讨论赛 题，但可以利用任何图书资料、互联网上的资料、任何类型的计算机和软件等，为充分发挥参赛学生的创造性提 供了广阔的空间。第一届MCM时，就有美国70所大学90个队参加，到1992年已经有美国及其它一些国家的189所大 学292个队参加，在某种意义下，已经成为一种国际性的竞赛，影响极其广泛。
美赛6种题型及通关详解
美赛6种题型及通关详解所谓6种题型，提示了部分题目的内容，但如果作为选题依据，作用非常有限。
如果是为了更好的选题，搞清楚MCM与ICM的区别，可能更有帮助。
选哪道题不是特别重要，重要的是应该“尽快”选题。
竞赛时间是固定的，选题的时间越长，做题的时间越少。
选题多花1小时，意味着建模和写论文的时间就少了1小时。
能获什么奖主要看实力，其次看运气。
准备越充分，胜算越大。
如果不想碰运气的话，早点动手准备吧。
六种题型怎么理解首先，MCM/ICM（2016年起）每年共有6道题，不是6种题，MCM是ABC三题，ICM是DEF三题。
对6道题目类型的描述，不是严格的划分，角度和依据都不相同。
continuous和discrete是指模型的类型，data insights是指问题数据的特征，operations research/network science和environmental science是指问题涉及到的学科，而environmental science和policy又是指问题本身的背景。
这不是按照同一标准对题目进行划集中在统计、模式识别等方向。
再比如D题如果是网络科学的问题的话，所用到模型、算法、软件比较集中，有章可循。
近几年网络科学是一个热门研究领域，算法、软件包括可视化的软件都很多，如果对这一领域的相关知识和软件都比较熟悉，选题时可以重点关注D题。
E题环境科学，大体上会集中在环境污染、资源短缺、可持续发展、生态保护等几个方面。
对问题的背景有一定的提示作用，但是范围仍然很广，模型、方法没有明显的特征。
所以，显然无法仅仅根据这些提示就进行选题，至多是，排除某个题目不考虑（如，计算能力差的队可以不选C题）。
如果仅从选题的角度出发，搞清楚MCM竞赛与ICM竞赛的区别，可能更有帮助。
MCM与ICM的区别国内常说的美国赛，其实是两个竞赛，MCM即Mathematical Contest in Modeling，直译为数学建模竞赛，和ICM即The Interdisciplinary Contest in Modeling，直译为交叉学科建模竞赛。
全国大学生数学建模竞赛简介PPT课件
194
35
225
39
224
38
262
46
223
43
队数
总数
中国
211
4
235
6
260
21
292
26
259
40
315
84
320
84
393
115
409
107
472
138
479
155
美国大学生数学建模竞赛
• 1985年开始举办数学建模竞赛(MCM), 1989年我国 (我校)学生开始参加。
• 1999年开始增办交叉学科竞赛(ICM).
竞赛宗旨
竞赛事项
❖ 答卷按省（市、自治区）和全国两级评奖； ❖ 每年赛题、优秀答卷及获奖名单刊登于次年
“工程数学学报”第1期； ❖ 全国组委会网址：
竞赛的社会影响不断扩大
❖ 99年的竞赛命名为“99’创维杯全国大学生数学建 模竞赛”;
❖ 2000年的竞赛命名为“2000网易杯全国大学生数 学建模竞赛”;
❖ A,C 为连续型题目; B,D为离散型题目
评奖标准
❖ 假设的合理性、建模的创造性、结果的正确 性和文字表述的清晰程度。
竞赛意义
大学阶段难得的一次近似于“真刀真枪” 的训练，模拟了毕业后工作时的情况，既丰 富、活跃了广大同学的课外生活，也为优秀 学生脱颖而出创造了条件.
竞赛意义
❖ 数学建模竞赛培养学生创新精神，提高 学生综合素质；
年 2000 2001 2002 2003 2004 2005
参赛国数 9 11 11 8 9 9
参赛总队数 495 579 628 638 742 808
美国大学生数学建模竞赛赛前培训心得体会
美国大学生数学建模竞赛赛前培训心得体会数学建模（Mathematical Modeding）是对现实世界的一个特定对象，为了一个特定目的，根据特有的内在规律，作出一些必要的简化假设，运用适当的数学工具，得到一个数学结构的过程[1].美国大学生数学建模竞赛（MCM/ICM），是一项国际级的竞赛项目，为现今各类数学建模竞赛之鼻祖。
MCM/ICM 是Mathematical Contest in Modeling 和InterdisciplinaryContest in Modeling 的缩写，即数学建模竞赛和交叉学科建模竞赛[2].MCM始于1985年，ICM始于2000年，由美国自然基金协会和美国数学应用协会共同主办，美国运筹学学会、工业与应用数学学会、数学学会等多家机构协办，比赛每年举办一次。
MCM/ICM着重强调研究问题、解决方案的原创性团队合作、交流以及结果的合理性。
竞赛形式为三名学生组成一队在四天内任选一题，完成该实际问题的数学建模的全过程，并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解（及软件）、检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出英文论文。
沈阳工业大学从2007年开始参加美国大学生数学建模竞赛，截至到2015年共参加了9届。
2015年共有16组美赛队伍，是我校参加美赛队伍最多一届。
前八届竞赛中，共获得一等奖 6 次，二等奖12 次，三等奖22 次。
2015 年获得一等奖2 组，二等奖3 组，三等奖6 组。
总结我校9 年来参加美国大学生数学建模竞赛的经验，笔者从美国大学生数学建模竞赛的赛前培训工作出发，总结几点心得体会，供同行们参考与讨论。
1 选拔优秀学生组队培训是美国大学生数学建模竞赛赛前培训的前提数学建模竞赛的主角是参赛队员，选拔参赛队员的成功与否直接影响到参赛成绩。
我们首先在参加全国大学生数学建模竞赛并获奖的同学中进行动员报名，经过一个阶段的培训后选拔出参加寒假集训队员，暑期集训结束后通过模拟最终确定参赛队员。
MCMTheMathematicalContestinModeling：MCM数学建模竞赛
MCM: The Mathematical Contest in ModelingICM: The Interdisciplinary Contest in ModelingContest Registration and Instructions(All instructions and rules apply to ICM as well as to MCM, except where otherwise noted.)To participate in MCM a team must be sponsored by a faculty advisor from their institution. The registration process must be completed by the advisor.PLEASE NOTE THE CHA NGES TO THE MCM/ICM RULES WHICH ARE HIGHLIGHTED IN RED BELOWThere are several procedures that a team's advisor must go t hrough at various times before, during, and after the contest. Please read these instructions carefully and be sure to complete all the steps involved. It is the advisor's responsibility to make sure that teams are correctly registered and that all steps required for participation in MCM/ICM are completed.We Suggest print ing a copy of these contest instructions for reference before, during, and after the contest.Note that COMAP is in the USA Eastern time zone; all t imes given in these instructions are in terms of Eastern time.If a team has been caught violat ing the rules, the faculty advisor will not be allowed to advise another team for one year and the advisor's instit ution will be put on one year's probation.Should a team from that institut ion be caught violating the rules a second t ime, then that school will not be allowed to compete for a period of at least one year.Before the contest registration deadline at 2pm EST on Thursday February 5, 2009 :Register your team online:The registration process will take you through a series of screens that askyou for your email address and contact information. Enter the requiredinformation as you step through the screens.IMPORTANT: Be sure to use a valid current email address so that we can use it tocontact you at any point before, during, or after the contest, if necessary.1.A ll teams must be registered before 2pm EST on Thursday February 5,2009 . At that time the registration system will stop accepting new teamregistrations; any team not registered by that time will not be able toparticipate in MCM 2009 . No exceptions will be made.2.T o guard against the possibility of interruptions in internet service werecommend that all teams complete the registration process well in advance ofthe deadline of 2pm EST on Thursday February 5, 2009 . COMAP cannotaccept late registrations for MCM/ICM under any circumstances, even if you are unable to reach our web site on the day of the contest. No except ions will be made.3.R egistration is via the contest web site. To register a team, go to/undergraduate/contests/mcm. If you are registering your first team for this year's contest, click on Register for 2009 Contest on the left-hand side of the screen.If you have already registered a team for this year's contest and want toregister an additional team, click on Advisor Login and then login with the email address and password that you used when you registered your first team.Once you're logged in, click on the Register Another Team link near the upper right corner of the page and follow the instructions there.An advisor may register at most two teams. If you already have two teams registered then the Register Another Team link will not appear and you cannot register another team.4.R egistration FeeOne of the final steps in the registration process is payment of the $ 100 registration fee per team. We accept payment via Mastercard or Visa, and payment must be made via our secure web site. Weregret that we are not able to accept other forms of payment.The pages that process your credit card payment on our site are secure pages, which means that your credit card number is protected with encryption while being transmitted from your computer to our server. Our system does notstore your credit card number; we only use it long enough to process your payment.5.O nce we have received approval from your financial institution (this takes only afew seconds), the system will issue a control number for your team. Your team is not fully registered until you have received a team control number. You should print out the page that gives your team control number; it also contains a reminder of the email address and password that you used when registering, and you will need these to complete the contest procedures.6.Y ou will not receive any email confirmation of your registration; the onlyconfirmation you will receive will be the screen giving your team's control number.7.T he screen giving your team's control number is your confirmation that yourteam has been registered. In order to participate in the contest, however, you will need to return to the contest web site several times to enter and confirm information about your team, and to print out your team's control andsummary sheets that you will use when preparing your team's solution packet.Please read the instructions below for details on these steps.If at any point before or during the contest you need to change any of theinformation (name, address, contact information, etc) that you specified whenyou registered, you can do so by logging in to the contest web site with theemail address and password that you used when registering (click on theAdvisor Login link on the left side of the screen). Once logged in, click on theEdit Advisor or Instit ution Data link near the upper right corner of thepage.8.R eturn to the contest web site regularly to check for any updated instructions orannouncements about the contest. Except in extreme circums tances, COMAPwill not send any confirmation, reminders, or announcements by email. Allcommunication regarding the contest will be via the contest web site.Before the contest begins at 8pm EST on Thursday February 5, 2009 : Choose your team members:1.Y ou must choose your team members before the contest begins at 8pm EST onThursday February 5, 2009 . Once the contest begins you may not add orchange any team members (you may, however, remove a team member, if heor she decides not to participate).2.E ach team may consist of a maximum of three students.3.N o student may be on more than one team.4.T eam members must be enrolled in school at the time of the contest, but do nothave to be full-time. They must be enrolled at the same school as the advisorand other team members.When the contest begins at 8pm EST on Thursday February 5, 2009 : Teams view the contest problems via the contest web site:1.T he contest problems will become available precisely at 8pm EST on ThursdayFebruary 5, 2009 ; team members can view them by visiting/undergraduate/contests/mcm. Nopassword will be needed to view the problems; simply go to the contest website at or after 8pm EST on Thursday February 5, 2009 and you will see a linkto view the problems.2.I f for some reason you cannot access our main web site at that time, go to ourmirror site at /mcm or click here . Thecontest site and the mirror site are on two completely different networks indifferent parts of the USA. If you cannot access either one of them then itprobably means that there is a problem with your local internet connection andyou should contact your ISP to resolve the issue.3.T he contest consists of a choice of three problems: A, B, and C.Important:o MCM teams should choose either problem A or problem B; anMCM team may submit a solution to only one of the problems. MCMteams should not choose problem C.o ICM teams should choose problem C. There is no choice for ICMteams. ICM teams should not choose problem A or B.Teams prepare solutions:1.T eams may use any inanimate source of data or materials --- computers,software, references, web sites, books, etc., however all sources used must becredited. Failure to credit a source will result in a team being disqualified fromthe competition.2.T eam members may not seek help from or discuss the problem with their advisoror anyone else, except other members of the same team. Input of any formfrom anyone other than student team members is strictly forbidden. Thisincludes email, telephone contact, personal conversation, communication viaweb chat or other question-answer systems, or any other form ofcommunication.3.P artial solutions are acceptable. There is no passing or failing cut-off score, norwill numerical scores be assigned. The MCM/ICM judges are primarilyinterested in the team's approach and methods.4.S ummary SheetThe summary is a very important part of your MCM paper. The judges place considerable weight on the summary, and winning papers are sometimesdistinguished from other papers based on the quality of the summary. To write a good summary, imagine that a reader may choose whether to read the body of the paper based on your summary. Thus, a summary should clearly describe yourapproach to the problem and, most prominently, what your most important conclusions were. The summary should inspire areader to learn the details of your work. Your concisepresentation of the summary should inspire a reader to learn the details of your work. Summaries that are mererestatements of the contest problem, or are a cut-and-paste boilerplate from the Introduction are generally considered to be weak.To Summarize:Restatement Clarification of the Problem - state in your own words whatyou are going to do.Assumptions with Rat ionale/Just ificat ion - emphasize thoseassumptions that bear on the problem. List clearly all variables used in yourmodel.Model Design and justification for type modelused/developed.Model Testing and Sensitivity Analysis, including erroranalysis, etc.Discuss strengths and weakness to your model or approach.Provide algorithms in words, figures, or flow charts (as a step by stepalgorithmic approach) for all computer codes developed.5.C onciseness and organization are extremely important. Key statements shouldpresent major ideas and results.Present a clarification or restatement of the problem, as appropriate.Present a clear exposition of all variables, assumptions, and hypotheses.Present an analysis of the problem, motivating or justifying the modeling to beused.Include a design of the model.Discuss how the model could be tested, including error analysis and stability(conditioning, sensitivity, etc.).Discuss any apparent strengths or weaknesses to your model or approach.6.P apers must be typed and in English.7.T he solution must consist entirely of written text, and possibly figures, charts, orother written material, on paper only. No non-paper support materials such ascomputer files or disks will be accepted.8.E ach page of the solut ion should contain the team control number andthe page number at the top of the page; we suggest using a page headeron each page, for example:9.10. Team # 321 Page 6 of 1311.12.The names of the students, advisor, or institution should not appear on anypage of the solution. The solution should not contain any identifyinginformation other than the team control number.13.Any preparation rule not followed is grounds for team disqualification.After the contest begins at 8pm EST on Thursday February 5, 2009 : Print Summary Sheet and Control SheetsWhile the team s are preparing their solutions, the advisor should1.L ogin to the contest web site (go to/undergraduate/contests/mcm. and click onAdvisor Login and enter your email address and password).2.E nter the team member names and confirm that they are correctly spelled.This is exact ly as the names and inst itut ions will appear on thecertificates. COMAP will not make any changes or reprint certificatesfor any reason.3.S pecify the problem that your team has chosen to solve.4.P rint one copy of the control sheet.5.P rint one copy of the team summary sheet.When the contest ends at 8pm EST on Monday February 9, 2009 : Prepare Solution Packet:1.H ave each student sign the control sheet, pledging that they have abided by thecontest rules and instructions.2.T ake the completed summary sheet that your team has prepared and makethree copies of it.3.M ake three copies of your team's solution paper. Staple one copy of thesummary sheet on top of each copy of the solution paper.4.S taple the control sheet on top of just one copy of the solution paper.5.Y ou are now required to include an electronic copy of your team’ssolution papers. Please enclose a CD-ROM with a PDF or Word file ofyour paper.DO NOT include programs or software on these disks as they will notbe used in the judging process.If you have more than one team it is recommended that you add allyour teams to a single CD-ROM and label it with contest, year, andteam control numbers.Example: Contest Year Control Numbers2009 MCM/ICM 10004, 10005Mail Solution Packet:1.A fter you have prepared your team's solution packet as above, mail it toMCM/ICM CoordinatorCOMAP, Inc.175 Middlesex Turnpike., Suite 3BBedford, MA 01730USA2.C OMAP must receive your solution on or before Friday February 20, 2009 . It isyour responsibility to make sure that your team's solution packet arrives atCOMAP by this deadline.3.U se registered or express mail if necessary to insure that your solution arrives atCOMAP by Friday February 20, 2009 .4.C OMAP will not accept late solutions under any circumstances.5.I f you require confirmation that your paper was received by COMAP, send thepacket via a carrier that provides package tracking. Due to the number ofpapers received, COMAP can not answer receipt inquiries or emails.After the contest is over:Confirm that your team's solution was received at COMAP:A few days after m ailing your solution packet, you m ay login to the contestweb site using the Advisor Login link to verify that your team's solution was received at COMAP. Please allow several days for us to process your packet before expecting to see this confirmation.JudgingJudging will be completed by May, 2009. The solutions will be recognized as Unsuccessful Participant, Successful Participant, Honorable Mention,Meritorious, or Outstanding Winner.Check ResultsReturn to the contest web si te periodically to check for the results of thecontest. It will take several weeks for the judges to evaluate the solutionsand for COMAP to process the results. We will post the results on the web site as soon as they are available. Please do not call or em ail COMAP asking when the results will be available; simply visit the contest web site regularly tocheck for them.Receive certificateAt som e point after the results have been issued, each team thatparticipated successfully will receive a certificate of participation. Allinternational teams will now ONLY receive an electronic (PDF)certificate. The certificate will be mailed or emailed to the advisor at theaddress used during the registration process. Please allow several weeksafter the results are posted to the contest web site before expecting toreceive your certificate.Prizes∙The Institute for Operations Research and the Management Sciences (INFORMS) will designate an Outstanding team from each of the three problems as anINFORMS winner∙The Society for Industrial and Applied Mathematics (S IAM) will designate one Outstanding team from each problem as a S IAM winner.∙The Mathematical Association of America (MAA) will designate one Outstanding team from each problem for the MCM as a MAA winner.Note: COMAP is the final arbiter of all rules and policies, and may disqualify or refuse to register any team that, in its sole discretion, does not follow these contest regulations and procedures.。
2003年AMC8试题
19th AMC 8 2003 1. Jamie counted the number of edges of a cube, Jimmy counted the number of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum? (A) 12 (B) 16 (C) 20 (D) 22
4. A group of children riding on bicycles and tricycles rode past Billy Bob’s house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there? (A) 2 (B) 4 (C) 5 (D) 6 cookies are trapezoids:
3 in
5 in
• Roger’s cookies are rectangles:
4 in
2 in
• Paul’s cookies are parallelograms:
2 in 3 in
• Trisha’s cookies are triangles:
5. If 20% of a number is 12, what is 30% of the same number? (A) 15 (B) 18 (C) 20 (D) 24 (E) 30
6. Given the areas of the three squares in the figure, what is the area of the interior triangle? (A) 13 (B) 30 (C) 60 (D) 300 (E) 1800
数学建模竞赛简介
• 目标函数与约束条件的选择
• 3个场馆一起设计，或3个场馆分开设计 • 结果的合理性
成功参赛的要素
• 浓厚的兴趣 • 敏锐的洞察力和活跃的思维； • 获取新知识的能力 • 扎实的数学基础 • 熟练的计算机编程 • 清晰的论文表达
院校数 79 101 196 259 337 373 400 460 517 529 571 638 724 795 864 969 1023 1137
队数 314 420 867 1234 1683 1874 2103 2657 3210 3861 4458 5406 6881 8492 9985 11742 12846 15042
数学建模竞赛 简介
dx rx dt
刘云
玉溪师范学院
数学建模竞赛的由来
• 1985年开始由美国工业与数学学会举办“美国大学生数学 建模竞赛”MCM（Mathematical Contest in Modeling）。 • 1989年我国大学生首次开始参加 MCM. • 1990年上海率先举办了“上海市大学生数学模型竞赛” • 1992年，教育部高教司和中国工业与应用数学协会联合举 办“中国大学生数学建模竞赛（CMCM)”。 • 1994年起由教育部高教司和CSIAM共同举办，每年一次(9 月) • 1999年， 美国大学生交叉学科建模竞赛ICM （Interdisciplinary Contest in Modeling)开始。 • 日前 CMCM 已经成为全国高校规模最大的课外科技活动
如何将这个调度问题抽象成 一个明确、完整的数学模型， 指出求解模型的方法；根据实际问题的要求，如果要设计 更好的调度方案，应如何采集运营数据。
C题
C题数学建模竞赛数学建模竞赛（Mathematical Contest in Modeling，缩写为MCM）于1985年最先出现于美国，1989年我国大学生开始参加美国大学生数学建模竞赛，1990年10月中国工业与应用数学学会（CSIAM）成立，CSIAM下属的数学模型专业委员会开始考虑创办我国自己的大学生数学建模竞赛。
1992年11月27日到29日由CSIAM数学模型专业委员会组织举办了“1992年全国大学生数学模型联赛”，10个城市79所院校的314个队参加，从此我国有了自己的大学生数学建模竞赛（China Undergraduate Mathematical Contest in Modeling，缩写为CUMCM）。
1993年12月教育部（前国家教委）高教司正式发文，要求在全国普通高校中陆续开展电子设计、数学建模、机械设计和结构设计竞赛，并且于1994年3月成立了由教育部高教司和CSIAM成员共同组成的第一届全国大学生数学建模竞赛组委会，于是从1994年开始，CUMCM成为教育部高教司和中国工业与应用数学学会共同主办、每年一届、面向全国高等院校学生的一项课外科技竞赛活动。
近20年来，CUMCM的规模平均每年以20％以上的增长速度健康发展，是目前全国高校中规模最大的课外科技活动之一。
2010年有33个省市、自治区及新加坡、澳大利亚的1197所院校的17317个队参加。
2011 年，来自全国33个省/市/自治区(包括香港和澳门特区)及新加坡、美国的1251所院校、19490个队（其中本科组16008队、专科组3482队）、58000多名大学生报名参加本项竞赛。
在数学建模活动开展20周年之际，有必要对以往的数学建模工作进行总结及对未来的发展进行预测。
请考虑完成以下任务：1. 利用附件1中的数据，试建立评价模型，给出广东赛区各校建模成绩的科学、合理的排序；并对广东赛区各院校2012年建模成绩进行预测；2. 利用附件2中的数据，给出全国各院校的自建模竞赛活动开展以来建模成绩的科学、合理的排序；3. 你认为如果科学、合理地进行评价和预测，除全国竞赛成绩、赛区成绩外，还需要考虑那些因素？附件1：2008年-2011年广东赛区成绩附件2：1994-2011年全国成绩（国家奖）。
全国大学生数学建模竞赛简介
MCM2004-A：指纹是独一无二的吗？ ：指纹是独一无二的吗？ 人们普遍认为世界上每一个活人的指纹都是不一样 的，请设计一个模型，并且用该模型分析以上说法 请设计一个模型， 正确的可能性， 正确的可能性，比较一下因为指纹相同导致确认身 份时产生错误的可能性和因为DNA相同导致产生错 份时产生错误的可能性和因为 相同导致产生错 误的可能性。 误的可能性。 MCM2008A:给大陆洗个澡 给大陆洗个澡 研究一下由于全球气温升高造成的北极冰帽融化对大 陆的影响。具体来说，为佛罗里达海岸今后50年，每 陆的影响。具体来说，为佛罗里达海岸今后50年 50 十年由于融化造成的影响建立模型， 十年由于融化造成的影响建立模型，要特别注意大型 都市区。提出一些适当的回应来处理这些问题。 都市区。提出一些适当的回应来处理这些问题。
竞赛的反响
• 学生欢迎：“一次参赛，终身受益” 学生欢迎： 一次参赛，终身受益” • 研究生导师们的认同 • 企业界的认同／赞助 企业界的认同／ • 教育改革同行的认同：“成功范例” 教育改革同行的认同： 成功范例” • 国际同行的认同
竞赛的反响（一例） 竞赛的反响（一例）
IBM 中国研究中心 招聘条件 中国研究中心Position title: Business Optimization(BJ) 1．Background in industrial engineering, operations ． research, mathematics, Artificial Intelligence, management science etc. 2. Knowledge in network design, job scheduling, data analysis, simulation and optimization 3. Award in mathematical contest in modeling is a plus 4. Experience in industry is a plus 5. Experience in eclipse or programming model / architecture design is a plus --Feb. 18, 2006, /cn/ibm/crl/careers/condition.shtml
美赛简介及竞赛规则
MCM/ICM竞赛简介享有数学建模“奥林匹克”之称的MCM/ICM竞赛是一项面向世界各国大学生的国际性赛事，包括The Mathematical Contest in Modeling(数学建模竞赛)、The Interdisciplinary Contest in Modeling(交叉学科建模竞赛)和MCM/ICM Media Contest(数学建模媒体竞赛)，由美国自然基金协会和美国数学及其应用联合会共同主办，运筹学与管理科学学会、工业与应用数学学会、数学学会等多家机构协办，目前已成为全世界最具影响力的大学生学科竞赛。
MCM(The Mathematical Contest in Modeling，数学建模竞赛)始于1985年，其宗旨是鼓励大学生通过对实际问题予以阐明、分析、建立数学模型并提出解法，来提高应用数学解决实际问题的能力和写作能力；ICM(The Interdisciplinary Contest in Modeling，交叉学科建模竞赛)始于2000年，其宗旨是发展并提升大学生运用数学方法解决交叉学科问题的能力和写作能力。
比赛每年举办一次。
竞赛形式为三名学生组成一队在四天内任选一题，完成该实际问题的数学建模的全过程，并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解（及软件）、检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出论文。
该项竞赛共设置四个奖项，分别为Outstanding Winner，Finalist，Meritorious Winner，Honorable Mentions。
在国内，约定俗成地将这四个奖项分别对应为特等奖、特等奖提名奖、一等奖、二等奖。
2013年吸引了来自中国、美国、加拿大、德国、印度、芬兰等15个国家和地区的6593支队伍参赛。
学习资料参赛规则【数学中国翻译】2014美国大学生数学建模竞赛（MCM/ICM）参赛规则中英文对照/thread-201325-1-1.html数学中国MCM/ICM参赛指南翻译（2014版）（任何单位转载须注明来源：）MCM:The Mathematical Contest in ModelingMCM：数学建模竞赛ICM:The InterdisciplinaryContest in ModelingICM：交叉学科建模竞赛ContestRules, Registration and Instructions比赛规则，比赛注册方式和参赛指南(All rules and instructions apply to both ICM and MCMcontests, exceptwhere otherwisenoted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）To participate in a contest, each team must be sponsoredby a faculty advisor fromits institution.每个MCM的参赛队需有一名所在单位的指导教师负责。
数学建模竞赛介绍
8
数学建模竞赛的历史
中国大学生数学建模竞赛（CUMCM）
• 1992年中国工业与应用数学学会(CSIAM)开始组织 • 1994年起教育部高教司和CSIAM共同举办(每年9月) • 1999年起竞赛分为本科组(甲组)、高职高专组(乙组) • 2008 年全国有31个省/市/自治区(包括香港)1023所院 校、12846个队、3万8千多大学生参加
量纲分析法 差分法 变分法 图论法 层次分析法 数据拟合法 回归分析法 类比法 数学规划（线性规划，非线性规划，整数规 划，动态规划，目标规划）
24
数学能力
数学建模常用的方法（2）
因子分析法 排队方法 对策方法 决策方法 模糊评判方法 时间序列方法 灰色理论方法 现代优化算法（禁忌搜索算法，模拟退火算 法，遗传算法，神经网络）
25
数学能力
吃透一本好的教材，参考若干书籍
姜启源：数学模型 第三版 高等教育出版社 叶其孝：大学生数学建模竞赛辅导 教材1-5 湖南教育出版社 数学建模（原书第三版）[美] 叶其孝 姜启源译 机械工业出版社
26
参加数学建模竞赛所需知识
1. 数学能力 2. 计算机能力 3. 论文写作与文献查阅能力
赛区获奖15%
•参赛对象：在校大学生（所有专业）
21
数学建模与数学建模竞赛
1.数学建模竞赛简介
2. 参加数学建模竞赛所需知识
3. 数学建模竞赛过程应注意的问题
22
参加数学建模竞赛所需知识
1. 数学能力 2. 计算机能力 3. 论文写作与文献查阅能力
4. 即时学习认知能力
23
数学能力
数学建模常用的方法（1）
第二天：能够初步建立模型，开始论文写作，给出 初步模型的简单求解； 第三天上午：改进模型，继续论文写作并开始写摘 要；
数模发展历程
什么是数学模型与数学建模简单地说：数学模型就是对实际问题的一种数学表述。
具体一点说：数学模型是关于局部现实世界为某种目的的一个抽象的简化的数学构造。
更确切地说：数学模型就是对于一个特定的对象为了一个特定目标，根据特有的内在规律，做出一些必要的简化假设，运用适当的数学工具，得到的一个数学构造。
数学构造可以是数学公式，算法、表格、图示等。
数学建模就是建立数学模型，建立数学模型的过程就是数学建模的过程〔见数学建模过程流程图〕。
数学建模是一种数学的思考方法，是运用数学的语言和方法，通过抽象、简化建立能近似刻划并"解决"实际问题的一种强有力的数学手段。
美国大学生数学建模竞赛的由来：1985年在美国出现了一种叫做MCM的一年一度大大学生数学模型〔1987年全称为Mathematical Competition in Modeling,1988年改全称为Mathematical Contest in Modeling,其所写均为MCM〕。
这并不是偶然的。
在1985年以前美国只有一种大学生数学竞赛〔The william Lowell Putnam mathematial Competition,简称Putman(普特南〕数学竞赛〕，这是由美国数学协会〔MAA--即Mathematical Association of America的缩写〕主持，于每年12月的第一个星期六分两试进展，每年一次。
在国际上产生很大影响，现已成为国际性的大学生的一项著名赛事。
该竞赛每年2月或3月进展。
我国自1989年首次参加这一竞赛，历届均取得优异成绩。
经过数年参加美国赛说明，中国大学生在数学建模方面是有竞争力和创新联想能力的。
为使这一赛事更广泛地展开，1990年先由中国工业与应用数学学会后与国家教委联合主办全国大学生数学建模竞赛〔简称CMCM〕，该项赛事每年9月进展。
数学模型竞赛与通常的数学竞赛不同，它来自实际问题或有明确的实际背景。
美赛
作为准备，你最好阅读历年竞赛的特等奖论文，这是非常重要的。这是唯一的渠道，当你阅读完一篇特等奖论文后，尝试猜猜评委们的观点，尽量与评委们保持一致！ 论文的写作工具在美赛中通常为LaTex，建议参赛的学生使用它，我们数学中国（）每年在竞赛前都会出来LaTex模板，直接套用即可，当然不会用LaTex也可以用word，推荐用word2007,因为他提供了即时翻译功能，是写作英文论文的必备。 在这里强调，不要试图通过写中文再翻译成英文，更不要指望任何人来帮你翻译，通常中文翻译成英文的文章，是那么的生涩难懂。在竞赛准备期间每个星期最少写2篇以上的英文科技小论文，写完之后请英语老师评价修改一下，这样有利于你的英文写作水平。
4、保持对问题的敏感性每 年的年底我们都会针对这一年国内外发生的事实进行总结，今年是个经济大灾年，全球金融危机。明年的题目是否会出到，尚未可知。但是经济危机的背景下，我们 是不是可以自己给自己出题目，自己做呢？比如经济危机对股市的影响、经济危机国际传染路线问题、政府救市的评估问题，这些都是可以用数学模型加以描述的。 也许有些同学会说，连诺贝尔经济学奖获得者都没有解决的问题，我们做有什么意思。呵呵，练笔与不练笔自己拿主意，只有经常做一些模型，才会提高自己建模的 水平。单单为了竞赛拿奖，没有平时的练笔。得奖的几率渺茫！
2000-2013美国数学建模竞赛(MCM、ICM)历年试题汇总
目录2000 年美国大学生数学建模竞赛MCM、ICM 试题 (3)2000 MCM A: Air Traffic Control (3)2000 MCM B: Radio Channel Assignments (3)2000 ICM: Elephants: When is Enough, Enough? (5)2001 年美国大学生数学建模竞赛MCM、ICM 试题 (7)2001 MCM A: Choosing a Bicycle Wheel (7)2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...). (8)2001 ICM: Our Waterways - An Uncertain Future (10)2002 年美国大学生数学建模竞赛MCM、ICM 试题 (14)2002 MCM A: Wind and Waterspray (14)2002 MCM B: Airline Overbooking (14)2002 ICM: Scrub Lizards (15)2003 年美国大学生数学建模竞赛MCM、ICM 试题 (19)2003 MCM A: The Stunt Person (19)2003 MCM B: Gamma Knife Treatment Planning (19)2003 ICM: Aviation Baggage Screening Strategies: To Screen or Not to Screen, that is the Question (20)2004 年美国大学生数学建模竞赛MCM、ICM 试题 (24)2004 MCM A: Are Fingerprints Unique? (24)2004 MCM B: A Faster QuickPass System (24)2004 ICM: To Be Secure or Not to Be? (24)2005 年美国大学生数学建模竞赛MCM、ICM 试题 (25)2005 MCM A: Flood Planning (25)2005 MCM B: Tollbooths (25)2005 ICM: Nonrenewable Resources (25)2006 年美国大学生数学建模竞赛MCM、ICM 试题 (27)2006 MCM A: Positioning and Moving Sprinkler Systems for Irrigation (27)2006 MCM B: Wheel Chair Access at Airports (27)2006 ICM: Trade-offs in the fight against HIV/AIDS (28)2007 年美国大学生数学建模竞赛MCM、ICM 试题 (32)2007 MCM A: Gerrymandering (32)2007 MCM B: The Airplane Seating Problem (32)2007 ICM: Organ Transplant: The Kidney Exchange Problem (33)2008 年美国大学生数学建模竞赛MCM、ICM 试题 (38)2008 MCM A: Take a Bath (38)2008 MCM B: Creating Sudoku Puzzles (38)2008 ICM: Finding the Good in Health Care Systems (38)2009 年美国大学生数学建模竞赛MCM、ICM 试题 (40)2009 MCM A: Designing a Traffic Circle (40)2009 MCM B: Energy and the Cell Phone (40)2009 ICM: Creating Food Systems: Re-Balancing Human-Influenced Ecosystems41 2010年美国大学生数学建模竞赛 MCM、ICM 试题 (42)2010 MCM A: The Sweet Spot (42)2010 MCM B: Criminology (43)2010 ICM: The Great Pacific Ocean Garbage Patch (44)2011年美国大学生数学建模竞赛 MCM、ICM 试题 (45)2011 MCM A: Snowboard Course (45)2011 MCM B: Repeater Coordination (45)2011 ICM: Environmentally and Economically Sound (46)2012年美国大学生数学建模竞赛 MCM、ICM 试题 (48)2012 MCM A: The Leaves of a Tree (48)2012 MCM B: Camping along the Big Long River (50)2012 ICM: Modeling for Crime Busting (51)2013年美国大学生数学建模竞赛 MCM、ICM 试题 (59)2013 MCM A: The Ultimate Brownie Pan (59)2013 MCM B: Water, Water, Everywhere (61)2013 ICM: NetworkModeling of Earth's Health (62)2000 年美国大学生数学建模竞赛MCM、ICM 试题2000 MCM A: Air Traffic ControlTo improve safety and reduce air traffic controller workload, the Federal Aviation Agency (FAA) is considering adding software to the air traffic control system that would automatically detect potential aircraft flight path conflicts and alert the controller. To that end, an analysit at the FAA has posed the following problems.Requirement A: Given two airplanes flying in space, when should the air traffic controller consider the objects to be too close and to require intervention? Requirement B: And airspace sector is the section of three-dimensional airspace that one air traffic controller controls. Given any airspace sector, how do we measure how complex it is from an air traffic workload perspective? To what extent is complexity determined by the number of aircraft simultaneously passing through that sector1.at any one instant?2.during any given interval of time?3.during a particular time of day?How does the number of potential conflicts arising during those periods affect complexity? Does the presence of additional software tools to automatically predict conflicts and alert the controller reduce or add to this complexity? In addition to the guidelines for your report, write a summary (no more than two pages) that the FAA analyst can present to Jane Garvey, the FAA Administrator, to defend your conclusions.2000 MCM B: Radio Channel AssignmentsWe seek to model the assignment of radio channels to a symmetric network of transmitter locations over a large planar area, so as to avoid interference. One basic approach is to partition the region into regular hexagons in a grix (honeycomb-style), as shown in Figure 1, where a transmitter is located at the center of each hexagon.An interval of the frequency spectrum is to be alloted for transmitter frequencies. The interval will be divided into regularly spaced channels, which we represent by integers 1,2,3, … . Each transmitter wil be assigned one positive integer channel. The same channel can be used at many locations, provided that interference from nearby transmitters is avoided.Our goal is to minimize the width of the interval in the frequency spectrum that is needed to assugn channels subject to some constraints. This is achieved with the concept of a span. The span is the minimum, over all assignments satisfying the constraints, of the largest channel used at any location. It is not required that every channel smaller than the span be used in an assignment that attains the span.Let s be the length of a side of one of the hexagons. We concentrate on the case that there are two levels of interference.Requirement A: There are several contrainsts on the frequency assignments. First, no two transmitters within distance 4s of each other can be given the same channel. Second, due to spectral spreading, transmitters within distance 2s of each other must not be given the same or adjacent channels: Their channels must differ by at least 2. Under these contraints, what can we say about the span in Figure 1?Requirement B: Repeat Requirement A, assuming the grid in the example spreads arbitrarily far in all directions.Requirement C: Repeat Requirements A and B, except assume now more generally that channels for transmitters within distance 2s differ by at least some given integer k, while those at distance at most 4s must still differ by at least one. What cna we say about the span and about efficient strategies for designing assignments, as a function of k?Requirement D: Consider generalizations of the problem, such as several levels of interference or irregular transmitter placements. What other factors may be important to consider?Requirement E: Write an article (no more than 2 pages) for the local newspaper explaining your findings.2000 ICM: Elephants: When is Enough, Enough?“Ultimately, if a habitat is undesirably changed by elephants, then their removal should be considered -even by culling.”National Geographic (Earth Almanac) –December 1999 A large National Park in South Africa contains approximately 11,000 elephants. Management policy requires a healthy environment that can maintain a stable herf of 11,000 elephants. Each year park rangers count the elephant population. During the past 20 years whole herds have been removed to keep the population as close to 11,000 as possible. The process involved shooting (for the most part) and occasionally relocating approximately 600 to 800 elephants per year.Recently, there has been a public outcry against the shooting of these elephants. In addition, it is no longer feasible to relocate even a small population of elephants each year. A contraceptive dart, however, has been developed that can prevent a mature elephant cow from conceiving for a period of two years.Here is some information about eh elephants in the Park:∙There is very little emigration of immigration of elephants.∙The gender ratio is very close to 1:1 and control measures have endeavored to maintain parity.∙The gender ratio of newborn calves is also about 1:1. Twins are born about 1.35% of the time.∙Cows first conceive between the ages of 10 and 12 and produce, on average, a calf every 3.5 years until they reach an age of about 60.Gestation is approximately 22 months.∙The contraceptive dart causes an elephant cow to come into oestrus every month (but not conceiving). Elephants usually have courtship only once in 3.5 years, so the monthly cycle can cause additional stress.∙ A cow can be darted every year without additional detrimental effects. A mature elephant cow will not be able to conceive for 2 years after thelast darting.∙Between 70% and 80% of newborn calves survive to age 1 year.Thereafter, the survival rate is uniform across all ages and is very high(over 95%), until about age 60; it is a good assumption that elephantsdie before reading age 70.There is no hunting and negligible poaching in the Park.The park management has a rough data file of the approximate ages and gender of the elephants they have transported out of the region during the past 2 years. This data is available on website: icm2000data.xls. Unfortunately no data is available for the elephants that have been shot or remain in the Park.Your overall task is to develop and use models to investigate how the contraceptive dart might be used for population control. Specifically:Task 1: Develop and use a model to speculate about the likely survival rate for elephants aged 2 to 60. Also speculate about the current age structure of the elephant population.Task 2: Estimate how many cows would need to be darted each year to keep the population fixed at approximately 11,000 elephants. Show how the uncertainty in the data at your disposal affects your estimate. Comment on any changes in the age structure of the population and how this might affect tourists. (You may want to look ahead about 30-60 years.)Task 3: If it were feasible to relocate between 50 and 300 elephants per year, how would this reduce the number of elephants to be darted? Comment on the trade-off between darting and relocation.Task 4: Some opponents of darting argue that if there were a sudden loss of a large number of elephants (due to disease or uncontrolled poaching), even if darting stopped immediately, the ability of the population to grow again would be seriously impeded. Investigate and respond to this concer.Task 5: The management in the Park is skeptical about modeling. In particular, they argue that a lack of complete data makes a mockery of any attempt to use models to guide their decision. In addition to your technical report, include a carefully crafted report (3-page maximum) written explicitly for the park management that responds to their concerns and provides advice. Also suggest ways to increase the park managers confidence in your model and your conclusions.Task 6: If your model works, other elephant parks in Africa would be interested in using it. Prepare a darting plan for parks of various sizes (300-25,000 elephants), with slightly different survival rates and transportation possibilities.2001 年美国大学生数学建模竞赛MCM、ICM 试题2001 MCM A: Choosing a Bicycle WheelCyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.Task 1. Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel. The table should include the wind speeds for different road grades startingfrom zero percent to ten percent in one percent increments. (Roadgrade is defined to be the ratio of the total rise of a hill divided by thelength of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportionalto the road grade. A rider will lose about 8 kph for a five percent grade over 100 meters.∙Task 2. Provide an example of how the table could be used for a specific time trial course.∙Task 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...)Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state. What is normally an easy two-hour drive took up to 18 hours to complete. Many cars simply ran out of gas along the way. Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston to Columbia. Plans to carry this out have been prepared (and posted on the Web) by the South Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown. Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip. (More accurate data, if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three. Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees (including some coming from farther north by other routes), so some traffic continues outbound on I-26 towards Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving Columbia going northwest was moving only very slowly. Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999. Here are the questions that need to be addressed:1.Under what conditions does the plan for turning the two coastal-boundlanes of I-26 into two lanes of Columbia-bound traffic, essentiallyturning the entire I-26 into one-way traffic, significantly improveevacuation traffic flow?2.In 1999, the simultaneous evacuation of the state's entire coastal regionwas ordered. Would the evacuation traffic flow improve under analternative strategy that staggers the evacuation, perhapscounty-by-county over some time period consistent with the pattern of how hurricanes affect the coast?3.Several smaller highways besides I-26 extend inland from the coast.Under what conditions would it improve evacuation flow to turn around traffic on these?4.What effect would it have on evacuation flow to establish moretemporary shelters in Columbia, to reduce the traffic leaving Columbia?5.In 1999, many families leaving the coast brought along their boats,campers, and motor homes. Many drove all of their cars. Under whatconditions should there be restrictions on vehicle types or numbers ofvehicles brought in order to guarantee timely evacuation?6.It has been suggested that in 1999 some of the coastal residents ofGeorgia and Florida, who were fleeing the earlier predicted landfalls ofHurricane Floyd to the south, came up I-95 and compounded the traffic problems. How big an impact can they have on the evacuation trafficflow? Clearly identify what measures of performance are used tocompare strategies. Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.Clearly identify what measures of performance are used to compare strategies. Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.2001 ICM: Our Waterways - An Uncertain FutureZebra mussels, Dreissena polymorpha, are small, fingernail-sized, freshwater mollusks unintentionally introduced to North America via ballast water from a transoceanic vessel. Since their introduction in the mid 1980s, they have spread through all of the Great Lakes and to an increasing number of inland waterways in the United States and Canada. Zebra mussels colonize on various surfaces,such as docks, boat hulls, commercial fishing nets, water intake pipes and valves, native mollusks and other zebra mussels. Their only known predators, some diving ducks, freshwater drum, carp, and sturgeon, are not numerous enough to have a significant effect on them. Zebra mussels have significantly impacted the Great Lakes ecosystem and economy. Many communities are trying to control or eliminate these aquatic pests. SOURCE: Great Lakes Sea Grant Network /.Researchers are attempting to identify the environmental variables related to the zebra mussel infestation in North American waterways. The relevant factors that may limit or prevent the spread of the zebra mussel are uncertain. You will have access to some reference data to include listings of several chemicals and substances in the water system that may affect the spread of the zebra mussel throughout waterways. Additionally, you can assume individual zebra mussels grow at a rate of 15 millimeters per year with a life span between 4 - 6 years. The typical mussel can filter 1 liter of water each day.Requirement A: Discuss environmental factors that could influence the spread of zebra mussels.Requirement B: Utilizing the chemical data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAChem1.xls, and the mussel population data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAPopulation 1.xls model the population growth of zebra mussels in Lake A. Be sure to review the Information about the collection of the zebra mussel data. Requirement C: Utilizing additional data on Lake A from another scientist provided at :ap/undergraduate/contests/icm/imagesdata/LakeAChem2.xls and additional mussel population data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAPopulation 2.xls corroborate the reasonableness of your model from Requirement B. As a result of this additional data, adjust your earlier model. Analyze the performance of your model. Discuss the sensitivity of your model. Requirement D: Utilizing the Chemical data from two lakes (Lake B and Lake C) in the United States provided atap/undergraduate/contests/icm/imagesdata/LakeB.xls and ap/undergraduate/contests/icm/imagesdata/LakeC.xls determine if these lakes are vulnerable to the spread of zebra mussels. Discuss your prediction.Requirement E: The community in the vicinity of Lake B (in requirement D) is considering specific policies for the de-icing of roadways near the lake duringthe winter season. Provide guidance to the local government officials regarding a policy on “de-icing agents.”In your guidance include predictions on the long-term impact of de-icing on the zebra mussel population. Requirement F: It has been recommended by a local community in the United States to introduce round goby fish. Zebra mussels are not often eaten by native fish species so they represent a dead end ecologically. However, round gobies greater than 100 mm feed almost exclusively on zebra mussels. Ironically, because of habitat destruction, the goby is endangered in its native habitat of the Black and Caspian Seas in Russia. In addition to your technical report, include a carefully crafted report (3-page maximum) written explicitly for the local community leaders that responds to their recommendation to introduce the round goby. Also suggest ways to help reduce the growth of the mussel within and among waterways.Information about the collection of the zebra mussel dataThe developmental state of the Zebra mussel is categorized by three stages: veligers (larvae), settling juveniles, and adults. Veligers (microscopic zebra mussel larvae) are free-swimming, suspended in the water for one to three weeks, after which they begin searching for a hard surface to attach to and begin their adult life. Looking for zebra mussel veligers is difficult because they are not easily visible by the naked eye. Settled juvenile zebra mussels can be felt on smooth surfaces like boats and motors. An advanced zebra mussel infestation can cover a surface, even forming thick mats sometimes reaching very high densities. The density of juveniles was determined along the lake using three 15×15 cm settling plates. The top plate remained in the water for the entire sampling season (S - seasonal) to estimate seasonal accumulation. The middle and bottom plates are collected after specific periods (A –alternating ) of time denoted by “Lake Days”in the data files.The settling plates are placed under the microscope and all juveniles on the undersides of the plate are counted and densities are reported as juveniles/m^2.2002 年美国大学生数学建模竞赛MCM、ICM 试题2002 MCM A: Wind and WatersprayAn ornamental fountain in a large open plaza surrounded by buildings squirts water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The water-flow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area. Your task is to devise an algorithm which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.2002 MCM B: Airline OverbookingYou're all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook-that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations. Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.Consider the overbooking issue in light of the current situation: Less flights by airlines from point A to point B Heightened security at and around airports Passengers' fear Loss of billions of dollars in revenue by airlines to dateBuild a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the company's revenue is maximized. Insure that your model reflects the issues above, andconsider alternatives for handling “bumped”passengers. Additionally, write a short memorandum to the airline's CEO summarizing your findings and analysis.2002 ICM: Scrub LizardsThe Florida scrub lizard is a small, gray or gray-brown lizard that lives throughout upland sandy areas in the Central and Atlantic coast regions of Florida. The Florida Committee on Rare and Endangered Plants classified the scrub lizard as endangered.You will find a fact sheet on the Florida Scrub Lizard at/undergraduate/contests/mcm/contests/2002/problem s/icm2002data/scrublizard.pdfThe long-term survival of the Florida scrub lizard is dependent upon preservation of the proper spatial configuration and size of scrub habitat patches.Task 1: Discuss factors that may contribute to the loss of appropriate habitat for scrub lizards in Florida. What recommendations would you make to the state of Florida to preserve these habitats and discuss obstacles to the implementation of your recommendations?Task 2: Utilize the data provided in Table 1 to estimate the value for Fa (the average fecundity of adult lizards); Sj (the survivorship of juvenile lizards- between birth and the first reproductive season); and Sa (the average adult survivorship).Table 1Summary data for a cohort of scrub lizards captured and followed for 4 consecutive years. Hatchling lizards (age 0) do not produce eggs during the summer they are born. Average clutch size for all other females is proportional to body size according to the function y = 0.21*(SVL)-7.5, where y is the clutch size and SVL is the snout-to-vent length in mm.Year Age Total NumberLivingNumber of LivingFemalesAvg. Female Size(mm)1 0 972 495 30.32 1 180 92 45.83 2 20 11 55.84 3 2 2 56.0Task 3: It has been conjectured that the parameters Fa , Sj , and Sa , are related to the size and amount of open sandy area of a scrub patch. Utilize the data provided in Table 2 to develop functions that estimate Fa, Sj , and Sa for different patches. In addition, develop a function that estimates C, the carrying capacity of scrub lizards for a given patch.Table 2Summary data for 8 scrub patches including vital rate data for scrub lizards. Annual female fecundity (Fa), juvenile survivorship (Sj), and adult survivorship (Sa) are presented for each patch along with patch size and the amount of open sandy habitat.Patch Patch Size (ha) Sandy Habitat (ha) Fa Sj Sa Density (lizards/ha)a 11.31 4.80 5.6 0.12 0.06 58b 35.54 11.31 6.6 0.16 0.10 60c 141.76 51.55 9.5 0.17 0.13 75d 14.65 7.55 4.8 0.15 0.09 55e 63.24 20.12 9.7 0.17 0.11 80f 132.35 54.14 9.9 0.18 0.14 82g 8.46 1.67 5.5 0.11 0.05 40h 278.26 84.32 11.0 0.19 0.15 115Task 4: There are many animal studies that indicate that food, space, shelter, or even reproductive partners may be limited within a habitat patch causing individuals to migrate between patches. There is no conclusive evidence on why scrub lizards migrate. However, about 10 percent of juvenile lizards do migrate between patches and this immigration can influence the size of the population within a patch. Adult lizards apparently do not migrate. Utilizing the data provided in the histogram below estimate the probability of lizards surviving the migration between any two patches i and patch j.Table 3HistogramMigration data for juvenile lizards marked, released, and recaptured up to 6 months later. Surveys for recapture were conducted up to 750m from release sites.Task 5: Develop a model to estimate the overall population size of scrub lizards for the landscape given in Table 3. Also, determine which patches are suitable for occupation by scrub lizards and which patches would not support a viable population.Patch size and amount of open sandy habitat for a landscape of 29 patches located on the Avon Park Air Force Range. See:/undergraduate/contests/icm/2002problem/map.jpg for a map of the landscape.Patch Identification Patch Size (ha) Sandy Habitat (ha)1 13.66 5.382 32.74 11.913 1.39 0.234 2.28 0.765 7.03 3.626 14.47 4.387 2.52 1.998 5.87 2.499 22.27 8.44。
2003年全国大学生英语竞赛C类初赛真题及答案
2003 National English Contest for College Students（Preliminary）Part I Listening Comprehension（30 minutes，30 points）Section A Dialogues（10 points）Directions：In this section ，you will hear 10 short dialogues．At the end of each dialogue，a question will be asked about what was said．Both the dialogue and the question will be read only once．After each question there will be a pause．during the pause，you must read the four choices marked A，B，C and D，and decide which is the best answer．Then m ark the corresponding letter on the Answer Sheet with a single line through the center．1．A．A sales clerk．B．A police officer C．A tailor．D．A nurse．2．A．By train．B．She walks C．By car．D．By bus．3．A．Fish is the only dish left．B．Chicken is the only dish left．C．V egetarian meals are not offered．D．There aren't any vegetarian meals left．4．A．He starts work next weekend．B．He'll be away．C．He'll be in the mountains．D．He's moving to Florida．5．A．In an elevator．B．At a dress store．C．On the seventh floor．D．At a department store．6．A．They felt it was disorganized．B．They were pleased with its Asian content．C．They felt it lacked Asian content．D．They felt it ignored recent events．7．A．He doesn't have enough time．B．He doesn't have a watch．C．The library doesn't have the articles he wants．D．He can't find the library．8．A．He wants the woman to dine out with them．B．He wants to work tomorrow．C．He wants the woman to finish dinner first．D．He wants to pay for the dinner．9．A．Twice a day．B．Twice a week．C．Once a week．D．Daily．10．A．At two o'clock．B．At four o'clock．C．At three thirty D．At eight o'clock．Section B News Items（10 points）Directions：In this section，you will hear 10 pieces of short news from BBC or VOA．There will be a question following each piece of news．Write down the answer to each question in no more than 15 words．11._______________________________________12_______________________________________13._______________________________________14_______________________________________15_______________________________________16_______________________________________17_______________________________________18._______________________________________19_______________________________________20._______________________________________Section C Compound Dictation（10 points）Directions：In this section，you will hear a passage three times．When the passage is read for the first time，you should listen carefully for its general idea．Then listen to the passage again．When the passage is read for the second time，you are required to fill in the blanks numbered from 21 to 28 with the exact words you have just heard．For blanks numbered from 29 to 30，you are required to fill in the missing information．Y ou can either use the exact words you have just heard or write down the main points in your own words．Finally，when the passage is read for the third time，you should check what you have written and rewrite the correct answers on the Answer Sheet．Although general Motors and General Electric are large multinational companies with operations around the globe，there are numerous smaller companies that engage in international trade．Because 95percent of the world's population and two-thirds of its(21)_____ power are located outside the United States，it is important for American(22)_____to be present in foreign markets．However，before we explain the different methods by which a company may (23)_____in international trade，we might first consider some important (24)_____that U.S．companies often fail to study before they sell products in a foreign country．These factors are (25)_____with differences in language，in values and attitudes，and in political (26)_____．When (27)_____Coca-Cola into the Chinese market in 1920，the company used a group of Chinese symbols that，when spoken，sounded like Coca-Cola．However，when read，these symbols meant，“a female horse fattened with wax”．Upon reentering the Chinese market in the 1970s，Coca-Cola used a series of Chinese (28)_____that translates into“happiness in the mouth”．(29)_________________________．Culture is the total pattern of human behavior that is practiced by a particular group of people．(30)_________________________．Part II Vocabulary and Structure（15 minutes，30 points）Section A Multiple Choice（20 points）Directions：Questions 31-50 constitute a complete passage．There are 20blanks in the passage．For each blank there are four choices marked A，B，C and D．Choose the one that best completes the sentence．Then mark the corresponding letter on the Answer Sheet with a single line through the centre．31．Senior Metropolitan police officers tried to dismiss the Noting Hill race riots which raged for five nights over the August bank holiday in 1958 as the work of“ruffians ，both colored and white”hell-bent on hooliganism ，according to _____ official files．A．recent revealed B．newly released C．previous disclosing D．earlier exposing32．But police eyewitness reports in the secret papers_____ that they wereoverwhelmingly the work of a white working class mob out to get the“niggers”．A．contain B．convince C．consist D．confirm 33．The ferocity of the Noting Hill“racial riots”，as the press called them at the time，shocked Britain into_____ for the first time that it was not above the kind of racial conflict then being played out in the American deep south．A．realizing B．witnessing C．watching D．identifying 34．The carnival，which will_____ the streets of west London _____more than 1.5 million people this weekend，was started in 1959 as a direct response to the riots．A．crowd；of B．pour；for C．fill；with D．emerge；in35．While senior officers tried to play down the racial aspects of the riots，the internal Metropolitan police files released this month at the public record office confirm that the disturbances were overwhelmingly _____ by 300 to 400 strong“Keep Britain White” mobs ，many of them Teddy boys armed with iron bars ，butcher's knives and weighted leather belts，who went“nigger-hunting”among the West Indian residents of Noting Hill and Noting Dale．A．erupted B．commenced C．triggered D．inaugurated36．The first night left five black men _____ on the pavements of Noting Hill．A．lying unconscious B．there died C．feel faint D．serious hurt37．The battles raged over the bank holiday weekend as the black _____responded in kind with counterattacks by large groups of“men of color”similarly armed．A．column B．army C．brigade D．community 38．Thomas Williams was stopped by the police as he came out of Bluey's Club on Talbot Road，Noting Hill．He _____a piece of iron down his left trouser leg，a petrol bomb in his right pocket and a razor blade in his inside breast pocket：“I have to protect myself，”he told the arresting officer．A．found to have B．was found to have C．found having D．was found having39．The _____ files，which were sealed under the 75-year rule but have been released early，show that senior officers tried to convince the then home secretary，“Rab”Butler，that there was not a racial element to the rioting．A．forbidden B．confidential C．incredible D．strict 40．In his official report，Detective Sergeant M.Walters of the Notting Hill police said the national press had been wrong to portray the“widespread series of street disturbances”as“racial”riots：“Whereas there certainly was some _____ feeling between white and colored residents in this area，it is abundantly clear much of the trouble was caused by ruffians，both colored and white，who seized on this opportunity to indulge in hooliganism ．”A．ill B．Sick C．painful D．hurt41．But the police witness statements and private statistics _____ ．A．told differently B．interpreted in a different wayC．existed m any differences D．told a different story42．The Met com missioner was told that _____ the 108people who were charged with offences ranging from grievous bodily harm to affray and riot and possessing offensive weapons，72 were white and 36 were “colored”．A．for B．From C．of D．in43．It is popularly believed that the riot began on the night of Saturday，August 20，when a 400-strong crowd of white men，_____“Teds”，attacked houses occupied by West Indians．A．they are all B．many of them C．some were D．most of them belong to44．Among the _____ was Majbritt Morrison ，a young white Swedish bride of a Jamaican．A．offenders B．rioters C．victims D．residents45．She was pelted with stones，glass and wood，and _____ in the back with an iron bar as she tried to get home．A．bruised B．struck C．patted D．scratched 46．The internal police witness statements provide graphic evidence of the motives of the mobs—at one point crowds several thousand strong roamed the streets of Notting Hill，_____ homes and attacking any West Indian they could find．A．plunging into B．breaking into C．seeking for D．searching for47．PC Richard Bedford said he had seen a mob of 300 to 400 white people in Bramley Road _____：“We will kill all black bastards．Why don't you send them home？”A．shouting B．to cry C．utter D．announced48．PC Ian McQueen on the same night said he was told：“Mind your own _____，cops．Keep out of it．We will settle these niggers our way．We'll murder the bastards．” A．matters B．affair C．things D．business49．The disturbances continued night after night until they finally petered out on September 5．At the Old Bailey Judge Salmon later handed down exemplary _____ of four years each on nine white youths who had gone“nigger hunting”．A．decisions B．statements C．trials D．sentences50．While those dealt with by the courts were overwhelmingly white ，the large number of black people also arrested and the official _____ there had not been a racial motive ensured a legacy of black mistrust of the Metropolitan police that has never really been eradicated．A．persistence B．perseverance C．insistence D．instanceSection B Error Correction（10points）Directions：The following passage contains 9 errors．In each case only one word is involved．Y ou should proofread the passage on the Answer Sheet and correct it in the following way：EXAMPLEOne night，quite late，I was still awake in the room I am shared with 1. ammy husband．I was lying on my right side and can hear a child crying． 2. couldGetting up，I went ∧ see if our son was all right． 3. to He was sleeping soundly，breathing deeply and gently． 4. √ The ZipperWhatever did we do before the invention of the zipper？In 1893 the world's first zipper was produced in Chicago．Although the inventor claimed that it was a reliable fasteningfor clothing，this was not the case．The Chicago zipper sprang 51．______ open without warning，or jammed shut，and it swiftly lostpopularity．Twenty years ago a Swedish-born engineer called 52．______ Sundback solved the problem．He attached tiny cups to thebacks of the interlocked teeth，and this meant that the teeth 53．______ could be enmeshed more firmly and reliably．At first zippers were made of metal．They were heavy，andif they got stuck it was difficult to free．Then came nylon 54．______ zippers which were lighter and easier to use，and had smallerteeth．The fashion industry liked the new zippers far betterbecause they didn‟t distort the line of the garment or weighing 55．______ down light fabrics．They were also easier for the machiniststo fit into the garment．Meanwhile a new fastening agent made its appearance atthe end of the twenty century: velcro. V elcro is another product 56．______ made from nylon．Nylon is a very tough synthetic fibre firstdeveloped in the 1930s，and bearing a name to mind the wearer 57．______of the two places where it was developed：NY for New Y ork andLON for London．V elcro is made with very small nylon hooks onone side of the fastening which caught tiny looped whiskers on the 58．______ other side of the fastening．It is strong and durable．V elcro is used on clothing，luggages and footwear．It is quick 59．______and easy to fasten and unfasten，and has taken a large part ofthe zipper's share of the market．It is also used in ways a zippercannot be used—for instance as an easily changed fastening onplaster casts，and to hold furnishing fabrics in a position．60．______ Part III Situational Dialogues（5 minutes，10 points）Directions：Complete the following dialogues by choosing the best answer．Then mark the corresponding letter on the Answer Sheet with a single line through the centre．61．Rob：Hey Jill，you're looking great．Jill：Thanks，Rob．____________Rob：Well，you did it．How？Jill：I jog every morning，and I go to aerobics every other day．A．I bought this dress yesterday．Really smart．B．Y ou are looking fine too．C．I'm recovering my strength after the flu．D．My New Year's resolution was to get in shape．62．Bob：Hi Jane．How are you？Jane：____________I didn't sleep a wink last night．The people next door were making a lot of noise again till very late at night．A．I'm feeling a bit out of sorts this morning．B．Fine，thank you．And you？C．I slept like a log and didn't want to get out of bed．D．It seems a bit unusual，you know．63．Ann ：Aah！He's gorgeous！Look at those big，golden paws．When did you get him？Roger：Y esterday．____________Ann ：Oh，right．What kind is she？Roger：A Labrador．A．Susan's got a more beautiful one．B．What's up？C．It's a she actually．D．Isn't it right？64．Tina：Wow，look at all the things on sale．____________Andrew：Y es，look，this shirt is 50 ％off．Tina：And look at these shoes．They are 30 ％off the normal price．A．I'd like to buy a skirt．B．There are some real bargains．C．Are the prices reasonable？D．These shoes are the same as mine．65．Woman：Have you finished the packaging？Man ：____________Woman：Good．Because the truck will be coming soon，this is a rush job．A．Don't hurry m or I'll break the glass．B．Almost．I just have to wrap the glass and put it into boxes．C．No，I haven't．Why didn't you help me with it？D．Y es，I have．What else can I do for you？66．Customs Officer ：________________________Mrs．John son ：No，nothing at all．Customs Officer ：No perfume，alcohol or cigarettes？Mrs．John son ：Well，I have 200 cigarettes；that's all．A．Do you have anything in the bag，ma'am？B．Do you have anything to declare，ma'am？C．Do you want to buy something，ma'am？D．Is there anything I can do for you，ma'am？67．Linda：Hello．I'd like to send this package，please．Clerk：____________________________________Linda：First class．How long will that take？Clerk：About three days．A．How would you like to send it？B．Which class are you in？C．Where do you want to send it to？D．Which class is it in？68．Assistant：Can I help you？Colin ：Y es，it's about this sports shirt．I washed it the other day．The colour ran and it shrank．Assistant：Oh dear，I see．________________________Colin ：I'm afraid not．Assistant：I'm sorry，but I'm not allowed to change anything without a receipt．A．Did you buy it here？B．Would you want to change it？C．Do you have the receipt？D．Could you tell me who sold it to you？69．James：Could I have my bill，please？Can I pay by credit card or eurocheque？Receptionist：____________James：I'll pay by credit card，then．Receptionist：That's fine．I hope you enjoyed your stay here．A．Here's your bill．B．Sorry，we don't take credit card．C．Y ou can pay by eurocheque．D．Y es，we take both．70．Husband：When is our anniversary？Wife：________________________Husband：No，it's just that I bought these flowers for you and I was hoping today was the day．A．Hmm ．．．I can't remember either．Why？B．Hey，are these flowers for me？C．Who cares？Do you want to give me a surprise？D．Are you joking？Have you really forgotten again？Part IV Reading Comprehension（25 minutes，40 points）Section A Multiple Choice（10 points）Directions：There is one reading passage in this part．The passage is followed by 5 questions or unfinished statements．For each of them there are four choices marked A，B，C and D．You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the centre．Questions 71 to 75 are based on the following passage：Taking a peep at what's going on in your headCARL Filer，18，a star salesman at a B＆Q hardware store in the UK，was called up for promotion within one week of starting work．But，instead of being made supervisor，he was sacked—after his employers saw the results of his psychometric test．Y ou might think that anyone who answers that he“strongly disagrees he is an over-achiever is asking for trouble，but Mr Filer already thought he had proved himself more than capable．This year，nearly half of UK firms—46 percent—will use psychometric tests to select trainees，compared with just 17 percent in 2000，according to a report for GTI，a publisher of graduate career guides．These tests，which rate candidates‟ ability and gauge their personality，have been usedin the UK since the 1980s．But assorted studies have shown most people—graduates in particular—are wholly cynical about the idea of their personality being“measured．“People tend to see them as either too silly or too clever， says Clive Fletcher，professor of occupational psychology at University of London．“But all the evidence indicates the tests do have some value．The first personality test as we know it，was developed by the American army in 1917 to filter out weak recruits．But it was not until the 1980s that the tests became popular in Britain．With a rising number of graduates going for a decreasing number of jobs，organizations began to see psychometric testing as a cheap，reliable alternative to the expensive，time-consuming interview．But today the tests are becoming alarmingly sophisticated and are edging towards probing the“dark side：pathology and personality disorders．Increasingly，tests are being used to try to detect promising young graduates who may，later in life，fly off the rails（go crazy）；or to stop psychopaths（having mental disorder）getting recruited．In the future，interviewees could even be given a mouth swab to reveal the genetic and biological markers of personality．“We are heading for the era of genetic screening，”warns Carolyn Jones，of the Institute for Employment Rights．“I think these tests are very flawed．And there are other problems with the tests．For starters，it is possible to fake it—even the test producers agree on this．But they have made it as hard as possible．For example，look at whether you agree or disagree with the following two statements：“New ideas come easily to me and“I find generating new concepts difficult． How long did it take you to realize they both could mean the same thing？The main argument，however，is that the tests are invalid and cannot quantify（put a numerical value on）something as changeable as personality．The golden rule is then，that a psychometric test should never be used as the sole basis of selection，but should always be followed by interviews．71．Most people's attitude towards the psychometric test is ______．A．contemptuous B．favorable C．tolerant D．confounded72．Which of the following is one of the reasons why psychometric testing wins an advantage over interviews？A．It doesn't cost any money．B．It requires no equipment．C．It is time-saving．D．It can be done within seconds．73．Which of the following statements is the author's idea？A．Psychometric tests are defective．B．Psychometric tests should not be the only way to recruit promising young graduates．C．Psychometric tests are invalid and cannot quantify something changeable as personality．D．Psychometric tests are golden rules．74．The test producers make the tests very complicated to ______．A．avoid cheating B．improve genetic screeningC．find out the best ideas D．generate new concepts75．Which of the following is not true according to the passage？A．The American army developed the first personality test to screen out weak recruits．B．In the future，interviewers could give a mouth swab to reveal interviewees‟ symptoms．C．There are possibilities for starters to cheat in the psychometric tests．D．Interviews still play an important role in evaluating interviewees．Section B Short Answer Questions（30 points）Directions：In this part there are 3 passages with 15 questions or incomplete statements．Read the passages carefully．Then answer the questions in the fewest possible words（not exceeding 10 words）．Remember to rewrite the answers on the Answer Sheet．Questions 76 to 80 are based on the following passage：The 8 Steps of Social Invention1．Get ready to play．Like other types of creativity，social inventiveness flourishes when you begin thinking outside conventional boundaries．Charlie Girsch，a St．Paul，Minnesota-based creativity consultant，suggests that you start by playing with obviously absurd explanations for everyday events．“If traffic is slow，you'll be tem pted to say，…Hmm．Must be an accident up ahead．‟ Instead，try saying，…Must be a family of turtles crossing the highway‟or…I expect there's some kind of alien abduction going on．‟Y ou'll be amazed how soon you will be look ing at familiar problems in new ways．”Girsch's book，Fanning the Creative Spirit（Creativity Central，1999）has scores of other exercises for limbering up the inventive part of your brain．2．Generate a zillion far-fetched ideas．Concerned about the homeless in your neighborhood？Imagine a Homeless Parliament，a Homeless Circus，homeless families forming an orchestra，a homeless museum ．．．and on and on．Generate like mad with no regard for feasibility in order，as social invention pioneer Nicholas Albery advises，to“overcome e worthy-but-dull ideas．”Eventually the two or three best ideas will begin to stand out．3．Take your wildest idea and bring it down to earth．How about that Homeless Circus？Could it turn into a forum for homeless people to display their creative talents？A performance series about homelessness？A neighborhood carnival with the homeless as guests of honor？Y our flakiest idea may have a germ of brilliance that actually makes it more attractive，and thus more feasible （and fundable），than its worthy-but-dull cousins．4．Look for in venations that solve more than one problem．The Slow Food Movement，born in Italy，boosts local farmers and regional cuisine traditions and restaurateurs and the same time that it“feeds”our hunger for authentic tastes，healthy eating，and a more leisurely，saner style of life．5．Accentuate the positive．“A very common question that I get when I work with people in communities is…Whydoesn't anybody care about our problems？‟”notes M chael Patterson，a social inventor and activist in Massachusetts．“What a worthless question．…Why‟？questions are for philosophers．Ask…How‟？and…What‟？questions—they are a lot more practical．”For instance，Patterson asks，“What would you do if you knew you couldn't fail？”6．Give it a rest．Walk away from your favorite idea for a while，forget about it，let it sleep．With your conscious mind out of the way，your subconscious gets to fiddle with the concept for a while，and you just might have an unexpected insight or breakthrough．7．Practice“yes and”in stead of“yes but”．No matter how tempted you are to say“Y es，but this will be hard because，”or“Yes，but a million other people are doing this，”shift the conjunction to“and”and see what sort of positive refinement or change emerges．“Y es，and we could concentrate on immigrants．”“Y es，and we can make it open to all ages．”8．Get your idea into the world．This is the tough part．Y ou might seek out the help of activists who will take a shine to your ideas．Or become an organizer yourself．Paul Glove，a New Y ork social inventor，coun-sels：“If you have an idea you believe in，write a pamphlet with your phone number on it and post it in Laundromats and bookstores．If three people call you，have lunch with them and call yourselves an organization．If five people call，meet with them and issue a press release．” Presto，you're launched．76．To generate far-fetched ideas helps to ______．77．Michael Patterson wants us to come up with“How”？and“What”？instead of“Why”？questions because he considers they are more practical than ______．78．The pur pose to practice“yes and”instead of“yes but”is to make yourself more ______．79．According to the article，when one has difficulty developing his favorite idea，he should ______．80．One should not only generate far-fetched ideas but also ______ because the latter step is the nearest to reality．Questions 81 to 85 are based on the following passage：Thin Slice of TV Has Big MarketIt is too early to write an obituary for bulky picture tubes，which will remain the most affordable TV sets for years to come．But，analysts and industry executives insist that thin screens already have started to become the dominant format for TV sets in the digital era．Sharp price cuts have brought plasma sets and other thin，flat televisions out of high-end electronic boutiques and into thousands of mass-market outlets such as Cosco，a wholesale buying club in the US，best known for offering members bulk items and big discounts．The least expensive plasma sets still cost a hefty US ＄3，000or more ，yet sales are growing so rapidly that many manufacturers are racing to boost production．That increase，combined with expanding production capacity and improved technology，could push the price of plasma sets down by one-third next year，according to analyst Richard Doherty of Envisioneering Group，a US research firm．But manufacturers are not just competing with each other；they are also trying to fend off challenges from competing thin-screen technologies，such as liquid crystal displays（LCD）．The demand for thin screens is fuelled in part by the advent of DVDs and digital TV broadcasts，which offer more detailed pictures and more lifelike colors than conventional analog TV signals．To see the difference，consumers need a set that can pack more information onto the screen than their current TVs can．This sharpness is most vivid on screens that are 40inches diagonal or larger．At that size，however，traditional direct view and projection TVs are so bulky that many consumers have trouble finding a place for them at home．Hence the interest in thin screens—models slender and light enough to hang on a wall．The glass panels at the heart of plasma and LCD sets come mainly from about a dozen companies with factories in Japan，South Korea and，increasingly，China．About 800，000 plasma panels will be shipped this year around the world，analysts say．That is a tiny amount compared with the overall market for TVs，which was about 140 million sets last year．But，industry experts said 2003would be a“breakout year” or plasma because shipments should double．Helping drive the growth are new or expanded manufacturing facilities．For example，Japanese electronics giant NEC last year doubled the capacity of its Japanese factory—reaching 300，000to 400，000 plasma panels．And it plans to double it again in 2003，officials said．As competition has heated up during the last four years，prices have fallen more than 50 percent．According to“NPD Tec world”，the average price of a plasma display sold in the US dropped from US ＄12，700in January 1999 to US ＄6，100in October 2002．The best markets for plasma screens have been in Asia，and about half of the sets have gone to businesses instead of homes．LCD TVs carry a premium price—they can be 10 times as expensive as a comparable tube-driven television—that knocks them out of most buye rs‟ budgets．But LCD panels are quickly taking over the market for computer monitors，and the tens of millions of panels being produced for that segment will help push down prices for LCD TVs，analysts predicted．Sharp Electronics，for one，is betting heavily on LCDs．Its chairman，Toshiaki Urushisako，has predicted that Sharp will switch completely from conventional tube sets to LCD TVs in Japan by 2005．Flat-panel refers to wafer-thin（3 inches or less）TVs，whereas flat-screen may actually describe traditional cathode-ray-tube sets（CRTs）whose glass front lacks the distorting curve that TVs have had for 50 years．Be aware of two things：One，flat-panel technology may not be high-definition TV；for eventual HDTV reception，some of these sets will require a separate HD tuner．Two，some flat-panel TVs are just the panel and lack speakers and sometimes。
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Aviation Baggage Screening Strategies:To Screen or Not to Screen, that is the QuestionYou are an analysis team in the Office of Security Operations for the TransportationSecurity Administration (TSA), responsible for the Midwest Region of the United States.New laws will soon mandate 100% screening of all checked bags at the 429 passenger airports throughout the nation by explosive detection systems (EDSs; see Figure 1).EDSs use computed tomography (CT) technology to scan checked bags, similar to how CAT scans are used in hospitals. Using multiple x-rays of each bag, EDSs create three-dimensional images of a bag’s content, showing the density of each item. This information is utilized to determine whether an explosive device is present. Experimentation with EDSs indicate that each device is operational about 92% of the time and each device can examine between 160 and 210 bags per hour.The TSA has been actively purchasing EDSs and deploying them at airports throughoutthe nation. Given that these devices cost nearly $1 million each, weigh as much aseight tons, and cost several thousand dollars to install in an airport, determining the correct number of devices to deploy at each airport and how to best use them (once operational) are important problems.Currently, manufacturers are not able to produce the expected number of EDSs required to meet the federal mandate of 100% screening of checked luggage. Because of the limited number of EDS machines available, the Director of Airport Security for the Midwest Region (Mr. Sheldon) is not surprised that the TSA is requesting a detailed analysis on the estimated number of EDSs required at all airports. In addition, given the limited space and funds available for each airport, Mr. Sheldon believes that at some point a detailed analysis of emerging technologies will be needed. Promising technologies with more modest space and labor costs will emerge in the coming decade (e.g. x-ray diffraction; neutron-based detection; quadropole resonance; millimeter wave imaging; and microwave imaging).Task 1: You have been tasked by your Director, Mr. Sheldon, to develop a model to determine the number of EDSs required at two of the largest facilities in the region, Airports A & B, which are described in the Technical Information Sheet (TIS)–Appendix A. Carefully describe the assumptions that you make in designing the model, then use your model to recommend the number of EDSs required usingthe data provided in Table 1 of the TIS.Task 2: Prepare a short (one page) position paper to accompany your model that describes the security-related objectives of the airlines and the constraints that the airlines must work within for the sets of flights described in Table 1 of the TIS.Task 3: Since security screening takes time and might delay passengers,the airport managers at Airports A & B request that you develop a model that can help the airlines determine how to schedule the departure of different types of flights within the peak hour. Carefully describe all the assumptions that you make in designing the model and use your model to produce a schedule for the two airports with the data provided in Table 1.Task 4: Based on your analysis, what can you recommend to Mr. Sheldon and the airlines about checked baggage screening for the flights during the peak hours at your two airports?Task 5: Mr. Sheldon realizes that your work may have national impact and requests that you write a memo explaining how your models can be adapted to determine the number of EDSs and airline scheduling for all 193 airports in the Midwest Region. He will send the memo along with the models and the analysis to the Director of the Office of Security Operations (his boss) at the TSA and to all security directors of other airports in the region for their comment and possible implementation.Additional security measures associated with higher risks may require that up to 20% of the passengers will need to have all their checked bags screened through both an EDSand an explosive trace detection (ETD) machine, even though an EDS is 98.5% accurate in identifying explosive devices in checked bags. ETD machines use mass spectrometry technology to detect minute particles of explosive compounds. Each ETD machine costs $45,000 to purchase, however, the labor cost to operate the ETD machine is approximately 10 times that of the EDS. ETD can process 40 to 50 bags per hour; they are operational 98% of the time, and they are 99.7% accurate in identifying explosive materials on checked bags. At this time, ETD machines have not been federally certified, but Mr. Sheldon believes that they will soon be an integral part of national airport security systems.Task 6: Modify your EDS models to incorporate the use of ETD machines and determine how many ETD machines are needed for Airports A & B and if the schedules need to be changed. Since thisinformation may affect national level decisions, write a memo to the Director of Homeland Security and the Director of TSA with a technical analysis of this enhanced screening policy. Is the cost of such a policy justified in light of the value that it provides? Should the ETDs replace any of the EDS devices?Task 7: The Director of Homeland Security must also decide how to best fund future scientific research programs. Use your EDS/ETD model to examine the possible effect of changes in the device echnology, cost, accuracy, speed, and operational reliability. Include recommendations for the science, technology, engineering, and mathematics (STEM) research areas that will have the biggest impact on security system performance. Add your recommendation to the memo prepared in Task 7.Appendix ATechnical Information Sheet (TIS)Table 1Peak Hour Flight Departures for Airports A and BNote: On average, 2% of flights are cancelled each dayAlthough all the flights in Table 1 depart during a peak hour, their actual departure times are set by the airline when designing their flight schedule. A flight cannot depart until all its checked bags are screened using an EDS. The airline has the flexibility to schedule their flights during the peak hour to avoid undesirable flight delays dueto unscreened bags.Historical data indicates that flights with 85 or fewer seats typically fly with between 70% and 100% of their seats occupied. Flights with between 128 and 215 seats typically fly with between 60% and 100% of their seats occupied. Flights with 350 seats typically fly with between 50% and 100% of their seats occupied. Passengers typically arrive for their flight between forty-five minutes and two hours prior to their scheduled departure time. For flights other than “shuttle” service, airlines claim that 20% of the passengers do not check any luggage, 20% check one bag, and the remaining passengers check two bags.Preliminary estimates indicate that it will cost $100,000 to modify existing infrastructure(reinforced flooring, etc.) to install each EDS at Airport A and $80,000 to install each EDS at Airport B.Figure 1: Explosive Detection System (EDS)。