2012美赛题目中英文对照
美国数学学会中学生数学竞赛真题和答案解析2012AMC8-solutions
American Mathematics Competitions
28th Annual
AMC 8
American Mathematics Contest 8 Tuesday, November 13, 2012
This Solutions Pamphlet gives at least one solution for each problem on this year’s exam and shows that all the problems can be solved using material normally associated with the mathematics curriculum for students in eighth grade or below. These solutions are by no means the only ones possible, nor are they necessarily superior to others the reader may devise. We hope that teachers will share these solutions with their students. However, the publication, reproduction, or communication of the problems or solutions of the AMC 8 during the period when students are eligible to participate seriously jeopardizes the integrity of the results. Dissemination at any time via copier, telephone, email, internet or media of any type is a violation of the competition rules.
2012美赛B题参考资料
Typical Day on the Rogue RiverIf you've never taken a river trip before, it may seem daunting, but read through this description and we think you'll be ready to climb aboard!MorningImagine waking to the smell of coffee brewing or bacon cooking. For the early birds we have coffee, fruit and juice ready by 7 or 7:30 and full breakfast by 8. Breakfast normally consists of something hearty and traditional like pancakes and bacon, french toast and sausage, or scrambled eggs and Canadian bacon. We also have juice, fruit, yogurt and cereal for those who want to eat lighter.Breakfast is a good time to talk about what the day will be like, so people can pack accordingly. For example, if there is a long hike planned, you might put your hiking shoes in your day bag so they will available for the hike.We will have everything packed and ready to hit the river by 9:30 or 10. We don't usually care to be on the river earlier, because it is too cool before then to be getting wet. You will have a chance to read, chat, hike, fish or otherwise relax while the rafts are being loaded.On The WaterRogue River rafting is done in three types of boats.An oar raft is a large raft that is rowed by the guide. Your job here is to relax, watch the scenery go by, and hang on in the rapids.A paddle raft is a bit smaller. Everyone gets a paddle, and works as a team to maneuver the raft. The guide sits in back, steers and give commands.An inflatable kayak, or ducky is a one- or two- person boat. With no guide, it is the most challenging -and fun-way to run the river.Unless you know what kind of boat you want to be in, we recommend that you rotate between boats a few times each day, in order to get the whole river experience.Once on the river we will float for two to three hours before stopping for lunch. We may also stop to take a short hike to a waterfall or other spot of interest.Lunch normally takes about an hour, and gives people another chance to stretch their legs with a short hike or relax.After lunch we float another two to three hours, again perhaps with an off-river activity. We arrive in camp between 3 and 5, depending on the miles we cover and the stops we make.CampWhen we hit camp you will grab your bag and find a nice place to camp. Again, there is time to hike, swim, read, fish, relax or play games. Often a guide will organize a game or a hike to a place of special interest.We serve hors d'oeuvre around 7 and dinner around 8. It is too warm to eat earlier. Dinner is usually a social time when everyone gathers to eat and share their day's experiences. The lead guide usually takes advantage of the gathering to tell everyone what tomorrow will bring.Some folks tend to stay up late, talking, perhaps singing. Instruments are welcome if they are small enough to pack (no pianos, please) and add a great deal to any camp scene. Sometimes, especially on the last night, people put together skits, make up songs, and otherwise celebrate the completion of a wonderful trip together.Dates and PricesTrip ItineraryBefore You Go....Trip Details。
美国数学建模题目2001至2012翻译
2001年A题（一）Choosing a Bicycle Wheel选择自行车车轮有不同类型的车轮可以让自行车手们用在自己的自行车上。
两种基本的车轮类型是分别用金属辐条和实体圆盘组装而成（见图1）。
辐条车轮较轻，但实体车轮更符合空气动力学原理。
对于一场公路竞赛，实体车轮从来不会用作自行车的前轮但可以用作后轮。
职业自行车手们审视竞赛路线，并且请一位识文断字的人推断应该使用哪种车轮。
选择决定是根据沿途山丘的数量和陡度，天气，风速，竞赛本身以及其他考虑作出的。
你所喜爱的参赛队的教练希望准备妥当一个较好的系统，并且对于给定的竞赛路线已经向你的参赛队索取有助于确定宜用哪种车轮的信息。
这位教练需要明确的信息来帮助作出决定，而且已经要求你的参赛队完成下面列出的各项任务。
对于每项任务都假定，同样的辐条车轮将总是装在前面，而装在后面的车轮是可以选择的。
任务1. 提供一个给出风速的表格，在这种速度下实体后轮所需要的体能少于辐条后轮。
这个表格应当包括相应于从百分之零到百分之十增量为百分之一的不同公路陡度的风速。
（公路陡度定义为一座山丘的总升高除以公路长度。
如果把山丘看作一个三角形，它的陡度是指山脚处倾角的正弦。
）一位骑手以初始速度45kph从山脚出发，他的减速度与公路陡度成正比。
对于百分之五的陡度，骑上100米车速要下降8kph左右。
任务2. 提供一个例证，说明这个表格怎样用于一条时间试验路线。
任务3. 请判明这个表格是不是一件决定车轮配置的适当工具，并且关于如何作出这个决定提出其他建议。
MCM2001B题Escaping a Hurricane's Wrath逃避飓风怒吼(一场恶风…)1999年，在Floyd飓风预报登陆之前，撤离南卡罗来纳州沿海地区的行动导致一场永垂青史的交通拥塞。
车水马龙停滞在州际公路I-26上，那是内陆上从Charleston通往该州中心Columbia相对安全处所的主要干线。
正常时轻松的两个小时驱车路要用上18个小时才能开到头。
2012大学生英语竞赛答案National English Contest for College Students (Level C - Preliminary)
2012大学生英语竞赛答案(Level C)权威发布2012 National English Contest for College Students (Level C - Preliminary) 参考答案及作文评分标准Part I Listening Comprehension (30 marks)Section A (5 marks)1—5 CBBAC Section B (10 marks)6—10 BAACB 11—15 CABCBSection C (5 marks)16—20 ACABA Section D (10 marks)21. disruption 22. air pressure 23. slow down 24.immune system 25.stimulates26. bear in mind 27. circulation 28. decreases 29. Consult 30. side effectsPart II Vocabulary and Structure (15 marks)31—35 BDABC 36—40 BDDAB 41—45 CADBCPart III Cloze (10 marks)46. likelihood 47. fortune 48. take 49. with 50. knowing51. dozens 52. least 53. burning 54.easy/simple 55. realizePart IV Reading Comprehension (40 marks) Section A (10 marks)56. describe 57. opportunity 58. honeymoon 59. transition 60. characterized Section B (10 marks)61. F 62. T 63. T64. The special depth that true friendship is about.65. They need to get over fear of confrontation and rejection. Section C (10 marks)66. High fatality 67. thrill seeking; risk taking 68. pushing out personal boundaries 69. C 70. A Section D (10 marks)71.“Linguistic”intelligence and“Logical mathematical”intelligence.72. The ability to gauge ones own mood, feelings and mental states, and the ability to gauge it in others and use the information.73.“Logical mathematical”intelligence and the“bodily-kinesthetic”intelligence.74. 他的观点引发了激烈的讨论，应如何定义智力。
2012年美国大学生数学建模竞赛B题特等奖文章翻译
We develop a model to schedule trips down the Big Long River. The goalComputing Along the Big Long RiverChip JacksonLucas BourneTravis PetersWesternWashington UniversityBellingham,WAAdvisor: Edoh Y. AmiranAbstractis to optimally plan boat trips of varying duration and propulsion so as tomaximize the number of trips over the six-month season.We model the process by which groups travel from campsite to campsite.Subject to the given constraints, our algorithm outputs the optimal dailyschedule for each group on the river. By studying the algorithm’s long-termbehavior, we can compute a maximum number of trips, which we define asthe river’s carrying capacity.We apply our algorithm to a case study of the Grand Canyon, which hasmany attributes in common with the Big Long River.Finally, we examine the carrying capacity’s sensitivity to changes in thedistribution of propulsion methods, distribution of trip duration, and thenumber of campsites on the river.IntroductionWe address scheduling recreational trips down the Big Long River so asto maximize the number of trips. From First Launch to Final Exit (225 mi),participants take either an oar-powered rubber raft or a motorized boat.Trips last between 6 and 18 nights, with participants camping at designatedcampsites along the river. To ensure an authentic wilderness experience,at most one group at a time may occupy a campsite. This constraint limitsthe number of possible trips during the park’s six-month season.We model the situation and then compare our results to rivers withsimilar attributes, thus verifying that our approach yields desirable results.Our model is easily adaptable to find optimal trip schedules for riversof varying length, numbers of campsites, trip durations, and boat speeds.No two groups can occupy the same campsite at the same time.Campsites are distributed uniformly along the river.Trips are scheduled during a six-month period of the year.Group trips range from 6 to 18 nights.Motorized boats travel 8 mph on average.Oar-powered rubber rafts travel 4 mph on average.There are only two types of boats: oar-powered rubber rafts and motorizedTrips begin at First Launch and end at Final Exit, 225 miles downstream.*simulates river-trip scheduling as a function of a distribution of trip*can be applied to real-world rivers with similar attributes (i.e., the Grand*is flexible enough to simulate a wide range of feasible inputs; andWhat is the carrying capacity of the riverÿhe maximum number ofHow many new groups can start a river trip on any given day?How should trips of varying length and propulsion be scheduled toDefining the Problemmaximize the number of trips possible over a six-month season?groups that can be sent down the river during its six-month season?Model OverviewWe design a model thatCanyon);lengths (either 6, 12, or 18 days), a varying distribution of propulsionspeeds, and a varying number of campsites.The model predicts the number of trips over a six-month season. It alsoanswers questions about the carrying capacity of the river, advantageousdistributions of propulsion speeds and trip lengths, how many groups canstart a river trip each day, and how to schedule trips.ConstraintsThe problem specifies the following constraints:boats.AssumptionsWe can prescribe the ratio of oar-powered river rafts to motorized boats that go onto the river each day.There can be problems if too many oar-powered boats are launched with short trip lengths.The duration of a trip is either 12 days or 18 days for oar-powered rafts, and either 6 days or 12 days for motorized boats.This simplification still allows our model to produce meaningful results while letting us compare the effect of varying trip lengths.There can only be one group per campsite per night.This agrees with the desires of the river manager.Each day, a group can only move downstream or remain in its current campsiteÿt cannot move back upstream.This restricts the flow of groups to a single direction, greatly simplifying how we can move groups from campsite to campsite.Groups can travel only between 8 a.m. and 6 p.m., a maximum of 9hours of travel per day (one hour is subtracted for breaks/lunch/etc.).This implies that per day, oar-powered rafts can travel at most 36 miles, and motorized boats at most 72 miles. This assumption allows us to determine which groups can reasonably reach a given campsite.Groups never travel farther than the distance that they can feasibly travelin a single day: 36 miles per day for oar-powered rafts and 72 miles per day for motorized boats.We ignore variables that could influence maximum daily travel distance, such as weather and river conditions.There is no way of accurately including these in the model.Campsites are distributed uniformly so that the distance between campsites is the length of the river divided by the number of campsites.We can thus represent the river as an array of equally-spaced campsites.A group must reach the end of the river on the final day of its trip:A group will not leave the river early even if able to.A group will not have a finish date past the desired trip length.This assumption fits what we believe is an important standard for theriver manager and for the quality of the trips.MethodsWe define some terms and phrases:Open campsite: Acampsite is open if there is no groupcurrently occupying it: Campsite cn is open if no group gi is assigned to cn.Moving to an open campsite: For a group gi, its campsite cn, moving to some other open campsite cm ÿ= cn is equivalent to assigning gi to the new campsite. Since a group can move only downstream, or remain at their current campsite, we must have m ÿ n.Waitlist: The waitlist for a given day is composed of the groups that are not yet on the river but will start their trip on the day when their ranking onthe waitlist and their ability to reach a campsite c includes them in theset Gc of groups that can reach campsite c, and the groups are deemed “the highest priority.” Waitlisted groups are initialized with a current campsite value of c0 (the zeroth campsite), and are assumed to have priority P = 1 until they are moved from the waitlist onto the river.Off the River: We consider the first space off of the river to be the “final campsite” cfinal, and it is always an open campsite (so that any number of groups can be assigned to it. This is consistent with the understanding that any number of groups can move off of the river in a single day.The Farthest Empty CampsiteOurscheduling algorithm uses an array as the data structure to represent the river, with each element of the array being a campsite. The algorithm begins each day by finding the open campsite c that is farthest down the river, then generates a set Gc of all groups that could potentially reach c that night. Thus,Gc = {gi | li +mi . c},where li is the groupÿs current location and mi is the maximum distance that the group can travel in one day.. The requirement that mi + li . c specifies that group gi must be able to reach campsite c in one day.. Gc can consist of groups on the river and groups on the waitlist.. If Gc = ., then we move to the next farthest empty campsite.located upstream, closer to the start of the river. The algorithm always runs from the end of the river up towards the start of the river.. IfGc ÿ= ., then the algorithm attempts tomovethe groupwith the highest priority to campsite c.The scheduling algorithm continues in this fashion until the farthestempty campsite is the zeroth campsite c0. At this point, every group that was able to move on the river that day has been moved to a campsite, and we start the algorithm again to simulate the next day.PriorityOnce a set Gc has been formed for a specific campsite c, the algorithm must decide which group to move to that campsite. The priority Pi is a measure of how far ahead or behind schedule group gi is:. Pi > 1: group gi is behind schedule;. Pi < 1: group gi is ahead of schedule;. Pi = 1: group gi is precisely on schedule.We attempt to move the group with the highest priority into c.Some examples of situations that arise, and how priority is used to resolve them, are outlined in Figures 1 and 2.Priorities and Other ConsiderationsOur algorithm always tries to move the group that is the most behind schedule, to try to ensure that each group is camped on the river for aFigure 1. The scheduling algorithm has found that the farthest open campsite is Campsite 6 and Groups A, B, and C can feasibly reach it. Group B has the highest priority, so we move Group B to Campsite 6.Figure 2. As the scheduling algorithm progresses past Campsite 6, it finds that the next farthest open campsite is Campsite 5. The algorithm has calculated that Groups A and C can feasibly reach it; since PA > PC, Group A is moved to Campsite 5.number of nights equal to its predetermined trip length. However, in someinstances it may not be ideal to move the group with highest priority tothe farthest feasible open campsite. Such is the case if the group with thehighest priority is ahead of schedule (P <1).We provide the following rules for handling group priorities:?If gi is behind schedule, i.e. Pi > 1, then move gi to c, its farthest reachableopen campsite.?If gi is ahead of schedule, i.e. Pi < 1, then calculate diai, the number ofnights that the group has already been on the river times the averagedistance per day that the group should travel to be on schedule. If theresult is greater than or equal (in miles) to the location of campsite c, thenmove gi to c. Doing so amounts to moving gi only in such a way that itis no longer ahead of schedule.?Regardless of Pi, if the chosen c = cfinal, then do not move gi unless ti =di. This feature ensures that giÿ trip will not end before its designatedend date.Theonecasewhere a groupÿ priority is disregardedisshownin Figure 3.Scheduling SimulationWe now demonstrate how our model could be used to schedule rivertrips.In the following example, we assume 50 campsites along the 225-mileriver, and we introduce 4 groups to the river each day. We project the tripFigure 3. The farthest open campsite is the campsite off the river. The algorithm finds that GroupD could move there, but GroupD has tD > dD.that is, GroupD is supposed to be on the river for12 nights but so far has spent only 11.so Group D remains on the river, at some campsite between 171 and 224 inclusive.schedules of the four specific groups that we introduce to the river on day25. We choose a midseason day to demonstrate our modelÿs stability overtime. The characteristics of the four groups are:. g1: motorized, t1 = 6;. g2: oar-powered, t2 = 18;. g3: motorized, t3 = 12;. g4: oar-powered, t4 = 12.Figure 5 shows each groupÿs campsite number and priority value foreach night spent on the river. For instance, the column labeled g2 givescampsite numbers for each of the nights of g2ÿs trip. We find that each giis off the river after spending exactly ti nights camping, and that P ÿ 1as di ÿ ti, showing that as time passes our algorithm attempts to get (andkeep) groups on schedule. Figures 6 and 7 display our results graphically.These findings are consistent with the intention of our method; we see inthis small-scale simulation that our algorithm produces desirable results.Case StudyThe Grand CanyonThe Grand Canyon is an ideal case study for our model, since it sharesmany characteristics with the Big Long River. The Canyonÿs primary riverrafting stretch is 226 miles, it has 235 campsites, and it is open approximatelysix months of the year. It allows tourists to travel by motorized boat or byoar-powered river raft for a maximum of 12 or 18 days, respectively [Jalbertet al. 2006].Using the parameters of the Grand Canyon, we test our model by runninga number of simulations. We alter the number of groups placed on thewater each day, attempting to find the carrying capacity for the river.theFigure 7. Priority values of groups over the course of each trip. Values converge to P = 1 due to the algorithm’s attempt to keep groups on schedule.maximumnumber of possible trips over a six-month season. The main constraintis that each trip must last the group’s planned trip duration. Duringits summer season, the Grand Canyon typically places six new groups onthe water each day [Jalbert et al. 2006], so we use this value for our first simulation.In each simulation, we use an equal number of motorized boatsand oar-powered rafts, along with an equal distribution of trip lengths.Our model predicts the number of groups that make it off the river(completed trips), how many trips arrive past their desired end date (latetrips), and the number of groups that did not make it off the waitlist (totalleft on waitlist). These values change as we vary the number of new groupsplaced on the water each day (groups/day).Table 1 indicates that a maximum of 18 groups can be sent down theriver each day. Over the course of the six-month season, this amounts to nearly 3,000 trips. Increasing groups/day above 18 is likely to cause latetrips (some groups are still on the river when our simulation ends) and long waitlists. In Simulation 1, we send 1,080 groups down river (6 groups/day?80 days) but only 996 groups make it off; the other groups began near the end of the six-month period and did not reach the end of their trip beforethe end of the season. These groups have negligible impact on our results and we ignore them.Sensitivity Analysis of Carrying CapacityManagers of the Big Long River are faced with a similar task to that of the managers of the Grand Canyon. Therefore, by finding an optimal solutionfor the Grand Canyon, we may also have found an optimal solution forthe Big Long River. However, this optimal solution is based on two key assumptions:?Each day, we put approximately the same number of groups onto theriver; and?the river has about one campsite per mile.We can make these assumptions for the Grand Canyon because they are true for the Grand Canyon, but we do not know if they are true for the Big Long River.To deal with these unknowns,wecreate Table 3. Its values are generatedby fixing the number Y of campsites on the river and the ratio R of oarpowered rafts to motorized boats launched each day, and then increasingthe number of trips added to the river each day until the river reaches peak carrying capacity.The peak carrying capacities in Table 3 can be visualized as points ina three-dimensional space, and we can find a best-fit surface that passes (nearly) through the data points. This best-fit surface allows us to estimatethe peak carrying capacity M of the river for interpolated values. Essentially, it givesM as a function of Y and R and shows how sensitiveM is tochanges in Y and/or R. Figure 7 is a contour diagram of this surface.The ridge along the vertical line R = 1 : 1 predicts that for any givenvalue of Y between 100 and 300, the river will have an optimal value ofM when R = 1 : 1. Unfortunately, the formula for this best-fit surface is rather complex, and it doesn’t do an accurate job of extrapolating beyond the data of Table 3; so it is not a particularly useful tool for the peak carrying capacity for other values ofR. The best method to predict the peak carrying capacity is just to use our scheduling algorithm.Sensitivity Analysis of Carrying Capacity re R and DWe have treatedM as a function ofR and Y , but it is still unknown to us how M is affected by the mix of trip durations of groups on the river (D).For example, if we scheduled trips of either 6 or 12 days, how would this affect M? The river managers want to know what mix of trips of varying duration and speed will utilize the river in the best way possible.We use our scheduling algorithm to attempt to answer this question.We fix the number of campsites at 200 and determine the peak carrying capacity for values of R andD. The results of this simulation are displayed in Table 4.Table 4 is intended to address the question of what mix of trip durations and speeds will yield a maximum carrying capacity. For example: If the river managers are currently scheduling trips of length?6, 12, or 18: Capacity could be increased either by increasing R to be closer to 1:1 or by decreasing D to be closer to ? or 12.?12 or 18: Decrease D to be closer to ? or 12.?6 or 12: Increase R to be closer to 4:1.ConclusionThe river managers have asked how many more trips can be added tothe Big Long Riverÿ season. Without knowing the specifics ofhowthe river is currently being managed, we cannot give an exact answer. However, by applying our modelto a study of the GrandCanyon,wefound results which could be extrapolated to the context of the Big Long River. Specifically, the managers of the Big Long River could add approximately (3,000 - X) groups to the rafting season, where X is the current number of trips and 3,000 is the capacity predicted by our scheduling algorithm. Additionally, we modeled how certain variables are related to each other; M, D, R, and Y . River managers could refer to our figures and tables to see how they could change their current values of D, R, and Y to achieve a greater carrying capacity for the Big Long River.We also addressed scheduling campsite placement for groups moving down the Big Long River through an algorithm which uses priority values to move groups downstream in an orderly manner.Limitations and Error AnalysisCarrying Capacity OverestimationOur model has several limitations. It assumes that the capacity of theriver is constrained only by the number of campsites, the trip durations,and the transportation methods. We maximize the river’s carrying capacity, even if this means that nearly every campsite is occupied each night.This may not be ideal, potentially leading to congestion or environmental degradation of the river. Because of this, our model may overestimate the maximum number of trips possible over long periods of time. Environmental ConcernsOur case study of the Grand Canyon is evidence that our model omits variables. We are confident that the Grand Canyon could provide enough campsites for 3,000 trips over a six-month period, as predicted by our algorithm. However, since the actual figure is around 1,000 trips [Jalbert et al.2006], the error is likely due to factors outside of campsite capacity, perhaps environmental concerns.Neglect of River SpeedAnother variable that our model ignores is the speed of the river. Riverspeed increases with the depth and slope of the river channel, makingour assumption of constant maximum daily travel distance impossible [Wikipedia 2012]. When a river experiences high flow, river speeds can double, and entire campsites can end up under water [National Park Service 2008]. Again, the results of our model don’t reflect these issues. ReferencesC.U. Boulder Dept. of Applied Mathematics. n.d. Fitting a surface to scatteredx-y-z data points. /computing/Mathematica/Fit/ .Jalbert, Linda, Lenore Grover-Bullington, and Lori Crystal, et al. 2006. Colorado River management plan. 2006./grca/parkmgmt/upload/CRMPIF_s.pdf .National Park Service. 2008. Grand Canyon National Park. High flowriver permit information. /grca/naturescience/high_flow2008-permit.htm .Sullivan, Steve. 2011. Grand Canyon River Statistics Calendar Year 2010./grca/planyourvisit/upload/Calendar_Year_2010_River_Statistics.pdf .Wikipedia. 2012. River. /wiki/River .Memo to Managers of the Big Long RiverIn response to your questions regarding trip scheduling and river capacity,we are writing to inform you of our findings.Our primary accomplishment is the development of a scheduling algorithm.If implemented at Big Long River, it could advise park rangerson how to optimally schedule trips of varying length and propulsion. Theoptimal schedule will maximize the number of trips possible over the sixmonth season.Our algorithm is flexible, taking a variety of different inputs. Theseinclude the number and availability of campsites, and parameters associatedwith each tour group. Given the necessary inputs, we can output adaily schedule. In essence, our algorithm does this by using the state of theriver from the previous day. Schedules consist of campsite assignments foreach group on the river, as well those waiting to begin their trip. Given knowledge of future waitlists, our algorithm can output schedules monthsin advance, allowing managementto schedule the precise campsite locationof any group on any future date.Sparing you the mathematical details, allow us to say simply that ouralgorithm uses a priority system. It prioritizes groups who are behindschedule by allowing them to move to further campsites, and holds backgroups who are ahead of schedule. In this way, it ensures that all trips willbe completed in precisely the length of time the passenger had planned for.But scheduling is only part of what our algorithm can do. It can alsocompute a maximum number of possible trips over the six-month season.We call this the carrying capacity of the river. If we find we are below ourcarrying capacity, our algorithm can tell us how many more groups wecould be adding to the water each day. Conversely, if we are experiencingriver congestion, we can determine how many fewer groups we should beadding each day to get things running smoothly again.An interesting finding of our algorithm is how the ratio of oar-poweredriver rafts to motorized boats affects the number of trips we can send downstream. When dealing with an even distribution of trip durations (from 6 to18 days), we recommend a 1:1 ratio to maximize the river’s carrying capacity.If the distribution is skewed towards shorter trip durations, then ourmodel predicts that increasing towards a 4:1 ratio will cause the carryingcapacity to increase. If the distribution is skewed the opposite way, towards longer trip durations, then the carrying capacity of the river will always beless than in the previous two cases—so this is not recommended.Our algorithm has been thoroughly tested, and we believe that it isa powerful tool for determining the river’s carrying capacity, optimizing daily schedules, and ensuring that people will be able to complete their trip as planned while enjoying a true wilderness experience.Sincerely yours,Team 13955。
2012美国大学生数学建模题目(英文原版加中文翻译)
2012 MCM ProblemsPROBLEM A:The Leaves of a Tree"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical mode l to describe and classify leaves. Consider and answer the following:• Why do leaves have the various shapes that they have?• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.“多少钱树的叶子有多重？”怎么可能估计的叶子（或树为此事的任何其他部分）的实际重量？会如何分类的叶子吗？建立了一个数学模型来描述和分类的叶子。
精编2012年全国大学生英语竞赛初赛真题+答案
2012 National English Contest forCollege Students(Level C – Preliminary)(总分：150分时间：120分钟)Part I listening Comprehension (30 marks)Section A (5 marks)In this section, you will hear five short conversations. Each conversation will be read only once .After each conversation, there will be a twenty-second pause. During the pause, read the question and the three choices marked A, B and C, and decide which is the best answer .Then mark the corresponding letter on the answer sheet with a single line through the centre.1.What does the man say we can do to deal with oil crisis?A. To make full use of oil.B. To use as little oil as possibleC. To find alternative energy.2. Where does this conversation most probably take place?A. In an insurance company.B. In a bank.C. In a supermarket.3. According to the man, who is going to take over the position they are talking about?A. Janice.B. Someone else.C. Meryl.4. What does the woman say about the man’s report for the meeting?A. He has to get it ready before tomorrow noon.B. He has done well enough.C. He has enough time to prepare it.5. How many people will be on the earth by the year 2020 according to the professor?A. Some 5.8 billion.B. Nearly 7 billion.C. Over 8.5 billion.Section B (10 marks)In this section, you will hear two long conversations. Each conversation will be read only once. At the end of each conversation, there will be a one-minute pause. During the pause, read the questions and the three choices marked A, Band C, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the centreConversation One6. What’s the main job of Simon’s organization?A. They send out radio signals to communicate with other planets.B. They look for life and intelligence on other planets.C. They study stars that have planets orbiting around them.7. Why does the organization search for radio signals from space?A. Their presence may prove the existence of aliens.B. They may help scientists find out how the universe started.C. They convey messages about life on the earth.8. Does Simon believe those stories about aliens visiting our planet?A. No, he doesn’t believe them at all.B. Yes, he does believe those stories because of his study.C. Yes, he believes them although he has no evidence.9. Which of the following factor is considered to be important in forming life according to the passage?A. Gravity.B. Minerals.C. Water.10. When did the “big bang” occur?A. No one knows.B. 12 billion years ago.C. 20 billion year ago.Conversation Two11. Why did Bob make the news last month?A. Because he criticized traditional jobsB. Because he earned a lot of money.C. Because he tried new strategies in finding a job.12. In which way do the bestsellers like “The Brand Called You” and “The Personal BrandingPhenomenon” help people?A. They advise people to promote themselves as brands.B. They teach people how to be a perfect partner.C. They give people tips for job interview.13. When did Bob come up with the idea of using the internet to find a job?A. Ten years ago when he was a college student.B. When he began to do research between jobs.C. After he launched the campaign “Give Bob a Job”.14. What was the purpose of Bob’s making the video?A. To fulfill his ambition as a director.B. To sell his products like Teddy bears and T-shirts.C. To advertise his skills and talents.15. How can the internet help Bob in his job search exactly?A. By helping him make friends.B. By passing on the video he made.C. By providing job information for him.Section C (5 marks)In this section, you will hear five short news items. After each item, which will be read only once, there will be a pause. During the pause, read the question and the three choices marked A, B and C, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the centre.16. How many troops are going to withdraw from Afghanistan by the end of next year?A. 43,000.B. 10,000.C. 33,000.17. What is the finding of the study?A. Low-calorie foods may lead to more weight.B. High-calorie foods may lead to more weight.C. High-calorie foods may lead to less weight.18. What do the conflicting reports show about radiation?A. The radiation level given by Tokyo Electric is much smaller than that given by othertests.B. The radiation level given by other tests is smaller than that given by Tokyo Electric.C. The radiation level is close to 10,000 times the normal level.19. Why are Caribbean Service and Europe Today shut down by BBC?A. Because of their outdated services.B. Because of cuts in government funding.C. Because of lack of target audience.20. What’s the cause of demonstrations in cities and towns across Syria?A. They are calling for more freedom.B. Workers demand higher pay.C. Some thirty people were killed by the police.Section D (10 marks)In this section, you will hear a short passage. There are 10 missing words or phrases. Fill in the blanks with the exact words or phrases you hear. The passage will be read twice. Remember to write the answers on the answer sheet.Recovery from jetlag can take as long as a day for every time zone crossed. So if you’re flying east-west for your holiday or on business, it is likely to mean a few days of feeling tired or even unwell.Jetlag is the (21)__________ of the body’s natural cycle and some factors make it worse. The artificial atmosphere inside a plane can affect the body in a number of ways and add to the effects of jetlag.Exercising before flights helps to offset the effects on the body of reduced (22) _________, and aerobic exercise afterwards helps to reoxygenate it. Drink plenty of water. Children may need more. Drinking carrot juice before flying overcomes oxygen deficiency.Eat light, frequent meals. Heavy meals (23) __________ the blood circulation, which can lead to dizziness and fainting. For two weeks before you fly, eat plenty of food containing vitamins A and E; they will build up your (24) __________ and help to keep you fit. Sleep as much as you can before the flight and on it. On board, wear earplugs and eye pads because darkness (25) __________ secretion of the hormones that enhance sleep.Avoid alcohol, which restricts the brain’s oxygen intake. Like tea and coffee, alcohol increases the dehydration effect of flying. If you need to drink to relax, (26) __________ that the cabin environment intensifies the effect of alcohol.Wear loose, comfortable, warm clothes and limber up during flight. Sitting down for several hours slows down the (27) _________, leading to local stiffness, cramps and dizziness. Re-adjustto local time as soon as you can. Bright light helps the body stay alert, so if you are going somewhere sunny, stay outside.Do not smoke before or during the flight since smoking (28) ___________ the blood oxygen level. If you need to calm your nerves, try aromatherapy oils which have a sedative effect.(29) _________ your doctor before flying if you are on medication. The effects of some drugs are strengthened at high altitudes and some may produce (30) _________.Part II Vocabulary and Structure (15 marks)There are 15 incomplete sentences in this section. 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. What we all work for is to free ________ time for the things we really want to do.A. offB. upC. asideD. in32. You _________ his words seriously. He was talking nonsense.A. won’t takeB. may not takeC. mustn’t have takenD. needn’t have taken33. Never hesitate to _________ the first opportunity that comes along.A. seizeB. drawC. who; thatD. obtain34. His mother ________ hated city life longed to return to the village in _______she grew up.A. that; whereB. who; whichC. who; thatD. who; where35. All things _______, I think I’d better take your advice.A. consideringB. to be consideredC. consideredD. have been considered36. Twelve European countries ________ over to the Euro on January 1st, 2002.A. transformedB. switchedC. reversedD. altered37. She isn’t anything ________ unpleasant as people say she is.A. as likeB. likeC. asD. like as38. Stop complaining. You really ________ my nerves.A. get downB. get alongC. get offD. get on39. There wasn’t _______ truth in what he said.A. a grain ofB. a ray ofC. a point ofD. a drop of40. ________ for my savings, I wouldn’t be able to survive these miserable days.A. Was it notB. Were it notC. Had it been notD. Hadn’t it been41. There was a power cut this morning. ________, I couldn’t do anything with my computer.A. SupposedlyB. PresumablyC. ConsequentlyD. Essentially42. Alarm clocks needlessly wake ______ households. I want to design something targeted atthe individual sleeper.A. wholeB. totalC. fullD. high43. _______ both parties agree on these issues will a contract be signed soon.A. If onlyB. UnlessC. ShouldD. Only if44.—I’ve run out of cash. Could you lend me a few pounds this evening?—_____ I’ll just have to find time to get to the bank and make a withdrawal.A.I can lend you some now.B. I’m not sure I’ve got any either.C. Sorry, I haven’t got a penny in my account.D. My credit card must be left home.45. —We’re all going to the New Skyline Restaurant for our end-of-year get-together. Canwe count you in?—Oh, thanks, Sara, but _____A. I didn’t find you then.B. I’ve been to the restaurant once.C. I’ll pass this time.D. I’ll meet you there at 5:00.Part III Cloze (10 marks)Read the following passage and fill in each blank with one word. Choose the correct word in one of the following three ways: according to the context, by using the correct form of the given word, or by using the given letters of the word. Remember to write the answers on the answer sheet.Did you know that for every 20,000 novels written, only one gets published? So the (46) ____ (likely) that I’ll ever fulfill my ambition of becoming a professional mystery writer doesn’t seem very high. But the prospect of turning my lifelong passion into my livelihood and achieving fame and (47) for ______ at the same time is just too exciting for me to be put off by dull statistics.So what does it (48) t_______ to become a writer? Reading is important—all writers need to research their genre thoroughly to familiarize themselves (49) _______ its codes and conventions. My bookshelves at home are stacked with the novels of all the great mystery writers, which I’ve read and in many cases, re-read, despite (50) _______ (know) all the time “who’d done it”.Of course, being a writer requires imagination. You have to develop your own personal style rather than simply copy the work of “the greats”. I’ve turned out (51) d________ of short crime stories for my university student magazine—some have been published, some not, but I’ve always aimed to produce original and imaginative material.Last but not (52) ________, successful writers possess enormous self-discipline. I’ve often sacrificed my social life in order to devote the necessary time and effort to producing a good quality story. And more than once that has meant (53) _______ the midnight oil.We’ve got a novel inside us. Getting it out in anywhere near publishable form is no (54) ______ task, but with imagination and determination, and the help of an expert on “master class”, who could possibly fail to (55) re_______ their ambition?Part IV Reading Comprehension (40 marks)Read the following passages. Each passage is followed by several questions. Respond to the questions using information from the passage. Remember to write the answers on the answer sheet.Section A (10 marks)Questions 56—60 are based on the following passage.The term culture shock was introduced forthe first time in 1958 to describe the anxietyproduced when a person moves to a completelynew environment. This term expresses thefeeling of not knowing what to do or how to dothings in a new environment. This termexpresses the feeling of not knowing what todo or how to do things in a new environment. We can describe culture shock as the physical and emotional discomfort a person suffers when coming to live in a place different from the place of origin.Often, the way that we live before is not accepted or considered as normal in the new place. Everything is different, for example, not speaking the language, not knowing how to use banking machines, not knowing how to use telephones, and so forth.The symptoms of culture shock can appear at different times. Although a person can experience real pain from culture shock, it is also an opportunity for growing and learning new perspectives. Culture shock can help people develop a better understanding of themselves and stimulate personal creativity.Culture shock has many stages. Each stage can be ongoing, or appear only at certain times. In the first stage, the new arrival may feel very happy about all of the new experience. This time is called the honeymoon stage. Afterward, the second stage presents itself. A person may encounter some difficulties in daily life. For example, communication difficulties may occur, such as not being understood. In this stage, there may be feelings of impatience, anger and sadness. Transition between the old methods and those of the new country is a difficult process and takes time to complete. The third stage is characterized by gaining some understanding of the new culture. A new feeling of pleasure and sense of humor may be experienced. A person may start to feel a psychological balance. The individual is more familiar with the environment and wants to belong. This starts an evaluation of the old ways versus those of the new. In the fourth stage, the person realizes that the new culture has goodand bad things to offer. This stage can be one of double integration or triple integration, depending on the number of cultures that the person has to process. This integration is characterized by a more solid feeling of belonging. The person starts to define himself or herself and establish goals for living. The fifth stage is the stage that is called the reentry shock. This occurs when a person returns to the newly acquired customs are considered improper in the old culture.Questions 56—60Complete the summary with words from the passage, changing the form where necessary, with only one word for each blank.Introduced in 1958, culture shock is a term used to (56) __________ physical and emotional discomfort people experience when they come to or live in a new place. Although many people suffer a lot from culture shock, it is an (57) _________ for personal improvement. The five stages of culture shock may last for a long time or show up once in a while. In the first stage, the (58) __________ stage, the new arrival might be OK with everything. Afterward, (59) ________ from old methods to the new one calls for time and energy. During the third and fourth stage, people may gain more understanding of the new culture and possess objective views. The double or triple integration is (60) __________ by a feeling of belonging. The last stage, called reentry shock, refers to the feeling people have when returning to their home country.Section B (10 marks)Questions 61-65 are based on the following passage.For some people, it would be unthinkable. But Gabe Henderson is finding freedom in a recent decision; he canceled his MySpace account. The 26 years old graduate student stopped his account after realizing that a lot of his online friends were really just acquaintances. “The superficial emptiness clouded the excitement I had once felt,” Henderson wrote in an article. “It seems we have lost, to some degree, the special depth that true friendship is about.”Journalism professor Michael Bugeja, who is a strong supporter of face-to-face communication, read Henderson’s column and saw it was a sign of hope. Though he’s not anti-technology, Bugeja often lectures students about “interpersonal intelligence”—knowing when, where, and for what purpose technology is most appropriate. He points out the studentshe’s seen walking across campus, holding hands with each other while talking on cell phones to someone else He’s also seen them in coffee shops, surrounded by people, but staring instead at a computer screen. “True friends,” he says, “need to learn when to stop blogging and go across campus to help a friend.”These days, young people are more wired than ever—but they’re also getting more worried. Increasingly, they’ve had to deal with online bullies, who are posting anything from embarrassing photos to online threats. And increasingly, young people also are realizing that things they post on their profiles can come back to hurt them when applying for schools or jobs.Social networking can be an “extremely effective”way to publicize events to large groups. It can even help build a sense of community on campus. People joined Facebook as a way to meet others. However, it has limitations. A good Internet pro make even the most boring person seem some what interesting. People are also not always happy with text messages on the cell phones. Cell phones can be a quick way to say “have a good day”. But friends can also cancel a night out with a text message to avoid having to explain. “Our generation needs to get over this fear of confrontation and rejection.” Henderson says. “The focus needs to be on quality communication, in all ways.”Back in his life, Henderson is enjoying spending more face-to-face time with his friends and less with his computer. He says his decision to quit his social-networking Internet accounts was a good one. “I’m not sacrificing friends,” he says, “because if a picture, some basic information about their life and a Web page is all my friendship has become, then there was nothing to sacrifice to begin with.”Questions 61—63Decide whether the following statements are true (T) or false (F) according to the passage.61. Although Henderson quit MySpace, most of his online friends are actually close friends.62. According to Bugeja, young people should know when to use technology and when to stop using it.63. Social networking helps build a sense of community but has a negative effect on young people’s life if it is used inappropriately.Questions 64—65Answer the following questions briefly according to the passage.64. What does Henderson lose by using social networking websites like Myspace?65. What do young people need to overcome in order to focus on quality communication?Section C (10 marks)Questions 66—70 are based on the following passage.“Five …Four …Three …Two …One …See ya! ”and Chance McGuire,twenty-five, is airborne off a 600 –footconcrete dam in Northern California. Inone second he falls 15 feet, in two seconds60 feet, and after three seconds and 130feet, he is flying at 66 miles an hour.McGuire is a practitioner of what hecalls the king of all extreme sports. BASE—an acronym for building, antenna, span (bridge) and earth (cliffs)—jumping has one of the sporting world’s highest fatality rates: inits 18-year history, forty –six participants have been killed. Yet the sport has never been more popular, with more than a thousand jumpers in the United States, and more seeking to get into it every day. It is an activity without margin for error. If your chute malfunctions, don’t bother researching for a reserve—there isn’t time. There are no second chances.Still, the sport may be a perfect fit with the times. Americans may have more in common with McGuire than they know or care to admit. America has embarked on a national orgy of thrill seeking and risk taking. The rise of adventure and extreme sports such as BASE jumping, snowboarding, ice climbing, skateboarding, and paragliding is merely the most vivid manifestation of this new national behavior.The rising popularity of extreme sports speaks of an eagerness on the part of millions of Americans to participate in activities closer to the edge, where danger, skill, and fear combine to give weekend warriors and professional athletes alike a sense of pushing out personal boundaries. According to American Sports Data Inc., a consulting firm, participation in so-called extreme sports is way up. Snowboarding has grown 113 percent in five years and now boasts nearly 5.5 million participants. Mountain hiking, skateboarding, scuba diving—their growth curves reveal a nation that loves to play with danger. Contrast that with activities such as baseball, touch football, and aerobics, all of which were in steady decline throughout the 1990s.The pursuits that are becoming more popular have one thing in common: the perception that they are somehow more challenging than a game of touch football. “Every human being with two legs and two arms is going to wonder how fast, how strong, how enduring he or she is,” says Eric Perlman, a mountaineer and film maker specializing in extreme sports. “We are designed to experience or die.”Questions 66—68Complete the following sentences with information given in the passage in a maximum of 4 words for each blank.66. _______ rates doesn’t stop people from getting into BASE jumping every day.67. The rise of extreme sports manifests the national behavior of _______ and ________.68. The combination of fear, skill and danger gives both amateurs and professionals a sense of______.Questions 69—70Choose the best answer according to the passage.69. Which of the following activities reveals a nation that loves to play activities closer to the edge?A. Touch football.B. Baseball.C. Scuba diving.D. Aerobics.70. What does Eric mean by saying “We are designed to experience or die”?A. Life with great challenges is a meaningful one.B. Life without great experiences is very common.C. People may die while doing extreme sports.D. Extreme sports are essential parts of human life.Section D (10 marks)Questions 71—75 are based on the following passage.Albert Einstein was one of the greatest thinkers the world has ever known. He formulated theories of relativity, successfully described the nature of the universe and came up with the most famous equation in the world. David Beckham is the footballer whose skills and precision have made him one of the most gifted sportsmen of his generation. Who is more intelligent?How Gardner’s theory of multiple intelligences (MI) dares us to put these two men on neighboring pedestals. Instead of regarding intelligence as a single quantity measurable by pen-and-paper tests, Gardner, an education professor at Harvard University, divides human intelligence into no fewer than eight separate categories ranging from mathematical tomusical competence. (74)His ideas have provoked vigorous debate about how one defines intelligence. Gardner’s point is that quantity measures only one capacity, the sort of mental agility that is valued in academic achievement, and that this single number does not do justice to human potential. So he has created his own spheres of achievement. Some categories are easily reconcilable with general perceptions about IQ. For example, “linguistic” intelligence confers a mastery of language, and is the preserve of such people as poets, writers and linguists. “Logical mathematical”intelligence marks out people who take a reasoning approach to physical things, and seek underlying principles. Einstein is the standard –bearer of this group, which also includes philosophers. These two categories are the main components of what we generally think of as “intelligence”.“Musical”intelligence characterizes musicians, composers and conductors. “Spatial”intelligence is about being able to picture perspective, to visualize a world in one’s head with great accuracy. Chess players, artists and architects would rate highly in this category. Dancers, athletes and actors are lumped under the “bodily-kinesthetic”heading; these individual, like Beckham, are able to control their bodies and movements very carefully.Then come two types of “personal” intelligence-intrapersonal, the ability to gauge one’s own mood, feelings and mental states, and interpersonal, being able to gauge it in others and use the information. These two categories could be interpreted as emotional intelligence. Psychiatrists are particularly adept at the former, while religious leaders and politicians are seen as people who can exploit the latter.Charles Darwin is perhaps the perfect embodiment of the eighth intelligence –“naturalist”. This label describes people with a deep understanding of the natural world and its objects. Zoologists and botanists can count themselves among this group.(75)These eight categories certainly reflect the fact that, in these areas, there is a spectrum of human ability ranging from the hopeless to the brilliant. But are these really intelligences, or could these competences be more accurately described as gifts or talents?Questions 71—73Answer the following questions briefly according to the passage.71. What are the main components of “intelligence” we generally think of?72. What kind of abilities does emotional intelligence involve?73. Which intelligences are represented by Einstein and Beckham respectively?Questions 74—75Translate the underlined sentences in the passage into Chinese.74. His ideas have provoked vigorous debate about how one defines intelligence.75. These eight categories certainly reflect the fact that, in these areas, there is a spectrum of human ability ranging from the hopeless to the brilliant.Part V Translation (10 marks)Translate the following sentences into English, using the hints given in brackets. Remember to write the answer on the answer sheet.76. 既然没有退路了，我们不妨试试他的方法。
2012年数学建模美赛B题
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Page 3 of 18
1 Introduction & Backgrounds
Tourism is the sum of relationships and the phenomena which happens in the process when people make the non resident trip in order to seek the spirit of the pleasant feeling. it is a kind of spiritual pursuit when people have met the material life. Every time when we plan to select a tourist destination, we are always considering many issues, such as: the safety, the quality, the time and so on. As the administrator of the tourism area, we hold the tourism resources, At the same time, in order to improve the safety of tourist and the quality of tourism, we must do our best to avoid too many tourists at the same time or in a given period of time to enter the scenic area. For hot spots and spots of limited opening hours, if conditions permit, improving the system to achieve the maximum utilization of resource is the problem to be solved urgently, in other words, as the managers, we must give access to more tourists in the case of quality assurance.
2012B国赛中文对照
2012年AMC8真题及英文详解
1. Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic?Solution 1Since Rachelle uses pounds of meat to make hamburgers, she uses pounds ofmeat to make one hamburger. She'll need 24 times that amount of meat for 24hamburgers, or .Solution 2Rachelle uses meat for hamburgers in the ratio. If we multiply this ratio on top and bottom by 3 to get 24 hamburgers on thebottom, we get. Therefore, she uses 9pounds of meat for 24 hamburgers, making the answer.2. In the country of East Westmore, statisticians estimate there is a baby born every hours and a death every day. To the nearest hundred, how many people areadded to the population of East Westmore each year?There are births and one death everyday in East Westmore. Therefore, the population increases by people everyday. Thus, thereare people added to the population every year. Rounding, we findthe answer is .3. On February 13 The Oshkosh Northwester listed the length of daylight as 10hours and 24 minutes, the sunrise was , and the sunset as . The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?The problem wants us to find the time of sunset and gives us the length of daylight and time of sunrise. So all we have to do is add the length of daylight to the time of sunrise to obtain the answer. Convert 10 hours and 24 minutes into in order to add easier.Adding, we find that the time of sunsetis .4. Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?Peter ate slices. The pizza has slices total. Taking the ratio of the amount of slices Peter ate to the amount of slices in the pizza, we find that Peterate of the pizza.5. In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , in centimeters?The figure is the same height on both sides, so the sum of the lengths contributing to the height on the left side will equal the sum of the lengths contributing to the height on the left side.Thus, the answer is .6. A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?First, we start with a sketch. It's always a good idea to start with a picture, although not as detailed as this one.In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is square inches. The height of the whole frame (including the photograph) would be , and the width of the whole frame, . Therefore, the area of the whole figure wouldbe square inches. Subtracting the area of the photograph from thearea of both the frame and photograph, we find the answer tobe .7. Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test?Isabella wants an average grade of on her 4 tests; this also means that shewants the sum of her test scores to be at least (if she goes over this number, she'll be over her goal!). She's already taken two tests, which sumto , which means she needs more points to achieve her desiredaverage. In order to minimize the score on the third test, we assume that Isabella will receive all points on the fourth test. Therefore, the lowest Isabella couldhave scored on the third test would be .8. A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price?Solution 1: With AlgebraLet the original price of an item be .First, everything is half-off, so the price is now .Next, the extra coupon applies 20% off on the sale price, so the price after this discount will be of what it was before. (Notice how this is not applied to the original price; if it were, the solution would be applying 50% + 20 % = 70% off the original price.)The price of the item after all discounts have been applied is . However, we need to find the percentage off the original price, not the currentpercentage of the original price. We then subtract from (the originalprice of the item), to find the answer, .Solution 2: FakesolvingSince the problem implies that the percentage off the original price will be the same for every item in the store, fakesolving is applicable here. Say we are buying an item worth 10 dollars, a convenient number to work with. First, it is clear that we'll get 50% off, which makes the price then 5 dollars. Taking 20% off of 5 dollars gives us 4 dollars. Therefore, we have saved a totalof9. The Fort Worth Zoo has a number of two-legged birds and a number offour-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?Solution 1: AlgebraLet the number of two-legged birds be and the number of four-legged mammals be . We can now use systems of equations to solve this problem.Write two equations:Now multiply the latter equation by .By subtracting the second equation from the first equation, we findthat . Since there were heads, meaning that therewere animals, there were two-legged birds.Solution 2: Cheating the SystemFirst, we "assume" there are 200 two-legged birds only, and 0 four-legged mammals. Of course, this poses a problem, as then there would onlybe legs.Now we have to do some swapping--for every two-legged bird we swap for afour-legged mammal, we gain 2 legs. For example, if we swapped one bird for one mammal, giving 199 birds and 1 mammal, there would be legs.If we swapped two birds for two mammals, there would be legs. If we swapped 50 birds for 50 mammals, there would be legs. Notice that we must gain legs. This means we must swapout birds. Therefore, there must be birds. Checking our work, we find that , and we are correct.10. How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?For this problem, all we need to do is find the amount of valid 4-digit numbers that can be made from the digits of , since all of the valid 4-digit number will always be greater than . The best way to solve this problem is by using casework.There can be only two leading digits, namely or .When the leading digit is , you can make such numbers.When the leading digit is , you can make such numbers.Summing the amounts of numbers, we find that there are such numbers.Notice that the first digit cannot be , as the number is greater than . Therefore,there are three digits that can be in the thousands.The rest three digits of the number have no restrictions, and therefore thereare for each leading digit.Since the two 's are indistinguishable, there are suchnumbers .11. The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and are all equal. What is the value of ?Since there must be an unique mode, and is already repeated twice, cannot beany of the numbers already listed (3, 4, 5, 7). (If it were, the mode would not be unique.) So must be , or a new number.Solution 1: Guess & CheckWe can eliminate answer choices and , because of the above statement. Now we need to test the remaining answer choices.Case 1:Mode:Median:Mean:Since the mean does not equal the median or mode, can also be eliminated. Case 2:Mode:Median:Mean:We are done with this problem, because we have found when , the conditionis satisfied. Therefore, the answer is .Solution 2: AlgebraNotice that the mean of this set of numbers, in terms of , is:Because we know that the mode must be (it can't be any of the numbers alreadylisted, as shown above, and no matter what is, either or a new number, it willnot affect being the mode), and we know that the mode must equal the mean, we can set the expression for the mean and equal:12. What is the units digit of ?The problem wants us to find the units digit of , therefore, we can eliminate the tens digit of , because the tens digit will not affect the final result. So our new expression is . Now we need to look for a pattern in the units digit.We observe that there is a pattern for the units digit which recurs every four powers of three. Using this pattern, we can subtract 1 from 2012 and divide by 4. Theremainder is the power of three that we are looking for, plus one. dividedby leaves a remainder of , so the answer is the units digit of , or . Thus,we find that the units digit of is .13. Jamar bought some pencils costing more than a penny each at the school bookstore and paid . Sharona bought some of the same pencils and paid . How many more pencils did Sharona buy than Jamar?We assume that the price of the pencils remains constant.Convert and to cents. Since the price of the pencils is more than one penny, we can find the price of one pencil (in cents) by taking the greatest commondivisor of and , which is . Therefore, Jamar bought pencilsand Sharona bought pencils. Thus, Sharonabought more pencils than Jamar.14. In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?This problem is very similar to a handshake problem. We use theformula to usually find the number of games played (or handshakes). Now we have to use the formula in reverse.So we have the equation . Solving, we find that the number of teams in the BIG N conference is15. The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numbers?To find the answer to this problem, we need to find the least common multipleof , , , and add to the result. The least common multiple of the four numbersis , and by adding , we find that that such number is . Now we need to find theonly given range that contains . The only such range is answer , and so ourfinal answer is .16. Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?In order to maximize the sum of the numbers, the numbers must have their digits ordered in decreasing value. There are only two numbers from the answer choiceswith this property: and . To determine the answer we will have to use estimation and the first two digits of the numbers.For the number that would maximize the sum would start with . The firsttwo digits of (when rounded) are . Adding and , we find that the firstthree digits of the sum of the two numbers would be .For the number that would maximize the sum would start with . The firsttwo digits of (when rounded) are . Adding and , we find that the firstthree digits of the sum of the two numbers would be .From the estimations, we can say that the answer to this problem is .In order to determine the largest number possible, we have to evenly distribute the digits when adding. The two numbers that show an example of thisare and . The digits can be interchangeable between numbers because we only care about the actual digits.The first digit must be either or . This immediately knocks out .The second digit must be either or . This doesn't cancel any choices.The third digit must be either or . This knocks out and .The fourth digit must be or . This cancels out .This leaves us with .17. A square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?The first answer choice , can be eliminated since there must be squares with integer side lengths. We then test the next largest sidelength which is . The square with area can be partitioned into squares with area and two squareswith area , which satisfies all the conditions of the problem. Therefore, the smallest possible value of the length of the side of the original square is .18. What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?The problem states that the answer cannot be a perfect square or have prime factors less than . Therefore, the answer will be the product of at least twodifferent primes greater than . The two smallest primes greaterthan are and . Multiplying these two primes, we obtain the number ,which is also the smallest number on the list of answer choices. So we are done, andthe answer is .19. In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar?Let be the number of red marbles, be the number of green marbles, and be the number of blue marbles.If "all but 6 are red marbles", that means that the number of green marbles and the number of blue marbles amount to . Likewise, the number of red marbles and bluemarbles amount to , and the number of red marbles and the number of greenmarbles amount to .We have three equations:We add all the equations to obtain a fourth equation:Now divide by on both sides to find the total number of marbles:Since the sum of the number of red marbles, green marbles, and blue marbles is thenumber of marbles in the jar, the total number of marbles in the jar is .Notice how we never knew how many of each color there were (there is 1 green marble, 5 blue marbles, and 3 red marbles).20. What is the correct ordering of the three numbers , , and , in increasing order?The value of is . Now we give all the fractions a common denominator.Ordering the fractions from least to greatest, we find that they are in the order listed.Therefore, our final answer is .Instead of finding the LCD, we can subtract each fraction from to get a commonnumerator. Thus,All three fractions have common numerator . Now it is obvious the order of thefractions. . Therefore, our answeris .21. Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?If Marla evenly distributes her square feet of paint between the 6 faces, eachface will get square feet of paint. The surface area of one of the faces of the cube is square feet. Therefore, there willbe square feet of white on each side.22. Let be a set of nine distinct integers. Six of the elements are 2, 3, 4, 6, 9, and 14. What is the number of possible values of the median of ?First, we find that the minimum value of the median of will be .We then experiment with sequences of numbers to determine other possible medians.Median:Sequence:Median:Sequence:Median:Sequence:Median:Sequence:Median:Sequence:Median:Sequence:Any number greater than also cannot be a median of set .There are then possible medians of set .23. An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?Let the perimeter of the equilateral triangle be . The side length of the equilateral triangle would then be and the sidelength of the hexagon would be .A hexagon contains six equilateral triangles. One of these triangles would be similar to the large equilateral triangle in the ratio , since the sidelength of the smallequilateral triangle is half the sidelength of the large one. Thus, the area of one of the small equilateral triangles is . The area of the hexagon isthen .Let the side length of the equilateral triangle be and the side length of the hexagonbe . Since the perimeters are equal, we must have which reducesto . Substitute this value in to the area of an equilateral triangle toyield .Setting this equal to gives us . Substitue into the area of a regular hexagon to yield .Therefore, our answer is .The area of an equilateral triangle with side length is .The area of a regular hexagon with side length is .24. A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?Draw a square around the star figure. The sidelength of this square is , because the sidelength is the diameter of the circle. The square forms -quarter circles aroundthe star figure. This is the equivalent of one large circle with radius , meaning that the total area of the quarter circles is . The area of the square is . Thus, thearea of the star figure is . The area of the circle is . Taking the ratio of thetwo areas, we find the answer is .25. A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length , and the other of length . What is the value of ?The total area of the four congruent triangles formed by the squares is .Therefore, the area of one of these triangles is . The height of one of these triangles is and the base is . Using the formula for area of the triangle, wehave . Multiply by on both sides to find that the value of is .To solve this problem you could also use algebraic manipulation.Since the area of the large square is , the sidelength is .We then have the equation .We also know that the sidelength of the smaller square is , since its area is . Then,the segment of length and segment of length form a right triangle whose hypotenuse would have length .So our second equation is .Square both equations.Now, subtract, and obtain the equation . We can deduce that the value of is .。
2012年数学建模美赛B题翻译
问题B：大量物种灭绝已经发生
亚马逊雨林是这个世界上最大的雨林，它拥有世界上最多的野生动物。
它座落在南美洲北面被巴西，玻利维亚等9个国家所分享。
因为乱砍乱伐的在雨林造成了致命的影响，所以这条信息需要普及。
虽然短期内砍伐能产生经济效益，但是长期下去会损害亚马逊雨林。
砍伐已经到达了历史的最低点，而在巴西仅仅只有50%的雨林处于被保护的状态。
但是栖息地遗失所产生的影响将在一段时间后会显示出来。
“砍伐在很短的时间内并不能杀死鸟类，长时间就会死亡，它们被挤在狭小的剩下的栖息地里，这样死亡率从就会逐渐提高”，生物学家这样说。
要求：
一．建立砍伐效应的模型,物种大灭绝是否会在未来近期发生。
二．用你的模型区预估多少物种会在未来20年会灭绝，考虑四种情景：
1.商业自由放任砍伐
2.出台一些规定
3.按照政府的规定目标，到2020年为止坚决减少80%的砍伐
4. 2020年终止采伐
三．写一份20页的报告（不包括摘要）表现出你对关于砍伐效应猜想的分析，保证包括政府在确保生态安全方面所扮演的角色。
2012年美国数学建模MCM题目(中英对照版)
2012 Contest ProblemsMCM PROBLEMSPROBLEM A: The Leaves of a Tree"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:• Why do leaves have the various shapes that they have?• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.“一棵树的叶子有多重？”怎么能估计树的叶子（或者树的任何其它部分）的实际重量？怎样对叶子进行分类？建立一个数学模型来对叶子进行描述和分类。
2012全国大学生英语竞赛决赛B类答案
2012National English Contestfor College Students(Level B-Final)参考答案及评分标准Part I.Listening Comprehension（30points）1—5CBCAB6—10CBBAC11—15BABCA16—20BCACA21.the nguage25.the telegraph 26.steam27.currency28.Europe29.depression30.relationshipsPart II.Multiple-choiceSection A(10points)31—35ABDAC36—40BDCCASection B(5points)41—45DAACDPart III.Cloze(10points)46.fail47.narrow48.distinguishing49.to50.geographic51.products52.account53.secondary54.capture55.strategiesPart IV.Reading comprehension(40points)Section A(10points)56.B57.C58.reproductive system59.enhance performance60.standard doping testsSection B(10points)61.They only got10%of the profits of the band’s merchandising.62.He used the profits to finance his club.63.Because his recording contract greatly favoured the label’s owner.64.He got less than half what the record company had been expecting to pay.65.He rejected a recording company’s offer to appear on the album and film of the music festival Woodstock. Section C(10points)66.most influential writers67.middle class family/Catholic family68.greatest20th-century novel 69.stream of consciousness70.the short-story collectionSection D(10points)71—73YNY1--74.在漆黑的煤窑里我悄悄地、尽可能近地爬到那两个正在说话的人旁边。
2012年大学生英语竞赛C类阅读题翻译
Section A“文化撞击”这一术语最早出现于1985年，人们用这一术语来描述人在进入全新的环境之后所产生的焦虑。
这种焦虑表现为：处于新环境之中不知道该做什么事，也不知道如何做事。
可以说，“文化撞击”是人们在进入一个不同于以往的新环境时所经历的精神与身体上的不适应的感觉。
通常情况下，新环境中的人们并不接受新成员原来的生活习惯，人们认为那些生活习惯是奇怪的。
所以对于新成员来说，一切都是新的，如：新的语言，不知道怎么使用的取款机，还有不会用的电话，等等。
在很多时候人们都会表现出“文化撞击”的症状。
虽然人们可能由于“文化撞击”而感受到真实的痛楚，但这也是成长和学习的机会，它可以帮助人更好地了解自己，并激发人们的创造力。
“文化撞击”可以分为许多阶段，有些阶段是彼此相连的，而有的阶段则是间隔开来，而且只在特定的时间表现出来。
第一阶段，又叫做“蜜月阶段”。
在这个阶段中，人们初次接触这个新的环境，这种体验让他们觉得很快乐。
随之而来的是第二个阶段，人们有可能会在日常生活中遇到一些困难，例如：交流上的障碍，其他人有可能无法听懂他们的话。
在这个阶段，人们有可能会失去耐心，变得忧伤，愤怒起来。
这个阶段中，人们从旧的生活方式向新的生活方式转变，而这是一个既耗时又费力的过程。
到了第三阶段，人们的一个特点是：他们开始初步了解新环境中的文化了，因此，他们会产生一种愉悦的感觉，还有可能伴随一点幽默感。
从心理上说，人们对新旧环境的感觉趋向于一致，这是因为：人们进一步熟悉了新环境并且开始对新环境产生了归属感。
此外，人们还会将新的生活方式与原来的生活方式加以对比和评价。
在第四阶段，人们认识到新的环境不仅有好的一面也有不好的一面，因此他们会将曾经体验过的两种或者三种文化融合起来。
这种融合的一大特点就是：这个过程中人们有一种强烈的归属感。
人们对开始对自我有了明确的定位，对生活也有了明确的目标。
第五阶段，又叫“二次撞击阶段”，这一阶段是人们回到原来的国家时经历的一个阶段。
2012年美国数学建模题目
2012 Contest ProblemsMCM PROBLEMSPROBLEM A: The Leaves of a Tree"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:• Why do leaves have the various shapes that they have?• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.PROBLEM B: Camping along the Big Long RiverVisitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish.. The government agency responsible formanaging this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river mana gers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings.。
2012 MCM Contest Problems(2012年美国赛题目—中英文版)
2012 MCM Contest Problems (2012年美国赛题目—中英文版) PROBLEM A:The Leaves of a Tree "How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:?6?1 Why do leaves have the various shapes that they have??6?1 Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape??6?1 Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure??6?1 How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.PROBLEM B:Camping along the Big Long River Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish.. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings.A“多少钱，树上的叶子重？”你如何估计的实际重量的叶（或对任何其他部分的树）？你如何分类的叶子？建立一个数学模型，描述和分类的叶子。
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2012 Contest Problems
MCM PROBLEMS
PROBLEM A: The Leaves of a Tree
"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:
• Why do leaves have the various shapes that they have?
• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?
• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?
• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?
In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.
2012美赛A题：一棵树的叶子
（数学中国翻译）
“一棵树的叶子有多重？”怎么能估计树的叶子（或者树的任何其它部分）的实际重量？怎样对叶子进行分类？建立一个数学模型来对叶子进行描述和分类。
模型要考虑和回答下面的问题：
• 为什么叶子具有各种形状？
• 叶子之间是要将相互重叠的部分最小化，以便可以最大限度的接触到阳光吗？树叶的分布以及树干和枝杈的体积影响叶子的形状吗？
• 就轮廓来讲，叶形（一般特征）是和树的轮廓以及分枝结构有关吗？
• 你将如何估计一棵树的叶子质量？叶子的质量和树的尺寸特征（包括和外形轮廓有关的高度、质量、体积）有联系吗？
除了你的一页摘要以外，给科学杂志的编辑写一封信，阐述你的主要发现。
PROBLEM B: Camping along the Big Long River
Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish.. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings.
2012美赛B题：沿着“大长河”露营
【数学中国翻译】
游客在“大长河”(225英里)可以享受到秀丽的风光和令人兴奋的白色湍流。
这条河对于背包客来说是进不去的，因此畅游这条长河的唯一办法就是在这条河上露营上几天。
这次旅行从开始的下水点到最终结束点，共225英里，且是顺流而下的。
乘客可以选择平均4英里/小时的以浆作为动力的橡胶筏或者平均8英里/小时的机动帆船旅行。
整个旅行从开始到结束会经历6至18个夜晚。
负责管理这条河的政府机构希望到这里的每一次旅行都能够享受到野外经历，以最少的接触到在河上其它的船只。
目前，每年在六个月期间(一年的其余部分的天气对于河流旅行来说太冷)，共有X次旅行，有Y处露营地，露营地均匀的分布整个河道。
由于漂流的受欢迎程度的上升，公园管理者已经被要求允许更多的旅行次数。
所以他们想确定怎样可能安排一个最优的混合的旅行方案，不同的时间(单位为夜)和推动方式(马达或浆)，最大限度的利用露营地。
换句话说，在长河的漂流季，将会有多少更多的乘船旅行可以加进来?河流的管理者现在雇佣你，为他们提出最佳排程方式和河流承载能力的建议，记住两个露营者不能在同一时
间内占据同一个露营地。
除了你的一页摘要，准备一页备忘录，对河流的管理者描述你的主要发现。
ICM PROBLEM
PROBLEM C: Modeling for Crime Busting
Click the title below to download a ZIP file containing the 2012 ICM Problem.
Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.
Modeling for Crime Busting
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