2012年AMC 10A竞赛真题及答案(英文版)
AMC10的真题答案及中文翻译
AMC10的真题答案及中文翻译AMC10的真题及中文翻译1、One ticket to a show costs $20 at full price. Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickets using a coupon that gives her a 30% discount. How many more dollars does Pam pay than Susan?(A) 2 (B) 5 (C) 10 (D) 15 (E) 20中文：一张展览票全价为20美元。
Susan用优惠券买4张票打七五折。
Pam用优惠券买5张票打七折。
Pam比Susan多花了多少美元？2、An aquarium has a rectangular base that measures 100cm by 40cm and has a height of 50cm. It is filled with water to a height of 40cm. A brick with a rectangular base that measures 40cm by 20cm and a height of 10cm is placed in the aquarium. By how many centimeters does that water rise?(A) 0.5 (B) 1 (C) 1.5 (D) 2 (E)2.5中文：一个养鱼缸有100cm×40cm的底，高为50cm。
它装满水到40cm的高度。
把一个底为40cm×20cm，高为10cm的砖块放在这个养鱼缸里。
鱼缸里的水上升了多少厘米？3、The larger of two consecutive odd integers is three times the smaller. What is their sum?(A) 4 (B) 8 (C) 12 (D) 16 (E) 20中文：2个连续的奇整数中较大的数是较小的数的3倍。
英语竞赛 2012 答案
2012全国英语竞赛C类试题答案2012 National English Contestfor 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 CBBACSection B (10 marks)6—10 BAACB 11—15 CABCBSection C (5 marks)16—20 ACABASection 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. characterizedSection 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 tak ing 68. pushing out personal boundaries 69. C 70. ASection D (10 marks)71.“Linguistic”intelligence and“Logical mathematical”intelligence.72. The ability to gauge one蒺s own mood, feelings and mental states, and the ability to gauge it in others anduse 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。
-年amc 10a和b竞赛真题及答案(英文版)
2010-2015年AMC 10A和B竞赛真题及答案（英文版）
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2010年AMC 10Aห้องสมุดไป่ตู้赛真题及答案（英文版）
2010年AMC 10B竞赛真题及答案（英文版）
2011年AMC 10A竞赛真题及答案（英文版）
2011年AMC 10B竞赛真题及答案（英文版）
Problem 4
2012年AMC 10A竞赛真题及答案（英文版）
go去wentgone
2012年AMC 10B竞赛真题及答案（英文版）
get得到gotgot
sink下沉sank / sunksunk / sunken
give给gavegiven
hit打hithit
不规则动词表
2013年AMC 10A竞赛真题及答案（英文版）
mistake误认mistookmistaken
grow成长grewgrown
think思考thoughtthought
2012全国大学生英语竞赛决赛答案
2012National English Contestfor College Students(Level C-Final)参考答案及作文评分标准Part I Listening Comprehension(30marks)Section A(5marks)1—5AABCBSection B(10marks)6—10ABAAC11—15ACBABSection C(5marks)16—20CAABCSection D(10marks)21.recycling industry22.designed to23.containing24.disposed of25.sufficient 26.failed to27.injustice28.in total29.otherwise30.discardedPart II Vocabulary and Structure(15marks)31—35BDCAA36—40CBCBD41—45DBCBDPart III Cloze(10marks)46.Joneses47.Instead48.around49.providing50.distribution51.majority52.reference53.decades54.about55.highPart IV Reading Comprehension(40marks)Section A(10marks)56.retarding/delaying/slowing(down)57.accelerate58.restriction59.modulate60.consequences Section B(10marks)61.T62.F63.F64.To know their coping strategies/To know a little about how their companion deals with difficult situations.65.Writing in journals.Section C(10marks)66.paralyzed inability67.exhaustion68.suspension69.C.70.A.Section D(10marks)71.No other biped can actually cover more than a tiny fraction of the walking distance that can be sustained by humans.72.It is equipped to support and balance an erect body and to produce the leverage necessary to propel the body forward in locomotion.73.It has undergone enormous design changes in cohering its 28bones,37joints and 107ligaments,and 32muscles and tendons to adapt to the body weight and numerous torsions.74.这些不同部分构成的错综复杂的网络，不仅需要支持和平衡沉重的身躯，还需要保证每天几百或几千次的动作。
AMC10A,2012年试题及答案
2012AMC10A ProblemsInstructions1.This is a25-question,multiple choice test.Each question is followed by answers markedA,B,C,D and E.Only one of these is correct.2.You will receive6points for each correct answer,1.5points for each problem leftunanswered,and0points for each incorrect answer.3.No aids are permitted other than scratch paper,graph paper,ruler,compass,protractorand erasers(No problems on the test will require the use of a calculator).4.Figures are not necessarily drawn to scale.5.You will have75minutes working time to complete the test.1.Cagney can frost a cupcake every20seconds and Lacey can frost a cupcake every30seconds.Working together,how many cupcakes can they frost in5minutes?2.A square with side length8is cut in half,creating two congruent rectangles.What are thedimensions of one of these rectangles?3.A bug crawls along a number line,starting at-2.It crawls to-6,then turns around and crawlsto5.How many units does the bug crawl altogether?4.Let and.What is the smallest possible degree measure forangle CBD?st year100adult cats,half of whom were female,were brought into the Smallville AnimalShelter.Half of the adult female cats were accompanied by a litter of kittens.The average number of kittens per litter was4.What was the total number of cats and kittens received by the shelter last year?6.The product of two positive numbers is9.The reciprocal of one of these numbers is4timesthe reciprocal of the other number.What is the sum of the two numbers?7.In a bag of marbles,of the marbles are blue and the rest are red.If the number of redmarbles is doubled and the number of blue marbles stays the same,what fraction of the marbles will be red?8.The sums of three whole numbers taken in pairs are12,17,and19.What is the middlenumber?9.A pair of six-sided dice are labeled so that one die has only even numbers(two each of2,4,and6),and the other die has only odd numbers(two of each1,3,and5).The pair of dice is rolled.What is the probability that the sum of the numbers on the tops of the two dice is7?10.Mary divides a circle into12sectors.The central angles of these sectors,measured indegrees,are all integers and they form an arithmetic sequence.What is the degree measure of the smallest possible sector angle?11.Externally tangent circles with centers at points A and B have radii of lengths5and3,respectively.A line externally tangent to both circles intersects ray AB at point C.What is BC?12.A year is a leap year if and only if the year number is divisible by400(such as2000)or isdivisible by4but not100(such as2012).The200th anniversary of the birth of novelistCharles Dickens was celebrated on February7,2012,a Tuesday.On what day of the week was Dickens born?13.An iterative average of the numbers1,2,3,4,and5is computed the following way.Arrangethe five numbers in some order.Find the mean of the first two numbers,then find the mean of that with the third number,then the mean of that with the fourth number,and finally the mean of that with the fifth number.What is the difference between the largest and smallest possible values that can be obtained using this procedure?14.Chubby makes nonstandard checkerboards that have squares on each side.Thecheckerboards have a black square in every corner and alternate red and black squares along every row and column.How many black squares are there on such a checkerboard?15.Three unit squares and two line segments connecting two pairs of vertices are shown.Whatis the area of?16.Three runners start running simultaneously from the same point on a500-meter circulartrack.They each run clockwise around the course maintaining constant speeds of4.4,4.8, and5.0meters per second.The runners stop once they are all together again somewhere on the circular course.How many seconds do the runners run?17.Let and be relatively prime integers with and=.What is?18.The closed curve in the figure is made up of9congruent circular arcs each of length,where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side2.What is the area enclosed by the curve?19.Paula the painter and her two helpers each paint at constant,but different,rates.Theyalways start at8:00AM,and all three always take the same amount of time to eat lunch.On Monday the three of them painted50%of a house,quitting at4:00PM.On Tuesday,when Paula wasn't there,the two helpers painted only24%of the house and quit at2:12PM.On Wednesday Paula worked by herself and finished the house by working until7:12P.M.How long,in minutes,was each day's lunch break?20.A x square is partitioned into unit squares.Each unit square is painted either white orblack with each color being equally likely,chosen independently and at random.The square is then rotated clockwise about its center,and every white square in a position formerly occupied by a black square is painted black.The colors of all other squares are leftunchanged.What is the probability the grid is now entirely black?21.Let points=,=,=,and=.Points,,,andare midpoints of line segments and respectively.What is the area of ?22.The sum of the first positive odd integers is212more than the sum of the first positiveeven integers.What is the sum of all possible values of?23.Adam,Benin,Chiang,Deshawn,Esther,and Fiona have internet accounts.Some,but not all,of them are internet friends with each other,and none of them has an internet friend outside this group.Each of them has the same number of internet friends.In how many different ways can this happen?24.Let,,and be positive integers with such that and.What is?25.Real numbers,,and are chosen independently and at random from the intervalfor some positive integer.The probability that no two of,,and are within1unit of each other is greater than.What is the smallest possible value of?2012AMC10A Solutions 1-5:DEECB6-10:DCDDC11-15:DACBB16-20:CCEDA21-25:CABED。
高中一年级美国数学竞赛试题(简称AMC10)2012年B卷39617197
Problem 1Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms?SolutionProblem 2A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?SolutionProblem 3The point in the xy-plane with coordinates (1000, 2012) is reflected across the line y=2000. What are the coordinates of the reflected point?SolutionProblem 4When Ringo places his marbles into bags with 6 marbles per bag, he has 4 marbles left over. When Paul does the same with his marbles, he has 3 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 6 marbles per bag. How many marbles will be left over?SolutionProblem 5Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is 10%. She leaves a 15% tip on the price of her meal before the sales tax is added, and the tax is calculated on the pre-tip amount. She spends a total of 27.50 dollars for dinner. What is the cost of her dinner without tax or tip in dollars?SolutionProblem 6In order to estimate the value of x-y where x and y are real numbers with x > y > 0, Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct?A) Her estimate is larger than x-y B) Her estimate is smaller than x-y C) Her estimate equals x-y D) Her estimate equals y - x E) Her estimate is 0SolutionProblem 7For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide?SolutionProblem 8What is the sum of all integer solutions to ?SolutionProblem 9Two integers have a sum of 26. When two more integers are added to the first two integers the sum is 41. Finally when two more integers are added to the sum of the previous four integers the sum is 57. What is the minimum number of even integers among the 6 integers?SolutionProblem 10How many ordered pairs of positive integers (M,N) satisfy the equation =SolutionProblem 11A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?SolutionProblem 12Point B is due east of point A. Point C is due north of point B. The distance betweenpoints A and C is , and = 45 degrees. Point D is 20 meters due Northof point C. The distance AD is between which two integers?SolutionProblem 13It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it?SolutionProblem 14Two equilateral triangles are contained in square whose side length is . The bases of these triangles are the opposite side of the square, and their intersection is a rhombus. What is the area of the rhombus?SolutionProblem 15In a round-robin tournament with 6 teams, each team plays one game against each other team, and each game results in one team winning and one team losing. At the end of the tournament, the teams are ranked by the number of games won. What is the maximum number of teams that could be tied for the most wins at the end on the tournament?SolutionProblem 16Three circles with radius 2 are mutually tangent. What is the total area of the circles and the region bounded by them, as shown in the figure?SolutionProblem 17Jesse cuts a circular paper disk of radius 12 along two radii to form two sectors, the smaller having a central angle of 120 degrees. He makes two circular cones, using each sector to form the lateral surface of a cone. What is the ratio of the volume of the smaller cone to that of the larger?SolutionProblem 18Suppose that one of every 500 people in a certain population has a particular disease, which displays no symptoms. A blood test is available for screening for this disease. For a person who has this disease, the test always turns out positive. For aperson who does not have the disease, however, there is a false positive rate--inother words, for such people, of the time the test will turn out negative, butof the time the test will turn out positive and will incorrectly indicate that the person has the disease. Let be the probability that a person who is chosen at random from this population and gets a positive test result actually has the disease. Which of the following is closest to ?SolutionProblem 19In rectangle , , , and is the midpoint of . Segmentis extended 2 units beyond to point , and is the intersection of and. What is the area of ?SolutionProblem 20Bernardo and Silvia play the following game. An integer between 0 and 999, inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds 50 to it and passes the result to Bernardo. The winner is the last person who produces a number less than 1000. Let be the smallest initial number that resultsin a win for Bernardo. What is the sum of the digits of ?SolutionProblem 21Four distinct points are arranged on a plane so that the segments connecting them have lengths , , , , , and . What is the ratio of to ?SolutionProblem 22Let be a list of the first 10 positive integers such that for eacheither or or both appear somewhere before in the list. How many such lists are there?SolutionProblem 23A solid tetrahedron is sliced off a wooden unit cube by a plane passing through two nonadjacent vertices on one face and one vertex on the opposite face not adjacent to either of the first two vertices. The tetrahedron is discarded and the remaining portion of the cube is placed on a table with the cut surface face down. What is the height of this object?SolutionProblem 23A solid tetrahedron is sliced off a wooden unit cube by a plane passing through two nonadjacent vertices on one face and one vertex on the opposite face not adjacent to either of the first two vertices. The tetrahedron is discarded and the remaining portion of the cube is placed on a table with the cut surface face down. What is the height of this object?SolutionProblem 24Amy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those girls but disliked by the third. In how many different ways is this possible?SolutionProblem 25A bug travels from to along the segments in the hexagonal lattice picturedbelow. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there?Retrieved from"/Wiki/index.php/2012_AMC_10B_Problems"。
2012全国大学生英语竞赛A类答案
2012 National English Contestfor College Students(Level A - Preliminary)参考答案及作文评分标准Part I Listening Comprehension (30 marks)SectionA (5 marks)1—5 BCCABSectionB (10 marks)6—8 CBA 9—10 AC 11—15 BABBCSectionC (5 marks)16—20 BBACCSectionD (10 marks)21. Italy; 22. capturing snakes; 23. set off fireworks; 24. set free; 25. immune; 26. Spain;27. throw tomatoes; 28.a fight; 29. safety glasses; 30. the firing of a rocketPart II Vocabulary and Structures (15 marks)31—35 CADCA 36—40 ACDBA 41—45 CABADPart III Cloze (10 marks)46. sensible; 47. to; 48. in; 49. read; 50. repeatedly; 51. lay; 52. filled; 53. vacant;54. indefatigable; 55. littlePart IV Reading Comprehension (40 marks)SectionA (10 marks)56. important features of companies; 57. freedom to develop ideas; 58. well -positioned (great) marketingstrategies; 59. scholarships; 60. make decisionsSectionB (10 marks)61. The basic function of Wikipedia.62. Info anarchy.63. Set upa website that can be edited by anyone they like.64. To prevent idiots, vandals and fanatics from defacing, deleting or pushing one-sided views.65. Disregard the importance of expertise.SectionC (10 marks)66. F; 67. F; 68.F69. 小型住宅和后花园，以及高层住宅的发展，不仅阻碍了人们饲养宠物，而且会加大人们对稀少的公共休憩用地的需求。
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。