18届华杯赛高年级初赛C卷试题及详解
18届2013年小高组华杯赛竞赛题初赛 决赛A卷 B卷 C卷 完美版
第十八届华罗庚金杯少年邀请赛初赛试题A(小学高年级组)(时间2013年3月23日10:00~11:00)一、选择题(每题10分,满分60分,以下每题的四个选项中,仅有一个是正确的,请将表示正确答案的英文字母写在每题的圆括号内。
)1.2012.25×2013.75-2010.25×2015.75=()。
A.5 B.6 C.7 D.82.2013年的钟声敲响了, 小明哥哥感慨地说: 这是我有生以来第一次将要渡过一个没有重复数字的年份。
已知小明哥哥出生的年份是19的倍数, 那么2013年小明哥哥的年龄是()岁。
A.16 B.18 C.20 D.223.一只青蛙8点从深为12米的井底向上爬, 它每向上爬3米, 因为井壁打滑, 就会下滑1米,下滑1米的时间是向上爬3米所用时间的三分之一。
8点17分时, 青蛙第二次爬至离井口3米之处, 那么青蛙从井底爬到井口时所花的时间为()分钟。
A.22 B.20 C.17 D.164.一个盒子里有黑棋子和白棋子若干粒, 若取出一粒黑子, 则余下的黑子数与白子数之比为9:7, 若放回黑子, 再取出一粒白子, 则余下的黑子数与白子数之比为7:5, 那么盒子里原有的黑子数比白子数多()个。
A.5 B.6 C.7 D.85. 右图ABCD 是平行四边形, M 是DC 的中点, E 和F 分别位于AB 和AD上, 且EF 平行于BD 。
若三角形MDF 的面积等于5平方厘米, 则三角形CEB 的面积等于( )平方厘米。
A .5B .10C .15D .206. 水池A 和B 同为长3米, 宽2米, 深1.2米的长方体。
1号阀门用来向A 池注水, 18分钟可将无水的A 池注满; 2号阀门用来从A 池向B 池放水, 24分钟可将A 池中满池水放入B 池。
若同时打开1号和2号阀门, 那么当A 池水深0.4米时, B 池有( )立方米的水。
A .0.9B .1.8C .3.6D .7.2二、填空题(每小题 10 分, 满分40分)7. 小明、小华、小刚三人分363张卡片, 他们决定按年龄比来分。
2018年华杯赛初赛小学高年级组试题6题
第1次 第2次 第3次
6:小王将一些同样大小的正三角形纸片摆放在桌上,第一次放1张纸片;第二次在这个小 正三角形纸片四周再放3张纸片;第三次在第二次摆放好的图形四周再摆放纸片;……摆 放要求是:每次摆放的每张纸片必须和上一次摆放的纸片至少有一条边重合,且纸片之间 除边之外,无重合(见下图),第20次摆放后,该图形共用了正三角形纸片多少张?
第1次 第2次 第3次 第4次 第5次 第6次
6:小王将一些同样大小的正三角形纸片摆放在桌上,第一次放1张纸片;第二次在这个小 正三角形纸片四周再放3张纸片;第三次在第二次摆放好的图形四周再摆放纸片;……摆 放要求是:每次摆放的每张纸片必须和上一次摆放的纸片至少有一条边重合,且纸片之间 除边之外,无重合(见下图),第20次摆放后,该图形共用了正三角形纸片多少张?
6:小王将一些同样大小的正三角形纸片摆放在桌上,第一次放1张纸片;第二次在这个小 正三角形纸片四周再放3张纸片;第三次在第二次摆放好的图形四周再摆放纸片;……摆 放要求是:每次摆放的每张纸片必须和上一次摆放的纸片至少有一条边重合,且纸片之间 除边之外,无重合(见下图),第20次摆放后,该图形共用了正三角形纸片多少张?
第1次 第2次
6:小王将一些同样大小的正三角形纸片摆放在桌上,第一次放1张纸片;第二次在这个小 正三角形纸片四周再放3张纸片;第三次在第二次摆放好的图形四周再摆放纸片;……摆 放要求是:每次摆放的每张纸片必须和上一次摆放的纸片至少有一条边重合,且纸片之间 除边之外,无重合(见下图),第20次摆放后,该图形共用了正三角形纸片多少张?
第1次 第2次 第3次 第4次 第5次 第6次 第7次 第8次 第20次
第1次 第2次 第3次 第4次 第5次 第6次 第7次 第8次 第20次
华杯赛小学高年级试卷合集(18-21)A3
初赛试卷 A(小学高年级组)试题 一、选择题
第十九届华罗庚杯少儿数学邀请赛
初赛试卷 A(小学高年级组)试题
1、平面上的四条直线将平面分割成八个部分,则这四条直线中至多有( A.0 B.2 C.3 D.4
5、右图 ABCD 是平行四边形,M 是 DC 的中点,E 和 F 分别位于 AB 和 AD 上,且 EF 平行于 BD,若三角形 MDF 的面积等于 5 平方厘米,则三角形 CEB 的面积等于 ( )平方厘米。 A.5 B.10 C.15 D.20
6、如图所示,AF=7cm,DH=4cm,BG=5cm,AE=1cm。若正方形 ABCD 内的四边形 EFGH 的面积为 78cm²,则正方形 的边长为( A.10 二、填空题 7、五名选手 A、B、C、D、E 参加“好声音”比赛,五个人站成一排集体亮相。他们胸 前有每人的选手编号牌,5 个编号之和等于 35。已知站在 E 右边的选手的编号和为 13;站在 D 右边的选 )cm。 B.11 C.12 D.13
10、 圣诞老人有 36 个同样的礼物,分别装在 8 个袋子中。 已知 8 个袋子中的礼物的个数 至少为 1 且各不相同。现要从中选出一些袋子,将选出的袋子中的所有礼物平均分给 8 个小朋友,恰好分完(每个小朋友至少分得一个礼物),那么,共 种不同的选择。
第二十一届华罗庚杯少儿数学邀请赛 第二十届华罗庚杯少儿数学邀请赛 一、选择题 1、现在从甲、乙、丙、丁四个人中选出两个人参加一项活动。规定:如果甲去,那么乙也去;如果丙不去, 那么乙也不去;如果丙去,那么丁不去。最后去参加活动的两个人是( A.甲、乙 B.乙、丙 C.甲、丙 ) A. 2017 B. 2016 C. 2015 D. 2014 初赛试卷 A(小学高年级组)试题 一、选择题 1. 算式 的计算结果中含有(
18~22届华杯赛小高组初赛试题及参考答案
第一章 计算篇
1、【第 18 届华杯赛初赛 A 第 1 题】
2012.25×2013.75-2010.25×2015.75=( )
(A)5
(B)6
(C)7
(D)8
2、【第 18 届华杯赛初赛 B 卷第 2 题】
2 2 3 2 3 3 2 3 3 3 2 33的个位数字是( )。
9个3
-4-
第三章 几何篇
1、【第 18 届华杯赛初赛 A 卷第 5 题】
右图 ABCD 是平行四边形,M 是 DC 的中点,E 和 F 分别位于 AB 和 AD 上,且 EF
平行于 BD。若三角形 MDF 的面积等于 5 平方厘米,则三角形 CEB 的面积等于( )
平方厘米。
(A)5
(B)10
(C)15
计算: 481 1 265 1 904 1 184 29 160 41 703 55 _____。
6
12
20
30
42
56
7、【第 20 届华杯赛初赛 C 卷第 1 题】
计算: 9 11 13 15 17 120 1 1 ( )
20 30 42 56 72
34
(A)42
(B)43
4、【第 19 届华杯赛初赛 A 卷第 9 题】 四个黑色 1×1×1 的正方体和四个白色 1×1×1 的正方体可以组成________种不 同的 2×2×2 的正方体(经过旋转得到相同的正方体视为同一种情况)。 5、【第 19 届华杯赛初赛 B 卷第 10 题】 从 1,2,3,…,2014 中取出 315 个不同的数(不计顺序)组成等差数列,其中组 成的等差数列中包含 1 的有________种取法;总共有________种取法。 6、【第 20 届华杯赛初赛 A 卷第 3 题】
(完整版)第十八届华杯赛初赛试卷_小高B及答案
第十八届华罗庚金杯少年数学邀请赛初赛试卷 B ( 小学高年级组)总分第十八届华罗庚金杯少年数学邀请赛初赛试卷 B(小学高年级组)(时间 : 2013 年 3 月 23 日 10:00 ~ 11:00)装一、选择题 ( 每题 10 分, 满分 60 分. 以下每题的四个选项中, 仅有一个是正确的 , 请将表示正确答案的英文字母写在每题的圆括号内 .)1.一个四位数 , 各位数字互不相同 , 全部数字之和等于 6, 并且这个数是 11 的倍数 , 则知足这类要求的四位数共有()个.(A)6(B)7(C)8(D)9订 2.22323323 3 3 2 3 3 的个位数字是().9个 3(A)2(B)8(C)4(D)63.在下边的暗影三角形中 , 不可以由右图中的暗影三角形经过旋转、平移获得的是图()中的三角形.( A )( B)(C)( D)线4.某日 , 甲学校买了 56 千克水果糖 , 每千克 8.06元 . 过了几天 , 乙学校也需要买相同的56 千克水果糖 , 可是正好追上促销活动 , 每千克水果糖降价0.56 元, 并且只需买水果糖都会额外赠予5% 相同的水果糖 . 那么乙学校将比甲学校少花()元.(A)20(B)51.36(C)31.36( D)10.365.甲、乙两仓的稻谷数目相同 , 爸爸 , 妈妈和阳阳独自运完一仓稻谷分别需要 10 天 , 12 天和 15 天. 爸爸妈妈同时开始分别运甲、乙两仓的稻谷 , 阳阳先帮妈妈 , 后帮爸爸 ,结果同时运完两仓稻谷 , 那么阳阳帮妈妈运了()天.(A)3(B)4(C)5(D)66.如图, 将长度为9 的线段AB 分红9 等份,那么图中全部线段的长度的总和是().(A)132(B)144(C)156(D)165二、填空题 ( 每题 10 分, 满分 40 分)7.将乘积 0.243 0.325233 化为小数,小数点后第2013位的数字是________.8.一只青蛙 8 点从深为 12 米的井底向上爬 , 它每向上爬 3 米 , 由于井壁打滑 , 就会下滑 1米, 下滑 1 米的时间是向上爬 3 米所用时间的三分之一 . 8 点 17 分时 , 青蛙第二次爬至离井口 3 米之处 , 那么青蛙从井底爬到井口时所花的时间为________分钟 .9.一个水池有三个进水口和一个出水口 . 同时翻开出水口和此中的两个进水口 , 注满整个水池分别需要 6 小时、 5 小时和 4 小时 ; 同时翻开出水口和三个进水口 , 注满整个水池需要 3 小时 . 假如同时翻开三个进水口 , 不翻开出水口 , 那么注满整个水池需要________小时 .10.九个相同的直角三角形卡片 , 用卡片的锐角拼成一圈 , 能够拼成近似右图所示的平面图形 . 这类三角形卡片中的两个锐角中较小的一个的度数有 ________种不一样的可能值 . (右图不过此中一种可能的状况)。
2018年大学生英语竞赛(C类初赛真题及详细答案-
2018年大学生英语竞赛(NECCS)C类初赛真题试及详细答案PartⅠSection A1.Some bacteria______extremely harmful,but______are regularly used in producing cheeses, crackers and many other foods.A is:the othersB has been:the othersC are:othersD have been:others2.It was once a very prosperous part of the city,but now many of the businesses have moved away or gone______.A bankruptcyB bankruptC bankruptedD to bankrupt3.When one is unfamiliar with the local customs,it is easy to make a______.A blameB blunderC commitmentD fault4.______your timely advice,I would never have known how to deal with the tough job.A But forB Except forC Not untilD Prior to5.I'd______his reputation with other drug dealers and business people in the city,and then make a decision about whether or not to______a loan.A account for:supportB make up for:objectC take account of:approveD wipe out:oppose6.______,a man who expresses himself effectively is sure to succeed more rapidly than a man whose command of language is poor.A Were other things equalB Other things to be equalC Other things being equalD To be equal to other things7.In the book The Storied Life of A.J.Fikry,a valuable book was lost for years when it turned up one day,quite out of the______.A blackB blueC redD white8.True patriotism______putting the interests of one's country above everything,includingone's own life.A copes withB derives fromC takes inD relies on9.My father decided to make me go back to college immediately,study my lessons carefully, and______.A a master's degree must attainB must attain my master's degreeC attain my master's degreeD my master's degree be attained10.Libraries have reference books______you can check out a physician's educational background,training,and other credentials.A from thatB of whichC through thatD by which11.The term BRIC was first______by Goldman Sachs economist Jim O'Neill in a research paper,______BRIC stands for Brazil,Russia,India and China.A coined:in whichB invented:of itC made up:andD produced:that12.Had Dickens foreseen that his novel would cause such a disturbance,he______it.A should not have writtenB would not have writtenC didn't writeD had not written13.—I'm concerned about your weight,I think you should go on a diet.—______—Good, then you might as well start right away.A You're so kind,but I don't have to do that.B Actually,I've been thinking about the same thing.C Definitely.What about my blood pressure then?D Oh my!You know it's such a tough job for me.14.—Let me ask you some questions about the accident you witnessed.—______—Thank you.When did the accident occur?A Yes,I really enjoyed it.B It's none of my business.C Sure,go ahead.D Oh,stop teasing me.15.—______—It should be good.I'm looking forward to taking it.A Do you like computer games?B How about cleaning the room with me?C What do you think the computer course will be like?D What are you going to do after you graduate from high school?PartⅡClozeBeing able to multi-task is hailed by most people as a welcome skill,but not according to a recent study which claims that young people between the ages of eight and eighteen of the so-called"Generation M"are spending a considerable amount of their time on【C1】______(fruit)efforts as they multi-task.It argues that,in fact,these young people are frittering away as much as half of their time again as they would if they performed the very same tasks one after another.Some young people are juggling an ever larger number of electronic devices as they study.At the same time as they are working,young adults are also【C2】sur______the Internet,or sending out emails to their friends,and/or answering the phone and listening to music on their iPods or on another computer. As some new device comes along,it too is added to the list rather than【C3】______(place)one of the existing devices.Other research has【C4】ind______that this multi-tasking is even affecting the way of families themselves function as young people are too wrapped up in their own isolated worlds to interact with the other people around them.They can【C5】______longer greet family members when they enter the house,nor can they eat at the family table.All this electronic wizardry is supposedly also seriously affecting young people's performance at【C6】uni______and in the workplace.When asked about their perception of the impact of modern gadgets on their performance of tasks,the overwhelming majority of young people gave a【C7】______(favour)response.The response from the academic and business worlds was not quite as positive.The former feel that multi-tasking with electronic gadgets by children affects later【C8】dev______of study skills,resulting in a decline in the quality of writing,for example,because of the lack of concentration on task completion.They feel that many undergraduates now urgently need remedial help with study skills.Similarly,employers feel that young people【C9】ent______the workforce need to be taught all over again,as they have become deskilled.While all this may be true,it must be borne in mind that more and more is expected of young people nowadays,in fact, too much.Praise rather than criticism is due【C10】______respect of the way today's youth are able to cope,despite what the older generation throw at them.1.【C1】2.【C2】3.【C3】4.【C4】5.【C5】6.【C6】7.【C7】8.【C8】9.【C9】10.【C10】PartⅢReading ComperhensionSection ALook at an atlas.How are mountains shown?Where are the highest mountains?A few mountains stand alone,such as Mount Egmont in New Zealand,and Mount Kenya in Africa.Most mountains are found in long chains called mountain ranges.The Pennines,the Cambrian Mountains, the Alps,the Andes and Rockies are examples of mountain ranges.The highest mountain range on the Earth is the Himalayas in Asia.In order to understand how mountains are formed,we need to know what the inside of the Earth is like.The Earth is made up of layers of rock.The outside layer of rock,the one we live on,is called the Earth's crust.Beneath the crust is a layer called the mantle. Near the top of the mantle,some of the rocks have melted and are a liquid,like sticky tar.Because all the rocks around it press on the mantle,the molten rock tries to force its way out.If the molten rock does find a weak spot,it bursts through the Earth's crust,forming a volcano.Some mountains were made by volcanoes.The Earth's crust is made up of large pieces,called plates,which fit together like the pieces of a jigsaw puzzle.Some of the plates carry continents,others carry oceans. The plates move slowly,floating on the molten rocks of the mantle below.As the plates move,theypush against each other,slowly pushing up the rocks in folds to form mountains.India used to be a long way from Asia,but gradually the plate with India on it moved closer to the plate bearing Asia. The rocks in the sea between India and Asia were pushed up in folds that now form the Himalayan mountain range.That is why it is sometimes possible to find seashells near the tops of the Himalayas.Many other mountain ranges,including the Alps,Rockies and Pen-nines,are similar great folds of rock.While some plates are pushing together,others are moving further apart. Europe and North America are slowly moving further apart.Each year the Atlantic Ocean is a few centimetres wider.As the rocks move,they often crack or break.These breaks are called faults. Sometimes,great blocks of rocks are pushed up between two faults.These blocks may be so large and high that they form mountains.Some of the highland areas of East Africa are block mountains, so are the Vosges mountains in France and the Sierra Nevada mountains in the western United States.Block mountains often have flat tops.A flat-topped highland is called a plateau.Questions56—60Complete the following form with no more than three words according to the passage.56.57.58.59.60.Section BBy studying the notebooks,correspondence,and conversations of some of the world's great thinkers in science,art,and industry,scholars have identified the following thinking strategies that enable geniuses to generate original ideas:【B1】______Sigmund Freud's analytical methods were designed to find details that didn't fit traditional paradigms in order to come up with a completely new point of view.To solve a problem creatively,you must abandon the first approach that comes to mind,which usually stems from past experience,and reconceptualize the problem.Geniuses do not merely solve existing problems:they identify new ones.【B2】______Geniuses develop visual and spatial abilities that allow them to display information in new ways.The explosion of creativity in the Renaissance was tied to the development of graphic illustration during that period,notably the scientific diagrams of Leonardo da Vinci and Galileo Galilei.Galileo revolutionized science by making his thought graphically visible while his contemporaries used more conventional means. Geniuses produce.Thomas Edison held1,093patents,still a record.He guaranteed a high level of productivity by giving himself idea quotas:one minor invention every ten days and a major invention every six months.Johann Sebastian Bach wrote a cantata every week even when he was sick.Wolfgang Mozart produced more than600pieces of music.【B3】______Like playful children with buckets of building blocks,geniuses constantly combine and recombine ideas,images, and thoughts.The laws of heredity were developed by Gregor Mendel,who combined mathematics and biology to create a new science of genetics.【B4】______Their facility to connect the unconnected enables geniuses to see things others miss.Da Vinci noticed the similarity between the sound of a bell and a stone hitting water-and concluded that sound travels in waves.【B5】______Whenever we attempt to do something and fail,we end up doing something else.That's the first principle of creative accident.We may ask ourselves why we have failed to do what we intended,which is a reasonable question.But the creative accident leads to the question:What have we done?Answering that one in a novel,unexpected way is the essential creative act.It is not luck, but creative insight of the highest order.This may be the most important lesson of all:When you find something interesting,drop everything and go with it.Too many talented people fail to make significant leaps of imagination because they've become fixated on their pre-conceived plan.Butnot the truly great minds.They don't wait for gifts of chance:they make them happen.Questions61—65Complete the passage with the following sentences.There are two extra sentences that you do not need to use.A.Geniuses make their thought visible.B.Geniuses prepare themselves for enhance.C.Geniuses make novel combinations.D.Geniuses look at problems from all angles.E.Geniuses have a really broad mind.F.Geniuses force relationships.G.Geniuses are powerful in lots of aspects.6.【B1】7.【B2】8.【B3】9.【B4】10.【B5】Section CThe Dragon Boat Festival,the5th day of the5th lunar month,has had a history of more than 2,000years.Here are some things you must know.There are many legends about the evolution of the festival,the most popular of which is in commemoration of Qu Yuan(340—278BC).Qu Yuan was minister of the State of Chu and one of China's earliest poets.In face of great pressure from the powerful Qin State,he advocated enriching the country and strengthening its military forces so as to fight against the Qin.However,he was opposed by aristocrats and later deposed and exiled by King Huai.In his exiled days,he still cared much for his country and people and composed immortal poems including Li Sao(The Lament),Tian Wen(Heavenly Questions)and Jiu Ge(Nine Songs), which had far-reaching influences.In278BC,he heard the news that Qin troops had finally conquered Chu's capital,so he finished his last piece Huai Sha(Embracing Sand)and plunged himself into the Miluo River,clasping his arms to a large stone.The day happened to be the5th of the5th month in the Chinese lunar calendar.After his death,the people of Chu crowded to the bank of the river to pay their respects to him.The fishermen sailed their boats up and down the river to look for his body.People threw into the water zongzi(pyramid-shaped glutinous rice dumplings wrapped in reed or bamboo leaves)and eggs to divert possible fish or shrimp from attacking his body.An old doctor poured a jug of realgar wine(Chinese liquor seasoned with realgar)into the water,hoping to turn all aquatic beasts drunk.That's why people later followed the customs such as dragon boat racing,eating zongzi and drinking realgar wine on that day.Dragon boat racing is an indispensable part of the festival,held all over the country.As the gun is fired,people will see racers in dragon-shaped canoes pulling the oars harmoniously and hurriedly,accompanied by rapid drums,speeding toward their destination.Folk tales say the game o-riginates from the activities of seeking Qu Yuan's body,but experts,after painstaking and meticulous research,conclude that dragon boat racing is a semi-religious,semi-entertaining program from the Warring States Period(475—221BC).On Dragon Boat Festival,parents also need to dress their children up with a perfume pouch.They first sew little bags with colorful silk cloth,then fill the bags with perfumes or herbal medicines,and finally string them with silk threads.The perfume pouch will be hung around the neck or tied to the front of a garment as an ornament.They are said to be able to ward off evil.Questions66—70Answer the following questions according to the passage.11.When do Chinese people celebrate the Dragon Boat Festival every year?12.What masterpieces of Qu Yuan are mentioned in the passage?13.Why did Qu Yuan commit suicide?14.How do people celebrate the Dragon Boat Festival now?15.Why do parents prepare perfume pouches for their children on Dragon Boat Festival?Section DWhile baseball is often described as the national sport of the United States of America,it probably developed from an eighteenth-century English game called rounders.There were severalversions of the game until1845,when Alexander J.Cartwright organized"a group of players to decide on one set of rules.The main change from rounders was that a runner had to be tagged or touched by a player holding the ball to be put out,rather than hit by a thrown ball.This meant that a smaller,harder ball could be used,which in turn made possible a faster,larger game.Until the mid-1860s,baseball was an amateur sport,which means that the players were not paid.The first professional team,the Cincinnati"Red Stockings",was organized in1869and within two years the sport was more or less professional.Nowadays the best players can earn millions of dollars playing baseball.Professional baseball in the United States and Canada consists of two leagues and for the first half of the twentieth century there were also separate leagues for black players.The black leagues produced many excellent players but it wasn't until the1940s,and the success of Jackie Robinson playing for the Brooklyn"Dodgers",that black players were integrated into white major-league baseball in the United States.Baseball has had a broad impact on popular culture, both in the United States and elsewhere.Dozens of English-language idioms have been derived from baseball,for instance,the baseball meaning of"out of the ball park"is to hit a home run,but its non-baseball equivalent is to do something well or exactly as it should be done.The baseball cap has become a worldwide fashion i-tem not only in the United States,but also in countries where the sport itself is not particularly popular,such as the United Kingdom.Baseball has inspired many works of art and entertainment.One of the first major examples,Ernest Thayer's poem"Casey at the Bat",appeared in1888.There have been many baseball movies,including the Academy Award-winning The Pride of the Yankees(1942)and the Oscar nominees The Natural(1984)and Field of Dreams(1989).Literary works connected to the game include the short fiction of Ring Lardner and novels such as Robert Coover's The Universal Baseball Association,Inc.,J.Henry Waugh,Prop.Baseball's literary canon also includes the beat reportage of Damon Runyon:the columns of Grantland Rice,Red Smith,Dick Young,and Peter Gammons:and the essays of Roger Angell.Questions71—75Complete the summary with words from the passage,changing the form where necessary,with no more than three words for each blank.Baseball is regarded as the national sport of the USA.Its history can be traced back to an eighteenth-century English game named【R1】______.There were several versions of the game until1845,【R2】______one set of rules was decided on.Baseball was originally【R3】______,but in1869the first professional team,the Cincinnati Red Stockings,was organized.For the first half of the twentieth century black players had separate leagues,but【R4】______began in the1940s because of the success of Jackie Robinson. Baseball extended its glamour to many other fields,such as fashion,language,art and entertainment. Many artists and film directors got【R5】______from the worldwide popular sport.16.【R1】17.【R2】18.【R3】19.【R4】20.【R5】PartⅣError CorrectionPeople often laugh when they see penguins walking.Penguins look very funnywaddle from side to side on their short little legs.However,Adelie penguins【M1】______can walk200 kilometers across the Antarctic sea ice to the place they lay【M2】______their eggs.Penguins are such good swimmers so early explorers thought they were【M3】______fish.They use their flippers'fly'through the water as other birds use their【M4】______wings to fly through the air. Emperor penguins,the big penguins,【M5】______can go as fast as50kilometers an hour.If Adelie penguin is swimming【M6】______quickly,it can jump2meters out of the water.They do this before they are【M7】______being chased by leopard seals,which like to eat them.Emperor penguins can hold its breath underwater for twenty minutes.【M8】______This means they can divevery deep to hunt for food.The deepest dive scientists know about is458meters.That's nearly half a kilometer!When the male emperor penguins are looking after eggs,they join together in tightly groups.In the middle of the group it might be38℃,【M9】______while on the outside of the group it might be-35℃.When the penguins【M10】______on the outside get too cold,they move slowly to the inside and others take their place on the outside.1.【M1】2.【M2】3.【M3】4.【M4】5.【M5】6.【M6】7.【M7】8.【M8】9.【M9】10.【M10】PartⅤTranslationSection A1.If your parents give you pocket money with no strings attached,I've got some bad news for you.Experts are now claiming that it may be harmful for teenagers to get"free"pocket money. They argue that it makes them lazy and they may even end up in poverty.What's more,they say that youngsters will never learn the value of money if they don't earn it.Studies also indicate that you can rarely expect teenagers to save their pocket money when they get it for free and often waste it on unnecessary things.However,if they have to do something in order to earn it,they usually learn to use their money wisely.Section B有些人的成功常常让周围的人大惑不解,因为他们似乎从来都不工作,或者没有长时间地工作。
第十八届华杯赛决赛小高C试题及详细解答
说明:试卷及答案由华杯赛官网下载,详细解答由广州启慧教育提供。
广州市决赛使用此卷。
详细解答:一、填空题:1、原式=827551153331138×+÷−×=827165533838×××=215(或7.5) 难易程度:☆2、周期问题。
答案是5,92012年12月21到2013年2月3,包含12月21在内,共(31-21+1)+31+3=45天 周期为9,45÷9=5,余0,故 五 九的最后一天,即:第 九 天难易程度:☆3、先分别求出a+b 的最大值与最小值:要使a+b 最大,则a 与b 应尽量大,由于b 不超过19,故b 最大为19,由ba 是最简分数,且4151<<b a ,当b=19时,利用商不变性质有:20519204<<a ,故a 最大可为4,因此,a+b 最大可为19+4=23。
同理,可求出a+b 的最小值:由4151<<b a 可得:82102<<b a ,b a 最小可为92,故a 最小可为2,b 最小可为9,a+b 最小可为2+9=11因此,所有的积是:23×11=253难易程度:☆☆4、面积问题。
答案是37.5总体思路是:直接求△PBQ 的面积不容易,转化为用正方形面积减去其他图形的面积。
故需要连接DQ ,把四边形DPQC 转化为二个三角形。
接下来,多次利用同顶点的三角形面积的关系即可求出。
正方形的面积为100,故边长为10(1)、以D 为顶点来看△DQC 与△DQA因为AQ :QC=4:1,所以△QDA 的面积是△QDC 的4倍,所以△DQC 的面积是△ADC 的1/5,而△ADC 的面积是正方形ABCD 的一半,故△DQC 的面积是100÷2÷5=10显然△BCQ 的面积与△DQC 的面积相等,也是10(2)、以Q 为顶点来看△QDP 与△QPA因为AP :PD=1:3,所以△QDP 的面积是△QAP 的3倍,所以△QDP 的面积是△QDA 的3/4,而△QDA 的面积是△ACD 的面积减去△DQC 的面积,也就是50-10=40,故,△QDP 的面积为30(3)、求△ABP 的面积:由于AP :PD=1:3,AD=10,因此,AP=2.5,故,△ABP 的面积是2.5*10/2=12.5综合以上结论,就可求出△PBQ 的面积为:100-10-10-30-12.5=37.5难易程度:☆☆5、和差问题。
2018年华杯赛初赛小学高年级组试题2题
2:如图,一个3×3的正方形网格,如果小正方形 边长是1,那么阴影部分的面积是多少?
2:如图,一个3×3的正方形网格,如果小正方形 边长是1,那么阴影部分的面积是多少?
2:如图,一个3×3的正方形网格,如果小正方 边长是1,那么阴影部分的面积是多少?
2:如图,一个3×3的正方形网格,如果小正方形 边长是1,那么阴影部分的面积是多少?
2:如图,一个3×3的正方形网格,如果小正方形 边长是1,那么阴影部分的面积是多少?
2:如图,一个3×3的正方形网格,如果小正方形 边长是1,那么阴影部分的面积是多少?
2:如图,一个3×3的正方形网格,如果小正方形 边长是1,那么阴影部分的面积是多少?
小学华杯赛中年级组初赛真题及答案(第十八届-第二十三届)
华罗庚金杯少年数学邀请赛(小学中年级组)初赛试卷及答案(第18届-第23届)共9套(内部资料)第十八届华罗庚金杯少年数学邀请赛初赛试卷A(小学中年级组)(时间:2013年3月23日10:00~11:00)一、选择题(每小题10分,满分60分。
以下每题的四个选项中,仅有一个是正确的,请将表示正确答案的英文字母写在每题的圆括号内。
)1.45与40的积的数字和是()。
(A)9(B)11(C)13(D)152.在下面的阴影三角形中,不能由右图中的阴影三角形经过旋转、平移得到的是图()中的三角形。
3.小东、小西、小南、小北四个小朋友在一起做游戏时,捡到了一条红领巾,交给了老师.老师问是谁捡到的?小东说不是小西;小西说是小南;小南说小东说的不对;小北说小南说的也不对。
他们之中只有一个人说对了,这个人是()。
(A)小东(B)小西(C)小南(D)小北4.2013年的钟声敲响了,小明哥哥感慨地说:这是我有生以来遇到的第一个没有重复数字的年份.己知小明哥哥出生的年份是19的倍数,那么2013年小明哥哥的年龄是()岁。
(A)16(B)18(C)20(D)225.如右图,一张长方形的纸片,长20厘米,宽16厘米,如果从这张纸片上剪下一个长10厘米,宽5厘米的小长方形,而且至少有一条边在原长方形的边上,那么剩下纸片的周长最大是()厘米。
(A)72(B)82(C)92(D)1026.张老师每周的周一,周六和周日都跑步锻炼20分钟,而其余日期每日都跳绳20分钟,某月他总共跑步5小时,那么这个月的第10天是()(A)周日(B)周六(C)周二(D)周一二、填空题(每小题10分,满分40分)7.如右图,一个正方形被分成了4个相同的长方形,每个长方形的周长都是20厘米,则这个正方形的面积是_______平方厘米。
8.九个同样的直角三角形卡片,拼成了如右图所示的平面图形,这种三角形卡片中的两个锐角较大的一个是_______度。
9.幼儿园的老师给班里的小朋友送来55个苹果,114块饼干,83块巧克力,每样都平均分发完毕后,还剩3个苹果,10块饼干,5块巧克力,这个班最多有_______位小朋友。
第18届华杯赛每周一练试题及答案(第十期)(竞赛)
第18届华杯赛每周一练试题及答案(第十期)试题一(小学高年级组)有3个不同的数字,排列3次,组成了3个三位数,这3个三位数相加之和为789,又知运算中没有进位,那么这3个数字连乘所得的积是多少?答案:10或者12 解析:由题意,3个三位数的百位之和为7,十位数之和为8,个位数之和为9,而在每个三位数里,3个数字都各出现了一次。
所以我们把百位之和、十位之和、个位之和再加在一起,就应该等于把三个数字各加了3次,也就等于3个数字之和的3倍。
由于7+8+9=24,也即3个数字之和的3倍为24,从而3个数字之和为8.又由题意,3个数字互不相同。
而3个数字互不相同,其和又等于8,容易知道3个数字只能是1、2、5或者1、3、4.题目要求3个数字连乘的积,所以答案是1×2×5=10或者1×3×4=12试题二(小学高年级组)在10、9、8、7、6、5、4、3、2、1这十个数的每相邻两个数之间都填上一个加号或一个减号,组成一个算式。
要求同时满足以下条件:①算式的结果等于37;②这个算式里所有前面填了减号的数的乘积尽可能大。
那么这个最大乘积是多少?答案:24.解析:我们把这十个数字前面填了减号的数归为一组,剩下的数归为另一组。
第一组里所有数之和记为乙。
首先,甲和乙的和,应该就是两组数全体数字之和,也就是从1到10这十个数之和;即55.其次,由于第一组数中每个数前面都填了减号,所以乙减去甲的差,应当就是题目中所说的那个算式的得数,即37.这样,用和差问题的解题方法,可以算出甲是9,乙是46.也就是说,所有前面填了减号的数的和是9,这就是分析里所说的那个约束条件。
现在我们要找一组合适的数,它们的和是9,而乘积要尽可能大,这很容易通过一一试验来得到。
最合适的一组数是2、3、4,它们的乘积是24,即为答案。
试题三(小学中年级组)某种商品的价格是:每1个1分钱,每5个4分钱,每9个7分钱。
(完整word版)第十八届华杯赛初赛小高组C卷试题及详解
第十八届华罗庚金杯少年数学邀请赛 初赛试题C (小学高年级组)(时间:2013年3月23 日)表示正确答案的英文字母写在每题的圆括号内.)、选择题(每小题10分,满分60分.以下每题的四个选项中,仅有一个是正1.如果 2013 2013 - 2014 2014 2012 卫(其中m 与n 为互质的自然数) m那么m+n 的值是( (A )1243 ( B )1343 ( C )4025 (D )4029 解答:B 。
在考试中,选择恰当的方法很重要。
这道题,看到这道题后,我第一个想法就是归纳。
2 2 2 2 2 23 1445、 、 、 ------------------------32 1 5 42 2 2 5 3 7 62 45-、写完前三个,发现第二个算式很不和8谐,又写出了第四个,仔细一想,原来第二个可以写成33身3,规律找到了,分子是原42 262013 式中分子部分的一个因数,分母比分子大3!答案一定是,很简单,第一题是很容易2016的年份题,等等,年份 2013这个数是我们非常熟悉的, 2013=3 X 11X 61,是3的倍数,那么加3不还是3的倍数么?可以约分,所以最后的答案是2013切所以选B !2016 672如果本题需要详细的过程,那么用规纳的方法是不合适的,因为这是不完全归纳法,你这么知道前几个适用的情况下,最后的 2013也适用呢,所以最正确的方法是这样思考:如 果这道题直接计算, 分别算出分子分母, 然后必然需要一个约分的过程(从选项可以看出),那么就太麻烦了,如果不计算出最后结果就可以约分, 是件好事儿,那么转化分子还是转化分母呢?我们都知道,当分子分母都是乘法的形式,是比较好约分的,所以要转化分母,要在分母中“凑”出 2013.具体过程是这样的:2014 (2013 1) 20122013 20132014 2013 2014 20122013 2013 2014 2013 2013 2 2013 20132013 6712013 (2014 2) 2016 672m n 671672 1343.这个题做完了,很容易得分的一道题,也是容易马虎的一个题,如果不仔细读题,忽略了“ m 与n 为互质的自然数”,那么就容易把答案写成 D 。
第18届“华杯赛”笔试决赛小学高年级组试题C及参考答案
三、解答下列各题(每题 15 分, 共 30 分, 要求写出详细过程)
13. 答案:
1 4
14. 答案: 10
第 1 页
共 3 页
小数 0. a b c 化成最简分数后, 分子有________不同情况. 8. 由四个完全相同的正方体堆积成如右图所示的立体 , 则立
体的表面上(包括底面)所有黑点的总数至少是________.
二、解答下列各题(每题 10 分, 共 40 分, 要求写出简要过程)
9. 右图中, 大正方形的周长比小正方形的周长多 80 厘米, 阴影部 分的面积为 880 平方厘米. 那么, 大正方形的面积是多少平方 厘米? 10. 某高中根据入学考试成绩确定了录取分数线, 录取了四分之一的考生. 所有 被录取者的成绩平均分比录取分数线高 10 分, 所有没有被录取的平均分比 录取分数线低 26 分, 所有考生的平均成绩是 70 分. 那么录取分数线是多少? 11. 设 n 是小于 50 的自然数, 求使得 3n+5 和 5n+4 有大于 1 的公约数的所有 n. 12. 一次数学竞赛中, 参赛各队每题的得分只有 0 分, 3 分和 5 分三种可能. 比赛 结束时, 有三个队的总得分之和为 32 分. 若任何一个队的总得分都可能达到 32 分, 那么这三个队的总得分共有多少种不同的情况?
2. 农谚 ‘逢冬数九’ 讲的是, 从冬至之日起, 每九天分为一段, 依次称之为一九, 二九, ……, 九九, 冬至那天是一九的第一天. 2012 年 12 月 21 日是冬至, 那 么 2013 年 2 月 3 日是________九的第________天. 3. 最简单分数
2018年华杯赛初赛小学高年级组试题7题
读了剩余的1/4还多15页
读了剩余的1/3还多18页
还剩42页未读
7:雷雷买了一本新书,非常喜欢,第一天读了这本书的 1/5还多12页,第二天读了剩余的1/4还多15页,第三天读 了剩余的1/3还多18页,这时还剩42页未读,那么这本书 的页数是多少?
这本书有多少页
读了这本书的1/5还多12页
7:雷雷买了一本新书,非常喜欢,第一天读了这本书的 1/5还多12页,第二天读了剩余的1/4还多15页,第三天读 了剩余的1/3还多18页,这时还剩42页未读,那么这本书 的页数是多少?
7:雷雷买了一本新书,非常喜欢,第一天读了这本书的 1/5还多12页,第二天读了剩余的1/4还多15页,第三天读 了剩余的1/3还多18页,这时还剩42页未读,那么这本书 的页数是多少?
这本书有多少页
读了这本书的1/5还多12页
读了剩余的1/4还多15页
读了剩余的1/3还多18页
还剩42页未读
7:雷雷买了一本新书,非常喜欢,第一天读了这本书的 1/5还多12页,第二天读了剩余的1/4还多15页,第三天读 了剩余的1/3还多18页,这时还剩42页未读,那么5页
7:雷雷买了一本新书,非常喜欢,第一天读了这本书的 1/5还多12页,第二天读了剩余的1/4还多15页,第三天读 了剩余的1/3还多18页,这时还剩42页未读,那么这本书 的页数是多少?
这本书有多少页
读了这本书的1/5还多12页
7:雷雷买了一本新书,非常喜欢,第一天读了这本书的 1/5还多12页,第二天读了剩余的1/4还多15页,第三天读 了剩余的1/3还多18页,这时还剩42页未读,那么这本书 的页数是多少?
2018年全国大学生英语竞赛C类初赛答案及听力录音原文
- 1 -2018 2018 National National English C ompetition Competition for College S tudents Students (Level C - Preliminary)参考答案及作文评分标准Part I Listening Comprehension Section A1―5 CBADB Section B6―10 TFTFT 10 TFTFT 1111―15 CDBCC Section C16―20 DADDC Section DDictation21. off the coast 22. tiny animals 23. lots of light 24. colours and patterns 25. not allowed to Summary26. abandoned 26. abandoned 27. subway system 27. subway system 28. being renovated 28. being renovated 29. Brooklyn Bridge Station 29. Brooklyn Bridge Station 30. significance Part II Vocabulary & Grammar31―35 DABDB 35 DABDB 3636―40 CAABC 40 CAABC 4141―45 ACBCA Part III Cloze46. ingredient47. up 48. whereas/while 49. intelligence 50. By 51. pessimists 52. at 53. exception 54. encourages 55. resignationPart IV Reading ComprehensionSection A56. landscapes 56. landscapes 57. began to emerge 57. began to emerge 58. birth of impressionism 59. portraits 60. beautiful background scenerySection B61―65 EADGB Section C66.They work hard and have many things to do. 67.They make the wax inside their bodies and squeeze it out from glands in their bellies.68.To store it as food for the time when they cannot visit flowers. 69.Female worker bees.70.Guard bees will not let her in the hive and soon she dies.Section D73. cheap entertainment 74. the participants 72. interacting with 73. cheap entertainment 74. the participants 75. expandsocial reasons 72. interacting with 71.social reasons Part V TranslationSection A76.北京大学是一所综合性国立重点大学,其校园,世称“燕园”,坐落在北京西郊海淀区,总面积2,743,532 平方米,与圆明园和颐和园相毗临。
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3.一只青蛙 8 点从深为 12 米的井底向上爬, 它每向上爬 3 米, 因为井壁打滑, 就会下滑 1 米, 下滑 1 米的时 间是向上爬 3 米所用时间的三分之一. 8 点 17 分时, 青蛙第二次爬至离井口 3 米之处, 那么青蛙从井底爬 到井口时所花的时间为( )分钟. (A)22 (B)20 (C)17 (D)16
二、填空题 (每小题 10 分, 满分 40 分) 7.有四个人去书店买书, 每人买了 4 本不同的书, 且每两个人恰有 2 本书相同, 那么这 4 个人 至少买了_______种书.
【解析】从简单的情况思考,若只有两个人,那么为了符合题意,一定有 6 本不同的书,我们可以给这 6 本数编号为 1、2、3、4、5、6,那么设甲买的是 1、2、3、4,乙买的是 1、2、5、6.这时候又来了第三个 人,我们称呼他为丙,这是丙为了符合题意,他可以选择不买其他的书,他买编号为 3、4、5、6 也符合题 意,这时要注意的是,当三个人,只买 6 本书的时候,当甲、乙买的书确定之后,丙购买的编号是唯一的, 就是丙不能买甲、乙都买的书,如果他买了一本甲乙都买的书,那么他就必须再买一本他自己“独有”的 书!列一个表格让我刚才说的更清晰: 1 甲 乙 丙 √ √ 2 √ √ √ √ 3 √ 4 √ √ √ √ √ 5 6
(2) 乙配得的糖水含糖率:
(3) 丙配得的糖水含糖率:
所以,丙最甜!其实我们还可以用另一种方法来解答,如果对概念理解的比较清晰的话,我们可以知道, 向共同的糖水中加另一种糖水,加的糖水的浓度越大,糖水质量越多就越甜。甲又加入的是浓度为:20%的 糖水 50 克 乙又加入的是浓度为 20÷(20+30)=40%的糖水 50 克 丙又加入的是浓度为 2÷(2+3)=40%的糖水 100 克 很明显,丙往里面加的糖水更甜,更多,所以最甜的一定是丙。
2.甲、乙、丙三位同学都把 25 克糖放入 100 克水中混合成糖水, 然后他们又分别做了以下事情: 再加入 50 克含糖 率 20%的糖水. 再加入 20 克糖 和 30 克水. 再加入 100 克糖与水的比是 2:3 的糖水.
海边教育—好未来(原学而思)旗下专业的中小学直播课堂!
4.已知正整数 A 分解质因数可以写成 A 2 3 5 , 其中 、 、 是自然数. 如果 A 的二分之一是完
全平方数, A 的三分之一是完全立方数,
A 的五分之一是某个自然数的五次方, 那么
的最小值
5 / 11
海边教育—好未来(原学而思)旗下专业的中小学直播课堂!
的最小值恰好是[2,5]=10; 的最小值恰好是[2,3]=6。 同时满足三个条件的 的最小值恰好是[3,5]=15;
所以, 的最小值是 15+10+6=31。
5.今有甲、乙两个大小相同的正三角形, 各画出了一条两边中点的连线. 如图, 甲、乙位置左右对称, 但甲、 乙内部所画线段的位置不对称. 从图中所示的位置开始 , 甲向右水平移动 , 直至两个三角形重叠后再离开. 在移动过程中的每个位置, 甲与乙所组成的图形中都有若干个三角形. 那么在三角形个数最多的位置, 图形 中有( )个三角形.
(A)9
(B)10
(C)11
(D)12
6.从 1~11 这 11 个整数中任意取出 6 个数, 则下列结论正确的有( ① 其中必有两个数互质; ② 其中必有一个数是其中另一个数的倍数; ③ 其中必有一个数的 2 倍是其中另一个数的倍数. (A)3 (B)2 (C)1 (D)0
)个.
二、填空题 (每小题 10 分, 满分 40 分) 7.有四个人去书店买书, 每人买了 4 本不同的书, 且每两个人恰有 2 本书相同, 那么这 4 个人 至少买了_______种书.
一、选择题 (每小题 10 分, 满分 60 分. 以下每题的四个选项中, 仅有一个是正确的, 请将表示正确答案的 英文字母写在每题的圆括号内.)
1.如果
2013 2013 n (其中 m 与 n 为互质的自然数), 那么 m+n 的值是( 2014 2014 2012 m
(B)1343 (C)4025 (D)4029
海边教育—好未来(原学而思)旗下专业的中小学直播课堂!
7 / 11
一定是两两互质的,而很容易想到,每相邻的两个数都是互质的,所以可以这样构造(1,2,3) (4,5) (6,7) (8,9) (10,11) 其实构造的方法不是唯一的, 还有很多构造方法如: 【 (1,3,4) (2,9) (8, 11) (5, 6) (7,10) 】 ; 第二句很容易举出反例, (6、7、8、9、10、11)最大的六个数就没有倍数关系,同样的还有: (4、5、 6、7、9、11) ; 第三句,根据第二句话的反例,可以看出,第三句话是成立的,那么就要严谨的证明一下,还是要构 造抽屉,按照什么构造呢,可以按照 1 到 11 中的 5 个质因数来构造 5 个抽屉,1 放在哪个抽屉里都可以, (1,2,4,8) (3,6,9) (5,10) (7) (11)这五个抽屉中,要任意取 6 个数,必有两个数在同一个抽屉中,就 必满足其中一个数的 2 倍是另一个数的倍数。 所以有两句是正确的,最后的答案是 B。
10.如右图, 正方形 ABCD 被分成了面积相同的 8 个三角形, 如果 DG = 5, 那么正方形 ABCD 面积是____.
海边教育—好未来(原学而思)旗下专业的中小学直播课堂!
3 / 11
试卷解析
第十八届华罗庚金杯少年数学邀请赛
初赛试题(小学高年级 C 组) (时间: 2013 年 3 月 23 日)
)得到的糖水最甜. (B)乙 (C)丙 (D)乙和丙
3.一只青蛙 8 点从深为 12 米的井底向上爬, 它每向上爬 3 米, 因为井壁打滑, 就会下滑 1 米, 下滑 1 米的时 间是向上爬 3 米所用时间的三分之一. 8 点 17 分时, 青蛙第二次爬至离井口 3 米之处, 那么青蛙从井底爬 到井口时所花的时间为( )分钟. (A)22 (B)20 (C)17 (D)16
4 / 11
最终,( (A)甲
)得到的糖水最甜. (B)乙 (C)丙 (D)乙和丙
【解析】根据题意和我们所学过的公式,可以分别求出三人得到的糖水的最终浓度!
(1) 甲配得的糖水含糖率:
25 50 20% 100% 20% ; 100 25 50 25 20 100% 25.7% ; 100 25 50 25 100 5 2 100% 28.9% . 100 25 100
8.每天, 小明上学都要经过一段平路 AB、 一段上坡路 BC 和一段下坡路 CD(如右图) . 已知 AB:BC:CD = 1:2:1,
海边教育—好未来(原学而思)旗下专业的中小学直播课堂!
2 / 11Leabharlann 并且小明在平路、上坡路、下坡路上的速度比为 3:2:4. 如果小明上学与放学回家所用的时间比是 与 n 是互质的自然数),那么 m+n 的值是 .
【解析】下滑 1 米的时间是向上爬 3 米所用时间的三分之一,即上爬和下滑的速度相同。如果以一上一下 为一个周期,那么实际上每上升 2 米用时 4 分钟。如果此周期计算,那么青蛙爬到井口需要经过 12÷2=6 个周期。 在经过 5 个周期后, 青蛙距离井口 12-2×5=2 米, 再进过 2 分钟即可爬到井口, 所以共用时 5×4+2=22 分钟。 检验:青蛙经过 4 个周期,到达距离井口 4 米处,此时青蛙已爬到距井口 3 米处 1 次,用时 4×4=16 分钟, 再向上爬 1 米重新回到距井口 3 米处,再经过 1 分钟,16+1=17(分钟) ,满足题意。
第十八届华罗庚金杯少年数学邀请赛
初赛试题(小学高年级 C 组) (时间: 2013 年 3 月 23 日)
一、选择题 (每小题 10 分, 满分 60 分. 以下每题的四个选项中, 仅有一个是正确的, 请将表示正确答案的 英文字母写在每题的圆括号内.)
1.如果
2013 2013 n (其中 m 与 n 为互质的自然数), 那么 m+n 的值是( 2014 2014 2012 m
).
(A)1243 【解析】
原式
2013 2013 2014 (2013 1 ) 2012 2013 2013 2014 2013 2014 2012 2013 2013 2014 2013 2013 2 2013 2013 2013 (2014 2) 671 672
(B)1343 (C)4025 (D)4029
).
(A)1243
2.甲、乙、丙三位同学都把 25 克糖放入 100 克水中混合成糖水, 然后他们又分别做了以下事情: 再加入 50 克含糖 率 20%的糖水. 再加入 20 克糖 和 30 克水. 再加入 100 克糖与水的比是 2:3 的糖水.
最终,( (A)甲
6.从 1~11 这 11 个整数中任意取出 6 个数, 则下列结论正确的有( ① 其中必有两个数互质; ② 其中必有一个数是其中另一个数的倍数; ③ 其中必有一个数的 2 倍是其中另一个数的倍数. (A)3 (B)2 (C)1 (D)0
)个.
【解析】对于“任意…必有”这样的语句,应该考虑到“抽屉原理” 。如果需要证明结论正确的话,那就要 构造抽屉,而抽屉的个数,应该是小于 6 的!看题: 第一句说必有两个数互质,如果这是正确的话,那么就要构造出小于 6 的抽屉,且每一组抽屉中的数
(A)9
(B)10
(C)11
(D)12
【解析】可以把所有的情况都画出来然后通过比较找出三角形最多的图形,再仔细的数一下,发现有 11 个, 所有的图如下:
海边教育—好未来(原学而思)旗下专业的中小学直播课堂!