四年级奥数等差数列二教师版

1、第五讲等差数列二解题方法某些问题以转化为求假设干个数的和解决这些问题时先要判断这些数是否成为等差数 列,如果是等差数列才可以运用它的一些公式.在解决自然数的数字问题时,应根据题目的具体特点,有时可考虑将题中的数适当分 组,并将每组中的数合理配对,使问题得以顺利解决.例题1小王看一本书第一天看了 20页,以后每天都比前一天多看 2页,第30天看了 78页正好看完.这本书共有多少页提示根据条件“以后每天比前一天多看2页可以知道他每天看的页数都是根据一定规律排列的数, 即20、22、24、76、78.要求这本书共有多少页也就是求出这列数的和.解：由题意可知,这列数是一个等差数列,首项 =20,末项=

2、78,项数=30,所以这本书共有 20+78 X 30+2=1470 页答：这本书共有1470页.引申1、文丽学英语单词,第一天学会了 3个,以后每天都比前一天多学会 1个,最后一天学会了 21 个.文丽在这些天中共学会了多少个英语单词解：文丽每天学会的单词个数是一个等差数列,即3、4、5、6、21.首项=3,末项=21,项数=21-3 +2+1=10.所以,文丽在这些天中共学会了3+21 X 10+ 2=120个答：文丽在这些天中共学会了120个英语单词.2、李师傅做一批零件,第一天做了 25个,以后每天都比前一天多做 2个,第20天做了 63个 正好做完.这批零件共有多少个答：25+63

3、X 20+ 2=880 个3、小李读一本短篇小说,她第一天读了20页这个等差数列共有多少项 答：这个等差数列共有29项.例题2建筑工地上堆着一些钢管如以下图,求这堆钢管一共有多少根.oooocboooo提示：根据图可以知道,这是一个以3为首项,以1为公差的等差数列,求钢管一共有多少根其实是求 这列数的和.解：求钢管一共有多少根 ,其实就是求3+4+5+9+10的和.项数=10-3 +1+1=8,根据公式求和为：3+4+5+9+10=3+10 X8 + 2=13X8+ 2=52根.答：这堆钢管一共有52根.引中1、一些同样粗细的圆木,像如以下图一样均匀地堆放在一起,最下面一层有70根.一共有多少

4、根圆木答案：2485根.2、用3根等长的火柴棍摆成一个等边三角形,用这样的等边三角形,按以下图所示铺满一个大的等边三角形,如果这个大的等边三角 形的底边能放10根火柴棒,那么这个大的等边三角形中一共要放 多少根火柴棒解：如果把图中最上端的一个三角形看做第一层,与第一层紧相连的3个三角形2个向上的三角形,一个向下的三角形看做第二层,那么这个图中一共有10层三角形.不难看出,这10层三角形每层所需火柴棒根数,自上而下依次为：3,6,9,3X10.它们成等差数列,且首项为3,公差为3,项数为10.求火柴的总根数,也就是求这个等差数列各项的和.即：3+6+9+ +30=3+30 X 10 + 2=33

5、 X 5=165卞艮答：这个大的等边三角形中一共要放16升艮火柴棒.3、用相同的小立方体摆成如以下图的形状,如果共摆成10层,那么最下面有多少个小立方体答案：55个例题3有50把锁的钥匙搞乱了 ,为了使每把锁都配上自己的钥匙,至多要试多少次提示：开第一把锁时,如果不凑巧,试了 4田巴钥匙还不行,那所剩的一把就一定能把它翻开,即开第 一把锁至多需要试4砍,同理,开第二把锁至多需要48次,开第三把锁至多需试47次,等翻开第4毋巴 锁,剩下的最后一把不用试,一定能翻开.解：根据以上分析,可以把此题转化为求一个等差数列的和,即 49+48+47+ +2+1=49+1 X49+ 2=1225次答：至多要

6、试1225次.引中1、有60把锁的钥匙搞乱了 ,为了使每把锁都配上自己的钥匙,至多试多少次解：59+58+57+2+1=(59+1) X 59+2=1770(次)2、有一些锁的钥匙搞乱了 ,至多要试28次,就能使每把锁都配上自己的钥匙.一共有几 把锁的钥匙搞乱了 答：一共有8把锁的钥匙搞乱了 .3、一辆公共汽车有66个座位,空车出发后,第一站上一位乘客,第二站上两位乘客,第三站上 三位乘客,依次类推,第几站后,车上坐满乘客答：第11站后,车上坐满乘客.例题4四(1)班45位同学举行一次同学联欢会,同学们在一起一一握手,且每两个人只能握一次手,同学们共握了多少次手提示：假设4游同学排成一队,第1

7、位同学一次与其他同学握手,一共握了 44次,第2位同学因与第1 位同学已握手,只需要与另外4啦同学握手,一共握了 43次,这卞¥第3位同学只需与另外的42位同学握手, 依次类推.握手的次数分别为：44,43,42,3,2,1 ,这样应用等差数列求和公式即可解答.解：根据以上分析,可以把此题转化为求一个等差数列的和即 44+43+42+ -+3+2+1=(44+1) X 44+2=990 (次)答：同学们共握了 990次手.引中1、学校进行书法大赛,每个选手都要和其他所有选手各赛一场.如果有16人参加比赛,一共要进行多少场比赛答案：15+14+13+ - +3+2+1= (15+1)

8、X 15+2=120 (场)2、在一次元旦晚会上,一共有48位同学和5位老师,每一位同学或老师都要和其他同学握一 次手.那么一共握了多少次手解：根据题意,一共有 48+5=53 (人)参加了这次晚会.所以,一共握手的次数为： 52+51+50+ +3+2+1= (52+1) X 52+2=1378 (次)答：一共握了 1378次手.3、一次朋友聚会,大家见面时总共握手28次.如果参加聚会的人和其余的每个人只握手一次,问参加聚会的共有多少人解：设共有n人参加了聚会,由于要求参加聚会的人和其余的每个人只握手一次,所以 一共握手(n-1 ) + (n-2) + +2+1=nX ( n-1 ) +2,

9、由于共握手 28次,所以 nx ( n-1 ) + 2=28,即nx (n-1 ) =56.又由于n是正整数,通过计算,可知 8X 7=56, n=8,所以参加聚会 的共有8人.Class:答：参加聚会的共有8人.Name:A.Morning !B.Hello !C.Hi !()2. Nice to see you again !A.How are you ?B.Nice to see you , too .C.How do you do ?()3.Good night,mom !A.Night !B.Good night !()4.How do you do ?A.How are you ?

10、B.Fine,thanks .()5.HowmanyC.Good evening .C.How do you do ?storybooksdoyouhave ?A.I have 10.B.I can see 10.()6.Do you have new teachers?A.Yes,we do .B.Yes,we don ' t.()7.Who'C.Thirty yuan.C.Yes,we have .syourartteacher ?A.Mr Zhu.B.Miss Zhu.C.He ' s tall.()8.What ' s he like?A.He'

11、 s tall and strong .B.Yes,he is.C.Mr Zhu.()9.Is your English teacher young?A.No,she isn ' t.B.Yes,she is .C.No,she is.()10.?Her name is Chen Jie.A.What' s your name ?B.What ' s she name ? C.What ' s her name ?()11.? I like Chinese,math and English.A.What classes do you like?B.What do

12、 you like?C.What are you like ?()12.? We have English and P.E.C.What do you have on Monday?()13.? It ' s Monday.A.What is it today ? B.What day is it today ?C.What day is today ?()14.? I watch TV and do my homework.A.What do you do ? B.What do you do in Mondays?C.What do you do on Sundays ?()15.

13、May I have a look ?A.Sure.Here you are .B.Look !C.Here you are .)24.Thisisapple.It()16.Our math teacher isCanada.A.fromB.inC.at()17.Ithree new teachers.A.hasB.amC.have()18.What ' sChinese teacher like ?A.youB.yourC.you ' re()19.My P.E.teacher isthin.A.tooB.soC.very()20.There aredays in a wee

14、k.A.sixB.sevenC.eight()21.There aremonth(月)in a year(年).A.tenB.elevenC.twelve()22.I often watch TVSaturday .A.onB.inC.at()23.I like P.E.I don ' t lime music.A.butB.andC.soisred apple.A.a , aB.an,anC.an, a()25.Whatdo you like ?A.classesB.classC.class ' s六年级英语测试题Class:Name:()1. How are you ?A.

15、Fine,thanks.B.Yes,it is.C.How are you()2. Nice to meet you !A.Fine,thank you.B.OK.C.Nice to meet you ,too()3. How do you go to school ?A.I go to Canada by plane. B.I go to school by bike.C.What about you()4.HowdoyougototheUSA ?A.I usually go to school by bus. B.I go to England by ship.C.I go by plan

16、e.()5.?My homeis near thepost office.A. Where is your home ? B.OK.C.See you then!()6. See you at 2 o' clock.A.See you then !B.The fifth floor.C.It ' s easy.()7.?You can go by the No.15bus.A.It ' s not far.B. How can I get to Zhongshan Park ?C.Sure.A.Next to the cinema.B.Thank you .C.You

17、' re welcome.()9. Excusehere ?A.Yes,there is .B.No,it()10.?office.A.Yes,there is .B.No,it()11.A. Where is the cinema ,please ?me ,isthere a cinema nears not far.C.It ' s near the post office.? It ' s near the posts not far.C. Where is the library? It ' s next to the hospital.B.Is it

18、far ?C.Go straight.()12. How can I get to the hospitalA.It ' s next to the hospital.B.You can go by the No.201 bus. C.Thank you.()13.Thank you .A.Thank you .B.OK.C.You' re welcome.()14. How can I get to the museum?A.Go straight.Then turn left.B.Thank you .C.It ' s east of the cinema .()1

19、5. Where is the post office ?A.Go straight.Then turn left.B.Thank you .C.It ' s east of the cinema .()16. What are you going to do thisevening ? A.I ' m going to the cinema . B.I go to school on foot.C.Yes,it is.()17. Is it far ?A.No,it is .B.Yes , it is .C.Yes,it isn ' t.()18.do you go

20、to school ?()19. I go to schoolbike.A.onB. byC.get()20. Can I gofoot ?A.byB.atC.on()21.How can Ito the post office ?A.nearB. getC.for()22.me.A. ExcuseB. HowC.next()23.birthday to you !A. AfterB.HappyC.First()24. The hospital isthe left.A. atB.inC.on()25.is the bookstore ?A.WhereB.HowC.When四年级英语测试题Cl

21、ass:Name:( )1.Good afternoon ! A.Hello! B.Hi ! C.Afternoon ! ( )2.Nice to see you again ! A.How are you ? B.Hello ! C.Nice to see you , too. ( )3.Good night,moom ! A.Good evening ! B.Good night ! C.Night ! ( )4.How are you ? A.Fine,thank you . B.I am 10. C.Nine . ( )5.How do you do ?A.Fine ,Thank yo

22、u . B.How are you ? C.How do you do ? ( )6.How old are you ?A.How are you ? B.I am 11. C.I have 11. ()7.? I have 23.A.How many books do you have ? B.How many books can you see? C.How many book do you have ? ()8.? I can see 6.A.How many lights do you have ? B.How many lights can you see ?C.How many l

23、ight can you see ?( )9.May I have a look ?A.Sure.Here you are . B.Look! C.Sure.Here are you .()10.? 50 yuan.A.How much is this schoolbag ? B.How many is this schoolbag ?C.How much are this schoolbag ?( )11.Where' s my seat ?A.It' s near the door. B.It' s on the door. C.It' s under th

24、e door.()12.Let ' s clean the desks and chairs.A.All right ! B.Hello ! C.It' s nice .()13.What' s this ?A.There is a board . B.It' s a bee. C.It' s bee.()14.? My name is Mike.A.Here are you ? B.What' s your name ? C.How do you do ?()15.Who ' s the inventor of paper ?A.Chi

25、nese people. B.Oh! Great ! C.Hello!()16.I a student. You a teacher.A.am ,am B.are, are C.am, are( )17.This a boy.His nameZhang Peng.A.is, is B.am , is C.is , are()18.Let clean the fish bowl.A.I B. meC.my()19.This isapple.It isred apple .A.an ,anB.a, aC.an, a()20.We a new classroom.A.areB.haveC.has( )21.There a bee in our classroom.A. is B.are C.am()22. have