四年级奥数第五讲等差数列二教师版Word文件下载.docx

1、3+4+5+9+10=（3+10）82=13 2=52（根）。这堆钢管一共有52根。1、一些同样粗细的圆木,像如图所示一样均匀地堆放在一起,已知最下面一层有70根。一共有多少根圆木？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:

2、3,6,9,310。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） 10=33 5=165（根）这个大的等边三角形中一共要放165根火柴棒。3、用相同的小立方体摆成如图所示的形状,如果共摆成10层,那么最下面有多少个小立方体?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?开第一把锁时，如果不凑巧，试了49把钥匙还不行，那所剩的一把就一定能把它打开，即开第一把锁至多需要试49次，同理，开第二把锁至多需要48次，开第三把锁至多需试47次，等打开第49把锁，剩下的最后一把不用试

3、，一定能打开。根据以上分析,可以把本题转化为求一个等差数列的和，即 49+48+47+2+1=（49+1）49=1225（次）至多要试1225次。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?59+58+57+2+1=（59+1）592=1770（次）2、有一些锁的钥匙搞乱了,已知至多要试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? 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?第11站后，车上坐满乘客。例题4 四（1）班45位同学举行一次

4、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？假设45位同学排成一队，第1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43位同学握手，一共握了43次，这样第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。根据以上分析，可以把本题转化为求一个等差数列的和即 44+43+42+3+2+1 =（44+1）44 =990（次）同学们共握了990次手。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

5、？答案: 15+14+13+3+2+1=（15+1）152=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？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）522=1378（次）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？设共有n人参加了聚会，因为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=n（n-1）2，因为共握手28

6、次，所以n2=28，即n（n-1）=56.又因为n是正整数，通过计算，可知87=56，n=8，所以参加聚会的共有8人。参加聚会的共有8人。Class: Name: （ ）1. Good morning! !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 ! C.Good evening . ）4.How do you do ?

7、 B.Fine,thanks . ）5.How many story books do you have ?A.I have 10. B.I can see 10. C.Thirty yuan. ）6.Do you have new teachers?A.Yes,we do . B.Yes,we dont. C.Yes,we have . ）7.Whos your art teacher ?A.Mr Zhu. B.Miss Zhu. C.Hes tall. ）8.Whats he like?A.Hes tall and strong . B.Yes,he is. C.Mr Zhu. ）9.Is

8、 your English teacher young?A.No,she isnt. B.Yes,she is . C.No,she is. ）10. ? Her name is Chen Jie.A.Whats your name ? B.Whats she name ? C.Whats her name ? ）11. I like Chinese,math and English.A.What classes do you like? B.What do you like? C.What are you like ? ）12. We have English and P.E.A.What

9、do you have on Mondays ? B.What do you have ?C.What do you have on Monday? ）13. Its 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.May I have a look ?A.Sure

10、.Here you are . B.Look ! C.Here you are . ）16.Our math teacher is Canada.A.from B.in C.at ）17.I three new teachers.A.has B.am C.have ）18.Whats Chinese teacher like ?A.you B.your C.youre ）19.My P.E.teacher is thin.A.too B.so C.very ）20.There are days in a week.A.six B.seven C.eight ）21.There are mont

11、h（月）in a year（年）.A.ten B.eleven C.twelve ）22.I often watch TV Saturday .A.on C.at ）23.I like P.E. I dont lime music.A.but B.and C.so ）24.This is apple. It is red apple.A.a , a B.an,an C.an, a ）25.What do you like ?A.classes B.class C.classs六年级英语测试题 ）1. How are you ?A.Fine,thanks. B.Yes,it is. C.How

12、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. How do you go to the USA ?A.I usually go to school by bus. B.I go to England by ship. C.I go by plane. ）5. My hom

13、e is near the post office.A. Where is your home ? C.See you then! ）6. See you at 2 oclock.A.See you then ! B.The fifth floor. C.Its easy. ）7. You can go by the No.15 bus.A.Its not far. B. How can I get to Zhongshan Park ? C.Sure. ）8. Where is the hospital?A.Next to the cinema. B.Thank you . C.Youre

14、welcome. ）9. Excuse me ,is there a cinema near here ?A.Yes,there is . B.No,its not far. C.Its near the post office. ）10.? Its near the post office. C. Where is the library? Its next to the hospital. A. Where is the cinema ,please ? B.Is it far ? C.Go straight. ）12. How can I get to the hospital ?A.I

15、ts next to the hospital. B.You can go by the No.201 bus. C.Thank you. ）13.Thank you .A.Thank you . ）14. How can I get to the museum?A.Go straight.Then turn left. C.Its east of the cinema . ）15. Where is the post office ? ）16. What are you going to do this evening ?A.Im going to the cinema . B.I go t

16、o school on foot. C.Yes,it is. ）17. Is it far ?A.No,it is . B.Yes , it is . C.Yes,it isnt. ）18. do you go to school ?A.What B.Where C.How ）19. I go to school bike. B. by C.get ）20. Can I go foot ?A.by B.at C.on ）21.How can I to the post office ?A.near B. get C.for ）22. me.A. Excuse B. How C.next ）23

17、. birthday to you !A. After B.Happy C.First ）24. The hospital is the left.A. at C.on ）25. is the bookstore ?A.Where B.How C.When 四年级英语测试题 ）1.Good afternoon !A.Hello! B.Hi ! C.Afternoon ! ）2.Nice to see you again ! C.Nice to see you , too. ）3.Good night,moom !A.Good evening ! C.Night ! ）4.How are you

18、 ?A.Fine,thank you . B.I am 10. C.Nine . ）5.How do you do ?A.Fine ,Thank you . B.How are you ? ）6.How old are you ? B.I am 11. C.I have 11. 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 l

19、ights can you see ?C.How many light can you see ? ）9.May I have a look ? B.Look! C.Sure.Here are you . 50 yuan. A.How much is this schoolbag ? B.How many is this schoolbag ?C.How much are this schoolbag ? ）11.Wheres my seat ?A.Its near the door. B.Its on the door. C.Its under the door. ）12.Lets clea

20、n the desks and chairs.A.All right ! C.Its nice . ）13.Whats this ?A.There is a board . B.Its a bee. C.Its bee. My name is Mike.A.Here are you ? B.Whats your name ? ）15.Whos the inventor of paper ?A.Chinese 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 name Zhang Peng.A.is, is , is C.is , are ）18.Let