代数式求值教案3巩固练习（五篇范文）

第一篇：代数式求值教案3巩固练习

代数式求值

巩固练习：

21．先化简，再求值：已知x3x20，求代数式(x1)(x1)x(2x3)的值.2．已知2a＋b－1＝0，求代数式(a2b2)（a1)(ab)的值． abxx2y22(xy)23．已知=3，求的值． yxyxyy2

x34x34.先化简，再求值:，其中x满足x23x40． x12x1x2x1

5.已知：x2+x－2=0，求代数式x2x(x3)(x3)(x1)的值.6.已知a是关于x的方程x240的解，求代数式a1aa1a7的值．

7．已知：4x25x10，求代数式2x1xx1x2x2的值.8.已知x24x10，求

9.已知x23x10，求代数式(x2)(x3)(2x1)(2x1)4x的值．

2(x1)x6的值.x4x2答案：

第二篇：《对数的概念3》巩固练习

涟水中学高一级部数学学科教学案（编号：024）

《对数的概念3》巩固练习

班级_________姓名_________等第_________日期_________

一、填空题

1、(lg2)2(lg5)22lg2lg5的值为

2、log281log216log220log230______________ 33333、①log148log13____________ ②lg222512lg48_____________

4、①2112log52=_________________ ② log2[log2(log381)]=_________________

lg12lg155、已知lg2a,lg3b，则

二、解答题

等于_________________

6、（1）若lg20.3010,lg30.4771,求lg

45;

b（2）已知log189a,185,试用a、b表示log365

7、已知 2x43y12,求63x2y的值

《对数函数1》预习材料和课堂笔记

涟水中学高一级部数学学科教学案（编号：024）第1页 【知识点分解与课堂探究】

一、课前预习

1、对数函数的概念：

2、对数函数的图象和性质：

例题

1、求下列函数的定义域：

(1)ylog0.2(4x)(2)ylogax1(a0,a1)

(3)y1log9(3x6)(4)ylog(x1)(3x)

例题

2、利用对数函数的性质，比较下列各组数中两个数的大小：

(1)log23.4 log23.8(2)log0.51.8 log0.52.1

(3)log75 log67(4)log25.1 log15.9 2

例题

3、（1）不等式lg(43x)1的解集为。

（2）不等式loga231的解集为。

例题

4、求下列函数的值域：

2xlog3x 1ylog1(x24)2ylog3(x9)3ylog32

二、随堂练习

1、解下列方程

152x12(2)lg(3x1)2

2、求函数的f(x)log1(x6x17)值域。

22涟水中学高一级部数学学科教学案（编号：024）第2页

第三篇：初中数学竞赛专题培训(6)：代数式的求值

初中数学竞赛专题培训 第六讲 代数式的求值

代数式的求值与代数式的恒等变形关系十分密切．许多代

所以

a+b+c=0或bc+ac+ab=0．

若bc+ac+ab=0，则 数式是先化简再求值，特别是有附加条件的代数式求值问题，往往需要利用乘法公式、绝对值与算术根的性质、分式的基本性质、通分、约分、根式的性质等等，经过恒等变形，把代数式中隐含的条件显现出来，化简，进而求值．因此，求值中的方法技巧主要是代数式恒等变形的技能、技巧和方法．下面结合例题逐一介绍．

1．利用因式分解方法求值

因式分解是重要的一种代数恒等变形，在代数式化简求值中，经常被采用．

分析 x的值是通过一个一元二次方程给出的，若解出x后，再求值，将会很麻烦．我们可以先将所求的代数式变形，看一看能否利用已知条件．

解 已知条件可变形为3x2+3x-1=0，所以

6x4+15x3+10x2

=(6x4+6x3-2x2)+(9x3+9x2-3x)+(3x2+3x-1)+1

=(3x2+3x-1)(2z2+3x+1)+1

=0+1=1．

说明 在求代数式的值时，若已知的是一个或几个代数式的值，这时要尽可能避免解方程(或方程组)，而要将所要求值的代数式适当变形，再将已知的代数式的值整体代入，会使问题得到简捷的解答．

例2 已知a，b，c为实数，且满足下式：

a2+b2+c2=1，①

求a+b+c的值．

解 将②式因式分解变形如下

即

(a+b+c)

2=a2

+b2

+c2

+2(bc+ac+ab)

=a2

+b2

+c2

=1，所以 a+b+c=±1．所以a+b+c的值为0，1，-1．

说明 本题也可以用如下方法对②式变形：

即

前一解法是加一项，再减去一项；这个解法是将3拆成1+1+1，最终都是将②式变形为两个式子之积等于零的形式．

2．利用乘法公式求值

例3 已知x+y=m，x

3+y3

=n，m≠0，求x2

+y2的值．

解 因为x+y=m，所以

m3

=(x+y)3

=x3

+y3

+3xy(x+y)=n+3m·xy，所以

求x2

+6xy+y2的值．

分析 将x，y的值直接代入计算较繁，观察发现，已知中x，y的值正好是一对共轭无理数，所以很容易计算出x+y与xy的值，由此得到以下解法．

解 x2

+6xy+y2

=x2

+2xy+y2

+4xy

=(x+y)2

+4xy

3．设参数法与换元法求值

如果代数式字母较多，式子较繁，为了使求值简便，有时可增设一些参数(也叫辅助未知数)，以便沟通数量关系，这叫作设参数法．有时也可把代数式中某一部分式子，用另外的一个字母来替换，这叫换元法．

分析 本题的已知条件是以连比形式出现，可引入参数k，用它表示连比的比值，以便把它们分割成几个等式．

x＝(a-b)k，y＝(b-c)k，z＝(c-a)k．

所以

x+y+z=(a-b)k＋(b-c)k+(c-a)k=0．

u+v+w=1，①

由②有

把①两边平方得

u2+v2+w2+2(uv+vw+wu)=1，所以u2+v2+w2=1，即

两边平方有

所以

4．利用非负数的性质求值

若几个非负数的和为零，则每个非负数都为零，这个性质在代数式求值中经常被使用．

例8 若x2-4x+|3x-y|=-4，求yx的值．

分析与解 x，y的值均未知，而题目却只给了一个方程，似乎无法求值，但仔细挖掘题中的隐含条件可知，可以利用非负数的性质求解．

因为x2

-4x+|3x-y|=-4，所以

x2

-4x＋4＋|3x-y|=0，即(x-2)2

+|3x-y|=0．

所以 yx

=62

=36．

例9 未知数x，y满足

(x2

＋y2)m2

-2y(x+n)m+y2

+n2

=0，其中m，n表示非零已知数，求x，y的值．

分析与解 两个未知数，一个方程，对方程左边的代数式进行恒等变形，经过配方之后，看是否能化成非负数和为零的形式．

将已知等式变形为

m2

x2

+m2y2

-2mxy-2mny+y2

+n2

=0，(m2x2

-2mxy+y2)+(m2y2

-2mny+n2)=0，即(mx-y)2

+(my-n)2

=0．

5．利用分式、根式的性质求值

分式与根式的化简求值问题，内容相当丰富，因此设有专门

讲座介绍，这里只分别举一个例子略做说明．

例10 已知xyzt=1，求下面代数式的值：

分析 直接通分是笨拙的解法，可以利用条件将某些项的形式变一变．

解 根据分式的基本性质，分子、分母可以同时乘以一个不为

3．已知a+b+c=3，a+b+c=29，a+b+c=45，求零的式子，分式的值不变．利用已知条件，可将前三个分式的分

ab(a+b)+bc(b+c)+ca(c+a)的值．(改)母变为与第四个相同．

2．已知x+y=a，x+y=b，求x+y的值．

(第一个分母改为x)

5．设a+b+c=3m，求(m-a)+(m-b)+(m-c)-3(m-a)(m-b)(m-c)的同理

8．已知13x-6xy+y-4x+1=0，求(x+y)^13·x^10的值．

1.383

2.(b+2ab-a)/2 3.42 4.2 5.0 6.2 分利用这种对称性，或称之为整齐性，来简化我们的计算．

7.8 8.8

值．

分析 计算时应注意观察式子的特点，若先分母有理化，计算反而复杂．因为这样一来，原式的对称性就被破坏了．这里所言的对称性是

同样(但请注意算术根！)

将①，②代入原式有

练习六

第四篇：名词性从句巩固练习3（精选）

名词性从句巩固练习

1．____he does has nothing to do with me.A.whateverB.No matter whatC.ThatD.If

2.The manager came over and asked the customer how____

A.did the quarrel came aboutB.the quarrel had come about

C.has the quarrel come aboutD.had the quarrel come about

3.Energy is ____makes thingwork..A.whatB.somethingC.anythingD.that

4.Information has been putforward ____ more middle school graduates will be admitted into

universities.A.whileB.thatC.whenD.as

5.This is ___the shenzhou V Spaceship landed.A.thereB.in whichC.whereD.when

6.They have no idea at all____.A.where he has goneB.where did he go

C.which place has he goneD.where has he gone

7.The doctor did a lot to reduce the patient’s fear ____he would die of the disease.A.thatB.whichC.of whichD.of that

8.The order came ___the soldiers ____the small village the next morning.A.that;had to leaveB.that;should leave

C./;must leaveD.when;should leave

9.___is no possibility ____Bob can win the first prize in the match.A.There;thatB.It;thatC.there;whetherD.It;whether

10.The question came up at the meeting_____ we had enough money for our research.A.thatB.whichC.whetherD.if

11.Is _____he said really true?

A.thatB.whatC.whyD.whether

12.____the meeting should last two days or three days doesn’t matter.A.ThatB.WhetherC.IfD.Where

13.It worried her a bit _____her hair was turning gray.A.whileB.ifC.thatD.for

14._____more countries can use natural energy in the future remains to be seen.A.WhetherB.ThisC.whoD.If

15.____he will go to work in a mountain village surprises all of us.A.WhatB.ThatC.WhetherD.If

16.____you don’t like him is none of my business.A.WhatB.ThatC.WhoD.How

17.____all the inventions have in common is ____they have succeeded.A.What;whatB.That;thatC.what;thatD.That;what

18.____appeared to me that he enjoyed the food very much.A.WhatB.ItC.All thatD.That

19.It is widely ______that smoking can cause cancer.A.believedB.thinkC.sayD.hoped

20.____caused the accident is still a complete mystery.A.WhatB.ThatC.HowD.Where

21.____he always serves the people very well is known.A.WhatB.ThatC.WhichD.Who

22.____has passed the test will get a prize.A.WhoeverB.No mater whoC.WhomeverD.Who

23.Is____ true that the famous scientist will give us a lecture next week?

A thatB itC hisD he

24.It has not been decided ___ they will leave for New York.A.whenB whyC thatD what

25.Obviously___ we do morning exercises every day ___ us good.A.that doB.if;doC what;doesD.that;doseIt is said____ ____ was all ___ he said.A that;that;thatB what;what;whatC that;which;whatD that;that;which

27___ gets home first is to cook the supper.A.WhoB WhomC.Those whoD.Whoever

28___ moved us most was___ he looked after the old man for more than twenty years.A.That;thatB.What;thatC What;whatD.That;what

29.___ you did it is not known to all.A.WhoB.WhatC.HowD.Which

30.___ you do should be well done.A HowB.ThatC.WhateverD Why

31.The reason I plan to go is___ she will be disappointed if I don’t.A.becauseB.thatC.thanks toD.what

32.What time do you think__?

A.will Tom come backB.Tom will come backC.is Tom coming backD.can Tom get here

33.The teacher said that light___ faster than sound.A.Has traveledB.traveledC.had traveledD.travels

34..___ is still a question___ will win.A.It;thatB.It;whoC.That;whoD.This;that

35.If you know___ it was that wrote A Tale of Two Cities, raise your hand.A.whomB.whichC.whoD.that

36.In some countries,___ are called “public schools” are not owned by the state.A.thatB.whichC.asD.what

37.Thinking___ you know___ in fact you don’t is a terrible mistake.A.that;thatB.what;whatC.that;whatD.what that

38.Whether ways will be found to stop pollution or not is just___ worries the public.A.whyB.whichC.thatD.what

39.Why don’t you bring___ to his attention that you are too busy to do it?

A.thatB.whatC.thatD.it

40.___ David says sounds right to Helen.That’s why she has made up her mind to live with him___ happens.A.whatever;whateverB.No matter what;whatever

C.No matter what;No matter whatD.Whatever;however

41.That is___ I was born and grew up.A.ThereB.in whichC.whereD.the place

42.___ she was invited to the ball made her very happy.A.WhatB.ThatC.WhenD.Because

43.___ we are doing has never been done before.A.ThatB.WhatC.WhichD.Whether

44.---Have you found your book yet?---No, I’m not sure___ I could have left it.A.whetherB.whereC.whenD.why

45.The doctor couldn’t answer the question___ the patient could survive that night.A.ifB.thatC.whetherD.what

46.I firmly believe___ he said at the meeting was right.A.thatB.whichC.that whatD.what that

47.---What were you trying to prove to the police?---___ I was last night.A.ThatB.WhenC.WhereD.What

48.I think, though I could be mistaken, __ he liked me.A.whoB.whichC.thatD.what

49.At the meeting, we discussed___ we should employ more workers.A.ifB.whetherC.thatD./

50.After___ seemed like hours he came out with a bitter smile.A.whichB.itC.whatD.that

答案1—5 ABABC6—10 AABAC11—15 BBCAB16—20 BCBAA21—25 BABAD

26—30 ADBCC 31—35 BBDBC36—40 DCDDA41—45 CBBBC46—50 CCCBC

1.The doctor did a lot to reduce the patient’s fear ____he would die of the disease.A.thatB.whichC.of whichD.of that

2.The idea ___ we should have more industry in this area is a good one.A.thatB.whichC.whatD.how

3.The suggestion ____we have a group of these records printed as soon as possible was accepted

by the committee.A.howB.whichC.thatD.what

4.He told me the news ____ the Queen would visit China the next month.A.thatB.whichC.itD.whether

5.The fact troubles me much ___ I have been unable to pass the driving test up to now.A.whichB.becauseC.whyD.that

6.The mother didn’t know to blame for the broken glass as it happened while she was out.A.who

B.whenC.howD.what（NMF, T 2002）

7.―I think it’s going to be a big problem.―Yes, it could be.―I wonderwe can do about it.（NMET 02）A.ifB.howC.whatD.that

8.When you answer questions in a job interview, please remember the golden rule: Always give the monkey exactlyhe wants.（上海2002春）

A.whatB.whichC.whenD.that

9.Jack said to meet the American friends.A.he is pleaseB.what he was pleasedC.that he was pleasedD.which he pleased

10.fewer and fewer students showed interest in her lessons.A.What;whyB.That;whatC.What;becauseD.Why;that：

11.He often writes to us expressing his thought _____ one day he’ll come to join us.A.whichB.thatC.whatD.whether

12.He made a suggestion ____ the English test be put off until next Wednesday.A.whichB.whatC.thatD.whether

13.The news _____ the football team won the game made us happy.A.thatB.whichC.in whichD.what

14.The mere fact______ most people believe nuclear war would be madness does not mean thatit will not occur.A.whatB.whichC.thatD.why

15.―Do you really believe there is human race in outer space?

---So far there is no proof ____ people from other planets do exist.A.whichB.howC.whatD.that

16.---I drove to Zhuhai for the air show last week.---Is that you has a few days off?

A.whyB.whenC.whatD.where

17.has helped to save the drowning girl is worth praising.A.WhoB.The oneC.AnyoneD.Whoever

18.caused the accident is still a complete mystery.A.WhatB.ThatC.HowD.Where

答案：1.A A C A D6.A C A C A11.BCACD16.ADA

第一部分：基础题

1._______ makes his shop different is that it offers more personal services.A.WhatB.WhoC.WhateverD.Whoever

2.—It’s thirty years since we last met.—But I still remember the story, believe it or not, _______ we got lost on a rainy night.A.whichB.thatC.whatD.when

3.See the flags on top of the building? That was _______ we did this morning.A.whenB.whichC.whereD.What

4.—Could you do me a favor?—

A.whichB.whicheverC.whatD.whatever

5.These shoes look very good.I wonder _______.A.how much cost they areB.how much do they cost

C.how much they costD.how much are they cost

6.Doris' success lies in the fact _______ she is co-operative and eager to learn from others.A.whichB.thatC.whenD.why

7.Mary wrote an article on _______ the team had failed to win the game.A.whyB.whatC.whoD.that

8.Do you have any idea _______ is actually going on in the classroom?

A.thatB.whatC.asD.which

9.—Why does she always ask you for help?—There is no one else _______, is there?

A.who to turn toB.she can turn to C.for whom to turnD.for her to turn

10.Elephants have their own way to tell the shape of an object and ___ it is rough or smooth.A./B.whetherC.howD.what

11.Danny left word with my secretary _______ he would call again in the afternoon.A.whoB.thatC.asD.which

12.Mum is coming.What present _______ for your birthday?

A.you expect she has gotB.you expect has she got

C.do you expect she has gotD.do you expect has she got

13.The way he did it was different ________ we were used to.A.in whichB.in whatC.from whatD.from which

14.Great changes have taken place in that school.It is no longer _______ it was 20 years ago, _______ it

was so poorly equipped.A.what;whenB.that;whichC.what;whichD.which;that

15.Some researchers believe that there is no doubt ________ a cure for AIDS will be found.A.whichB.thatC.whatD.whether

第二部分：强化题

1.We haven’t settled the question of _______ it is necessary for him to study abroad.A.ifB.whereC.whetherD.that

2.A warm thought suddenly came to me _______I might use the pocket money to buy some flowers for my mother’s birthday.A.ifB.whenC.thatD.which

3.There is much chance _______ Bill will recover from his injury in time for the race.A.thatB.whichC.untilD.if

4.Please remind me _______ he said he was going.I may be in time to see him off.A.whereB.whenC.howD.what

5.We saw several natives advancing towards our party, and one of them came up to us._______ we

gave some bells and glasses.A.to whichB.to whomC.with whomD.with which

6.With his work completed, the businessman stepped back to his seat, feeling pleased _______ he was

a man of action.A.whichB.thatC.whatD.whether

A.No matter whatB.No matter whichC.WhateverD.Whichever

that makes him so excited.A.why it doesB.what he doesC.how it isD.what it is

9.___ is our belief that improvements in health care will lead to a stronger , more prosperouseconomy.A.AsB.ThatC.ThisD.It

10.Nobody believed his reason for being absent form the class ______ he had to meet his

uncle at the airport.A.whyB.thatC.whereD.because

11.The shopkeeper did not want to sell for _______ he thought was not enough.A.whereB.howC.whatD.which

12.He noticed that the straight part of the dance was different in the afternoon from _______ it had

been in the morning.A.thatB.whereC.whatD.which

13.I’d like to work with _______ is honest and easy to get on with.(2006年山东模拟题)

A.whoB.whoeverC.whomeverD.no matter who

14.When you are reading, make a note of _______ you think is of great importance.A.whichB.thatC.whatD.when

15.—Can we get everything ready by the weekend?

—It all depends on _______ we can get Mr.Green’s cooperation.A.thatB.whatC.whetherD.if基础题：1.ABDCC6.BABBB11.BCCAB

强化题：1.CCABB6.BDDDB11.CCBCC

第五篇：列代数式 教案

列代数式

教学目标

1． 使学生在了解代数式概念的基础上，能把简单的与数量有关的词语用代数式表示出来;

2． 初步培养学生观察、分析和抽象思维的能力.教学重点和难点

重点：列代数式.难点：弄清楚语句中各数量的意义及相互关系.课堂教学过程设计

一、从学生原有的认知结构提出问题

1用代数式表示乙数：(投影)

(1)乙数比x大5；(x+5)

(2)乙数比x的2倍小3；(2x-3)

(3)乙数比x的倒数小7；(1/x-7)

(4)乙数比x大16%((1+16%)x)

(应用引导的方法启发学生解答本题)

2在代数里，我们经常需要把用数字或字母叙述的一句话或一些计算关系式，列成代数式，正如上面的练习中的问题一样，这一点同学们已经比较熟悉了，但在代数式里也常常需要把用文字叙述的一句话或计算关系式(即日常生活语言)列成代数式本节课我们就来一起学习这个问题

二、讲授新课

例1 用代数式表示乙数：

(1)乙数比甲数大5；(2)乙数比甲数的2倍小3；

(3)乙数比甲数的倒数小7；(4)乙数比甲数大16%

分析：要确定的乙数，既然要与甲数做比较，那么就只有明确甲数是什么之后，才能确定乙数，因此写代数式以前需要把甲数具体设出来，才能解决欲求的乙数

解：设甲数为x，则乙数的代数式为

(1)x+5(2)2x-3；(3)1/x-7；(4)(1+16%)x

(本题应由学生口答，教师板书完成)最后，教师需指出：第4小题的答案也可写成x+16%x

例2 用代数式表示：

(1)甲乙两数和的2倍；

(2)甲数的1/3与乙数的1/2的差；

(3)甲乙两数的平方和；

(4)甲乙两数的和与甲乙两数的差的积；

(5)乙甲两数之和与乙甲两数的差的积

分析：本题应首先把甲乙两数具体设出来，然后依条件写出代数式

解：设甲数为a，乙数为b，则

(1)2(a+b)；(2)1/3 a-1/2b；(3)a2+b2；

(4)(a+b)(a-b)；(5)(a+b)(b-a)或(b+a)(b-a)

(本题应由学生口答，教师板书完成)

此时，教师指出：a与b的和，以及b与a的和都是指(a+b)，这是因为加法有交换律但a与b的差指的是(a-b)，而b与a的差指的是(b-a)两者明显不同，这就是说，用文字语言叙述的句子里应特别注意其运算顺序

例3 用代数式表示：

(1)被3整除得n的数；

(2)被5除商m余2的数

分析本题时，可提出以下问题：

(1)被3整除得2的数是几?被3整除得3的数是几?被3整除得n的数如何表示?

(2)被5除商1余2的数是几?如何表示这个数?商2余2的数呢?商m余2的数呢?

解：(1)3n；(2)5m+2

(这个例子直接为以后让学生用代数式表示任意一个偶数或奇数做准备)

例4 设字母a表示一个数，用代数式表示：

(1)这个数与5的和的3倍；(2)这个数与1的差的1/4 ；

(3)这个数的5倍与7的和的一半；(4)这个数的平方与这个数的1/3的和

分析：启发学生，做分析练习如第1小题可分解为“a与5的和”与“和的3倍”，先将“a与5的和”例成代数式“a+5”再将“和的3倍”列成代数式“3(a+5)”

解：(1)3(a+5)；(2)1/4(a-1)；(3)1/2(5a+7)；(4)a2+1/3a

(通过本例的讲解，应使学生逐步掌握把较复杂的数量关系分解为几个基本的数量关系，培养学生分析问题和解决问题的能力)

例5 设教室里座位的行数是m，用代数式表示：

(1)教室里每行的座位数比座位的行数多6，教室里总共有多少个座位?

(2)教室里座位的行数是每行座位数的2/3，教室里总共有多少个座位?

分析本题时，可提出如下问题：

(1)教室里有6行座位，如果每行都有7个座位，那么这个教室总共有多少个座位呢?

(2)教室里有m行座位，如果每行都有7个座位，那么这个教室总共有多少个座位呢?

(3)通过上述问题的解答结果，你能找出其中的规律吗?(总座位数=每行的座位数×行数)解：(1)m(m+6)个；(2)(3/2 m)m个

三、课堂练习

1设甲数为x，乙数为y，用代数式表示：(投影)

(1)甲数的2倍，与乙数的1/3的和；(2)甲数的1/4与乙数的3倍的差；

(3)甲乙两数之积与甲乙两数之和的差；(4)甲乙的差除以甲乙两数的积的商

2用代数式表示：

(1)比a与b的和小3的数；(2)比a与b的差的一半大1的数；

(3)比a除以b的商的3倍大8的数；(4)比a除b的商的3倍大8的数

3用代数式表示：

(1)与a-1的和是25的数；(2)与2b+1的积是9的数；

(3)与2x2的差是x的数；(4)除以(y+3)的商是y的数

〔(1)25-(a-1)；(2)；(3)2x2+2；(4)y(y+3)〕

四、师生共同小结

首先，请学生回答：

1怎样列代数式?2列代数式的关键是什么?

其次，教师在学生回答上述问题的基础上，指出：对于较复杂的数量关系，应按下述规律列代数式：

(1)列代数式，要以不改变原题叙述的数量关系为准(代数式的形式不唯一)；

(2)要善于把较复杂的数量关系，分解成几个基本的数量关系；

(3)把用日常生活语言叙述的数量关系，列成代数式，是为今后学习列方程解应用题做准备要求学生一定要牢固掌握

五、作业

1用代数式表示：

(1)体校里男生人数占学生总数的60%，女生人数是a，学生总数是多少?

(2)体校里男生人数是x，女生人数是y，教练人数与学生人数之比是1∶10，教练人数是多?

2已知一个长方形的周长是24厘米，一边是a厘米，求：(1)这个长方形另一边的长；(2)这个长方形的面积.学法探究

已知圆环内直径为acm，外直径为bcm，将100个这样的圆环一个接着一个环套环地连成一条锁链，那么这条锁链拉直后的长度是多少厘米？

分析：先深入研究一下比较简单的情形，比如三个圆环接在一起的情形，看

有没有规律.当圆环为三个的时候，如图：

此时链长为，这个结论可以继续推广到四个环、五个环、…直至100个环，答案不难得到：

解：

=99a+b(cm)