第一篇：代數(shù)式求值教案3鞏固練習(xí)

代數(shù)式求值

鞏固練習(xí)：

21．先化簡，再求值：已知x?3x?2?0，求代數(shù)式(x?1)(x?1)?x(2x?3)的值.2．已知2a＋b－1＝0，求代數(shù)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.先化簡，再求值:?，其中x滿足x2?3x?4?0． ?x?1??2?x?1?x?2x?1

5.已知：x2+x－2=0，求代數(shù)式?x?2??x(x?3)?(x?3)(x?1)的值.6.已知a是關(guān)于x的方程x2?4?0的解，求代數(shù)式?a?1??a?a?1??a?7的值．

7．已知：4x2?5x?1?0，求代數(shù)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，求代數(shù)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：《對數(shù)的概念3》鞏固練習(xí)

漣水中學(xué)高一級部數(shù)學(xué)學(xué)科教學(xué)案（編號：024）

《對數(shù)的概念3》鞏固練習(xí)

班級_________姓名_________等第_________日期_________

一、填空題

1、(lg2)2?(lg5)2?2lg2?lg5的值為

2、log281?log216?log220?log230?______________ 33333、①log148?log13?____________ ②lg222512?lg48?_____________

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

lg12lg155、已知lg2?a,lg3?b，則

二、解答題

等于_________________

6、（1）若lg2?0.3010,lg3?0.4771,求lg

45;

b（2）已知log189?a,18?5,試用a、b表示log365

7、已知 2x?43y?12,求63x?2y的值

《對數(shù)函數(shù)1》預(yù)習(xí)材料和課堂筆記

漣水中學(xué)高一級部數(shù)學(xué)學(xué)科教學(xué)案（編號：024）第1頁 【知識點分解與課堂探究】

一、課前預(yù)習(xí)

1、對數(shù)函數(shù)的概念：

2、對數(shù)函數(shù)的圖象和性質(zhì)：

例題

1、求下列函數(shù)的定義域：

(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)

例題

2、利用對數(shù)函數(shù)的性質(zhì)，比較下列各組數(shù)中兩個數(shù)的大?。?/p>

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

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

例題

3、（1）不等式lg(4?3x)?1的解集為。

（2）不等式loga23?1的解集為。

例題

4、求下列函數(shù)的值域：

2x?log3x ?1?y?log1(x2?4)?2?y?log3(x?9)?3?y?log32

二、隨堂練習(xí)

1、解下列方程

?1?52x?1?2(2)lg(3x?1)?2

2、求函數(shù)的f(x)?log1(x?6x?17)值域。

22漣水中學(xué)高一級部數(shù)學(xué)學(xué)科教學(xué)案（編號：024）第2頁

第三篇：初中數(shù)學(xué)競賽專題培訓(xùn)(6)：代數(shù)式的求值

初中數(shù)學(xué)競賽專題培訓(xùn) 第六講 代數(shù)式的求值

代數(shù)式的求值與代數(shù)式的恒等變形關(guān)系十分密切．許多代

所以

a+b+c=0或bc+ac+ab=0．

若bc+ac+ab=0，則 數(shù)式是先化簡再求值，特別是有附加條件的代數(shù)式求值問題，往往需要利用乘法公式、絕對值與算術(shù)根的性質(zhì)、分式的基本性質(zhì)、通分、約分、根式的性質(zhì)等等，經(jīng)過恒等變形，把代數(shù)式中隱含的條件顯現(xiàn)出來，化簡，進(jìn)而求值．因此，求值中的方法技巧主要是代數(shù)式恒等變形的技能、技巧和方法．下面結(jié)合例題逐一介紹．

1．利用因式分解方法求值

因式分解是重要的一種代數(shù)恒等變形，在代數(shù)式化簡求值中，經(jīng)常被采用．

分析 x的值是通過一個一元二次方程給出的，若解出x后，再求值，將會很麻煩．我們可以先將所求的代數(shù)式變形，看一看能否利用已知條件．

解 已知條件可變形為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．

說明 在求代數(shù)式的值時，若已知的是一個或幾個代數(shù)式的值，這時要盡可能避免解方程(或方程組)，而要將所要求值的代數(shù)式適當(dāng)變形，再將已知的代數(shù)式的值整體代入，會使問題得到簡捷的解答．

例2 已知a，b，c為實數(shù)，且滿足下式：

a2+b2+c2=1，①

求a+b+c的值．

解 將②式因式分解變形如下

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的值為0，1，-1．

說明 本題也可以用如下方法對②式變形：

即

前一解法是加一項，再減去一項；這個解法是將3拆成1+1+1，最終都是將②式變形為兩個式子之積等于零的形式．

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 因為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 將x，y的值直接代入計算較繁，觀察發(fā)現(xiàn)，已知中x，y的值正好是一對共軛無理數(shù)，所以很容易計算出x+y與xy的值，由此得到以下解法．

解 x2

+6xy+y2

=x2

+2xy+y2

+4xy

=(x+y)2

+4xy

3．設(shè)參數(shù)法與換元法求值

如果代數(shù)式字母較多，式子較繁，為了使求值簡便，有時可增設(shè)一些參數(shù)(也叫輔助未知數(shù))，以便溝通數(shù)量關(guān)系，這叫作設(shè)參數(shù)法．有時也可把代數(shù)式中某一部分式子，用另外的一個字母來替換，這叫換元法．

分析 本題的已知條件是以連比形式出現(xiàn)，可引入?yún)?shù)k，用它表示連比的比值，以便把它們分割成幾個等式．

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①兩邊平方得

u2+v2+w2+2(uv+vw+wu)=1，所以u2+v2+w2=1，即

兩邊平方有

所以

4．利用非負(fù)數(shù)的性質(zhì)求值

若幾個非負(fù)數(shù)的和為零，則每個非負(fù)數(shù)都為零，這個性質(zhì)在代數(shù)式求值中經(jīng)常被使用．

例8 若x2-4x+|3x-y|=-4，求yx的值．

分析與解 x，y的值均未知，而題目卻只給了一個方程，似乎無法求值，但仔細(xì)挖掘題中的隱含條件可知，可以利用非負(fù)數(shù)的性質(zhì)求解．

因為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 未知數(shù)x，y滿足

(x2

＋y2)m2

-2y(x+n)m+y2

+n2

=0，其中m，n表示非零已知數(shù)，求x，y的值．

分析與解 兩個未知數(shù)，一個方程，對方程左邊的代數(shù)式進(jìn)行恒等變形，經(jīng)過配方之后，看是否能化成非負(fù)數(shù)和為零的形式．

將已知等式變形為

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、根式的性質(zhì)求值

分式與根式的化簡求值問題，內(nèi)容相當(dāng)豐富，因此設(shè)有專門

講座介紹，這里只分別舉一個例子略做說明．

例10 已知xyzt=1，求下面代數(shù)式的值：

分析 直接通分是笨拙的解法，可以利用條件將某些項的形式變一變．

解 根據(jù)分式的基本性質(zhì)，分子、分母可以同時乘以一個不為

3．已知a+b+c=3，a+b+c=29，a+b+c=45，求零的式子，分式的值不變．利用已知條件，可將前三個分式的分

ab(a+b)+bc(b+c)+ca(c+a)的值．(改)母變?yōu)榕c第四個相同．

2．已知x+y=a，x+y=b，求x+y的值．

(第一個分母改為x)

5．設(shè)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 分利用這種對稱性，或稱之為整齊性，來簡化我們的計算．

7.8 8.8

值．

分析 計算時應(yīng)注意觀察式子的特點，若先分母有理化，計算反而復(fù)雜．因為這樣一來，原式的對稱性就被破壞了．這里所言的對稱性是

同樣(但請注意算術(shù)根！)

將①，②代入原式有

練習(xí)六

第四篇：名詞性從句鞏固練習(xí)3（精選）

名詞性從句鞏固練習(xí)

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：基礎(chǔ)題

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：強化題

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年山東模擬題)

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基礎(chǔ)題：1.ABDCC6.BABBB11.BCCAB

強化題：1.CCABB6.BDDDB11.CCBCC

第五篇：列代數(shù)式 教案

列代數(shù)式

教學(xué)目標(biāo)

1． 使學(xué)生在了解代數(shù)式概念的基礎(chǔ)上，能把簡單的與數(shù)量有關(guān)的詞語用代數(shù)式表示出來;

2． 初步培養(yǎng)學(xué)生觀察、分析和抽象思維的能力.教學(xué)重點和難點

重點：列代數(shù)式.難點：弄清楚語句中各數(shù)量的意義及相互關(guān)系.課堂教學(xué)過程設(shè)計

一、從學(xué)生原有的認(rèn)知結(jié)構(gòu)提出問題

1用代數(shù)式表示乙數(shù)：(投影)

(1)乙數(shù)比x大5；(x+5)

(2)乙數(shù)比x的2倍小3；(2x-3)

(3)乙數(shù)比x的倒數(shù)小7；(1/x-7)

(4)乙數(shù)比x大16%((1+16%)x)

(應(yīng)用引導(dǎo)的方法啟發(fā)學(xué)生解答本題)

2在代數(shù)里，我們經(jīng)常需要把用數(shù)字或字母敘述的一句話或一些計算關(guān)系式，列成代數(shù)式，正如上面的練習(xí)中的問題一樣，這一點同學(xué)們已經(jīng)比較熟悉了，但在代數(shù)式里也常常需要把用文字?jǐn)⑹龅囊痪湓捇蛴嬎汴P(guān)系式(即日常生活語言)列成代數(shù)式本節(jié)課我們就來一起學(xué)習(xí)這個問題

二、講授新課

例1 用代數(shù)式表示乙數(shù)：

(1)乙數(shù)比甲數(shù)大5；(2)乙數(shù)比甲數(shù)的2倍小3；

(3)乙數(shù)比甲數(shù)的倒數(shù)小7；(4)乙數(shù)比甲數(shù)大16%

分析：要確定的乙數(shù)，既然要與甲數(shù)做比較，那么就只有明確甲數(shù)是什么之后，才能確定乙數(shù)，因此寫代數(shù)式以前需要把甲數(shù)具體設(shè)出來，才能解決欲求的乙數(shù)

解：設(shè)甲數(shù)為x，則乙數(shù)的代數(shù)式為

(1)x+5(2)2x-3；(3)1/x-7；(4)(1+16%)x

(本題應(yīng)由學(xué)生口答，教師板書完成)最后，教師需指出：第4小題的答案也可寫成x+16%x

例2 用代數(shù)式表示：

(1)甲乙兩數(shù)和的2倍；

(2)甲數(shù)的1/3與乙數(shù)的1/2的差；

(3)甲乙兩數(shù)的平方和；

(4)甲乙兩數(shù)的和與甲乙兩數(shù)的差的積；

(5)乙甲兩數(shù)之和與乙甲兩數(shù)的差的積

分析：本題應(yīng)首先把甲乙兩數(shù)具體設(shè)出來，然后依條件寫出代數(shù)式

解：設(shè)甲數(shù)為a，乙數(shù)為b，則

(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)

(本題應(yīng)由學(xué)生口答，教師板書完成)

此時，教師指出：a與b的和，以及b與a的和都是指(a+b)，這是因為加法有交換律但a與b的差指的是(a-b)，而b與a的差指的是(b-a)兩者明顯不同，這就是說，用文字語言敘述的句子里應(yīng)特別注意其運算順序

例3 用代數(shù)式表示：

(1)被3整除得n的數(shù)；

(2)被5除商m余2的數(shù)

分析本題時，可提出以下問題：

(1)被3整除得2的數(shù)是幾?被3整除得3的數(shù)是幾?被3整除得n的數(shù)如何表示?

(2)被5除商1余2的數(shù)是幾?如何表示這個數(shù)?商2余2的數(shù)呢?商m余2的數(shù)呢?

解：(1)3n；(2)5m+2

(這個例子直接為以后讓學(xué)生用代數(shù)式表示任意一個偶數(shù)或奇數(shù)做準(zhǔn)備)

例4 設(shè)字母a表示一個數(shù)，用代數(shù)式表示：

(1)這個數(shù)與5的和的3倍；(2)這個數(shù)與1的差的1/4 ；

(3)這個數(shù)的5倍與7的和的一半；(4)這個數(shù)的平方與這個數(shù)的1/3的和

分析：啟發(fā)學(xué)生，做分析練習(xí)如第1小題可分解為“a與5的和”與“和的3倍”，先將“a與5的和”例成代數(shù)式“a+5”再將“和的3倍”列成代數(shù)式“3(a+5)”

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

(通過本例的講解，應(yīng)使學(xué)生逐步掌握把較復(fù)雜的數(shù)量關(guān)系分解為幾個基本的數(shù)量關(guān)系，培養(yǎng)學(xué)生分析問題和解決問題的能力)

例5 設(shè)教室里座位的行數(shù)是m，用代數(shù)式表示：

(1)教室里每行的座位數(shù)比座位的行數(shù)多6，教室里總共有多少個座位?

(2)教室里座位的行數(shù)是每行座位數(shù)的2/3，教室里總共有多少個座位?

分析本題時，可提出如下問題：

(1)教室里有6行座位，如果每行都有7個座位，那么這個教室總共有多少個座位呢?

(2)教室里有m行座位，如果每行都有7個座位，那么這個教室總共有多少個座位呢?

(3)通過上述問題的解答結(jié)果，你能找出其中的規(guī)律嗎?(總座位數(shù)=每行的座位數(shù)×行數(shù))解：(1)m(m+6)個；(2)(3/2 m)m個

三、課堂練習(xí)

1設(shè)甲數(shù)為x，乙數(shù)為y，用代數(shù)式表示：(投影)

(1)甲數(shù)的2倍，與乙數(shù)的1/3的和；(2)甲數(shù)的1/4與乙數(shù)的3倍的差；

(3)甲乙兩數(shù)之積與甲乙兩數(shù)之和的差；(4)甲乙的差除以甲乙兩數(shù)的積的商

2用代數(shù)式表示：

(1)比a與b的和小3的數(shù)；(2)比a與b的差的一半大1的數(shù)；

(3)比a除以b的商的3倍大8的數(shù)；(4)比a除b的商的3倍大8的數(shù)

3用代數(shù)式表示：

(1)與a-1的和是25的數(shù)；(2)與2b+1的積是9的數(shù)；

(3)與2x2的差是x的數(shù)；(4)除以(y+3)的商是y的數(shù)

〔(1)25-(a-1)；(2)；(3)2x2+2；(4)y(y+3)〕

四、師生共同小結(jié)

首先，請學(xué)生回答：

1怎樣列代數(shù)式?2列代數(shù)式的關(guān)鍵是什么?

其次，教師在學(xué)生回答上述問題的基礎(chǔ)上，指出：對于較復(fù)雜的數(shù)量關(guān)系，應(yīng)按下述規(guī)律列代數(shù)式：

(1)列代數(shù)式，要以不改變原題敘述的數(shù)量關(guān)系為準(zhǔn)(代數(shù)式的形式不唯一)；

(2)要善于把較復(fù)雜的數(shù)量關(guān)系，分解成幾個基本的數(shù)量關(guān)系；

(3)把用日常生活語言敘述的數(shù)量關(guān)系，列成代數(shù)式，是為今后學(xué)習(xí)列方程解應(yīng)用題做準(zhǔn)備要求學(xué)生一定要牢固掌握

五、作業(yè)

1用代數(shù)式表示：

(1)體校里男生人數(shù)占學(xué)生總數(shù)的60%，女生人數(shù)是a，學(xué)生總數(shù)是多少?

(2)體校里男生人數(shù)是x，女生人數(shù)是y，教練人數(shù)與學(xué)生人數(shù)之比是1∶10，教練人數(shù)是多?

2已知一個長方形的周長是24厘米，一邊是a厘米，求：(1)這個長方形另一邊的長；(2)這個長方形的面積.學(xué)法探究

已知圓環(huán)內(nèi)直徑為acm，外直徑為bcm，將100個這樣的圓環(huán)一個接著一個環(huán)套環(huán)地連成一條鎖鏈，那么這條鎖鏈拉直后的長度是多少厘米？

分析：先深入研究一下比較簡單的情形，比如三個圓環(huán)接在一起的情形，看

有沒有規(guī)律.當(dāng)圓環(huán)為三個的時候，如圖：

此時鏈長為，這個結(jié)論可以繼續(xù)推廣到四個環(huán)、五個環(huán)、…直至100個環(huán)，答案不難得到：

解：

=99a+b(cm)