直接间接引语练习题

直接间接引语练习题（精选7篇）

直接间接引语练习题 篇1

2.She asked me, “Is this book yours or his?”

3.The teacher asked, “How did you repair it?”

4.She said, “He will be busy.”

5.She said to Tom, “Can you help me?”

6.The teacher said, “The earth goes round the sun.”

7.My father said, “Practice makes perfect.”

8.The boy said to us, “ I usually get up at six every day.”

9.He said, “We are still students.”

10.He said to me, “I was born in 1978.”

11.He said, “I have studied English since .”

12.I said to him, “I have finished it.”

13.She said to us,“ I’ll come here tomorrow.”

14.“Where does your chemistry teacher live, Jane?” the young man asked.

15.“I have gotten the first place in the mathematics competition,” the little boy said happily.

16.“Light travels faster than sound,” the physics teacher said to the boys and girls.

17.“Will you go to the concert with me this evening?” Mary asked me.

直接间接引语练习题 篇2

Jenny said, "I’m going to London with my father."

珍妮说:"我要和父亲到伦敦去。" (引号内是直接引语)

Jenny said that she was going to London with her father.

珍妮说, 她要和她父亲去伦敦。 (宾语从句是间接引语)

一、如何变人称

下面有一句顺口溜“一主, 二宾, 三不变”。“一主”是指在直接引语变间接引语时, 如果从句中的主语是第一人称或被第一人称所修饰。从句中的人称要按照主句中主语的人称变化, 如:

He said, "My brother wants to go with me."→He said his brother wanted to go with him.

“二宾”是指直接引语变间接引语时, 若从句中的主语及宾语是第二人称。或被第二人称所修饰。从句中的人称要跟引号外的主句的宾语一致。如果引号外的主句没有宾语。也可以用第一人称, 如:

She said to Bob"How is your sister now?"→She asked Bob how his sister was then.

“三不变”是指直接引语变间接引语时。如果从句中的主语及宾语是第三人称或被第三人称所修饰从句中的人称一般不需要变化如:

Mr Smith said, “Jack is a good worker.”→Mr Smith said Jack was a good worker.

二、如何变时态

直接引语在改为间接引语时、时态需要做相应的调整。

现在时它需改为过去时态;过去时态改为完成时;过去完成时则保留原来的时态。如:

(1) She said, “I have lost a pen.”→She said she had lost a pen.

(2) She said, “We hope so.”→She said they hoped so.

(3) She said, “He will go to see his friend.”→She said he would go to see his friend.

但要注意在以下几种情况下, 在直接引语变为间接引语时, 时态一般不变化。

(1) 直接引语是客观真理。

“The earth moves around the sun and the moon moves around the earth”, the teacher told me.→The teacher told me the earth moves around the sun and the moon moves around the earth.

(2) 直接引语是过去进行时, 时态不变。如:

Jack said, “John, where were you going when I met you in the street?”→Jack asked John where he was going when he met him in the street.

(3) 直接引语中有具体的过去某年、某月、某日作状语, 变为间接引语时, 时态不变。如:

Xiao Wang said, “I was born on April 2l, 1980.”→Xiao Wang said he was born on April 20, 1980.

(4) 直接引语如果是一般现在时, 表示一种反复出现或习惯性的动作, 变间接引语, 时态不变。如:

He said, “I get up at six every morning.”→He said he gets up at six every morning.

(5) 如果直接引语中的情态动词没有过去时的形式 (例:ought to, had better, used to) 和已经是过去时的形式时, (例:could, should, would, might) 不再变。如:

Lucy said, "You had better come here today."→Lucy said I had better go there that day.

三、如何变状语

直接引语变间接引语, 状语变化有其内在规律, 时间状语由“现在”改为“原来” (例:now变为then, yesterday变为the day before yesterday) 地点状语, 尤其表示方向性的, 或用指示代词修饰的状语, 由“此”改为“彼” (例:this改为that) , 如:

He said, "These books are mine."→He said those books were his.

四、如何变句型

(1) 直接引语如果是陈述句, 间接引语应改为由that引导的宾语从句。如:She said, "Our bus will arrive in five minutes."→She said that their bus would arrive in five minutes.

(2) 直接引语如果是反意疑问句, 选择疑问句或一般疑问句, 间接引语应改为由whether或if引导的宾语从句。如:He said, "Can you swim, John?"→He asked John if he could swim.

"You have finished the homework, haven’t you?"my mother asked.→My mother asked me whether I had finished the homework.

"Do you go to school by bus or by bike?"→He asked me if I went to school by bus or by bike.

(3) 直接引语如果是特殊问句, 间接引语应该改为由疑问代词或疑问副词引导的宾语从句 (宾语从句必须用陈述句语序) 。

She asked me, "When do they have their dinner?"→She asked me when they had their dinner.

(4) 直接引语如果是祈使句, 间接引语应改为"tell (ask, order, beg等) sb (not) to do sth."句型。如:

"Don’t make any noise, "she said to the children.→She told (ordered) the children not to make any noise."Bring me a cup of tea, please, "said she.→She asked him to bring her a cup of tea.

(5) 直接引语如果是以“Let’s”开头的祈使句, 变为间接引语时, 通常用“suggest+动词 (或从句) 。”如:

直接引语与间接引语 篇3

1． 直接引语是陈述句时

间接引语为that引导的宾语从句（口语中that可以省略），主句的引述动词主要有say, tell, repeat, explain, think等。

He said, “You are younger than I.”→He said(that) I was younger than him.

2.直接引语是疑问句时

间接引语为陈述语序：主句的谓语动词say改为ask,或改为wonder, do not know, want to know, be not sure, be puzzled等。

（1）一般疑问句或反意疑问句变为if (whether)引导的宾语从句。

She said, “Do you often come here to read newspapers?”

→She asked me if (或whether) I often went there to read newspapers.

（2）选择疑问句变为whether…/or宾语从句。

I asked him, “Will you stay at home or go to a film tonight?”

→I asked him whether he would stay at home or go to a film that night.

(3)特殊疑问句变为由原来的疑问词引导的宾语从句。

He asked, “Where do you live?” →He asked me where I lived.

3.直接引语是祈使句时

间接引语为不定式，作ask, tell, beg, order, warn, advise等动词的宾语补足语（don’t变为not）。

The teacher said to the boy, “Open the window.”→The teacher told the boy to open the window.

His father said to him, “Don’t leave the door open.”→His father told him not to leave the door open.

[注意]

（1）有些表示建议、提议、劝告或要求的祈使句，可以用suggest, insist等动词加以转述。例如：

He said, “Let’s go to the theatre.”

→He suggested(our) going to the theatre.或He suggested that we(should) go to the theatre.

(2)“Would you mind opening the window?” he asked.

→He asked me to open the window.

“Why don’t you take a walk after supper?” he asked.

→He advised me to take a walk after supper.

4.直接引语是感叹句时

间接引语为what 或how 引导，也可以用that 引导。

She said, “What a lovely day it is!”

→She said what a lovely day it was.或She said that it was a lovely day.

5．如果主句谓语动词为各种现在时或一般将来时，则间接引语中的动词仍保持直接引语原来时态。如果主句谓语动词为过去时，间接引语中的动词时态按下列变化：

（1）一般现在时变为一般过去时

（2）现在进行时变为过去进行时

（3）一般将来时变为过去将来时

（4）现在完成时变为过去完成时

（5）一般过去时变为过去完成时

（6）过去完成时不变，仍为过去完成时

[注意]

（1）如果直接引语是表示客观真理时，变为间接引语，一般现在时不改为一般过去时。如：

The teacher said “The earth goes round the sun.”

→The teacher said that the earth goes round the sun.

（2）如果直接引语中有明确表示过去时间的状语，变为间接引语时，一般过去时不改为过去完成时。如：

He said to me, “I was born in 1973.”

→He told me that he was born in 1973.

(3)如果直接引语所述事实在当时和目前同样生效，变为间接宾语时，一般现在时不改为一般过去时。如：

He said, “I’m a boy, not a girl.”

→He said that he is a boy, not a girl.

(4)如果直接引语中的谓语动词表示一种反复出现或习惯动作，在变为间接引时，一般现在时不改为一般过去时。如：

The girl said, “I get up at six every morning.”

→The girl said that she gets up at six every morning.

(5)如果直接引语中含有since, when, while 引导的表示过去时间的状语从句，在变为间接引语时，只改变主句中的谓语动词，从句的一般过去时则不变。如：

He said to me, “I have taught English since he came here.”

→He told me that he had taught English since he came here.

(6)如果直接引语中含有情态动词must, need, had better以及情态动词的过去式could, might, should, would,在变为间接引语时，这些情态动词没有时态的改变。例如：

The teacher said to me. “You must pay more attention to your pronunciation.”→The teacher told me that I must (have to) pay more attention to my pronunciation.

6.代词等一般地应作相应的变化。

指示代词 this—that these—those

表示时间的词 now—then today—that day

this week(month, etc)—that week(month, etc)

yesterday—the day before

last week(month)—the week(month) before

three days(a year)ago—three days(a year) before

tomorrow—the next(following ) day

next week(month)—the next(following) week(month)

表地点的词 here—there

直接引语转换为间接引语的技巧 篇4

一、人称的转换

1. 直接引语中的第一人称，一般转换为第三人称

如：He said，“I am very sorry.”→He said that he was very sorry.

2. 直接引语中的第二人称，如果原话是针对转述人说的，应转换为第一人称

如：“You should be more careful next time.”my father told me.→ My father told me that I should be more careful the next time.

3. 直接引语中的第二人称，如果原话是针对第三人称说的，要转换成第三人称

如：She said to her son， “I’ll check your homework tonight.”→ She said to her son that she would check his homework that night.

4. 人称的转换包括人称代词、物主代词和名词性物主代词等

如：He asked me，“Will you go to the station with me to meet a friend of mine this afternoon？”→He asked me whether I would go to the station with him to meet a friend of his that afternoon.

5. 口诀巧记人称变化

口诀：“一主、二宾、三不变”。

（1）“一主”指当直接引语中的第一人称变为间接引语时，要和主句中的主语在人称上保持一致。

如：He said，“I am forty.”→ He said that he was forty.

（2）“二宾”指当直接引语中的第二人称变为间接引语时，要和主句中的间接宾语保持人称上的一致。

如：He said，“Are you coming tomorrow？”→He asked me if I was coming the next day.

（3）“三不变”指当直接引语中的第三人称变为间接引语时，人称不变。

如：He said，“Is she an English teacher？”→ He asked if she was an English teacher.

另外请同学们注意，直接引语为复数，引述者主语为单数时，间接引语的主语要相应变为复数。

如：He said，“Are you interested in English？”→ He asked us if we were interested in English.

总之，人称的转换不是固定的，具体情况具体对待，要符合逻辑。

二、时态的转换

直接引语转换为间接引语时，主句中的谓语动词如果是过去时，从句（即间接引语部分）中的谓语动词在时态方面要做相应的变化，变成过去时范畴的各种时态（实际这也是宾语从句对时态的要求），变化如下：

如：“I am very glad to visit your school”，she said. →She said she was very glad to visit our school.

Tom said，“We are listening to the pop music.”→ Tom said that they were listening to the pop music.

Mother asked，“Have you finished your homework

before you watch TV？” → Mother asked me whether I had finished my homework before I watched TV.

He asked the conductor，“Where shall I get off to change to a No. 3 bus？”→ He asked the conductor where he would get off to change to a No. 3 bus.

“Why did she refuse to go there？” the teacher asked. →The teacher asked why she had refused to go there.

三、句子结构的变化

1. 直接引语为陈述句时，用连词that引导，that在口语中常省略。主句的谓语动词可用said，也可用told来代替。请注意，可以说said that， said to sb. that或者told sb. that，不可直接说told that。

如：He said，“I have been to the Great Wall.”→He said to us that he had been to the Great Wall.

He said，“I’ll give you an examination next Monday.”→He told us that he would give us an examination the next Monday.

如果间接引语是由that引导的两个或两个以上的并列从句，第一个连词可以省略，以后的连词一般不省略，以免混乱。

如：The doctor said，“You are not seriously ill， you will be better soon.”→The doctor said（that）I was not seriously ill and that I would be better soon.

2. 直接引语为一般疑问句时，间接引语用连词whether或if引导，原主句中的谓语动词said要改为asked，语序是陈述句的语序，这一点非常重要。

如：He said，“Do you have any difficulty with

pronunciation？”→He asked（me） whether/if I had any difficulty with my pronunciation.

He said，“You are interested in English， aren’t you？”→He asked whether I was interested in English.

3. 直接引语为选择疑问句时，间接引语用whether...or...表达，而不用if...or...，也不用either...or...，语序是陈述句语序。

如：He asked，“Do you speak English or French？”→ He asked me whether I spoke English or French.

I asked，“Will you take bus or take train？”→ I asked him whether he would take bus or take train.

4. 直接引语为特殊疑问句时，原来的疑问词作为间接引语的连词，主句的谓语动词用ask（sb.）来表达，语序改为陈述句语序。

如：He asked，“What’s your name？”→He asked（me）what my name was.

He asked us，“How many car factories have been built in your country？”→He asked us how many car factories had been built in our country.

5. 直接引语为祈使句时，间接引语用带to的不定式表达，谓语动词常是ask， advise， tell， warn， order，request等。如ask sb. to do（用于肯定祈使句），ask sb. not to do（用于否定祈使句）。不定式短语中的时间状语、地点状语、人称及时态都做相应的变化。

如：He said，“Be seated， please.”→ He asked us to be seated.

“Do be careful with your handwritting.”he said →He told me to be careful with my handwriting.

“Don’t touch anything in the lab without permission”，the teacher said. → The teacher warned the students not to touch anything in the lab without permission.

6. 有些直接引语含有“建议”“劝告”的祈使句，可用suggest，insist，offer等动词转述。

如：He said，“Let’s have a rest.”→He suggested us having a rest.

He said，“Let me help you.”→ He offered to help me.

7. 当直接引语形式上是疑问句，有表示“请求”“建议”的意义时，可用ask sb. to do sth.，advise sb. to do sth.等形式转述。

如：“Would you mind opening the door？”he asked. →He asked me to open the door.

“Why not going out for a walk？”he asked us. →He advised us to go out for a walk.

8. 直接引语是感叹句时，可用what或how引导，也可用that引导。

如：She said，“What a lovely day it is！” → She said what a lovely day it was. /She said that it was a lovely day.

四、从句时态无须改变的情况

1. 当主句的谓语动词是一般现在时时

如：He always says，“I am tired out.”→ He always says that he is tired out.

2. 当主句的谓语动词是一般将来时时

如：He will say，“I’ll try my best to help you.”→ He will say that he will try his best to help me.

3. 当直接引语部分带有具体的过去时间状语时

如：He said，“I went to college in 1994.”→ He told us that he went to college in 1994.

4. 当直接引语中有以when， while引导的从句，表示过去的时间时

如：He said，“When I was a child， I usually played football after school.” →He said that when he was a child， he usually played football after school.

5. 当直接引语是客观真理或自然现象时

如：Our teacher said to us，“Light travels faster than sound.” →Our teacher told us that light travels faster than sound.

6. 当直接引语是谚语、格言时

如：He said，“Practice makes perfect.” → He said that practice makes perfect.

7.当直接引语中有情态动词should，would，could，had better，would rather，might，must，ought to，used to，need时

如：The doctor said，“You’d better drink plenty of water.” → The doctor said I’d better drink plenty of water.

He said， “She must be a teacher.” → He said that she must be a teacher.

He said，“She ought to have arrived her office by now.” →He said that she ought to have arrived her office by then.

She asked，“Must I take the medicine？” → She asked if she had to take the medicine.

直接间接引语练习题 篇5

直接证明与间接证明作业

一、选择题

1．函数y＝f(x)在(0,2)上是增函数，有 f(x＋2)=f(x)，则f(1)，f(2.5)，f(3.5)的大小关系是()

A．f(2.5)f(1)> f(2.5)

C．f(3.5)>f(2.5)>f(1)D．f(1)>f(3.5)>f(2.5)

2．用反证法证明：若整系数一元二次方程ax2＋bx＋c＝0(a≠0)有有理数根，那么a、b、c中至少有一个偶数时，下列假设正确的是()

A．假设a、b、c都是偶数

B．假设a、b、c都不是偶数

C．假设a、b、c至多有一个偶数

D．假设a、b、c至多有两个偶数

3．设a，b，c，d∈(0，＋∞)，若a＋d＝b＋c且|a－d|<|b－c|，则有()

A．ad＝bcB．ad

C．ad>bcD．ad≤bc

4．设a＝lg 2＋lg 5，b＝ex(x＜0)，则a与b大小关系为()

A．a＞b

C．a＝bB．a＜b D．a≤b

5．要证a2＋b2－1－a2b2≤0，只需证明()

A．2ab－1－ab≤0

a＋b2－1－a2b2≤0222a4＋b4B．a＋b－1－0 222D．(a2－1)(b2－1)≥0

二、填空题

1．设a＝＋2，b＝2，则a，b的大小关系为________．

2．用反证法证明命题“若实数a，b，c，d满足a＋b＝c＋d＝1，ac＋bd＞1，则a，b，c，d中至少有一个是非负数”时，第一步要假设结论的否定成立，那么结论的否定是________．

三、解答题

1．若a＞b＞c＞d＞0且a＋d＝b＋c，d＋a＜bc.2．已知a，b，c是互不相等的实数．

求证：由y＝ax2＋2bx＋c，y＝bx2＋2cx＋a和y＝cx2＋2ax＋b

确定的三条抛物线至少有一条与x轴有两个不同的交点．

3．已知a＞0，求证：

4．已知a>0，－>1，求证：1＋a>a2＋22≥a＋－2.aa1111

ba11－b

直接证明与间接证明作业

一、选择题

1—5：BBCAD

二、填空题

1.a＜b2.a，b，c，d全是负数”

三、解答题

1.证明： d＋a＜b＋c，只需证d＋a)2＜b＋c)2，即a＋d＋2ad＜b＋c＋2bc，因a＋d＝b＋c，只需证ad＜bc.即ad＜bc，设abcdt，abt,dct

adbc(bc)tt2bc

adbc

故命题得证

2.证明：假设题设中的函数确定的三条抛物线都不与x轴有两个不同的交点

(即任何一条抛物线与x轴没有两个不同的交点)，由y＝ax2＋2bx＋c，y＝bx2＋2cx＋a，y＝cx2＋2ax＋b，得Δ1＝(2b)2－4ac≤0，Δ2＝(2c)2－4ab≤0，Δ3＝(2a)2－4bc≤0.上述三个同向不等式相加得，4b2＋4c2＋4a2－4ac－4ab－4bc≤0，∴2a2＋2b2＋2c2－2ab－2bc－2ca≤0，∴(a－b)2＋(b－c)2＋(c－a)2≤0，∴a＝b＝c，这与题设a，b，c互不相等矛盾，因此假设不成立，从而命题得证．

3.证明：要证只要证a2＋22≥a＋－2，aaa2＋2a＋2.aa

212a＋2，a＋22≥aa21111∵a＞0，故只要证

1即a2＋24 11aa2＋2＋4≥a2＋2＋222a＋＋2，aaa

a2＋2≥ 2a＋，aa1111从而只要证2

1212只要证4a＋2≥2a＋2＋2，aa

1即a2＋2.a

4.11证明：∵－>1，a>0，ba∴011＋a·1－b>1，1－b

只需证1＋a－b－ab>1，只需证a－b－ab>0，即a－b11>1，即－>1.abba

直接证明与间接证明 篇6

教学目标：

重点：综合法，分析法与反证法的运用．

难点：分析法和综合法的综合应用．

能力点：能用三种方法解决简单的证明问题及三种证明方法的综合应用．

教育点：体会数学证明的思考过程及特点，提升分析解决问题的能力．

自主探究点：主要考察函数、导数、不等式的证明等基础知识，同时要综合运用数学知识进行推理论证，以及化归与转化的思想．

易错点：① 利用反证法证明数学问题时，要假设结论错误，并用假设命题进行推理，没有用假设命题推理而推出矛盾结果，其推理过程是错误的；

② 不会用分析法分析，找不到解决问题的切入口；

③ 不会用综合法表述，从而导致解题格式不规范．

学法与教具：

1．学法：自主探究、练习法2．教具：多媒体

一、【知识结构】

二、【知识梳理】

1．直接证明

（1）综合法

①定义：利用已知条件和某些数学定义、定理、公理等，经过一系列的________，最后推导出所要证明的结论________，这种证明方法叫做综合法． ②框图表示：PQ1Q1Q2Q2Q3QnQ（其中P表示已知条件，Q表

示要证的结论）．

（2）分析法

①定义：从________________出发，逐步寻求使它成立的__________，直至最后，把要证明的结论归结为判定一个明显成立的条件（已知条件、定理、定义、公理等）．这种证明的方法叫做分析法． ②框图表示：QP1P1P2P2P3得到一个明显成立的条件．

2． 间接证明 反证法：假设原命题__________（即在原命题的条件下，结论不成立），经过正确的推理，最后得出_____，因此说明假设错误，从而证明了原命题成立，这样的证明方法叫做反证法．利用反证法证题的步骤①假设命题的结论不成立，即假设结论的反面成立；②由假设出发进行正确的推理，直到推出矛盾为止；③由矛盾断言假设不成立，从而肯定原命题的结论成立．简言之，否定→归谬→断言．

三、【范例导航】 例1已知xyz1，求证：x2y2z2

3．【分析】综合法往往以分析法为基础，是分析法的逆过程，但更要注意从有关不等式的定理、结论或题设条件出发，根据不等式的性质推导证明． 综合法证明不等式，要特别注意基本不等式的运用和对题设条件的运用．由基本不等式x2y22xy,得到关于x、y、z的三个不等式，将三式相加整理变形,然后利用xyz1得(xyz)21从而可证．

【解答】法一：x2y22xy,y2z22yz,z2x22zx,(xy)(yz)(zx)2xy2yz2zx 3(xyz)xyz2xy2yz2zx,即3(x2y2z2)(xyz)21，xyz法二：xyz

1

322

213

．



(3x3y3z1)

222

[3x3y3z(xyz)] 13

[(xy)(yz)(zx)]0

(3x3y3zxyz2xy2xz2yz)

xyz

．

法三：证明：a1,a2,,anR,a1a2an1，则a1a2an

222

构造函数f(x)(xa1)(xa2)(xan)

1n

成立．

nx2(a1a2an)xa1a2annx2xa1a2an．

222

因为对于一切xR，都有f(x)0，所以44n(a1a2an)0,22222222

从而证得：a1a2an

222

1n

222，当n3时，即xyz

成立．

【点评】利用综合法证明不等式是不等式证明的常用方法之一，即充分利用已知条件与已知的基本不等式，经过推理论证推导出正确结论，是顺推法或由因导果法．其逻辑依据是三段论式的演绎推理方法，这就需保证前提正确，推理合乎规律，这样才能保证结论的正确．其基本流程表述如下：

变式训练：设a0,b0,ab1,求证

1a



1b1a



1ab1b

8.1ab

abab

1ab

2ab

【解答】方法一：a0,b0,ab1,又ab1,ab

14,

2ab

2

1，8.方法二：

ab1,

ba

ab

abab

1a



1b



1ab



4aba



abb



abab

112ab

2248 ab2()2

例2（1）用分析法证明：acbd

11（2）已知a0,

1．

ba【分析】（1）由于a,b,c,dR,故要分acbd0或acbd0两种情况，然后用分析法证明．（2）

要证明知条件

1b1a

不等式两边都是整数，可通过同时平方，化为有理式运算，通过化简得出已

1，可得证．

【解答】证明（1）①若acbd0，结论显然成立； ②(ac

若

acbd0，2

要

b

证

ac

d

b成立c，d只需

证

b)2

)c

(adbc)0显

2abcdadbc，即证ac2abcdbdacadbcbd，2222222222

然成立，综上所述acbd（2）要

证

成立，只需证1a

abab

11b1b，只需证(1a)(1b)

1a

1b

1,(b1,即1a

1baab1，abab,只需证1，即1．由已知a0,1成立，

【点评】分析法的特点和思路是“执果索因”，即从“未知”看“需知”，逐步靠拢“已知”或本身已经

成立的定理、性质或已经证明成立的结论等．通常采用“欲证——只需证——已知”的格式，在表达中要注意叙述形式的规范．在解答本题时有两点容易造成失分：（1）不去分类，而是直接平方作差判断．（2）在平方作差变形时运算失误或对等号成立的条件说明不到位而失分． 注意解题技巧： 1．逆向思考是用分析法证题的主要思想，通过反推，逐步寻找使结论成立的充分条件．正确把握转化方向是使问题顺利获解的关键．

2．在求解实际问题时，对于较复杂的问题，可以采用“分析-综合法”即两头凑的办法，即通过分析法找出某个与结论等价（或充分）的中间结论，然后通过综合法由条件证明这个中间结论，使原命题得证． 变式训练： 已知ABC三边a,b,c的倒数成等差数列，证明：B为锐角． 【解答】要证明B为锐角，根据余弦定理，也就是证明cosB

acb

2ac

20，即需证

acb0，由于acb2acb，要证acb0，只需证2acb0，a,b,c的倒数成等差数列，

1a



1c



2b,即2acb(ac)．要证2acb0，只需证b(ac)b0，即

b(acb)0．上述不等式显然成立．B 必为锐角．

2中至少有一个成立．

yx

【分析】当一个命题的结论是以“至多”、“至少”、“惟一”或以否定形式出现时，宜用反证法来证，反证法的关键是在正确的推理下得出矛盾，分析可得本题适合用反证法，从题目中可以看出“至少”这样的存

1x1y

在量词，于是可设2与2结论的反面成立，即两个不等式都不成立．通过推理可得出

yx

2与

xy2的结论，与已知xy2矛盾，所以假设不成立，原命题正确．

例3若x,y都是正实数，且xy2，求证：

1x1y

【解答】假设

1xy

2与

1yx

则有2都不成立，1xy

2与

1yx

因为x0且y0，2同时成立，所以1x2y，且1y2x，两式相加得，2xy2x2y，所以xy2，这与已知xy2相矛盾，因此

1xy

2与

1yx

2中至少有一个成立．

【点评】用反证法证明问题的一般步骤：（1）反设: 假定所要证的结论不成立，即结论的反面（否定命

题）成立；（否定结论）（2）归谬：将“反设”作为条件，由此出发经过正确的推理，导出矛盾——与已知条件、已知的公理、定义、定理及明显的事实矛盾或自相矛盾；（推导矛盾）（3）结论：因为推理正确，所以产生矛盾的原因在于“反设”的谬误．既然结论的反面不成立，从而肯定了结论成立．（结论成立）． 注意：（1）当结论的反面呈现多样性时，必须罗列出各种可能结论，缺少任何一种可能，反证法都是不完全的．（2）利用反证法证明问题时，要注意与之矛盾的定理不能是用本题的结论证明的定理，否则，将出现循环论证的错误．（3）反证法中常见词语的否定形式

变式训练：（2011．安徽）设直线l1:yk1x1，l2:yk2x1，其中实数k1,k2满足k

1k

220． 证明：l1与l2相交．

【解答】反证法．假设l1与l2不相交，则l1与l2平行，有k1k2，代入k1k220，得k1220，这与k1为实数的事实相矛盾，从而k1k2，即l1与l2相交．

四、【解法小结】

1．分析法的特点是：从未知看需知，逐步靠拢已知． 2．综合法的特点是：从已知看可知，逐步推出未知．

3．分析法和综合法各有优缺点．分析法思考起来比较自然，容易寻找到解题的思路和方法，缺点是思路逆行，叙述较繁；综合法从条件推出结论，较简捷地解决问题，但不便于思考．实际证题时常常两法兼用，先用分析法探索证明途径，然后再用综合法叙述出来． 4．应用反证法证明数学命题，一般分下面几个步骤： 第一步：分清命题“pq”的条件和结论； 第二步：作出与命题结论q相矛盾的假定q；

第三步：由p和q出发，应用正确的推理方法，推出矛盾结果；

第四步：断定产生矛盾结果的原因，在于开始所作的假定q不真，于是原结论q成立，从而间接地证明了命题pq为真．

第三步所说的矛盾结果，通常是指推出的结果与已知公理矛盾、与已知定义矛盾、与已知定理矛盾、与已知条件矛盾、与临时假定矛盾以及自相矛盾等各种情况．

五、【布置作业】

必做题：

1．关于x的方程axa10在区间(0,1)内有实根，则实数a的取值范围是__________． 2．设ab0，m

n，则m,n的大小关系是__________．

3．设x,y,z是空间的不同直线或不同平面，且直线不在平面内，下列条件中能保证“若xz，且（填写所有正确条件的代号）yz，则x∥y”为真命题的是________．①x为直线，y,z为平面；②x,y,z为平面；

③x,y为直线，z为平面；④x,y为平面，z为直线； ⑤x,y,z为直线．

．如果a,b应满足的条件是__________________． 5．（1）设x是正实数，求证：(x1)(x21)(x31)8x3；

（2）若xR，不等式(x1)(x21)(x31)8x3是否仍然成立？如果成立，请给出证明；如果不成立，请举出一个使它不成立的x的值．

必做题答案：1．(,1)2．mn 3．①③④4．a0,b0且ab

35．（1）证明 x是正实数，由基本不等式

知x1，1x2

2x，x1，故

(x1)(x1)x(1)

3x23． 8x（当且仅当x1时等号成立）

（2）解：若xR，不等式(x1)(x21)(x31)8x3仍然成立．由（1）知，当x0时，不等式成立；当x0时，8x30，而(x1)(x21)(x31)(x1)2(x21)(x2x1)

(x1)(x1)[(x

2)

4]0，此时不等式仍然成立．

选做题：

1．若a,b,c为RtABC的三边，其中c为斜边，那么当n2，nN时，anbn与cn的大小关系为____________． 2．下面有3个命题：

x

①当x0时，2

x的最小值为2；



6②将函数ysin2x的图象向右平移个单位，可以得到函数ysin(2x



6)的图象；

③在RtABC中，ACBC，ACa，BCb，则

ABC的外接圆半径r

．类比到空

间，若三棱锥SABC的三条侧棱SA、SB、SC两两互相垂直，且长度分别为a、b、c则三棱锥

S

ABC的外接球的半径R

其中错误命题的序号为________． ．．

．

3．已知f(x)xaxb．（1）求：f(1)f(3)2f(2)；

（2）求证：f(1),f(2),f(3)中至少有一个不小于选做题答案：

1．abc2．①②

3．解f(1)ab1，f(2)2ab4，f(3)3ab9，f(1)f(3)2f(2)2．（2）证明假设f(1),f(2),f(3)都小于

n

n

n

．

．则

f(1)

12,

f(2)

12,

f(3)

12,12f(2)1，1f(1)f(3)1．2f(1)f(3)2f(2)2．

透视直接引语变间接引语 篇7

我们转述别人的话时，可以引用别人的原话，被引用的部分称为直接引语；用自己的话转述别人的意思，被转述的部分称为间接引语。间接引语多数构成宾语从句。

二、直接引语改为间接引语时连词的使用：

1.直接引语为陈述句时，间接引语的连词用that，that可以省略。如：

“I have lived in the south for years,” Mrs Duncan said.

→Mrs Duncan told me (that) she had lived in the south for years.

Duncan夫人说她在南方住了许多年。

“I shall tell him exactly what I think,” she said.

→She said (that) she would tell him exactly what she thought. 她说她将会告诉他她所想的。

2.直接引语为一般疑问句时，间接引语的连词用if/whether。如：

He said, “Are you interested in English?”

→He asked (me) if I was interested in English. 他问我是否对英语感兴趣。

He said，“Did you see him last night?”

→He asked (me) whether I had seen him the night before.

他问我前一天晚上是否见到了他。

3.直接引语为特殊疑问句时，间接引语的连词用特殊疑问句本身所带的疑问词如when，where， who， why， how， how many， how old等等。如：

“What do you want?” he asked me.

→He asked me what I wanted. 他问我想要什么。

“How can we improve the condition of the soil?” the farmers asked him.

→The farmers asked him how they could improve the condition of the soil.

农民们询问他如何才能提高土壤的质量。

4.直接引语为祈使句时，间接引语不用连词，而是将直接引语改为动词不定式用作句子的宾语补足语。如：

She said to us，“Please sit down. ”

→She asked us to sit down.

He said，“Don’t make so much noise， boys. ”

→He told the boys not to make so much noise.

“Please explain why you’re two and a half hours late,” the boss said.

→The boss asked him to explain why he was two and a half hours late.

“Don’t give up!” Father shouted at him.

→Father told him in a loud voice not to give up.

“Get everything ready in half an hour,” the teacher said to the students.

→The teacher ordered the students to get everything ready in half an hour.

注意：

主句的谓语动词有时要根据直接引语的情态和语气作相应的变化，如say说； tell sb. 告诉某人；ask问/请求； suggest建议； order命令等等。

三、时态的变化：

如主句的谓语动词为现在时态范畴，间接引语中的时态一般不作变化；但如果主句的谓语动词为过去时态范畴，则间接引语多改用相应的过去时态。其规律见下表：

如：“She’s preparing her lessons,” I said.

→I said that she was preparing her lessons.

I said to them，“He’ll get excited. ”

→I told them that he would get excited.

He said to me，“Jane spent all her time doing that.”

→He told me that Jane had spent all her time doing that.

注意：

1.直接引语如果有表示具体的过去时间状语(如in 1992, last week等)，在变为间接引语时时态可以不变。如：

My father said to me，“I read the book in 1986.”

→My father told me he read the book in 1986.

2.直接引语表达的意思是客观真理时，时态可以不变。如：

The geography teacher said to us，“The earth turns around the sun.”

→The geography teacher told us that the earth turns around the sun.

四、间接引语中人称代词的变化：

要根据句子的意义作相应的变动。其规律是：一主二宾三不变，即第一人称代词指的是句子的主语；第二人称代词指的是句子的宾语；第三人称代词不用变化。如：

“I haven’t brought my dictionary,” the student said.

→The student said that he hadn’t brought his dictionary.

五、指示代词、时间、地点状语的变化：

通常总是由近指改为远指。其规律见下表：

如：

“I’ll come and see you again this evening， Tom,” he said.

→He told Tom that he would go and see him again that evening.

注意：

如果现场转述别人的话或当句子的意义不会引起误解的情况下，则勿须改变以上内容。如：

“I’ll come here again today,” she said.

→She said that she’d come here again today.

六、语序的使用：

间接引语中总是使用陈述语序。如：

She asked，“What is it? What’s going to happen now?”

→She asked what it was and what was going to happen then.

The boy was wondering，“How does the computer work?”

→The boy was wondering how the computer worked.

He asked me，“Do you study English or French?”

→He asked me whether I studied English or French.

“It’s Mary， isn’t it?” asked Jane.