Unit 4 I used to be afraid of the dark 单元闯关试题 2025-2026学年上学期初中英语人教版九年级全册

中小学教育资源及组卷应用平台
Unit 4 I used to be afraid of the dark 单元闯关试题
2025-2026学年上学期初中英语人教版九年级全册
一、完形填空
阅读短文，从每小题所给的 A、B、C、D四个选项中，选出可以填入空白处的最佳选项。
I'm in my middle fifties and I don't feel old yet. However, sometimes I look back on my childhood and 1 things with the way of life of today's kids. Some things have 2 changed.
One area of change is television. Some changes have been improvements. Some changes, however, have been 3 .
When I started school, most families in my village didn't have a television; televisions were just beginning to get 4 . They were new and expensive. My father 5 money for a whole year and bought a small black and white set. I 6 remember watching my favorite cartoon on that fascinating machine. I even invited all my friends over. That was 7 ！
Now, televisions have come to every home in my village and many families 8 more than one television. The pictures are in full color and far 9 . The screens are so wonderful that they are more 10 those of movies. The variety(种类) and quantity(数量) of programs have 11 greatly, too. There are over one hundred channels(频道) 12 . As for the programs, there are many fine educational shows. On the other hand, there is a lot of 13 that most parents don't want their kids to watch. Experts 14 that television has a very big influence on kids and a lot of it is negative(消极的).
Television isn't 15 it used to be. I wonder what it will be like when today's kids are my age. What do you think
1．A．miss B．invent C．compare D．imagine
2．A．suddenly B．mostly C．normally D．certainly
3．A．plans B．problems C．dreams D．symbols
4．A．similar B．personal C．traditional D．popular
5．A．saved B．lost C．spent D．changed
6．A．yet B．still C．ever D．again
7．A．exciting B．boring C．lucky D．unlucky
8．A．sell B．own C．fix D．break
9．A．clearer B．smaller C．more difficult D．more expensive
10．A．about B．with C．like D．against
11．A．appeared B．increased C．competed D．moved
12．A．absent B．necessary C．comfortable D．available
13．A．rubbish B．attention C．trouble D．knowledge
14．A．hope B．doubt C．warn D．promise
15．A．how B．what C．when D．where
二、阅读理解
阅读三篇短文，从每小题所给的 A、B、C、D四个选项中，选出一个与短文内容相符的最佳选项。
A
“What should I wear today？” That's a question you might ask yourself in the morning. For some kids，the answer is the same every day─a school uniform.
More than 10 years ago，3 percent of all public schools in the US required that students wear uniforms. Now，that number is closer to 10 percent. Some people support the policy（政策），hoping that uniforms will encourage students to focus on（专注于）their work. Opponents，however，say students should be allowed to express themselves through their clothing.
Yes！ ◆"My school has a strict uniform policy. At school my friends and I don't have the need to discuss clothes，and we enjoy just being together and learning. The best thing I like about our uniform is the style，especially the shirts and sweaters，"said fourth grader Clifton Harris.
◆"It helps save parents' money，"a mother said. ◆“I think uniforms help students focus on their studies rather than their clothes，”Megan Mannion said. Her school，Rankin Elementary School，has had a uniform policy since 1995.
No！ ◆“I think students should choose their own clothing styles，rather than be told to wear a specific uniform，” fifth grader Kaylie Vilayvong said. Her classmate Wade Fleetwood agrees，"Kids should be allowed to wear different styles of clothes.” ◆Some parents are worried about the expense（花费）.Most schools offer uniforms at a price between $16 and $26 “What's the school going to do for people who can't afford them？” asked a father. ◆“Adults make their own clothing choices and are free to express themselves through their look，” a teacher said." Students should be allowed to choose their own clothing，too.”
16．What percent of public schools in the US ask students to wear uniforms now？
A．Far less than3%. B．Nearly 3%.
C．Nearly 10%. D．More than 10%.
17．What does the underlined word "Opponents" mean in Chinese？
A．支持者 B．反对者 C．消费者 D．生产者
18．According to Clifton Harris，what's the best thing about his school uniform？
A．It has a good style. B．It is very comfortable.
C．It saves his parents' money. D．It helps him focus on his studies.
19．Which of the following is TRUE？
A．Wade Fleetwood agrees that students should wear school uniforms.
B．Most schools in the US offer school uniforms at a price of over $26.
C．Most teachers think students should make their own clothing choices.
D．Rankin Elementary School has had a school uniform policy for over 20years.
20．How does the writer develop this passage？
A．By telling some stories. B．By giving some examples.
C．By introducing study results. D．By comparing different opinions.
B
As a student, I was most afraid to answer questions in class, and I found that the students around were just like me. At the beginning of each class, when the teacher asked a question, I always lowered my head because I was afraid that the teacher saw me. One day, in a foreign language class, Mr. Black gave us a lesson. He wanted us to be active in class, so he asked us some questions, but no one answered. “Let me tell you a story first,” he said. “When I came to the United States to study, the university often invited famous people to make speeches. Before the beginning of every speech, I found an interesting thing. The students around me always took a card board folded (折叠的) in half, wrote their names boldly with the most eye-catching color, and then placed the cardboard on the seat. So when the speaker needed the answers from the students, he could see and call a listener’s name directly.”
“I couldn’t understand that. My classmate told me the speakers were all top people who meant chances. When your answer was to his surprise, it meant he might give you more chances. In fact, I really saw a few students got great chances because of that.”
After listening to the story, I understood that the chance would not find you itself. You must show yourself all the time so that you could find a chance on the card.
21．What did Mr. Black want the students to do in his class
A．Read loudly. B．Take notes carefully.
C．Be active. D．Listen to him quietly.
22．How did the writer’s classmates behave when they were asked questions
A．They raised their hands. B．They shook their heads.
C．They closed their eyes. D．They lowered their heads.
23．How did the speaker get to know the students’ names
A．He got them from the computer. B．He saw the cardboards on the seats.
C．He asked the students for their names. D．He got them from the name list on the teacher’s desk.
24．What does the underlined word “eye-catching” in Paragraph 1 mean in Chinese
A．引人注目的 B．眼睛疼痛的 C．目光呆滞的 D．睡眼朦胧的
25．What does the writer mainly tell us
A．Doing as others do is necessary. B．Answering questions bravely is easy.
C．Attracting others’ attention is interesting. D．Showing yourself bravely can win chances.
C
At my primary school, I was one of the smartest kids there. I never studied, but always got perfect scores. I thought I was born clever. At least I believed so. I was also a prodigy in music according to myself. I could sing better than almost everyone else in my school. I was pretty sure that once I got to sixth grade, everyone would be surprised by me. But actually, they weren’t.
When I arrived at my new class, I couldn’t wait to show everyone what I could do. However, there was always someone else who could do them better. My grades began to suffer. More talented girls often sang solo（独唱）. I believed I wasn’t talented. I believed I was a failure.
Over the next two years, I had to work very hard. Every prize for the singing competition was given to me for hard work and efforts. Grades were still very low but improving little by little. I worked really hard. However, I was never the best at everything.
I haven’t realized until recently that I really don’t have to be the best at everything. I was too hard on myself. In fact, when I did badly in a test, my classmates never laughed at me.
No one is perfect. There will probably always be someone better than me at something. Anyway, there are about seven billion people in this world. I will never be the number one at everything, and that’s really okay.
26．What does the underlined phrase “a prodigy” probably mean
A．A smart kid. B．A crazy fan.
C．A common child. D．A lazy girl.
27．When the writer was at the new class, ____________.
A．she lost her interest in music B．she had difficulty in learning
C．she surprised everyone in solos D．she got on badly with her classmates
28．What happened to the writer during the next two years
A．She won many prizes without any efforts.
B．She found the best way to become perfect.
C．She gave up trying because of the low scores.
D．She failed to be perfect though she worked hard.
29．What has the writer realized recently
A．There is no success without effort.
B．Being talented is the key to success.
C．Don’t expect too much of yourself.
D．It’s not necessary to care about the result.
30．Which would be the best title for this passage
A．No one is perfect B．My past life as a young girl
C．Hard work doesn’t work D．What to do when you’re not perfect
请阅读下面短文，根据短文内容，从所给的选项中选出能填入空白处的最佳选项，使短文意思通顺。选项中有一项为多余项。）
When I was a kid, I was a little fat. And I was always tired because of that. At last I had to make a decision: 31 . So a few weeks after my birthday, I started to lose weight.
Walking was all I could do at first. I started walking to a subway stop every day. On weekends, I walked in Central Park. A year later, I started to run. At first I could run for only two minutes, but I kept on.
It made a difference. I was losing nine or ten pounds a month. And there was something about running: It made me feel like a kid again. 32 .
I started to think about the New York City Marathon, which goes right past my apartment building. For years，I thought I could never do that. 33 . That summer, I started running for the marathon. And on the morning of the November 1st, I stood on the Verrazano Bridge in Staten Island with more than 40,000 other runners，waiting for the event to start.
34 , handing me cups of water. In Harlem, my mom and brother stood on a street corner to see me. And then I crossed the finish line in Central Park, and somebody put a medal (奖牌) around my neck. At the moment, I knew: 35 .
A．I enjoyed it
B．What I have to do is running every day
C．If I put my mind to something, nothing is impossible
D．I was going to start losing weight
E．But now I realized that maybe I could
F．When we started moving, it was an amazing feeling to have people cheering me on
三、选词填空
阅读短文，从方框中选择适当的词并用其正确形式填空，使短文通顺、意思完整。每空限填一空，每词限用一次。
one, scare, actual, he, toy, reach, possible, clever, wake, move
Adam was an English senior high student living in Liverpool. He regarded himself as the 36 student in his class.
One day, Adam wanted to see 37 uncle in London, so he bought a train ticket from Liverpool to London. When he 38 the train station, the train had already filled with passengers. There were no free seats in the carriage. Then, Adam saw a man selling 39 . He suddenly had a good idea.
Adam bought a rubber snake and threw it into the carriage. All the passengers were very 40 when they saw the “snake”. They all shouted for help. People ran out of the carriage as quickly as 41 . Adam saw several empty berths (卧铺) and lay down on 42 of them. He soon fell asleep.
After a while, Adam 43 up. He found the train was not 44 and thought it had stopped at a station. He asked a railway man, “Which station is it ”
The railway man replied, “It is Liverpool. 45 , there was a snake in this carriage. So it was separated and left behind here, the other carriages have left for London.
四、读写综合
请阅读下面短文，根据所提供的信息，回答五个问题，要求所写答案语法正确，语义完整切题。
In American countryside, people often park their cars in the yard when they are at home. So you can easily understand whether people are at home or not. But I used to park my car in the car barn (车库) when I was on holiday.
It was a Sunday morning. I got up early and went to the garden behind our house with my husband. We planted some flowers and trees there. About one hours later, I heard our lazy dog yipping (犬吠) in our house. I at once realized that something must be happening in the house. Quickly, my husband and I came back to the house and saw a boy rush out of our house and run away.
“Come in and see what was gone.” My husband said. “He must think nobody is in.”
“Shall I go to run after him or call the police ” my husband asked.
“No, after all, we have nothing lost.” I replied.
Some days later, a woman with the boy came to my house and asked, “Is it your dog I found that it killed my chicken yesterday, and I wanted to kill it. But my son said it was yours.”
When I was shaking hands with the boy to thank him. I felt something hard in my hand. I wanted to say something, but he has run away again.
46．How can you know whether people are at home in American countryside （不超过15词）
47．Where was the writer when the dog yipped （不超过6词）
48．The couple (夫妇) found （仅填1词）missing after the boy ran away
49．The woman want to kill the dog because （不超过5词）
50．The writer feel （仅填1词） when she knew the fact.
第二节 书面表达
时光荏苒，跟三年前的自己相比较，你会有很多变化。请以“I Have Changed a Lot!”为题，根据以下要求与提示，用英语写一篇短文，具体描述你最重要的变化及其是如何发生的。
要求：
1. 短文不得出现任何真实人名、校名及其他相关信息；
2. 100 词左右。
提示：
1. What did you use to be like
2. What is the most important change
3. And how did it happen Tell a story about it.
I Have Changed a Lot!
__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
答案
1．C 2．D 3．B 4．D 5．A 6．B 7．A 8．B 9．A 10．C 11．B 12．D 13．A 14．C 15．B
【分析】文章介绍了作者小时候和现在的孩子生活的不同，有的东西变得更好了，有的改变成了问题。主要介绍了过去的电视和现在的不同之处。
1．句意：有时往回看看我的童年，比较现在的孩子和我的童年的一些东西。根据compare---with---把---和---进行比较；A. miss思念，错过；B. invent发明；C. compare比较；D. imagine想象；故选C
2．句意：一些东西确实改变了。A. suddenly突然；B. mostly主要地；C. normally正常地；D. certainly的确；根据One area of change is television. Some changes have been improvements. Some changes, however, have been 　　3　　. 可知，是一些东西确实改变了；故选D
3．句意：然而一些改变成了问题。A. plans计划； B. problems问题；C. dreams梦想；D. symbols象征；根据后文On the other hand, there is a lot of 　　13　　 that most parents don't want their kids to watch. Experts 　　14　　 that television has a very big influence on kids and a lot of it is negative(消极的). 可知是问题；故选B
4．句意：电视刚刚开始流行。A. similar相似的；B. personal个人的；C. traditional传统的；D. popular流行；根据They were new and expensive. My father 　　5　　 money for a whole year and bought a small black and white set.可知，是刚刚流行；故选D
5．句意：我爸爸攒了一年的钱，买了一个小的黑白电视机。A. saved节省；B. lost丢失；C. spent花费；D. changed改变；根据They were new and expensive.可知，是攒了一整年的钱；故选A
6．句意：我仍然记得在这个极好的机器上看我最喜欢的动画片。A. yet还，尚（通常用于否定句和疑问句）；B. still仍然；C. ever曾经；D. again又；根据句意记得过去发生的事情，所以是仍然记得；故选B
7．句意：那很激动。A. exciting激动的；B. boring 无聊的；C. lucky幸运的；D. unlucky不幸的；根据I even invited all my friends over可知，邀请所有的朋友来看电视，应该是激动的；故选A
8．句意：许多家庭拥有多于一个的电视。A. sell卖；B. own拥有；C. fix修理；D. break打破；根据Now, televisions have come to every home in my village可知，是许多家庭拥有多于一个的电视；故选B
9．句意：画面更鲜艳更清晰。A. clearer更清晰；B. smaller更小；C. more difficult更难；D. more expensive更贵；根据The pictures are in full color可知是更清晰；故选A
10．句意：屏幕是如此的好以至于它们更像那些电影。A. about关于；B. with和；C. like像；D. against反对；根据The screens are so wonderful 和be like像；故选C
11．句意：电视节目的种类和数量也有很大的增加。A. appeared出现；B. increased增加；C. competed比赛；D. moved移动；根据The variety(种类) and quantity(数量)可知是增加；故选B
12．句意：有100多个频道能找到。A. absent缺席的；B. necessary必须的；C. comfortable舒服的；D. available可找到的；根据The variety(种类) and quantity(数量) of programs have 　　11　　 greatly, too.可知，是有100多个频道能找到；故选D
13．句意：有许多的垃圾。A. rubbish垃圾；B. attention注意；C. trouble麻烦；D. knowledge知识；根据most parents don't want their kids to watch可知，是垃圾；故选A
14．句意：专家警告电视对孩子有很大的影响。A. hope希望；B. doubt质疑；C. warn警告；D. promise保证；根据a lot of it is negative(消极的)可知，是警告；故选C
15．句意：电视不再是过去的样子。A. how怎样；B. what什么；C. when什么时候；D. where哪里；根据句意应是是什么样；故选B
16．C 17．B 18．A 19．D 20．D
【分析】这篇短文主语是一篇关于是否在学校穿校服的问题的讨论。
16．细节理解。根据文中More than 10 years ago，3 percent of all public schools in the US required that students wear uniforms. Now，that number is closer to 10 percent.可知，现在是10%。故选C。
17．词句猜测。根据上文. Some people support the policy（政策），hoping that uniforms will encourage students to focus on（专注于）their work.及say students should be allowed to express themselves through their clothing.可知这里opponents的意思是“反对者”。故选B。
18．细节理解。根据文中The best thing I like about our uniform is the style，especially the shirts and sweaters，"said fourth grader Clifton Harris.可知，这里是说款式。故选A。
19．推理判断。根据文中”Megan Mannion said. Her school，Rankin Elementary School，has had a uniform policy since 1995.可知，Rankin Elementary学校有20多年的校服政策。故选D。
20．文中结构。通读整篇短文可知在，这篇短文作者通过比较不同人对是否穿校服来写这篇短文。故选D。
21．C 22．D 23．B 24．A 25．D
【导语】本文是一篇记叙文。主要讲述了“我”很害怕在课堂上回答问题，布莱克老师为了让“我们”积极起来，讲述了他自己的亲身经历，告诉我们：机会不会主动找你，只有积极主动参与，充分展示自己，才能获得更多的机会。
21．细节理解题。根据“He wanted us to be active in class”可知，他想要我们在课堂上积极一些，故选C。
22．推理判断题。根据“I always lowered my head because I was afraid that the teacher saw me”及“so he asked us some questions, but no one answered”可知，“我”不想回答问题时会低下头，其他同学和“我”一样，由此猜测出他们也会低下头，故选D。
23．细节理解题。根据“The students around me always took a card board folded in half, wrote their names boldly with the most eye-catching color, and then placed the cardboard on the seat.”可知，演讲者从座位上的写字板上得知学生们的名字，故选B。
24．词句猜测题。根据“So when the speaker needed the answers from the students, he could see and call a listener’s name directly.”“老师想要找人回答问题时，直接能够看到”可推知，eye catching是“引人注目的”，故选A。
25．主旨大意题。通读全文，尤其是通过老师讲述自身的经历可知，本文告诉我们：勇敢地展示自己能够赢得机会，故选D。
26．A 27．B 28．D 29．C 30．A
【分析】作者通过对自己学习经历的叙述，阐述了“人无完人”的人生道理。
26．词义猜测题。根据文中句子“I could sing better than almost everyone else in my school.”可以推断出，作者在音乐方面也是一个聪明的孩子。故选A。
27．推理判断题。根据文中的“When I arrived at my new class”和“My grades began to suffer.”以及后文中“Over the next two years”和“Grades were still very low”可推断，作者到了新班以后，在学习方面遇到了困难，故选B。
28．细节理解题。根据文中“Over the next two years”和“I worked really hard. However, I was never the best at everything”可知，在之后的两年间，作者仍然不完美，尽管她已经很努力了，故选D。
29．细节理解题。根据“I haven’t realized until recently that I really don’t have to be the best at everything.”可知，作者意识到不要对自己期望太高。故选C。
30．最佳标题题。根据整个文章的理解可知，本文主要叙述了作者尽力使自己在各方面都很突出，力求完美，结果失败的故事。最后懂得了“人无完人”的道理，所以A选项比较符合，故选A。
31．D 32．A 33．E 34．F 35．C
【分析】我小时候很胖，因此总是感到疲劳。我决定减肥，开始步行到地铁站，一年后跑步，先是跑几分钟， 我坚持锻炼，最后参加了马拉松比赛，获得奖牌。此时我意识到：世上无难事，只怕有心人。
31．D. I was going to start losing weight我正要开始减肥。根据第一段最后一句So a few weeks after my birthday, I started to lose weight.在我的生日后的几个星期，我开始减肥，可知我那时正要开始减肥，故选D。
32．A. I enjoyed it 我喜欢它。根据前一句It made me feel like a kid again.跑步使我感觉像个孩子，可推测我喜欢跑步。故选A。
33．E. But now I realized that maybe I could但是现在我意识到或许我会的。根据后一句That summer, I started running for the marathon.那年夏天我开始跑马拉松，可知我意识到我或许能够跑步，故选E。
34．F. When we started moving, it was an amazing feeling to have people cheering me on 当我们开始移动时，有人为我欢呼是一种奇妙的感觉。根据后面的handing me a cup of water递给我一杯水可知，描述我们在长跑的起始线上，感觉很奇妙，故选F。
35．C. If I put my mind to something, nothing is impossible 如果我专心于做某事，没有不可能的。这里作者通过自己参加长跑的经历是告诉我们：世上无难事，只怕有心人，故选C。
36．cleverest 37．his 38．reached 39．toys 40．scared 41．possible 42．one 43．woke 44．moving 45．Actually
【导语】本文主要讲述了Adam聪明反被聪明误的故事。
36．句意：他认为自己是班上最聪明的学生。根据“He regarded himself as the...student in his class.”和下文可知，Adam认为他自己是班上最聪明的学生；clever符合语境，此处要用最高级cleverest。故填cleverest。
37．句意：有一天，Adam想去伦敦看他的叔叔，所以他买了一张从利物浦到伦敦的火车票。根据“uncle”可知，此处指Adam他的叔叔，应用he的形容词性物主代词his。故填his。
38．句意：当他到达火车站时，火车上已经坐满了乘客。根据“the train station”可知，此处指到达火车站，reach符合语境；时态为一般过去时，动词要用过去式。故填reached。
39．句意：然后，Adam看到一个人在卖玩具。根据下文“Adam bought a rubber snake and threw it into the carriage.”可知，Adam看到一个人在买玩具；toy符合语境，此处应用复数toys。故填toys。
40．句意：当他们看到那条“蛇”时，所有的乘客都很害怕。根据“when they saw the ‘snake’ ”可知，车厢里的人看到“蛇”时，都很恐惧；scare符合语境，此处要用形容词scared“恐惧的”作表语。故填scared。
41．句意：人们尽可能快地从车厢里跑出来。根据“People ran out of the carriage as quickly as...”可知，as...as possible“尽可能……”，固定表达。故填possible。
42．句意：Adam看到几个空铺位，就在其中一个铺位上躺了下来。根据“lay down on ... of them”可知，Adam在其中一个铺位上躺了下来；one符合语境，one of“……中的一个”。故填one。
43．句意：过了一会儿，Adam醒了。根据上文“He soon fell asleep.”可知，他睡着了，所以此处指他醒来了；wake符合语境，wake up“醒来”；时态为一般过去时，故此处要用wake的过去式woke。故填woke。
44．句意：他发现火车不动了，以为它停在某个车站了。根据“thought it had stopped at a station”可知，火车没有移动，move符合语境；再根据空前的“was”可知，时态过去进行时，故此处要用move的分词moving。故填moving。
45．句意：事实上，这节车厢有一条蛇。根据下文“So it was separated and left behind here, the other carriages have left for London.”可知，因为车厢里有蛇，所以这节车厢被脱离开来了；actual符合语境，此处要用副词actually“事实上”来说明原因；句首首字母大写，故填Actually。
46．People often park their cars in the yard when they are at home. 47．In the garden behind their house. 48．nothing. 49． it killed her chicken yesterday. 50．embarrassed
【分析】本文是记叙文，作者讲述了和丈夫在花园里种花时，邻居男孩偷偷跑进她家，但他们没有报警；几天后才知道是自家的狗吃了邻居的鸡，男孩母亲想杀死作者家的狗，正是男孩阻止了他的母亲。
46．根据第一段“In American countryside, people often park their cars in the yard when they are at home. So you can easily understand whether people are at home or not”，可知人们在家时经常把车停在院子里，故填People often park their cars in the yard when they are at home。
47．根据第二段“I got up early and went to the garden behind our house with my husband…I heard our lazy dog yipping in our house”，可知作者在他们房子后面的花园里，故填In the garden behind their house。
48．根据第五段丈夫的话“after all, we have nothing lost”，可知没丢东西，故填nothing。
49．根据第六段“I found that it killed my chicken yesterday, and I wanted to kill it”，可知是因为那只狗昨天咬死了她的鸡，故填 it killed her chicken yesterday。
50．根据最后一段“When I was shaking hands with the boy to thank him”，可知作者误会了男孩应该是感到尴尬，需作肯定回答，故填embarrassed。
【答案】例文
I Have Changed a Lot!
Time goes by quickly. My life has changed a lot in the past few years. Let me show you my changes.
I used to be really short and thin. Because I used to be shy and quiet, I was always silent in class. But now I have changed a lot. The most important change in my life is that I become more outgoing. What made me change a lot I remember when I was in Grade Eight, there was an English speech contest in our school. I wanted to take part in it, but I was afraid of it. Our English teacher, Mr. Wang encouraged me to take part in it. He guided me a lot, and I practiced a lot every day. Finally, I won the first prize in the speech contest. I felt very proud and happy. Since then, I have become more outgoing.
I hope my life will become better and better.
3.2 函数的基本性质--函数的单调性和最大（小）值 常见题型总结练 2025-2026学年数学高一年级人教A版（2019）必修第一册
一：图象法求单调区间
1.如图是函数的图象，则函数的单调递减区间为（ ）
A． B． C． D．
2.函数的单调递增区间是（ ）
A． B． C． D．
3.已知函数的图象如图所示，则该函数的减区间为（ ）

A． B．
C． D．
4.定义在上的函数的单调递减区间是 .
二：函数单调性的判断
1．已知四个函数的图象如图所示，其中在定义域内具有单调性的函数是（ ）
A． B．
C． D．
2.（多选题）在区间上为减函数的是（ ）
A． B． C． D．
3.(多选题)下列函数中，在R上是增函数的是（ ）
A．y=|x| B．y=x
C．y=x2 D．y=
4.下列函数中，在上单调递增的是（ ）
A． B． C． D．
三：证明或判断函数的单调性
1.下列函数中，满足“对任意，，当时，都有”的是（ ）
A． B． C． D．
2.函数在上的最小值为（ ）
A．1 B． C． D．
3.下列函数中，在区间上为增函数的是（ ）
A． B． C． D．
4.已知函数的定义域为，则下列说法中正确的是（ ）
A．若满足，则在区间内单调递增
B．若满足，则在区间内单调递减
C．若在区间内单调递增，在区间内单调递增，则在区间内单调递增
D．若在区间内单调递增，在区间内单调递增，则在区间内单调递增
四：求函数的单调区间
1.函数的单调增区间为（ ）
A． B． C．和 D．
2.函数的单调递增区间是（ ）
A．（，1] B．[1，） C．[1，4] D．[2，1]
3.已知，则函数的单调增区间是 .
4.（24-25高一上·全国·课堂例题）已知函数，，根据图象写出它的单调区间．．
五：函数单调性的应用
1.已知函数在区间上是减函数，则整数a的取值可以为（ ）
A． B． C．0 D．1
2.若函数在区间上单调递减，则实数的取值范围是（ ）
A． B． C． D．
3.若函数（为实数）是R上的减函数，则（ ）
A． B． C． D．
4.若在上为减函数，则实数的取值范围为（ ）
A． B． C． D．
六：利用单调性比较大小或解不等式
1.若函数在上单调递增，且，则实数的取值范围是（ ）
A． B． C． D．
2.已知函数f（x）的定义域为R，且对任意的x1，x2且x1≠x2都有[f（x1）﹣f（x2）]（x1﹣x2）＞0成立，若f（x2+1）＞f（m2﹣m﹣1）对x∈R恒成立，则实数m的取值范围是（　　）
A．（﹣1，2） B．[﹣1，2]
C．（﹣∞，﹣1）∪（2，+∞） D．（﹣∞，﹣1]∪[2，+∞）
3.设函数在区间上有意义，任意两个不相等的实数，下列各式中，能够确定函数在区间上单调递增的是（ ）
A． B．
C． D．
4.(多选题)设函数在上为减函数，则（ ）
A．
B．
C．
D．
E．
函数的最大（小）值
一：利用图象求函数最值
1.定义在R上的偶函数在[0,7]上是增函数，在[7，＋∞)上是减函数，又f(7)＝6，则f(x)(　　)
A．在[－7,0]上是增函数，且最大值是6
B．在[－7,0]上是减函数，且最大值是6
C．在[－7,0]上是增函数，且最小值是6
D．在[－7,0]上是减函数，且最小值是6
2.函数y＝f（x）在[－2，2]上的图象如图所示，则此函数的最小值、最大值分别是(　　)．
A．f（－2），0 B．0，2 C．f（－2），2 D．f（2），2
3.若函数，它的最大值为，则实数的取值范围是（ ）
A． B． C． D．
4.函数在区间上的值域为
二：利用单调性求函数最值
1.函数y＝在[2，3]上的最小值为（ ）
A．2 B．
C． D．－
2.已知函数在区间上的最大值为A，最小值为B，则A-B等于（ ）
A． B． C．1 D．-1
3.函数在区间上的最小值为（ ）
A． B．1 C． D．2
4.若函数y＝在区间[2，4]上的最小值为5，则k的值为(　　)
A．5 B．8
C．20 D．无法确定
三：求二次函数的最值
1.已知函数在区间上有最大值5，最小值1，则的值等于（ ）
A． B．1 C．2 D．3
2.定义域为R的函数满足，且当时，，则当时，的最小值为(　　)
A． B． C． D．
3.（多选题）关于函数（）在上最小值的说法不正确的是（ ）
A．4 B．
C．与的取值有关 D．不存在
4.（多选题）已知在区间上的最小值为，则可能的取值为（ ）
A． B．3 C． D．1
四：判断二次函数的单调性和求解单调区间
1.函数在区间上递增，则实数的取值范围是(　　)
A． B． C． D．
2.若函数在上是减函数，则实数m的取值范围是（ ）
A． B． C． D．
3.若函数在上是减函数，则实数m的取值范围是（ ）
A． B． C． D．
4.（多选题）已知函数的定义域为，值域为，则的可能的取值是（ ）
A．1 B．2 C．3 D．4
五：函数最值的实际应用
1.如图所示是函数的图象，图中曲线与直线无限接近但是永不相交，则以下描述正确的是（ ）
A．函数的定义域为
B．函数的值域为
C．此函数在定义域中不单调
D．对于任意的，都有唯一的自变量x与之对应
2.若是偶函数，且对任意∈且，都有，则下列关系式中成立的是（ ）
A． B．
C． D．
3.向一个圆台形的容器(如图所示)中倒水,且任意相等的时间间隔内所倒的水体积相等,记容器内水面的高度y随时间t变化的函数为,则以下函数图象中,可能是的图象的是(　　).
A． B．
C． D．
4.（23-24高一上·全国·课后作业）一水池有2个进水口，1个出水口，进出水速度如图甲、乙所示．某天0点到6点，该水池的蓄水量如图丙所示（至少打开一个水口）.

给出以下4个论断，其中正确的是（　　）
A．0点到3点只进水不出水
B．3点到4点不进水只出水
C．3点到4点只有一个进水口进水
D．4点到6点不进水也不出水
答案
一：图象法求单调区间
根据题意，结合函数图象可得函数的单调递减区间为：.
故选：.
函数的定义域需要满足，解得定义域为，
因为在上单调递增，所以在上单调递增，
故选：D.
函数的图象在区间和是下降的，在区间和是上升的，
故该函数的减区间为．
故选：C.
，取
如图所示：
单调递减区间是
故答案为
二：函数单调性的判断
对于A，函数分别在及上单调递增，
但存在，使，故A不符合题意；
对于C，函数分别在及上单调递增，
但存在，使，故C不符合题意；
对于D，函数分别在及上单调递减，
但存在，，使，故D不符合题意；
只有B完全符合增函数的定义，具有单调性.
故选:B.
解：函数是上的减函数，
函数在区间上单调递减，
函数在区间单调递减.
函数在区间单调递增，
所以A，B，C符合要求；D项不符合要求.
故选：ABC.
解：选项A，，当x<0时单调递减，不符合题意；
选项B，显然在R上是增函数，符合题意；
选项C，y=x2，当x<0时单调递减，不符合题意；
选项D，作出草图如下，实线部分，观察图象可得函数在R上为增函数，符合题意.

故选：BD
对于A中，函数在上单调递减，所以A不符合题意；
对于B中，函数在上单调递减，单调递增，所以B符合题意；
对于C中，函数在上单调递减，所以C不符合题意；
对于D中，时函数在上单调递减，所以D符合题意.
故选：D.
三：证明或判断函数的单调性
因为对任意，，当时，都有，所以在上为增函数，
A选项，在上为增函数，不符合题意.
B选项，在上为减函数，不符合题意.
C选项，在上为增函数，符合题意.
D选项，在上为增函数，不符合题意.
故选：C.
因为在上单调递增，且恒成立，
可知函数在上单调递减，
当时，，所以函数在上的最小值为.
故选：B.
选项A：，开口向下，对称轴为，所以函数在区间上为减函数，故选项A错误；
选项B：，所以函数在区间上为增函数，故选项B正确；
选项C：可以看作由函数向左平移一个单位得到，所以函数在区间上为减函数，故选项C错误；
选项D：，开口向下，对称轴为，所以函数在区间上为减函数，故选项D错误.
故选：B.
对于AB：函数满足，或，特值并不具有任意性，
所以区间端点值的大小关系并不能确定函数在区间上的单调性，故A，B错误；
对于C：区间和有交集，故函数在区间内单调递增，故C正确，
对于D：区间和没有交集，故不能确定函数在区间内的单调性.
例如在和上递增，但，故D错误．
故选：C.
四：求函数的单调区间
由可得且，
因为开口向下，其对称轴为，
所以的减区间为和
所以的单调增区间为和
故选：C
由，得，解得，
令，则，
因为在上递增，在上递减，而在上递增，
所以在上递增，在上递减，
所以的单调递增区间是，
故选：D
解：因为，对称轴为 ，又开口向下，
又，∴函数的单调递增区间为．
故答案为：
，
函数图象如图所示．
由图象可知，函数的单调递增区间为，单调递减区间为．
五：函数单调性的应用
解：由题意可得，解得，
∴整数a的取值可以为.
故选：A
函数的对称轴为，
由题意可知，解得，
所以实数的取值范围是.
故选：B.
由题意知，解得
故选：D
为上的减函数， 时， 递减，即，①， 时， 递减，即，②且 ，③ 联立①②③解得， .
故选：C.
六：利用单调性比较大小或解不等式
在上单调递增，，，解得：，
实数的取值范围为.
故选：C.
解：由题意，可知：
∵对任意的x1，x2且x1≠x2都有[f（x1）﹣f（x2）]（x1﹣x2）＞0成立，
∴函数f（x）在定义域R上为增函数．
又∵f（x2+1）＞f（m2﹣m﹣1）对x∈R恒成立，
∴x2+1＞m2﹣m﹣1，
∴m2﹣m﹣1＜1，
即：m2﹣m﹣2＜0．
解得﹣1＜m＜2．
故选：A．
解：函数在区间上单调递增，则任意两个不相等的实数，与应该同号，所以，
故选：C.
由题意，函数在上为减函数.
当时，，，，
则，，，故ACD错误；
对于B，因为，所以，
所以，故B正确；
对于E，因为，所以，故E正确.
故选：BE.
函数的最大（小）值
一：利用图象求函数最值
∵函数是偶函数，而且在[0，7]上为增函数，
∴函数在[-7，0]上是减函数.
又∵函数在x=7和x=-7的左边是增函数，右边是减函数，且f(7)=f(-7)，
∴最大值为f(7)=f(-7)=6.
故选B.
试题分析：由图观察可知函数在和上单调递增，在上单调递减．
所以函数在处取的最大值为．
又由图观察可知，所以函数的最小值为．故C正确．
由题意，函数表示开口向上，且对称轴为的抛物线，
要使得当，函数的最大值为，则满足且，
解得，所以实数的取值范围是.
故选D.
由题：，函数在单调递减，在单调递减，
可以看成函数向右平移1个单位，再向上平移1个单位，作出图象：
所以函数在递减，在递减，，，
所以函数的值域为.
故答案为：
二：利用单调性求函数最值
y＝在[2，3]上单调递减，所以x=3时取最小值为，
故选：B.
函数在区间是减函数，
所以时有最大值为1，即A=1，
时有最小值，即B=，
则,
故选：A.
由知，在上是增函数，所以在上递增，所以.
故选：C
∴或∴k＝20.选C.
三：求二次函数的最值
由题意，函数，
可得函数在区间上单调递增，在区间上单调递减，
当时，则函数在区间上单调递增，其最小值为，
显然不合题意；
当时，则函数在区间上单调递增，在区间上单调递减，
故函数的最大值为，
因为，令，即，即，
解得或，
又因为，所以.
故选： D.
设，则，则，又，∴，∴当时，取到最小值为.
由题意得：二次函数（）的对称轴为，且函数图象开口向上，
则该函数在上单调递减，
所以，
故选：BCD.
解：因为函数，函数的对称轴为，开口向上，
又在区间上的最小值为，
所以当时，，解得（舍去）或；
当，即时，，解得（舍去）或；
当，即时，．
综上，的取值集合为．
故选：BC．
四：判断二次函数的单调性和求解单调区间
函数,二次函数图像开口向上，
若在区间上递增，
则对称轴x=-a,
即a
故选D.
函数的对称轴为，
由于在上是减函数，所以.
故选：B
函数的对称轴为，
由于在上是减函数，所以.
故选：B
因为函数在区间上单调递减，在上单调递增，
所以在R上的最小值为，且，
（1）当时，由的值域为，可知必有
所以且，解得，此时
（2）当时，由的值域为，可知必有
所以且，解得，此时
综上可知，
所以的可能的取值为
故选：BCD
五：函数最值的实际应用
1 由图知：的定义域为，值域为，A、B错；
显然在分别递增，但在定义域上不单调，C对；
显然，对应自变量x不唯一，D错.
故选：C
∵对任意的x1，x2∈（0，+∞），都有，
∴函数f（x）在（0，+∞）上单调递减，
又∵，
∴，
又∵f（x）是偶函数，∴f（﹣）＝f（）.
∴.
故选：A.
由容器的形状可知，在相同的变化时间内，高度的增加量越来越小，
故函数的图象越来越平缓，
故选：D.
由甲，乙图得进水速度为1，出水速度为2，
对A，由题意可知在0点到3点这段时间，每小时进水量为2，即2个进水口同时进水且不出水，所以A正确；
对BC，从丙图可知3点到4点水量减少了1，所以应该是有一个进水口进水，同时出水口也出水，故B错误C正确；
对D，当两个进水口同时进水，出水口也同时出水时，水量保持不变；也可由题干中的“至少打开一个水口”知D错，故D错误．
故选：AC
21世纪教育网 www.21cnjy.com 精品试卷·第 2 页 （共 2 页）
21世纪教育网(www.21cnjy.com)