Unit 4 I used to be afraid of the dark 单元检测试题 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 单元检测试题
2025-2026学年上学期初中英语人教版九年级全册
一、完形填空
Everyone changes in his or her life. Mostly these changes take place because of an experience. For me, high school was such an experience. High school has taught me about myself, and that is the most 1 lesson I have ever learned.
I used to be quiet and 2 , not wanting to show my inner self (内在自我). I would 3 talk about what was in my mind. I was afraid that someone would criticize (批评) me or tell me I was 4 . I cared too much about what others thought of me.
Now I am no longer afraid to tell others my 5 and let them know how I feel. I have changed a lot with the 6 of my teachers and friends. They teach me that it is not a big deal to 7 in something as long as I have learned from my mistakes. By finding the courage (勇气) to believe in, I have become much 8 in mind. The thought of a challenge used to make me feel afraid, 9 now I want to work even harder to 10 the difficulties that stand in my way. I have realized that the ideas I had in the past can now contribute (贡献) to the world.
1．A．important B．interesting C．difficult D．useless
2．A．shy B．happy C．clever D．sad
3．A．never B．even C．always D．usually
4．A．right B．free C．wrong D．sick
5．A．business B．worries C．address D．scores
6．A．exercise B．work C．help D．secret
7．A．fail B．waste C．succeed D．believe
8．A．quicker B．stronger C．richer D．bigger
9．A．and B．but C．so D．because
10．A．look up B．give up C．deal with D．work on
二、阅读理解
I am a middle school student. My name is Wang Jing. My grandfather is 70 years old. He often says life has changed a lot. It becomes better and better. I ask him what life was like when he was a child. The following is what he says.
When he was a child, he used to feel hungry. There didn’t use to be enough food for him to eat. He has two brothers and two sisters. His parents were both farmers. They were very poor and couldn’t let their children eat as much as possible. As for clothes, they didn’t use to have enough clothes. They didn’t use to buy new clothes. The younger brothers and sisters often wore their elder brothers’ and sisters’ clothes. My grandfather is the youngest. Only he went to school and had a job in the city. His brothers and sisters didn’t get an education (教育) and live in the countryside now. Now my grandfather has retired and lives a happy life. He can eat any food that he wants. He can buy clothes that he wants to buy. He says he is much happier than before. He often asks me to study hard. He says if I work hard, I can have a good future.
根据材料内容选择最佳答案。
11．When did Wang Jing’s grandfather not have enough food
A．When he was young. B．When he was old.
C．When he has children. D．When he was a child.
12．How many children do Wang Jing’s grandfather’s parents have
A．Three. B．Four. C．Five. D．Six.
13．Whose clothes did her grandfather use to wear
A．His brothers’. B．His mother’s.
C．His own. D．His father’s.
14．Why couldn’t her grandfather’s brothers or sisters go to school
A．Because they didn’t want to go to school.
B．Because their parents didn’t want them to go to school.
C．Because they were poor.
D．Because they were rich.
15．How is her grandfather’s life now
A．He doesn’t feel happy.
B．Now her grandfather has retired and lives a happy life.
C．We don’t know.
D．He still can’t buy clothes that he wants to buy.
Everyone knows that China is changing and developing very quickly at the moment. Many young people from home and abroad thought about the changes. The following are some comments (评论) which young people made on a website message board.
I’m a Chinese student. I’m very proud of China and I’d love to make a real contribution to the development of my country. When I finish my training in Canada, I will go back to China and start a business, so I can give something back to the country. —Carmon, Toronto
I’m a Chinese student. My hometown used to be very poor. But it has changed now. Most people in my hometown have a better life and some can now afford (买得起) cars. I’m very happy with these changes and very proud of them. —Zhou Li, Guangxi
I spent two years in Beijing as a student in the late 1990s and I recently went back there on holiday. I couldn’t believe the changes which had taken place in such a short time. And I admire Chinese people for their wish to succeed, and their family values. I think these qualities will be very important if China is to continue developing. —Jackson, Oxford
I hope that China will become a successful and prosperous (繁荣的) country. There is still a long way to go. There are many challenges and difficulties ahead, but I am sure we can get them over if we work together. —Susan, Hong Kong
16．Who is not Chinese
A．Jackson. B．Susan. C．Zhou Li. D．Carmon.
17．Where is Carmon now
A．In Guangxi. B．In Oxford. C．In Toronto. D．In Hong Kong.
18．When did Jackson study in Beijing
A．In 1990. B．In the early 1990s.
C．Less than 10 years ago. D．More than 20 years ago.
19．What is Zhou Li’s hometown like now
A．It’s still very poor. B．Some people have enough money to buy cars.
C．There are green trees everywhere. D．There are many tall buildings.
20．What can we learn from the text
A．Carmon doesn’t want to start a business in China.
B．China is changing and developing very fast now.
C．Jackson dislikes Chinese family values.
D．Susan studied in Beijing for two years.
Fred was a poor man who lived alone in a small village. He was lazy so he didn’t want to find a job. He had no friends or relatives. He used to beg for food for his living.
One day, a kind man gave Fred a large bowl of rice. Fred didn’t eat up the rice in one go. He put the remaining（剩余的）rice on the table. He lay on his bed and kept an eye on it. After a while, Fred fell asleep and had a dream. He dreamed that there was a famine（饥荒）in his village. He sold his remaining rice and got some money. He used the money to buy a pair of goats（山羊）. His goats had kids in months, so he got more goats. He sold some goats and became rich. He bought a large house. He fell in love with a beautiful lady and they got married.
Fred dreamed that he was dancing with his wife. He felt so excited that he kicked in air and his leg hit the bowl on the table. The bowl with rice dropped and broke into pieces. The noise woke him up. At once, Fred realized that he had been dreaming. He also realized that he could get nothing if he didn’t make a change. Then he decided to get rid of his laziness. Soon he found a job and worked hard.
21．How did Fred get some money in his dream
A．By selling his goats. B．By selling the remaining rice.
C．By selling his bowl. D．By selling his house.
22．Fred kicked in air when he dreamed that ________.
A．he became a rich man B．he had more goats
C．he was dancing with his wife D．he had a large house
23．The underlined phrase “get rid of” is similar to ________.
A．get out of B．leave out C．get into D．cut off
24．Which of the following is TRUE according to the passage
A．Fred was a rich man before he had a dream.
B．Fred got a large bowl of rice from a lady.
C．In Fred’s dream, he bought a pair of horses.
D．The bowl dropped and the noise woke Fred up.
25．We can learn from the story that ________.
A．begging can help us become rich
B．the remaining rice can take you into good dreams
C．it’s impossible to gain without hard work
D．a beggar can also make his dream come true
三、任务型阅读
阅读短文，回答问题。
I live in a large neighborhood. I have lived here since I was born. I have a lot of friends here. Mr. Wang is one of them. He is 85 years old. I enjoy visiting Mr. Wang because he tells me exciting stories about Hong Kong in the past. He also shows me old photos. Yesterday, I visited Mr. Wang after school. I asked him how long he had lived here. This is what he told me:
“I have lived in the neighborhood since 1993.Before I moved here, I lived in a small village called Pak Mong on Lantau Island. There were many people living in the village when I was young. These years, there are only a few families left. Most families moved to the city for work. I left the village in 1993, when my son moved to the city.
Pak Mong is an old village. There are watchtowers (瞭望塔) around the village. In the old days, soldiers used to stand in the watchtowers and keep guard (站岗). Here is a photo of my school. I went to that school a very long time ago. The school has been closed since 1985.
I enjoy going to the Kowloon Walled City Park, because it makes me think of my old village. I have visited the park three times since 2004.Would you and your family members like to go to the park with me next weekend ”
26．How old is Mr. Wang
27．Were there more people in the village in 1993 than these years
28．When did Mr. Wang leave the village
29．How many times has Mr. Wang been to the Kowloon Walled City Park
30．What does Mr. Wang want to do next weekend
四、短文填空
A Better Town for Teenagers
I believe there are many things that we can do to make life in our town a lot better for teenagers.
First of all, I think more bike lanes（车道）should be built. A lot of teenagers in my town bike everywhere, but it’s very dangerous 31 there is a lot of traffic. If there are more bike lanes in 32 future, it will be much safer for us.
33 (two), I believe that we need more places. 34 my opinion, teenagers won’t cause problems in the street if there are more places for us 35 (go) to. So we need more 36 (club) and other places where we can meet.
Thirdly, teenagers here need more sports facilities（设施）. There 37 (be) places to play ball games so far like tennis and basketball, but what about other sports, like 38 (skate) and rollerblading
Finally, I’m sure we 39 (make) the town better if we don’t drop litter everywhere. If we all do 40 (anything) helpful now, our town will be much better in the future.
五、完成句子
41．你过去很矮，不是吗
You short, you
42．自从我们上次见到我们的小学同学已经有三年了。
three years we last saw our primary school classmates.
43．我过去常常看到他每天在图书馆里读书。
I see him in the library every day.
44．但是看看他现在是多么高大、强壮!
But look now!
45．我过去在学校里不受欢迎。
I in school.
六、书面表达
46．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!
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参考答案
题号 1 2 3 4 5 6 7 8 9 10
答案 A A A C B C A B B C
题号 11 12 13 14 15 16 17 18 19 20
答案 D C A C B A C D B B
题号 21 22 23 24 25
答案 B C A D C
1．A 2．A 3．A 4．C 5．B 6．C 7．A 8．B 9．B 10．C
【导语】本文主要讲述了作者在高中阶段，从安静害羞变得自信勇敢的个人经历。
1．句意：高中教会我认识了自己，这是我学到的最重要的一课。
important重要的；interesting有趣的；difficult困难的；useless无用的。根据“that is the most ... lesson I have ever learned.”可知，高中这段经历让我学到了最重要的一课，important符合语境。故选A。
2．句意：曾经的我是安静害羞的，不想展现内心的自我。
shy害羞的；happy开心的；clever聪明的；sad悲伤的。根据“not wanting to show my inner self”可知，作者性格是害羞的。故选A。
3．句意：我永远不会谈论我的想法。
never从不；even甚至；always总是；usually通常。根据“not wanting to show my inner self ”可知，作者不想展示自己的内心，所以“从不”谈论自己想法。故选A。
4．句意：我担心有人会批评我或者告诉我我错了。
right正确的；free空闲的；wrong错误的；sick生病的。根据“I was afraid that someone would criticize me”并结合常识可知，不表达自己的内心是害怕别人说自己是“错误的”。故选C。
5．句意：现在我不再害怕告诉别人我的烦恼，让他们知道我的感受。
business商业；worries担忧；address地址；scores分数。根据“let them know how I feel”可知，此处指告诉他人我的忧虑。故选B。
6．句意：在老师和同学的帮助下，我已经改变了很多。
exercise练习；work工作；help帮助；secret秘密。本句讲述作者的改变得益于别人的帮助，with the help of...“在……的帮助下”。故选C。
7．句意：他们教会我，只要我从错误中吸取教训，在某件事上失败没什么大不了的。
fail失败；waste浪费；succeed成功；believe相信。根据“it is not a big deal to...in something as long as I have learned from my mistakes”可知，在错误中吸取教训，说明某件事情“失败”了。故选A。
8．句意：通过找到相信的勇气，我的内心变得越来越坚强。
quicker更快的；stronger更坚强的；richer更富有；bigger更大。根据“By finding the courage to believe in”可知，有了信任的勇气，作者内心变得更坚强。故选B。
9．句意：挑战的想法曾经让我感到害怕，但现在我想更加努力地工作，以应对阻碍我前进的困难。
and和；but但是；so所以；because因为。根据“The thought of a challenge used to make me feel afraid,...now I want to...”可知，本句讲述作者之前和现在想法的改变，内容构成转折关系。故选B。
10．句意：挑战的想法曾经让我感到害怕，但现在我想更加努力地工作，以应对阻碍我前进的困难。
look up查找；give up放弃；deal with应对、处理；work on从事于……。根据“...the difficulties that stand in my way”可知，对于困难需要“处理”。故选C。
11．D 12．C 13．A 14．C 15．B
【导语】本文是一篇记叙文，讲述了作者爷爷小时候的贫穷生活，并和今天的幸福生活进行对比，说明生活正在变得越来越好。
11．细节理解题。根据“When he was a child, he used to feel hungry.”可知，当他是小孩的时候，他经常吃不饱。故选D。
12．细节理解题。根据“He has two brothers and two sisters.”可知，爷爷的父母总共有5个孩子。故选C。
13．细节理解题。根据“The younger brothers and sisters often wore their elder brothers’ and sisters’ clothes. My grandfather is the youngest.”可知，爷爷小的时候穿的是他哥哥们的衣服。故选A。
14．推理判断题。根据“They were very poor and couldn’t let their children eat as much as possible.”可推知，爷爷的哥哥姐姐没有上学是因为贫穷。故选C。
15．细节理解题。根据“Now my grandfather has retired and lives a happy life.”可知，现在她的爷爷退休了，过着幸福的生活。故选B。
16．A 17．C 18．D 19．B 20．B
【导语】本文是一些年轻人谈论中国的变化与发展。
16．细节理解题。根据“I spent two years in Beijing as a student in the late 1990s and I recently went back there on holiday... I admire Chinese people for their wish to succeed, and their family values.”和“Jackson, Oxford”可知，Jackson不是中国人。故选A。
17．推理判断题。根据“When I finish my training in Canada, I will go back to China and start a business, so I can give something back to the country.”可知，Carmon现在在加拿大；再根据“Carmon, Toronto”推知，Carmon在加拿大的多伦多。故选C。
18．推理判断题。根据“I spent two years in Beijing as a student in the late 1990s”可知，Jackson上个世纪末在北京学习，现在是2023年，由此推知他是20多年前在北京学习。故选D。
19．细节理解题。根据“Most people in my hometown have a better life and some can now afford (买得起) cars.”可知，大多数人都过上了更好的生活，有些人现在买得起汽车了。故选B。
20．细节理解题。根据“Everyone knows that China is changing and developing very quickly at the moment.”可知，中国现在变化和发展非常快。故选B。
21．B 22．C 23．A 24．D 25．C
【导语】本文是一篇记叙文，文章主要讲述了弗雷德因为懒惰，生活过得十分贫困潦倒，靠乞讨为生，一天，弗雷德梦到自己勤劳致富了，靠自己的努力过上了幸福的生活，也因为这个梦，弗雷德打算改变自己懒惰的习性，认真工作。
21．细节理解题。根据“He sold his remaining rice and got some money.”可知弗雷德靠卖剩余的粮食获得了一些钱。故选B。
22．细节理解题。根据“Fred dreamed that he was dancing with his wife. He felt so excited that he kicked in air and his leg hit the bowl on the table.”可知弗雷德梦见他在和妻子跳舞。他感到非常兴奋，一脚踢向了空中。故选C。
23．词句猜测题。根据“He also realized that he could get nothing if he didn’t make a change. Then he decided to get rid of his laziness. Soon he found a job and worked hard.”可知弗雷德意识到了他需要做出改变，猜测此处的get rid of...意为“摆脱”。故选A。
24．细节理解题。根据“The bowl with rice dropped and broke into pieces. The noise woke him up.”可知碗碎了，弗雷德惊醒了。故选D。
25．推理判断题。通读全文，可知文章主要讲述了一个懒惰的乞丐因为一场梦，意识到自己需要做出改变，通过努力，摆脱懒惰，才能过上幸福的生活。选项C“不努力是不可能获得的。”符合文章的核心思想。故选C。
26．He is 85 years old. 27．Yes, there were. 28．In 1993. 29．Three times. 30．He wants to go to the park next weekend.
【导语】本文是一篇记叙文，介绍我与一位八十五岁的邻居的友好相处以及老人在小村庄生活的经历和感受。
26．根据文中“Mr. Wang is one of them. He is 85 years old.”可知，王先生85岁，故填He is 85 years old.
27．根据文中“There were many people living in the village when I was young. These years, there are only a few families left. Most families moved to the city for work. ”可知，当我小的时候，这个村住着很多人，但是这些年很多家庭搬去城里工作了，所以在1993年，村里的人比这些年要少，故填Yes, there were.
28．根据第二段“ I left the village in 1993, when my son moved to the city.”可知，王先生是1993年离开这个村的，故填In 1993.
29．根据文中“I enjoy going to the Kowloon Walled City Park, because it makes me think of my old village. I have visited the park three times since 2004.”可知，王先生曾经去过九龙寨城公园3次了，故填Three times。
30．根据文中“Would you and your family members like to go to the park with me next weekend ”可知，王先生下周末打算去这个公园，故填He wants to go to the park next weekend.
31．because 32．the 33．Secondly 34．In 35．to go 36．clubs 37．have been 38．skating 39．will make 40．something
【导语】本文主要介绍了如何建立一个为青少年服务的更好的城镇。
31．句意：我镇上到处都是骑自行车的青少年，但这很危险，因为车流量很大。根据“...it’s very dangerous ...there is a lot of traffic.”可知此处前后句是因果关系，需填连词because“因为”。故填because。
32．句意：如果将来有更多的自行车道，对我们来说会更安全。根据“If there are more bike lanes in...future...”可知此处是固定短语in the future“在未来”。故填the。
33．句意：第二，我认为我们需要更多的场地。根据“First of all”可知此处表达“第二”需使用序数词的副词形式secondly，位于句首，首字母需大写。故填Secondly。
34．句意：在我看来，如果有更多的地方可供我们去，青少年就不会在街上惹麻烦。此处为固定短语in one’s opinion“在某人看来”，位于句首，首字母需大写。故填In。
35．句意：在我看来，如果有更多的地方可供我们去，青少年就不会在街上惹麻烦。根据“...if there are more places for us...to.”可知此处需使用动词不定式作定语来修饰places。故填to go。
36．句意：所以我们需要更多的俱乐部和其他可以见面的地方。根据“more”可知此处需填名词club“俱乐部”的复数形式。故填clubs。
37．句意：到目前为止，已经有网球和篮球等打球的地方了，但其他运动呢，比如滑冰和滑旱冰？根据“so far”可知此处谓语需使用现在完成时，其结构为have/has done，句子主语为名词复数places，选用助动词have。故填have been。
38．句意：到目前为止，已经有网球和篮球等打球的地方了，但其他运动呢，比如滑冰和滑旱冰？根据“like...and rollerblading ”可知此处需填动名词作宾语。故填skating。
39．句意：最后，如果我们不到处乱扔垃圾，我相信我们会让这个城市变得更好。根据“I’m sure we...the town better if we don’t drop litter everywhere.”可知此处是if引导的条件状语从句，遵循主将从现的原则。故填will make。
40．句意：如果我们现在都做一些有益的事情，我们的城市将来会更好。根据“If we all do...helpful now, our town will be much better in the future.”可知此处是陈述句，表达“一些有益的事情”，需使用不定代词something。故填something。
41． used to be didn’t
【详解】“过去常常做某事”used to do sth；“short”是形容词，所以这里是用used to be表示“过去是”；根据反意疑问句“前肯后否”原则可知，疑问部分用否定句，前半部分的陈述句是一般过去时，所以疑问部分的助动词用didn’t来反问。故填used to be；didn’t。
42． It’s been since
【详解】根据语境可知，这件事已经发生，时态为现在完成时，由since“自从”引导的时间状语从句；主句是“It’s been three years”；从句是“we last saw our primary school classmates.”。因此主句和从句用连词since连接；第一个空后been可知是现在完成时，因为是时间，因此主语是it，谓语动词应用助动词has，因为一个空，it has要使用它的缩写形式It’s，第二个空填been；第三个空是连词“自从”since。故填It’s；been；since。
43． used to reading
【详解】“过去常常做某事”used to do sth；see sb doing sth“看见某人在做某事”，固定短语；“读”read。故填used to；reading。
44．how big and strong he is
【详解】空处缺少“他是多么高大、强壮”的英文表达，是一个感叹句，“高大”big ，“强壮”strong，两者之间用and连接，感叹句的中心词是形容词，所以引导词用how；“他”he；“是”is，结合感叹句结构“How+形容词+主谓！”，故填how big and strong he is。
45．didn’t use to be popular
【详解】“过去常常做某事”used to do sth；根据汉语可知，这里是否定句，要借助助动词didn’t完成，其后动词变回原形；“受欢迎的”popular。故填didn’t use to be popular。
46．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.
【详解】[总体分析]
① 题材：本文是一篇材料作文；
② 时态：“一般过去时”为主；
③ 提示：写作要点已给出，考生注意不要遗漏提示中的要点，可适当添加细节，并突出写作要点。
[写作步骤]
第一步，先总述和之前相比，自己改变了很多；
第二步，再描述你之前是什么样子的，例如可以从之前的外貌、性格等方面来描述；接着描述自己发生了哪些变化，其中最重要的变化是什么，这个变化是如何发生的。
第三步，书写结束语，表达自己对未来生活的憧憬。
[亮点词汇]
① used to be 过去是
② take part in 参加
③ be afraid of 害怕
④ encourage sb to do 鼓励某人做某事
[高分句型]
① Because I used to be shy and quiet, I was always silent in class.（because引导的原因状语从句）
② The most important change in my life is that I become more outgoing.（that引导的表语从句）
③ I remember when I was in Grade Eight, there was an English speech contest in our school.（when引导的时间状语从句和there be句型）
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
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