限时训练参考答案.pdf

88
8m
8m
9m 当且仅当

2
，即 m 4 时等号成立.故△ABO与△AFO面积之和的最小值为 3.故选 B.
8m
3
9. 解析
π
tan tan

tan


π
3


1

tan

3 π tan
2
1 2
3 3

2 3 12 3
12 3 1 2 3
6. 解析 解法一（特殊位置法）：由甲、乙二人均不能从事 A 工作，可知 A 工作有 C13 种分 配方法，则剩余的 B ， C ， D 三项工作有 A34 种分配方法.所以由分步乘法计数原理，可得 不同的工作分配方案有 C13 C34 72（种）. 解法二（特殊元素法）：甲参加，乙不参加，有 C13 A33 18（种）分配方案；

a
，由题意得
2

a

0
，解得
1 .故选 A.
1 2a 0
a 2
2. 解析
B
x x 1或x 1
，所以
U
B

x 1 x 1 .把 U B 与集合 A 在数轴表示
出来，如图所示.由图可知， A U B x 0 x 1 .故选 B.
自信是迈向成功的第一步



则 OA m2 , m ，OB n2 , n ，O A O B m 2 n 2 m n 2 ，解得 mn 1（舍）或 mn 2 .
设直线 lAB的方程为 m2 n2 y n m n x n2 ，即 m n y n x n2 ，令

九年级英语限时训练（附参考答案）一．根据句意及首字母和汉语提示完成句子。

1.The official newspaper c_________the news of Tiangong-I,for it took a big step forward into space.2.The idiom(成语）:“Meng zi’s mother makes three moves”tells of a mother who did all she could to provide the best e_________for her child.3.The young lady w _______hair is blond comes from Australia.4.Sometimes, you won’t know the true value of a moment u_______it becomes a memory.5.Good _______(发音）will impress others and make yourself confident.二．完形填空（共10小题；每小题1分，满分10分）There was a garden full of plants. In the corner of the garden, a 6 rose grew. She was the most beautiful flower there. She was as white as snow, 7 the plants around her were shocked at her beauty. But the white rose couldn’t see 8 , so she didn’t know how beautiful she was.Sometimes, she was even a little envious (羡慕的) of the sunflowers around her. She hoped that she could be as 9 as them.One sunny day, a girl went into the 10 . She walked around and was amazed at the beauty of na ture. Suddenly, she saw the white rose. “It hasn’t rained for days,” said the girl. “And the weather report says it will continue to be 11 for a few days. If the rose stays here, it will 12 soon. I’ll take it home and put it in my beautiful vase(花瓶).”The white rose was put in a lovely vase by the window. From the reflection in the window, the white rose saw herself for the 13 time. “Is that me?” she was shocked. “Till now I didn’t 14 how beautiful I looked.”Sometimes, we think other people are very great and 15 know our own advantages. This makes us feel less confident of ourselves. Look into your heart, and you’ll find how great you are.6. A. white B. red C. blue7. A. or B. but C. and8. A. herself B. himself C. yourself9. A. quiet B. lovely C. lonely10. A. park B. corner C. garden11. A. rainy B. cloudy C. sunny12. A. leave B. die C. cancel13. A. first B. second C. third14. A. improve B. realize C. suppose15. A. always B. usually C. never三．综合填空（共10小题；每小题2分，满分20分）根据短文内容，用方框中所给词语的适当形式填空，使文章通顺、完整。

高三数学限时训练（十九）一．填空题（本大题共14小题，每题5分，满分70分）1．已知集合2112{|lg 0},{|222,}x M x x N x x Z -+===<<∈,则M N = ．2．已知等差数列{a n },其中,33,4,31521==+=n a a a a 则n 的值为 _ ．3．已知函数log ()a y xb 的图象如右图所示,则b a = _4．设函数lg |2|,2()1,2x x f x x -≠⎧=⎨=⎩，若关于x 的方程0)()(2=++c x bf x f 恰有5个不同的实数解x 1、x 2、x 3、x 4、x 5则f(x 1＋x 2＋x 3＋x 4＋x 5)＝ ． 5．直线Ax ＋By ＋C ＝0与圆x 2＋y 2＝4相交于两点M 、N ，若满足C 2＝A 2＋B 2，则OM ·ON （O 为坐标原点）＝ _ ．6．设椭圆的两个焦点分别为F 1、、F 2，过F 2作椭圆长轴的垂线交椭圆于点P ，若△F 1PF 2为等腰直角三角形，则椭圆的离心率是 ．7．已知α,β均为锐角,且21sin sin -=-βα,1cos cos 3αβ-=,则cos()αβ-= _ ．8．已知变量x 、y 满足条件6200x y x y x y +≤⎧⎪-≤⎪⎨≥⎪⎪≥⎩，若目标函数z ax y =+ (其中0a >)，仅在(4，2)处取得最大值，则a 的取值范围是 ．9．在△ABC 中,若a ＝7,b ＝8,13cos 14C =,则最大内角的余弦值为 ．10．一个几何体的三视图中，正视图和侧视图都是矩形，俯视图是等腰直角三角形（如图），根据图中标注的长度，可以计算出该几何体的表面积是 ．第10题11．已知双曲线2212y x -=的焦点为F 1、F 2，点M 在双曲线上且120,MF MF ⋅=则点M 到x 轴的距离为 ．12．设()y f x =是定义在R 上的函数，给定下列三个条件：①()y f x =是偶函数；②()y f x =的图象关于直线1x =对称；③2T =为()y f x =的一个周期．如果将上面①、②、③中的任意两个作为条件，余下一个作为结论，那么构成的三个命题中真命题的个数有 个．13．在△ABC 中,1=BC ,2=AB ,1cos 4B =，则sin(2)A B +的值为 ．14．对于函数⎩⎨⎧>≤=.cos sin ,cos ;cos sin ,sin )(x x x x x x x f 给出下列四个命题：①该函数是以π为最小正周期的周期函数；②当且仅当x k ππ=+()k Z ∈时，该函数取得最小值－1； ③该函数的图象关于ππk x 245+=()k Z ∈对称； ④当且仅当πππk x k 222+<<()k Z ∈时，.22)(0≤<x f 其中正确合题的序号是 （请将所有正确命题的序号都．填上）．二．解答题（本大题有2个题，每小题15分，共30分） 15．（本大题满分15分）已知△ABC 的面积S 满足3≤S ≤33且BC AB BC AB 与,6=⋅的夹角为α． （Ⅰ）求α的取值范围；（Ⅱ）求ααααα22cos 3cos sin 2sin )(++=f 的最小值．16．（本大题满分15分）如图，在平面直角坐标系xOy中，平行于x轴且过点A(33，2)的入射光线l1被直线l：y=33x反射．反射光线l2交y轴于B点，圆C过点A且与l1, l2都相切．（1）求l2所在直线的方程和圆C的方程；（2）设P，Q分别是直线l和圆C上的动点，求PB+PQ的最小值及此时点P的坐标．限时训练（十九）答案一．填空题1．{}1- 2．50 3．27 4．3lg2 5．-2 61 7．59728．a>19．71-10．12+42 11 12．3 13．16153 14．③④二．解答题15．解：（Ⅰ）由题意知6cos ||||=⋅=⋅αBC AB BC ABαcos 6||||=⋅BC AB αααααπtan 3sin cos 621sin ||||21)sin(||||21=⨯⨯=⋅=-⋅=BC AB BC AB S 333≤≤S3tan 133tan 33≤≤≤≤∴αα即BC AB 与是α 的夹角 ],0[πα∈∴]3,4[ππα∈∴． （Ⅱ）=++=++=ααααααα222cos 22sin 1cos 2cos sin 2sin )(f)42(222cos 2sin 22πααα++=++]3,4[ππα∈)(3121142απαππαf 时即当当==+∴有最小值为233+． 16．解：（1）直线1l ：y=2，设1l 交l 于点D ，则D （23，2） ∵l 的倾斜角为30° ∴2l 倾斜角为60°∴32=k ∴反射光线2l 所在的直线方程为y —2=)32(3-x 即043=--y x已知圆C 与1l 切于点A ，设C （a ，b ） ∵圆心C 在过点D 且与l 垂直的直线上 ∴83+-=a b ……① 又圆心在过A 且与1l 垂直的直线上 ∴33=a ……② 由①②得 33=a 1-=b 圆C 的半径r=3故所求圆的方程为9)1()33(22=++-y x ． （2）设点B （0，—4）关于l 的对称点B ＇（00,y x ） 则2332400x y ⋅=-，且340-=+x y ∴B ＇（—23，2）固定点Q 可发现，当B ＇、P 、Q 共线时，PB+PQ 最小 故PB+PQ 的最小值为B ＇C —3∴PB+PQ 的最小值B ＇C —3=221—3．。

限时训练4参考答案（2014-12-23）
31.（11分）
答案:(1)高压（1分）低压(1分)
(2)西北(偏北) (1分)②(1分)②地等压线密集,水平气压梯度力较大(2分)
(3)低温晴朗(1分)冷锋过境后,④地受高压脊控制。

(2分)
(4)受冷锋活动影响,将经历一次大风、降雨(雪)、降温等天气。

(2分)
32.（14分）
（1）A（1分）海陆热力性质差异（1分） D （1分）
（2）冬季风（西北风）（1分）亚洲高压（蒙古、西伯利亚高压）（1分）（3）西南季风（1分）东南信风（1分）
夏季由于阳光直射点北移，气压带和风带北移，南半球的东南季风越过赤道，受地转偏向力的影响偏转为西南季风。

（2分）
（4）C（2分）
（5）阿留申低压（1分）中纬西风气流（1分）温和多雨（1分）。

31、只有永远躺在泥坑里的人，才不会再掉进坑里。——黑格尔 32、希望的灯一旦熄灭，生活刹那间变成了 34、形成天才的决定因素应该是勤奋。——郭沫若 35、学到很多东西的诀窍，就是一下子不要学很多。——洛克
限时训练试卷答案讲评
11、获得的成功越大，就越令人高兴 。野心 是使人 勤奋的 原因， 节制使 人枯萎 。 12、不问收获，只问耕耘。如同种树 ，先有 根茎， 再有枝 叶，尔 后花实 ，好好 劳动， 不要想 太多， 那样只 会使人 胆孝懒 惰，因 为不实 践，甚 至不接 触社会 ，难道 你是野 人。(名 言网) 13、不怕，不悔(虽然只有四个字，但 常看常 新。 14、我在心里默默地为每一个人祝福 。我爱 自己， 我用清 洁与节 制来珍 惜我的 身体， 我用智 慧和知 识充实 我的头 脑。 15、这世上的一切都借希望而完成。 农夫不 会播下 一粒玉 米，如 果他不 曾希望 它长成 种籽； 单身汉 不会娶 妻，如 果他不 曾希望 有小孩 ；商人 或手艺 人不会 工作， 如果他 不曾希 望因此 而有收 益。-- 马钉路 德。

2020年广东中考英语阅读理解限时训练（一）AAre you learning English and do you need help with grammar?Do you want to learn new vocabulary?Well,try to get help from the following top five free English learning centers online.Dave's ESL CafeOur center can help you learn and practice English.You can read many stories and do a lot of exercises to test yourself.You can also post questions and answers onto the Learners'Corner.Classroom by Voice of AmericaYou can watch videos and listen to news stories to improve your listening and vocabulary.You can also listen to English words and their meanings.About EnglishYou can take free English courses in our center,and you'll get regular(定期的)e­mails that will help you learn English.Newbury House Dictionary of American English Do you need to find the definition(定义)of a word?Use this online dictionary to find simple and clear definitions,as well as example sentences and idioms(习语)．You can also find different cultural facts.Personal English Portal(门户网站)on YouTube We offer you series(系列)of videos to develop your listening skills.You can also do a search on YouTube to find other videos.This is a good way to practice English and have fun.()1.Linda is interested in Dave's ESL Cafe.What can she do in the center?A．Watch videos.B．Listen to news stories.C．Find the meanings of words.D．Post questions and answers.()2.From Newbury House Dictionary of American English，what can you find?A．Example sentences and idioms.B．English songs.C．English grammar exercises.D．Many videos.()3.About English often sends e­mails to its visitors to help them ________.A．get relaxed B．have funC．become famous D．learn English()4.If you want to develop your listening skills and have fun，you can go to________.A．Newbury House Dictionary of American EnglishB．YouTubeC．Dave's ESL CafeD．the Classroom by V oice of America()5.Where may we read the above information?A.In the science fiction.B．In a newspaper.C.In a story book.D．In a science report.BNo matter who you are and where you live，the most important thing is what kind of person you are.There are many good qualities(品质)that can benefit you a lot in your life.Among them，the following qualities are the most helpful ones.Have a positive attitude(态度).Life is not always a bed of roses. When you face difficulties，don't lose heart.Do you know what can help you overcome difficulties?It's your attitude.Cheer up！Life is like a mirror.When you smile in front of it，it will also smile at you.Keep learning.Maybe you are used to your present life.Every day you have so much work to do that you can't find any time to learn. However，the world around you is changing all the time.Never be satisfied with yourself，or you will fall behind others.Keeping learning can help you get success in the future.Be creative.In the modern world，the students who have creative thinking are needed most.Being creative means coming up with new ideas and having creative imagination.Those who are creative have more choices in their life.Be honest and keep your promise.Honesty is the best policy(原则). Nobody likes a person who tells lies.The one who keeps his words is popular everywhere.As long as you have these qualities mentioned above，you will be excellent and make a difference to the world.Albert Einstein once said，“Try not to become a man of success but rather try to become a man of value.”()6.From the passage，we know that_____can help you overcome difficulties.A.rosesB.attitudeC.mirrorsD.learning ()7.The underlined word“benefit”probably means____in Chinese in this passage.A.影响B.补贴C.有益D.救济()8.In the writer's opinion，there are_____qualities that can benefit you most in your life.A.threeB.fourC.fiveD.six ()9.Which of the following is NOT true according to the passage？A.Since there is too much work to do，you needn't find time tolearn.B.If you think creatively，you will have more chances to choosein your life.C.When you keep your words，you usually promise to do whatyou have said.D.Albert Einstein thought we should become a man of value.()10.Which one might be the best title of this passage？A.Keeping Your PromiseB.Being a Man of SuccessC.Trying to Think CreativelyD.The Most Helpful Qualities of a ManAMany students find it difficult to learn English.Some of them even want to give up.They wonder how they can learn it well.Here are four English classes in Yucai Training Center.Have a look,maybe they can help you to improve it.Class 1:For speaking Time:7：30p ．m.—9：30p ．m.everyTuesday Teacher:John Smith (the USA)Price:￥150for a monthIntroduction:In this class,you will learn how to talk with others in English and how to sing English songs.Class 2:For reading Time:8：00p ．m.—10：00p ．m.on Mondays Teacher:Jeff Green (the UK)Price:￥180for 6weeks Introduction:We'll tell you some useful reading strategies and skills.Some for daily reading and some for exam reading.Class 3:For listening Time:7：00p ．m.—8：30p ．m.onWednesdays Teacher:Lin Tao (CHN)Price:￥100for 3weeksIntroduction:This class will give you some helpful advice to practice listening.Class 4:For writing Time:7：00p ．m.—9：00p ．m.every Thursday Teacher:Rose (Australia)Price:￥120for 4weeks Introduction:Rose is an experienced teacher.She has her special ways for you to improve your writing.She is also here to be your pen pal.For more information,you can read tomorrow's newspaper or contact (联系)Mr.Zheng at 0769­6653221or e­mail him at yucai @ .2020年广东中考英语阅读理解限时训练（二）()1.There is(are)________class(es)for you to improve your English in Yucai Training Center.A．one B．twoC．three D．four()2.If you want to join all the classes in this training center,you should pay________for them.A．￥150B．￥180C．￥220D．￥550()3.________will teach Mr.Chen to improve his speaking.A．John Smith B．Jeff GreenC．Lin Tao D．Rose()4.You can read this advertisement________.A．in a storybook B．in a newspaperC．in a magazine D．on the Internet()5.Which is the correct order for the class in Yucai Training Center according to the time you can join in?①Class1:For speaking②Class2:For reading③Class3:For listening④Class4:For writingA．①②③④B．②①③④C．②①④③D．③④②①BPinyin,a system that uses the Latin letters,tells us how to pronounce Chinese characters.What you learned in your first Chinese class in primary school was probably pinyin.The year2018marks pinyin's sixtieth birthday.In1958,Chinese linguist(语言学家)Zhou Youguang and his team designed pinyin.Before that,Chinese people used many other methods to denote(标注)the pronunciation of Chinese characters.In ancient China, people denoted Chinese characters using other Chinese characters that had the same pronunciation.Some of the symbols are Chinese character strokes(笔画)．For example,a vertical stroke(一竖)pronounced as“i”in pinyin.Some people in Taiwan still use this method.However,these methods are not as simple as pinyin.Because of pinyin,many illiterate(不识字的)people have learned how to read.We use pinyin to type Chinese characters into computers and phones.Pinyin has been useful in other ways,too.It helps to promote the use of Standard Chinese,or Mandarin, so people who speak different dialects(方言)can still understand each other.Pinyin is not only popular in China.Many people around the world start to learn Chinese by learning pinyin.You might say“nihao”instead of “hello”to a foreign friend.The Oxford English Dictionary(《牛津英语词典》)includes more than100Chinese words in pinyin,such as zhongguomeng for“Chinese dream”，and wanggou for“online shopping”．Pinyin is not only a language tool,but also a cultural bridge that connects China to the world,Guangming Daily noted.Pinyin is still young.But it has been and will still be a useful tool in the future.()6.The underlined word“promote”in the second paragraph may mean“________”in the passage.A．解释B．改善C．表达D．介绍()7.Paragraph2mainly tells us about________.A．the history of pinyin B．the designers of pinyinC．the problems of pinyin D．the future of pinyin()8.The writer talks about the Oxford English Dictionary to tell us ________.A．pinyin is popular only in ChinaB．pinyin is popular all over the worldC．pinyin will not be used in the futureD．English will be replaced(代替)by pinyin()9.We can learn from the passage________.A．pinyin has been used since ancient ChinaB．people in Taiwan prefer to use pinyinC．pinyin is useful in many waysD．we will not use pinyin in the future()10.We can infer from the passage that the writer feels________ about the future of pinyin.A．doubtful B．unsureC．hopeful D．sad2020年广东中考英语阅读理解限时训练（三）AHello,lovely boys and girls.I would like to introduce our English language holidays for you.As English is one of the most widely spoken languages in the world，millions of people look forward to studying English abroad(在国外)during holidays.English language holidays are taken in English­speaking countries like England，the USA，Australia and so on.There，you study in a language school with students from many different countries.You live with local(本地的)people，and often stay with a host family.The English language holiday has become a very popular way of learning English because it has many advantages.●Constant Experience(持续的体验)Because you are in an English­speaking country，from the time you wake up and have breakfast with your host family until late evening，you have no opportunity to escape the English language.●Mixed(混合的)ClassesOn a language holiday，students come from all over the world.It is possible that nobody in your class will speak your language，so you will just have to speak English.●Free From PressureOn a language holiday，you may forget the everyday pressure of school.You feel more relaxed and you can learn easily.●Cultural UnderstandingLearning a language is not only about learning words.Different countries have different cultures.People think and behave(表现)differently.By visiting and living in a foreign country，you learn to understand the culture and the people，and so understand the language better.If you want to know more about it,don't forget to attend our introduction meeting on time.It will be held at eight tomorrow morning in our school hall.You won't realize its advantages until you experience it by yourself.()1.The followings are all English­speaking countries EXCEPT ______according to the passage.A.EnglandB.the USAC.RussiaD.Australia()2.While you are having an English language holiday，you cannot ______.A.just do what you likeB.study in a language schoolC.stay with a host familyD.live with local people()3.What does the underlined word“escape”mean in Chinese?A.教育B.逃避C.表达D.进去()4.The number of advantages of English language holidays is ______.A.oneB.twoC.threeD.four()5.What's the best title of this passage?A.English language holidays.B.English language holidays are popular.C.The advantages of English language holidays.D.The disadvantages of English language holidays.BDo you know what smart phones can do for us?We can make phone calls，take photos，call a Didi Taxi，send short messages or e­mails，check e­mails，surf the Internet and watch videos almost anywhere.Especially，smartphone shopping has become more and more popular in our life because people can buy almost everything they need there.You are wondering how to shop on smartphones?Let me show you.If you live in the central part of the city,and you need to buy some fresh grapes from the east of the city,you can use your smartphone.To start with，all you need to do is download a shopping app(应用程序)and find a suitable store you like.Shopping on the smartphone has a lot of advantages，of which the most important is perhaps its convenience.People don't have to waste a lot of energy and time to go from one shop to another to choose things they like.This is especially good for the old，the sick and the busy people who cannot go to the shops by themselves.However，shopping on the smartphone also has its disadvantages. The first disadvantage is that people can't see the goods or try them on by themselves.Sometimes，the real goods may not be the same as what they have seen on the smartphone.The second disadvantage is that some shops on the Internet are not registered(登记的).They will never deliver(递送)anything to you after they get the money from you.Once you are cheated，you will find that you have nowhere to go to complain(投诉).()6.Smartphone shopping has become more and more popular in our life because______.A.we can take photos and send short messagesB.we can buy almost everything we needC.we can check e­mails and surf the InternetD.we can make phone calls and call a Didi Taxi()7.If you want to shop on smartphones，you should______at first.A.go to the storeB.find a suitable storeC.send e­mails to the shopD.download a shopping app()8.What does the underlined word“convenience”mean in Chinese?A.麻烦B.方便C.舒适D.交流()9.The number of disadvantages of shopping on smartphones is ______.A.oneB.twoC.threeD.four()10.What's the best title of this passage?A.Smartphone shopping.B.The usages of smartphone shopping.C.The advantages of smartphone shopping.D.The disadvantages of smartphone shopping.AHow winter weather influences the subway serviceWhen temperatures drop,and ice and snow fall on the tracks,know more service changes by:☆listening to your local traffic broadcasts☆visiting our website ☆signing up for email or text message warnings on our website☆following us on Twitter(NYCTSubwayScoop)☆calling our travel information line at 718-330-1234Our goal is to keep as many trains in service as possible and to keep you informed.Depending on how bad the weather is,here’s what you can expect:Service on these lines may run local on different parts of their routes:A,E,D,F,N,Q,2,3,4,5Service will change on these lines:G —Service between Court Square and 71st Street will stop for some time.7—Reduced service 11p.m.—1a.m.After 1a.m.normal late night service startsagain.S —*42nd Street train runs all night*Dyre Road trains go farther to 149th Street*Rockaway Park train goes farther to Euclid RoadExpect service on these weekday lines to end earlier than normal:B(take D or Q instead),V(take F instead),W(take N instead)Please allow for more travel time and listen for broadcasts.Thank you.2020年广东中考英语阅读理解限时训练（四）()11.People can know about subway service changes in winter through_____ ways.A.threeB.fouC.fiveD.six()12.The subway website will_____.A.send emails to some passengersB.keep all the underground trains in serviceC.follow the passengers around in the stationD.call the travel information line to know about the changes()13.What service changes there will be depends on_____.A.the weatherB.the seasonC.passengersD.the temperature()14.The service of_____lines will change if necessary.A.tenB.fourteenC.sixteenD.eighteen()15.When Line V ends earlier,passengers can take_____.A.Line7B.Line QC.Line5D.Line FBWould you like to live in a city where buildings turn the lights off for you,and self-driving cars will find the nearest parking space themselves?Although it might sound a little far from you,living in a“smart”city like this could happen sooner than you think.Great changes have taken place in towns that we have lived in for centuries, while completely new cities are being built.One such place is the city of Songdo. Every home there will have a“tele-presence system(远程遥控系统)”allowing users to control the heating and locks,take part in video meetings,and receiveeducation,health care and government services.Around the city,escalators(自动扶梯)will only move when someone is on them,and offices and schools will all be connected to the system.The great mind behind Songdo is from the company Cisco.In fact,technology companies around the world such as IBM,Siemens and Microsoft are already in the business.“About75%of the world’s population will live in cities by2050,so cities will need to be more modern to deal with the coming problems.Making cities smarter is one way out,and I think this will in turn make cities greener,”said Dan Hill, head of a research company.()16.According to the text,living in a“smart”city_____.A.is not a green wayB.will be far from youC.will soon become trueD.is completely impossible()17.The underlined phrase“in turn”means_____in Chinese.A.反过来B.轮流C.依次地D.翻转()18._____offers the great mind to build Songdo.A.CiscoB.IBMC.SiemensD.Microsoft()19.Dan Hill thinks that making cities smarter is one way to_____.A.drive people out of citiesB.control the world’s populationC.develop his own companyD.solve the cities’coming problems()20.Which of the following might be the best title for the text?A.Future EducationB.Smart Citiesernment ServicesD.Famous Companies【参考答案】训练一1-5 D A D B B 6-10 B C B A D 训练二1～5 D D A B B 6～10 D A B C C　训练三1~5C A B D C6~10B D B B A 训练四1-5 C A A C D 6-10 C A A D B。

八年级下册物理限时训练（二）1．关于力、力和运动的关系，下列说法中不正确的是（）A．施力物体一定也是受力物体B．物体不受力，运动状态一定不改变C．两个不接触的物体间一定没有力的作用D．力不能脱离物体而单独存在2.忽略空气阻力,抛出的铅球在空中运动轨迹如图所示,则下列对抛出后的铅球,分析正确的是（）A．铅球受到沿运动方向的推力，在这个力作用下继续运动B．铅球受到重力和推力，在这两个力作用下继续运动C．铅球不受力，靠惯性继续运动D．铅球受到重力作用，运动状态不断发生变化3.下列现象中，不能用惯性解释的是（）A．人走路时有时会绊倒B．子弹从枪膛飞出枪外后，继续向前运动C．用力将伞上的水甩掉D．地上滚动的球最终会停下来4.如图所示，跳水运动员站在跳板上静止不动，下列说法正确的是（）A．跳板被压弯说明力可以改变物体的运动状态B．运动员对跳板的压力和运动员所受的重力是一对平衡力C．跳板对运动员的支持力和运动员对跳板的压力是一对平衡力D．跳板对运动员的支持力和运动员所受的重力是一对平衡力5.如图所示的各种情形中，两个力是平衡力的是（）A． B． C． D．6.如图是运动员顶足球时的情景，忽略空气阻力，下列说法正确的是（）A．球被顶出，说明力可以改变物体的运动状态B．顶出去的球在上升过程中，受到平衡力的作用C．球在上升过程中，受到一个向上的力D．顶出去的球最终落地，是由于球具有惯性7.下列实例中，目的是为了增大摩擦的是（）A．旅行箱安装小轮子B．给自行车的车轴上机油C．自行车轴承中装有滚珠 D．自行车轮胎上制有凹凸的花纹8.如图所示，某同学沿水平方向用75N的力推箱子，下列分析不正确的是（）A．若该同学没有推动箱子，箱子所受摩擦力为75NB．若箱子被推动，箱子在滑行过程中所受摩擦力大小为75N，方向水平向左C．若该同学推箱子的推力增大，箱子所受摩擦力也可能增大D．若箱子被推动，箱子在滑行过程中撤去推力，箱子会由于惯性继续运动一段时间9.秋千荡到最高点时，如果受到的力全部消失，下列现象可能会发生的是（）A．继续来回摆动 B．做匀速直线运动C．保持静止状态 D．做匀速圆周运动10.下列关于惯性的说法中，正确的是（）A．人走路时没有惯性，被绊倒时有惯性B．交通规则中要求司机系安全带，是为了减小司机的惯性C．物体没有受外力作用时有惯性，受外力作用后惯性被克服了D．物体的惯性与物体的运动状态及受力情况均无关11.2022年3月23日，“天宫课堂”上王亚平轻推静止的“冰墩墩”，“冰墩墩”沿直线运动到对面叶光富的手中。

限时训练(四)says the support he gets online has encouraged himself to keep working. In return, his example has inspired many others to improve themselves and try to change their own destiny(命运)．At present Tao gets 100 yuan each day from the building site, but thanks to his live streaming(网上直播), his income can reach up to 8，000 yuan. This has really helped him a lot. And he's planning to get married and become a father one day. He wants to do everything he can to change his destiny, rather than stay as a builder.()1.What does Tao Jinjin do at present?A．An actor. B．A director.C．A reporter. D．A building worker.()2.Why did Tao choose to do his work at the beginning?A．He wanted to make more money.B．He wanted to be pitied by others.C．He wanted to show he could live on hisown.D．He couldn't do any other work.()3.Tao's videos get so much attention on the Internet because ________．A．Internet users are interested in some work like carrying bricks on the building site B．many people want to know how to get 8，000 yuan a month from the videosC．the videos encourage people to improve themselves and spread positive energyD．these videos can always bring much pleasure to Internet users()4.What can we know from the passage?A．The Internet has really changed Tao Jinjin's life.B．Tao Jinjin's mother takes care of him every day.C．Tao Jinjin is always living a long and painful life.D．Tao Jinjin keeps his live streaming because of his father.Ⅱ.语法填空阅读下面短文，在空白处填入一个适当的词，或填入括号中所给单词的正确形式(每空不多于3个单词)。

2023届高三英语晚自习限时训练一、阅读理解AParis is the most wooded city in Europe, and around one quarter of its area is taken up by parks, gardens and other green spaces.Jardin des Plantes: over 28 hectaresThis impressive botanical garden is home to four museums, including the Natural History Museum, which houses a variety of African animals. The gardens themselves boast thousands of species of plants. This is a lovely place to relax and explore the beautiful surroundings.Parc des Buttes-Chaumont: over 24 hectaresIf you want to get off the tourist trail and hang out with true Parisians, this park is the perfect spot for a relaxing picnic or a leisurely wander. It is in the 19th district and is one of the largest parks in Paris. Cross its lake on the suspension bridge, or admire the waterfalls and attractive temples.Jardin du Luxembourg: over 25 hectaresThese beautiful gardens were first laid out in 1612 as the gardens of the Luxembourg Palace. They include a geometric forest, French and English style gardens, as well as a large pond. There is so much to see and do with activities especially for children, such as slides, rides and puppet shows, as well as leisure and sporting activities for adults. The gardens are home to more than one hundred sculptures.Le Parc de la Villette: 55 hectaresThis urban cultural park is so much more than just a park as it is home to numerous music venues, exhibition spaces and cafes. It is also home to no less than 12 gardens, which all follow different themes. The Passenger Gardens, for example, which are built on what was once the sheep market, support a variety of ecosystems, demonstrating the importance of biodiversity.1. Which green space probably suits students who are interested in botany?A．Jardin des Plantes. B．Parc des Buttes-Chaumont.C．Jardin du Luxembourg. D．Le Parc de la Villette.2. Which is special about Jardin du Luxembourg?A．They used to be royal gardens. B．They are Parisian favourite gardens. C．They feature American style gardens. D．They house a variely of African animals.3. What can visitors do in Le Parc de la Villette?A．Visiting museums. B．Attending concerts.C．Admiring waterfalls. D．Watching puppet shows.BA team of researchers at ETH Zurich has the perfect long-lasting solution to our fog problem. They have developed a very thin and gold-based transparent coating (涂层) that can convert sunlight into heat, which can be applied to glass and other surfaces to prevent them from fogging.The special coating is developed using titanium oxide and gold particles. It selectively absorbs infrared radiations (红外线照射) from the sunlight and creates a heating effect that is powerful enough to keep fog away from the surface of an object.The coating basically employs heat to stop fogging. The coating absorbs a large part of the infrared radiation, which causes it to heat up-by up to 8℃.Previously, products like anti-fogging sprays create a very thin film of water on the surface to remove fog. The problem with such surfaces is pollution. Along with water, the sprays also attract dirt, dust, oil, and various other dirty substances, and just a little dirt on the surface makes it useless. However, the new coating repels (排斥) water. Furthermore, the coating is significantly thinner, which makes it more transparent as well as flexible. It is heated passively and requires, during daytime, no additional energy source.Gold might be expensive, but the researchers stress that their coating requires solittle that the material costs remain low. Their coating is produced with standardized and readily scalable methods, all cost-effectively. However, although this product can work at very low levels of solar irradiation, it does rely on a certain amount of light.The researchers will develop the coating further for other applications. In the process, they will examine whether other metals work just as well as gold. There is no need to fear. However, this would cause a car or a building to heat up more in the summer. The researchers have already filed a patent. Hopefully, this groundbreaking product will soon be available on the market.；4. How does the new coating work to remove fog?A．By reflecting part of sunlight selectively.B．By keeping cool air away from the object.C．By creating a thin film of water on the surface.D．By absorbing infrared radiations to heat the coating.；5. Why does the author mention previous anti-fogging products?A．To stress the advantages of the new coating.B．To introduce the inspiration behind the new coating.C．To prove the difficulty of creating anti-fogging products.D．To explain the reason for the anti-fogging coating being popular .；6. What is the limitation of the new coating?A．It is considerably expensive.B．It depends on sunlight to work.C．It takes too much time to produce.D．It is difficult to clean and maintain.；7. What do the researchers plan to do next?A．Apply for a patent for the invention.B．Develop the product for more practical uses.C．Explore the environmental impact of the coating.D．Seek a cheaper material as an alternative to gold.CAn exhibition of vivid photographs and a restored documentary give fresh insight into the Antarctic explorer, who died a century ago.One hundred years ago, the leader of the last great expeditio n of the heroic age of polar exploration died from a heart attack as his ship, Quest, headed for Antarctica. The announcement of the death of Ernest Shackleton on 30 January 1922 was greeted with an outpouring of national grief.This was the man, after all, who had saved the entire crew of his ship Endurance —which had been crushed and sunk by ice in 1915 — by making a daring trip in a tiny open boat over 750 miles of polar sea to raise the alarm at a whaling station in South Georgia.It remains one of the greatest rescue stories of modern history and led to the idolising of Shackleton in the United Kingdom, a reputation that survived undamaged for the rest of the century. As his contemporary Raymond Priestley, the geologist and Antarctic explorer, later put it: “When disaster strikes and all hope is gone, get down on your knees and pray for Shackleton.”And here and now in 2022, his death is being marked with an elaborately illustrated exhibition —Shackleton’s legacy and the power of early Antarctic pho tography — which opens at the Royal Geographical Society (RGS), and which includes a range of images and artefacts from his expeditions. Additionally, a digitally remade version of South, a documentary film of Shackleton’s 1914-16 Endurance expedition, is being screened at the British Film Institute.The film and most of the exhibition’s finest images are the handiwork of Frank Hurley, who sailed with Shackleton and who was one of the 20th century’s greatest photographers and film-makers. Both film and exhibition feature striking camera work and provide vivid accounts of the hardships that Shackleton and his men endured as they headed off to explore Antarctica.Even after he survived the great expedition, he still longed for another trip to Antarctica, and after long negotiations set sail in Quest, from England, with the aim of circumnavigating (环航) Antarctica, Shackleton was by now very ill and had suffered at least one heart attack. On 2 January 1922, he wrote in his diary: “I grow old and tired but must a lways lead on.” Three days later he had a major heart attack and died a few hours later. He is buried on South Georgia, scene of his greatest triumph.“Shackleton was an inspirational leader. He had an innate sense of what was possible and achievable. He also had a huge personality but led by example. At the same time, he was sensitive to the needs of the individuals he was leading. For example, after Endurance broke up, his men had lost their protection and shelter. Their social fabric had been destroyed. There would have been disagreement. Yet Shackleton succeeded in keeping them together and made sure they survived.”8. People were overcome with grief when Ernest Shackleton died because .A．it was a huge pity that such a brave explorer should ha ve died from a heart attack B．he was the man that wrote about one of the greatest rescue stories of modern history C．he came to his entire crew’s rescue and symbolised hope in extreme circumstances D．there was no one to pray to anymore when disaster came and there was no hope9. What can we learn about the exhibition?A．It presents Shackleton’s 1914-16 Endurance expedition with powerful Antarctic photos.B．It celebrates the 100th anniversary of the great explorer Ernest Shackleton’s birth. C．It consists of vivid photographs, artefacts, and documentaries of Ernest Shackleton.D．It is created by Frank Hurley, who witnessed Shackleton’s heroic acts with his own eyes.10. Which of the following is NOT true about Ernest Shackleton according to the passage? A．He was the leader of a heroic exploration to the South pole, who died from a heart attack off shore.B．He saved the crew members of the sunken Endurance by travelling to raise the alarmin a tiny boat.C．He is universally recognised as the greatest Antarctic explorer who has enjoyed enduring fame.D．He was inspirational, practical, responsible, sensitive towards his men, but had a strong character.11. What does “Their social fabric had been destroyed. ” in the last paragraph most probably mean?A．What they wore would not be accepted by others upon returning.B．They could no longer socialise with others even if they went back.C．The ship could not keep them together even if they survived.D．They could not function socially as they had when there was shelter.二、七选五阅读Do you want lots of success in school and in your friendship? If you want to learn how to balance your friendship and study, read on.• Talk about your goals for school.Share what academic success looks like for both of you. 12 Before the semester starts, sit down and discuss what you’d both like to achieve.• Share tips and tricks with each other.Exchange study techniques to learn how to be more successful. Maybe you know some learning methods like making a list of key ideas and reviewing them one hour a day. Chat about how you’ll both try to master your subjects. 13• Remind each other to take your health seriously.Put your wellness above everything else to succeed in school. 14 Get at least 8 hours of rest. Make sure to eat nutritious meals that will keep you energized. When you take care of yourselves, you’ll both reduce stress and improve your academic performances.• 15Remember that you both can overcome any challenge s with enough effort. In orderto get the most out of your studies, keep a “growth mindset”, an optimistic outlook that lets you see any difficult topic or task as an opportunity to learn.• Prioritize (优先安排) exams and finals.16 When you and your friend are in the middle of a finals week or have a huge assignment to prepare for, that should come first. Block out times on your schedules that need all your focus.A．Keep positive attitudes about school.B．Fight for any challenges enthusiastically.C．Your methods will be always encouraging.D．Give each other space during more intense periods.E．It’s important to be clear about what your goals are.F．You’ll lift each other up and get an extra edge in class.G．So you can both be at your best physically and mentally.三、完型填空When I was 13, I climbed my first mountain near my home. I was overweight thenand 17 when I reached the top. But I loved the 18 .Two years ago, my friend Mel Olsen and I drove to Oregon to climb 11,240-foot Mount Hood.As we went higher, the trail (山路) grew 19 and steeper. At around 9 a.m., we reached an ice step. Confident I was safe, I put my full 20 on it. Suddenly, I heard a 21 , and the ice broke off the step, right under my foot.In a second, I fell backward. Soon, I came to a stop on a flat slope. I 22 my whole body, feeling 23 that I was fine, except that I was suffering from a sharp painin my left 24 and couldn’t move.I 25 for help, and immediately Mel and other climbers came to assist me and called Mountain Rescue. Then I was loaded into a(n) 26 and taken to a hospital,27 I stayed for four days. The doctors told me it would be a year before I could 28 again, but I was back on the trails within six months.The fall has made me more 29 . One slip (滑倒) on a mountain can change everything. But the experience also made me 30 as a person. Since the accident, I’ve climbed another 60 mountains. I’m not going to let one fall 31 me from doing my favorite thing.17. A．out of danger B．out of trouble C．out of balance D．out of breath18. A．opportunity B．memory C．challenge D．mountain19. A．wider B．flatter C．narrower D．nearer20. A．body B．strength C．foot D．weight21. A．cry B．crack C．crash D．call22. A．calmed B．looked C．tested D．checked23. A．fortunate B．satisfied C．grateful D．confident24. A．arm B．shoulder C．leg D．eye25. A．yelled B．asked C．begged D．arranged26. A．car B．ambulance C．truck D．shelter27. A．which B．that C．where D．when28. A．jump B．move C．drive D．climb29. A．positive B．cautious C．frightened D．anxious30. A．grow B．develop C．feel D．act31. A．protect B．ban C．addict D．keep四、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

2
2
2
11. 解析 由 cos2 A b c 1 cos A ，即1 b 1 cos A ，得 b cos A .
2 2c
2
c
c
sin B
解法一（正弦定理）：由正弦定理，得 cos A
，
sin C
所以 sin B sin C cos A sin π A C
c
b
所以直线 F1Q 的斜率为 ，可得直角顶点 Q0,b ，
c
π 且 FQO ，故 b c .
4
cc
2
所以椭圆的离心率 e
.
a b2 c2 2
自信是迈向成功的第一步
3
8. 解析 据三棱锥的三视图，还原几何体 P ABC ，且 PA 平面 ABC ，底面△ABC
1
1
5
为等腰三角形， S△ ABC

2
2
2

2
， S△PAB

S△PAC

1 2
5
，
2
1
S△ PBC

2 2
5
5，
55 因此三棱锥的表面积为 S△PAB S△PAC S△ABC S△PBC 2 5 2 5 2 .
2
16. 解析 设椭圆的左焦点为 F1 c,0 ，依题意 OF OQ OF1 .
1 又点 O 为 F1F2 的中点，所以 OQ 2 FF1 ，
则△QFF1 为直角三角形，得 FQ F1Q .
b 又直线 l : y x 垂直于 FQ ，故 F1Q//l ，
对于选项 B：若 m,n ， m // ， n// ，不一定推出 // ，

y A'
所以直线 EA 的方程为 y x+4 .
由

y x+4 y2 16x
，消去
x
得
y2
16
y

64

0
，
2
即 y 8 0 ，得 yA 8 ，
1
1
所以 S△AEF EF yA 8 8 32 .
2
2
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O
A
F 4x
自信是迈向成功的第一步

0

5 3

x

3

.故选
A.
y
B M A
O
DC
x
9.解析 作出满足不等式组的可行域 D ，如图中阴影部分所示.
x 2 y 6 x 4 2 y 1
y 1
则z

x4
x4

1
2

x

4

.
y 1
令 z
，问题转化为求 z 的最大值.
B
C
b
O
2a
A
8.解析 根据题意作图，如图所示.
设圆 x2 y2 6x 5 0 的圆心为 C ，化为标准形式后得 C 3, 0 ，
设弦 AB 的中点为 M x, y ，由 AM BM ，得 CM AB .
1
3
取 OC 的中点为 D ，则 DM OC .
2
2
3
2
4.解析
因为 cos π 2 cos 2 1 2sin2
2
81

1

高一英语限时训练 1答案解析阅读理解A）篇. 主题语境：人与社会——科学与技术本文是论说文。

一些科学家对人工智能的强大功能和快速发展表示了担心。

1. B。

理解主旨要义。

根据第二段中的Some recent models can ... Some can ... Others can ...可知，本段是对第一段最后一句Quite powerful AI tools have surprised even their creators with what they can do的延伸和展开说明，作者主要通过举例的方式介绍了当前人工智能工具的一些强大功能。

2. D。

理解目的。

根据第三段内容及第四段中的a more powerful model和The rapid progress and more general skills of recent AI models可知，作者在这里提到GPT-4是为了表明人工智能工具发展迅速。

3. C。

推断。

根据第四段中的many computer experts wrote an open letter calling for a six-month pause for any work on AI tools stronger than GPT-4和第五段内容可知，许多计算机科学家写公开信呼吁暂停人工智能工具研究，因为他们担心人工智能工具过于强大而不可控。

由此可推知，他们写这封信是为了减缓人工智能的发展。

4. D。

推断。

根据第六段内容可知，许多人工智能专家都不支持该信的观点：一些专家说这封信夸大了人工智能工具的能力；另一些专家说应该更关注当前人工智能工具的问题，而不是臆想未来会出现的问题。

B）篇主题语境：人与自然——自然生态本文是说明文。

科学家在南极海岸发现了一个新的帝企鹅群。

5. A。

理解具体信息。

根据第一段内容可知，由于帝企鹅的自然家园环境恶劣，人们无法接近一些企鹅群，这使得帝企鹅难以研究。

解得 v1＝B4qmd. 设粒子刚好打在上极板右边缘时， 由图知：R22＝L2＋(R2－d2)2，所以 R2＝4L24＋ d d2， 又 R2 ＝ mBvq2，解得 v2＝Bq(44Lm2＋ d d2). 综上分析，要使粒子不打在极板上，
其入射速率应满足以下条件：
v<B4qmd或
Bq(4L2＋d2)
C E b. B
限时训练七：一、二.选择题
学无 止 境
题号
1
2
3
4
5
6
7
8
9
答案
B
B
D
C
AB
AC
BC
BD
AB
三．非选择题：
10.解：由题意可知，导电棒在运动的过程中受到安培力和摩擦力
的作用，如图所示：
由左手定则可知，磁场方向向上；
当电流为 2A 时，导电棒作匀速运动，有
BI1L = f
（1） 当电流为 4A 时，有： BI 2 L − f = ma
限时训练十二：一、二.选择题
题号
1
2
3
4
5
6
7
8
9
答案
C
C
A
B
BD
AB
AD
CD
三．非选择题：
10.解析：(1)电流稳定后，导体棒做匀速运动，受力平衡，
有 F 安＝G，即 BIL＝mg ①(2 分) 解得 B＝ImLg ②(2 分)
(2)由法拉第电磁感应定律得导体棒产生的感应电动势 E＝BLv ③(1 分) 闭合电路中产生的感应电流 I＝ER ④(1 分) 由②③④式解得 v＝Im2gR(2 分)
（2）
由 （ 1）（ 2） 得 ： B= 0.3T

英语参考答案听力：1-5 ACAAC 6-10 BACAB 11-15 BCCBB 16-20 CBAAC单选：21-25 AADBB 26-30 BBDAC 31-35 CDCCD完型：36-40 BDACB 41-45 BDACD 46-50 CADAC 51-55 BCADB阅读：56-58 DDB 59-61 CDB 62-65 ABAC 66-70 BDACA71. making 72. deserve 73. options/choices/alternatives 74. similar 75. covers 76. wisdom 77. harmony 78. winding 79. acted/functioned/served 80. migrationPossible version:Despite the fact that constructing your future with goals is tough, it does make a difference during the process of your life, as it guarantees your right direction of constant achievements.Personally, it can never be too true that life can not shine without goals. No matter what you do, so long as you are determined to achieve, goals are necessary.Everybody has his own goals with no exception of me. Being a man useful to society is my long-term goal. However, at present, to an ideal university is undoubtedly my desire. Few people can survive well unless equipped with abundant knowledge.In an effort to realize my dream, hard work seems the best and only choice. Not only will I make my study plans in detail, but the most important is to put my plans into real action. Only with great efforts can I attain further education and eventually step into future with great confidence.阅读理解注解A56. 选D。

1限时训练（三十七）答案部分一、选择题题号 1 2 3 4 5 6 7 8 9 10 11 12 答案DDBBCBCBCCCB二、填空题13. 1 14.1215 15. 3胜 16. 960解析部分 （1）解析 依题意，{}14A x x =<<，{}2B x x =>，则()2,4A B =.故选D.评注 试题以考生最熟悉的知识呈现，体现面向全体考生、注重考查基础知识的特点.试卷以简单题目开始，稳定了考生的情绪，对考生在考试中正常发挥起到了重要的作用.（2）解析 由i 12i z =-，得12i2i iz -==--，则2i z =-+，所以z 的虚部为1.故选D.评注 试题的设计可以将复数运算的基本方法展现在解题过程中，考查考生对复数概念的理解以及复数运算法则的掌握情况.（3）解析由已知条件和等差数列的通项公式，得123122313a a aa d =⎧⎨+=+=⎩，得3d =，所以()4565133442a a a a a d ++==+=.故选B.评注 试题把等差数列的通项公式与求和作为考查的重点，体现了新课程标准对数列这部分内容的要求.试题的设计将对基础知识的考查和对能力的考查有机结合，而且以考生最熟悉的知识呈现，消除了考生的紧张情绪，有助于考生稳定发挥.（4）解析 依题意，从四个球中随机选取三个球，所选三个球上的数字能构成等差数列的情况有两种，即“2”“3”“4”，“2”“4”“6”.因此，所选三个球上的数字能构成等差数列的概率是3421C 2=.故选B. （5）解析 依题意，抛物线216y x =的准线方程是4x =-.又因为AB =，所以可得(A -，(4,B -，则22161a -=，得 24a =，所以2a =，故实轴长24a =.故选C.（6）解析 借助长方体，在长方体中构建几何体.据三视图分析可得，还原后的几何体如图所示，三棱锥P ABC -.该几何体的体积1142323V =⨯⨯⨯=.故选B.（7）解析 由22log e log 21a =>=，122log e log e 1b ==-<-，()221e 0,1e c -==∈， 因此a c b >>.故选C.（8）解析 依题意，由余弦定理得2222225643cos 22564b c a A bc +-+-===⨯⨯， 所以sin 22sin cos 22436cos sin sin 545A A A a AB B b ⨯===⨯=.故选B. （9）解析 第1次执行循环体后，16sin60 3.132S =⨯⨯︒<，不满足退出循环的条件，则12n =；第2次执行循环体后，112sin 303 3.132S =⨯⨯︒=<，不满足退出循环的条件，则24n =； 第3次执行循环体后，124sin 15 3.1056 3.132S =⨯⨯︒=<，不满足退出循环的条件，则48n =；第4次执行循环体后，148sin 7.5 3.132 3.132S =⨯⨯︒=>，满足退出循环的条件，所以输出的n 值为48.故选C.（10）解析 依题意，设双曲线C 的右焦点为(),0Fc ，右顶点为(),0A a ，圆222x y b +=与x 轴正半轴交点(),0B b ，且2a c b +=，则()22224a c b c a +==-，即4a c c a +=-，得53c e a ==，所以45b c =，又点(),0B b 到渐近线0ay bx ±=的距离2165b d c ==， 因此4b =，5c =，3a =，双曲线C 的方程为221916x y -=.故选C. （11）解析 解法一:设数列{}n a 的公比为q .由题设可得()21110a q +=，()315a q q +=，3解得12q =，18a =，从而()1411118*22n n n n a a q n ---⎛⎫⎛⎫==⨯=∈ ⎪⎪⎝⎭⎝⎭N .由4112n n a -⎛⎫= ⎪⎝⎭，可得4n ，所以12n a a a 的最大值为123464aa a a =.故选C. 解法二:设数列{}n a 的公比为q ，由题设可得()21110a q +=，()315a q q +=，解得18a =，12q =，从而41112n n n a a q --⎛⎫== ⎪⎝⎭，故()()3473242212111222n nn n n n a a a -+----++-⎛⎫⎛⎫⎛⎫=== ⎪⎪ ⎪⎝⎭⎝⎭⎝⎭，由于()2717492228n n n -⎛⎫=--⎪⎝⎭，故当3n =或4n =时，21749228n ⎛⎫-- ⎪⎝⎭取得最小值，最小值为6-，所以12n a a a 的最大值为64.故选C. （12）解析 因为()32534f x x x x =-++，所以()2361f x x x '=-+，故()66f x x ''=-， 令()0f x ''=，则1x =，所以()f x 的对称中心为11,4⎛⎫⎪⎝⎭.（再通过初等方法证明）()()122f x f x +-=. 因为()()2f x f x +-=()()()3232553232244x x x x x x -+++---+-+=323x x -+3225518126123122442x x x x x x x ++--+--+-++=，所以函数()y f x =的图像关于点11,4⎛⎫⎪⎝⎭中心对称， 则201711220171009100910091009k k f f f f =⎛⎫⎛⎫⎛⎫⎛⎫=+++= ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭∑201720161100910091009f f f ⎛⎫⎛⎫⎛⎫+++ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭ ，则2017112201710092k k f =⎛⎫=⨯ ⎪⎝⎭∑，得20171201710094k k f =⎛⎫=⎪⎝⎭∑.故选B. （13）解析 解法一：（利用模长用平方的原理去求解）因为平面向量,,abc 不共线，且两两所成角相等，所以2,,,3π〈〉=〈〉=〈〉=a b b c a c ，()22++=++=a b c a b c 22++a b 2+c 222⋅+⋅+⋅=a b a c b c 22222112211cos 212cos 21233ππ+++⨯⨯⨯+⨯⨯⨯+⨯⨯⨯2cos 13π=，所以1++=a b c .解法二：（数形结合思想求解）依题意，向量,,abc .如图所示，+a b 与c 反向共线，且1+=a b ，故211++=-=a b c .（14）解析 当1x =时，()31264nn-==，所以6n =，()63x -的展开式中， ()616C 3rr r r T x -+=-.令2r =，得()22436C 3T x =-，即2x 的系数为246C 31215=.（15）解析 由题意可得，甲、乙、丙、丁四支足球队举行“组合杯”足球友谊赛，每支球队都要与其他三支球队进行比赛，且比赛要分出胜负.则只需进行24C 6=场.因为每场都会产生胜方和负方，所以6场比赛共产生6胜6负.又甲、乙、丙三队的比赛成绩分别是两胜一负、全败、一胜两负，共有3胜6负，所以丁队的比赛成绩是3胜.故填3胜.（16）解析 解法一：分别将1,2,,59n = 代入()111nn n a a n ++-=+中，得212a a -=，323a a +=，434a a -=，545a a +=， ，585758a a -=，595859a a +=，605960a a -=， 从而131a a +=，571a a +=， ，57591a a +=，所以1357575915a a a a a a ++++++= ，又()()()21436059a a a a a a -+-++-= ()246601359a a a a a a a ++++-+++=()3026024609302⨯++++== ，所以601260S a a a =+++=()13599302930215960a a a ++++=+⨯= .解法二：由题设得()111nn n a a n ++-=+，令2n k =，得()2212121kk k a a k ++-=+，即21221k ka a k ++=+，再令21n k =-，得()2122112k k k a a k --+-=，即2212k k a a k --=，所以21211k k a a +-+=，因此601260S a a a =+++= ()21436059a a a a a a -+-++-+5()()135922*********a a a +++=++++⨯= .。

2023-2024学年八年级上学期人教版数学阶段限时训练卷（第11~13章）一．选择题（共10小题，满分30分，每小题3分）1．（3分）下面有4个汽车标致图案，其中不是轴对称图形的是（）A．B．C．D．2．（3分）下列每组数据分别是三根小木棒的长度，用这些木棒能摆成三角形的是（）A．5cm，5cm，11cm B．13cm，12cm，20cmC．8cm，7cm，15cm D．3cm，4cm，8cm3．（3分）如图，工人师傅门时，常用木条EF固定长方形门框，使其不变形，这样做的根据是（）A．三角形的稳定性B．两点确定一条直线C．两点之间，线段最短D．四边形的不稳定性4．（3分）下列条件不能得到等边三角形的是（）A．有两个内角是60°的三角形B．三个外角都相等的三角形C．有两个角相等的等腰三角形D．有一个角是60°的等腰三角形5．（3分）如图，AB∥CD，∠AFE＝135°，∠D＝80°，则∠E等于（）A．55°B．45°C．80°D．50°6．（3分）如图，已知AC∥BD，∠A＝∠C，则下列结论不一定成立的是（）A．∠B＝∠D B．OA＝OCC．OA＝OD D．AD＝BC7．（3分）如图，已知MB＝ND，∠MBA＝∠NDC，下列条件中不能判定△ABM≌△CDN的是（）A．∠M＝∠N B．AM∥CNC．AB＝CD D．AM＝CN8．（3分）等腰三角形一腰上的高与另一腰的夹角为60°，则等腰三角形的底角度数为（）A．15°B．30°C．15°或75°D．30°或150°9．（3分）如图所示，在Rt△ACB中，∠C＝90°，AD平分∠BAC，若BC＝16，BD＝10，则点D到AB的距离是（）A．9B．8C．7D．610．（3分）如图，BE、CF是△ABC的角平分线，∠A＝50°，BE、CF相交于D，则∠BDC的度数是（）A．115°B．110°C．100°D．90°二．填空题（共7小题，满分28分，每小题4分）11．（4分）点P（2，﹣3）关于y轴对称的点的坐标是．12．（4分）已知在△ABC中，∠A＝40°，∠B﹣∠C＝40°，则∠C＝．13．（4分）已知a，b是等腰三角形的两边长，且a，b满足（a+b﹣13）2＝0，则此等腰三角形的周长为．14．（4分）如图，在△ABC中，AB＝AC，点D在AC上，且BD＝BC＝AD，则∠ABD＝．15．（4分）如图Rt△ABC中，∠A＝30°，AB+BC＝12cm，则AB＝cm．16．（4分）一艘海轮位于灯塔P的南偏东70°方向的M处，它以每小时40海里的速度向正北方向航行，2小时后到达位于灯塔P的北偏东40°的N处，则N处与灯塔P的距离为．17．（4分）如图，等边△ABC中，E是AC边的中点，AD是BC边上的中线，P是AD上的动点，若AD＝6，则EP+CP的最小值为．三．解答题（共8小题，满分62分）18．（6分）如图，AE＝CF，AD＝CB，DF＝BE，求证：△ADF≌△CBE．19．（6分）一个多边形的内角和比它的外角和的2倍还大180度，求这个多边形的边数．20．（6分）如图，已知AC＝AE，∠B＝∠D，∠1＝∠2，求证：AB＝AD．21．（8分）如图，△ABC的周长为20，其中AB＝8，（1）用直尺和圆规作AB的垂直平分线DE交AC于点E，垂足为D，连接EB；（保留作图痕迹，不要求写画法）（2）在（1）作出AB的垂直平分线DE后，求△CBE的周长．22．（8分）如图，在平面直角坐标系中，A（﹣3，2），B（﹣4，﹣3），C（﹣1，﹣1）．（1）在图中作出与△ABC关于y轴对称的△A1B1C1（要求点A与A1，点B与点B1，点C和点C1相对应）；写出点A1，B1，C1的坐标（直接写答案）：A1；B1；C1；（2）请直接写出△A1B1C1的面积是．23．（8分）如图，在△ABC中，已知AB＝AC，BD平分∠ABC，AE为BC边的中线，AE、BD相交于点D，其中∠ADB＝125°，求∠BAC的度数．24．（10分）如图，△ABC中，AB＝AC，D、E、F分别为AB、BC、AC上的点，且BD＝CE，∠DEF＝∠B．（1）求证：∠BDE＝∠CEF；（2）当∠A＝60°时，求证：△DEF为等边三角形．25．（10分）（1）如图①，把△ABC纸片沿DE折叠，使点A落在四边形BCED的内部点A′的位置，试说明2∠A＝∠1+∠2；（2）如图②，若把△ABC纸片沿DE折叠，使点A落在四边形BCED的外部点A′的位置，此时∠A与∠1、∠2之间的等量关系是（无需说明理由）；（3）如图③，若把四边形ABCD沿EF折叠，使点A、D落在四边形BCFE的内部点A′、D′的位置，请你探索此时∠A、∠D、∠1与∠2之间的数量关系，写出你发现的结论并说明理由．2023-2024学年八年级上学期人教版数学阶段限时训练卷（第11~13章）参考答案与试题解析一．选择题（共10小题，满分30分，每小题3分）1．【解答】解：A．是轴对称图形，故此选项不合题意；B．是轴对称图形，故此选项不合题意；C．是轴对称图形，故此选项不合题意；D．不是轴对称图形，故此选项符合题意；故选：D．2．【解答】解：A、5+5＜11，不能组成三角形，故此选项错误；B、13+12＞20，能组成三角形，故此选项正确；C、8+7＝15，不能组成三角形，故此选项错误．D、3+4＜8，不能够组成三角形，故此选项错误；故选：B．3．【解答】解：用木条EF固定长方形门框，得到了△AEF，使其不变形，这样做的根据是三角形的稳定性，故选：A．4．【解答】解：A、两个内角为60°，因为三角形的内角和为180°，可知另一个内角也为60°，故该三角形为等边三角形；故本选项不符合题意；B、三个外角相等说明该三角形中三个内角相等，故该三角形为等边三角形；故本选项不符合题意；C、等腰三角形的两个底角是相等的，故不能确定该三角形是等边三角形．故本选项符合题意；D、有一个角是60°的等腰三角形是等边三角形，故本选项不符合题意；故选：C．5．【解答】解：∵AB∥CD，∠AFE＝135°，∴∠DGF＝∠AFE＝135°，∴∠DGE＝180°﹣∠DGF＝45°，∵∠D＝80°，∴∠E＝180°﹣∠D﹣∠DGE＝55°，故选：A．6．【解答】解：A、∵AC∥BD，∴∠A＝∠D，∠C＝∠B，∵∠A＝∠C，∴∠B＝∠D，正确，故本选项不符合题意；B、∵∠A＝∠C，∴OA＝OC，正确，故本选项不符合题意；C、根据已知不能推出OA＝OD，错误，故本选项符合题意；D、∵∠A＝∠C，∠B＝∠D，∴OA＝OC，OD＝OB，∴OA+OD＝OC+OB，即AD＝BC，正确，故本选项不符合题意；故选：C．7．【解答】解：A、∠M＝∠N，符合ASA，能判定△ABM≌△CDN，故A选项不符合题意；B、AM∥CN，得出∠MAB＝∠NCD，符合AAS，能判定△ABM≌△CDN，故B选项不符合题意．C、AB＝CD，符合SAS，能判定△ABM≌△CDN，故C选项不符合题意；D、根据条件AM＝CN，MB＝ND，∠MBA＝∠NDC，不能判定△ABM≌△CDN，故D选项符合题意；故选：D．8．【解答】解：在等腰△ABC中，AB＝AC，BD为腰AC上的高，∠ABD＝40°，当BD在△ABC内部时，如图1，∵BD为高，∴∠ADB＝90°，∴∠BAD＝90°﹣46°＝30°，∵AB＝AC，∴∠ABC＝∠ACB（180°﹣30°）＝75°；当BD在△ABC外部时，如图2，∵BD为高，∴∠ADB＝90°，∴∠BAD＝90°﹣60°＝30°，∵AB＝AC，∴∠ABC＝∠ACB，而∠BAD＝∠ABC+∠ACB，∴∠ACB∠BAD＝15°，综上所述，这个等腰三角形底角的度数为75°或15°．故选：C．9．【解答】解：∵BC＝16，BD＝10∴CD＝6由角平分线的性质，得点D到AB的距离等于CD＝6．故选：D．10．【解答】解：∵∠A＝50°，∴∠ABC+∠ACB＝180°﹣50°＝130°，∵BE、CF是△ABC的角平分线，∴∠EBC∠ABC，∠FCB∠ACB，∴∠EBC+∠FCB（∠ABC+∠ACB）＝65°，∴∠BDC＝180°﹣65°＝115°，故选：A．二．填空题（共7小题，满分28分，每小题4分）11．【解答】解：点P（2，﹣3）关于y轴对称的点的坐标为：（﹣2，﹣3）．故答案为：（﹣2，﹣3）．12．【解答】解：∵在△ABC中，∠A＝40°，∴∠B+∠C＝140°①，∵∠B﹣∠C＝40°②，∴①﹣②得，2∠C＝100°，解得∠C＝50°．故答案为：50°．13．【解答】解：∵（a+b﹣13）2＝0，∴a﹣b+3＝0，a+b﹣13＝0，∴a＝5，b＝8，∵a，b是等腰三角形的两边长，∴等腰三角形的三边长为5，5，8或5，8，8，∴5+5+8＝18或5+8+8＝21，∴等腰三角形的周长为18或21，故答案为：18或21．14．【解答】解：设∠ABD＝x，∵BC＝AD，∴∠A＝∠ABD＝x，∵BD＝BC，∴∠C＝∠BDC，根据三角形的外角性质，∠BDC＝∠A+∠ABD＝2x，∵AB＝AC，∴∠ABC＝∠C＝2x，在△ABC中，∠A+∠ABC+∠＝180°，即x+2x+2x＝180°，解得x＝36°，即∠ABD＝36°．故答案为：36°．15．【解答】解：∵Rt△ABC中，∠A＝30°，∴BC AB．设BC＝xcm，则有AB＝2xcm∴x+2x＝12，∴x＝4，∴AB＝8cm．故答案为：8．16．【解答】解：如图∠NPM＝180°﹣70°﹣40°＝70°，∵向北的方向线是平行的，∴∠M＝70°，∴∠NPM＝∠M，∴NP＝MN＝40海里×2＝80海里，故答案为：80海里．17．【解答】解：作点E关于AD的对称点F，连接CF，∵△ABC是等边三角形，AD是BC边上的中线，∴AD⊥BC，∴AD是BC的垂直平分线，∴点E关于AD的对应点为点F，∴CF就是EP+CP的最小值．∵△ABC是等边三角形，E是AC边的中点，∴F是AB的中点，∴CF是△ABC的中线，∴CF＝AD＝6，即EP+CP的最小值为6，故答案为6．三．解答题（共8小题，满分62分）18．【解答】证明：∵AE＝CF，∴AE﹣EF＝CF﹣EF，∴AF＝CE．在△ADF和△CBE中，∴△ADF≌△CBE（SSS）．19．【解答】解：设这个多边形的边数为n，由题意得，（n﹣2）•180°＝2×360°+180°，解得n＝7，答：这个多边形的边数是7．20．【解答】证明：∵∠1＝∠2，∴∠1+∠CAD＝∠2+∠CAD，∴∠BAC＝∠DAE，在△ADF和△CBE中，，∴△ADF≌△CBE（AAS），∴AB＝AD．21．【解答】解：（1）如图，BE为所作；（2）∵DE是AB的垂直平分线，∴EA＝EB，∴EB+EC＝EA+EC＝AC，∵△ABC的周长为20，∴AC+BC＝20﹣AB＝20﹣8＝12，∴△CBE的周长＝BE+EC+BC＝AE+EC+BC＝AC+BC＝12．22．【解答】解：（1）如图所示，△A1B1C1即为所求；故答案为：（3，2），（4，﹣3），（1，﹣1）；（2）如图所示，S△ABC＝S梯形BCDE﹣S△ACD﹣S△ABE3×（5+3）2×31×5＝12﹣2.5﹣3＝6.5．故答案为：6.523．【解答】解：∵AB＝AC，AE为BC边的中线，∴AE⊥BC，∴∠AEB＝90°，又∵∠ADB＝125°，∴∠DBE＝∠ADB﹣∠AEB＝35°，∵BD平分∠ABC，∴∠ABC＝2∠DBE＝70°，∵AB＝AC，∴∠C＝∠ABC＝70°，∴∠BAC＝180°﹣∠ABC﹣∠C＝40°．24．【解答】证明：（1）∵∠DEC是△BDE的一个外角，∴∠B+∠BDE＝∠DEF+∠CEF，∵∠DEF＝∠B，∴∠BDE＝∠CEF；（2）由（1）可知∠BDE＝∠CEF，∵AB＝AC，∠A＝60°∴∠B＝∠C＝60°，∴∠DEF＝60°，在△BDE和△CEF中∴△BDE≌△CEF（ASA），∴DE＝EF，∴△DEF为等边三角形．25．【解答】解：（1）如图，根据翻折的性质，∠3（180﹣∠1），∠4（180﹣∠2），∵∠A+∠3+∠4＝180°，∴∠A（180﹣∠1）（180﹣∠2）＝180°，整理得，2∠A＝∠1+∠2；（2）根据翻折的性质，∠3（180﹣∠1），∠4（180+∠2），∵∠A+∠3+∠4＝180°，∴∠A（180﹣∠1）（180+∠2）＝180°，整理得，2∠A＝∠1﹣∠2；（3）根据翻折的性质，∠3（180﹣∠1），∠4（180﹣∠2），∵∠A+∠D+∠3+∠4＝360°，∴∠A+∠D（180﹣∠1）（180﹣∠2）＝360°，整理得，2（∠A+∠D）＝∠1+∠2+360°．。

你永远是最棒的限时训练（七）参考答案答案部分一、选择题⎡ 3⎫13. 314. 8415. 516. ⎢-2, +∞ ⎪2⎣ ⎭解析部分1. 解析 A = (0, 2) ，B = ( -∞ , -1) (1, +∞) ，故 R B = [ -1,1]. 由数轴分析可得 AR B =(0,1] ．故选 C.2. 解析 根据题意可设 z = a + i ，则 z = a 2+ 1 .2< 4 ，所以 z ∈ ⎡)．故选 B ．因为-1 < a < 2 ，则0 a ⎣1, 5 3. 解析 如图所示，从图中5 个点中任意选出2 个点组成一条线段，有C 52= 10 （种）不同的选择方案，其中距离小于正方形边长的有 4 种，则距离大于或等于正方形边长的有6 种，其概率为P = 6 = 3.故选 A.10 5ABEDC 4. 解析 当k = 1时，易推知△OAB 的面积为 1，充分性成立；2当△OAB 的面积为 1时，由题可得 OA = OB = 1 ，2且 S = 1 OA OB sin ∠AOB = 1 ，所以∠AOB = π，222， 由图形性质转化到直线l 到圆心O 的距离d 为221=，解得k = ±1，必要性不成立.故选 A. 即d = 22 2自信是迈向成功的第一步你永远是最棒的⎛ π π ⎫时，2 x +π ⎛π 2π ⎫5. 解析 当 x ∈ -,⎪∈ -,⎪ ，36 3 3 ⎝ ⎭ ⎝ 3⎭故不在 y = sin x 的某一单调增区间内，故 A 错误；y = cos 4x - sin 4x = (cos 2 x - sin 2 x )(cos 2 x + sin 2 x ) = cos 2 x - sin 2 x = cos 2x ，即T = π ，故 B 错误；把 x =π⎛π ⎫ 代入 y = cos x +⎪ ，得 y = 0，故 C 正确；3 6 ⎝⎭正切函数没有对称轴，仅有对称中心，故 D 错误.故选 C.6. 解析 分析知该几何体为圆柱的一半，故体积为V = 12 ⨯ ( π⨯12⨯ 2) = π .故选 D.因此随着 的变化而变化，且呈现以 为周期的循环， 故当i = 2016 = 672 ⨯3 时，退出循环，因此 A = 2 .故选 D.c2+ 18. 解析 如图所示，易知2a + c =c ，即e = =55 = .故选 A.a 5 - 1 2y2a +ccO2cx9. 解析 由题意得0 < n < m ，故根据 y = 2x在R 上单调递增，A 错误；自信是迈向成功的第一步你永远是最棒的作差比较或根据函数 y = x 在(- 1, +∞) 上单调递增，B 错误；x + 1由题意得0 < 1 < 1，根据 y = ln x 在(0, +∞)上单调递增，C 正确； m n根据 y = x 3+ x 在R 上单调递增，D 错误.故选 C.评注 问题的本质就是研究函数的单调性.10. 解析 在 f ⎡ f ( x )⎤ = 0 中令t = f (x ) ，则 f (t )= 0 .⎣ ⎦ 若a = 0 ，验证易知此时不符合题意；若a ≠ 0 ，分a > 0 ，a < 0 讨论其图像大致如图所示．由 f (t ) = 0 知，t = f ( x ) = 1 ，问题转化为t = f ( x ) = 1 有且仅有一个实数解. 因此当a < 0 时，此式恒成立；当a > 0 时， f ( x ) 与 y 轴的交点(0, a ) 必须在 y = 1的下方，故0 < a < 1.综上所述：a ∈ ( -∞, 0 ) (0,1) .故选 A.y32 a a >01–3 –2 –1 O 1 2 3 x a <0 –1a–2–311. 解析 分解问题， y 2 x - 1 ⎧ y - 2 x + 1, x < 1-1 ⇔ ⎨ ；⎩ y 2 x - 3, x 1x 2 - y 2- 2 x + 2 y 0 ⇔ ( x - 1) 2 - ( y - 1) 2 0 ⇔( x - y )( x + y - 2 ) 0 ⇔ ⎧x - y 0⎧x - y 0⎨或⎨.⎩x + y - 2 0 ⎩x + y - 2 0画出可行域，如图所示，分析知点P 到直线 y = - 2 x + 1 的距离为PQ 的最小值，故 PQ = = 3 5 .故选 D.min5评注( x - 1) 2 - ( y - 1) 2 0 也可以等价为 x - 1y -1 ，采用分类讨论解决.自信是迈向成功的第一步你永远是最棒的 yy =-2x +1y =2x-3y =-x +243 y =x21QP–2 –1O 123x–112. 解析 解法一：以点 A 为坐标原点，建立如图所示的平面直角坐标系. 设 A (0，0) ，∠BAC = θ ，则B (6cos θ , 6sin θ ) ，C (10, 0) .取 AC 的中点D ，连接OD ，则OD ⊥ AC .1⎛ 1⎫因为OD = OA + AD =AC - x AB - y AC =- y ⎪AC - x AB ， 2 ⎝ 2⎭⎡ ⎛ 1 ⎫ ⎤⎛ 1 ⎫ 2 故OD ⋅ AC = ⎢  - y ⎪ AC - x AB ⎥ ⋅ AC =- y ⎪ AC - x AB ⋅ AC =22 ⎣ ⎝ ⎭ ⎦⎝ ⎭ ⎛ 1⎫- y ⎪ ⨯ 100 - 60 x cos θ = 0 ，即5 -10 y - 6 x c os θ = 0 ，2 ⎝ ⎭把2 x + 10 y = 5 代入化简得2x - 6 x cos θ = 0 ，得 x = 0 或cos θ = 1 . 1 1 3①当 x = 0 时， y =， 所以 AO = AC ，所以O 点与D 点重合，22 1即△ABC 为直角三角形，故S = ⨯ 6 ⨯ 8 = 24 ；21 时，sin θ = 2，②当cos θ = 23 3故 S = 1⨯ AB ⨯ AC ⨯ sin θ = 20 2 .2综上所述，△ABC 的面积为24 或20 2 .故选 D.yB (6cos θ,6sin θ) OA D C (10,0) x自信是迈向成功的第一步你永远是最棒的5解法二（构造法）：延长 AB 到点E ，使 AE =AB ，取 AC 中点D .2 2 x ⎛ 5⎫⎛ 1⎫ 2x因为 AO =AB ⎪ + 2 yAC ⎪ =AE + 2 y AD ，55 ⎝ 2 ⎭⎝ 2 ⎭又因为2 x + 10 y = 5 ，即2x+ 2 y = 1，因此O ， E ，D 三点在一条直线上.5若 O 与E 重合，则与O 在 AB 的垂直平分线上矛盾；若 O 与D 重合，即DA = DB = DC ，所以△ABC 为直角三角形，且 ∠B = π ，故S = 1⨯ 6 ⨯ 8 = 24 ；2 2若 O 不与D ，E 重合，则由三点共线知ED ⊥ AC .因为 AD = 5 ， AE = 15 ，故cos A =1，3此时sin A =22，故S =1⨯ AB ⨯ AC ⨯ sin A = 202 .32综上所述，△ABC 的面积为24 或20 2 .故选 D.ADOBCE13. 解析 S = 1 bc sin A =3c =3，故c = 2.24 2由余弦定理得a 2= b 2+ c 2- 2bc cos A = 1 + 4 - 2 ⨯ 1 ⨯ 2 ⨯ 1= 3 ，故a = 3 .214. 解析 展开式的第r + 1 项为T = C r(2x )7-r⎛ 1 ⎫r= C r 27 - r x 7 -2r ， ⎪ r +177⎝ x ⎭ 故令7 - 2 r = -3，即r = 5 ，所以 1的系数为C 5 2 7 -5= 21 ⨯ 4 = 84 ．x 37 15. 分析 通过常规的配凑无法实现，故尝试计算几个观察规律.因为a n ⋅ a n -1 = a n -1 -1，且a n -1 ≠ 0，故a n =a n -1 - 1，an -1因此a 2 = 5 ，a 3 = 4，a 4 = - 1，a 5 = 5 ，…，5 4故数列{a n } 是以3 为周期的数列．自信是迈向成功的第一步你永远是最棒的又因为2015 = 3⨯ 671+ 2 ，因此a 2015 = 5．16.解析 由题意得 x M = λ + (1- λ ) ⨯ 2 = -λ + 2 ，⎛ 2 - λ , 2- λ -1 ⎫，λ ∈[0,1].故M⎪⎝2 - λ ⎭⎛ 3 ⎫ ⎛ 3 3 ⎫ON = λ OA + (1 - λ )OB = λ (1, 0 ) + (1 - λ ) 2,⎪ = 2 - λ ,-λ ⎪ .2⎝⎭⎝2 2 ⎭31 12 - λ ) + 1MN= λ - 2 + λ = - λ -= -2 2 2 2 22 - λ令t = 2 - λ，则t ∈[1,2]，问题转化为k围．令 g (t ) =t+1-3，因为 g ( t ) =22 t增，0 故 g ( t ) min= g () =-3221⎡3⎤因此+-∈ ⎢ 0,- 2 ⎥2 ⎦自信是迈向成功的第一步。