天津市第一中学2020届高三下学期第四次月考英语试题 PDF版含答案
天津一中2020届高三上学期第一次月考英语试题 PDF版含答案
天津一中2019-2020-1高三年级一月考英语试卷第I卷（选择题，共115分）第一部分：听力测试（共两节，满分20分）第一节(共5小题；每小题1分，满分5分)听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你将有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1.What will the man go to London to do?A.Attend a meeting.B.Go sightseeing.C.Visit someone.2.What’s wrong with the man’s alarm clock?A.It doesn’t work well.B.It tells wrong time.C.It rings all the time.3.What’s the man’s nationality?A.Canadian.B.British.C.American.4.What’s the weather going to be like tomorrow?A.Cloudy.B.Rainy.C.Sunny.5.What is the man going to do first after school today?A.Play basketball.B.Study at the library.C.Go home.第二节听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A,B,C三个选项中选出最佳选项，并标在试卷的相应位置。
每段对话或独白读两遍。
听第6段材料，回答第6~7题。
6.What can we know about Peter?A.He has just got married.B.He met his girlfriend unexpectedly.C.He has returned home from abroad.7.What will the man go to Pairs for?A.Business.B.Sightseeing.C.Honeymoon.听第7段材料，回答第8~10题。
2020届高三11月月考试题 英语(应历)Word版含答案
姓名，年级：时间：2019～2020学年度三年级11月份月考试卷英语试卷命题人：徐雨生审题人：本试卷分第I卷（选择题，共100分）和第II卷（非选择题，共50分）两部分。
总分150分，考试时间120分钟.第Ⅰ 卷注意事项：1．答题前，考生务必将自己的姓名、班级、考号用0.5毫米的黑色墨水签字笔填写在答题卡上。
并检查条形码粘贴是否正确。
2．1—60小题选出答案后，用2B铅笔填涂在答题卡对应题目标号的位置上，非选择题用0。
5毫米黑色墨水签字笔书写在答题卡对应框内，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。
第一部分听力第二部分：阅读理解（共两节，满分40分)第一节（共15小题;每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C和D)中，选出最佳选项,并在答题卡上将该项涂黑。
AWhistle for WillieBy Ezra Jack KeatsThe Blue Ribbon DayBy Katie CouricToo Loud LilyBy Sofie LagunaA。
I Like Me。
B. Too Loud Lily。
C. Whistle for Willie。
D. The Blue Ribbon Day.22。
What can we know about Ezra Jack Keats?A. He’s a character of The Snowy Day。
B. He was awarded a big book prize.C。
He is a co—author of I Like Me。
D. He helped Peter train his dog.23. What do the four books have in common？A. They are for disabled children B。
They are on building confidence.C. They are adapted from fairy tales。
2020-2021学年天津市实验中学高三英语月考试题及答案解析
2020-2021学年天津市实验中学高三英语月考试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AAs a nation, we are getting bigger and eating more. But there are effective ways to control your appetite and eat only as much as you need.Keep away from low-nutrition snacksThat means ice cream, sweets, chips biscuits, cakes and any other salty orsugary snacks you eat between meals. Although we have a tendency to eat them, you can learn to live without these unhealthy-and-fattening-additions to your diet. Try to make it a habit to eat them only when offered at social events or as a special treat.Leave half an hour between main course and dessertHaving a break between courses gives your brain time to receive the fullness signal and make you more likely to refuse the sweet stuff. And, in fact, as soon as you feel the first signals of fullness, remove your plate from the table. That will tell your brain that food time is over.Make yours a small helpingPut an end to super-sized portions. You won’t be missing out—today’s small was the medium or large of a few decade ago. Select or serve yourself a modest portion and eat it slowly enjoying the flavors. Before you know it, small will feel just right. What’s more, ordering the smaller size leads to wearing the smaller size.Distract yourselfWhen you find yourself hunting down food, even though you’re even hungry, do something else for 20 minutes. Drink a large glass of water as thirst is often confused with a desire for food. Choose something that engages your brain as well as your hands, such as writing a letter or listening to a song. You could also go for a short walk or do something that you enjoy. If you think you really are hungry, set an alarm for 20 minutes’ time and if you still want to eat when it rings, fine. If not, the urge will have passed.1. Which way suits you better if you tend to order a large portion of food?A. Distract yourself.B. Make yours a small helping.C. Keep away from low-nutrition snacks.D. Leave half an hour between main course and dessert.2. Why should you have a break between main course and dessert?A. To give people time to chat.B. To have a good appetite for sweet stuff.C. To reduce appetite for dessert.D. To give the host time to remove your plate.3. When you find yourself pursuing for food, what should you do?A. Eat some biscuits.B. Eat some sugary snacks.C. Have some soft drinks.D. Listen to a lovely melody.BMost people around the world are right-handed. This also seems to be true in history. In 1799, scientists studied works of art made at different times from 1,500 B.C. to the 1950s. Most of the people shown in these works are right-handed, so the scientists guessed that right-handedness has always been common through history. Today, only about 10% to 15% of the world’s population is left-handed.Why are there more right-handed people than left-handed ones? Scientists now know that a person’s two hands each have their own jobs. For most people, the left hand is used to find things or hold things. The right hand is used to work with things. This is because of the different work of the two sides of the brain. The right side of the brain, which makes a person’s hands and eyes work together, controls the left hand. The left-side of the brain, which controls the right hand, is the centre for thinking and doing problems. These findings show that more artists should be left-handed, and studies have found that left-handedness is twice as common among artists as among people in other jobs.No one really knows what makes a person become right-handed instead of left-handed. Scientists have found that almost 40% of the people become left-handed because their main brain is damaged when they are born. However, this doesn’t happen to everyone, so scientists guess there must be another reason why people become left-handed. One idea is that people usually get right-handed from their parents. If a person does not receive the gene(基因) for right-handedness, he / she may become either right-handed or left-handed according to the chance and the people they work or live with.Though right-handedness is more common than left-handedness, people no longer think left-handed people are strange or unusual. A long time ago, left-handed children were made to use their right hands like other children, but today they don’t have to.4. After studying works of art made at different times in history, the scientists found _______.A. the art began from 1,500B.C.B. the works of art ended in the 1950sC. most people shown in the works of art are right-handedD. most people shown in the works of art are left-handed5. What is the left hand for most people used to do?A. It’s used to find or hold things.B. It’s used to work with things.C. It’s used to make a person’s eyes work together.D. It’s the centre for thinking and doing problems.6. According to the passage, which of the following is NOT true?A. No one really knows what makes a person become right-handed.B. Left-handedness is cleverer than right-handedness.C. Today children are not made to use their right hands only.D. Scientists think there must be some reason why people become left-handed.7. The best title for this passage is _______.A. Scientists’ New InventionsB. Left-handed PeopleC. Which HandD. Different Brains, Different HandsCTo hear people talk about Internet friendships, you would think it was one giant web of cat-fishing and e-crime. While we all undoubtedly have to take measures to remain safe online, assuming every friendship or connection made on Instagram, Twitter or Facebook is cheating or insincere would be a mistake.As a woman who works in the creative industry, I have found real joy in seeking out a community I couldn’t find elsewhere, and making some great friends along the way. My first online friendship was on Twitter with my(now) best friend, during the university exam period. We exchanged study notes in dozens of direct messages, set a study date, and haven’t looked back since.Drawn to each other by similar circumstances, friendships online are similar to offline in that they tend to begin because of shared interest or common ground-maybe they’ve read the post on Instagram. Maybe they have the same taste in food or politics. Or maybe they just love memes too. If online friendships start similar to friendships offline, they grow in the same way, too. Often through mutual support: apart from calling a friend tocongratulate him on that new job, you also re-tweet his jokes and praise his Instagram story.Despite my positive experiences when I tell people, most are still suspicious. Eyebrows are raised higher when I explain not only have I found a community online but have made friendships with people I meet face-to-face too. Actually, these are just as valid as other friendships, according to behavioural psychologist Jo Hemmings, who says online friendships can be real.So how do you know if people are there for the real you or just because you’re popular on Instagram? Hemmings has simple rules. She tells me “You have to equally feel comfortable that you’re getting something of each other instead of being used to enable something that isn’t friendship.”Therefore, if all a “friend” online is asking you to do is to promote their work or personal brand and rarely takes an interest in you, then there may be room to question the basis of the friendship. On that note it is worth remembering that just because someone has a lot of followers, it doesn’t necessarily mean they have lots of friends.8. What is most people’s attitude towards online friendship?A. Negative.B. Positive.C. Objective.D. Neutral.9. Why does the writer share her own experience in paragraph 2?A. To introduce the background information of the text.B. To convey the writer’s attitude and give the related example.C. To prove the likely risk for people to develop friendship online.D. To remind people of the various benefits of making friends online.10. How can online and offline friendships be deepened?A. They should be based on shared interest.B. They need to have common ground.C. They require support from each other.D. They can’t live without social media.11. According to the author, what’s the golden rule to make friends online?A. A friend to all is a friend to none.B. Without confidence there is no friendship.C. A friend without faults will never be found.D. Friendship cannot stand always on one side.DPablo Picasso was born on October25 inMalaga. Spain in 1881. Taking after his father, Picasso shared apassion（热爱）for painting and art. Even though he wasn't the best student in school, Picasso excelled at drawing. Noticing his amazing talent, Picasso's father, an artist, taught him everything he knew. Before long, Picasso could paint and draw much better than his father. With this rich talent, Picasso paid less and less attention to his schoolwork and spent the majority of his day sketching and drawing in notepads and sketchbooks.When he was a little bit older, Picasso moved twice and was accepted into two fine art programs. However, he didn't care very much for the special techniques they taught and often wandered the streets by himself drawing the scenes around him. After moving to these two places, Picasso moved back home toBarcelonaand decided that he would develop new techniques of art and painting based on what he saw.Later, Picasso decided to move toParis,France, where he began perfecting his own techniques of painting, drawing and other forms of art. His drawings. paintings, and an included pieces about sadness, poverty, classics and self-portraits. One of his major types of work is calledcubism（立体派），which includes art with all sizes of geometric shapes together on the piece of an. This type of art is very important because no other artists had come up with the idea before. Picasso decided to try something new, and as a result, cubismis widely accepted today as a classic style of art.Picasso inspires us to always be thinking. He tells us to think outside the box and come up with fresh new ideas that can change the world. He surely plays a significant role in the art field.12. What do we know about Picasso as a student at school?A. He hated doing his homework.B. He was very proud of his talent.C. He showed great talent for drawing.D. He was often praised by his teacher.13. What did Picasso's father do when he found Picasso's gift?A. He tried his best to help Picasso.B. He blamed Picasso for his laziness.C. He asked Picasso to finish his work on time.D. He encouraged Picasso to do better at school.14. What was Picasso's attitude towards the special techniques at that time?A. He thought highly of them.B. He took no interest in them.C. He was confused about them.D. He was concerned about them.15. What does the author tell us in the last two paragraphs?A. Picasso has great faith in art.B. Picasso has changed the world a lot.C. Picasso can do anything he wants to.D. Picasso is a highly creative artist.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020年高考数学【真题母题解密】比较大小（天津卷）（解析版）
『高考真题·母题解密』『分项汇编·逐一击破』专题06比较大小【母题来源】2020年高考数学天津卷【母题题文】设，则的大小关系为（）0.80.70.713,,log 0.83a b c -⎛⎫=== ⎪⎝⎭,,a b c A. B. C. D. a b c <<b a c <<b c a <<c a b<<【答案】D【试题解析】利用指数函数与对数函数的性质，即可得出的大小关系.,,a b c 【详解】因为，，，0.731a =>0.80.80.71333b a-⎛⎫==>= ⎪⎝⎭0.70.7log 0.8log 0.71c =<=所以.故选：D.1c a b <<<【命题意图】本题考查的是有关指数幂和对数值的比较大小问题，在解题的过程中，注意应用指数函数和对数函数的单调性，确定其对应值的范围.【命题方向】这类试题在考查题型上主要以选择题的形式出现．试题难度不大，多为低档题，是历年高考的热点．考查对简单函数单调性的理解及不等式的有关知识；常见的命题角度有：与常用基础函数如：幂函数、指数函数、对数函数等知识结合.【方法总结】比较指对幂形式的数的大小关系，常用方法：（1）利用指数函数的单调性：，当时，函数递增；当时，函数递减；x y a =1a >01a <<（2）利用对数函数的单调性：，当时，函数递增；当时，函数递减；log a y x =1a >01a <<（3）借助于中间值，例如：0或1等.1．【2020·天津九校高三下学期4月联考】设，，则（）．0.5log 0.8a = 1.10.8b log =0.81.1c =A. B. b a c <<b c a <<C. D. a b c <<a c b<<【答案】A 【解析】【分析】结合指数和对数函数的单调性分别与0和1比较，易得，，，所以.0a 1<<b 0<c 1>b<a<c 【详解】解：因为0.50.50.50log 1a log 0.8log 0.51=<=<=所以 故选A1.1 1.1b log 0.8log 10=<=0.80c 1.1 1.11=>=b<a<c 【点睛】本题考查了指数和对数函数性质的运用，在指数和对数比较大小过程中一般先比较与0,1的大小关系.2．【2020·天津市北辰区高三高考模拟】已知函数是定义在上的偶函数，且在上单调递增，则三个数，，的大小关系为（）A. B.C.D.【答案】C 【解析】【分析】根据奇偶性得：，通过临界值的方式可判断出自变量之间的大小关系，再利用函数的单调性得到的大小关系.【详解】；，即：为偶函数又在上单调递增，即本题正确选项：【点睛】本题考查利用函数单调性判断大小的问题，关键是能够利用奇偶性将自变量变到同一单调区间内，再通过指数、对数函数的单调性，利用临界值确定自变量的大小关系.3．【2020·天津市北辰区2020届高三第一次诊断测试】已知函数的定义域为，且函数()y f x =(),ππ-的图象关于直线对称，当时，（其中是()2y f x =+2x =-()0,x π∈()ln 'sin 2f x x f xππ⎛⎫=- ⎪⎝⎭()'f x 的导函数），若,,，则的大小关系是（ ）()f x ()log 3a f π=13log 9b f ⎛⎫= ⎪⎝⎭13c f π⎛⎫= ⎪⎝⎭,,a b c A B. C. D. b a c >>a b c>>c b a>>b c a>>【答案】D 【解析】【分析】求出,可得的值，能确定的解析式，分类讨论可确定的符号，可得在()'f x '2f π⎛⎫ ⎪⎝⎭()'f x ()'f x ()f x 上递增，再利用指数函数、对数函数的单调性比较的大小关系，结合函数的奇()0,π13log 32ππ、、()f x 偶性与单调性可得结果.【详解】，，()ln 'sin 2f x x f x ππ⎛⎫=- ⎪⎝⎭ ()''cos 2f x f xx ππ⎛⎫∴=- ⎪⎝⎭，，'2'cos 2222f f πππ⎛⎫⎛⎫=-= ⎪ ⎪⎝⎭⎝⎭()'2cos f x xx π=-当时，；当时，，2x π≤<π()2cos 0,'0x f x ≤>02x π<<()2,2cos 2,'0x f x x π><∴>即在上递增，的图象关于对称，()f x ()0,π()2y f x =+ 2x =-向右平移2个单位得到的图象关于轴对称，()2y f x ∴=+()y f x =y 即为偶函数，，，()y f x =()()13log 922b f f f ⎛⎫==-= ⎪⎝⎭0log 1log 3log 1ππππ=<<=，即，，1103212πππ=<<<130log 32πππ<<<<()()132log 3f f f ππ⎛⎫∴>> ⎪⎝⎭即.故选D.b c a >>【点睛】本题主要考查函数的奇偶性、对数函数的性质、指数函数的单调性及比较大小问题，属于难题. 在比较，，，的大小时，首先应该根据函数的奇偶性与周期性将，()1f x ()2f x ()n f x ()f x ()1f x ，，通过等值变形将自变量置于同一个单调区间，然后根据单调性比较大小．()2f x ()n f x 4．【2020·天津市滨海新区三校2020届高三高考数学5月份模拟】已知奇函数f （x ）在R 上是减函数，若a ＝﹣f （1og 3），b ＝f （），c ＝f （2﹣0.8），则a ，b ，c 的大小关系为（ ）A ．a ＜b ＜cB ．a ＜c ＜bC ．b ＜c ＜aD ．c ＜a ＜b【答案】B【分析】结合函数的单调性及奇偶性进行比较函数值的大小．解：奇函数f （x ）在R 上是减函数，∵log 34∈（1，2），0，2﹣0.8∈（0，1），∵a ＝﹣f （1og 3）＝f （log 34），b ＝f （），c ＝f （2﹣0.8）＝f （），则a ＜c ＜b ，故选：B ．5．【2020·天津市部分区2020届高考二模】已知，，，则，，的大小3log 0.3a =0.3log 2b =0.23c =a b c 关系是（ ）A B. C. D. a b c >>b c a>>c b a >>c a b>>【答案】C 【解析】【分析】由题意结合指数函数、对数函数的单调性可知，即可得解.10a b c <-<<<【详解】由题意，，，331log 0.3log 13<=-0.30.30.3log log 2lo 1013g 10=<<-=0.20331>=所以.10a b c <-<<<故选：C.【点睛】本题考查了指数式、对数式的大小比较，考查了指数函数、对数函数单调性的应用，属于基础题.6．【2020·天津市第一百中学2020届高三高考模拟】已知函数是定义在上的偶函数，且在()f x R 上单调递增，则三个数，，的大小关系为[)0,∞+()3log 13a f =-121log 8b f ⎛⎫= ⎪⎝⎭()0.62c f =A. B. a b c >>a c b >>C. D. b a c >>c a b>>【答案】C 【解析】【分析】根据奇偶性得：，通过临界值的方式可判断出自变量之间的大小关系，再利用函数的单调()3log 13a f =性得到的大小关系.,,a b c 【详解】；，3332log 9log 13log 273=<<=1221log log 838==0.610222<<=即：为偶函数 0.6312102log 13log 8<<<()f x ()()33log 13log 13a f f ∴=-=又在上单调递增，即()f x [)0,+∞()()0.61321log log 1328f f f ⎛⎫∴>> ⎪⎝⎭b a c>>本题正确选项：C【点睛】本题考查利用函数单调性判断大小的问题，关键是能够利用奇偶性将自变量变到同一单调区间内，再通过指数、对数函数的单调性，利用临界值确定自变量的大小关系.7．【2020·天津市第一中学2020届高三下学期第四次月考】已知奇函数，且在()f x ()()g x xf x =上是增函数.若，，，则a ，b ，c 的大小关系为[0,)+∞2(log 5.1)a g =-0.8(2)b g =(3)c g =A. B. C. D. a b c <<c b a<<b a c<<b c a<<【答案】C【解析】【详解】因为是奇函数，从而是上的偶函数，且在上是增函数，()f x ()()g x xf x =R [0,)+∞，22(log 5.1)(log 5.1)a g g =-=，又，则，所以即，0.822<4 5.18<<22log 5.13<<0.8202log 5.13<<<，0.82(2)(log 5.1)(3)g g g <<所以，故选C ．b ac <<【考点】指数、对数、函数的单调性【名师点睛】比较大小是高考常见题，指数式、对数式的比较大小要结合指数函数、对数函数，借助指数函数和对数函数的图象，利用函数的单调性进行比较大小，特别是灵活利用函数的奇偶性和单调性数形结合不仅能比较大小，还可以解不等式.8．【2020·天津市东丽区耀华滨海学校高三年级上期第二次统练】已知，则0.20.32log 0.2,2,0.2a b c ===A. B. C. D. a b c <<a c b<<c a b<<b c a<<【答案】B 【解析】【分析】运用中间量比较，运用中间量比较0,a c 1,b c【详解】则．故选B ．22log 0.2log 10,a =<=0.20221,b =>=0.3000.20.21,<<=01,c a c b <<<<【点睛】本题考查指数和对数大小的比较，渗透了直观想象和数学运算素养．采取中间变量法，利用转化与化归思想解题.9．【2020·天津市和平区2020届高三高考二模】已知：，，，则a ，b ，c 的11ln 4a =113eb ⎛⎫= ⎪⎝⎭11log 3e c =大小关系为（ ）A. B. C. D. c a b >>c b a>>b a c>>a b c>>【答案】A 【解析】【分析】利用指数函数，对数函数的性质求解.【详解】因为，，11111ln ln log ln 343e e a c =<=<==1111033eb ⎛⎫⎛⎫<= ⎪ ⎪⎝⎭⎝⎭<=所以a ，b ，c 的大小关系为.c a b >>故选：A【点睛】本题主要考查指数函数，对数函数的性质，还考查了转化问题的能力，属于基础题.10．【2020·天津市河北区高三高考数学一模】已知函数f （x ）是定义在R 上的偶函数，且f （x ）在[0，+∞）单调递增，设a ＝f （），b ＝f （log 37），c ＝f （﹣0.83），则a ，b ，c 大小关系为（ ）A ．b ＜a ＜c B ．c ＜b ＜aC ．c ＜a ＜bD ．a ＜c ＜b【答案】C 【解析】根据题意，由偶函数的性质可得c ＝f （﹣0.83）＝f （0.83），又由指数、对数的性质可得0.83＜1log 3log 37，结合函数的单调性分析可得答案．根据题意，函数f （x ）是定义在R 上的偶函数，则c ＝f （﹣0.83）＝f （0.83），又由f （x ）在[0，+∞）单调递增，且0.83＜1log 3log 37，则有c ＜a ＜b ，故选：C ．【点评】本题考查函数的奇偶性与单调性的综合应用，涉及对数值的大小比较，属于基础题．11．【2020·天津市河北省区2019届高三总复习质量检测】.已知，则13241log 3log 72a b c ⎛⎫=== ⎪⎝⎭,，的大小关系为（ ）,,a b c A. B. C. D. a c b <<b a c<<c a b<<a b c<<【答案】A 【解析】【分析】容易得出，再根据对数函数的性质将b 化为与c 同底的对数，即可比较出大01,a <<12,12b c <<<<小.【详解】解：，，，所以.故选A.1312a ⎛⎫= ⎪⎝⎭ 01a ∴<<244log 3log 9log 71b c ==>=>b c a >>【点睛】本题考查指数与对数大小的比较，考查对数换底公式以及对数函数的单调性，属于基础题.12．【2020·天津市红桥区2020届高三高考二模】已知，，，则（ ）131log 2a =121log 3b =32log 3c =A. B. C. D. b a c >>a b c>>c b a>>a c b>>【答案】A 【解析】【分析】根据对数函数单调性得到，，，得到答案.01a <<l b >0c <【详解】，，，111333110log 1log log 123a =<=<=112211log log 132b =>=332log log 310c =<=故.b a c >>故选：A.【点睛】本题考查了利用对数函数单调性比较数值大小，意在考查学生对于函数性质的灵活运用.13．【2020·天津高三一模】已知函数．若，，()25x f x x =+131log 2a f ⎛⎫= ⎪⎝⎭(3log b f =．则a ，b ，c 的大小关系为（）()0.26c f =A. B. C. D. a b c >>a c b>>c a b>>c b a>>【答案】D 【解析】【分析】先根据对数函数与指数函数的性质，得到，，再根据函数单调性，即可判13310log log 12<<<0.261>断出结果.【详解】因为，，113333310log 1log log log lo 2g 312=<=<<=0.261>函数与都是增函数，所以也是增函数，2xy =5y x =()25x f x x =+因此，即.故选：D.(()0.21331log log 62f f f ⎛⎫< ⎪<⎝⎭c b a >>【点睛】本题主要考查由函数单调性比较大小，熟记指数函数与对数函数的性质即可，属于常考题型.14．【2020·天津市六校高三上学期期初检测】已知，，，则，，的大ln a π=lg125b =0.31c e ⎛⎫= ⎪⎝⎭a b c 小关系是（ ）A. B. a b c >>b a c >>C. D. 以上选项都不对c a b >>【答案】B 【解析】【分析】利用指数对数函数的图像和性质确定的范围即得它们的大小关系.,,a b c 【详解】由题得，2ln ln ln 2e a e π<=<=所以.12a <<,2lg125lg102b =>=,0.3011()1c e e ⎛⎫=<= ⎪⎝⎭所以.b a c >>故选：B【点睛】本题主要考查指数函数和对数函数的图像和性质，意在考查学生对这些知识的理解掌握水平.15．【2020·天津市南开区南开中学高三下学期第一次月考】设，则0.231012143a b og c lg =-==，，a ，b ，c 的大小关系是（ ）A. B. C. D. a c b<<b c a<<c a b<<c b a<<【答案】A 【解析】【分析】判断每个数的大致范围再分析即可.【详解】,,0.2221,0a >=∴< 331031,13log log b >=∴> ,,故选：A ．1410,01lg lg lg c <<∴<< a c b ∴<<【点睛】本题主要考查了函数值大小的关系,属于基础题型.16．【2020·天津高三一模】已知定义在上的函数满足，且函数在上是减函数，若 ，则的大小关系为（）A. B.C. D.【答案】A 【解析】【分析】化简，根据指数函数的单调性以及对数函数的单调性分别判断出，的取值范围，结合的单调性与奇偶性即可得结果.【详解】，是偶函数，，，，，，，又因为在上递减，，，即，故选A.【点睛】本题主要考查函数的奇偶性与单调性，以及指数函数与对数函数的性质，属于综合题. 在比较，，，的大小时，首先应该根据函数的奇偶性与周期性将，，，通过等值变形将自变量置于同一个单调区间，然后根据单调性比较大小．17．【2020·天津南开中学高三月考】已知奇函数在上是增函数，若，()f x R 21log 5a f ⎛⎫=- ⎪⎝⎭，，则的大小关系为()()2log 4.1b f =()0.82c f =,,a b c A. B. C. D. a b c <<b a c<<c b a<<c a b<<【答案】C 【解析】由题意：，且：，()221log log 55a f f ⎛⎫=-= ⎪⎝⎭0.822log 5log 4.12,122>><<据此：，结合函数的单调性有：，0.822log 5log 4.12>>()()()0.822log 5log 4.12f f f >>即.本题选择C 选项.,a b c c b a >><<【考点】 指数、对数、函数的单调性【名师点睛】比较大小是高考常见题，指数式、对数式的比较大小要结合指数函数、对数函数，借助指数函数和对数函数的图象，利用函数的单调性进行比较大小，特别是灵活利用函数的奇偶性和单调性数形结合不仅能比较大小，还可以解不等式.18．【2020·天津市实验中学滨海分校2020届高三模拟考试（】已知定义在R 上的奇函数满足()f x ，且在区间[1，2]上是减函数，令，，，则(2)()f x f x +=-ln 2a =121(4b -=12log 2c =的大小关系为（ ）(),(),()f a f b f c A. B. ()()()f b f c f a <<()()()f a f c f b <<C. D. ()()()f c f b f a <<()()()f c f a f b <<【答案】C 【解析】【分析】由满足，且在区间[1，2]上是减函数，确定在上是增函数，再由奇函数()f x (2)()f x f x +=-()f x [1,0]-性质得在上递增，在上单调递增．然后把自变量的值都转化到上，比较大小．()f x [0,1][1,1]-[1,1]-【详解】设，则，又在上递减，1210x x -≤<≤121222x x ≤+<+≤()f x [1,2]∴，而，，∴，即12(2)(2)f x f x +>+11(2)()f x f x +=-22(2)()f x f x +=-12()()f x f x ->-，∴在是递增，12()()f x f x <()f x [1,0]-∵是奇函数，∴在上递增，从而在上单调递增，，()f x ()f x [0,1][1,1]-(0)0f =，，，，ln 2(0,1)a =∈121()24b -==12log 21c ==-()(2)(0)0(0)f b f f f ==-==∴由得，即．10ln 2-<<(1)(0)(ln 2)f f f -<<()()()f c f b f a <<故选：C ．【点睛】本题考查函数的奇偶性与单调性．解题关键是确定函数的单调性，难点在于由满足()f x ，且在区间[1，2]上是减函数，确定在上是增函数，然后就是这类问题的常(2)()f x f x +=-()f x [1,0]-规解法，确定出上单调性，转化比较大小[1,1]-19．【2020·天津和平区高三第三次质检】设正实数分别满足，则,,a b c 2321,log 1,log 1a a b b c c ⋅===的大小关系为( ),,a b c A. B. C. D. a b c >>b a c>>c b a>>a c b>>【答案】C 【解析】【分析】把看作方程的根，利用数形结合思想把方程的根转化为函数图象交点的横坐标，则可以利用图象比,,a b c 较大小.【详解】由已知可得231112,log ,log ,a b c ab c ===作出函数的图象，它们与函数图象的交点的横坐标分别为，232,log ,log xy y x y x ===1y x =,,a b c 如图所示，易得.故选C.c b a >>【点睛】本题考查函数与方程，基本初等函数的图象.对于含有指数、对数等的方程，若不能直接求得方程的根，一般可以利用数形结合思想转化为函数图象的交点问题.20．【2020·天津市芦台一中2020届高三年级第二次模拟】已知定义在R 上的函数的图象关于()f x 1-对称，且当时，单调递减，若，，，则x 1=x 0>()f x ()0.5a f log 3=()1.3b f 0.5-=()6c f 0.7=a ，b ，c 的大小关系是 ()A. B. C. D. c a b >>b a c>>a c b>>c b a>>【答案】A 【解析】【分析】先根据对称性将自变量转化到上，再根据时单调递减，判断大小.0x >0x >()f x 【详解】∵定义在上的函数的图像关于对称，∴函数为偶函数，R ()1f x -1x =()f x ∵，∴，∴，，0.50.5log 3log 10<=()()0.52log 3log 3f f =2221log 2log 3log 42=<<= 1.31.30.522-=>．∵当时，单调递减，∴，故选A ．600.71<<0x >()f x c a b >>【点睛】比较两个函数值或两个自变量的大小：首先根据函数的性质把两个函数值中自变量调整到同一单调区间，然后根据函数的单调性，判断两个函数值或两个自变量的大小。
天津市第一中学2021届高三下学期第四次月考英语试题
2020-2021-2天津-中高三年级第四次月考英语听力测试卷听力A卷第一节（共5小题；每小题1分，满分5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你将有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
例: How much is the shirt?A. £19. 15.B. £9. 15C. £9. 181. What do the speakers need to buy?A. A fridgeB. A dinner table.C. A few chairs.2. Where are the speakers?A. In a restaurant.B. In a hotel.C. In a school3. What does the woman mean?A. Cathy won’t be at the party.B. Cathy is too busy to come.C. Cathy is going to be invited.4. Why does the woman plan to go to town?A. To pay her bills in the bank.B. To buy some books in a bookstore.C. To get some money from the bank.5. What is the woman trying to do?A. Finish some writing.B. Print an article.C. Find a newspaper.第二节（共10小题；每小题1. 5分，满分15分）听下面几段材料。
每段材料后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
天津市天津市第一中学2022届高三英语上学期第二次月考试题(含解析)
第I卷（选择题，共115分）
第一部分：听力测试（共两节，满分20分）
第一节听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷相应的位置。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话后仅读一遍。
【答案】B
【解析】
【详解】考查动词辨析。句意：春节期间，由于安全和噪音污染，我国大部分城市都取消了烟花表演。A. defended辩护；B. cancelled取消；C. burst爆炸；D. broadened拓展。根据句意可知选B。
5பைடு நூலகம்—I ________ so busily recently that I ________ no time to help you with your maths.
A. 2. B. 3. C. 4.
听第9段材料，回答第13至16题。
13. How did the woman probably find the party?
A. Boring. B. Exciting. C. Relaxing.
14. What did the man call the woman for yesterday?
8. What is the woman suffering from?
A. A headache. B. A fever. C. A severe disease.
9. Why didn’t the woman take any medicine?
A. Because she couldn’t find any in her house. B. Because her doctor asked her not to do that.
天津市第一中学2023-2024学年高三下学期第四次月考英语试卷
天津市第一中学2023-2024学年高三下学期第四次月考英语试卷学校:___________姓名：___________班级：___________考号：___________一、单项选择1．—Have you heard the news that Mrs Smith will be appointed as our head?— _______. She is just an assistant.A．You said it B．By all means C．You don’t say D．You bet2．-You look sleepy today.- ______not to miss the flight, I didn’t dare to close my eyes the whole night.A．Having reminded B．Reminded C．Being remindedD．To be reminded3．Some people think that watching violence on TV is one of the major causes of ______ behavior and crime in society.A．abstract B．ridiculous C．aggressive D．visual4．It is said that body language ________ 55 per cent of a first impression while what you say just 7 percent.A．lies in B．accounts forC．consists of D．goes with5．The magician picked several persons ______ from the audience and asked them to help with his performance.A．at random B．on the whole C．on average D．in general 6．Each means ______to solve the problem, but none is effective.A．have been tried out B．were tried out C．is tried outD．has been tried out7．I advise you to stay away from Mary. Although she is usually easy-going, she ______be quite annoying sometimes.A．can B．need C．must D．should 8．These MBAs are undeniably expensive and ______ pose the question as to how much value and payback they can provide.A．essentially B．absolutely C．consistently D．consequently 9．—Will you take over at the next service area? I want a short rest.—Sure. You ______ for over four hours by then.A．have driven B．have been drivingC．will be driving D．will have been driving10．In schools, it is required that no parent should ______to classrooms during class time.A．have possession B．have connection C．have accessD．have contact11．Don’t let such an unimportant matter as this come between us _____ we can concentrate on the major issue.A．so that B．in caseC．because D．on condition that12．When you visit Beijing, you can go to theaters and teahouses ________ you can experience a truly Chinese way of life.A．that B．which C．where D．when 13．— I’ve been eating a healthy diet for a year.— Oh, great! ______.A．Same to you B．Keep it up C．Cheer up D．Good luck 14．Dr. Hart says ______ he really admires is the way ______ she has acknowledged good health not only makes her more beautiful, but happier too.A．which, that B．that, what C．what, that D．that, which 15．If you see things in a negative light, you will find faults and problems where there are really ______.A．nothing B．some C．many D．none二、完形填空After a whole week of rain we finally had a comfortable, beautiful summer day outside. My family and I were driving to a nearby town when my daughter 16 a yard sale. Then, a few miles down the road, we saw another, and another, and another, We saw tables full of knickknacks. We saw plates, glasses, and silverware. 17 , we saw lots of smiling people talking, laughing, sitting, and standing in the sunshine.Seeing all of this brought back 18 of my childhood. Most of the clothes in my closet back then came from 19 . My mom was a talented yard sale-shopper. When I was little, she would drag me along with her. I used to 20 going to them, until onespecial day when I saw that they also sold old 21 . After that, I always browsed through the books until it was time to 22 . Sometimes mom would 23 me one too. Soon, a large part of my home library came from yard sale books. For me, these books were more 24 than their first editions.Why do we have yard sales? It certainly isn’t for the 25 . For all the time and 26 people put into them, they would hardly make minimum wage from the sales. I think, rather, it is yard sales that 27 us together. We 28 our old things and we buy “new” old things. We talk and 29 old friends and new neighbors. We get a 30 to give and share. We 31 through kindness and love among all the old stuff. It’s all about 32 , both in goods and between people.I think yard sales teach us something about 33 too. We can’t really34 anything here, after all; all we get is 35 possession of our stuff, then it comes time for us to let it go and pass it on.16．A．announced B．spotted C．prepared D．recalled 17．A．Even so B．In short C．At least D．Above all 18．A．problems B．memories C．realities D．dreams 19．A．markets B．neighbors C．yard sales D．shopping malls 20．A．imagine B．enjoy C．practice D．hate 21．A．books B．paintings C．plates D．toys 22．A．go B．start C．work D．register 23．A．award B．write C．buy D．lend 24．A．popular B．useful C．different D．priceless 25．A．fun B．money C．relaxation D．responsibility 26．A．love B．resource C．fund D．effort 27．A．mix B．bring C．guide D．inspire 28．A．get rid of B．put away C．go through D．make use of 29．A．pass by B．look for C．catch up with D．face up to 30．A．tradition B．goal C．chance D．job 31．A．extend B．connect C．learn D．compete 32．A．communication B．information C．deliveryD．exchange33．A．life B．ethics C．economy D．society 34．A．purchase B．explore C．own D．trust 35．A．temporary B．legal C．normal D．full三、阅读理解With the rapid development of computer science, the Internet is changing quickly out of our expectations. In the past, we just had the Internet while now we have the Internet of Things (IoT), which aims to get everything and everyone talking. Attaching sensors to “things”, such as cows, cars and refrigerators, and then assigning them unique IP addresses allow them to “talk” to the Internet. Of course, the IoT will involve much more than a handful of sensors. Networking company Cisco estimates that 50 billion Internet-connected devices and objects will be sending over data by 2020.36．How do researchers get everything and everyone talking?A．By establishing the IoT and launching a handful of sensors.B．By sending people to track them day and night and collect useful data.C．By communicating with them all the time through the IoT.D．By connecting sensors with them and appointing them unique IP addresses. 37．According to the passage, which of the following is NOT TRUE?A．IoT can help people do preventive maintenance and save money.B．IoT can help people monitor energy usage and observe price changes timely.C．IoT can help people adjust their habits and use electrical appliances more wisely.D．IoT can help people investigate things and update a lot of important data. 38．Besides its probably ending up being a fashion, what else do critics worry about the IoT?A．People will lose interest in it as quckly as the thrill over last year’s smartphone.B．Whether related companies will provide long-term software updates or not.C．Refrigerators and washing machines will be replaced by other devices in a few years.D．The software provided by companies will be outdated easily and quickly. 39．According to the passage, when owners of the Tesla Model S electric car received a recall notice, they ___.A．just waited in the car while the maintenance is being done through wireless update B．were required to go to the nearest 4S store to make some adjustments or repairsC．could definitely depend on the IoT to send them the charger plug to be fixedD．had to confirm the update with the help of the equipment provided by the company 40．What would be the best title for the passage?A．Craze is disappearing!B．It’s time to change!C．It’s all connected!D．The Internet is coming!It was a cold May morning when I received an intriguing (有趣的) email from an old high school friend inviting me to join a 10-day all-girls surf trip. I knew I had to say yes.The trip seemed simple enough. Ten women aged 30 to 45, all complete strangers, gathered on the coast of Portugal to try something new: surfing in the Atlantic Ocean.I have always loved traveling, so I eagerly sent an email to my boss seeking permission from him to make the once-in-a-life trip.If there’s one thing I’ve learned over my past 33 years, it’s that adults typically spend their days mastering the things they’ve done before. It seems like we pride ourselves on becoming experts in whatever field we’ve fallen into, knowing more and more about less and less.Now, in theory, this is a great strategy, as it allows you to become really, really good at one particular thing, but it also kind of ends up leaving some skills lacking.I met my new surfing companions on the grass of the hotel lawn in a small surf town called Ericeira. Despite our different personalities and backgrounds, we were all united in a relentless desire to challenge ourselves, learn, tackle and grow.The shores at Ericeira, where the beginners learn to surf, are shallow and covered with slippery rocks. They make for softer waves but are difficult to navigate.Guided by our amazing coaches, together, we faced the waves. Sometimes, it poured with rain, and the waves crashed around us, but we were still out there. And with every slip and fall, words of encouragement filled the air.Honestly, I probably spent most of my days frozen to the bone, but that didn’t matter because a new level of genuine joy and personal achievement had been unlocked. Learning a new skill taught me the humility that can come from doing badly at something new, and the pride that develops when you finally manage to grasp something you’ve been working on.While surfing might not be my calling, trying it out inspired me to take more risks in life, to step outside of my comfort zone and to never stop believing in myself. You never know what you’re capable of if you don’t go out there and try.41．What motivated the author to join the surf trip to Portugal?A．Her love for surfing and improving existing skills.B．Her desire to reconnect with a high school friend and make new friends.C．Her passion for embracing challenges and exploring new places.D．The chance to take a break in Portugal from work.42．What is the author’s view on adults focusing on mastering one field?A．It blocks creativity and exploration.B．It is essential for career success.C．It disturbs one’s work-life balance.D．It narrows one’s abilities.43．Which of the following words best describe the author’s surfing experience?A．Tough but rewarding.B．Relaxing but unpredictable.C．Difficult but interesting.D．Tiring but meaningful.44．What can be inferred about the author?A．She discovered her true calling atter the trip.B．She used to lack confidence in herself.C．She became more willing to challenge herself.D．She went on to become an expert surfer.45．What wisdom did the author gain from the experience with surfing?A．The need to seek professional training in all new skills.B．The value of pushing your limits and running the risk of something unpleasant.C．The benefit of exploring new places with unknown companions.D．The importance of being an expert in on field.The Internet has completely changed the workplace over the past three decades. Artificial Intelligence is now all set to do the same, and businesses that don’t take advantage of the technology risk being left behind.Global tech giants like Amazon have been leading the change, and businesses of all sizes are now using the technology for employing and managing their staff.Among them is L’Oreal. With about a million applicants for roughly 15,000 new positions each year, the company is using AI to hire.“We really wanted to save time and focus more on quality, diversity and candidate experience. And AI solutions were the best way to go faster on these challenges,” said Eva Azoulay, global vice-president of L’Oreal’s Human Resources Department.The company uses Mya, a chatbot, to save employers’ time during the first stage of the process. It handles routine questions from candidates, and checks details such as availability and visa requirements. Should candidates make it to the next round, they’ll run into Seedlink, an AI software that scores applicants based on their answers to open-ended interview questions. These scores don’t replace human judgment, said Azoulay, but they do exclude candidates who might not seem like obvious choices.Early results have been promising. For one internship program, where 12,000 people apply for about 80 spots, employers claim they saved 200 hours of time while hiring the most diverse group to date.Other businesses have gone beyond employment and are using AI to help manage employees. Some UK firms have started using Isaak, a system designed by the London-based company StatusToday, to track how many hours staff spend online and the number of emails they receive. London real estate agent JBrown has been using this system since March. CEO James Brown said it helps the firm understand employees’ habits and prevent them from overworking. “It enables us to solve bottleneck problems and relieve overburdened employees,” he said.Despite these examples of good practice, there is still a long way for AI to reach its full potential, and the technology comes with risks. Another AI danger could be its impact on jobs through automation.McKinsey predicts AI could add $13 trillion to the global economy by 2030, with early adopters doubling their cash flow over that period. But the demand for repetitive (重复的) or digitally-unskilled jobs could drop by around 10%, the consulting firm said in a 2018 report. 46．What can we learn about AI technology from Paragraph 1?A．It causes a great problem in workplace.B．It will become a necessary part of business.C．It requires businesses to invest much money.D．It will replace the Internet in the future.47．L’Oreal uses AI in its hiring process to _____.A．pick out the most suitable candidates directlyB．come up with more questions unlimitedlyC．improve the company’s hiring efficiencyD．save money by replacing human judgment48．What’s the meaning of the underlined word “exclude” in the 5th paragraph?A．Prepare.B．Consider.C．Remove.D．Include. 49．Firms with the system Isaak can _____.A．prevent their employees from surfing the InternetB．force their employees to form good working habitsC．monitor the contents of all their employees’ emailsD．help their employees avoid being overstressed at work50．What is the main idea of the passage?A．What AI will bring to the workplace.B．Why AI could be good for the workplace.C．How businesses can prepare for an AI future.D．How to use AI to improve workplace efficiency.Culture can affect not just language and customs, but also how people experience the world on surprisingly basic levels.Researchers, with the help of brain scans, have uncovered shocking differences in perception (感知) between Westerners and Asians, what they see when they look at a city street, for example, or even how they perceive a simple line in a square, according to findings published in a leading science journal.In western countries, culture makes people think of themselves as highly independent individuals. When looking at scenes, Westerners tend to focus more on central objects than on their surroundings. East Asian cultures, however, emphasize inter-dependence. When Easterners look at a scene, they tend to focus on surroundings as well as the object.Using an experiment involving two tasks, Dr Hedden asked subjects to look at a line simply to estimate its length, a task that is played to American strengths. In another, they estimated the line’s length relative to the size of a square, an easier task for the Asians. The level of brain activity, by tracking blood flow, was then measured by Brain Scanners. The experiment found that although there was no difference in performance, and the tasks were very easy, the levels of activity in the subjects’ brains were different. For the Americans, areas linked to attention lit up more, when they worked on the task they tended to find more difficult — estimating the line’s length relative to the square. For the Asians, the attention areas lit up more during the harder task also — estimating the line’s length without comparing it to the square. The findings are a reflection of more than ten years of previous experimental research into east-west differences.In one study, for instance, researchers offered people a choice among five pens; four red and one green. Easterners were more likely to choose a red pen while Westerners were more likely’ to choose the green one.Culture is not affecting how you see the world, but how you choose to understand and internalize it. But such habits can be changed. Some psychological studies suggest that when an Easterner goes to the West or vice versa, habits of thought and perception also begin to change. Such research gives us clues on how our brain works and is hopeful for us to developprograms to improve our memory, memory techniques and enhance and accelerate our learning skills.51．According to the passage, Chinese people are most likely to ___.A．more emphasize independent thinkingB．always focus more on their surroundingsC．think of Westerners as highly independent individualsD．focus more on the context as well as the object52．We know from the passage that people’s brains will be more active when ___.A．the task is much easier B．the blood flow is trackedC．the task is more difficult D．people begin to choose colors 53．What do the findings of the experiment mentioned in the 4th paragraph indicate?A．They indicate that culture has a great impact on the way people talk and behave.B．They show that Easterners and Westerners have great differences in perceiving the world.C．They suggest that people’s habits of thought and-perception can be changed indifferent cultures.D．They make it clear that Easterners and Westerners lay emphasis on different things. 54．It can be inferred from the passage that ____.A．Easterners prefer collectivism to individualismB．East Asian cultures lay more emphasis on independenceC．It took over ten years to find out how to improve our brainpowerD．Americans will change their habits of perception when they’re in Britain 55．Which of the following will be the best title of the passage?A．Chinese culture: why it has an advantage over Western culture?B．Western culture and Chinese culture: which will be more suitable for us?C．Western culture and Chinese culture: why we should learn from both?D．Western culture vs. Chinese culture阅读短文, 按照题目要求用英语回答问题。
天津市第一中学2023-2024学年高三第四次月考数学试卷(解析版)
天津一中2023—2024-2高三年级第四次月考数学试卷本试卷总分150分，考试用时120分钟．考生务必将答案涂写在答题卡上，答在试卷上的无效．一、选择题（本大题共9小题，每小题5分，共45分）1. 已知集合，则（ ）A. B. C. D. 【答案】C 【解析】【分析】根据题意，求得集合，结合集合交集的运算，即可求解.【详解】由不等式，解得，所以，又由，所以.故选：C.2. 将收集到的天津一中2021年高考数学成绩绘制出频率分布直方图，如图所示，则下列说法中不正确的是（ ）A. B. 高三年级取得130分以上的学生约占总数的65%C. 高三年级的平均分约为133.2D. 高三年级成绩的中位数约为125【答案】D 【解析】【分析】对于A ，由各个矩形面积之和为1即可列式求解；对于B ，求最右边两个矩形面积之和即可验算；对于C ，D 分别由平均数计算公式、中位数计算方法即可判断.{}{}2|3100,33A x x x B x x =--<=-≤≤A B = (2,3]-[)3,5-{1,0,1,2,3}-{3,2,1,0,1,2,3,4}---{}1,0,1,2,3,4A =-23100x x --<25x -<<{}1,0,1,2,3,4A =-{}33B x x =-≤≤{}1,0,1,2,3A B ⋂=-0.028a =【详解】对于A ，，故A 正确；对于B ，高三年级取得130分以上的学生约占总数的，故B 正确；对于C ，高三年级的平均分约为，故C 正确；对于D ，设高三年级成绩的中位数为，由于，所以，故D 不正确.故选；D.3. 已知，条件，条件，则是的（ ）A. 充分不必要条件 B. 必要不充分条件C 充要条件D. 既不充分也不必要条件【答案】A 【解析】【分析】结合绝对值的性质，根据不等式的性质及充分条件、必要条件的定义分析判断即可.【详解】因为，所以由得，故由能推出；反之，当时，满足，但是；所以是的充分不必要条件.故选：A .4. 函数的图象大致为（ ）A. B.C. D.【答案】B 【解析】.()1100.0010.0090.0250.037100.028a =-⨯+++÷=⎡⎤⎣⎦()0.0280.03710100%65%+⨯⨯=()1050.0011150.0091250.0251450.0281350.03710133.2⨯+⨯+⨯+⨯+⨯⨯=x 0.010.090.250.350.500.350.370.72++=<<+=130140x <<0a >:p a b >2:q a ab >p q 0a >a b >2a ab ab >≥:p a b >2:q a ab >10,2a b =>=-212a ab =>=-122a =<-=p q ()21cos 31x f x x ⎛⎫=-⋅ ⎪+⎝⎭【分析】根据函数奇偶性即可排除CD ，由特殊点的函数值即可排除A.【详解】，则的定义域为R ，又，所以为奇函数，图象关于原点对称，故排除CD ，当时，，故排除A .故选：B.5. 已知函数是上的偶函数，且在上单调递增，设，，，则a ，b ，c 的大小关系是（ ）A. B. C. D. 【答案】B 【解析】【分析】结合偶函数的性质，函数单调性，只需比较对数、分数指数幂的大小即可得解.【详解】因为函数是上的偶函数，且在上单调递增，所以，即.故选：B.6. 多项式展开式中的系数为（ ）A. 985B. 750C. 940D. 680【答案】A 【解析】分析】由二项式定理即可列式运算，进而即可得解.【详解】多项式展开式中的系数为.故选：A.7. 已知斜三棱柱中，为四边形对角线的交点，设三棱柱的体积【2()(1)cos 31xf x x =-⋅+()f x ()()()22321cos 1cos 1cos 313131x x x xf x x x x f x -⎛⎫⨯⎛⎫⎛⎫-=-⋅-=-⋅=-+⋅=- ⎪ ⎪ ⎪+++⎝⎭⎝⎭⎝⎭()f x πx =()ππ22π1cos π103131f ⎛⎫-=< ⎪++⎝⎭=-+()f x R ()f x [0,)+∞12e a f ⎛⎫= ⎪⎝⎭12b f ⎛⎫= ⎪⎝⎭1ln 2c f ⎛⎫= ⎪⎝⎭a b c <<b<c<ac<a<bb a c<<()f x R ()f x [0,)+∞()()1211ln 2ln 1e 22b f f f c f ff a ⎛⎫⎛⎫⎛⎫=<==<<== ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭b<c<a ()52(71)52x x++2x ()52(71)52x x++2x 32350555C 712C 7159805985⋅⋅⋅+⋅⋅⋅=+=111ABC A B C -O 11ACC A 111ABC A B C -为，四棱锥的体积为，则（ ）A. B. C. D. 【答案】A 【解析】【分析】如图，延长，连接，则、，进而得，即可求解.【详解】如图，延长，连接，则，所以，又O 为的中点，所以点到平面的距离是点到平面的距离的2倍，则，所以，即故选：A8. 已知函数（为常数，且）的一个最大值点为，则关于函数的性质，下列说法错误的有（ ）个.1V 11O BCC B -2V 21:V V =1:31:41:62:31OA 11,,OB OB A B 111123A BCC B V -=11122A BCC B V V -=12223V V =1OA 11,,OB OB A B 11111111,3A ABC A BCCB A ABC V V V V V ---=+=111123A BCCB V -=1AC 1A 11BCC B O 11BCC B 11111222A BCC B O BCC B V V V --==12223V V =2113V V =()sin cos f x a x b x =+,a b 0,0a b >>π3x =()sin 2cos 2g x a x b x =+①的最小正周期为；②的一个最大值点为；③在上单调递增；④的图像关于中心对称．A. 0个 B. 1个C. 2个D. 3个【答案】B 【解析】【分析】根据三角函数的性质，求的关系，再根据辅助角公式化简函数，再利用代入的方法，判断函数的性质.【详解】函数，，平方后整理为，所以，，函数的最小正周期为，故①正确；当时，，此时函数取得最大值，故②正确；当时，，位于单调递增区间，故③正确；，故④错误，所以错误的只有1个.故选：B9. 已知双曲线的左焦点为，过作渐近线的垂线，垂足为，且与抛物线交于点，若，则双曲线的离心率为（ ）A.B.C.D.【答案】B 【解析】()g x π()g x π6()g x 2π,π3⎛⎫⎪⎝⎭()gx 7π,012⎛⎫⎪⎝⎭,a b ()g x ()sin cos f x a x b x =+12b +=()20a =a π()sin 2cos 22sin 26g x x b x b x ⎛⎫=+=+ ⎪⎝⎭0b >()g x 2ππ2=π6x =πππ2662⨯+=()g x 2π,π3x ⎛⎫∈⎪⎝⎭π3π13π2,626x ⎛⎫+∈ ⎪⎝⎭77ππ4π2sin 22sin 0121263g b b π⎛⎫⎛⎫=⨯+=≠ ⎪ ⎪⎝⎭⎝⎭22221(0,0)x y a b a b-=>>1(,0)F c -1F P 212y cx =M 13PM F P =【分析】首先利用等面积法求出点坐标，再根据，求出坐标，再将坐标带入抛物线化简即可求解出双曲线离心率.【详解】据题意，不妨取双曲线的渐近线方程为，此时，，∴，且是直角三角形，设，则，，代入中，得，即；设,则，，由，则，，∴，则；又在抛物线上，，即，化简得，分子分母同时除以，，且，，.故选：B二、填空题（本大题共6小题，每小题5分，共30分）10. 已知，且满足（其中为虚数单位），则_________．【答案】2【解析】【分析】根据复数相等得到关于的方程组，解该方程组即可.【详解】由题意，可得，P 13PM F P =M M 212y cx =by x a=-1F P b =1OF c =OP a =1OPF (,)p p P x y 11122OPF p S ab cy== p aby c ∴=b y xa =-2p a x c =-2(,a ab P c c-(,)M xy 2,a ab PM x y c c ⎛⎫=+- ⎪⎝⎭ 221,,a ab b ab F P c cc c c ⎛⎫⎛⎫=-+= ⎪ ⎪⎝⎭⎝⎭ 13PM F P = 223a b x c c+=⋅3ab ab y c c -=⋅2234,b a ab x y c c -==2234(,)b a abM c c -M 212y cx =22243()12ab b a cc c-∴=()()()2222222222221612316123a b b aca c a c a a c ⎡⎤=-⇔-=--⎣⎦422491640c a c a -+=4a 4291640e e ∴-+=1e >2e ∴===e ∴=,R a b ∈(12i)(i)3i a b ++=-i 22a b +=,a b (12i)(i)3i a b ++=-(2)(2)i 3i a b a b -++=-所以，解得，所以.故答案为：211. 著名的“全错位排列”问题（也称“装错信封问题”是指“将n 个不同的元素重新排成一行，每个元素都不在自己原来的位置上，求不同的排法总数．”，若将个不同元素全错位排列的总数记为，则数列满足，．已知有7名同学坐成一排，现让他们重新坐，恰有两位同学坐到自己原来的位置，则不同的坐法有_________种【答案】【解析】【分析】根据数列递推公式求出项，再结合分步计数原理求解.【详解】第一步，先选出两位同学位置不变，则有种，第二步，剩下5名同学都不在原位，则有种，由数列满足，，则，，，则不同的做法有种.故答案为：.12. 已知在处的切线与圆相切，则_________．【答案】或【解析】【分析】根据导数的几何意义，求得切线方程，再由直线与圆相切，列出方程，即可求解.【详解】由函数，可得，则且，所以函数在处的切线方程为，即，又由圆，可得圆心，半径为，2321a b a b -=⎧⎨+=-⎩1575a b ⎧=⎪⎪⎨⎪=-⎪⎩222a b +=n n a {}n a 120,1a a ==()12(1)(3)n n n a n a a n --=-+≥9242776C 2121⨯==⨯5a {}n a 120,1a a ==()12(1)(3)n n n a n a a n --=-+≥()()321312a a a =-+=()()432419a a a =-+=()()5435144a a a =-+=2144924⨯=9242()ln f x x x =-1x =22:()4C x a y -+==a -0x y -=2()ln f x x x =-1()2f x x x=-'(1)1f '=(1)1f =()f x 1x =11y x -=-0x y -=22:()4C x a y -+=(,0)C a 2r =因为与圆，解得.故答案为：.13. 元旦前夕天津-中图书馆举办一年一度“猜灯谜”活动，灯谜题目中逻辑推理占，传统灯谜占，一中文化占，小伟同学答对逻辑推理，传统灯谜，一中文化的概率分别为，，，若小伟同学任意抽取一道题目作答，则答对题目的概率为______，若小伟同学运用“超能力”，抽到的5道题都是逻辑推理题，则这5道题目中答对题目个数的数学期望为______.【答案】 ①. ##②. 【解析】【分析】根据全概率公式求解概率，根据二项分布列的期望公式求解即可.【详解】设事件“小伟同学任意抽取一道题目作答，答对题目”，则.由题意小伟同学任意抽取一道逻辑推理题作答，则答对题目的概率为，根据二项式分布知，所以，即的数学期望为.故答案为：，14. 在中，设，，其夹角设为，平面上点满足，，交于点，则用表示为_________．若，则的最小值为_________．【答案】 ①. ②.【解析】【分析】由和三点共线，得到和，得出方程组，求得的值，得到，再由，化简得到，得出，结合基本不等式，即可求解.0x y -=C 2a =±±20%50%30%0.20.60.7X 0.5511201A =()0.20.20.50.60.30.70.55P A =⨯+⨯+⨯=0.2()5,0.2X B ~()50.21E X =⨯=X 10.551ABC ,AB a AC b ==u u u r r u u u r r θ,D E 2AD AB = 3AE AC =,BE DC O AO ,a b65AO DE DC BE ⋅=⋅ cos θ4355AO a b =+ ,,D O C ,,B O E 2(1)AO ta t b =+- ()33AO ua u b =+-2133t ut u =⎧⎨-=-⎩,t u 4355AO a b =+ 65AO DE DC BE ⋅=⋅ 2248209a b a b ⋅=+ 22209cos 48a b a bθ+=【详解】因为三点共线，则存在实数使得，又因为三点共线，则存在实数使得，可得，解得，所以，由，因为，可得，整理得，可得，所以又因为所以，当且仅当时，即时，等号成立，所以.故答案为：15. 设函数，若函数与直线有两个不同的公共点，则的取值范围是______.【答案】或或【解析】【分析】对于，当可直接去绝对值求解，当时，分和,,D O C t (1)2(1)AO t AD t AC ta t b =+-=+-,,B O E u ()()133AO u AB u AE ua u b =+-=+-2133t u t u =⎧⎨-=-⎩24,55t u ==4355AO a b =+ 32,2,3DE AE AD b a DC AC AD b a BE AE AB b a =-=-=-=-=-=- 65AO DE DC BE ⋅=⋅ 436()(32)(2)(3)555a b b a b a b a +⋅-=-⋅-2248209a b a b ⋅=+ 2248cos 209a b a b θ=+ 22209cos 48a b a bθ+=22209a b+≥ 22209cos 48a b a b θ+=≥ 22209a b = 3b cos θ4355AO a b =+ 22()21f x x ax ax =-++()y f x =y ax =a 2a <-21a -<<-2a >221y x ax =-+0∆≤0∆>a <-a >论，通过和图像交点情况来求解.详解】由已知，即，则必过点，必过，对于，当时，，此时恒成立，所以，令，即，要有两个不同的公共点，则，解得或或，当时，或当时，和图象如下：此时夹在其两零点之间的部分为，令，得无解，则有两个根有两个根，即有两个解，，符合要求；当和图象如下：【221y x ax =-+()1y ax x =-22()21f x x ax ax ax =-++=()2211x ax ax x -+=-()1y ax x =-()()0,0,1,0221y x ax =-+()0,1221y x ax =-+280a ∆=-≤a -≤≤2210x ax -+≥()222()2121f x x ax ax a x ax =-++=+-+()221a x ax ax +-+=()22210a x ax +-+=()21Δ442020a a a ⎧=-+>⎨+≠⎩2a -≤<-21a -<<-2a <≤280a ∆=->a <-a >a <-221y x ax =-+()1y ax x =-221y x ax =-+-2221x ax ax ax -+-=-+()221a x -=()2211x ax ax x -+=-()2211x ax ax x ⇔-+=-()22210a x ax +-+=()2Δ4420a a =-+>a <-a >221y x ax =-+()1y ax x =-或令，根据韦达定理可得其两根均为正数，对于①，则，解得，对于②，则，解得，综上所述，的取值范围是或或.【点睛】方法点睛：对于方程的根或者函数零点问题，可以转化为函数图象的交点个数问题，图象直观方便，对解题可以带来很大的方便.三、解答题（本大发共5小题，共75分）16. 已知中，角A ，B ，C 的对边分别为a ，b ，c ，且，．（1）求；（2）若，求的面积．【答案】（1（2【解析】【分析】（1）利用正弦定理求关系，再利用余弦定理求出，再利用两角和的正弦定理计算即可；（2）利用三角形的面积公式求解即可.【小问1详解】2210x ax -+=011⎧<<⎪⎪>3a >011⎧<<⎪⎪<3a <<a 2a <-21a -<<-2a >ABC sin cos sin 22C CB =2223a c b -=πsin 3B ⎛⎫+⎪⎝⎭1b =ABC ,,a b c cos B因为，所以，由正弦定理得，所以，即，所以，在中，，所以【小问2详解】由（1）得当时，，所以17. 已知四棱台，下底面为正方形，，，侧棱平面，且为CD 中点．（1）求证：平面；（2）求平面与平面所成角的余弦值；（3）求到平面的距离．【答案】（1）证明见详解 （2）sincos sin 22C CB =sin 2sinC B =2c b =2222223347b a b c b b +=+===a 222cos 2a cb B ac +-===ABC sin B ==π11sin sin 322B B B ⎛⎫+=== ⎪⎝⎭1b =2a c ==122ABC S =´´=1111ABCD A B C D -ABCD 2AB =111A B =1AA ⊥ABCD 12,AA E =1//A E 11BCC B 11ABC D 11BCC B E 11ABC D 15（3【解析】【分析】（1）直接使用线面平行的判定定理即可证明；（2）构造空间直角坐标系，然后分别求出两个平面的法向量，再计算两个法向量的夹角余弦值的绝对值即可；（3）使用等体积法，从两个不同的方面计算四面体的体积即可求出距离.【小问1详解】由于，，故，而，故四边形是平行四边形，所以，而在平面内，不在平面内，所以平面；【小问2详解】如上图所示，以为原点，为轴正方向，建立空间直角坐标系.则，，，，，，设平面与平面的法向量分别是和，则有和，1EAD B 11∥A B AB CE AB ∥11CEA B 1111122CE CD AB A B ====11CEA B 11A E B C ∥1B C 11BCC B 1A E 11BCC B 1//A E 11BCC B 1A 11111,,A A A D A B,,x y z ()2,0,0A ()10,1,0D ()2,0,2B ()10,0,1B ()10,1,1C ()()()()11110,0,2,2,1,0,2,0,1,0,1,0AB AD BB B C ==-=--=11ABC D 11BCC B ()1,,n p q r = ()2,,n u v w =11100n AB n AD ⎧⋅=⎪⎨⋅=⎪⎩ 212110n BB n B C ⎧⋅=⎪⎨⋅=⎪⎩即，，从而，，.故我们可取，，而，故平面与平面所成角的余弦值是.【小问3详解】设到平面的距离为，由于，而，所以.所以到平面18. 已知椭圆的左右顶点为A ，B ，上顶点与两焦点构成等边三角形，右焦点（1）求椭圆的标准方程；（2）过作斜率为的直线与椭圆交于点，过作l 的平行线与椭圆交于P ，Q 两点，与线段BM 交于点，若，求．【答案】（1）（2）【解析】【分析】（1）根据上顶点与两焦点构成等边三角形求出即可；（2）设出直线方程，利用弦长公式求出求出，，利用点到直线的距离求出点到直线的距离和点到直线的距离，再根据列式计算即可.【小问1详解】2020r p q =⎧⎨-+=⎩200u w v --=⎧⎨=⎩0r v ==2p q =20u w +=()11,2,0n = ()21,0,2n =-11cos ,5n 11ABC D 11BCC B 15E 11ABC D L 111111332E AD B AD B V LS L AD AB L -==⋅⋅⋅= 111142333E AD B B AD E AEB ABCD V V S S --==⋅⋅=⋅= 43=L =E 11ABC D 22221(0)x y a b a b +=>>(1,0)F A (0)k k >l M F N 2AMN BPQ S S =△△k 22143x y +=k =,a b AM PQ N AM B PQ 2AMN BPQ S S =△△由已知在等边三角形中可得，则椭圆的标准方程为为；【小问2详解】设直线的方程为：，联立消去得，则，得，，设直线的方程为：，设，联立，消去得，易知，则，所以，由得，所以直线的方程为，即，联立得，所以点到直线的22,a c b ====22143x y +=l ()2y k x =+()222143y k x x y ⎧=+⎪⎨+=⎪⎩y ()2222341616120k x k x k +++-=221612234M k x k --=+226834M k x k-=+226834Mk AM x k -=-=-=+PQ ()1y k x =-()()1122,,,P x y Q x y ()221143y k x x y ⎧=-⎪⎨+=⎪⎩y ()22223484120k x k x k +-+-=0∆>221212228412,3434k k x x x x k k-+==++PQ ==()2212134k k +=+226834M k x k -=+222681223434M k k y k k k ⎛⎫-=⋅+= ⎪++⎝⎭BM ()2221234268234kk y x k k +=---+()324y x k=--()()3241y x k y k x ⎧=--⎪⎨⎪=-⎩222463,4343k k N k k ⎛⎫+ ⎪++⎝⎭N AM点到直线，因为，所以，解得.【点睛】方法点睛：直线与椭圆联立问题第一步：设直线方程：有的题设条件已知点，而斜率未知；有的题设条件已知斜率，点不定，都可由点斜式设出直线方程．第二步：联立方程：把所设直线方程与椭圆方程联立，消去一个元，得到一个一元二次方程．第三步：求解判别式：计算一元二次方程根的判别式.第四步：写出根之间的关系，由根与系数的关系可写出．第五步：根据题设条件求解问题中的结论．19. 已知数列满足对任意的，均有，且，，数列为等差数列，且满足，．（1）求，的通项公式；（2）设集合，记为集合中的元素个数．①设，求的前项和；②求证：，．【答案】（1），B PQ 2AMN BPQ S S =△△()221211122234k k +=⨯+k =∆0∆>{}n a *N n ∈212n n n a a a ++=12a =24a ={}n b 11b =2105b b a +={}n a {}n b {}*1N n n k n A k a b a +=∈<≤n c n A ()2n n n p b c =+{}n p 2n 2n P *N n ∀∈122121111176n n c c c c -++++< 2n n a =32n b n =-（2）①；②证明过程见解析【解析】【分析】（1）根据等比中项的性质，结合等差数列的通项公式、等比数列的通项公式进行求解即可；（2）①根据不等式的解集特征，结合累和法、等比数列的前项和公式分类讨论求出的表达式，最后根据错位相减法进行求解即可；②运用放缩法，结合等比数列前项和公式进行运算证明即可.【小问1详解】因为数列满足对任意的，均有，所以数列是等比数列，又因为，，所以等比数列的公比为，因此；设等差数列的公差为，由；【小问2详解】因为，，所以由，因此有，即有，，当时，有于是有当为大于2的奇数时，()2122122n n P n n +=-⋅+-12322,n n k k +*<-≤∈N n n c n {}n a *N n ∈212n n n a a a ++={}n a 12a =24a ={}n a 212a a =1222n n n a -=⨯={}n b d ()210511932313132n b d d d b b n n a ⇒+++=⇒=⇒=+-=+-=2n n a =32n b n =-11,2322,nn n k n a b a k k k *+*+<≤∈⇒<-≤∈N N {}{}{}{}{}123452,3,4,5,6,7,8,9,10,11,12,13,,22A A A A A ===== {}623,24,,43,A =1234561,1,3,5,11,21,c c c c c c ======234512233445562,42,82,162,322,c c c c c c c c c c +=+==+==+==+== 12,n n n c c ++= 2,N n n *≥∈112,n n n c c --+=1112,n n n c c -+--=n ()()()243122431122221n n n n n n n c c c c c c c c -----=-+-+-+=+++++，显然也适合，当为大于2的偶数时，，显然也适合.①，，，设，则有，两式相减，得，，；②设，显然，，当时，有，因此，12214211143n n -⎛⎫- ⎪+⎝⎭=+=-11c =n ()()()244222442222221n n n n n n n c c c c c c c c -----=-+-++-+=+++++ 122214211143nn ⎛⎫- ⎪-⎝⎭=+=-21c =()()()21,21,N 221,2,Nn n n n n n n k k p b c n n k k **⎧+=-∈⎪=+=⎨-=∈⎪⎩()()212342121321242n n n n n P P P P P P P P P P P P P --=++++++=+++++++ ()()132124212132321221222424222n nn n n n -⎡⎤⎡⎤=⨯++⨯+++-⋅+-+⨯-+⨯-++⋅-⎣⎦⎣⎦()()()123212122232212221234212n n n n n n -⎡⎤=⨯+⨯+⨯++-⋅+⋅+-+-+--⎣⎦ ()()12321212223221222n n S n n -=⨯+⨯+⨯++-⋅+⋅ ()()234221212223221222nn S n n +=⨯+⨯+⨯++-⋅+⋅ 123212212222222n n n S n -+-=+++++-⋅ ()()2212121222212212n n n S n S n ++-⇒-=-⋅⇒=-⋅+-()2122122n n P n n +=-⋅+-()()11321k k k k c *+=∈+-N ()11332121k k k k c +=≤-+-()4213224k k k --⨯=-4,N k k *≥∈()()344213224042132212kk kkkk k--⨯=->⇒->⨯⇒<-()1133421221k k k k k c +=≤<-+-所以当时，，即，显然当时，有成立.【点睛】关键点点睛：本题的关键由可以确定从第几项开始放缩，根据数列的通项公式的形式，得到，这样可以进行放缩证明.20. 已知函数．（1）讨论的单调区间；（2）已知，设的两个极值点为，且存在，使得的图象与有三个公共点；①求证：；②求证：．【答案】（1）答案见解析 （2）证明见解析【解析】【分析】（1）首先求函数的导数，再讨论，结合函数的定义域，即可求函数的单调区间；（2）①要证，即证，只需证，构造函数，，借助导数即可得证；②同①中证法，先证，则可得，利用、是方程的两根所得韦达定理，结合即可得证.【小问1详解】，，N k *∈4512321111111111143222k k k c c c c c -⎛⎫+++++<++++++ ⎪⎝⎭ 43123211111111122114312k k k c c c c c --⎛⎫- ⎪⎝⎭⇒+++++<+++⨯- 312321111171171171322326k k k c c c c c --⎛⎫+++++<+-<+= ⎪⎝⎭ 2k n =122121111176n n c c c c -++++< 171111632=+++()1133421221k k k k k c +=≤<-+-2()24ln f x x ax x =-+()f x [4,6]a ∈()f x ()1212,λλλλ<b ∈R ()y f x =y b =()123123,,x x x x x x <<1212x x λ+>31x x -<∆1212x x λ+>2112x x λ>-()()1112f x f x λ<-()()()12x g x f x f λ=--()10,x λ∈2232x x λ+<()()2312123122x x x x x x λλ=++<---1λ2λ220x ax -+=[4,6]a ∈()()222422x ax f x x a x x-+'=-+=0x >其中，，当时，即，此时恒成立，函数在区间单调递增，当时，即或当时，在区间上恒成立，即函数在区间上单调递增，当，得或当时，，时，，所以函数的单调递增区间是和，单调递减区间是，综上可知，当的单调递增区间是；当的单调递增区间是和，单调递减区间是；【小问2详解】①由（1）知，当时，函数的单调递增区间是和，单调递减区间是，、是方程的两根，有，，又的图象与有三个公共点，故，则，()22tx x ax =-+28a ∆=-0∆≤a -≤≤()0f x '≥()f x ()0,∞+0∆>a <-a >a <-()0f x ¢>()0,∞+()f x ()0,∞+a >()0t x =1x =1x =0x <<x >()0f x ¢>x <<()0f x '<()f x ⎛ ⎝⎫+∞⎪⎪⎭a ≤()f x ()0,∞+a >()f x ⎛ ⎝⎫+∞⎪⎪⎭[4,6]a ∈()f x ()10,λ()2,λ+∞()12,λλ1λ2λ220x ax -+=122λλ=12a λλ+=()y f x =y b =()123123,,x x x x x x <<112230x x x λλ<<<<<1112x λλ->要证，即证，又，且函数在上单调递减，即可证，又，即可证，令，，由，则恒成立，故在上单调递增，即，即恒成立，即得证；②由，则，令，，则，故在上单调递增，即，1212x x λ+>2112x x λ>-1112x λλ->()f x ()12,λλ()()1122f x f x λ<-()()12f x f x b ==()()1112f x f x λ<-()()()12x g x f x f λ=--()10,x λ∈()()()()212222422x ax x x f x x a x x xλλ-+--'=-+==()()()()()112211122222x x xx x g x x λλλλλλλ------'=+-()()()()()1221112222x x x x x x x λλλλλλ+--+-=-⋅-()()222211*********x x x x x x xx x λλλλλλλλ-+++--+=-⋅-()()()()()12221111222420x x x x x x x λλλλλλλ--=-⋅=>--()g x '()10,λ()()()()111102g x g f f λλλλ<=--=()()1112f x f x λ<-112230x x x λλ<<<<<2322x λλ-<()()()22x h x f x f λ=--()2,x λ∈+∞()()()()()122221222222x x xx x h x x λλλλλλλ------'=+-()()()()()2112222222x x x x x x x λλλλλλ+--+-=-⋅-()()221122212222222x x x x x x xx x λλλλλλλλ-+++--+=-⋅-()()()()()22112222222420x x x x x x x λλλλλλλ--=-⋅=>--()h x '()2,λ+∞()()()()222202h x h ff λλλλ>=--=即当时，，由，故，又，故，由，，函数在上单调递减，故，即，又由①知，故，又，故.【点睛】关键点点睛：最后一问关键点在于先证，从而借助①中所得，得到.()2,x λ∈+∞()()22x f x f λ>-32x λ>()()3232f x f x λ>-()()32f x f x =()()3222f x f x λ>-2322x λλ-<122x λλ<<()f x ()12,λλ2322x x λ<-2232x x λ+<1212x x λ+>()()2312123122x x x x x x λλ=++<---2122λλ-==≤=31x x -<2232x x λ+<1212x x λ+>()()2312123122x x x x x x λλ=++<---。
天津市第一中学2020届高三语文上学期第一次月考试题PDF
天津一中2019-2020-1高三年级语文学科一月考质量调查试卷本试卷分第I 卷（选择题）和第II 卷（非选择题）两部分，共150分，考试时间150分钟。
考生务必将答案涂写在答题卡的规定位置上，答在试卷上的无效。
祝各位考生考试顺利!第Ⅰ卷（39分）一、语言文字运用（共24分，每小题3分）1.阅读下面的文字，完成题目①黄狗为了表示同主人的意见一致，也便在翠翠身边汪汪汪的吠着。
其余的商人皆笑着，一时不能走路。
祖父气嘘嘘．．．的赶来了，把钱强迫．．塞到那个人手里。
②洋先生不准他革命，他再没有别的路；从此决不能望有白盔白甲的人来叫他，他所有的抱负．．，志向，希望，前程，全被一笔勾销．．．．了。
至于闲人们传扬开去，给小D 王胡等辈笑话，倒是还在其次的事。
③古老的教堂和卡西莫多之间有种心电感应，相互吸引，意气相投．．．．，外表相像，使得他紧紧黏附于它，就像乌龟黏附在甲壳．．上一样，那凹凸不平的教堂正是他的甲壳。
④黛玉忙拦道：“这宝姐姐也忒胶柱鼓瑟．．．．，矫糅造作．．．．了。
这两首虽于史鉴上无考，咱们虽不曾看这些外传，不知底里，难道咱们连两本戏也没见过不成！”文中加点字的字音、字形及语段出处文常，全部正确的一项是（）A.气嘘嘘强．迫（qiǎng ）沈从文《边城》B.抱负一笔勾销鲁迅《阿Q 正传》C.甲壳．（qiào ）意气相投巴尔扎克《高老头》D.胶柱鼓瑟矫糅造作曹雪芹《红楼梦》2.下列加点字的注音全部正确的一项是（）A.休憩．（qì）蓦．然（mù）不更．事（gēng ）退避三舍．（shè）B.翕．张（xī）内讧．（hòng ）拧．毛巾（níng ）不稂．不莠（láng ）C.狡黠．（xié）噱．头（xué）冠．心病（guàn ）情不自禁．（jīn ）D.谙．熟（àn ）木讷．（nè）独角．戏（jiǎo ）钻．木取火（zuàn ）3.下列词语中没有错别字的一项是（）A.题纲发祥地别出心裁大海里捞针B.渎职敲竹杠步履为艰快刀斩乱麻C.忖度破天荒声名雀起人不可貌相D.幅员开倒车察言观色礼轻情意重4.下列词语中，字形和加点字的字音全部正确的一项是（）A.轻歌曼舞一年之季在于春拙．劣（zhuó）力能扛．鼎（gāng）B.雍荣典雅百炼钢化为绕指柔打烊．（yáng）寅吃卯．粮（mǎo）C.毋庸赘言流水不腐，户枢不蠹果脯．（fǔ）焚膏继晷．（guǐ）D.大厅广众盛名之下，其实难副履．历（lǚ）瘦削．不堪（xuē）5.下列句子中，词语使用最恰当的一项是（）①据英国广播公司报道，3·11日本大地震五周年之后，录像、证言的公开在世人面前愈发模糊，福岛第一核电站事故真相越来越了。
天津市第一中学2022-2023学年高三上学期第一次月考英语试题
天津一中2022-2023-1高三年级一月考英语试卷第I卷（选择题，共115分）第一部分：听力测试（共两节，满分20分）第一节(共5小题；每小题1分，满分5分)听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你将有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1.What does the man mean?A.The alarm bell is very good.B.The gate keeper should replace the alarm bell.C.They don’t have to change the alarm bell.2.When will the man arrive?A.At8:45.B.At9:15.C.At9:50.3.Who will make the decision?A.The man.B.The woman.C.The waiter.4.Where does this conversation take place?A.At an airport.B.At a railway station.C.At a post office.5.Why was the man late?A.His daughter was sick.B.He didn’t want to work.C.He had a stomachahce.第二节（共10小题，每小题1.5分，满分15分）听下面3段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段材料读两遍。
听第6段材料，回答第6至8题。
6.How long did the man sleep last night?A.For five hours.B.For two hours.C.For three hours.7.Why didn’t the man come to the party?A.He didn’t like the party.B.He got home late.C.He left work late and had a headache.8.What does the woman advise the man to do first?A.Take a sleep pill.B.Take a painkiller.C.Have some exercise.听第7段材料，回答第9至11题。
天津市第一中学2022-2023学年高三上学期第三次月考英语试题(含答案)
天津一中2022-2023-1高三年级英语学科第三次月考试卷第I卷（共95分）本试卷分为第I卷（选择题）、第II卷（非选择题）和第III卷（听力）三部分，共150 分, I卷、第II卷考试用时100分钟。
第I卷4页，第II卷1页，第III卷2页。
考生务必将答案涂写规定的位置上, 答在试卷上的无效。
祝各位考生考试顺利!第一部分英语知识运用（共两节,满分45分）第一节单项填空（共15小题；每小题1分，满分15分）从A、B、C、D四个选项中,选出可以填入空白处的最佳选项。
1. —Going to the pub Viking Burger to watch the final of the World Cup tonight?—______! Will you join us?A. You thereB. You betC. You got meD. You know better2. The Five Avenues Area is a very popular tourist ______ in Tianjin.A. digestB. drawC. distinctionD. division3. For a senior high student, ______ good use you have made of your time to study, there is still room for improvement.A. whateverB. howeverC. thoughD. whether4. With the ever-serious pollution, many species, including endangered ones, are known ______ by ocean plastics in the past decades.A. to have been affectedB. to have affectedC. having been affectedD. having affected5. Sometimes parents’ control of young kids will be thought to be such an invisible rope with which to tie them tightly that they ______ tried to cut it.A. extremelyB. thoroughlyC. desperatelyD. obviously6. There is a sign over there, saying no person ______ bring food and drinks into the reading room.A. shallB. shouldC. willD. must7. Such a simple experiment ca n effectively ______ people’s doubts about the new technology, so they are willing to embrace the innovation.A. bring forthB. go overC. put awayD. wipe out8. The Palace Museum is ______ the royal families used to live and it’s now a historical museum with collections of valuable antiques.A. whatB. whichC. whereD. how9. Prof. Wu says that the best way to help the tradition ______ is passing it down from generation to generation.A. surviveB. recoverC. preserveD. function10. Although members of one culture do not express their emotions as openly as _______ of another do, it does not mean that they do not experience emotions.A. itB. oneC. thatD. those11. Cambridge University says it ______ gaokao scores for years, requiring the admitted students to rank in the top 0.1 percent on the test in their province.A. has been consideringB. had consideredC. is consideringD. considers12. Hate speech on the internet causes violence, undermines diversity and social unity, thus ______ the common values and principles that bind us together.A. to threatenB. having threatenedC. threateningD. threatened13. Reciting does much good in language learning and it ______ helps to learn science subjects better.A. in returnB. by chanceC. in turnD. for once14. China will allow all couples to have three children, ______, in my opinion, is helpful to cope with the increasingly aging society.A. thatB. whichC. whatD. who15. —Because they were all team players, the task was fulfilled.—Well, ______.A. a bird in the hand is worth two in the bushB. a good beginning is half doneC. where there is a will, there is a wayD. many hands make light work第二节完形填空（共20小题；每小题1.5分，满分30分）阅读下面短文,从16-35各题所给的A、B、C、D四个选项中,选出最佳选项。
天津市耀华中学2024-2025学年高三上学期第一次月考英语试卷(含答案)
天津市耀华中学2025届高三年级第一次月考英语试卷第Ⅰ卷(共115分)第一部分：听力(共两节，满分20分)第一节(共5小题;每小题1分，满分5分)听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C 三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你将有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What will the man do nextA. Get something to drink.B. Have a meeting.C. Make a phone call.2. What does the man advise the woman to doA. Take some exercise.B. Creates new ideas.C. See a doctor.3. How will the boy go home nowA. By bike.B. By bus.C. By underground.4. Why didn’t the woman buy the coatA. It di dn’t fit her.B. It would cost her too much.C. She didn’t like it very much.5. Where are the speakersA. At the man’s house.B. In a hospital.C. At a drugstore.第二节(共10小题;每小题1.5分，满分15分)听下面几段材料。
每段材料后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段材料前，你将有时间阅读各个小题，每小题5秒钟;听完后，各小题将给出5秒钟的作答时间。
每段材料读两遍。
听下面一段对话，回答第6至第8小题。
6. What are the speakers mainly talking aboutA. The arrangement of a trip.B. The details of the matches.C. The plan for their holiday.7. What will the team do in ScotlandA. Go to the beach.B. Play five matches.C. Go to the mountains.8. How many matches will the team play in GreeceA. Two.B. Thee.C. Four.听下面一段对话，回答第9至第11小题。
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2019-2020-2天津一中高三年级第四次月考英语听力测试卷试卷A（选择题，共20分）第一节（共5小题；每小题1分，满分5分）听下面五段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你将有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1．Which color does the man prefer?A．Blue.B．Red.C．White.2．Where does this conversation probably take place?A．At a repair shop.B．At a gas station.C．In a parking lot.3．What do we know from this conversation?A．The wind has stopped.B．The rain has stopped.C．It is still raining.4．What does the woman tell us about Paul?A．He spends too much money.B．He likes expensive watches.C．He really does like television.5．What is the most probable relationship between the speakers?A．Schoolmates.B．Colleagues.C．Partners.第二节（共10小题；每小题1.5分，满分15分）听下面几段材料。
每段材料后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段材料前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段材料读两遍。
听下面一段对话，回答第6至第8小题。
6．Why does the man want to go to Florida?A．To have a holiday.B．To attend a sports meet.C．To get some information.7．What sport is the man probably interested in?A．Golf.B．Tennis.C．Sailing.8．Where does the conversation probably take place?A．In a bookstore.B．In a sports center.C．In a travel agency.听下面一段对话，回答第9至第11小题。
9．What are the speakers mainly talking about?A．An art project.B．Art homework.C．A famous painting.10．How does the man feel about the woman’s message?A．Excited.B．Confused.C．Disappointed.11．Why is the man going to the art room?A．To talk to the teacher.B．To see a new painting.C．To sign up for a class trip.听下面一段独白，回答第12至第15小题。
12．Who is the speaker?A．A librarian.B．An officer.C．A student.13．What is the function of the Student Center?A．To offer job opportunities.B．To assist students to register.C．To provide services and amusement.14．Where will the students register?A．In the library.B．In the lecture hall.C．In the Student Center.15．What is the main topic of the talk?A．How to use the library.B．Some important locations on campus.C．Assistance offered by the Student Center.2019-2020-2天津一中高三年级四月考英语听力测试卷试卷B（选择题，共20分）第一节（共5小题；每小题1分，满分5分）听下面五段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你将有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1．Where does this conversation most probably take place?A．At a gym.B．At a bus stop.C．At a train station.2．What are the speakers talking about?A．A historical book.B．A western movie.C．A science course.3．How does the woman feel?A．Tired.B．Excited.C．Hungry.4．What will the man probably do?A．Lend the woman some money.B．Pay for the woman’s lunch.C．Get the woman’s purse.5．What does the man mean?A．He does not enjoy classical music.B．He is not interested in the CD.C．He has heard the new CD.第二节（共10小题；每小题1.5分，满分15分）听下面几段材料。
每段材料后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段材料前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段材料读两遍。
听下面一段对话，回答第6至第8小题。
6．How long will the man have to wait for a one-bedroom apartment?A．For a month.B．For two weeks.C．For three weeks.7．How much should one pay for a two-bedroom apartment?A．$150a month.B．$175a month.C．$185a month.8．What does the woman probably do?A．A hotel clerk.B．A house agent.C．A housekeeper.听下面一段对话，回答第9至第11小题。
9．Why does the woman talk to the professor?A．She wants to take an advanced course.B．She wants him to recommend books.C．She wants him to give her a good grade.10．How does the woman feel about the course she has already taken?A．Much too easy.B．Hard to keep up.C．Unsatisfied with her grade.11．What does the professor promise to do?A．Ask another professor for his opinion.B．Let her register for an easier course.C．Pick out some books for her.听下面一段独白，回答第12至第15小题。
12．Why does the speaker introduce Pugh?A．Pugh is a well-known person.B．The speaker admires Pugh.C．Pugh is often seen on TV.13．What did Pugh say in a TV interview?A．The swim could raise awareness of crises.B．It was dangerous to swim in the ocean.C．He once considered quitting the swim.14．Why did Pugh swim in the Arctic Ocean?A．To become a top swimmer.B．To be close to wildlife in the ocean.C．To show his concern about climate change.15．What made Pugh interested in animals and environment?A．His childhood in England.B．His experiences in South Africa.C．The challenges he met in the ocean.2019-2020-2天津一中高三年级第四次月考英语试卷本试卷分为第I卷（选择题）、和第II卷（非选择题）两部分，共130分，考试用时100分钟。
考生务必将答案填写在答题卡上，答在试卷上的无效。
考试结束后，将答题卡交回。
祝各位考生考试顺利!第I卷（选择题，共95分）第一部分英语知识运用（共两节，满分45分）第一节单项填空（共15小题；每小题1分，满分15分）从A、B、C、D四个选项中，选出可以填入空白处的最佳选项。
1.The paper was due next month,and I am working seven days______week,often long into______night.A.a,theB.the,/C.a,aD./,the2.Studying hard is,of course,important,but enough rest is no doubt______or even more important.rgelyB.merelyC.equallyD.partly3.______skills,David is believed to be one of the best and most talented basketball players in our team.A.In need ofB.In favor ofC.In terms ofD.In honor of4.Believe it or not,some English idioms are very difficult to understand______you know the meaning of each word.A.as ifB.in caseC.now thatD.even if5.To produce the goods satisfying the environmental______,the company has brought in advanced technology to remove the chemicals in the course of production.A.burdensB.requirementsC.pollutionD.evolution6.Mr.Li is a good man who always thinks more of others than himself,______we should follow the example of.A.itB.himC.oneD.that7.No country in the world can______these problems alone,such as climate change, hunger and disease,etc.Therefore,all the countries should cooperate to get rid of them.A.addressB.cancelC.replaceD.involve8.Before we come to a decision,we must make sure we have______all the relevant facts.A.set foot onB.set fire toC.made way forD.taken account of9.Delete the short message at once!Many a man______by such tricks up to now.A.are cheatedB.is cheatedC.have been cheatedD.has been cheated10.-I’m travelling to Iceland next week.Would you tell me about your experiences there?-______.Let’s talk about it over coffee.A.By all means.B.Take your time.C.That’s all right.D.It’s up to you.11.Despite some difficulties,there are special moments______make it worthwhilefor moms to take care of children at home.A.whenB.whereC.whichD.what12.The energy program______at reducing our dependence on fossil fuels hasmade considerable breakthroughs in the past decades.A.aimB.aimedC.being aimingD.to aim13.We______him that he ought to make the bar more attractive with variousmethods.He finally sees the light.A.toldB.would tellC.have been tellingD.had told14.For British people,somebody standing too close may make them focus less onwhat others are saying than on______close he or she is to them.A.whatB.whereC.whichD.how15.The beautiful girl chose to teach in a village school,though she_____in a big city for an easier life.A.could stayB.could have stayedC.must have stayedD.must stay第二节完形填空（共20小题；每小题1.5分，满分30分）阅读下面短文，掌握其大意，然后从16-35各题所给的四个选项A、B、C、D四个选项中，选出最佳选项。