湖南四大名校内部资料试卷-长沙市第一中学2019-2020高一第一学期期中

2019-2020学年高一上英语期中模拟试卷含答案第Ⅰ卷选择题第一部分：听力（共两节，满分２０分）请听下面５段对话，选出最佳选项．1. Which sport does the woman like best?A.BaseballB.BadmintonC.Volleyball2. What are the two speakers going to do ?A.Going shoppingB.See a filmC. Have hair cut.3. Where does the conversation probably take place?A. At a hospital.B.At a shopC.At a post office.4. What’s the probable relation between the two speakers?A.Colleagues.B.Friends.C.Couple.5. What does the woman probably do?A.A reporter.B.A student.C.A tour guide.第二节请听下面５段对话或独白，选出最佳选项．请听第６段对话材料，回答第６—７题６. What happened to the man?A.He lost his job.B.He failed his final test.C.He was late for school.7. How is the man’s feeling to the woman?A.Frightened.B.Grateful.C.Disappointed.请听第７段材料，回答第８—９题．8. Where will the woman take the boys to?A. SchoolB.ParkC.Hospital9. What is the man planning to do?A.Open a savings account.B.Bake a birthday cake.C.Buy a birthday present. 请听第８段材料，回答第10—12题．10. What kind of music does the woman prefer?A.Classical music.B.Pop music.C.Country music.11. What does the man say about classical music？A.He listens to it when cooking.B.It is good for his brain.C.It can help reduce stress.12. What does the woman tell the man in the end?A.He can find some recordings on the Internet.B.He can buy some new CDs online.C.He can listen to Mozart’s music.请听第９段材料，回答第13—16题。

2019-2020学年湖南省长沙市第一中学高一上学期期中数学试题一、单选题1．设集合{|21,}A x x k k ==+∈Z ，则（ ） A ．3A ⊆ B ．3A ∈ C ．3A ∉ D ．3 A【答案】B【解析】根据元素与集合的关系以及表示方法即可求解. 【详解】由21,x k k =+∈Z ，可得x 表示的是奇数， 所以3A ∈， 故选：B 【点睛】本题考查了元素与集合之间的关系以及表示方法，属于基础题. 2．下列函数既是偶函数又有零点的是（ ） A ．21y x =+ B ．||2x y = C ．2y x x =+ D ．1lg ||y x =+【答案】D【解析】利用函数的奇偶性定义以及函数的零点定义即可求解. 【详解】对于A ，函数21y x =+为偶函数，令210y x =+=，方程无解，故函数无零点，A 不选；对于B ，函数||2x y =为偶函数，令||20x y ==，方程无解，故函数无零点，B 不选；对于C ，函数2y x x =+为非奇非偶函数，C 不选；对于D ，函数1lg ||y x =+为偶函数，令1lg ||0y x =+=，解得110x =±，故函数有零点，D 符合题意； 故选：D 【点睛】本题考查了函数的奇偶性以及函数的零点，需掌握函数奇偶性定义和零点定义，属于基础题.3．函数f （x ），g （x ）由如下表格给出，则f （g （3））=（ ）A ．4B ．3C ．2D ．1【答案】A【解析】通过表格求出g （3）的值，然后求解f （g （3））的值． 【详解】由表格可知，g （3）＝2， ∴f （g （3））＝f （2）＝4． 故选：A ． 【点睛】本题考查函数值的求法，考查两次对应，考查计算能力．4．函数()f x 为定义在R 上的奇函数，当0x ≥时，()4x f x m =+，则12f ⎛⎫-= ⎪⎝⎭( ) A ．1 B ．2- C ．1-D ．32-【答案】C【解析】由题意可得()00f =，进而求出1m =-，再利用函数为奇函数可得1122f f ⎛⎫⎛⎫-=- ⎪ ⎪⎝⎭⎝⎭，代入解析式即可求解 【详解】由函数()f x 为定义在R 上的奇函数，当0x ≥时，()4xf x m =+，则()00f =，即040m +=，解得1m =-， 所以()41xf x =-又1122f f ⎛⎫⎛⎫-=- ⎪ ⎪⎝⎭⎝⎭，1214112f ⎛⎫=-= ⎪⎝⎭，所以112⎛⎫-=- ⎪⎝⎭f ， 故选：C 【点睛】本题考查了奇函数的性质，利用函数的奇偶性求函数值，解题的关键是求出参数值，属于基础题.5．函数()f x 与()xg x a =互为反函数，且()g x 过点()2,4-，则()()12f f +=( )A ．1-B ．0C ．1D ．14【答案】A【解析】利用反函数的定义以及性质求出()f x 的解析式，代入即可求解. 【详解】由题意可得()log a f x x =，又()g x 过点()2,4-，则()4,2-在()f x 上，即2log 4a -=，解得12a =，所以()12log f x x =，所以()()1122log 1l 1og 20121f f +=+=-=-，故选：A 【点睛】本题考查了指数函数与对数函数的关系以及反函数的性质，属于基础题.6．根据表格中的数据，可以断定方程e 20x x --=的一个根所在的区间是( )A ．(1,0.5)-B ．()1,0-C ．()1,2D ．()2,3【答案】C【解析】利用零点存在性定理即可判断.【详解】令()2xf x e x =--，由表中数据可得()1 2.7230.280f =-=-<，()27.394 3.390f =-=>，所以()()120f f ⋅<， 故函数零点所在的区间为()1,2. 故选：C 【点睛】本题考查了零点存在性定理的应用，需熟记定理的内容，属于基础题.7．如图，在直三棱柱111ABC A B C -(侧棱1AA 垂直于底面ABC 中，D 为11A B 的中点，12AB BC BB ===，25AC =，则异面直线BD 与AC 所成的角为（ ）A ．30°B ．45°C ．60°D ．90°【答案】C【解析】取11B C 的中点E ，连接,DE BE ，得BDE ∠或其补角为所求，在DEB ∆中求解角即可. 【详解】如图，取11B C 的中点E ，连接,DE BE ，则11DE AC AC P P ， 故BDE ∠或其补角为所求异面直线BD 与AC 所成的角，又5BD BE ==5DE所以DEB ∆为等边三角形，所以60DEB ∠=o ， 故选：C 【点睛】本题考查了求异面直线所成角的大小，解题的关键是找到与异面直线所成角的大小相等的两角，属于基础题.8．我们处在一个有声世界里,不同场合,人们对声音的音量会有不同要求．音量大小的单位是分贝()dB ,对于一个强度为I 的声波，其音量的大小η可由如下公式计算：10lgII η=⋅(其中0I 是人耳能听到的声音的最低声波强度)，设170dB η=的声音强度为1I ，260dB η=的声音强度为2I ，则1I 是2I 的（ ） A ．76倍 B ．10倍C ．7610倍D ．7ln 6倍【答案】B【解析】根据题意代入170dB η=，260dB η=，得到方程组，然后将两式相减，整理化简后得到12I I 的值，得到答案. 【详解】因为010lgI I η=⋅， 代入170dB η=，260dB η=，得10207010lg 6010lg I I I I ⎧=⋅⎪⎪⎨⎪=⋅⎪⎩，两式相减，得12001010lglg I I I I ⎛⎫=⋅- ⎪⎝⎭得到12lg1I I =，即1210II =， 故选：B. 【点睛】本题考查利用已知函数模型解决问题，对数运算公式，属于简单题. 9．下列不等式中不成立的是（ ）A ．0.50.556<B ．22log 3log 5<C ．0.23log 0.83-<D ．0.30.40.10.1<【答案】D【解析】利用指数函数、对数函数、幂函数的图像与性质，即可判断. 【详解】对于A ，0.5y x =为增函数，0.50.556∴<，故A 正确； 对于B ，2log y x =为增函数，22log 3log 5∴<，故B 正确； 对于C ，33log 0.8log 10<=，0.230->，0.23log 0.83-∴< ，故C 正确；对于D ，0.1xy =为减函数，则0.30.40.10.1>，故D 不正确； 故选：D 【点睛】本题考查了指数函数、对数函数、幂函数的性质，属于基础题.10．若三棱锥P ABC -中，PA PB ⊥，PB PC ⊥，PC PA ⊥，且1PA =，2PB =，3PC =，则该三棱锥外接球的表面积为（）A ．72π B ．14π C ．28π D ．56π【答案】B【解析】将棱锥补成长方体，根据长方体的外接球的求解方法法得到结果. 【详解】根据题意得到棱锥的三条侧棱两两垂直，可以以三条侧棱为长方体的楞，该三棱锥补成长方体，两者的外接球是同一个，外接球的球心是长方体的体对角线的中点处。

一中高一第三次月考数 学时量：120分钟 满分：150分一、选择题(共12小题，每小题5分，共60分)1.若集合{}2,0,2M =-，{}220N x x x =+=，则M N =( ) A.{}2- B.{}0 C.{}2,0-D.{}2,0,2- 2.经过点()0,1，斜率为1的直线的方程为( )A.10x y +-=B.10x y -+=C.10x y ++=D.10x y --= 3.已知函数()27x f x x =+-，则()f x 的零点所在的区间为( )A.()0,1B.()1,2C.()2,3D.()3,4 4.已知函数()()3,f x ax bx a b =+∈R ，()2log 310f =，则12log 3f ⎛⎫= ⎪⎝⎭( ) A.10 B.10- C.110 D.110- 5.已知函数()()1223,3log 1,3x x f x x x +⎧+≤⎪=⎨-->⎪⎩，且()2f a =-，则()7f a -=( ) A.72B.52C.34-D.14- 6.函数()lg 10x f x x =⋅的图象是( )A. B. C. D.7.已知圆锥的母线长为5，高为4，则这个圆锥的表面积为( )A.21πB.24πC.33πD.39π8.已知函数()ln f x x =，若()2a f =，()0.32b f =，()2log 5c f =，则( )9.已知直线l 经过两直线320x y -+=和25180x y +-=的交点，且垂直于4350x y --=，则直线l 的方程为( )A.34200x y +-=B.34200x y ++=C.3440x y --=D.43100x y --=10.已知a ，b 为不同的直线，α，β为不重合的平面，则下列说法中正确的个数是( )①若//a b ，b a ⊂，则//a α.②若a b ⊥，则a ，b 相交③若//a α，//b α，则//a b④若a α⊥，b β⊥，//αβ，则//a bA.0B.1C.2D.311.已知三棱锥P ABC -的所有顶点都在球O 的球面上，PA ⊥平面ABC ，6AB =，8BC =，10AC =.若三棱锥P ABC -的体积为16，则球O 的表面积为( ) A.3043π B.3113π C.108π D.104π12.用()C A 表示非空集合A 中的元素个数，定义()()()()()(),,C B C A C B A B C A C A C B ≥⎧⎪*=⎨<⎪⎩.若{}1,2,3A =，()(){}22220B x x ax x ax =+++=，且3A B *=，则实数a 的取值范围是( )A.()22,⎡-∞-+∞⎣， B.(()22-∞-+∞，，C.⎡-⎣D.(-二、填空题(本大题共4个小题，每小题5分，共20分) 1lg 2⎫- 14.一条光线从点()1,1A -出发射向x 轴，经过x 轴上的点P 反射后经过点()2,5B ，则点P 的坐标为__________.15.若不等式210x x a +-+>在区间()2,2-上恒成立，则实数a 的取值范围是__________.16.设()2x xe ef x --=，()2x x e eg x -+=，给出如下结论： ①()f x 为奇函数且在R 上单调递增；②对任意实数x ，都有()()()222g x g x f x ⎡⎤=+⎡⎤⎣⎦⎣⎦； ③存在实数0x ，使()()22000g x f x -=⎡⎤⎡⎤⎣⎦⎣⎦；④对任意实数x ，都有()()()22f x f x g x =.其中所有正确结论的序号是__________.三、解答题(本大题共6个小题，共70分)17.(本小题满分10分)已知对数函数()f x 过点()8,3(1)求函数()f x 的解析式，并写出函数()f x 的定义域；(2)若()()11f x f x ->+，求x 的取值范围.18.(本小题满分12分)如图，在三棱柱111ABC A B C -中，1AA AC ⊥且1AA AC =，点E ，F 分别为11B C 和BC 的中点，1B A 与1A B 相交于点G .(1)证明：平面//EFG 平面11A ACC ；(2)求异面直线GE 和AC 所成角的大小.已知直线()():311530l m x m y m +++--=(1)求证：无论m 为何实数，直线l 恒过一定点M ；(2)若直线l 与x 轴、y 轴分别相交于A ，B 两点，点M 为线段AB 的中点，求直线l 的方程.20.(本小题满分12分)如图所示，在四棱锥A BCDE -中，//CD BE ，BE ⊥平面ABC ，1AB BC ==，2BE =，2AC =. (1)求证：AB DE ⊥；(2)当三棱锥D ACE -的体积等于16时，求二面角A DE B --的平面角的正切值.某企业计划投资生产甲、乙两种产品，根据长期收益率市场预测，投资生产甲产品的利润与投资额成正比，投资生产乙产品的利润与投资额的算术平方根成正比，已知投资1万元时，甲、乙两类产品的利润分别为0.125万元和0.5万元.(1)分别写出两类产品的利润与投资额x 的函数关系式；(2)该企业有100万元资金，全部用于生产甲、乙产品，问怎样分配资金能使得利润之和最大，最大利润为多少万元？22.(本小题满分12分)设D 是函数()y f x =定义域．．．内的一个子集，若存在0x D ∈，使得()00f x x =，则称0x 是函数()y f x =的一个“不动点”，也称()f x 在区间D 上不存在不动点.(1)已知()2f x x bx c =++，若对于任意实数b ，函数()f x 恒有两个不相等的不动点，求实数c 的取值范围；(2)已知()()2log 421x x g x a =+⋅-，若()g x 在区间[]1,2上存在不动点，求实数a 的取值范围.。

2019-2020学年长沙市第一中学高三英语期中试卷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AWhen the weather is bad or when the flu breaks out, we can let the kids do some fun things at home, which can be beneficial to kids.Reading out loudIf your children are young enough, don't forget to read books to them out loud! Few children dislikehaving a good book read to them, and it's great for the development of their brains. However, if your children are a bit older and have moved onto more advanced books, there is always the choice of listening to an audiobook. This can also be done while they're doing something else.Playing board gamesMaybe your children's table is full of board games, which have been forgotten for a long time. It's a good time to bring them out when playing outside is no longer a choice. Surely, playing board games is a great way to connect with children. In addition, many board games are designed to get children thinking!Having a dance partyConsidering that all you need is a speaker or maybe just a phone, you can have a dance party wherever you are! This is a great way to get kids’ bodies moving when they are inside. Play some of your children's favorite music and let them dance to it. Not only is it good exercise, but it will help your children feel time is flying!Doing jigsaw (拼图) puzzlesFor most people that have children, it's common to have at least one jigsaw puzzle at home. Jigsaw puzzles are great because everyone can do them on their own time. Besides, your whole family will have a sense of achievement when everyone is smiling over the finished product.1. What do reading out loud and playing board games have in common?A. They both develop children's team spirit.B. They both improve children's listening ability.C. They both do good to children's thinking ability.D. They both focus on interaction between children.2. Which of the following combines exercise and music?A. Reading out loud.B. Playing board games.C. Doing jigsaw puzzles.D. Having a dance party.3. What is the purpose of the text?A. To list four interesting children's parties.B. To recommend four children's favorite books.C. To introduce some activities for children inside.D. To show some funny things for children outside.BExperts are warning about the risks of extremely picky(挑剔的)eating after a teenager living on a diet of chips and crisps developed lasting sight loss. Eye doctors inBristolcared for the 17-year-old after his sight had gone to the point of blindness. Tests showed he had serious vitamin deficiency(缺乏). Dr. Denize Atan, who treated him at the hospital, said, “His diet was basically a portion of chips from the local fish and chip shop every day. He also used to snack on crisps and sometimes white bread and ham, and not really any fruit and vegetables.”The teenager saw his doctor at the age of 14 because he had been feeling tired and unwell. At that time he suffered from vitamin B12 deficiency, but he did not stick with the treatment or improve his poor diet. Three years later, he was taken to theBristolEyeHospitalbecause of progressive sight loss.He was not overweight or underweight, but he had lost minerals from his bones, which was really quite shocking for a boy of his age. In terms of his sight loss, he met the standards of being blind. “He had blind spots right in the middle of his sight,” said Dr Denize Atan, “That means he can’t drive and would find it reallyarduousto read, watch TV or recognize faces.”Dr Denize Atan said that parents should learn about the harm that can be caused by picky eating, and turn to experts for help. For those who are concerned , she advised, “It’s best not to be anxious about picky eating , and instead calmly introduce one or two new foods with every meal.” She said multivitamin tablets can supplement(补充) a diet, but cannot take the place of eating healthily. “It’s much better to take in vitamins through a varied and balanced diet,” she said, adding that too manycertain vitamins , including vitamin A, can be harmful ,“so you don’t want to overdo it.”4. What does Dr Denize Atan imply in paragraph 1?A. The diet of the boy is not balanced.B. Fruit and vegetables are rich in vitamins.C. Picky eating is common among teenagers.D. The cause of the boy’s disease is unknown.5. Why did the boy go to see his doctor at the age of 14?A. To improve his poor diet.B. To get some help to lose weight.C. To be treated for his discomfort.D. To slow down his progressive sight loss.6. What does the underlined word “arduous” in paragraph 3 probably mean?A. Important.B. Easy.C. Necessary.D. Difficult.7. What does the last paragraph mainly talk about?A. Reasons why the boy is seriously ill.B.Suggestions for the boy’s family to care for him.C. Advice for parents worried about picky eating.D. Waysof taking in enough vitamins and minerals.CThursday, two Russian submarines(潜艇) dived down 2.5 miles into the Arctic Ocean and planted a national flag onto a piece of continental shelf known as the Lomonosov Ridge. Rising from the center of the Arctic Basin, the flag sent a clear message to the surrounding nations: Russia had just laid claim(权利) to the vast oil and gas reserves contained in this underwater area.AfterRussia, theUnited States,Norway,SwedenandFinlandare all trying to gain profit. Projections show that the area of land and sea that falls within theArctic Circleis home to an estimated 90 billion barrels of oil, an incredible 13% of Earth’s reserves. It’s also estimated to contain almost a quarter of untapped global gas resources. But long before this oil race began, how did theArcticbecome so rich in energy?“The first thing you realize is that theArctic—unlike the Antarctic—is an ocean surrounded by continents”, Alastair Fraser, a geoscientist from Imperial College London, said. Firstly, this means there’s a huge quantity of organic material available, in the form of dead sea creatures such as plankton and algae, which form the basis of what will ultimately become oil and gas. Secondly, the surrounding ring of continents means that the Arctic Basin contains a high proportion of continental crust(大陆地壳), which makes up about 50% of its oceanic area. That’s significant because continental crust typically contains deep depressions called basins, into which organic matter sinks.Here, it gets inserted in rock and preserved in anoxic(缺氧) waters, meaning they contain little oxygen.“Normally, in a shallow sea with lots of oxygen, it would not be preserved. But if the sea is deep enough, the oxygenated waters at the top will be separated from the anoxic conditions at the base,” Fraser explained. Conserved within these oxygen-free basins, the matter maintains compounds that finally make it useful as an energy source for millions of years in the future.8. Why didRussiaplant a national flag onto the Lomonosov Ridge?A. To tell surrounding countries its armed forces.B. To show its advanced technology of submarines.C. To show abundant natural resources in theArcticBasin.D. To claim its privilege to explore for oil and gas in the area.9. What’s the function of the last sentence in paragraph 2?A. Making a comparison.B. Serving as a connecting link.C. Analyzing the cause and effect.D. Drawing the conclusion of the text.10. What can we know from the last paragraph?A. Oxygen only exists in the top part of the ocean.B. Organic materials mostly exist in the basins with oxygen.C. Water containing oxygen turns organic materials into oil and gas.D. Oxygen-free environment counts in the formation of the arctic’s rich energy.11. What can be a suitable title for the text?A. What makes theArcticattractive?B. Why do many nations focus on theArctic?C. Why is there so much oil in theArctic?D. How does theArcticBasincome into being?DOn World Oceans Day, which falls on June 8, the US National Geographic Society announced it would recognize the Southern Ocean in Antarctica, bringing the global total to five.Unlike the Arctic, Atlantic, Indian and PacificOceans—which are defined by the continents that bound them—the Southern Ocean is instead characterized by the Antarctic Circumpolar Current（南极洋流）. According to the National Geographic, the Southern Ocean includes most of the waters surrounding Antarcticaout to 60 degrees south latitude（纬度）."Encircled by the powerfully swift ACC, it is the only ocean to touch three others and to completely embrace a continent rather than being embraced by them," Sylvia Earle, a marine biologist and oceanographer, told the Daily Mail.Those familiar with the Southern Ocean know it's unlike any other. "Anyone who has been there will struggle to explain what's so charming about it, but they'll all agree that the glaciers are bluer, the air colder, the mountains more awful and the landscapes morecaptivatingthan anywhere else you can go," Seth Sykora-Bodie, a marine scientist at the National Oceanic and Atmospheric Administration, told National Geographic.National Geographic hopes their revised maps will bring public awareness to the region, thereby encouraging Southern Ocean conservation—but its significance is beyond that."We think it's really important from an educational standpoint, as well as from a map-labeling standpoint, to bring attention to the Southern Ocean as a fifth ocean," Alex Tait, National Geographic Society geographer, told The Post. "So when students learn about parts of the ocean world, they learn it's an interconnected ocean, and they learn there are these regions called oceans that are really important, and there's a distinct one in the icy waters around Antarctica."12. Why is the Southern Ocean different from other oceans?A. It has never been explored before.B. It surrounds the Antarctic all around.C. It is enclosed by the fast-flowing ACC.D. It has ecologically distinct environment.13. What does the underlined word "captivating" in paragraph 4 probably mean?A. Strange.B. Unusual.C. Attractive.D. Informal.14. What does the National Geographic think of the Southern Ocean?A. It will be instructive for students.B. It will promote tourism development.C. It will encourage public to treasure water.D. It will draw scientists to study in the Antarctic.15. What is the best title for the text?A. World Oceans DayB. Revised Antarctic MapsC. Adding a New OceanD. New Discovery under the Sea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。

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2019届湖南省重点中学高一上学期期中考试试题数学试卷第I 卷 （选择题， 共60分）一、选择题（共12小题，每小题5分，共60分，每小题只有一个正确答案)在每小题给出的四个选项中，只有一项是最符合题目要求的，选出正确的选项并将该选项在答题卡上涂黑。

1．已知集合A ={x ｜log 2x >0}，B ={x |x 2–2x –3〈0}，则A ∪B =（ ） A ．(–1，+∞） B ．（–∞，3） C ．（–1,1）D ．（1，3）2．与610°角终边相同的角的集合( ）A ．{α|α＝k ·360°＋230°,k ∈Z }B ．｛α｜α＝k ·360°＋250°，k ∈Z ｝C ．{α｜α＝k ·360°＋70°，k ∈Z ｝D ．{α|α＝k ·360°＋270°，k ∈Z } 3。

下列函数中,在定义域内既是奇函数又是增函数的为（ )A ．1y x =+B ．3y x =-C ．1y x=D ．||y x x =4．当a 〉0且a ≠1时，函数f （x ）=a x –2–3的图象必过定点（ ） A ．（0，–3) B ．(2,–2）C ．（2，–3)D ．（0，1）5．已知角α的终边经过点(－4，3），则cos α＝（ ）A ．错误!B ．错误!C ．－错误!D ．－错误!6．函数f （x ）=ln （x +1）–2x的零点所在的大致区间是（ ）A ．（3,4)B ．（2，e)C ．（1，2）D ．(0，1)7.已知一扇形的弧所对的圆心角为54°，半径r ＝20cm ，则扇形的周长为（ ）A ．（40＋6π）cmB ．1120cmC ．6πcmD ．1 080cm8.设05log 06a ．＝．，11log 06b ．＝．,0611c ．＝．，则（ ） A ．a b c << B ．b c a <<C ．b a c <<D ．c a b <<9．已知幂函数y =pqx ,（p ，q ∈Z ）的图象如图所示，则( ）A ．p ，q 均为奇数，且pq>0 B ．q 为偶数，p 为奇数,且p q<0 C ．q 为奇数，p 为偶数，且pq〉0 D ．q 为奇数，p 为偶数，且pq〈0 10．函数f (x ）=log 0.5（2–x )+log 0.5(2+x ）的单调递增区间是（ ） A ．(2，+∞） B ．（–∞，–2） C ．(0，2）D ．（–2，0）11．已知f （x ）是定义在R 上的偶函数,且在区间（–∞，0］上单调递增．若实数a 满足f (22log a )〉f （–3），则a 的取值范围是（ ）A ．（–∞，–3）B ．（0，3）C ．(3，+∞）D ．（–3，+3）12．已知函数()21,0log ,0kx x f x x x +≤⎧=⎨>⎩，则当0k >时，函数()1y f f x =+⎡⎤⎣⎦的零点个数是 A ．1 B ．2 C ．3 D ．4第Ⅱ卷二、填空题(本题共4小题，每小题5分，共20分）13. 若，则=_________．14．已知()1ln f x x x=-在区间(1，2）内有一个零点x 0,若用二分法求x 0的近似值(精确度为0.2)，则最少需要将区间等分的次数为 _________________.15.若函数)(x f y =的定义域是]4,2[，则)(log 21x f y =的定义域是_____________.16．把物体放在冷空气中冷却，如果物体原来的温度是 o 1C θ，空气的温度是 o 0C θ，min t 后物体的温度 o C θ可由公式()0.24010e t θθθθ-=+-求得．把温度是 o 100C 的物体，放在o 10C 的空气中冷却min t 后，物体的温度是o 40C ，那么t 的值约于 ．（保留三位有效数字，参考数据：ln 3取1.099,ln 2取0.693)三、解答题（本大题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤） 17．（本题满分10分)求值：（1）计算:715log 2043210.064()70.250.58----++⨯；（2）已知lg 2a =，103b =，用,a b 表示．6log 3018．（本题满分12分) 已知集合{}{}21216,21318x A x B x m x m -=≤≤=+≤≤- （1）求集合A（2）若B ⊆A ，求实数m 的取值范围.19.已知是定义在R 上的奇函数，当时，．（1）求函数的解析式;（2）若函数为R 上的单调减函数，求a 的取值范围；20。

2019年湖南省高一上学期期中考试数学试卷【含答案及解析】姓名 ____________ 班级 _______________ 分数 ____________题号-二二三总分得分、选择题1. 函数： - .j 亠一 的定义域是（）A -2A •B .________________________________C • I • ________________________D •「，A ?石-?〔,则下图中3.已知函数 rw-L.、厂 补，则f ⑴一广仃）・（ ）A .-B.C.__________________________________ D . 允4.设"占 | , b = | 訂,c = log 3 0.7 ，则有（ ）A .]•：、： ::.:.二 ___________B .举怎誉応魯 _________________________C . b 亡吃 < C ______________D . C <b2.设全集 —.;,---------------------- C ■5•已知I I ,若:心心r ：，则，处€紈逾耳()A- __________________________________ B -— L---------------------------------------------------------- C -. ------------------------------------------------------------------- D■1讣M6. 函数| 的值域是( )A •(Q.Z ) ________________________________B • f 0,|------------------------------------------------------- C • 1 -. -------------------------------------------------------------7. 已知二次函数 -门- -2/w.r + 1在区间■内是单调函数，则实数'的取值范围是 ( )A . 一’’或；：：：_ ： B2 <;?z<3C . -•或 _D • - _8.若函数，I ，■ ■_ ' 「在|| 上的最大值和最小值之和为■，贝V ‘■的值为（） A .丄B •-4T__________________________________ C . 2 D . 49. 已知.i 满足：当.一 •时,则丿；化+坯」；等于（ ）A .—?4 -----------------------------------------io. 给出定义：若一--「•一（其中•为整数），则，叫做离实数-7 ?最近的整数，记作 二，即：」".在此基础上给出下列关于函数 ，「：-.'：的四个命题：当：时，「 I '1i53，值域是 ------- ■①函数；I .;的定义域是.J厂7②函数，,! I . I的图像关于：F轴对称；③函数I -的图像关于坐标原点对称；④ 函数•二:在一"打|上是增函数;则其中正确命题的个数是( )•A • 1 B• 2CD •4二、填空题已知集合.■- j I ■■一；：，二〉| 则'■- =12. 已知函数• I 满足关系式■ I. : - | ，则函数I 恒过定点为 _________ .13. 函数―一「:、•：在区间rod 上的最大值为，最小值为■，则不等式log tf（x_ Q ^0的解集为____________ •14. 定文运免：&働壇甘推爲/（I）二3^财______________ •15. 给出以下四个命题：①若集合: ,贝U 「②若函数的定义域为•胆订，则函数. 的定义域为| ;③函数「：的单调递减区间是：| I ■；Y④已知集合厂—八- ■-J. I ■-,则映射•■一中满足越;i的映射共有3个;⑤若＞■- ■,且心=1 ,型.型』.虫空L空型=加托AD r⑶r（20B） rm ⑸其中正确的命题有____________________________ （写出所有正确命题的序号）.三、解答题16.求值: 11I' - ■ + '- ■ '' - : 1「17.已知全集匕三R ，集合月■取卜1} ,8・{丫卜&5€6}.(1 ) 求、肾和，■」£'； (2 )求「；(3)定义 / 一£ = & 乂且工 E 占}，求, A ~(A - B) 18. 设集合P ・ 曙传3卫■网七rd}I…‘八i(1) 化简集合，并求当.三：时，打的真子集的个数.(2 )若 厂厂•.；匚，求实数的取值范围.19. 已知函数.i 是定义在 门心匕-上的偶函数，且当•.,时,门a .(1) 求出函数，f 、j 的解析式； (2)画出函数|的图象,并根据图象写出函数|f(y ］的增区间；(3)设，.、 I I ,对任意 二■,存在 --使•或叮;屮軌爲，求的取值范围.20. 某蔬菜基地种植西红柿，由历年市场行情得知，从二月一日起的 200天内，西红柿的种植成本与上市时间的关系用图 1的抛物线弧表示，西红柿市场售价与上市时间的关 系用图2的一条线段表示 (注：市场售价和种植成本的单位：元/100kg,时间单位：天)I 一二+*0.75" +(2吕)3(1(2))（1）写出图1表示的种植成本与时间的函数关系式^ / I ,写出图2表示的市场售价与时间的函数关系式（2 ）认定市场售价减去种植成本为纯收益，问何时上市的西红柿收益最大？21. 设「：—=—，为常数2T + L（1）若.，为奇函数，求，「；（2）判断.•,在匸上的单调性，并用单调性的定义予以证明.（3）在（1 ）的条件下，不等式.| ：- I对；.-■ j ■/恒成立，求z的取值范围.参考答案及解析第1题【答案】【解析】试题井析：因为固数蚀二后厶-所以F律严沦°且应选C.x-2 "2工0第2题【答案】【解析】试题分析？因^A={xeN\-l<x<10}= ^V0.L23,4,5,6,7,8,91C}, B -| £A | x?- t 6 = 0 2J};所IA Ar\ B= $}故应选A.第3题【答案】【解析】试题分析：因为/(1)-/(3]=/(+)-10 = 17-10=7 ,斯以殛-第4题【答案】试题分折；由fh)=\~可知;,loe30.7<0 ,所X 、【解析】所以应选D.第5题【答案】B【解析】试题分折：令再&)=如恥4丛是奇囲数，所^/(2015) = ^ 2015^4^. 2015 + 1 = ^PPff 20152<tt5-bi-2015 = jt-l ,馭十(一201巧=g (-2015尸”+,(-2015)+1 (2015严口占.(201,)£》1 講2 - &应选D・第10题【答案】第7题【答案】A【解析】试题汁析；由题意可亀 二次團数严十-2mx+l 的对莉軸为2朋」因为画数在区间（23）内是单 调函数』所以梆兰2或故应选山第8题【答案】B【解析】试題井析；当衣A ］时,兀心1 +吟+ 1。

长沙市一中2018级高一第一学期期末考试试卷一、选择题（本大题共12小题，每小题5分，满分60分。

在每小题给出的四个选项中，只有一项是符合题目要求的）1.满足{}{}11,2,3A ⊆⊆的集合A 的个数是( ) A.2B.3C.4D.82.已知幂函数()a f x x =的图像过点()4,2，若()3f m =，则实数m 的值为（ ） A.3B.3±C.9±D.93.454sincos tan 363πππ⎛⎫⋅⋅- ⎪⎝⎭的值是（ ） A.33-B.33C.34-D.344.已知直线123:210,:250,:310l x y l x ny l mx y +-=++=++=，若12l l P 且13l l ⊥，则m n +的值为（ ） A.-10B.-2C.10D.25.已知2510a b ==，则11a b+=（ ） A.12B.1C.2D.26.如图所示，已知正方体1111ABCD A B C D -，则直线11B D 与平面11ABC D 所成的角 的大小是（ ） A.30oB.45oC.60oD.90o7.已知tan 2θ=，则22sin sin cos 2cos θθθθ+-等于（ ）A.43- B.54C.34-D.458.设,m n 是两条不同的直线，,αβ是两个不同的平面，下列命题中正确的事是（ ） A.若,,,m n αβαβ⊥⊂⊂则m n ⊥B.若,,,m n αβαβ⊂⊂P 则m n PC.若,,,m n m n αβ⊥⊂⊂则αβ⊥D.若,,,m m n n αβ⊥P P 则αβ⊥9.已知函数())ln 1f x x =+，则()1lg 2lg 2f f ⎛⎫+= ⎪⎝⎭（ ）A.-1B.0C.1D.210.若存在正数x 使12xx a ⎛⎫-< ⎪⎝⎭成立，则a 的取值范围是（ ） A.(),-∞+∞B.()2,-+∞ C .()2,+∞D.()1,-+∞11.如图，有一个水平放置的透明无盖的正方体容器，容器高4cm ，将一个球放在容器口，再向容器内注水，当球面恰好接触水面时测得水深为3cm ，如果不计容器的厚度，则球的体积为（ ）A.31256cm π B.343312cm π C.33436cm π D.32563cm π 12.已知()f x 是定义在R 上的单调函数，满足()1xf f x e ⎡⎤-=⎣⎦，且()()f a f b e <<。

长沙市第一中学2019-2020学年度高一第一学期第一次阶段性检测数 学时量：120分钟 满分：150分一、选择题(共12小题，每小题5分，共60分) 1.集合{},a b 的子集个数是( )A.1B.2C.3D.42.设U =R ，集合{P x y ==，{Q y y ==，则()U P Q =( )A.[)1,+∞B.∅C.[)0,1D.[)1,1-3.函数()023x f x +=的定义域为( )A.33,2⎡⎤-⎢⎥⎣⎦B.3333,,222⎡⎫⎛⎫---⎪ ⎪⎢⎣⎭⎝⎭ C.33,2⎡⎫-⎪⎢⎣⎭D.3333,,222⎡⎫⎛⎤---⎪ ⎢⎥⎣⎭⎝⎦4.已知集合{}24M x x ==，{}4N x ax ==，若N M ⊆，则实数a 的取值集合为( )A.{}2B.{}2,2-C.{}2,0D.{}2,2,0-5.已知函数()()210,1x f x aa a -=+>≠的图象过定点P ，则P 的坐标是( )A.()0,1B.()0,2C.()2,1D.()2,26.已知函数()223f x x x =-+在区间[]0,t 上的最大值是3，最小值是2，则实数t 的取值范围是( )A.[]1,2B.(]0,1C.[)1,+∞D.(]0,27.已知函数()()21310,2,3,2x a x a x f x a x -⎧-+≤⎪=⎨+>⎪⎩是定义域R 上的减函数，则实数a 的取值范围是( )A.1,12⎡⎫⎪⎢⎣⎭B.11,32⎡⎫⎪⎢⎣⎭C.1,12⎛⎫⎪⎝⎭D.1,13⎛⎫⎪⎝⎭8.已知函数()37f x ax bx =-+(其中a ，b 为常数)，若()717f -=-，则()7f 的值为( )A.31B.17C.17-D.159.定义在R 上的函数()f x 满足：对任意12,x x ∈R ，()()()12121f x x f x f x +-=+，则下列说法中一定正确的是( )A.()f x 为奇函数B.()f x 为偶函数C.()1f x +为奇函数D.()1f x +为偶函数10.函数2211x y x -=+的值域为( )A.[)1,1-B.[]1,1-C.(]1,1-D.()1,1-11.已知()12g x x =-，()()2210x f g x x x -=≠⎡⎤⎣⎦，则12f ⎛⎫⎪⎝⎭等于( ) A.15B.1C.3D.3012.若函数()f x 是R 上的单调函数，且对任意实数x ，则()2log 3f =( ) A.1B.45C.12D.0二、填空题(本大题共4个小题，每小题5分，共20分)13.已知定义在(),0-∞上的函数()22f x x =+，且()6f a =，则a =__________.14.某小学五年级1班共有40名同学，在某次摸底测试中语文20人优秀，数学23人优秀，两门都不是优秀者6人，则两门都是优秀的同学共有__________人.15.若定义在R 上的偶函数()f x 在()0,+∞单调递增，且()20f -=，则()0xf x <的解集为__________. 16.已知函数()1112x k f x x -++=-+，若对任意的实数1x ，2x ，3x ，不等式()()()123f x f x f x +≥恒成立，则实数k 的取值范围是__________. 三、解答题(本大题共70分) 17.(本小题满分10分)计算：(1)0.5201354164π-⎛⎫⎛⎫⨯÷ ⎪ ⎪⎝⎭⎝⎭；已知集合{}721A x a x a =-<-≤，集合()(){}120B x x x =-+≤.(1)若0a =，求AB ，A B ；(2)若B A ⊆，求实数a 的取值范围.19.(本小题满分12分) 函数()()110f x x x=-> (1)画出函数()f x 的图象，并写出单调区间；(不要求证明)(2)是否存在正实数(),m n m n <，使函数()f x 的定义域为[],m n 时值域为,66m n ⎡⎤⎢⎥⎣⎦，若存在，求m ，n 的值；若不存在，请说明理由.20.(本小题满分12分) 已知函数()1ln1x f x x +=- (1)判断函数()f x 的奇偶性，并给出证明； (2)判断函数()f x 在()1,+∞上的单调性；(3)解不等式：()()2232470f x x f x x +++-+->.某公司为提高员工的综合素质，聘请专业机构对员工进行专业技术培训，其中培训机构费用成本为12000元.公司每位员工的培训费用按以下方式与该机构结算：若公司参加培训的员工人数不超过30人时，每人的培训费用为850元；若公司参加培训的员工人数多于30人，则给予优惠：每多一人，培训费减少10元.已知该公司最多有60位员工可参加培训，设参加培训的员工人数为x 人，每位员工的培训费为y 元，培训机构的利润为Q 元.(1)写出y 与x (0x ＞，*x ∈N )之间的函数关系式；(2)当公司参加培训的员工为多少人时，培训机构可获得最大利润？并求最大利润.22.(本小题满分12分)设函数()xxf x ka a -=-(0a >且1a ≠，k ∈R )，()f x 是定义在R 上的奇函数.(1)求k 的值； (2)已知()312f =，函数()()224x xg x a a f x -=+-，[]1,2x ∈，求()g x 的值域； (3)若1a >，()()xh x a f x =-，对任意[],1x λλ∈+，不等式()()2h x h x λ+≤⎡⎤⎣⎦恒成立，求实数λ的取值范围.。