湖南衡阳第八中学2018-2019学年高一数学上学期12月九科联赛试题

衡阳市八中高一年级下学期联赛英语试卷时量：120分钟总分：150分注意事项：1. 答第Ⅰ卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

2. 选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。

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第Ⅰ卷第一部分听力做题时，先将答案标在试卷上，录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题，每小题1.5分，满分7.5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。

每段对话仅读一遍。

第二部分阅读理解（共两节，满分35）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。

AShould online learning be encouraged?Editor’s note: As many parents have tried to give their children a head start, online education services, with their relatively cheap prices, are mushrooming across the world. What do you think? Should this way of teaching be encouraged?Ted M (UK)Online education is not new. It has been found effective in many countries where access(进入) to schools is difficult. It lacks the opportunity for social learning of course, but in most systems there are weekend, summer and winter “camps” where students can arr ange to meet and interact with others as part of the courses. Such education is valuable for remote(远程的) learning in inaccessible regions.Linda (China)I find that children today spend less and less time playing outdoors than we did when we were young. We have the technology to enable us to teach students to learn with an amazing variety of resources but I do hope not at the cost of losing their childhood.Breathing (Canada)I think education is not about learning or gathering only textbook knowledge. It’s about communicating with others, discussing, group work etc. Online education means distance education. At present it is spread all over the world. It has some good results too. But I like face-to-face education. It helps a student to build up his or her mental and physical strength besides textbook knowledge.Jimmy (US)It really depends on what kind of learner you are. If you are a self-motivated student and can manage your own time, online learning is for you. So long as you have the ability to learn on your own.Sunny (Australia)Online schools offer students with customized learning and help them gain access to courses that may not be provided in their assigned school. This is one of the primary reasons for the increased demand in online learning. Online learning is providing new choices for kids and more choices for parents.21. Which of the following is Linda’s opinion on online learning?A. It lacks the opportunity for social learning.B. It is valuable for learning in remote regions.C. It limits the time children spend playing outdoors.D. It is very popular all over the world.22. Who is totally supportive to online learning?A. SunnyB. BreathingC. JimmyD. Ted M23. What is the purpose of the passage?A. To introduce the access to online learning.B. To list the benefits of online learning.C. To show the quick spread of online learning.D. To present different opinions on online learning.BAt thirteen, I was diagnosed(诊断) with a kind of attention disorder. It made school difficult for me. When everyone else in the class was focusing on tasks, I could not.In my first literature class, Mrs. Smith asked us to read a story and then write on it, all within 45 minutes. I raised my hand right away and said," Mrs. Smith, you see, the doctor said I have attention problems. I might not be able to do it.”She glanced down at me through her glasses，"You are not different from your classmates, young man.”I tried，but I did not finish the reading when the bell rang. I had to take it home.In the quietness of my bedroom, the story suddenly all become clear to me. It was about a blind person, Louis Braille. He lived in a time when the blind couldn’t get much education. But Louis didn’t give up. Instead，he invented a reading system of raised dots（点）, which opened up a whole new world of knowledge to the blind.Wasn’t I the“blind”in my class，being made to learn like the “sighted”students？My thoughts spilled out and my pen started to dance. I completed the task within 40 minutes. Indeed，I was not different from others；I just needed a quieter place. If Louis could find his way out of his problems，why should I ever give up？I didn’t expect anything when I handed in my paper to Mrs. Smith，so it was quite a surprise when it came back to me the next day--with an “A” on it. At the bottom of the paper were these words: “See what you can do when you keep trying？”24.The author didn’t finish the reading in class because __________.A. he was new to the classB. he had an attention disorderC. he wanted to take the task homeD. he was tired of literature25．What do we know about Louis Braille from the passage？A. He had good sight.B. He gave up reading.C. He made a great invention.D. He learned a lot from school.26．What was Mrs. Smith’s attitude to the author at the end of the story？A. Angry.B. Encouraging.C. Impatient.D. Sympathetic.27．What is the main idea of the passage？A. The disabled should be treated with respect.B. Everyone needs a hand when faced with challenges.C. A teacher can open up a new world to students.D. One can find his way out of difficulties with efforts.CIndia has a growing number of millionaires – at present there are 200, 000 Indians worth a million dollars or more. According to Forbes, India is also home to the fourth-highest number of billionaires in the world. It’s notsurprising, given India’s large population and the rapid increase in its economic fortunes in the past two decades.This rise in the rich has led to a growing industry that meets the needs of its wealthy and picky（挑剔的）clients（客户）. These businesses offer excellent services tailored to the strict standards of the ultra-wealthy（超级富豪）, their unique tastes and lifestyles. From matchmaking（做媒）to private jets and from lifestyle management to expensive fine art, no matter how unusual the demand sounds, no request will be refused.Like mi llionaires elsewhere, India’s rich “want access to the best things in life, but don’t have the time, nor the connections, to acquire them,” says Tanu Jian, head of marketing at the Gurgaon office of Quintessentially Lifestyle, a firm that offers round-the-clock personalized（针对个人的）services to its ultra-wealthy members. With the company’s unique network of contacts, Jain has helped clients secure an autographed Roger Federer tennis racket （球拍）, and a limited edition John Lennon pen.When it comes to serving the super-rich, the “customer is king” approach guides everything. Each client is assigned a personal “lifestyle manager” who carefully “studies the behavior of each member and accordingly recommends a personalized solution for each request,” says Jain.The rapid increase in India’s super-rich has touched off a race among service providers who are trying to break into the market. India is exploding with entrepreneurial (企业的) energy. So is the industry whose business is to know where the super-rich want to spend their money.28. Which of the following is Not the reason for the fast growth of India’s super-rich service businesses?A. Indian government’s putting increasing emphasis on service industry.B. India’s fast economic advance over the last twenty years.C. India’s large number of super-rich relative to its total population.D. Human beings’ natural desire for good things in life.29. Which of the following can best explain the underlined word “tailored”?A. done right after someone’s extra ordinary request.B. done passionately for someone’s strict demand.C. done immediately for someone’s original intention.D. done specially for someone’s particular need.30. According to the passage, which of the following statements is Not True?A. India ranks fourth on the list of the number of billionaires.B. “Customer is king” is the best policy to the businesses serving the Indian super-riches.C. The best things are not available to India’s rich because of some bans from the government.D. If a rich Indian woman wants to seek an ideal husband, she can turn to some businesses.31. Which one can serve as the best title of the passage?A. What Specific Needs India’s Super-Rich Have.B. What India’s Super-Rich Bring About.C. Why India’s Super-Rich’s Need List Is Growing.D. How India’s Super-Rich Get Done Their Needs.DWe are lucky to live in a world that is full of incredible technology. Our living rooms are packed with computers, LCD TVs, video game systems, and Blue-ray players that help us enjoy the latest entertainment. Although these items bring us joy and convenience, they also create a lot of junk. Each device needs its own plug （插头）and adaptor（适配器）to keep its batteries（电池）recharged, and over time these wires get tangled (缠绕在一起的). Thankfully, something has come along to help rid our homes of this mess while still supplying these devices with the power they need. It’s cal led wireless（无线的）charging（充电）and this trend is just starting.Wireless charging has a lot of potential for smart phones and other electronic devices. Electronic devices can absorb（吸收）the electricity once they’re placed on a special charging mat. There a re several advantages that wireless charging offers over traditional methods. For starters, cords (电线) have a tendency to wear out with use. Wireless charging users never have to worry about buying replacement cords. Wireless charging is also far more convenient for medical implants（移植物）, as patients won’t need to recharge their devices through the skin using cords. In turn, this cuts down on the risks of infection（感染）. Wireless charging can also bring safety benefits, as wired charging devices that come in contact with water can increase the chances of getting an electric shock（触电）. Wireless charging gets rid of that danger completely.Still, there are a few drawbacks to wireless charging. The first is speed. It takes a bit longer to charge devices wirelessly than it does if the device is plugged in. The process also requires more heat, so devices tend to get a bit hotter, which could create other safety issues. Also, since devices must be left on a special pad while charging, it is harder to operate them while they are powering up. This limitation may be gotten rid of in the future, as researchers are developing transmitters (发射器) that can charge several different devices in a room without the need to connect to a charging pad. Although wireless-charging technology may be far from perfect, it seems like a step in the right direction as we move towards a less-tangled future.32. What is a problem with many modern appliances?A. They go out of style too quickly.B. They are not very entertaining.C. Most people can’t afford to pay for them.D. They can cause a lot of junk around the house.33. Why is wireless charging beneficial for medical patients?A. It makes maintenance（维护）of their devices much easier.B. Wireless charging has shown to cure people of serious diseases.C. It often brings down the cost for their medical bills.D. It’s being used as a replacement for many pills.34. Which of the following is a disadvantage of wireless charging?A. Wireless charging means devices take up more space.B. People can now buy fewer devices for their homes.C. People can’t plug in their devices conveniently.D. It takes longer to charge your battery wirelessly.35. What seems to be the author’s attitude towards wireless chargin g?A. Cautious.B. Uncaring.C. Disapproving.D. Favorable.第二节（共5小题，每小题2分，满分10分。

数学参考答案二、填空题11. 12. 425)23()2(22=-++y x 13.或1 14. 15.6 16.①③ 三、解答题 17.（1）（2）{}62)(≤<-=⋃x x B A C U18. （1）证明：连接AC 交BD 于，连接. ∵四边形ABCD 是正方形， ∴是AC 的中点。

又∵是PA 的中点， ∴PC ∥.∵PC ⊄平面， ⊂平面 ∴PC ∥平面；（2）∵侧棱PA ⊥底面ABCD ，且PA=2，Q 是PA 的中点。

∴棱锥的高QA=1，又∵底面ABCD 是边长为2的正方形， ∴棱锥的底面面积=2， ∴32123131=⨯⨯=⋅=∆-QA S V ABD BAD Q 19.12121221)(+-=+-=x x x x f20. （1）∵正方形∴∵面AC ABC ACDE ABC ACDE =⋂⊥面面面,∴,∴ ∵,∴（2）取EO CO O AB ,,连接中点∵AC BC BC AC ⊥==，2,∴222,===⊥AB AO CO AB CO ，AC ABC ACDE ABC ACDE AC AE =⋂⊥⊥面面面面,,∴CO AE ABC AE ⊥∴⊥,面ABE CO A AB AE 面⊥∴=⋂,,∴成的角与面为ABE EC CEO ∠在直角三角形3362tan 6===∠=EO CO COE EO AEO ，中， 21、解：长为的直线方程为设的坐标为（到直线距离为1041)23(31232222--=++-=a a a d41)23(21212--=⨯=∆a d AC S ABC ∵，∴∴），（，此时时面积最大为23,4981023B a =-22、（1）圆的方程化为m y x -=-+-5)2()1(22， 圆心 C(1,2),半径，则圆心C(1,2)到直线的距离为：5121422122=+-⨯+=d由于|MN|=,则|MN|=， 有，∴,解得m=4 (2)假设存在直线，使得圆上有四点到直线l 的距离为, 由于圆心 C(1,2)，半径r=1， 则圆心C(1,2)到直线的距离为：5515121422122-<=+-⨯+=d 解得。

衡阳市一中2018年下学期高一期末考试数学考试时量：120分钟考试总分：150分一、选择题：本大题共 12小题，每小题5分，共60分，在每小题给出的四个选项中，只有 一项符合题目要求的.1 •已知集合 A = {—1,2},B = {x1 兰 x 兰 2}，则 A 「|B = A. 1x1 <X <2} B.1-1,2] C. *D.{2}2•下面是属于正六棱锥的侧视图的是3•给出以下命题：①经过三点有且只有一个平面；②垂直于同一直线的两条直线平行；③ 一个平面内有两条直线与另一个平面平行，则这两个平面平行；④垂直于同一平面的两 条直线平行•其中正确命题的个数有 A . 1个B . 2个C . 3个D . 4个4.下列命题正确的是A •幕函数的图象都经过（0,0）、（1,1）两点B •当n = 0时，函数y =x n 的图象是一条直线C. 如果两个幕函数的图象有三个公共点，那么这两个函数一定相同D. 如果幕函数为偶函数，则图象一定经过点（-仏1）5.直线y 二k （x • 2）被圆x 2 y^4截得的弦长为2 3，则直线的倾斜角为2A. Ji 6B.Ji3C. D.R ，贝y a 的取值范围是1 6•若函数y=log a（x -ax 1）定义域为A . 0 a 1 B. 0 a 2 且a =1 C. 1 a 2 D. a —217•如图，在直角梯形 ABCD 中， A =90°, AD//BC,AD = AB BC =1，将 ABD2沿BD 折起，使得平面 ABD _平面BCD .在四面体 A - BCD 中，下列说法正确的是 A. 平面ABD _平面ABC B. 平面ACD _平面ABC C. 平面ABC _平面BCD D. 平面ACD _平面BCD8•中国古代数学名著《九章算术》中 ，将顶部为一线段，下底为一矩形的拟柱体称之为刍甍 (m eng)，如图几何体为刍甍，已知面ABCD 是边长为 3的正方形， EF //AB ,9 •我们从这个商标' 中抽象出一个图像为右图，其对应的函数可能是10.已知二棱锥P -'ABC 的二条侧棱PA, pB, PC 两两垂直，且PA = PB = PC = 1，则 三棱锥P-ABC 的外接球的表面积为A. 16二B.12二C.4 二D.3 二11.若实数x, y 满足x 23，则的取值范围是x —2E F=2, EF 与面ABCD 的距离为2,则该多面体的体积为615A. B.2C. 8D.9A . f(x)二一^ Bx -1C.f (x)二 f (x)二X —11A. -3 八3B.C. | 3 ,、、3D.(,-：：，-'、3 U 3, ■He )12 .设函数y = f (x)有5个零点x i , X 2, X 3, X 4,X 5 ,且对一切实数x 均满足 f ( x 4) f (-x) = 0，贝y x 1x 2 x 3 x 4 x 5 二A. 8B.10 C. 16 D. 20二、填空题：本大题共 4小题，每小题5分，共20分，把答案填在答题卡中对应题号的横 线上. 13•给出下列平面图形：①三角形；②四边形；③五边形；④六边形.则过正方体中心的截面图形可以是 ________________ (填序号)14. 已知 m R ，则直线 11 : (m 1)x 「(m -3)y -4 二 0 与直线 l 2: (m 1)x 「(m 「3)y=0的距离的最大值为 _____________lnx(x A 0)15. 已知函数f(x) = <2，则函数g(x)= f(x) + x-a 恰好存在一个零点I-x 1 2—2x(x")时，实数a 的取值范围为 _______________ .16. 圆锥A0底面圆半径为1，母线AB 长为6，从AB 中点M 拉一条绳子，绕圆锥一周转到B 点，则这条绳子最短时长度为 _______________三、解答题：本大题共 6小题，共70分。

湖南省衡阳市第八中学2019-2020学年高一数学上学期第三次月考试题请注意：时量150分钟 满分150分一、单选题（每小题5分，共计60分）1．已知{}{}|35,4A x x B x x =-<<=>，则A B =（ ） A ．{}|35x x -<<B ．{}|5x x >C ．{}|45x x <<D ．{}|34x x -<< 2．下列结论中正确的是（ ）A ．半圆弧以其直径为轴旋转一周所形成的曲面叫做球B ．直角三角形绕一直角边为轴旋转一周得到的旋转体是圆锥C ．夹在圆柱的两个平行截面间的几何体还是一个旋转体D ．用一个平面截圆锥底面与截面组成的部分是圆台3．函数1()ln(2)f x x x=--的零点所在的大致区间是（ ） A ．（2，3）B ．（3，4）C ．（4，5）D ．（5，6） 4．如图所示的是水平放置的三角形直观图，D '是△A 'B 'C '中B 'C '边上的一点，且D '离B '比D '离C '近，又A 'D '∥y '轴，那么原△ABC 的AB 、AD 、AC 三条线段中（ ）A ．最长的是AB ，最短的是AC B ．最长的是AC ，最短的是ADC ．最长的是AD ，最短的是AC D ．最长的是AB ，最短的是AD5．已知函数()f x 为奇函数,且当0x >时, ()220f x x x=+>,则()2f -=（ ） A ．2 B ．1 C ．-2D ．-5 6．在一个长方体1111ABCD A B C D -中，已知6AB =，5BC =，14BB =，则从点A 沿表面到点1C 的最短路程为（ ）．A ．B C ．D ．15 7．设函数1()ln 1x f x x x-=+，则函数的图像可能为（ ）A ．B ．C ．D ．8．鲁班锁是中国传统的智力玩具，起源于古代汉族建筑中首创的榫卯结构，这种三维的拼插器具内部的凹凸部分（即榫卯结构）啮合，十分巧妙，外观看是严丝合缝的十字立方体，其上下、左右、前后完全对称，从外表上看，六根等长的正四棱柱分成三组，经90榫卯起来，如图，若正四棱柱的高为8，底面正方形的边长为2，现将该鲁班锁放进一个球形容器内，则该球形容器的表面积的最小值为（ ）（容器壁的厚度忽略不计）A ．21πB ．40πC ．41πD ．84π9．已知2log (4)log (21)a a a a -<-，则a 的取值范围是（ ）A ．()2+∞，B ．1,22⎛⎫ ⎪⎝⎭C ．()23，D ．1,32⎛⎫ ⎪⎝⎭10．设m ，n 是两条不同的直线α，β，γ是三个不同的平面，给出下列四个命题：（1）若m α⊥，//n α，那么m n ⊥；（2）若m n ⊥，m α⊥，//n β，那么αβ⊥；（3）若//αβ，m α⊂，那么//m β；（4）若αγ⊥，βγ⊥，则αβ∥,其中正确命题的序号是（ ）A ．（1）（2）B ．（2）（3）C ．（1）（3）D ．（2）（4）11．函数()f x 的定义域为D ，若存在闭区间[],a b D ⊆ ,使得函数()f x 同时满足:（1）()f x 在[],a b 内是单调函数；（2）()f x 在[],a b 上的值域为[],(0)ka kb k >,则称区间[],a b 为()f x 的“k 倍值区间”.下列函数：①()f x lnx =；②()()10fx x x =>；③()()20f x xx =≥；④()()2011x f x x x =≤≤+.其中存在“3倍值区间”的有（ ） A ．①③ B ．②③ C ．②④ D ．①②③④12．如图，在棱长为2的正方体1111ABCD A B C D -中，点E F 、分别是棱BC ，1CC 的中点，P 是侧面11BCC B 内一点，若1A P //平面AEF ，则线段1A P 长度的取值范围是（ ）A ．B ．C ．[2D ． 二、填空题（每小题5分，共计20分）13．求值：3log 43lg -+= . 14．已知三棱锥P ­ABC 中，△ABC 为等边三角形，PA ＝PB ＝PC ＝2，PA ⊥PB ，则三棱锥P ­ABC 的外接球的体积为 .15．设常数a R ∈，则方程||1x x a e +⋅=的解的个数组成的集合是A = .16．在矩形ABCD 中，AB ＜BC ，现将△ABD 沿矩形的对角线BD 所在的直线进行翻折，在翻折的过程中，给出下列结论：①存在某个位置，使得直线AD 与直线BC 垂直；②存在某个位置，使得直线AC 与直线BD 垂直；③存在某个位置，使得直线AB 与直线CD 垂直．其中正确结论的序号是________．三、解答题（第17题10分，18-22每小题12分，共计70分）17．（10分）已知集合{})2(log 22x y x A --==，集合{}a y y B x +==-23 （1）当1=a 时，求B A ，B A ；（2）若B B A = ，求a 的取值范围.18．（12分）如图所示，有一块矩形铁皮ABCD ，4=AB ，剪下一个半圆面作圆锥的侧面，余下的铁皮内剪下一个与其相切的圆面，恰好作为圆锥的底面.试求：（1）矩形铁皮AD 的长度；（2）做成的圆锥体的体积.19．（12分）如图三棱柱111C B A ABC -中ABC AA 平面⊥1且21=AA ，底面ABC 是边长为2的等边三角形，点D 是11B A 的中点.（1）求证：C A 1 平面D BC 1；（2）求异面直线C A 1与1BC 所成角的大小.20．（12分）某市为创建全国卫生城市，引入某公司的智能垃圾处理设备。