郑州市2017高三一测答案(正版)

髙三英语试题卷范I 页（共12页）2017年高中毕业年级第-次质量预测英语试题卷柏—和的”）利和小选和）卄旅”护120劝*150 叙听力如鼻作”分）。

”应首钠读柿卡上的丈杓仏"在和卡上住・ 虑试曲4上作备尢*tc第I 卷償“,佔”血站上。

"内專2后•你将有两卄的时耐心上漳案 转涂到答题卡上。

第一节（共5小題;毎小超15分.満分7.5分）听下fH 5段对话。

毎段对话后有-个小题•从题中所给的A 、B 、C 三44M 中送岀量隹 选项•并标在试卷的相应位置。

听完每段对话后•你都有10秒钟的时间来回沖关小题和阅读下一小题。

毎段对话仅读一迴。

1. When was the piano bought?A ・ but y"T ・B. Lart wsk. 2. How much should the man pay?A. S16.B. $32・ 3. Where will they have lunch today 。

A ・ In a resuurant.B ・ At a coffee shop.4・ What will the weadiei piuLably be like tomorrow?A. Soowy. B ・ Wnnn ・5. What will tbe man probably do this weekend^A. Go hiking; with hb friends ・B. Stay with his friend Lewis ・Q Mak. a decision with Lewis. 第二节（*15 d4B;毎小題1・5分■满分22.5分）昕下面5段财话或独白・毎段对话或独白后有几个小建•从题中所给的A 、B 、C 三个选项中逢岀■佳迭項,并标在试卷的相应位直。

听毎段对话或独白前•你将有时间阅读各个小 副•毎小题5秒常;听完后•各小題将給出5秒仲的作答时何.毎段对话或強门读两第_部分听力（共两节，满分30分）C. Last month. C ・ $60 C. In the dining hall. C. Rainy.16. 奇三英语试题衿第2页（共12页）C. The result of her interview. What does the man think of the woman?B ・ She is too anxious.A ・ She i ・ very calm ・ 听第10段材料•回答第17至20越° What is the announcement mainly about?A. A visit to the (oretl. B ・ Safety in the mountains ・ CBoss and employee. Wrong. Excited. She is so confident.A trip to the countryside.18. Where are the »tudento Roing to camp?A. In the fo^at. B・ By the river.19 Why thouldn9! the students go into the thick pan of the forest?A. Hwy may get lo&l in it.B・Hiere it ■ river in the forest.C・ There are wild animals there・20. WTiat can we le<ni from the announcement?A. Students will make a fire «t the camping ・ite・B・ Students need to pay for some of the activities・C. Students arc coins to the forest together by bus.离三英语试题卷第3页（共|2页）Nfce. France□ncd with palm trees and froi-class hotels, the city ol Nice, lociied «> 上French Riviera, offere& 心卜coa&dine of Mediterranean beaches. Becwwe they're in the heart of the city, th* 皿* attract a large crowd・Soifywre looking for wmething more private, yg'll have to U”" a "w mil" outside of the city center.Hibadeo, SpainAt low "de. PUya de las Catedralet in Ribadeo v Spain it the perfect beach to take in the Zura! wonders without urban amutemenU like resUuranU, bare or huge crowds・ Il boasts unique rock formations making it tnily picture worthy.2】・What makes Dubrovnik w special?A・ It is surrounded by stone walls・B・ Il has the most attractive coastline.C・ It the longest beach tcMon. D・B. It has the most attractive coastline.It is the traixung center of Hairy Poiter.If you plan to go to a beach in the city. where should you go?A・ Mykonos・ B. Sicily・ C. Nice. D. Ribadeo・23. Which of the following i& true about Ribadeo?A. Visiton can try snorkeling there.B・ It offers visitors boteb.C. It has restaurants, ban and huge crowds.D・ Visitors can enjoy unique rock formations there.24. What do all the beaches have in common?A. Hiey have beautiful wild flowers.B. They are famous European beaches.C・ Hiey are well known for their green water.D. They provide risitor® with urban amutementi.Yearo a«o, my wife and 1 volunteered at a homeless shelter in downtown L M Angeles, US, preparing meali for thousands of people. I got to talk with one of the guys in line9 Albert. He s&id he liked my socks・"Want to see mine?" he asked, lifting his leg. He was barefoot. He said he had been meaning to buy a pair but he hadn*t got around to it. I felt ■ sinking feeling in my stomach.The next day, after work, I slopped at R OM and filled up a cart with socks・[stuffed my trunk with th«n・That next morning, I Mt my alarm for 5 and drove over to Santa Moniol PaliM^et "A. ^>ich is a common destination lor homeleu people.高三英语试題卷第4页（共12页）harmless but is actually damaging, is the pressure on sun to have their photos taken with exotic （奇舁的）animal. Fwnous people who are “ked to have photon taken with wild 高三英语试题卷第5页（共12页）animals for a magazine spread or who do so while on vacation always have good intentionB °nd even loveanimals. This makes them easy targets for the often pvedjr amu^mcnt parf（・ ami 川如1 animal centen・Kind people are naturally drawn to places that chim （丙称）to offer exotic ammals safety and are eager to see elephants paint, to hug baby beae or to Rwim with dolphin* However t it turns out that many of these businets persons are breeder!（饲养动韌者"）・（^ea^cr> or exhibitors that are using famous peopled goodwill for their own purposes・Many business persons continually keep the animals just to theyll have a constant supply young animals in order to charge money for photos. Of courw. the babies are lovely but they grow fart, and within a few weeks they are too big to handle. Theyl） ftpend the rest of their sometimes decades, in small and empty cages or even be killed.In some Asian countries t elephants are kept in camps・A few campe are working Io help elephants in trouble, but the vast majority are not, and training methods are bart>aric （野蛮的）and croel. As soon as the cameras are gone after someone like Prince William has a photo taken widi an elephant, the chains go back on.Fan叭tell the start： stay ・tr・y from exotic animal photos, and the animah will be grateful.28 ・ What does the author intend to <k> with this passage?A. To show how &lan influence cultural trends.B. To urge governments to look into ilk"） animal centen.C. To persuade stars not to have photoe taken with exotic animals.D. To remind people to think about how to treat wild animah kindly.29. According to the passage we can learn that many busing person® _________________ ・A・ make a great effort to provide safety for animalsB. take advantage of stars* good intentions to make profitsC. aim to offer good chances for people to get close to animalsD. expect there to be little competition as exotic animals are rare30. Why do many busineM persons continually keep young animals?A. They expect to exchange them for money at the market.B・ Hiey intend to increase the number of endangered animals.C・ *H>ey can rescue more animals and get them out of trouble.D・ H>ey want to make sure of having enough of them for photos.c. Media expcmire haa （ailed to ha^e «y effect on fampu・ people.D. Sun fed symp^hedc and concerned about miMreated animab.DIt — dui tochnohgy could be ch^nf tbe phce. where we 聪 A project conducted by J3Shu. . 2 lectuwr M the UniZy ci HertfonWure*. School ci Tenng and Technology, has buill OQ the unirerwtya ImwHone project aimed to create a home 屁f per vtoM people livii« at bone who are weak or elderiy.-We've developed a wn^Und type M device （養■）・” 2 JS Siau, -which «Uow " to monitor the ccndibon of an elderiy pemm t« whoever it rearing the device. It allo" «• to collect （hte of a perwn （o see if tbe pence has faDen ar is away from where they are Mjppoeed to be. It coonects an elderly penon with an a*uted living type of device with the InierHonw. The Mtbtcd project it part of the univenrt/t wider InterHome project, which b the development of a smart house. The bouse scores the usage p&Uexm of the penon living there and can adapt to make it use as little energy as pouible. Connecting the two together and building the service element （元素）allow us to introduce the auMed living idea to care for the elderly. It1® very UBportmt that these lechnolopes are there to help and gupport rather than to replace any af the exiting Mrnces.The IntcrHame is not just a prototype （样品）or a vehicle far mearch. Ifs ■ study tool to help ftuJents 6wi different scientific bockgrouiMb learn about and develop technology. The InferHome oomhinoi the hteet broadband technology, mobile data and commtimcabon. Reseaxchen andmake oure thM all the te chnology wuris togecher. Students get expenence by developing new haidware ■nd teftware Hiclvei. It requires a variety of skills from students—electromc en^ineerB, computer Mudentt. doti<n icudenti and ao on. ** Tbe present plan we are working g it ■ smart home project in Witford with Mroe cxxnmercud companies^ Mid Johann Sian * We ara looking at how a wwuter home can provide extra value services."32. m underiined word “ superviMs" in Paragraph 1 probably means -人wa«ch« over B・ gives support to C・ directs 33. Whit M the Interfiome project intended to do?B. Hovide better care and services for the elderly.C・ Cany out all the wort the exitiing services do.D glop iet that mainly aim to save energy.34. W）ui cm, w. le»n about the InterHome project Z the article?A. It is a li© collection of many existing technologies.B. k i» JUM • platfonn to help studente to do reaearchC. It is a smart home project developed by 出亦“ univeraiiies. D・ comfortsCall oc the students to cm for old people.D. It allowi students i<> put into ute and txy out what they" lcamed35. What is the main purpose rf the author in writing this article?A. To build up a new platform for students to develop new technology-B. To show bow future buildinsB wiU change eldeHy 怦町“股.C・ To describe a new project that aims （o develop a tma" home ：or the 7deriy・D. To introduce a new kind of technoJogy to help people to enjoy ■ better life. 第二节（其5小毎小題2分曲分10分）根据短文内容•从短文后的选項中选岀能填入空白处的最佳选琐•并在答题卡上将该项涂愿。

郑州市2017届高三上学期第一次质量预测试题数学（文）本试卷分第I 卷（选择题）和第Ⅱ卷（非选择题）两部分，考试时间120分钟，满分150分．考生应首先阅读答题卡上的文字信息，然后在答题卡上作答，在试题卷上作答无效．交卷时只交答题卡．第I 卷一、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，只有一项是符合题目要求的．1．已知集合{}{}|2,|A x x B x x m =>=<,且A B R = ，那么m 的值可以是 A ．0 B ．1 C ．2 D ．32．复数1iz i+=（i 是虚数单位）在复平面内对应的点在 A. 第一象限 B ．第二象限 C ．第三象限 D ．第四象限3． 2.5PM 是指大气中直径小于或等于2.5微米的颗粒 物，也称为可入肺颗粒物，右图是据某地某日早7点至晚8 点甲、乙两个 2.5PM 监测点统计的数据（单位：毫克／每立方米）列出的茎叶图，则甲、乙两地浓度的方差较小的是 A ．甲 B ．乙C ．甲乙相等D ．无法确定4．如图，某几何体的正视图和俯视图都是矩形，侧视 图是平行四边形，则该几何体的体积为A ．B ．C ．D ．5．已知曲线23ln 4x y x =-的一条切线的斜率为2，则切点的横坐标为 A.3 B. 2 C ．1 D ．126．已知各项不为0的等差数列{}n a 满足2478230a a a -+=，数列{}n b 是等比数列，且77b a =，则212b b 等于A ．1B ．2C ．4D ．87．若1sin()34πα-=，则cos(2)3πα+A.78- B ．14- C ．14 D ．788．已知抛物线22(0)y px p =>，过其焦点且斜率为-1的直线交抛物线于A ，B 两点，若线段AB 的中点的纵坐标为－2，则该抛物线的准线方程为A ．x=lB ．2x =C ．1x =-D ．2x =-9．设函数())cos(2)()2f x x x πϕϕϕ=+++<，且其图象关于直线0x =对称，则A ．()y f x =的最小正周期为π，且在(0,)2π上为增函数 B ．()y f x =的最小正周期为2π，且在(0,)4π上为增函数 C ．()y f x =的最小正周期为π，且在(0,)2π上为减函数 D ．()y f x =的最小正周期为2π，且在(0,)4π上为减函数10．双曲线22221(0,0)x y a b a b+=>>的左、右焦点分别是1F 、2F ，过1F 作倾斜角为30 的直线交双曲线右支于M 点，若2MF ⊥x 轴，则双曲线的离心率为B D 11．已知向量a 是与单位向量夹角为60 的任意向量，则对任意的正实数t,的最小值是A. 0B.12D. 112. 定义在R 上的函数32()(0)f x ax bx cx a =++≠的单调增区间为（-1，1），若方程23(())2()0a f x bf x c ++=恰有4个不同的实根，则实数a 的值为．A ．12 B ．12- C ．1 D ．－1第Ⅱ卷本卷包括必考题和选考题两部分．第13—21题为必考题，每个试题考生都必须作答，第22—24题为选考题，考生根据要求作答．二、填空题：本大题共4小题，每小题5分，共20分．13．设,x y 满足约束条件1,3,0,x y x y y -≥-⎧⎪+<⎨⎪>⎩， 则z x y =-的取值范围为________．14．执行右面的程序框图，若输出的78S =，则输入的整 数p 的值为__________．15.已知三棱柱111ABC A B C -的侧棱垂直于底面，各顶 点都在同一球面上，若12,2,1AA AB AC ===．60BAC ∠= ，则此球的表面积等于_________．16．整数数列{}n a 满足21()n n n a a a n N *++=-∈，若此数列的前800项的和是2017，前813项的和是2000，则其前2017项的和为__________．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．（本小题满分12分） 已知函数()sin(2)(0,0)f x A x A ϕϕπ=+><<，当3x π=-时取得最小值-4．(I)求函数()f x 的解析式；(Ⅱ)若等差数列{}n a 前n 项和为n S ，且24(0),()6a f a f π==，求数列1n S ⎧⎫⎨⎬⎩⎭的前n 项和n T . 18．（本小题满分12分）郑州市为了缓解城市交通压力，大力发展公共交通，提倡多坐公交少开车,为了调查市民乘公交车的候车情况，交通主管部门从在某站台等车的45名候车乘客中随机抽取15人，按照他们的候车时间（单位：分钟）作为样本分成6组，如下表所示：(I)估计这45名乘客中候车时间少于12分钟的人数；(Ⅱ)若从上表第四、五组的5人中随机抽取2人做进一步的问卷调查，求抽到的2人恰好来自不同组的概率．19.（本小题满分12分）在三棱柱111ABC A B C -中，侧面11ABB A 为矩形，11,AB AA ==D 为1AA 的中点，BD 与1AB 交于点O ，CO ⊥侧面11ABB A ． (I)证明：1BC AB ⊥；(Ⅱ)若OC OA =，求三棱锥1C ABC -的体积． 20．（本小题满分12分）已知△ABC 的两顶点坐标(1,0),(1,0)A B -，圆E 是△ABC 的内切圆，在边AC ，BC ，AB 上的切点分别为P ，Q ，R ，1CP =（从圆外一点到圆的两条切线段长相等），动点C 的轨迹为曲线M ．(I)求曲线M 的方程；(Ⅱ)设直线BC 与曲线M 的另一交点为D ，当点A 在 以线段CD 为直径的圆上时，求直线BC 的方程．21.（本小题满分12分） 已知函数(1)()ln ,()k x f x x x g x x-==． (I)当k e =时，求函数()()()h x f x g x =-的单调区间和极值；； (Ⅱ) 若()()f x g x ≥恒成立，求实数k 的值。

2020届河南省郑州市2017级高三一模考试英语试卷★祝考试顺利★(含答案)第二部分阅读理解（共两节,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和D四个选项中,选出最佳选项。

ALooking for work?Tutors Wanted:Mall/Science/Humanities+Test PreparationJob Posted:2 days agoWage:$27-30 per hourJob Type: Part-limeSchedule: Afternoons,evenings,weekdays,weekendsJob description:We're looking for tutors lo join us before the next school year starts.Our suitable candidate will be able to assist middle and high school students with test preparation and academic work in Math,Science and/or Humanities.We'll pay for your training before this fall and can also offer flexible summer tutoring chances, including teaching group classes.Once our fall semester starts on August 21, we'll have even higher demand for tutoring sessions on Sundays from 1 p. m. to 8 p. m. as well as from 3 p. m. to 9 p. m. from Monday to Thursday.What we offer:＊Flexible scheduling. Tutors work from 15 to 30 hours per week depending on availability and students' demand.＊Free Sunday dinners during the academic year.＊Fun staff gatherings.＊Health insurance reimbursement(报销）for staff working over 30 hours per week.＊We are 5 minutes' walking distance from the Menlo Park Station.Applicants must:＊Have a good command of the subjects which they tutor students in.＊Be willing to tutor students through the full academic year.Application instructions:＊Email us your resume(简历）。

2017年高中毕业年级第一次质量预测英语参考答案一、选择题（1-60）：1.C2.B3.A4.C5.B6.A7.C8.C9.A 10.B 11.C 12.B 13.A 14.A 15.C 16.B 17.C 18.A 19.C 20.B 21.A 22.C 23.D 24.B 25.D 26.A 27.C 28.C 29.B 30.D 31.B 32.A 33.B 34.D 35.C 36.B 37.D 38.A 39.G 40.F 41.B 42.A 43.D 44.C 45.B 46.C 47.A 48.D 49.C 50.A 51.B 52.D 53.A 54.D 55.C 56.B57.D 58.C 59.B 60.A二、英语知识运用第二节（61-70）：61. itself 62. was described 63. preventing 64. that 65. is66. The 67. flowers 68. at 69. held 70. as三、短文改错：Last weekend we went for camping in the mountains with our teacher, Anna. When wearrived, we made a camp fire first. Then, Anna taught us to catch fish so that they could have morewefood to eat that night. I liked the airs there because it was fresh and clean. Many stars were upairhighly in the sky and the moon looked bright. We all sat around the fire, listening ∧Anna’s high to stories about her childhood. She was born into a poor family or she had worked very hard to beandsuccessful. I was very touched that I couldn’t sleep the whole night, thought about being a teacher so thinkingin the future. When I get home, I said to my parents, “Everything was great about the camping. I gotwant to be the teacher like Anna in the future.”a（注：第6处，若把or改为so或but亦可；第8处，若在thought前加and亦可。

河南省郑州市2017届高中毕业年级第一次质量预测数学（文科）第Ⅰ卷（共60分）一、选择题：本大题共12个小题,每小题5分,共60分.在每小题给出的四个选项中，只有一项是符合题目要求的.1.已知集合{}2|1M x x =<，{}|21xN x =>，则MN =（ ）A ．∅B ．{}|01x x <<C ．{}|0x x <D ．{}|1x x <2.若复数z 满足)3i z i =（i 为虚数单位），则z 的共轭复数为（ ）A iB iC ．1+D ．13.已知命题p ：114a >，命题q ：x R ∀∈，210ax ax ++>，则p 成立是q 成立的（ ） 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4.在ABC ∆中，||3||AB AC AB AC +=-，||||3AB AC ==，则CB CA ⋅=（ ） A ．3B ．3-C ．92D ．92-5.我们可以用随机模拟的方法估计π的值，如图程序框图表示其基本步骤（函数RAND 是产生随机数的函数，它能随机产生(0,1)内的任何一个实数）．若输出的结果为781，则由此可估计π的近似值为（ ） A ．3.119 B ．3.124C ．3.132D ．3.1516.某几何体的三视图如图所示，则其体积为（ ）A ．207B ．92162π-C ．21636π-D ．21618π-7.函数sin 2cos 2y x x =+如何平移可以得到函数sin 2cos 2y x x =-图象（ ） A ．向左平移2π B ．向右平移2π C ．向左平移4π D ．向右平移4π 8.函数12()()cos 12xxf x x -=+的图象大致为（ ）9.如图直三棱柱'''ABC A B C -中，ABC ∆为边长为2的等边三角形，'4AA =，点E 、F 、G 、H 、M 分别是边'AA 、AB 、'BB 、 ''A B 、BC 的中点，动点P 在四边形EFGH 内部运动，并且始终有 //MP 平面''ACC A ，则动点P 的轨迹长度为（ ） A ．2B ．2πC．D ．410.已知双曲线的焦点到渐进线的距离等于实半轴长，则该双曲线的离心率为（ ） A．12B ．2CD．11.已知a ，b R +∈，且115a b a b+++=，则a b +的取值范围是（ ） A ．[]1,4 B ．[2,)+∞ C ．(2,4) D ．(4,)+∞12.已知函数()ln f x x x x =+，若m Z ∈，且(2)(2)()m x f x --<对任意的2x >恒成立，则m 的最大值为（ ）A ．4B ．5C ．6D ．8第Ⅱ卷（共90分）二、填空题（每题5分，满分20分，将答案填在答题纸上）13.在平面直角坐标系xOy 中，已知角α的顶点和点O 重合，始边与x 轴的非负半轴重合，终边上一点M坐标为，则tan()4πα+= ．14.已知实数x ，y 满足不等式组360,240,20,x y x y y -+≥⎧⎪+-≤⎨⎪+≥⎩则z x y =+的最小值为 ．15.如果满足60A ∠=︒，6BC =，AB k =的锐角ABC ∆有且只有一个，那么实数k 的取值范围是 ．16.对于函数()f x 与()g x ，若存在{}|()0x R f x λ∈∈=，{}|()0x R g x μ∈∈=，使得||1λμ-≤，则称函数()f x 与()g x 互为“零点密切函数”，现已知函数2()3x f x e x -=+-与2()4g x x ax x =--+互为“零点密切函数”，则实数a 的取值范围是 ．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. （本小题满分12分）已知数列{}n a 的前n 项和22n n nS +=，*n N ∈．（1）求数列{}n a 的通项公式；（2）设2(1)n an n n b a =+-，求数列{}n b 的前2n 项和．18. （本小题满分12分）如图，在四棱锥S ABCD -中，底面梯形ABCD 中，//AD BC ，平面SAB ⊥平面ABCD ，SAB ∆是等边三角形，已知24AC AB ==，22BC AD CD ===M 是SD 上任意一点，SM mMD =，且0m >．（1）求证：平面SAB ⊥平面MAC ；（2）试确定m 的值，使三棱锥S ABC -体积为 三棱锥S MAC -体积的3倍．19. （本小题满分12分）近年来郑州空气污染较为严重，现随机抽取一年（365天）内100天的空气中 2.5PM 指数的监测数据，统计结果如下：记某企业每天由空气污染造成的经济损失为S （单位：元）， 2.5PM 指数为x ．当x 在区间[]0,100内时对企业没有造成经济损失；当x 在区间(100,300]内时对企业造成经济损失成直线模型（当 2.5PM 指数为150时造成的经济损失为500元，当 2.5PM 指数为200时，造成的经济损失为700元）；当 2.5PM 指数大于300时造成的经济损失为2000元． （1）试写出()S x 的表达式；（2）试估计在本年内随机抽取一天，该天经济损失S 大于500元且不超过900元的概率； （3）若本次抽取的样本数据有30天是在供暖季，其中有8天为重度污染，完成下面列联表，并判断是否有95%的把握认为郑州市本年度空气重度污染与供暖有关？22()()()()()n ad bc K a b c d a c b d -=++++，其中n a b c d =+++．20. （本小题满分12分）已知坐标平面上动点(,)M x y 与两个定点(26,1)P ，(2,1)Q ，且||5||MP MQ =． （1）求点M 的轨迹方程，并说明轨迹是什么图形；（2）记（1）中轨迹为C ，过点(2,3)N -的直线l 被C 所截得的线段长度为8，求直线l 的方程．21. （本小题满分12分） 已知函数()ln f x x =． （1）证明：()1f x x ≤-；（2）若对任意0x >，不等式1()1a f x ax x-≤+-恒成立，求实数a 的取值范围．请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分.22. （本小题满分10分）选修4-4：坐标系与参数方程在平面直角坐标系xOy 中，曲线1C 的参数方程为2cos sin x y ϕϕ=⎧⎨=⎩（ϕ为参数），在以O 为极点，x 轴的正半轴为极轴的极坐标系中，曲线2C 是圆心为(3,)2π，半径为1的圆．（1）求曲线1C ，2C 的直角坐标方程；（2）设M 为曲线1C 上的点，N 为曲线2C 上的点，求||MN 的取值范围．23. （本小题满分10分）选修4-5：不等式选讲已知0a >，0b >，函数()||||f x x a x b =++-的最小值为4． （1）求a b +的值； （2）求221149a b +的最小值．数学（文科）参考答案一、选择题1-5:BDACB 6-10:BDCDC 11、12：AC 二、填空题13.2- 14.14-15. 16.[]3,4三、解答题17.解：（1）当1n =时，111a S ==；当2n ≥时， 1a 也满足n a n =，故数列{}n a 的通项公式为n a n =.（2）由（1）知n a n =，故2(1)n n n b n =+-. 记数列{}n b 的前2n 项和为2n T ，则1222(222)(12342)n n T n =++++-+-+-+.记122222nA =+++，12342B n =-+-+-+，[](12)(34)(21)2B n n n =-++-+++--+=.故数列{}n b 的前2n 项和21222n n T A B n +=+=+-.18.（1）证明：在ABC ∆中，由于2,4,AB AC BC ===∴222AB AC BC +=,故AB AC ⊥．又平面SAD ⊥平面ABCD ，平面SAB 平面ABCD AB =，AC ABCD ⊂平面，∴AC SAB ⊥平面，又AC MAC ⊂平面，（22m =．19. 解：（1）根据在区间]100,0[对企业没有造成经济损失;在区间]300,100(对企业造成经济损失成直线模型（当PM2.5指数为150时造成的经济损失为500元,当PM2.5指数为200时,造成的经济损失为700元）;当PM2.5指数大于300时造成的经济损失为2000元,可得：[]0,0,100,()4100,(100,300],2000,(300,).x S x x x x ⎧∈⎪=-∈⎨⎪∈+∞⎩（2）设“在本年内随机抽取一天，该天经济损失S 大于200元且不超过600元”为事件A ， 由200600,<≤S 得150250,<≤w 频数为39（32K 的观测值 所以有95%的把握认为空气重度污染与供暖有关． 20. 解：(Ⅰ)由题意，得5MP MQ=化简，得：2222230x y x y +---=， 所以点M 的轨迹方程是22(1)(1)25x y -+-=. 轨迹是以(1,1)为圆心，以5为半径的圆．（II ）当直线l 的斜率不存在时，:l 2x =-，所以:l 2x =-符合题意．当直线l 的斜率存在时，设l 的方程为3(2)y k x -=+，即230,-++=kx y k 圆心到l 的距离所以直线l 的方程为即512460x y -+=． 综上，直线l 的方程为2x =-或512460x y -+=. 21. 解：（Ⅰ）令()()(1)g x f x x =--,则 1() 1.g x x'=- 当1,()0.x g x '==所以01()0,x g x '<<>时， 1()0,x g x '><时， 即()g x 在()0,1递增；在()1,+∞递减； 所以()(1)0g x g ≤=，() 1.f x x ≤- （Ⅱ）记,ln 1)(x xa ax x h --+=则在),0(+∞上，1)(≥x h ， ()()()22221111110,a x x a ax x a a h x a x x x x x⎛⎫+-- ⎪--+-⎝⎭'=+-==> ①若102a <≤，111a-+>，(0,1)x ∈时，0)('>x h ，)(x h 单调递增，012)1()(≤-=<a h x h ， 这与),0(+∞上1)(≥x h 矛盾；②若112a <<，1011a <-+<，),1(+∞上)(,0)('x h x h >递增，而112)1(<-=a h ，这与),0(+∞上1)(≥x h 矛盾；③若1≥a ，011≤+-a，∴)1,0(∈x 时0)('<x h ，)(x h 单调递减；(1,)x ∈+∞时0)('>x h ，)(x h 单递增；∴min ()(1)211h x h a ==-≥，即()1h x ≥恒成立； ④若0=a ，()21xx x h +-='，()1,0∈x 时，()0>'x h ，()x h 单调递增；()+∞∈,1x 时，()0<'x h ，()x h 单调递减，∴()()110h x h ≤=-<，这与),0(+∞上1)(≥x h 矛盾；⑤若0<a ，011<+-a，()1,0∈x 时，()0>'x h ，()x h 单调递增；()+∞∈,1x 时，()0<'x h ，()x h 单调递减，∴()()1210,h x h a ≤=-<这与),0(+∞上1)(≥x h 矛盾．综上，实数a 的取值范围是[1,)+∞．22.解：（1）消去参数ϕ可得1C 的直角坐标方程为曲线2C 的圆心的直角坐标为)3,0(， ∴2C 的直角坐标方程为1)3(22=-+y x ．（2）设),sin ,cos 2(ϕϕM1sin 1≤≤-ϕ，∴,2||min 2=MC ，4||max 2=MC .根据题意可得,112||min =-=MN ，,514||max =+=MN 即||MN 的取值范围是[]1,5．23. 解：（1所以()f x a b ≥+，当且仅当0))((<-+b x a x 时，等号成立，又0,0a b >>， 所以||a b a b +=+，所以()f x 的最小值为a b +,所以4a b +=． （2）由（1）知4,4a b b a +==-，。

2017年高中毕业年级第一次质量预测物理 参考答案一、选择题（本题共11小题，每小题4分，共44分。

全部选对的得4分，选对但不全的得2分，有选错或不答的得0分。

答案填涂在答题卡的相应位置。

）1．C 2．B 3．D 4．A 5．D 6．C 7．AC 8．BC 9．AD 10．BC 11．BD二、实验题（本题共2小题，共17分。

请把分析结果填在答题卡上或按题目要求作答。

）12．(1)错误！未找到引用源。

（2分），(2)m ＜＜M （1分），(3)错误！未找到引用源。

（2分），小于（1分）。

13．(1) 0.830 mm （2分）(2) ①（1分），④（1分），R 1（1分）(3)21.3 Ω（2分） (4) 错误！未找到引用源。

（2三、计算题（本题共4小题，共39分。

解答时应写出必要的文字说明、方程式和重要演算步骤。

只写最后答案的不能得分。

有数值计算的题，答案中必须写出数值和单位。

）14．(1)两车减速运动的加速度为错误！未找到引用源。

（1分）甲车减速到v 2所用时间为错误！未找到引用源。

， 走过的距离为 错误！未找到引用源。

，甲车从匀速运动到栏杆打开所用时间为 错误！未找到引用源。

甲车从减速到栏杆打开的总时间为 t 甲=错误！未找到引用源。

（2分）乙车减速行驶到收费岛中心线的时间为 错误！未找到引用源。

，从减速到栏杆打开的总时间为 错误！未找到引用源。

（1分）人工收费通道和ETC 通道打开栏杆放行的时间差错误！未找到引用源。

（1分）(2) 解法一乙车从收费岛减速带到恢复正常行驶，所用时间为 t 乙=t 3+t 0+t 3=31s乙车从收费岛减速带到恢复正常行驶，走过的距离为 x 乙=x +d +x =160m （1分）甲车从收费岛减速带到乙车恢复正常行驶，所用时间为 t 甲=t 1+t 2+t 1+t显然t 甲=t 乙，即t =2t 3+t 0-2t 1-t 2=21s甲车从收费岛减速带到乙车恢复正常行驶，走过的距离为x甲=x1+x2+x1+v1t=560m （2分）所以，两车驶离收费站后相距最远为△x=x甲-x乙=400m （1分）（2）解法二乙车从收费岛中心线开始出发又经t3=8 s加速到v1=72 km/h，与甲车达到共同速度，此时两车相距最远。

2017年河南郑州高三一模英语试卷-学生用卷一、阅读理解（共两节）1、【来源】 2017年河南郑州高三一模第1~4题8分Traveling to Europe to see famous monuments like the Eiffel Tower in Paris and the Colosseum（古罗马竞技场）in Rome, is not exactly the ideal vacation for kids. Fortunately, Europe has more to offer than lots of old churches and ancient history. You can enjoy some fun with your kids in the sun at some of the famous beaches of the continent.Mykonos, GreeceThe closer you get to the equator, the longer the beach season is, and Greece is wonderful for that. You can enjoy beautiful green water, public chairs and lovely umbrellas at the beaches in Mykonos. Dubrovnik, CroatiaThere's nothing more attractive than the beautiful beaches bordering Dubrovnik, Croatia's most beautiful city. It's surrounded by stone walls like a castle. It almost makes you feel like you're suntanning （晒黑皮肤）at Hogwarts, where the hero Harry Porter of the story is trained!Sicily, ItalyRabbit Beach on the island of Sicily offers shallow and crystal clear waters, making it a perfect beach for families with young children. And if you want to add interest to your experience, try snorkeling（徒手潜水）.Nice, FranceLined with palm trees and first﹣class hotels, the city of Nice, located on the French Riviera, offers a whole coastline of Mediterranean beaches. Because they're in the heart of the city, these beaches attract a large crowd. So if you're looking for something more private, you'll have to travel a few miles outside of the city center.Ribadeo, SpainAt low tide, Playa de las Catedrales in Ribadeo, Spain is the perfect beach to take in the natural wonders without urban amusements like restaurants, bars or huge crowds. It boasts beautiful wild flowers and unique rock formations making it truly picture worthy.(1) What makes Dubrovnik so special?A. It is surrounded by stone walls.B. It has the most attractive coastline.C. It has the longest beach season.D. It is the training center of Harry Porter.(2) If you plan to go to a beach in the city, where should you go?A. Mykonos.B. Sicily.C. Nice.D. Ribadeo.(3) Which of the following is true about Ribadeo?A. Visitors can try snorkeling there.B. It offers visitors first-lass hotels.C. It has restaurants, bars and huge crowds.D. Visitors can enjoy unique rock formations there.(4) What do all the beaches have in common?A. They have beautiful wild flowers.B. They are famous European beaches.C. They are well known for their green water.D. They provide visitors with urban amusements.2、【来源】 2017年河南郑州高三一模第5~7题6分(每题2分)Years ago, my wife and I volunteered at a homeless shelter in downtown Los Angeles, U.S., preparing meals for thousands of people, I got to talk with one of the guys in line, Albert. He said he liked my socks. "Want to see mine？" he asked, lifting his leg. He was barefoot. He said he had been meaning to buy a pair but he hadn't got around to it. I felt a sinking feeling in my stomach.The next day, after work, I stopped at Ross and filled up a cart with socks. I stuffed my trunk with them. The next morning, I set my alarm for 5 a.m. and drove over to Santa Monica's Palisades Park, which is a common destination for homeless people.I took one of the bags from my trunk. It was still dark out. I headed for a group of three men around a tree, probably using it as a windbreaker. Two were asleep under heavy blankets, and the third was digging through his collection. As I walked toward him, he watched me, perhaps questioning my motives. "I thought you guys might need some fresh new socks. " I said, handing him a pair. He looked confused at first but took them and said, "thank you." I gave him two more pairs for his friends.I moved on. An hour later, I had given out all the socks.Most people were sleeping, and I felt like Santa. I knew that when they woke up they would find a very meaning present.That was nine years ago. Every week I'll hand out as many socks as I can. If I'm on vacation or on a business trip for more than a week, I bring a bag of socks with me and hand them out to the homeless on the streets in other states and countries.It's extremely satisfying to operate "under the radar" to help make some people's lives a little bit easier. Part of me hopes to see Albert out there one of these days, but even if I don't I like to think one of the pairs will find him.(1) What caused the author to hand out socks to the homeless？A. Albert's desire to get free socks.B. The approach of Christmas Day.C. His hard work at a homeless shelter.D. The conversation between him and Albert.(2) Which is true about the author according to the passage？A. He believed it felt good to help the homeless．B. He went to Rose to buy a pair of socks for Albert．C. He handed out socks to the homeless as Christmas gifts．D. He was often questioned about why he was giving out socks．(3) What could be the best title for the passageA. Santa Clause Brings Christmas GiftsB. Kindness Is Rewarded With KindnessC. Every Sock Helps Make Somebody's DayD. Socks Are Passed on From Hand to Hand3、【来源】 2017年河南郑州高三一模第8~11题8分Famous people have a lot of influence on cultural trends, like it or not. However, one trend that seems harmless but is actually damaging, is the pressure on stars to have their photos taken with exotic （奇异的） animals. Famous people who are asked to have photos taken with wild animals for a magazine spread or who do so while on vacation always have good intentions and even love animals. This makes them easytargets for the often greedy amusement parks and illegal animals centers. Kind people are naturally drawn to places that claim（声称）to offer exotic animals safety and are eager to see elephants paint, to bug baby bears or to swim with dolphins. However, it turns out that many of these business persons are breeders（饲养动物者）, dealers or exhibitors that are using famous people's goodwill for their own purposes.Many business persons continually keep the animals just so they'll have a constant supply of young animals in order to charge money for photos. Of course, the babies are lovely but they grow fast, and within a few weeks they are too big to handle. They'll spend rest of their lives. something decades, in small and empty cages or even be killed.In some Asian countries, elephants are kept in camps. A few camps are working to help elephants in trouble, but the vast majority are not, and training methods are barbaric（野蛮的）and cruel. As soon as the cameras are gone after someone like Prince William has a photo taken with an elephant, the chains go back on.Fans, tell the stars: stay away from exotic animals photos, and the animals will be grateful.(1) What does the author intend to do with this passageA. To show how stars influence cultural trendsB. To urge governments to look into illegal animals centersC. To remind people to think about how to treat wild animals kindlyD. To persuade stars not to have photos taken with exotic animals(2) According to the passage we can learn that many business persons.A. make a great effort to provide safety for animalsB. aim to offer good chances for people to get close to animalsC. take advantage of star's good intentions to make profitsD. expect there to be little competition as exotic animals are rare(3) Why do many business persons continually keep young animals？A. They expect to exchange them for many at the marketB. They intend to increase the number of endangered animalsC. They want to make sure of having enough of them for photosD. They can rescue more animals and get them out of trouble(4) What can be inferred from the passage？A. Stars can have photos taken with exotic animals free of chargeB. Many people follow stars and have photos taken with exotic animalsC. Media exposure has failed to have any effect on famous peopleD. Stars feel sympathetic and concerned about mistreated animals4、【来源】 2017年河南郑州高三一模第12~15题8分It seems that technology could be changing the places where we live. A project conducted by Johann Sinu, a senior lecturer at the University of Hertfordshire's School of Engineering and Technology, has built on the university's InterHome project aimed to create a home that TAL#NBSP supervises people living at home who are weak or elderly."We've developed a wristband type of device（装置）, "said Johann Siau, "which allows us to monitor the condition of an elderly person, or whoever is wearing the device. It allows us to collect data of a person to see if the person has fallen or is away from where they are supposed to be. It connects an elderly person with an assisted living type of device with the InterHome. " The assisted living project is part of the university's wider InterHome project, which is the development of a smart house. The house stores the usage patterns of the person living there and can adapt to make it use as little energy as possible. Connecting the two together and building the service element（元素）allow us to introduce the assisted-living idea to care for the elderly. It's very important that these technologies are there to help and support rather than to replace any of the existing services.The InterHome is not just a prototype or a vehicle for research, it's a study tool to help students from different scientific backgrounds learn about and develop technology. The InterHome combines the latest broadband technology, mobile data and communication. Researchers and students make sure all the technology works together. Students s get experience by developing new hardware and software themselves. It requires a variety of skills from students—electronic engineers, computer students, design students and so on. "The present plan we are working on is a smart home proj ct inWatford with some commercial companies, " said Johann Siau. "We are looking at how a smarter home can provide extra value services. "(1) The underlined word "supervises" in the paragraph 1 is probably means"".A. gives support toB. watches overC. directsD. comforts(2) What is the InterHome project intended to doA. Call on the students to care for old peopleB. Provide better care and services for the elderlyC. Carry out all the work the existing services doD. Develop houses that mainly aim to save energy(3) What can we learn about the Interhome project from the articleA. It is a large collection of many existing technologiesB. It is just a platform to help students to do research workC. It is a smart home project developed by different universitiesD. It allows students to put into use and try out what they're learned(4) What is the main purpose of the author in writing this articleA. To build up a new platform for students to develop new technologyB. To describe a new project that aims to develop a smart home for the elderlyC. To show how future building will change elderly people's way of lifeD. To introduce a new kind of technology to help people to enjoy a better life5、【来源】 2017年河南郑州高三一模第15~20题10分Do people Need Small Talk to Be Happy?Psychologists（心理学家）have long said that connecting with others is an important part of happiness, but just how much conversation we require is under examination. In one study, researchers found that small talk made up only 10% of their conversation related withhappiness.1Scientists believe that small talk could promote bonding. Late last year, Princeton researchers reported that small talk keeps closeness with loved ones, and isn't merely the stuff of awkward exchanges with strangers.Still, chatting with strangers could brighten your morning.In a series of experiments, psychologists gave Chicago passengers different directions about whether to talk with fellow passengers—something they typically avoided.2None of the chatters reported being rejected.Small talk can also help us feel connected to our surroundings. People who smiled at, made eye contact with, and briefly spoke with their Starbucks baristas（服务员）reported a greater sense of belonging than those who rushed through the transaction（交易）.3One report found that when volunteers broke the silence to chat with gallery goers, the visitors felt happier and more connected to the exhibit than those who were not approached.4none study, people who were rated"less curious"by researchers had getting a conversation rolling on their own, and had greater luck building closeness with others when they were supplied with questions that encouraged personal disclosure （透露）. But people who were considered "curious" needed no help when transforming conversations about ordinary things into personal exchanges.5A. The same is true of gallery goers.B. But don't play down small talk just yet.C. They found that small talk is related with happiness.D. Those told to chat with others reported a more pleasant journey.E. Making small talk is an important skill for all the social situations.F. A“curious mindset", the author concl uded, can lead to "positive social interactions".G. Of course, some people are better than others at turning small talk into something bigger.二、英语知识运用（共两节）6、【来源】 2017年河南郑州高三一模第21~40题30分2017~2018学年安徽合肥庐阳区合肥市第六中学高一上学期期中第21~40题30分2017~2018学年11月内蒙古呼和浩特高三上学期月考第41~60题30分I remember the first day when I saw Sally playing basketball. I watched in wonder as she struggled her way through the crowd of boys on the playground. She seemed so1, but she managed to shoot jump shots just over their heads and into the net. The boys always tried to stopher2nobody could.I began to notice Sally at other times, basketball in hand, playing3. She practiced dribbling（运球）and4over and over.One day I asked Sally why she5so much. Without a moment of hesitation she said, "I want to go to college. The only way I can go is to geta6. I'm going to play college basketball and I want to be the best one. I believe that if I am7enough, I will get one. My father has told me that if the dream is big enough, the facts don't8. "I9her through those junior high years and into high school. Every week, she led her team to10. One day in her senior year, I saw her sitting on the grass, her head11in her arms. Slowly and quietly,I12nd sat down beside her. "What's wrong? " I asked. "Oh, nothing, "came a soft reply, "I am just too short. "The13told her that at 165cm she would probably never play for a top team-still less she would be14 a scholarship-so she should stop dreaming about college.I felt she was extremely15. I asked her if she had talked to her dad about it yet. She told me that her father said those coaches were16. They didn't understand the17of a dream.The next year, Sally was seen by a college basketball coach after a big game. Shewas18offered a scholarship and19to the college team. She was going to get the college education that she had20and worked toward for all those years.It's true: if the dream is big enough, the facts don't count.A. silentB. smallC. strongD. hugeA. butB. andC. soD. forA. stillB. againC. wellD. aloneA. passingB. runningC. shootingD. strugglingA. studiedB. practicedC. expectedD. improvedA. titleB. prizeC. scholarshipD. rewardA. goodB. braveC. carefulD. activeA. lackB. talkC. appearD. countA. encouragedB. respectedC. watchedD. helpedA. victoryB. confidenceC. responsibilityD. professionA. droppedB. buriedC. coveredD. sunkA. walked offB. walked outC. walked aroundD. walked upA. coachB. teacherC. captainD. leaderA. suggestedB. sentC. promisedD. offeredA. worriedB. excitedC. disappointedD. surprisedA. greatB. wrongC. strictD. cruelA. pressureB. valueC. causeD. powerA. exactlyB. naturallyC. reallyD. normallyA. takenB. admittedC. introducedD. appointedA. dreamed ofB. picked upC. benefited fromD. carried out7、【来源】 2017年河南郑州高三一模第41~50题15分Tea is consumed around the world more than any other drink except water. Originating in China, tea has long established1（it）as the national drink of this country.A century before the birth of Christ, tea2（describe）in Chinese texts as a health drink that made one live longer. Today, it is still being regarded as such. Both green and black teas are claimed to be effective for3（prevent）cancer, heart disease, and many other deadly diseases. There is only one point4people need to be aware of when they drink tea—it should not be drunk along with meals.Tea, a popular drink in China and many other countries,5（be）carefully prepared according to local customs.6Chinese put loose tea in teapots, add boiling water, and serve it in teacups: The strong tea from China's Fujian Province is drunk in tiny cups before dinner. Lighter teas with jasmine（茉莉）, rose orother7（flower）, usually served after dinner, are special to China's Changjiang River regions.Many English people, travelling away from home, feel8 a loss if their favourite teabags are not available. Afternoon tea in England is still a time-honoured tradition. It's a good opportunity for people to socialize or discuss business matters.In Japan, a tea ceremony is often held while people are drinking tea. The ceremony,usually9（hold） in a teahouse, dates back to the 16th century. Guestsfollow strict rules set up then and the tea used is a powdered green tea. Though still practised today, the ceremony may not be as popular10it used to be.三、写作（共两节）8、【来源】 2017年河南郑州高三一模第51题10分2020~2021学年四川成都高新区电子科技大学实验中学高二上学期开学考试第71题10分假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。

郑州市2017届高三上学期第一次质量预测试题数学（理）本试卷分第I 卷（选择题）和第Ⅱ卷（非选择题）两部分，考试时间120分钟，满分150分．考生应首先阅读答题卡上的文字信息，然后在答题卡上作答，在试题卷上作答无效．交卷时只交答题卡．第I 卷一、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，只有一项是符合题目要求的．1．已知集合{}{}|2,|2A x x B x x m =>=<,且，那么m 的值可以是A ．1B ．2C ．3D ．42．复数1iz i+=（i 是虚数单位）在复平面内对应的点在 A. 第一象限 B ．第二象限 C ．第三象限 D ．第四象限3． 2.5PM 是指大气中直径小于或等于2.5微米的颗粒 物，也称为可入肺颗粒物，右图是据某地某日早7点至晚8 点甲、乙两个 2.5PM 监测点统计的数据（单位：毫克／每立方米）列出的茎叶图，则甲、乙两地浓度的方差较小的是 A ．甲 B ．乙C ．甲乙相等D ．无法确定4．如图，某几何体的正视图和俯视图都是矩形，侧视 图是平行四边形，则该几何体的表面积为A ．15+B ．C ．30+．5．已知曲线23ln 4x y x =-的一条切线的斜率为12-，则切点的横坐标为 A.3 B. 2 C ．1 D ．126．已知各项不为0的等差数列{}n a 满足2478230a a a -+=，数列{}n b 是等比数列，且77b a =，则2811b b b 等于A ．1B ．2C ．4D ．87．二项式6(ax 的展开式的第二项的系数为-，则22a x dx -⎰的值为A.3 B ．73 C ．3或73 D ．3或103-8．已知抛物线22(0)y px p =>，过其焦点且斜率为-1的直线交抛物线于A ，B 两点，若线段AB 的中点的横坐标为3，则该抛物线的准线方程为A ．x=lB ．2x =C ．1x =-D ．2x =-9．设函数())cos(2)()2f x x x πϕϕϕ=+++<，且其图象关于直线0x =对称，则A ．()y f x =的最小正周期为π，且在(0,)2π上为增函数 B ．()y f x =的最小正周期为π，且在(0,)2π上为减函数 C ．()y f x =的最小正周期为2π，且在(0,)4π上为增函数 D ．()y f x =的最小正周期为2π，且在(0,)4π上为减函数10．已知a ，b 是两个互相垂直的单位向量，且1c a c b ==，则对任意的正实数t ， 1c ta b t++的最小值是A.2 B ． C ．4 D ．11．已知椭圆221:12x y C m n -=+与双曲线222:1x y C m n+=有相同的焦点，则椭圆1C 的离心率e 的取值范围为A. B. C. (0,1) D. 1(0,)212.已知数列{}n a 的通项公式为)n a n N *=∈，其前n 项和为n S ，则在数列1S 、2S 、…2014S 中，有理数项的项数为A ．42B ．43C ．44D ．45第Ⅱ卷本卷包括必考题和选考题两部分．第13—21题为必考题，每个试题考生都必须作答，第22—24题为选考题，考生根据要求作答．二、填空题：本大题共4小题，每小题5分，共20分．13．设,x y 满足约束条件1,3,0,x y x y y -≥-⎧⎪+<⎨⎪>⎩， 则z x y =-的取值范围为________．14．执行右面的程序框图，若输出的3132S =，则输入的整 数p 的值为__________．15.已知三棱柱111ABC A B C -的侧棱垂直于底面，各顶2,1AB AC ==．60ABC ∠= ，则此球的表面积等于_________．16．定义在R 上的函数32()(0)f x ax bx cx a =++≠的单 调增区间为（-1，1），若方程23(())2()0a f x bf x c ++=恰有6个不同的实根，则实数a 的取值范围是__________．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．（本小题满分12分） 如图△ABC 中，已知点D 在BC 边上，满足0,AD AC ⋅=sin BAC AB BD ∠=== (I)求AD 的长; (Ⅱ)求cosC ．18.（本小题满分12分）为迎接2017年“马”年的到来，某校举办猜奖活动，参与者需先后回答两道选择题，问题A 有三个选项，问题B 有四个选项，但都只有一个选项是正确的，正确回答问题A 可获奖金a 元，正确回答问题B 可获奖金b 元．活动规定：参与者可任意选择回答问题的顺序，如果第一个问题回答正确，则继续答题，否则该参与者猜奖活动终止．假设一个参与者在回答问题前，对这两个问题都很陌生．(I)如果参与者先回答问题A ，求其恰好获得奖金a 元的概率；(Ⅱ)试确定哪种回答问题的顺序能使该参与者获奖金额的期望值较大．19.（本小题满分12分）在三棱柱111ABC A B C -中，侧面11ABB A 为矩形，11,AB AA ==D 为1AA 的中点，BD 与1AB 交于点O ，CO ⊥侧面11ABB A ． (I)证明：1BC AB ⊥；(Ⅱ)若OC OA =，求直线1C D 与平面ABC 所成角的 正弦值． 20．（本小题满分12分）已知△ABC 的两顶点坐标(1,0),(1,0)A B -，圆E 是△ABC 的内切圆，在边AC ，BC ，AB 上的切点分别为P ，Q ，R ，1CP =（从圆外一点到圆的两条切线段长相等），动点C 的轨迹为曲线M ．(I)求曲线M 的方程；(Ⅱ)设直线BC 与曲线M 的另一交点为D ，当点A 在 以线段CD 为直径的圆上时，求直线BC 的方程．21.（本小题满分12分） 已知函数()ln ,()(1)f x x x g x k x ==-． (I)若()()f x g x ≥恒成立，求实数k 的值；(Ⅱ)若方程()()f x g x =有一根为11(1)x x >,方程'()'()f x g x =的根为0x ，是否存在实数k ，使1?x k x =若存在，求出所有满足条件的k 值；若不存在，说明理由， 请考生在第22、23、24题中任选一题作答，如果多做，则按所做的第一题计分． 22.（本小题满分10分）选修4-1:几何证明选讲如图，A ，B ，C ，D 四点在同一圆上，BC 与AD 的延长线交于点E ，点F 在BA 的延长线上．(I)若1,13EC ED CB DA ==，求DCAB的值； (Ⅱ)若2BCEF FA FB =⋅，证明：EF ∥CD ．23.（本小题满分10分）选修4-4:坐标系与参数方程已知曲线12cos :1sin x t C y t =-+⎧⎨=+⎩ (t 为参数)，24cos :3sin x C y θθ=⎧⎨=⎩(q 为参数)．(I)化1C ，2C 的方程为普通方程，并说明它们分别表示什么曲线;(Ⅱ)过曲线2C 的左顶点且倾斜角为4π的直线l 交曲绒1C 于A ，B 两点，求AB .24.（本小题满分10分）选修4-5：不等式选讲 设函数()4(4)f x x x a a =-+-<. (I)若()f x 的最小值为3，求a 值； (Ⅱ)求不等式()3f x x ≥-的解集，2017年高中毕业年级第一次质量预测数学（理科） 参考答案一、 选择题ADACB DBCBB AB 二、 填空题13.[1,3)-； 14.5； 15. 8π； 16.12a <-. 三、解答题17．解：(1) 因为AD AC ⊥，所以sin sin()cos 2BAC BAD BAD π∠=+∠=∠,即cos BAD ∠=,…………………………….2分 在ABD ∆中，由余弦定理可知2222cos BD AB AD AB AD BAD =+-⋅⋅∠， 即28150AD AD -+=，解之得5AD =或 3.AD = ……………………………………………….6分由于AB AD >，所以 3.AD =…………………………………………………..7分 (2) 在ABD ∆中，由正弦定理可知sin sin BD ABBAD ADB=∠∠，又由cos BAD ∠=可知1sin 3BAD ∠=，所以sin sin AB BAD ADB BD ∠∠==, 因为2ADB DAC C C π∠=∠+∠=+∠,所以cos C =.……………………………………………………..12分 18．解：随机猜对问题A 的概率113P =，随机猜对问题B 的概率214P =．………… 2分 ⑴设参与者先回答问题A ，且恰好获得奖金a 元为事件M ,则12131()(1)344P M P P =-=⨯=, 即参与者先回答问题A ，其恰好获得奖金a 元的概率为14. ………………4分⑵参与者回答问题的顺序有两种，分别讨论如下：①先回答问题A ，再回答问题B ．参与者获奖金额ξ可取0,,a a b +， 则()12013P P ξ==-=，()()12114P a P P ξ==-=，()121.12P a b PP ξ=+==②先回答问题B ，再回答问题A ，参与者获奖金额η，可取0,,b a b +，则()23014P P η==-=，()()21116P b P P η==-=，()211.12P a b P P η=+==()3110.4612124a bE b a b η=⨯+⨯++⨯=+………… 10分32.12a bE E ξη--= 于是，当23a b >，时E E ξη>，即先回答问题A ，再回答问题B ，获奖的期望值较大； 当23a b =，时E E ξη=，两种顺序获奖的期望值相等；当23a b <，时E E ξη<，先回答问题B ，再回答问题A ，获奖的期望值较大.…………………………12分 19.解：(1)证明：由题意11tan tan AD AB ABD AB B AB BB ∠==∠==, 注意到10,2ABD AB B π<∠∠<,所以1ABD AB B ∠=∠,所以1112ABD BAB AB B BAB π∠+∠=∠+∠=,所以BD AB ⊥1, ……………………3分又⊥CO 侧面11A ABB ，1.AB CO ∴⊥ 又BD 与CO 交于点O ，所以CBD AB 面⊥1,又因为CBD BC 面⊂,所以1AB BC ⊥.……………………………6分(2)如图，分别以1,,OD OB OC 所在的直线为,,x y z 轴， 以O 为原点，建立空间直角坐标系xyz O -则(0,A，(B ，C，1B，D ， 又因为12CC AD =，所以1C …………8分所以(AB =，AC =，1DC =设平面ABC 的法向量为(,,)n x y z =，则根据0,0AB n AC n ⋅=⋅=可得n =是平面ABC 的一个法向量,设直线1C D 与平面ABC 所成角为α，则11||sin ||||DC n DC n α⋅==………………12分20.⑴解：由题知||||||||||||2||||4||,CA CB CP CQ AP BQ CP AB AB +=+++=+=> 所以曲线M 是以,A B 为焦点，长轴长为4的椭圆（挖去与x 轴的交点），设曲线M ：22221(0,0)x y a b y a b+=>>≠，则2222||4,()32AB a b a ==-=， 所以曲线M ：221(0)43x y y +=≠为所求.---------------4分 ⑵解：注意到直线BC 的斜率不为0，且过定点(1,0)B ， 设1122:1,(,),(,)BC l x my C x y D x y =+，A由221,3412,x my x y =+⎧⎨+=⎩ 消x 得22(34)690m y my ++-=，所以1,2y =， 所以1221226,349,34m y y m y y m ⎧+=-⎪⎪+⎨⎪=-⎪+⎩-------------------------------------8分因为1122(2,),(2,)AC my y AD my y =+=+,所以212121212222222(2)(2)(1)2()49(1)12794.343434AC AD my my y y m y y m y y m m m m m m ⋅=+++=+++++-=--+=+++注意到点A 在以CD 为直径的圆上,所以0AC AD ⋅= ,即m =,-----11分所以直线BC的方程330x +-=或330x -=为所求.------12分21.⑴解:注意到函数()f x 的定义域为(0,)+∞, 所以()()f x g x ≥恒成立()()f xg x x x⇔≥恒成立, 设(1)()ln (0)k x h x x x x-=->, 则221()k x kh x x x x -'=-=, ------------2分当0k ≤时,()0h x '>对0x >恒成立,所以()h x 是(0,)+∞上的增函数, 注意到(1)0h =,所以01x <<时,()0h x <不合题意.-------4分 当0k >时,若0x k <<,()0h x '<;若x k >,()0h x '>. 所以()h x 是(0,)k 上的减函数,是(,)k +∞上的增函数,故只需min ()()ln 10h x h k k k ==-+≥. --------6分 令()ln 1(0)u x x x x =-+>,11()1xu x x x-'=-=, 当01x <<时,()0u x '>; 当1x >时,()0u x '<. 所以()u x 是(0,1)上的增函数,是(1,)+∞上的减函数. 故()(1)0u x u ≤=当且仅当1x =时等号成立.所以当且仅当1k =时,()0h x ≥成立,即1k =为所求. --------8分 ⑵解:由⑴知当0k ≤或1k =时,()()f x g x =,即()0h x =仅有唯一解1x =,不合题意; 当01k <<时, ()h x 是(,)k +∞上的增函数,对1x >,有()(1)0h x h >=，所以()()f x g x =没有大于1的根,不合题意. ---------8分当1k >时,由()()f x g x ''=解得10k x e -=,若存在110k x kx ke -==, 则111ln()(1)k k k keke k ke ---=-,即1ln 10k k e --+=,令1()ln 1(1)xv x x e x -=-+>,11()x x xe exv x e x xe--'=-=, 令(),()xxs x e ex s x e e '=-=-,当1x >时,总有()0s x '>, 所以()s x 是(1,)+∞上的增函数,即()(1)0xs x e ex s =->=, 故()0v x '>,()v x 在(1,)+∞上是增函数,所以()(1)0v x v >=,即1ln 10k k e --+=在(1,)+∞无解.综上可知,不存在满足条件的实数k . ----------------------12分 22.解：⑴ D C B A ,,,四点共圆，∴EBF EDC ∠=∠，又AEB ∠为公共角，∴ECD ∆∽,EAB ∆ ∴.DC EC EDAB EA EB== ∴2111...428DC EC ED EC ED AB EA EB EB EA ⎛⎫==== ⎪⎝⎭.∴DC AB =. ……………………………………………………………… 6分⑵ FB FA EF ⋅=2， ∴FEFB FA EF =， 又 BFE EFA ∠=∠， ∴FAE ∆∽FEB ∆，∴EBF FEA ∠=∠，又 D C B A ,,,四点共圆，∴EBF EDC ∠=∠，∴EDC FEA ∠=∠， ∴//.EF CD .…………………………………………………… 10分 23.解：⑴222212:(2)(1)1,: 1.169x y C x y C ++-=+= 曲线1C 为圆心是(2,1)-，半径是1的圆．曲线2C 为中心是坐标原点，焦点在x 轴上，长轴长是8，短轴长是6的椭圆．……4分⑵曲线2C 的左顶点为(4,0)-，则直线l的参数方程为4,,x s y s ⎧=-+⎪⎪⎨⎪=⎪⎩（s 为参数） 将其代入曲线1C整理可得：240s -+=，设,A B 对应参数分别为12,s s ，则1212 4.s s s s +==所以12||||AB s s =-==. ……………………………10分24.解：⑴因为,4)()4(4-=---≥-+-a a x x a x x因为4a <,所以当且仅当4a x ≤≤时等号成立,故43,1a a -=∴=为所求.……………………4分⑵不等式x x f -≥3)(即不等式x a x x -≥-+-34)4(<a ， ①当a x <时，原不等式可化为43,x a x x -+-≥-即 1.x a ≤+所以，当a x <时，原不等式成立.②当4≤≤x a 时，原不等式可化为43.x x a x -+-≥-即 1.x a ≥-所以，当4≤≤x a 时，原不等式成立.③当4>x 时，原不等式可化为43.x x a x -+-≥- 即7,3a x +≥由于4<a 时74.3a +>所以，当4>x 时，原不等式成立.综合①②③可知： 不等式x x f -≥3)(的解集为R.……………………10分。

2017年河南省郑州市高中毕业年级第一次质量预测一、选择题（共12小题；共60分）1. 设，，，则A. B.C. D.2. 若复数满足（为虚数单位），则的共轭复数为A. B. C. D.3. 命题“，”的否定是A. ，B. ，C. ，D. ，4. 《张丘建算经》卷上第题为：“今有女善织，日益功疾．初日织五尺，今一月日织九匹三丈．”其意思为今有女子善织布，且从第天起，每天比前一天多织相同量的布，若第一天织尺布，现在一个月（按天计）共织尺布．则该女最后一天织多少尺布?A. B. C. D.5. 我们可以用随机数法估计的值，如图所示的程序框图表示其基本步骤（函数是产生随机数的函数，它能随机产生内的任何一个实数），若输出的结果为，则由此可估计的近似值为A. B. C. D.6. 某几何体的三视图如图所示，则该几何体的体积为A. B. C. D.7. 设，则的展开式中常数项是A. B. C. D.8. 函数的图象大致为A. B.C. D.9. 已知数列满足，且对任意都有，则实数的取值范围为A. B. C. D.10. 设正实数，满足，，不等式恒成立，则的最大值为A. B. C. D.11. 已知直线与双曲线相切于点，与双曲线的两条渐近线交于，两点，则的值为A. B.C. D. 与的位置有关12. 已知函数，若，且对任意的恒成立，则的最大值为A. B. C. D.二、填空题（共4小题；共20分）13. 在平面直角坐标系中，已知角的顶点和点重合，始边与轴的非负半轴重合，终边上一点的坐标为，则．14. 已知实数，满足不等式组则的最小值为．15. 过抛物线的焦点作一条倾斜角为的直线交抛物线于，两点，则．16. 若函数满足：，都有，且，，则．三、解答题（共7小题；共91分）17. 巳知的外接圆直径为，角，，所对的边分别为，，，．（1）求的值；（2）若，求的面积．18. 如图，已知四棱锥，底面梯形中，，平面平面，是等边三角形，已知，．（1）求证：平面平面；（2）求二面角的余弦值．19. 北京时间月日下午，谷歌围棋人工智能AlphaGo与韩国棋手李世石进行最后一轮较量，AlphaGo获得本场比赛胜利，最终人机大战总比分定格在．人机大战也引发全民对围棋的关注，某学校社团为调查学生学习围棋的情况，随机抽取了名学生进行调查．根据调查结果绘制的学生日均学习围棋时间的频率分布直方图如图所示，将日均学习围棋时间不低于分钟的学生称为“围棋迷”．附：，其中．（1）根据已知条件完成下面的列联表，并据此资料判断是否有的把握认为“围棋迷”与性别有关?非围棋迷围棋迷合计男女合计（2）将上述调查所得到的频率视为概率．现在从该地区大量学生中，采用随机抽样方法每次抽取名学生，抽取次，记被抽取的名学生中的“围棋迷”人数为．若每次抽取的结果是相互独立的，求的分布列，期望和方差．20. 已知圆（）与直线相切，设点为圆上一动点，轴于，且动点满足，设动点的轨迹为曲线．（1）求曲线的方程；（2）直线与直线垂直且与曲线交于，两点，求（为坐标原点）面积的最大值．21. 设函数．（1）若当时，函数的图象恒在直线上方，求实数的取值范围；（2）求证：．22. 在平面直角坐标系中，曲线的参数方程为为参数，在以为极点，轴的正半轴为极轴的极坐标系中，曲线是圆心为，半径为的圆．（1）求曲线的普通方程，的直角坐标方程；（2）设为曲线上的点，为曲线上的点，求的取值范围．23. 已知，，函数的最小值为．（1）求的值；（2）求的最小值．答案第一部分 1. B2. D【解析】依题意得，则复数 的共轭复数为 ． 3. A 【解析】依题意得，命题“ ，”的否定是“ ， ”．4. C【解析】依题意得，织女每天所织的布的尺数依次排列形成一个等差数列，设为 ，其中 ，前 项和为 ，于是有，解得 ，即该织女最后一天织 尺布． 5. B【解析】在空间直角坐标系 中，不等式组表示的区域是棱长为 的正方体区域，相应区域的体积为 ；不等式组表示的区域是棱长为 的正方体区域内的 球形区域，相应区域的体积为，因此，即 ． 6. B【解析】如图所示，题中的几何体是从直三棱柱 中截去一个三棱锥 后所剩余的部分，其中底面 是直角三角形， ， ， ， ，因此题中的几何体的体积为7. A【解析】依题意得， ，的展开式的通项．令 ，得 ．因此的展开式中的常数项为． 8. C【解析】依题意，注意到，因此函数 是奇函数，其图象关于原点对称，结合各选项知，选项A ，B 均不正确；当 时，，， ，因此结合选项知，C 正确．9. D 【解析】依题意得，当时，，又，因此，，数列是以为首项，为公比的等比数列，等比数列的前项和等于，因此实数的取值范围是．10. C【解析】依题意得，，，即，当且仅当即时，取等号，因此的最小值是，，的最大值是．11. A 【解析】依题意，设点，，，其中，则直线的方程是，题中双曲线的两条渐近线方程为，即．①当时，直线的方程是或．由得此时，同理可得当直线的方程是时，．②当时，直线的方程是．由得，（）又，因此（）即是，，，．综上所述，．12. B 【解析】通解依题意得，对任意的恒成立．令，则，令，则，所以函数在上单调递增．因为，，所以方程在上存在唯一实数根，且满足，即有，．当时，，即，当时，，即，所以函数在上单调递减，在上单调递增，所以所以．故整数的最大值是．优解依题意得，当时，，即，因此满足题意的最大整数的可能取值为．当时，记，即，则，当时，，在区间上单调递减；当时，，在区间上单调递增．因此，的最小值是，于是有恒成立．所以满足题意的最大整数的值是．第二部分13.【解析】依题意得，．14.【解析】作出不等式组表示的平面区域，如图中阴影部分所示，由图知，当目标函数经过点时取得最小值，即．15.【解析】依题意，设点，，题中的抛物线的焦点坐标是，直线的方程为，即．由消去得，即，，．16.【解析】通解依题意，在已知等式中，取，，得．取，，得，，由此归纳猜想．下面用数学归纳法证明的正确性．①当时，成立．②假设当时，均成立，则取，，得，即当时，成立．综上所述，，因此．优解由已知得．取，易验证满足．由，得由此解得，，故，．第三部分17. （1）因为，所以，，．所以．（2）由，得，，即，又，所以，解得或舍去．所以．18. （1）在中，由于，，，所以，故．又平面平面，平面平面，平面，所以平面，又平面，故平面平面．（2）如图，建立空间直角坐标系，则，，，，，，，设平面的法向量，令，则，，所以．设平面的法向量，令，所以．所以，所以二面角的余弦值为．19. （1）由频率分布直方图可知，在抽取的人中，“围棋迷”有人，从而列联表如下：非围棋迷围棋迷合计男女合计将列联表中的数据代入公式计算，得因为，所以没有的把握认为“围棋迷”与性别有关．（2）由频率分布直方图知抽到“围棋迷”的频率为，将频率视为概率，即从该地区学生中抽取一名“围棋迷”的概率为．由题意知，，从而的分布列为：，．20. （1）设动点，，因为轴于，所以，由题意得，，所以圆的方程为．因为，所以，即将代入圆中，得动点的轨迹方程为．（2）由题意，设直线，，，联立直线与椭圆的方程得消去，得，，解得，，又点到直线的距离，，所以，当且仅当，即时，等号成立．故面积的最大值为．21. （1）令，，则，，．①当时，由于，有，于是在上单调递增，从而，因此在上单调递增，即；②当时，由于，有，于是在上单调递减，从而，因此在上单调递减，即，不符合题意；③当时，令，当时，，于是在上单调递减，从而，因此在上单调递减，即，不符合题意．综上可知，所求实数的取值范围是．（2）对要证明的不等式等价变形如下：对于任意大于的正整数，不等式恒成立，等价于，相当于（）的③中，的情形，在上单调递减，即，取，都有成立，令，原不等式得证．22. （1）消去参数可得的普通方程，曲线的圆心的直角坐标为，所以的直角坐标方程为．（2）设，曲线的圆心为，则因为，所以，．根据题意可得，，即的取值范围是．23. （1）因为，所以，当且仅当时，等号成立，又，，所以，所以的最小值为，所以．（2）由（）知，，，当且仅当，时，的最小值为．。