安徽省2017届安师大附中、马鞍山二中高三阶段性测试

注意事项：1.本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

2.答卷前，考生务必将自己的姓名、准考证号、座位号及考试科目用2B铅笔涂写在答题卡上。

2.每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号。

不能答在试卷上。

3.本试卷满分150分，考试时间为120分钟。

第Ⅰ卷第一部分听力 (共两节，满分30分)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 are the speakers talking about?A. The man’s weekend activities.B. The woman’s favorite sport.C. The city they live in.2. What might the man be?A. A businessman.B. A doctor.C. A student.3. When did the speakers start talking?A. At 2:50.B. At 3:00.C. At 3:10.4. What does the woman want to do?A. Borrow money from the man.B. Work in the bank.C. Start up a business.5. What i s the man’s research field?A. Education.B. Insects.C. Finance.第二节 (共15小题；每小题1.5分，满分22.5分)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。

2017届安师大附中、马鞍山二中统一考试试卷英语试题本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

全卷满分150分，考试时间120分钟。

考生注意事项：1. 答题前，务必在试卷、答题卡规定的地方填写自己的姓名、座位号，并认真核对答题卡上所粘贴的条形码中姓名、座位号与本人姓名、座位号是否一致。

务必在答题卡背面规定的地方填写姓名的座位号后两位。

2. 答第Ⅰ卷时，每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再先涂其他答案标号。

3. 答第Ⅱ卷时，必须使用0.5毫米的黑色墨水签字笔在答题卡上书写，要求字体工整、笔迹清晰。

必须在题号所指示的答题区域作答，超出答题区域书写的答案无效，在试题卷、．．．．．草稿纸上答题无效．．．．．．．．。

第Ⅰ卷第一部分听力（共两节，满分30分）回答听力部分时，请先将答案标在试卷上。

听力部分结束前，你将有两分钟的时间将你的答案转涂到客观题答题卡上。

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。

1. Where is this bus going?A. South.B. East.C. North.2. How does the woman probably feel?A. Excited.B. Nervous.C. Unhappy.3. Where does the man want to visit?A. Spain.B. Italy.C. France.4. What are the speakers talking about?A. A nice hairstyle.B. Their wedding.C. An old photo.5. What has the bear been doing?A. Eating campers’ food.B. Chasing the tourists.C. Attacking the park rangers (护林员).第二节（共15小题；每小题1.5分，满分22.5分）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。

安徽师大附中2017届马鞍山二中 12月高三阶段性测试理科综合卷注意事项：1．答题前，考生务必将自己的姓名、班级、准考证号填写在答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。

用2B铅笔将答题卡上试卷类型A方框涂黑。

2．选择题的作答：每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。

答在试题卷、草稿纸上无效。

3．填空题和解答题作答：用黑色墨水签字笔将答案直接答在答题卡上对应的答题区域内。

答在试题卷、草稿纸上无效。

4．选考题的作答：先把所选题目的题号在答题卡上指定的位置用2B铅笔涂黑。

考生应根据自己选做的题目准确填涂题号，不得多选。

答题答在答题卡上对应的答题区域内，答在试题卷、草稿纸上无效。

可能用到的相对原子质量：O—16 Al—27 Si—28 Ca—40 Fe—56第Ⅰ卷（共126分）一、选择题：本题共13小题，每小题6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．下列与实验有关的叙述正确的是( )A．探究温度对酶活性的影响时，将过氧化氢酶和过氧化氢先各自在某一温度下保温一段时间后再混合B．在“探究酵母菌细胞呼吸方式”实验中，通过观察澄清石灰水是否变混浊来判断其呼吸方式C．在模拟性状分离的实验中，盒子代表生殖器官，彩球代表配子，两个盒子的彩球数量要求相同D．同位素标记法被用于鲁宾和卡门实验、卡尔文循环实验2．生物膜将真核细胞分隔成不同的区室，使得细胞内能够同时进行多种化学反应，而不会相互干扰。

下列叙述正确的是( )A．线粒体将葡萄糖氧化分解成CO2和H2OB．高尔基体是肽链合成和加工的场所C．细胞核是mRNA合成和加工的场所D．溶酶体合成和分泌多种酸性水解酶3．研究发现，直肠癌患者体内存在癌细胞和肿瘤干细胞。

用姜黄素治疗，会引起癌细胞内BAX等凋亡蛋白高表达，诱发癌细胞凋亡；而肿瘤干细胞因膜上具有高水平的ABCG2蛋白，能有效排出姜黄素，从而逃避凋亡，并增殖分化形成癌细胞，下列说法不正确的是( ) A．肿瘤干细胞与癌细胞中基因的执行情况不同B．肿瘤干细胞的增殖及姜黄素的排出都需要消耗ATPC．编码BAX蛋白和ABCG2蛋白的基因都属于原癌基因D．用ABCG2抑制剂与姜黄素联合治疗，可促进肿瘤干细胞凋亡4．如图为一种溶质分子跨膜运输的示意图。

安徽师大附中2017届马鞍山二中12月高三阶段性测试理科综合化学卷注意事项：1．答题前，考生务必将自己的姓名、班级、准考证号填写在答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。

用2B铅笔将答题卡上试卷类型A方框涂黑。

2．选择题的作答：每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。

答在试题卷、草稿纸上无效。

3．填空题和解答题作答：用黑色墨水签字笔将答案直接答在答题卡上对应的答题区域内。

答在试题卷、草稿纸上无效。

4．选考题的作答：先把所选题目的题号在答题卡上指定的位置用2B铅笔涂黑。

考生应根据自己选做的题目准确填涂题号，不得多选。

答题答在答题卡上对应的答题区域内，答在试题卷、草稿纸上无效。

可能用到的相对原子质量：O—16 Al—27 Si—28 Ca—40 Fe—567．化学与人类关系密切。

下列说法不正确的是（）A．PM 2.5是指大气中直径接近2.5×10-6 m的颗粒物，它分散在空气中形成胶体B．用钢瓶储存液氯或浓硫酸C．用灼烧的方法可以区分蚕丝和人造纤维D．水泥、玻璃、陶瓷是人们在生产生活中用量最大的无机非金属材料8．设N A表示阿伏加德罗常数的值。

下列说法正确的是（）A．1 molNaN3所含阴离子总数为3N AB．0.1 mol氯化氢气体溶于水所得溶液中含有0.1 N A个HCl分子C．标准状况下，22.4L C12通入到足量FeBr2溶液中，被氧化的Br-数目为2N AD．32g O2和O3的混合气体含有的分子总数小于N A9．如图所示有机物的一氯取代物有(不含立体异构) （）A．5种B．6种C．7种D．8种10．下列实验方案的设计、结论正确的是（）A．用NaHCO3溶液可一次鉴别出稀盐酸、NaOH溶液、AlCl3溶液、NaAlO2溶液B．高锰酸钾试剂瓶内壁上黑色物质可用稀盐酸洗涤C．除去SO2中少量HCl，将其通入饱和的Na2SO3溶液D．将硝酸铵晶体溶于水，测得水温下降，证明硝酸铵水解是吸热的11．下列各组离子，在指定的环境中一定能大量共存的是（）A．使甲基橙变红色的溶液：Al3+、Cu2+、I－、S2O32－B．能使淀粉碘化钾试纸显蓝色的溶液：K+、SO42－、S2－、SO32－C．常温下c(H+)／c(OH－)=1012的溶液：Fe3+、Mg2+、NO3－、Cl－D．不能使酚酞变红的无色溶液：Na+、CO32－、K+、ClO－、AlO2－12．a、b、c、d为短周期元素，a的M电子层有1个电子，b的最外层电子数为内层电子数的2倍，c的最高化合价为最低化合价绝对值的3倍，c与d同周期，d的原子半径小于c。

安师大附中2017届马鞍山二中 12月高三阶段性测试理科综合卷可能用到的相对原子质量：O—16 Al—27 Si—28 Ca—40 Fe—56第Ⅰ卷（共126分）一、选择题：本题共13小题，每小题6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．下列与实验有关的叙述正确的是( )A．探究温度对酶活性的影响时，将过氧化氢酶和过氧化氢先各自在某一温度下保温一段时间后再混合B．在“探究酵母菌细胞呼吸方式”实验中，通过观察澄清石灰水是否变混浊来判断其呼吸方式C．在模拟性状分离的实验中，盒子代表生殖器官，彩球代表配子，两个盒子的彩球数量要求相同D．同位素标记法被用于鲁宾和卡门实验、卡尔文循环实验2．生物膜将真核细胞分隔成不同的区室，使得细胞内能够同时进行多种化学反应，而不会相互干扰。

下列叙述正确的是( )A．线粒体将葡萄糖氧化分解成CO2和H2OB．高尔基体是肽链合成和加工的场所C．细胞核是mRNA合成和加工的场所D．溶酶体合成和分泌多种酸性水解酶3．研究发现，直肠癌患者体内存在癌细胞和肿瘤干细胞。

用姜黄素治疗，会引起癌细胞内BAX等凋亡蛋白高表达，诱发癌细胞凋亡；而肿瘤干细胞因膜上具有高水平的ABCG2蛋白，能有效排出姜黄素，从而逃避凋亡，并增殖分化形成癌细胞，下列说法不正确的是( ) A．肿瘤干细胞与癌细胞中基因的执行情况不同B．肿瘤干细胞的增殖及姜黄素的排出都需要消耗ATPC．编码BAX蛋白和ABCG2蛋白的基因都属于原癌基因D．用ABCG2抑制剂与姜黄素联合治疗，可促进肿瘤干细胞凋亡4．如图为一种溶质分子跨膜运输的示意图。

下列相关叙述错误的是( ) A．载体①逆浓度运输溶质分子B．载体②具有A TP酶活性C．载体①和②转运方式不同D．载体②转运溶质分子的速率比自由扩散快5．下面有关孟德尔豌豆的一对相对性状杂交实验的说法，其中错误的是( )A．正确运用统计方法，孟德尔发现在不同性状的杂交实验中，F2的分离比具有相同的规律B．解释实验现象时，提出的“假说”之一：F1产生配子时，成对的遗传因子分离C．根据假说，进行“演绎”：若F1产生配子时，成对的遗传因子分离，则测交实验后代应出现两种表现型，且比例为1：1D．由于假说能解释F1自交产生3：1分离比的原因，所以假说成立6．图为基因的作用与性状的表现流程示意图。

二、选择题，本题共8小题，每小题6分，在每小题给出的四个选项中，第14～18题只有一项是符合题目要求的，第19～21题有多项符合题目要求。

全部选对的得 6 分，选对但不全的得 3 分，有错选的得 0 分。

14．万有引力定律中的引力常量G 是物理学中一个重要的常数，它的单位用基本单位来表示，下列选项中表示正确的是（ ）A ．kg·m/s 2B ．N·m 2/kgC ．m 3/ （kg·s 2）D ．kg 2/m 2 【答案】C 【解析】考点：单位制；万有引力定律【名师点睛】单位制是由基本单位和导出单位组成的，在国际单位制中，除了七个基本单位之外，其他物理量的单位都是导出单位，可以由物理公式推导出来。

15．如图所示，一个热气球与沙包的总质量为m ，在空气中沿竖直方向匀速下降，为了使它以3g的加速度匀减速下降，则应该抛掉的沙包的质量为（假定整个过程中空气对热气球的浮力恒定，空气的其它作用忽略不计）（ ）A ．3mB ．4m C ．23m D ．34m【答案】B 【解析】试题分析：设空气对热气球的浮力大小为F ．为了使它匀减速下降，则应该抛掉的沙的质量为△m ．以热气球与沙包整体为研究对象，匀减速下降时，根据牛顿第二定律得：F-（m-△m ）g =（m-△m ）a ；匀速下降时，由平衡条件有：mg=F ；联立解得：△m=4m，故选B. 考点：牛顿第二定律【名师点睛】分析物体的受力情况，确定合力是运用牛顿第二定律的关键．分析时，要注意抓住题设的条件：浮力不变.16. 如图所示是一固定光滑斜面，A 物体从斜面顶端由静止开始下滑，当A 物体下滑L 距离时，B 物体开始从离斜面顶端距离为2L 的位置由静止开始下滑，最终A 、B 两物体同时到达斜面底端，则该斜面的总长度为（ ）A ．49LB ．817L C ．3L D ．4L【答案】A 【解析】考点：匀变速直线运动的规律【名师点睛】此题是匀变速直线运动的规律的应用问题；关键是抓住两物体运动的位移关系及时间关系列方程求解.17. 如图AB 和CD 为圆上两条相互垂直的直径，圆心为O ，将电荷量分别为＋q 和－q 的两点电荷固定在圆周上，其位置关于AB 对称且距离等于圆的半径，要使圆心处的电场强度为零，可在圆周上适当的位置再放一个点电荷Q ，则该点电荷（ ）A.可放在A 点，Q ＝－2qB.可放在B 点，Q ＝+2qC.可放在C 点，Q ＝－qD.可放在C 点，Q ＝+ q 【答案】C【解析】试题分析：两个点电荷在0点产生的场强大小都为2qkr,两个场强的方向互成120°，根据平行四边形定则，合场强大小为2q k r ，方向水平向左．所以最后一个电荷在O 点产生的场强大小为2qk r，方向水平向左．所以该电荷若在C 点，为+q ，若在D 点，为-q ．故C 正确，ABD 错误．故选C. 考点：场强的叠加【名师点睛】解决本题的关键掌握点电荷的场强公式E=2qkr，以及会利用平行四边形定则进行合成。

安徽省马鞍山二中、安师大附中2017届高三12月阶段性测试英语试卷第Ⅰ卷第一部分听力（共两节,满分30分）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 are the speakers talking about? ________A．The man’s weekend activities.B．The woman’s favorite sport.C．The city they live in.2．What might the man be? ________A．A businessman.B．A doctor.C．A student.3．When did the speakers start talking? ________A．At 2:50.B．At 3:00.C．At 3:10.4．What does the woman want to do? ________A．Borrow money from the man.B．Work in the bank.C．Start up a business.5．What is the man’s research field? ________A．Education.B．Insects.C．Finance.第二节（共15小题;每小题1.5分,满分22.5分）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.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.每段对话或独白读两遍.听第6段材料,回答第6至7题.6．What kind of job did the woman take after graduation? ________A．Teaching.B．Marketing.C．V olunteering.7．What does the woman think the man should do? ________ A．Take his job immediately.B．Not worry about the money.C．Make a decision and stick to it.听第7段材料,回答第8至9题.8．Where does the woman advise the man to apply for a job? ________ A．In a newspaper office.B．In a travel agency.C．In a car factory.9．What does the man ask the woman about the job? ________ A．The pay.B．The working conditions.C．The experience.听第8段材料,回答第10至12题.10．Why didn’t the man realize his childhood dream? ________ A．His parents didn’t support him.B．He was offered another job.C．He lost interest in it later.11．What did the woman want to be when she was a little girl? ________ A．A pilot.B．A scientist.C．A teacher.12．What language is the woman good at? ________A．English and French.B．English and Italian.C．French and Italian.听第9段材料,回答第13至16题.13．Who is Jenny? ________A．The man’s wife.B．The woman’s colleague.C．The man’s sister.14．How long has it been since the speaker’s graduation? ________ A．Three years.B．Ten years.C．Thirteen years.15．What do we know about the man? ________A．He continued his studies after graduation.B．He once worked at a law firm.C．He is working in a trade company.16．When will the speakers meet each other again? ________A．This Saturday.B．This Sunday.C．Next Saturday.听第10段材料,回答第17至20题.17．What is Bill Gates famous for according to the speaker? ________A．His family background.B．His education in university.C．His contribution to the computer.18．What did Bill Gates do in 1975? ________A．He went to Harvard University.B．He began to design new software.C．He sold his inventions to MITS.19．When did Bill Gates leave Microsoft? ________A．In 2000.B．In 2008.C．In 2014.20．What do we know about Bill Gates from the talk? ________A．He was born in New York.B．His mother worked as a lawyer.C．He founded the Microsoft Company.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.AA cat with his own Facebook page and Instagram account is taking the Internet by storm thanks to his expressive eyebrows. Curious-looking Sam has racked up 150 000 Instagram followers and 530 000 likes on Facebook since bursting onto the scene in 2012.Owner Amanda Collazo, 26, from New York, has been handling the large amount of requests from fans and media for the past three years. She said, “There have definitely been situations where I have had to ignore friends, family or work to take the time to do Sam’s posts or answer emails on his behalf. Everyone gets a little annoyedwhen I’m on my phone and not paying attention to them. I never thought Sam would be so popular.”Amanda’s mum, Ivette Rodriguez, noticed the abandoned cat outside her home one evening.Ivette said, “I saw a little niche（壁龛）next to the house and there was a cat in there. He willingly gave himself up to me—I guess he was so tired of being outside.”Amanda created an Instagram account for Sam after a friend pointed out his expressive brows. She said, “I didn’t notice his eyebrows initially.”“He had about 800 followers at first—but in February someone posted his photo on Reedit and he blew up overnight—I woke up with 1600 followers. From there we made a Facebook and all other social media accounts.”Amanda posts pictures to Sam’s account every two days, but spends most of her day keeping up with al l of his fans. But the effort she puts into her pet’s social media has paid off—and she has bigger plans for Sam’s future, including merchandise（商品）.“Right now we’re trying to share him in a freeway. Eventually we’ll sell Sam merchandise, because I know many people do like having cute little mugs, Sam mugs, or posters, T-shirts.”21．Why does Amanda sometimes ignore her friends? ________A．She is absorbed in her work.B．She is popular with her fans.C．She gets along badly with her friends.D．She is busy wit h Sam’s business.22．How did Amanda get the cat called Sam? ________A．She bought it from her friend.B．One of her friends gave it to her.C．Her mother found it and adopted it.D．The text didn’t mention it.23．What does Amanda plan to do about Sam? ________A．She plans to post Sam’s photo on Reedit on the Internet.B．She plans to post pictures to Sam’s account every day.C．She plans to buy more cats.D．She plans to sell Sam products.BWhenever something looks interesting or beautiful, there is a natural desire of us to capture（捕捉）and preserve it—which means, in this day and age, that we are likely to reach for our phones to take a picture.Though this would seem to be an ideal solution, there are two big problems associated with taking pictures. Firstly, we are likely to be so busy taking pictures that we forget to look at the world whose beauty and interest encourage us to take a photograph in the first place. And secondly, because we feel the pictures are safely stored on our phones, we never get around to looking at them, so sure are we that we’ll get around to them one day.The first person to notice the problems was the English art critic（评论家）, John Ruskin. He was a keentraveler who realized that most tourists make a poor job of noticing or remembering the beautiful things they see. He argued that humans have a natural tendency to respond to beauty and desire to have it, but there are better and worse expressions of this desire. At worse, we get into buying souvenirs or taking photographs. But, in Rus kin’s eyes, there’s just one thing we should do—attempting to draw the interesting things we see, regardless of whether we happen to have any talent for doing so.Ruskin said, “Drawing can teach us to see: to notice properly rather than gaze absent-mindedly. In the process of recreating with our own hand what lies before our eyes, we naturally move from a position of observing beauty in a loose way to one where we acquire a deep understanding of its parts.”Ruskin deplored the blindness and hurry of modern tourists, especially those who prided themselves on travelling around the whole Europe in a week by train, “No changing of places at a hundred miles an hour will make us stronger, happier, or wiser. There was always more in the world than men could see, if they ever walked slowly; they will see it no better for going fast. The really precious things are thoughts and sights, not pace.”24．According to Paragraph 2, when taking pictures, people tend to ________.A．forget to appreciate something attractive on the spotB．find it hard to learn skills of taking good picturesC．find a good way to keep things in their mindsD．have a chance to meet the challenge of new technology25．According to Ruskin, what should travelers do to best express their appreciation of and desire for something beautiful? ________A．To speak it out openly.B．To photograph it instantly.C．To purchase it directly.D．To paint it immediately.26．From the fourth paragraph, we can infer that Ruskin encourages us to be ________.A．considerate and determinedB．active and adventurousC．creative and thoughtfulD．sensitive and ambitious27．The underlined word “deplored” in the last paragraph is closest in meaning to ________.A．appreciatedB．criticizedC．favoredD．ignoredCWhen Marco Polo travelled to Hangzhou, China 700 hundred years ago, never had he thought he’d be creating a job of social media ambassador in the 21st century in China.On May 20, one lucky foreigner would be selected to become the modern-day Marco Polo, getting a free 15-day trip to the scenic city of Hangzhou in China, and rewarded $55 000 in the next year for working part-time to promote the city to the global audience. Five finalists from Australia, Romania, U.S, Switzerland and France were in the final race. They came from a pool of 700 applicants from around the world, carefully selected by the Hangzhou Tourism Commission on their familiarity with China, social media presence and adventurous spirit.Located about 100 miles southwest to Shanghai, Hangzhou is home to 844 million population and among China’s richest cities as measures by per-capita GDP. Traditionally, Hangzhou is known for its charming West Lake, a UNESCO world heritage site with traditional Chinese stories and tales, and the Grand Canal, which travels from Hangzhou to Beijing and was a key route of transportation in ancient China. The city’s mild climate and charming environment drew 97 million tourists last year, contributing to 6.5% of the city’s GDP.The lucky winner would start an all-expense-paid trip to Hangzhou, which, in addition to visits to tourist sites and tastings of delicious food, also would include a four-day ride along the Grand Canal and three evenings spent at a local resident’s home.“It is in fact a part-time job. How you work that out efficiently is your problem,” Liam Bates, perhaps the strongest competitor because of his fluent Chinese, said. “We will see how hard it is to meet these numbers.”28．The purpose of Hangzhou choosing a social media ambassador is to ________.A．keep Marco Polo in people’s memoriesB．attract more foreign tourists to ChinaC．encourage more foreigners to speak ChineseD．explore a new route of transportation29．From paragraph 3, we know that ________.A．Hangzhou is 100 miles northwest to ShanghaiB．8.8 million visitors came to Hangzhou in 2015C．tourism plays an important in the GDP of HangzhouD．the Grand Canal travels from Hangzhou to Shanghai30．Liam Bates was most likely to get the job mainly due to his ________.A．travel experienceB．fluent ChineseC．adventurous spiritD．excellent videos31．Which of the following might be the best title for this passage? ________A．Hangzhou rewards international visitors to ChinaB．Liam Bates creates a dream job of social media ambassadorC．Dream job in China—$55 000 to the contemporary Marco PoloD．Hangzhou, a famous city for West Lake and the Great CanalDChinese car makers have narrowed the quality gap with their foreign rivals in the world’s largest vehicle market to the smallest level in seven years, according to research.But the improvements have not been enough to see an obvious drop in the market share for local car companies this year, raising questions about their ability to be global competitors.The annual quality survey of China’s car market by J.D. Power, a Californian market research company, tracks the number of mechanical and design problems reported per 100 vehicles by more than 21 000 Chinese drivers.It documented 131 problems per 100 domestic（国内的）vehicles, compared with 95 per 100 foreign vehicles. The 36-poin t gap was the narrowest in the study’s seven-year history. When China overtook the US as the world’s largest car maker in the 2009, the gap between domestic and foreign cars was 145 points. “It’s evidence to the improvements that domestic brands have been making,” said Geoff Broderick, head of J.D. Power’s operations. “By 2018 the domestic and the global brands will be equal in terms of quality.”Despite the steady improvement in quality, local vehicle makers have been performing poorly this year. According to the China Association of Automobile Manufacturers, domestic brand’s share of the market for cars—not including SUVs—has fallen from about 25 percent to 20 percent.“Chinese customers are very picky in the world because they have been trained to distrust products,” said Mr Broderick, citing scandals（丑闻）affecting baby milk powder and toys.They go into a situation expecting there could be quality issues, whereas in the West we trust the brands. 32．What was the gap between Chinese vehicles and foreign vehicles in 2016? ________A．131 points.B．145 points.C．95 points.D．36 points.33．The data in the fourth paragraph shows that ________.A．the market share of the domestic cars has droppedB．the quality of domestic vehicles have been improvedC．China’s cars have many mechanical and design problemsD．J.D. Power has done many surveys in the past seven years34．J.D. Power is ________.A．a name of a companyB．a car makerC．a head of an associationD．a milk brand35．According to what Mr. Broderick said in the last two paragraphs, we can learn that ________.A．Chinese car market will be optimistic as is expectedB．Chinese and western consumers have different attitudes to productsC．H e doesn’t like Chinese customers because they don’t trust productsD．It is easier fo r China’s car companies to sell cars to the West第二节（共5小题;每小题2分,满分10分）根据短文内容,从短文后的选项中选出能填入空白处的最佳选项,选项中有两项为多余选项.Why is volunteering important?When it comes to service work, it is important to realize that the actual goal should be getting the most out of your volunteering work. 36Gaining new/social experiencesV olunteering allows students to get involved with new things and develop social and academic skills that couldn’t be learned in a classroom environment. 37Giving back and helping othersV olunteers create better environments for others; they create healthier communities and they brighten lives. Jill, a senior student, has been a volunteer in her community for more than three years.38 “They always tell me how great we sound and how th ey wish they had taken time to learn an instrument in their youth.”Creating connections with people39 Not only does the volunteer work you do show who you are as a person, but it reflects many positive qualities that possibly employers and admission officers want to see. V olunteering allows you to meet a wide variety of people from all sorts of walks of life.40V olunteering isn’t one of the most attractive jobs, but it is one of the most beneficial and up lifting（令人振奋的）. It’s taking some time out of your day and helping others. V olunteer work makes us feel good. It builds self-confidence and lifts up the spirits.A．Building career choices.B．Developing a sense of achievement.C．V olunteering means a lot more.D．Building relationships with people is very important.E．V olunteering is an excellent way to improve your independence.F．She volunteers by performing in concerts for senior citizens.G．V olunteering allows you to experience different environments and situations.第三部分英语知识运用（共两节,满分45分）第一节完形填空（共20小题;每小题1.5分,满分30分）阅读下面短文,从短文后各题所给的四个选项（A、B、C和D）中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑.This is a story about a student, who kept a diary filled with private memories. Some were 41 memories from childhood when he felt hurt, confused, lonely and insecure. He had 42 fragments（片段）of dreams and personal 43 of anger and hatred, as well as things he 44 such as magic shops, coin dealers andChristmas reunion.Then a 45 thing happened. After dinner one night he realized that he had 46 his diary in the dining hall outside the campus. He was afraid that someone might 47 it and find out the truth about him, so he 48 back from the campus, only to find that it was gone.Weeks passed, and eventually he gave up the 49 of ever finding it again. A month later, he was hanging up his jacket in the same place 50 he saw his old brown diary, just where he had left it. 51 he flickered （快速翻阅）through the pages and found that a stranger had written this entry: “God bless you. I am a lot like yo u, only I don’t keep a diary. I am 52 to know there are others like me. I hope things 53 well for you.”Tears came to his eyes. He had never 54 that someone could know his inner feelings and also feel things just like the 55 he did.So whether you are rich or poor, brilliant or 56 , attractive or plain, there are people like you. One of the most deadly 57 we have is that we are not satisfying others. Perhaps you feel you won’t impress others 58 they are more confident, successful, intelligent or attractive than you. Such 59 is misguided. Get rid of your fears of not measuring up, and 60 yourself as you are.41．A．false B．valuable C．painful D．pleasant 42．A．described B．copied C．proved D．reported 43．A．secrets B．feelings C．belongings D．experiments 44．A．studied B．enjoyed C．hated D．misunderstood 45．A．terrible B．common C．moving D．strange 46．A．left B．brought C．stored D．opened 47．A．read B．sell C．steal D．destroy 48．A．looked B．jumped C．rushed D．wandered 49．A．belief B．hope C．life D．habit 50．A．which B．while C．where D．when 51．A．Patiently B．Nervously C．Calmly D．Unwillingly 52．A．unaware B．sorry C．grateful D．disappointed 53．A．work out B．take off C．turn over D．give up 54．A．expected B．seen C．promised D．explained 55．A．theory B．means C．way D．method 56．A．humorous B．average C．lazy D．generous 57．A．fears B．weaknesses C．diseases D．efforts 58．A．until B．so C．although D．because 59．A．finding B．practice C．thinking D．rule 60．A．amuse B．accept C．improve D．treat第Ⅱ卷英语试卷答案1~5．ACBCB 6~10．BCACA 11~15．BCABC 16~20．ACCBC21~25．DCDAD 26~30．CBBCB 31~35．CDBAB 36~40．CGFDB41~45．CABBA 46~50．AACBC 51~55．BCAAC 56~60．BACCB 61．The62．whose63．pleasure64．happier65．was talked66．is67．how68．them69．towards70．thankful71．picking→picked72．去掉so73．exciting→excited74．the→a75．try→trying76．head→headed77．book→books78．to→for79．quick→quickly80．someone后加whoGreener Life, Cleaner AirIt is not easy to forget the heavy smog’s that have occurred frequently this year. It lasted for about one week or more and affected many areas in China, causing much inconvenience and even harm to our life and health.The incident warned us to take action to fight for clean air before it’s too late! And I believe a green lifestyle can make a big difference to the air quality. Firstly, it’s good to take buses or other means of public transportation rather than cars whenever possible. What’s more, be aware to save water, electricity and paper. Moreover, recycle whatever we can. Last but n ot least, don’t forget to influence those around you to follow!英语试卷解析30．B细节推理题.根据最后一段Liam Bates, perhaps the strongest competitor because of his fluent Chinese可知他的优势是能说流利的汉语,故选B．31．C主旨大意题.文章讲述了杭州为了更好发展旅游业从外国人中严格选拔社会媒体大使这一事件,大使待遇优厚竞争很激烈.故选C．34．A细节推理题.根据第三段J.D．Power, a Californian market research company可知J.D．Power是一家公司的名字,故选A．35．B推理判断题.根据最后两段中Chinese customers are very picky in the world because they have been trained to distrust products和They go into a situation expecting there could be quality issues, whereas in the West we trust the brands.可知中国消费者和西方消费者对产品的态度和要求不同,故选B．38．F考查对上下文的理解和推理判断能力.根据上文Jill, a senior student, has been a volunteer in her community for more than three years.一个中学生吉尔为她们社区做志愿者已经三年多了.再根据下文“They always tell me how great we sound and how they wish they had taken time to learn an instrument in their youth.他们总是告诉我听起来棒极了,并希望他们年轻时也能学一件乐器该多好啊.F项:她通过为老人们演奏来做志愿者工作承接上文,故选F.39．D考查对上下文的理解和推理判断能力.根据上文Creating connections with people做志愿者可以和人们建立联系,可知本段应该讲这方面的知识.D项:和人们建立关系很重要符合本段意思,故选D．40．B考查对上下文的理解和推理判断能力.根据下文Volunteering isn’t one of the most attractive jobs, but it is one of the most beneficial and up lifting(令人振奋的). 做志愿者虽然不是最吸引人的工作,但是最有益的和令人振奋的工作之一、V olunteer work makes us feel good. It builds self-confidence and lifts up the spirits. 做志愿者可以使我们感觉很好,建立自信,鼓舞精神.可知本段应该讲做志愿者的意义在于发展成就感,故选B．44．B考查动词.A．studied学习;B．enjoyed喜爱;C．hated恨;D．misunderstood误解.根据句中的magic shops, coin dealers and Christmas reunion.可知这些都是孩子们喜欢的东西,根据常识选B．45．A考查形容词.A．terrible可怕的;B．common普通的;C．moving感人的;D．strange奇怪的.根据本段内容可知他的日记丢了,日记里面承载着他的很多感情,所以对他来说丢日记是可怕的事,根据情境选A．46．A考查动词.A．left留;B．brought带来;C．stored储存;D．opened打开.此处指他把日记本忘在了校外的餐厅,故选A．47．A考查动词.A．read读;B．sell卖;C．steal偷;D．destroy发现.因为日记本丢在了外面所以他怕有人会偷看他的日记,根据常识选A．48．C考查动词.A．looked看;B．jumped跳;C．rushed匆忙;D．wandered徘徊.因为意识到日记本丢了想找回来,所以匆忙返回去找.根据情境选C．49．B考查名词.A．belief信仰;B．hope希望;C．life生命;D．habit习惯.此处指几周过去了日记本也没找到,所以他放弃了能找到的希望,故选B．50．C考查副词.A．which哪一个;B．while当……的时候;C．where在……地方;D．when当……的时候.句中包含定语从句,先行词是place在定语从句中做状语,指在那个地方他看到了他的日记本.故选C．56．B考查形容词.A．humorous幽默的;B．average普通的;C．lazy懒惰的;D．generous慷慨的.此处和brilliant 反义,指杰出还是普通.故选B．57．A考查名词.A．fears担心,恐惧;B．weaknesses弱点;C．diseases疾病;D．efforts努力.句意:我们有的最致命的担心就是不能使别人满意.根据句意选A．58．C考查连词.A．until直到……才;B．so所以;C．although尽管;D．because因为.或许你没有感觉到给别人留下了深刻印象尽管他们比你自信、聪明、成功、有魅力.此处表示转折,故选C．68．them.考查代词.用于care about后面做宾语用宾格,指关心他们.故填them. 69．towards. 考查介词.表示“对…的态度”用attitude towards,故填towards. 70．thankful.考查形容词.动词be后用形容词做表语,指我总是很感激的.故填thankful.写作亮点:本篇条理清楚,要点全面,结构连贯.其句式上的变化既使得文章生动而流畅,也体现了作者驾驭句式的能力.例如:定语从句that have occurred frequently this year.非谓语动词causing much inconvenience.宾语从句whatever we can. It做形式主语.文章还运用了harm to, take action, fight for, make a big difference, rather than, be aware 等词汇及Firstly, What’s more, Last but not least等连接词.。

数学（理）试卷 第Ⅰ卷（选择题）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.已知复数)5z i i i =-（i 为虚数单位），则复数z 的共轭复数为（ ）A ．2i -B ．2i +C ．4i -D ．4i +2.“2a =-”是“直线1:30l ax y -+=与()2:2140l x a y -++=互相平行”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3.如下程序框图的算法思路源于数学名著《几何原本》中的“辗转相除法”，执行该程序框图（图中“m MOD n ”表示m 除以n 的余数），若输入的,m n 分别为495，135，则输出的m = （ ）A ．0B ．5C ． 45D ． 904. 将三颗骰子各掷一次，记事件A =“三个点数都不同”，B =“至少出现一个6点”，则条件概率()()|,|P A B P B A 分别是（ ） A ．601,912 B ．160,291 C ．560,1891 D ．911,21625. 某几何体的三视图如图所示，则该几何体的体积为（ ）A ．12B ．18C ．24D ．306. 已知点,,P A B 在双曲线22221x y a b-=上，直线AB 过坐标原点，且直线PA PB 、的斜率之积为13，则双曲线的离心率为（ ）A B ．2 D 7.在边长为1的正ABC ∆中，,D E 是边BC 的两个三等分点（D 靠近于点B ），则AD AE 等于（ ） A ．16 B ．29 C ．1318 D ．138. 已知函数()()sin 0,0,2f x A x A πωϕωϕ⎛⎫=+>>< ⎪⎝⎭的部分图象如图所示，若将()f x 图象上的所有点向右平移6π个单位得到函数()g x 的图象，则函数()g x 的单调递增区间为（ ）A ．,,44k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦ B ．2,2,44k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦ C ．,,36k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦ D ．2,2,36k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦9. 已知数列{}n a 是首项为a ，公差为1的等差数列，数列{}n b 满足1nn na b a +=，若对任意的*n N ∈，都有8n b b ≥成立，则实数a 的取值范围是（ ）A ．()8,7--B ．[)8,7--C ．(]8,7--D ．[]8,7--10.函数4cos xy x e =-（e 为自然对数的底数）的图像可能是（ ）A ．B ．C ．D ．11. 当,x y 满足不等式组22472x y y x x y +≤⎧⎪-≤⎨⎪-≤⎩时，22kx y -≤-≤恒成立，则实数k 的取值范围是（ ）A ．[]1,1--B ．[]2,0-C ．13,55⎡⎤-⎢⎥⎣⎦D ．1,05⎡⎤-⎢⎥⎣⎦12. 已知底面为边长为2的正方形，侧棱长为1的直四棱柱1111ABCD A B C D -中，P 是面1111A B C D 上的动点．给出以下四个结论中，则正确的个数是（ ）①与点D P 形成一条曲线 ；②若//DP 平面1ACB ，则DP 与平面11ACC A 所成角的正切值取值范围是,3⎫+∞⎪⎪⎣⎭；③若DP =DP 在该四棱柱六个面上的正投影长度之和的最大值为． A ．0 B ．1 C ．2 D ．3第Ⅱ卷（非选择题 ）二、填空题（本大题 共4小题 ，每题5分，满分20分，将答案填在答题纸上） 13.已知()f x 是定义在R 上的奇函数，且当0x <时，()2xf x =，则()4log 9f =____________．14.若0,,cos 224ππααα⎛⎫⎛⎫∈-= ⎪ ⎪⎝⎭⎝⎭，则sin 2α= ____________． 15.在数列{}n a 及{}n b 中，11111,1n n n n n n a a b a b a b ++=+=+==．设11n n nc a b =+，则数列{}n c 的前2017项和为 ____________．16.已知点A 在椭圆221259x y +=上，点P 满足()()1AP OA R λλ=-∈，有72OA OP =，则线段OP 在x 轴上的投影长度的最大值为____________．三、解答题 （本大题共6小题，第17题 至21题每题 12分，在第22、23题中任选一题10分，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，在ABC ∆中，12,cos 3AB B ==，点D 在线段BC 上．（1）若34ADC π∠=，求AD 的长；（2）若2,BD DC ACD =∆sin sin BADCAD∠∠的值． 18.（本小题满分12分）近年来我国电子商务行业迎来发展的新机遇．2016年“618”期间，某购物平台的销售业绩高达516亿元人民币，与此同时，相关管理部门推出了针对电商的商品和服务的评价体系．现从评价系统中选出200次成功交易，并对其评价进行统计，对商品的好评率为0.6，对服务的好评率为0.75，其中对商品和服务都做出好评的交易为80次．（1）请完成关于商品和服务评价的22⨯列联表，并判断能否在犯错误的概率不超过0.001的前提下，认为商品好评与服务好评有关？（2）若将频率视为概率，某人在该购物平台上进行的3次购物中，设对商品和服务全为好评的次数为随机变量X ：①求对商品和服务全为好评的次数X 的分布列： ②求X 的数学期望和方差． 附临界值表：2K 的观测值：()()()()()2n ad bc k a b c d a c b d -=++++（其中n a b c d =+++）关于商品和服务评价的22⨯列联表：19.（本小题满分12分）已知四棱锥P ABCD -中，底面ABCD 是梯形，//BC AD ，AB AD ⊥，且1,2AB BC AD ===，顶点P 在平面ABCD 内的射影H 在AD 上，PA PD ⊥．（1）求证：平面PAB ⊥平面PAD ；（2）若直线AC 与PD 所成角为60°，求二面角A PC D --的余弦值． 20.（本小题满分12分）已知焦点为F 的抛物线()21:20C x py p =>，圆222:1C x y +=，直线l 与抛物线相切于点P ，与圆相切于点Q ．（1）当直线l的方程为0x y -=时，求抛物线1C 的方程； （2）记12,S S 分别为,FPQ FOQ ∆∆的面积，求12S S 的最小值． 21.（本小题满分12分） 已知函数()()ln ,x af x m a m R x-=-∈在x e =（e 为自然对数的底）时取得极值，且有两个零点记为12,x x ．（1）求实数a 的值，以及实数m 的取值范围； （2）证明: 12ln ln 2x x +>．选做题 （在第22、23两题中任选一题作答，若两题都做，按第22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，圆C的参数方程为53x ty t⎧=-⎪⎨=+⎪⎩（t 为参数），在以原点O 为极点，x 轴的非负半轴为极轴建立的极坐标系中，直线l的极坐标方程为cos 4πρθ⎛⎫+= ⎪⎝⎭（1）求圆C 的普通方程和直线l 的直角坐标方程；（2）设直线l 与x 轴，y 轴分别交于,A B 两点，点P 是圆C 上任一点，求,A B 两点的极坐标和PAB ∆面积的最小值．23. （本小题满分10分）选修4-5：不等式选讲 已知函数()2f x x =-．（1）解不等式：()()12f x f x ++≤；（2）若0a <，求证：()()()2f ax af x f a -≥．参考答案一、选择题二、填空题 13. 13- 14. 151615. 4034 16. 15 三、解答题17.（1）在三角形中，∵1cos 3B =，∴sin 3B =．．．．．．．．．．．．．．．．．．．2分又ADC S ∆=ADC S ∆=．．．．．．．．．．．．．．．．．．．7分∵1sin 2ABC S AB BC ABC ∆=∠，∴6BC =， ∵11sin ,sin 22ABD ADC S AB AD BAD S AC AD CAD ∆∆=∠=∠，2ABD ADC S S ∆∆=，∴sin 2sin BAD ACCAD AB∠=∠，．．．．．．．．．．．．．．．．．．．．9分 在ABC ∆中，由余弦定理得2222cos AC AB BC AB BC ABC =+-∠，∴AC =sin 242sin BAD ACCAD AB∠==∠．．．．．．．．．．．．．．．．．．．．．．．．．12分 18.解：（1）由题 意可得关于商品和服务评价的22⨯列联表如下：()222008010407011.11110.8281505012080K ⨯⨯-⨯==>⨯⨯⨯，故能在犯错误的概率不超过0.001的前提下，认为商品好评与服务好评有关．．．．．．．．．．．．．．．．．．．．．．．．4分 （2）①每次购物时，对商品和服务全为好评的概率为25，且X 取值可以是0，1，2，3．其中()()()32211233327235423360;1;25125551255512P X P X C P X C ⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫========= ⎪ ⎪⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭；()3033238355125P X C ⎛⎫⎛⎫===⎪ ⎪⎝⎭⎝⎭， X 的分布列为：．．．．．．．．．．．．．．．．．．．．．．．．8分 ②由于23,5X B ⎛⎫⎪⎝⎭，则()()2622183,31555525E X D X ⎛⎫=⨯==⨯⨯-= ⎪⎝⎭．．．．．．．．．．．．12分19.解析：（1）∵PH ⊥平面,ABCD AB ⊂平面ABCD ，∴PH AB ⊥， ∵,,,AB AD ADPH H AD PH ⊥=⊂平面PAD ，∴AB ⊥平面PAD ，又AB ⊂平面PAB ，∴平面PAB ⊥平面PAD ．．．．．．．．．．．．．．．．5分 （2）以A 为原点，如图建立空间直角坐标系A xyz -，∵PH ⊥平面ABCD ， ∴x 轴//PH ．则()()()0,0,0,1,1,0,0,2,0A C D ，设(),02,0AH a PH h a h ==<<>， ∴()0,,P a b ，()()()0,,,0,2,,1,1,0AP a h DP a h AC ==-=， ∵PA PD ⊥，∴()220AP DP a a h =-+=， ∵AC 与BD 所成角为60°． ∴()21cos ,222AC DP a ==-， ∴()222a h -=，∴()()210a a --=，∵02a <<，∴1a =，∵0h >，∴1h =，∴()0,1,1P ．．．．．．．．．．．．．．．．．．．．．．8分 ∴()()()()0,1,1,1,1,0,1,0,1,1,1,0AP AC PC DC ===-=-，设平面APC 的法向量为(),,n x y z =，由n AP y z n AC x y ⎧=+=⎨=+=⎩，得平面APC 的一个法向量为()1,1,1n =-，设平面DPC 的法向量为(),,m x y z =，由00m PC x z m DC x y ⎧=-=⎨=-=⎩，得平面DPC 的一个法向量为()1,1,1，∴1cos ,3m nm n m n ==． ∵二面角A PC D --的平面角为钝角，∴二面角A PC D --的余弦值为13-．．．．．．．．．．．．．12分20.解：（1）设点200,2x P x p ⎛⎫ ⎪⎝⎭，由()220x py p =>得，22x y p =，求导x y p '=， 因为直线PQ 的斜率为1，所以1x p =且20002x x p -=，解得p = 所以抛物线1C的方程为2x =．（2）因为点P 处的切线方程为：()20002x x y x x p p-=-，即200220x x py x --=， 根据切线与圆切，得d r =1=，化简得4220044x x p =+， 由方程组20022422002201440x x py x x y x x p ⎧--=⎪+=⎨⎪--=⎩，解得20042,2x Q x p ⎛⎫- ⎪⎝⎭，所以002P Q PQ x x =-=-=，点0,2p F ⎛⎫⎪⎝⎭到切线PQ的距离是d ==，所以2220010211224p x p x S PQ d p x +-==⨯=，20122Q p S OF x x ==， 而由4220044x x p =+知，24200440p x x =->，得02x >，所以()()()()()() ()222242222 222000000000012422 20000 222442222422424443324x p x x x x x x xxx p xSS p x p p x x xxx+-+---+-=⨯===---=++≥-当且仅当224424xx-=-时取“=”号，即24x=+p=．所以12SS的最小值为3．21.（1）()()21ln1lnax x a a xxf xx x--+-'==，由()10af x x e+'=⇒=，且当1ax e+<时，()0f x'>，当1ax e+>时，()0f x'<，所以()f x在1ax e+=时取得极值，所以10ae e a+=⇒=，．．．．．．．．．．．．．．．．．．．．2分所以()()()2ln1ln,0,x xf x m x f xx x-'=->=，函数()f x在()0,e上递增，在(),e+∞上递减，()1f e me'=-，()00x x→>时，();f x x→-∞→+∞时，()(),f x m f x→-有两个零点12,x x，故101,0mmeem⎧->⎪<<⎨⎪-<⎩，．．．．．．．．．．．．．．．．．．．．．．．5分（2）不妨设12x x<，由题意知1122lnlnx mxx mx=⎧⎨=⎩，则()()221121221121lnln,lnxx xx x m x x m x x mx x x=+=-⇒=-．需证12ln ln2x x+>，只需证明212x x e>，只需证明：()12ln2x x >，只需证明：()122m x x+>，即证：()122211ln2x x xx x x+>-，即证2122111ln21x x x x x x +>-，设211x t x =>，则只需证明：1ln 21t t t ->+． 也就是证明：1ln 201t t t -->+．．．．．．．．．．．．．．．．．．．．．9分 记()()1ln 2,11t u t t t t -=->+，∴()()()()222114011t u t t t t t -'=-=>++， ∴()u t 在()1,+∞单调递增，∴()()10u t u >=，所以原不等式成立，故212x x e >，则12ln ln 2x x +>得证．．．．．．．．．．．．12分22.（1）由53x t y t⎧=-+⎪⎨=+⎪⎩，消去参数t ，得()()22532x y ++-=，所以圆C 的普通方程为()()22532x y ++-=， 由cos 4πρθ⎛⎫+= ⎪⎝⎭cos sin 2ρθρθ-=-， 所以直线l 的直角坐标方程为20x y -+=．．．．．．．．．．．．．．．．．．．．．5分（2）直线l 与x 轴，y 轴的交点为()()2,0,0,2A B -，化为极坐标为()2,,2,2A Bππ⎛⎫⎪⎝⎭，设P 点的坐标为()5,3t t -++，则P点到直线l的距离为d==∴min d ==AB = 所以PAB ∆面积的最小值是1222242S '==．．．．．．．．．．．．．．．．．．．．．10分 23.（1）由题意，得()()112f x f x x x ++=-+-， 因此只须解不等式122x x -+-≤，当1x ≤时，原不等式等价于232x -+≤，即112x ≤≤； 当12x <≤时，原不等式等价于12≤，即12x <≤； 当2x >时，原不等式等价于232x -≤，即522x <≤． 综上，原不等式的解集为15|22x x ⎧⎫≤≤⎨⎬⎩⎭．．．．．．．．．．．．．5分 （2）由题意得()()()222222222f ax af x ax a x ax a ax ax a ax a f a -=---=-+-≥-+-=-=，所以()()()2f ax af x f a -≥成立．．．．．．．．．．．．．．．．．．．．．．．．．10分。

数学（理）试卷 第Ⅰ卷（选择题）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.已知复数)5z i i i =-（i 为虚数单位），则复数z 的共轭复数为（ ） A ．2i - B ．2i + C ．4i - D ．4i +2.“2a =-”是“直线1:30l ax y -+=与()2:2140l x a y -++=互相平行”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3.如下程序框图的算法思路源于数学名著《几何原本》中的“辗转相除法”，执行该程序框图（图中“m MOD n ”表示m 除以n 的余数），若输入的,m n 分别为495，135，则输出的m = （ ）A ．0B ．5C ． 45D ． 904. 将三颗骰子各掷一次，记事件A =“三个点数都不同”，B =“至少出现一个6点”，则条件概率()()|,|P A B P B A 分别是（ ） A ．601,912 B ．160,291 C ．560,1891 D ．911,21625. 某几何体的三视图如图所示，则该几何体的体积为（ ）A ．12B ．18C ．24D ．306. 已知点,,P A B 在双曲线22221x y a b-=上，直线AB 过坐标原点，且直线PA PB 、的斜率之积为13，则双曲线的离心率为（ ）A ．3 B ．3 C ．2 D ．27.在边长为1的正ABC ∆中，,D E 是边BC 的两个三等分点（D 靠近于点B ），则AD AE 等于（ ） A ．16 B ．29 C ．1318 D ．138. 已知函数()()sin 0,0,2f x A x A πωϕωϕ⎛⎫=+>>< ⎪⎝⎭的部分图象如图所示，若将()f x 图象上的所有点向右平移6π个单位得到函数()g x 的图象，则函数()g x 的单调递增区间为（ ）A ．,,44k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦ B ．2,2,44k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦ C ．,,36k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦ D ．2,2,36k k k Z ππππ⎡⎤-+∈⎢⎥⎣⎦9. 已知数列{}n a 是首项为a ，公差为1的等差数列，数列{}n b 满足1nn na b a +=，若对任意的*n N ∈，都有8n b b ≥成立，则实数a 的取值范围是（ ）A ．()8,7--B ．[)8,7--C ．(]8,7--D ．[]8,7--10.函数4cos xy x e =-（e 为自然对数的底数）的图像可能是（ ）A ．B ．C ．D ．11. 当,x y 满足不等式组22472x y y x x y +≤⎧⎪-≤⎨⎪-≤⎩时，22kx y -≤-≤恒成立，则实数k 的取值范围是（ ）A ．[]1,1--B ．[]2,0-C ．13,55⎡⎤-⎢⎥⎣⎦D ．1,05⎡⎤-⎢⎥⎣⎦12. 已知底面为边长为2的正方形，侧棱长为1的直四棱柱1111ABCD A BC D -中，P 是面1111A B C D 上的动点．给出以下四个结论中，则正确的个数是（ ）①与点D P 形成一条曲线 ，且该曲线的长度是2；②若//DP 平面1ACB ，则DP 与平面11ACC A 所成角的正切值取值范围是3⎫+∞⎪⎪⎣⎭；③若DP ，则DP 在该四棱柱六个面上的正投影长度之和的最大值为 A ．0 B ．1 C ．2 D ．3第Ⅱ卷（非选择题 ）二、填空题（本大题 共4小题 ，每题5分，满分20分，将答案填在答题纸上） 13.已知()f x 是定义在R 上的奇函数，且当0x <时，()2xf x =，则()4log 9f =____________．14.若0,,cos 224ππααα⎛⎫⎛⎫∈-= ⎪ ⎪⎝⎭⎝⎭，则sin 2α= ____________． 15.在数列{}n a 及{}n b 中，1111b 1,1n n n n n n a a b a b a b ++=+=+==．设11n n nc a b =+，则数列{}n c 的前2017项和为 ____________．16.已知点A 在椭圆221259x y +=上，点P 满足()()1AP OA R λλ=-∈，有72OA OP =，则线段OP 在x 轴上的投影长度的最大值为____________．三、解答题 （本大题共6小题，第17题 至21题每题 12分，在第22、23题中任选一题10分，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，在ABC ∆中，12,cos 3AB B ==，点D 在线段BC 上．（1）若34ADC π∠=，求AD 的长；（2）若2,BD DC ACD =∆sin sin BAD CAD∠∠的值． 18.（本小题满分12分）近年来我国电子商务行业迎来发展的新机遇．2016年“618”期间，某购物平台的销售业绩高达516亿元人民币，与此同时，相关管理部门推出了针对电商的商品和服务的评价体系．现从评价系统中选出200次成功交易，并对其评价进行统计，对商品的好评率为0.6，对服务的好评率为0.75，其中对商品和服务都做出好评的交易为80次．（1）请完成关于商品和服务评价的22⨯列联表，并判断能否在犯错误的概率不超过0.001的前提下，认为商品好评与服务好评有关？（2）若将频率视为概率，某人在该购物平台上进行的3次购物中，设对商品和服务全为好评的次数为随机变量X ：①求对商品和服务全为好评的次数X 的分布列： ②求X 的数学期望和方差． 附临界值表：2K 的观测值：()()()()()2n ad bc k a b c d a c b d -=++++（其中n a b c d =+++）关于商品和服务评价的22⨯列联表：19.（本小题满分12分）已知四棱锥P ABCD -中，底面ABCD 是梯形，//BC AD ，AB AD ⊥，且1,2AB BC AD ===，顶点P 在平面ABCD 内的射影H 在AD 上，PA PD ⊥．（1）求证：平面PAB ⊥平面PAD ；（2）若直线AC 与PD 所成角为60°，求二面角A PC D --的余弦值． 20.（本小题满分12分）已知焦点为F 的抛物线()21:20C x py p =>，圆222:1C x y +=，直线l 与抛物线相切于点P ，与圆相切于点Q ．（1）当直线l的方程为0x y -=时，求抛物线1C 的方程； （2）记12,S S 分别为,FPQ FOQ ∆∆的面积，求12S S 的最小值． 21.（本小题满分12分） 已知函数()()ln ,x af x m a m R x-=-∈在x e =（e 为自然对数的底）时取得极值，且有两个零点记为12,x x ．（1）求实数a 的值，以及实数m 的取值范围； （2）证明: 12ln ln 2x x +>．选做题 （在第22、23两题中任选一题作答，若两题都做，按第22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，圆C的参数方程为53x ty t⎧=-⎪⎨=+⎪⎩（t 为参数），在以原点O 为极点，x 轴的非负半轴为极轴建立的极坐标系中，直线l的极坐标方程为cos 4πρθ⎛⎫+= ⎪⎝⎭（1）求圆C 的普通方程和直线l 的直角坐标方程；（2）设直线l 与x 轴，y 轴分别交于,A B 两点，点P 是圆C 上任一点，求,A B 两点的极坐标和PAB ∆面积的最小值．23. （本小题满分10分）选修4-5：不等式选讲 已知函数()2f x x =-．（1）解不等式：()()12f x f x ++≤；（2）若0a <，求证：()()()2f ax af x f a -≥．参考答案一、选择题二、填空题 13. 13-14. 151615. 4034 16. 15 三、解答题17.（1）在三角形中，∵1cos 3B =，∴sin B =．．．．．．．．．．．．．．．．．．．2分又ADC S ∆=ADC S ∆=．．．．．．．．．．．．．．．．．．．7分∵1sin 2ABC S AB BC ABC ∆=∠，∴6BC =， ∵11sin ,sin 22ABD ADC S AB AD BAD S AC AD CAD ∆∆=∠=∠，2ABD ADC S S ∆∆=，∴sin 2sin BAD ACCAD AB∠=∠，．．．．．．．．．．．．．．．．．．．．9分 在ABC ∆中，由余弦定理得2222cos AC AB BC AB BC ABC =+-∠，∴AC =sin 242sin BAD ACCAD AB∠==∠．．．．．．．．．．．．．．．．．．．．．．．．．12分18.解：（1）由题 意可得关于商品和服务评价的22⨯列联表如下：()222008010407011.11110.8281505012080K ⨯⨯-⨯==>⨯⨯⨯，故能在犯错误的概率不超过0.001的前提下，认为商品好评与服务好评有关．．．．．．．．．．．．．．．．．．．．．．．．4分 （2）①每次购物时，对商品和服务全为好评的概率为25，且X 取值可以是0，1，2，3．其中()()()32211233327235423360;1;25125551255512P X P X C P X C ⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫========= ⎪ ⎪⎪⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭；()3033238355125P X C ⎛⎫⎛⎫===⎪ ⎪⎝⎭⎝⎭， X 的分布列为：．．．．．．．．．．．．．．．．．．．．．．．．8分 ②由于23,5X B ⎛⎫⎪⎝⎭，则()()2622183,31555525E X D X ⎛⎫=⨯==⨯⨯-=⎪⎝⎭．．．．．．．．．．．．12分19.解析：（1）∵PH ⊥平面,ABCD AB ⊂平面ABCD ，∴PH AB ⊥， ∵,,,AB AD ADPH H AD PH ⊥=⊂平面PAD ，∴AB ⊥平面PAD ，又AB ⊂平面PAB ，∴平面PAB ⊥平面PAD ．．．．．．．．．．．．．．．．5分 （2）以A 为原点，如图建立空间直角坐标系A xyz -，∵PH ⊥平面ABCD ， ∴x 轴//PH ．则()()()0,0,0,1,1,0,0,2,0A C D ，设(),02,0AH a PH h a h ==<<>， ∴()0,,P a b ，()()()0,,,0,2,,1,1,0AP a h DP a h AC ==-=， ∵PA PD ⊥，∴()220AP DP a a h =-+=， ∵AC 与BD 所成角为60°． ∴()21cos ,222AC DP a ==-， ∴()222a h -=，∴()()210a a --=，∵02a <<，∴1a =，∵0h >，∴1h =，∴()0,1,1P ．．．．．．．．．．．．．．．．．．．．．．8分 ∴()()()()0,1,1,1,1,0,1,0,1,1,1,0AP AC PC DC ===-=-，设平面APC 的法向量为(),,n x y z =，由n AP y z n AC x y ⎧=+=⎨=+=⎩，得平面APC 的一个法向量为()1,1,1n =-，设平面DPC 的法向量为(),,m x y z =，由00m PC x z m DC x y ⎧=-=⎨=-=⎩，得平面DPC 的一个法向量为()1,1,1， ∴1cos ,3m nm n m n ==． ∵二面角A PC D --的平面角为钝角，∴二面角A PC D --的余弦值为13-．．．．．．．．．．．．．12分20.解：（1）设点200,2x P x p ⎛⎫ ⎪⎝⎭，由()220x py p =>得，22x y p =，求导x y p '=， 因为直线PQ 的斜率为1，所以01x p =且2002x x p-=，解得p = 所以抛物线1C的方程为2x =．（2）因为点P 处的切线方程为：()20002x x y x x p p-=-，即200220x x py x --=，根据切线与圆切，得d r =1=，化简得4220044x x p =+，由方程组20022422002201440x x py x x y x x p ⎧--=⎪+=⎨⎪--=⎩，解得20042,2x Q x p ⎛⎫- ⎪⎝⎭，所以002P Q PQ x x =-=-=，点0,2p F ⎛⎫⎪⎝⎭到切线PQ的距离是d ==所以2220010211224p x p x S PQ d p x +-==⨯=，20122Q pS OF x x ==， 而由4220044x x p =+知，24200440p x x =->，得02x >，所以()()()()()() ()222242222 222000000000012422 20000 222442222422424443324x p x x x x x x xxx p xSS p x p p x x xxx+-+---+-=⨯===---=++≥-当且仅当224424xx-=-时取“=”号，即24x=+p=所以12SS的最小值为3．21.（1）()()21ln1lnax x a a xxf xx x--+-'==，由()10af x x e+'=⇒=，且当1ax e+<时，()0f x'>，当1ax e+>时，()0f x'<，所以()f x在1ax e+=时取得极值，所以10ae e a+=⇒=，．．．．．．．．．．．．．．．．．．．．2分所以()()()2ln1ln,0,x xf x m x f xx x-'=->=，函数()f x在()0,e上递增，在(),e+∞上递减，()1f e me'=-，()00x x→>时，();f x x→-∞→+∞时，()(),f x m f x→-有两个零点12,x x，故101,0mmeem⎧->⎪<<⎨⎪-<⎩，．．．．．．．．．．．．．．．．．．．．．．．5分（2）不妨设12x x<，由题意知1122lnlnx mxx mx=⎧⎨=⎩，则()()221121221121lnln,lnxx xx x m x x m x x mx x x=+=-⇒=-．需证12ln ln2x x+>，只需证明212x x e>，只需证明：()12ln2x x >，只需证明：()122m x x+>，即证：()122211ln2x x xx x x+>-，即证2122111ln21x x x x x x +>-，设211xt x =>，则只需证明：1ln 21t t t ->+．也就是证明：1ln 201t t t -->+．．．．．．．．．．．．．．．．．．．．．9分 记()()1ln 2,11t u t t t t -=->+，∴()()()()222114011t u t t t t t -'=-=>++，∴()u t 在()1,+∞单调递增，∴()()10u t u >=，所以原不等式成立，故212x x e >，则12ln ln 2x x +>得证．．．．．．．．．．．．12分22.（1）由53x ty t⎧=-+⎪⎨=⎪⎩，消去参数t ，得()()22532x y ++-=，所以圆C 的普通方程为()()22532x y ++-=， 由cos 4πρθ⎛⎫+= ⎪⎝⎭cos sin 2ρθρθ-=-， 所以直线l 的直角坐标方程为20x y -+=．．．．．．．．．．．．．．．．．．．．．5分（2）直线l 与x 轴，y 轴的交点为()()2,0,0,2A B -，化为极坐标为()2,,2,2A B ππ⎛⎫⎪⎝⎭，设P 点的坐标为()5,3t t -++，则P 点到直线l的距离为d==∴min d ==AB = 所以PAB ∆面积的最小值是1222242S '==．．．．．．．．．．．．．．．．．．．．．10分 23.（1）由题意，得()()112f x f x x x ++=-+-， 因此只须解不等式122x x -+-≤，当1x ≤时，原不等式等价于232x -+≤，即112x ≤≤； 当12x <≤时，原不等式等价于12≤，即12x <≤； 当2x >时，原不等式等价于232x -≤，即522x <≤． 综上，原不等式的解集为15|22x x ⎧⎫≤≤⎨⎬⎩⎭．．．．．．．．．．．．．5分 （2）由题意得()()()222222222f ax af x ax a x ax a ax ax a ax a f a -=---=-+-≥-+-=-=，所以()()()2f ax af x f a -≥成立．．．．．．．．．．．．．．．．．．．．．．．．．10分。