中原工学院期末考试卷2017B

中原名校2016-2017学年高二下学期英语期末考试试卷一、完形填空1. 完形填空One day after school I was just finishing up some math homework. My dad came back from work and sat right beside me1over my homework with me. We made corrections 2 After that we3and my dad said,＂ I will always4every moment spending time talking with you.＂I remember my Dad telling me his stories of when he was5My dad didn't have a father6He was always moving from place to place with my 7My dad wasn't the easiest kid to 8He would9with kids at school, which made my grandma worried. He'd act out to release the anger he had from not having his father present in his10and teenage years.At high school, things got a little 11 He made a football team, he did well and didn't get into as much 12as before. He also made many friends13those friends was my uncle. My Dad and Uncle were friends all throughout high school. It was through my uncle14my Mom and Dad met15Later, they got married. After I was born, my dad felt that becoming a 16was an honorand that he would not be17in my life.I suddenly looked up to see my Dad18at me. I could see in my Dad's eyes how he longed for a19 like this. I continued to do my math homework and20my Dad say,＂ I love you, always.＂（1）A . takingB . lookingC . gettingD . handing（2）A . equallyB . insteadC . togetherD . hardly（3）A . thoughtB . plannedC . listenedD . talked（4）A . wasteB . organizeC . treasureD . choose（5）A . youngB . oldC . tiredD . poor（6）A . growing upB . turning upC . settling downD . breaking away（7）A . momB . uncleC . grandpaD . grandma（8）A . connectB . handleC . changeD . recognize（9）A . fightB . danceC . competeD . study（10）A . strugglingB . travellingC . childhoodD . adulthood （11）A . harderB . easierC . worseD . larger（12）A . troubleB . debtC . sadnessD . anxiety（13）A . BetweenB . Apart fromC . AmongD . As for（14）A . whoB . whenC . howD . that（15）A . practicallyB . officiallyC . especiallyD . entirely（16）A . fatherB . motherC . fighterD . student（17）A . presentB . differentC . absentD . strict（18）A . glaringB . pointingC . aimingD . smiling（19）A . appearanceB . relationshipC . backgroundD . behavior （20）A . feltB . foundC . heardD . made二、阅读理解2. 阅读理解What's going on under Liverpool?A Rainy Day in LiverpoolDark clouds appear over the River Mersey and a cold wind is blowing. A few rain drops are beginning to fall. We're in the famous city of Liverpool and we're going to spend this rainy day in the Williamson Tunnels.An Interesting Life StoryJoseph Williamson was born into a poor family in 1769，but left home and went to work for a tobacco company aged 11. He began at the bottom, and finally became head of the business. An Unsolved MysteryNobody knows why Williamson dug tunnels under most of Liverpool, but many think it was to create jobs. Perhaps half of Liverpool's population worked for him. The industry of war had made enormous amounts of money, but now Liverpool was in a terrible financial situation.The King of Edge HillI went on a guided tour starting close to where his empire began in Edge Hill. In the tunnels, the steps leading from rooms below ground to those buildings, which no longer exist, seem particularly ghostly.Incredible EngineeringWe go into the Double Tunnel. It's just been discovered that it's actually a triple tunnel - but nobody knows why the three tunnels were built on top of each other.We finish the tour and decide we'll have a coffee in the Williamson Tunnels Cafe Bar. There, I notice lots of flyers for bands and theater groups that are coming to play there.Why Liverpool?Apart from the obvious attractions like the football clubs, or anything to do with the Beatles, Liverpool has a lot to offer. Princes Park and Croxteth Park were royal hunting grounds and the trees are 200 years old. Renshaw Street displays are an unusual mix of architecture styles. The nightlife is exciting. If you want to experience a part of the British Isles with a character entirely different from London, you should definitely come to Liverpool.1.（1） Which of the following is TRUE about JosephWilliamson?A . He was born in the early 1700s.B . He left home when he turned 18.C . He worked for a tobacco company when he was young.D . He started his business by himself but ended up broke.2.（2） Where did Williamson start his business?A . Princes Park.B . Edge Hill.C . Croxteth Park.D . Renshaw Street.3.（3） What can you do in Liverpool?a. Join football clubs.b. Enjoy Beatles music.c. Visit famous tourist spots.d. Enjoy the beautiful beach.A . abdB . bcdC . acdD . abc3. 阅读理解In January, 2016, Harry Styles made a bold decision. He left the popular boy band One Direction and went solo (单飞). Now he is making his own voice heard. The 23-year-old British singer released his first solo single called Sign of the Times. His self-titled album (个人同名专辑) is coming out on May 12.Going solo is a journey for him to find his identity (身份).Though at the time, he was uncertain about his future, hekept a word in his mind - “honesty”. “I didn't want to write‘stories',” he told Rolling Stone. “I wanted to write mystories, things that happened to me. The number-one thing was I wanted to be honest. I hadn't done that before.”He is indeed full of stories since beginning his solocareer. Last fall, he spent two months recording on aremote island in Jamaica (牙买加).Along with somemusicians, he filled a two-floor house with instruments.They hung out at the bar that looked like a tree house.Many mornings began with a swim in the river down the hill.They watched many romantic comedies. Styles always helda black notebook and looked like a college student who wasstudying, Rolling Stone reported.His coming album is about rock music. In fact, he grewup with it. His father Desmond was a rock music fan. When Styles was very young, he danced to The Dark Side of the Moon, a classic song by British rock band Pink Floyd. “Icouldn't really get it. But I just remember (thinking that) this is really cool.”Harry said, “At the very beginning, all I wanted was to be the granddad with the best stories.” Surely, now he is on the right track (轨道).4.（1） Why did Styles go solo?A . He wanted to travel with his friends.B . He was certain that he would succeed.C . He wanted to be independent from the hand.D . He wanted to do the things that he hadn't done before.5.（2） From the article, which of the followings is true?A . Styles，next album is about his father.B . Styles wanted to be a man with “stories”.C . He left the band because of its dishonesty.D . Styles couldn't find his identity after going solo.6.（3） What Styles did on the island in Jamaica didn'tinclude .A . making a recordB . hanging out at the barC . swimming in the riverD . studying like a college student.7.（4） What is the article mainly about?A . Styles' “stories” about his solo career.B . Styles' favoriate sportsC . The band One DirectionD . Styles' achievements in music.4. 阅读理解French writer Frantz Fanon once said: “To speak alanguage is to take on a world, a culture.” Since the world changes every day, so does our language.More than 300 new words and phrases have recentlymade it into the online Oxford Dictionary, and in one way or another they are all reflections of today's changing world.After a year that was politically unstable, it's not hard to understand the fact that people's political views are one of the main drives of our expanding vocabulary. One example is “clicktivism”, a compound of “click” and “activism”. Itrefers to “armchair activists” — people who support apolitical or social cause, but only show their support from behind a computer or smartphone. And “otherize” is a verb for “other” that means to alienate (使疏远) people who are different from ourselves — whether that be different skin color, religious belief or sexuality.Lifestyle is also changing our language. For example, “fitspiration” — a compound of fit and inspiration — refers to a person or thing that encourages one to exercise and stay fit and healthy.The phrase “climate refugee” — someone who is forced to leave their home due to climate change — reflects people's concern for the environment.According to Stevenson, social media was the main source for the new expressions. “People feel much freer to coin their own words these days,” he said.But still, not all newly-invented words get the chance to make their way into a mainstream (主流的) dictionary. If you want to create your own hit words, Angus Stevenson, Oxford Dictionaries head of content development, suggests that you should not only make sure that they are expressive (有表现力的) and meaningful, but also have an attractive sound so that people will enjoy saying them out loud.8.（1） What is the article mainly about?A . Some new word that got included into the online Oxford Dictionary.B . The application of new words and phrases.C . How a language mirrors the changing world.D . The impact of social media on our language.9.（2） The underli ned word “coin” in the second-to-lastparagraph probably means ________.A . useB . recordC . changeD . create10.（3） How is the article mainly developed?A . By giving examples.B . By making comparisons.C . By following a timeline.D . By presenting research findings.11.（4） According to Stevenson, to make the wordsyou invent popular, they should ________.A . be easy to rememberB . have unique meaningsC . reflect the changing worldD . be meaningful, expressive and catchy5. 阅读理解Being seen in a fancy sports car or enjoying a beachholiday in a five-star hotel were once signs of having “made it”.But a new study suggested that having people think ofyou as constantly busy and overworked is now a far better way to show social status.According to Harvard University in the US, people areincreasingly leaning toward the phenomenon of“humblebragging (谦虚自夸)”. This is when people make a seemingly modest statement that actually draws attention to something they want to brag (吹嘘) about.Phrases such as “I have no life” and “I desperately need a holiday” are now used to imply social standing, while ordering food and shopping online is the perfect way to prove to neighbors that you are simply too busy and important to go to the supermarket.“Mo vies, magazines, and popular TV shows often highlight (强调) the abundance (富足) of money and leisure time among the wealthy,” said Neeru Paharia, an assistant professor at Harvard University.“In recent years, featuring wealthy people relaxing by the pool or on a yacht (游艇), playing tennis or skiing and hunting are being replaced with advertisements featuring busy individuals who work long hours and have very limited leisure time,” he said. “Displaying (how busy you are at work) and a lack of leisure time operates as a visible signal of status in the eyes of others.”The researchers pointed out that the Wall StreetJournal's 2016 advert campaign featured celebrities (名人) complaining about their busy lives, with the slogan (标语). “People who don't have t ime, make time to read the WallStreet Journal.”The report, which was published in the Journal ofConsumer Research, also found that brands that marketed themselves as timesaving were becoming increasingly high-status, because of the people who used them.According to the authors, this trend of humblebragging is due to people's shit of focus-they now value “thepreciousness und scarcity (稀缺) of individuals" more than “the preciousness and scarcity of goods”.“Busy individuals possess desirable characteristics, leading them to be viewed as scarce and in demand,” the authors concluded.12.（1） The main idea of this article is about ?A . the trend of “humblebragging”.B . characteristics of people who lead a busy life.C . why people today are becoming increasingly busy.D . why some people like to brag about their social status.13.（2） People today prefer to to display theirsocial statusA . share their passion for tennis or skiingB . show how fast-paced their work life isC . tell people about the wonderful holidays they takeD . show off their abundance of money and leisure time14.（3） The Wall Street Journal's 2016 advertcampaign implies that .A . busy people always have a better life than othersB . it's important to read newspapers however busy you areC . busy individuals should learn to manage their time betterD . a lack of time is a typical characteristic of people of high social status15.（4） From the article we can conclude that Americapeople today .A . all brag about themselives.B . value individuals, the preciousness and scarcityC . order food and shop online to show they are richD . work long hours and don't have enough leisure time.三、任务型阅读6. 任务型阅读Many people think of guys as being carefree when it comes to their appearance. But in fact, a lot of guys spend plenty of time in front of the mirror. They care just as much as girls do about their body image.Body image is a person's opinions and feelings about his or her own body and physical appearance________You appreciate your body for its capabilities and accept its imperfections.________ Here are some ideas.Recognize your strengths. Different body types are good fordifferent things. What does your body do well? Maybe your speed, strength, or coordination makes you better than others at a certain sport. That may be basketball, table tennis, mountain hiking, dancing, or even running. Or perhaps you have non-sports skills, like drawing, painting singing, playing a musical instrument, writing, or acting________Exercise regularly. Exercise can help you look well and feel about yourself. Good physiques (体形) don't justhapped________A healthy habit can be as simple as exercising 20 minutes to I Hour three days a week. Working out can also lift your spirits.Respect your body. Practicing good habits-regular showering; taking care of your teeth, hair, and skin; wearing clean clothes, and so on—can help you build a positive body image.________ Your body is just one part of who you are. Your talent for comedy a quick wit (智慧), and all the other things make you unique. So try not to let small imperfections take over.A. Be yourself.B. Just explore talents that you feel good about.C. They take hard work, regular workouts, and a healthy diet.D. So, what can you do to develop a positive body image?E. Use this as an opportunity to discover what you're good at.F. The good news is that self-image and body image can be changed.G Having a positive body image means feeling satisfied with the way you look.四、短文改错7. 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。

第一部分听力（共两节，满分30分）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;每小題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秒钟的时间回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. Where does the conversation probably tae place?A. In an office.B. In a restaurant.C. In a theatre.2. How old is the man now?A. About 20 years old.B. Nearly 40 years old.C. Over 60 years old.3. What will the man do net?A. Go to the information center.B. Chec the price of the ticet.C. Tae a train to leave New Yor.4. What can we learn about the man?A. He gave up his job.B. He has two job offers.C. He is doing a part-time job.5. What does Mr. Anderson do?A. A teacher.B. A librarian.C. A repairman.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。

中原名校2016—2017学年期末检测高二数学(理)试题第Ⅰ卷（选择题）一、选择题：本大题共12小题，每小题5分，共60分.在每个小题给出的四个选项中，有且只有一项符合题目要求.1.已知集合U R =，集合{}2|40M x x =-≤，则U C M = A. {}|22x x -<< B. {}|22x x -≤≤ C. {}|22x x x <->或 D.{}|22x x x ≤-≥或 2.设复数z 满足()()225z i i --=，则z =A. 23i +B. 23i -C. 32i +D.32i -3.若双曲线()222210,0x y a b a b-=>>A. 2y x =±B. y =C. 12y x =±D.y x = 4.设x R ∈，向量()()1,,2,6a x b ==-，且//a b ，则a b ⋅=A. -4B.C.D.20 5.下列四个结论：①若“p q ∧”是真命题，则p ⌝可能是真命题；②命题“2000,10x R x x ∃∈--<”的否定是“2,10x R x x ∃∈--≥”；③“5a >且5b >-”是“0a b +>”的充要条件；④当0a <时，幂函数ay x =在区间()0,+∞上单调递减.其中正确的结论个数是A.0个B.1个C. 2个D. 3个 6.在单调递减等差数列{}n a 中，若32431,4a a a ==，则1a = A. 1 B. 2 C.32D. 37.从4名男生和2名女生中任选3人参加某项活动，则所选的3人中女生人数不少于1人的概率是 A.45 B. 35 C. 25 D.158.把边长为1的正方形ABCD 沿对角线BD 折起，形成的三棱锥A-BCD 的正视图与俯视图如图所示，则其几何体的表面积为A.22+B.C. 1D. 1+9.函数22sin 33,00,1441x y x xππ⎛⎫⎡⎫⎛⎤=∈-⎪ ⎪⎢⎥⎣⎭⎝⎦⎝⎭+的图象大致是10.如果函数()f x 在区间D 上是增函数，且()f x x在区间上是减函数，则称函数()f x 在区间D 上是缓增函数，区间D 叫做缓增区间.若函数()21322f x x x =-+在区间D 上是缓增函数，则缓增区间D 是A.[)1,+∞ B. ⎡⎣ C. []0,1 D.⎡⎣11.若函数()3211232b f x x x bx ⎛⎫=-++ ⎪⎝⎭在区间[]3,5上不是单调函数，则函数⎡⎣在R 上的极大值为 A.232136b b - B. 3223b - C. 0 D. 423b - 12.已知函数()22ln x e f x k x x x ⎛⎫=-+ ⎪⎝⎭，若2x =是函数()f x 的唯一极值点，则实数k 的取值范围是A. (],e -∞B. []0,eC. (),e -∞D.[)0,e二、填空题：本大题共4小题，每小题5分，共20分.13.()cos 5sin aax x x -+=⎰ .14.曲线()ln f x x x =在点()()1,1f 处的切线方程为 .15.若将函数sin y x x =+的图象向右平移()0ϕϕ>个单位长度得到函数sin y x x =-的图象，则ϕ的最小值为 .16.已知函数()312x x f x x x e e=-+-，其中e 是自然对数的底数，若()()2120f a f a -+≤，则实数a 的取值范围为 .三、解答题：本大题共6小题，共70分.解答应写出必要的文字说明或推理、验算过程.17.（本题满分12分）已知命题P 函数()()2log 1m f x x =+是增函数，命题Q 2,10.x R x mx ∀∈++≥（1）写出命题Q 的否命题Q ⌝，并求出实数m 的取值范围，使得命题Q ⌝为真命题； （2）如果P Q ∨是真命题，P Q ∧是假命题，求实数m 的取值范围.18.（本题满分12分）如图，在长方体1111ABCD A B C D -中，11,AB AA E ==为BC 的中点. （1）求证：11C D D E ⊥;（2）若二面角1B AE D --的大小为90，求AD 的长.19.（本题满分12分）已知椭圆()222210x y a b a b+=>>的左、右焦点分别为12,F F ，A是椭圆的上顶点，直线2AF 交椭圆于另一点B. （1）若190F AB ∠=，求椭圆的离心率；（2）若22132,2AF F B AF AB =⋅=，求椭圆的方程.20.（本题满分12分）设等差数列{}n a 的公差0d >，且10a >，记12231111.n n n T a a a a a a +=+++（1）用1,a d 分别表示123,,T T T ，并猜想n T ； （2）用数学归纳法证明你的猜想.21.（本题满分12分）已知()()2ln , 3.f x x x g x x ax ==-+-（1）求函数()f x 在区间[](),20t t t +>上的最小值；（2）对一切实数()()()0,,2x f x g x ∈+∞≥恒成立，求实数a 的取值范围； （3）证明：对一切()0,x ∈+∞，12ln xx e ex>-恒成立.22.（本题满分10分）选修4-4：参数方程与极坐标系 在平面直角坐标系xoy 中，直线1l 的参数方程为2x ty kt=+⎧⎨=⎩（t 为参数），直线2l 的参数方程为2x m my k =-+⎧⎪⎨=⎪⎩（m 为参数），设直线1l ，2l 的交点为P,当变化时，P 的轨迹为曲线.（1）写出曲线C 的普通方程；（2）以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系，设()3:cos sin 0l ρθθ+=，M 为3l 与C 的交点，求M 的极径.23.（本题满分10分）选修4-5：不等式选讲已知函数()()24,1 1.f x x ax g x x x =-++=++-（1）当1a =时，求不等式()()f x g x ≥的解集；（2）若不等式()()f x g x ≥的解集包含，求实数a 的取值范围.中原名校2016—2017学年期末检测高二数学(理)答案一、选择题 1．C 2．A 3．D 4．D 5．B 6．B7．A8．B 9．A 10．D11．D12．A1．C 【解析】因为{}240M x x =-≤{}22x x =-≤≤，全集U R =，所以U C M ={}22x x x <->或，故选C.2．A 【解析】利用方程思想求解复数并化简.由(－2i)(2－i)＝5，得＝2i ＋52－i ＝2i ＋5(2＋i)(2－i)(2＋i)＝2i ＋2＋i ＝2＋3i.3．D 【解析】由条件e ＝3，即c a ＝3，得c 2a 2＝a 2＋b 2a 2＝1＋b 2a 2＝3，所以ba ＝2，所以双曲线的渐近线方程为y ＝±22．故选D4．D 【解析】∵a ＝(1，)，b ＝(2，－6)且a ∥b ，∴－6－2＝0，＝－3，∴a ＝(1，－3)，a ·b ＝20，故选D ．5．B 【解析】①若p q ∧是真命题，则p 和q 同时为真命题，p ⌝必定是假命题；②命题“2000,10x R x x ∃∈--<”的否定是“2,10x R x x ∀∈--≥”； ③“5a >且5b >-”是“0a b +>”的充分不必要条件；④a y x =1'a y a x -⇒=⋅，当0a <时，'0y <，所以在区间()0+∞，上单调递减. 选B ．6．B 【解析】由题知，a 2＋a 4＝2a 3＝2，又∵a 2a 4＝34，数列{a n }单调递减，∴a 4＝12，a 2＝32．∴公差d ＝a 4－a 22＝－12．∴a 1＝a 2－d ＝2．7．A 【解析】设所选女生人数为，则服从超几何分布，其中N ＝6，M ＝2，n ＝3，则P (1)＝P (＝1)＋P (＝2)＝212436C CC 错误！未找到引用源。

中原名校2016—2017学年期末检测高二数学(文)试题第Ⅰ卷（选择题）一、选择题：本大题共12小题，每小题5分，共60分.在每个小题给出的四个选项中，有且只有一项符合题目要求.1.已知集合U R =，集合{}2|40M x x =-≤，则U C M = A. {}|22x x -<< B. {}|22x x -≤≤ C. {}|22x x x <->或 D.{}|22x x x ≤-≥或 2.设复数z 满足()()225z i i --=，则z =A. 23i +B. 23i -C. 32i +D.32i -3.为了判断两个分类变量与Y 之间是否有关系，应用独立性检验法算得2K 的观测值为6，附：临界值表如下：则下列说法正确的是A. 有95%的把握认为与Y 有关系B. 有99%的把握认为与Y 有关系C.有99.5%的把握认为与Y 有关系D. 有99.9%的把握认为与Y 有关系 4.设x R ∈，向量()()1,,2,6a x b ==-，且//a b ，则a b ⋅=A. -4B.C.D.20 5.下列四个结论：①若“p q ∧”是真命题，则p ⌝可能是真命题；②命题“2000,10x R x x ∃∈--<”的否定是“2,10x R x x ∃∈--≥”；③“5a >且5b >-”是“0a b +>”的充要条件；④当0a <时，幂函数ay x =在区间()0,+∞上单调递减.其中正确的结论个数是A.0个B.1个C. 2个D. 3个6.已知函数()133xxf x ⎛⎫=- ⎪⎝⎭，则()f xA. 是偶函数，且在R 上是增函数B. 是奇函数，且在R 上是增函数C.是偶函数，且在R 上是减函数D. 是奇函数，且在R 上是减函数7. 在单调递减等差数列{}n a 中，若32431,4a a a ==，则1a = A. 1 B. 2 C.32D. 3 8.已知()f x 是定义在R 上的奇函数，且当()0,x ∈+∞时，()20182018log xf x x =+，则函数()f x 的零点的个数是 A. 1 B. 2 C. 3 D. 4 9.函数22sin 33,00,1441x y x xππ⎛⎫⎡⎫⎛⎤=∈-⎪ ⎪⎢⎥⎣⎭⎝⎦⎝⎭+的图象大致是10.若将函数sin y x x =的图象向右平移()0ϕϕ>个单位长度得到函数sin y x x =-的图象，则ϕ的最小值为A. 6πB. 2πC. 3πD.23π11.如果函数()f x 在区间D 上是增函数，且()f x x在区间上是减函数，则称函数()f x 在区间D 上是缓增函数，区间D 叫做缓增区间.若函数()21322f x x x =-+在区间D 上是缓增函数，则缓增区间D 是A.[)1,+∞B. ⎡⎣C. []0,1D.⎡⎣12.已知函数()22ln x e f x k x x x ⎛⎫=-+ ⎪⎝⎭，若2x =是函数()f x 的唯一极值点，则实数k 的取值范围是A. (],e -∞B. []0,eC. (),e -∞D.[)0,e二、填空题：本大题共4小题，每小题5分，共20分.13.已知()f x 的定义域为[]1,1-，则()2log f x 的定义域为 . 14.若曲线ln y x =的切线过原点，则此切线的斜率为 .15.已知()f x 是R 上的偶函数，()g x 是R 上的奇函数，且()()1g x f x =-，若()22f -=，则()2018f = .16.已知函数()ln 2x f x -=的定义域为A,不等式()21log a x x -<在x A ∈时恒成立，则实数a 的取值范围为 .三、解答题：本大题共6小题，共70分.解答应写出必要的文字说明或推理、验算过程. 17.（本题满分12分）设函数()()22280f x x ax aa =-->，记不等式()0f x ≤的解集为A.（1）当1a =时，求集合A;（2）若()1,1A -⊆，求实数a 的取值范围.18.（本题满分12分）若二次函数()()2,f x ax bx c a b R =++∈满足()()12f x f x x +-=，且()0 1.f =（1）求()f x 的解析式；（2）若在区间[]1,1-上，不等式()2f x x m >+恒成立，求实数m 的取值范围.19.（本题满分12分） 如图，在长方体1111ABCD A B C D -中，,E F 分别为111,DD C D 的中点.（1）证明：平面11ADC B ⊥平面1A BE ； （2）证明：1//B F 平面1A BE ；（3）若正方体棱长为1，求四面体11A B BE -的体积.20.（本题满分12分）已知椭圆C 的中心在原点，一个焦点为()2,0F -，且长轴与短轴长的比是2（1）求椭圆C 的方程；（2）设点(),0M m 在 椭圆C 的长轴上，点P 是椭圆上任意一点，当PM 最小时，点P 恰好落在椭圆的右顶点上，求实数m 的取值范围.21.（本题满分12分）已知()()2ln , 3.f x x x g x x ax ==-+-（1）求函数()f x 在区间[](),20t t t +>上的最小值；（2）对一切实数()()()0,,2x f x g x ∈+∞≥恒成立，求实数a 的取值范围.22.（本题满分10分）选修4-4：参数方程与极坐标系在平面直角坐标系xoy 中，直线1l 的参数方程为2x ty kt =+⎧⎨=⎩（t 为参数），直线2l 的参数方程为2x mmy k =-+⎧⎪⎨=⎪⎩（m 为参数），设直线1l ，2l 的交点为P,当变化时，P 的轨迹为曲线.（1）写出曲线C 的普通方程；（2）以坐标原点O 为极点，x 轴的正半轴为极轴建立极坐标系，设()3:cos sin 0l ρθθ+=，M 为3l 与C 的交点，求M 的极径.23.（本题满分10分）选修4-5：不等式选讲已知函数()()24,1 1.f x x ax g x x x =-++=++-（1）当1a =时，求不等式()()f x g x ≥的解集；（2）若不等式()()f x g x ≥的解集包含，求实数a 的取值范围.中原名校2016—2017学年下期期末检测高二数学(文)答案一、选择题1.C2.A3.A4.D5.B6.B7.B8.C9.A10.D 11.D 12.A1．C 【解析】因为{}240M x x =-≤{}22x x =-≤≤，全集U R =，所以U C M ={}22x x x <->或，故选C.2．A 【解析】利用方程思想求解复数并化简.由(－2i)(2－i)＝5，得＝2i ＋52－i ＝2i ＋5(2＋i)(2－i)(2＋i)＝2i ＋2＋i ＝2＋3i.3．A 【解析】依题意，2＝6，且P (2≥3．841)＝0．05，因此有95%的把握认为“和Y 有关系”，选A ．4．D 【解析】∵a ＝(1，)，b ＝(2，－6)且a ∥b ，∴－6－2＝0，＝－3，∴a ＝(1，－3)，a ·b ＝20，故选D ． 5．B 【解析】①若p q ∧是真命题，则p 和q 同时为真命题，p ⌝必定是假命题； ②命题“2000,10x R x x ∃∈--<”的否定是“2,10x R x x ∀∈--≥”； ③“5a >且5b >-”是“0a b +>”的充分不必要条件；④a y x =1'a y a x -⇒=⋅，当0a <时，'0y <，所以在区间()0+∞，上单调递减. 选B ．6．B 【解析】()()113333xxxx f x f x --⎛⎫⎛⎫-=-=-=- ⎪⎪⎝⎭⎝⎭，所以函数是奇函数，并且3x 是增函数，13x⎛⎫⎪⎝⎭是减函数，根据增函数-减函数=增函数，所以函数是增函数，故选A.7．B 【解析】由题知，a 2＋a 4＝2a 3＝2，又∵a 2a 4＝34，数列{a n }单调递减，∴a 4＝12，a 2＝32．∴公差d ＝a 4－a 22＝－12．∴a 1＝a 2－d ＝2．8．C 【解析】作出函数y ＝2 018和y ＝－log 2 018的图象如图所示，可知函数f ()＝2 018＋log 2 018在∈(0，＋∞)上存在一个零点，又f ()是定义在R 上的奇函数，所以f ()在∈(－∞，0)上只有一个零点，又f (0)＝0，所以函数f ()的零点个数是3，故选C.9．A 【解析】因为函数22sin ()11xy f x x==+可化简为222sin ()1x x f x x =+可知函数为奇函数关于原点对称，可排除答案C ；同时有42224sin 2cos 2cos ''()(1)x x x x x xy f x x ++==+ 3222(2sin cos cos )(1)x x x x x x x ++=+，则当(0,)2x π∈ '()0f x >,可知函数在2x π=处 附近单调递增，排除答案B 和D ，故答案选A ．10．D 【解析】因为y ＝sin ＋3cos ＝2sin ⎝ ⎛⎭⎪⎫x ＋π3，y ＝sin －3cos ＝2sin ⎝ ⎛⎭⎪⎫x －π3，所以把y ＝2sin ⎝ ⎛⎭⎪⎫x ＋π3的图象至少向右平移2π3个单位长度可得y ＝2sin ⎝ ⎛⎭⎪⎫x －π3的图象．所以选D 。

（满分100分，考试时间90分钟） 第Ⅰ卷（选择题，共44分）一、选择题（本题共11小题；每小题4分，共44分。

在每小题给出的四个选项中，第1-7题只有一项符合题目要求，第8-11题有多项符合题目要求。

全部选对的的4分，选不全对的的2分，有选错或不答的得0分）1.如图，一电荷量为q 的正点电荷位于电场中的A 点，受到的电场力为F 。

若把该点电荷换为电荷量为2q 的负点电荷，则A 点的电场强度E 为( )A.F/q ，方向与F 相反B.F/2q ，方向与F 相反C.F/q ，方向与F 相同D.F/2q ，方向与F 相同2.如图所示1L 灯与2L 灯的电阻相同，当滑动变阻器R 的滑片P 向上滑动时，两灯亮度变化情况是( )A.1L 灯变亮，2L 灯变亮 B.1L 灯变暗，2L 灯变亮 C.1L 灯变暗，2L 灯变暗 D.1L 灯变亮，2L 灯变暗3.带电质点在匀强磁场中运动，某时刻速度方向如图所示，此时，所受的重力和洛伦兹力的合力恰好与速度方向相反，不计阻力，则在此后的一小段时间内，带电质点将（ ）A. 可能做直线运动B. 可能做匀减速运动C. 一定做曲线运动D. 可能做匀速圆周运动4.在光滑水平面上，一质量为m 、速度大小为v 的A 球与质量为2m 静止的B 球碰撞后，A 球的速度方向与碰撞前相反，则碰撞后B 球的速度大小可能是( ) A. 0.6v B. 0.4v C. 0.3v D. 0.2v5.氢原子的能级如图所示，用光子能量为12.75eV 的光照射一群处于基态的氢原子，最多能观测到氢原子发射不同波长的光有( ) A. 3种 B. 4种 C. 5种 D. 6种6.U 23892放射性衰变有多种途径，其中一种途径是先衰变成Bi 21083，而Bi 21083可以经一次衰变变成X a210（代表某种元素），也可以经一次衰变变成Ti b 81，X a 210和Ti b81最后都衰变变成Pb 20682，衰变路径如图所示，则由图可判断下列说法正确的是（ ）A.过程①是β衰变，过程③是α衰变；过程②是α衰变，过程④是β衰变B.过程①是β衰变，过程③是α衰变；过程②是β衰变，过程④是α衰变C.过程①是α衰变，过程③是β衰变；过程②是α衰变，过程④是β衰变D.过程①是α衰变，过程③是β衰变；过程②是β衰变，过程④是α衰变7.太阳因核聚变释放出巨大能量，同时其质量不断减少。

绝密★启用前【全国校级联考】河南省中原名校2016-2017学年高二下期期末检测数学（理）试题考试范围：xxx ；考试时间：120分钟；命题人：xxx学校:___________姓名：___________班级：___________考号：___________注意事项．1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上第I 卷（选择题）一、选择题（题型注释）1、已知集合，集合，则A ．B ．C ．D ．【答案】C 【解析】略 2、设复数满足，则（） A ．B ．C ．D ．【答案】A 【解析】试题分析：,综上所试卷第2页，共15页述, 故选A.考点：复数加减乘除法的运算. 3、若双曲线的离心率为，则其渐近线方程为 A ．B ．C ．D ．【答案】D 【解析】由离心率为 ，得，所以渐近线的方程为 ，故选B. 4、设，向量，且，则A ．-4B ．C ．D ．20【答案】D【解析】∵a ＝(1，x )，b ＝(2，－6)且a ∥b ，∴－6－2x ＝0，x ＝－3，∴a ＝(1，－3)，a ·b ＝20，故选D ． 5、下列四个结论： ①若“”是真命题，则可能是真命题；②命题“”的否定是“”；③“且”是“”的充要条件； ④当时，幂函数在区间上单调递减.其中正确的结论个数是A ．0个B ．1个C ．2个D ．3个【答案】B 【解析】①若是真命题，则和同时为真命题，必定是假命题；②命题“”的否定是“”；③“且”是“”的充分不必要条件； ④，当时，，所以在区间上单调递减. 选B6、在单调递减等差数列中，若，则A ．1B ．2C ．D ．3【答案】B【解析】由题知，a 2＋a 4＝2a 3＝2，又∵a 2a 4＝ ，数列{a n }单调递减， ∴a 4＝ ，a 2＝ ．∴公差．∴a 1＝a 2－d ＝2．故选B.7、从4名男生和2名女生中任选3人参加某项活动，则所选的3人中女生人数不少于1人的概率是A ．B ．C ．D ．【答案】A【解析】由题意可知所选人中女生人数不超过 人，则包括女生有一个人和女生有零个人，当女生有一个人时的概率，当女生有零个人时的概率，所以事件的概率为，故选A.8、把边长为1的正方形ABCD 沿对角线BD 折起，形成的三棱锥A-BCD 的正视图与俯视图如图所示，则其几何体的表面积为A ．B ．C ．D ．【答案】B【解析】由题意及三视图可知，平面平面，设的中点为 ，则可得试卷第4页，共15页平面，所以， 由勾股定理可得，该几何体的表面积是两个等腰直角三角形与那两个正三角形面积之和，即，故选B.9、函数的图像大致是（ ）A ．B ．C ．D ．【答案】A【解析】因为函数y =f (x )=可化简为，可知函数为奇函数关于原点对称，可排除答案C ； 同时有y ′=故函数在x ∈(0,)时>0,则x ∈(0,)上单调递增，排除答案A 和D ，故选：B.点睛：识别函数的一般主要观察以下几点：定义域，奇偶性，单调性，特殊值，端点值，极限等等. 10、如果函数在区间D 上是增函数，且在区间上是减函数，则称函数在区间D 上是缓增函数，区间D 叫做缓增区间.若函数在区间D 上是缓增函数，则缓增区间D 是 A ．B ．C ．D ．【答案】D【解析】试题分析：在上是增函数，在上是减函数的缓增区间为.考点：1、函数的单调性；2、导数的应用.【方法点晴】本题考查函数的单调性、导数的应用，涉及函数与方程思想、数形结合思想和转化化归思想，考查逻辑思维能力、等价转化能力、运算求解能力，综合性较强，属于较难题型. 首先利用数形结合思想由在上是增函数，在上是减函数的缓增区间为. 11、若函数在区间上不是单调函数，则函数在R 上的极大值为 A ．B ．C ．0D ．【答案】D 【解析】，在区间上不单调， ，在 上递增，在上递减，在上的极大值为，故选D.【方法点睛】本题主要考查利用导数判断函数的单调性以及函数的极值，属于难题.求函数极值的步骤：(1) 确定函数的定义域；(2) 求导数；(3) 解方程求出函数定义域内的所有根；(4) 列表检查在的根左右两侧值的符号，如果左正右负（左增右减），那么在处取极大值，如果左负右正（左减右增），那么在处取极小值.12、已知函数，若是函数的唯一极值点，则实数的取值范围是 A ．B ．C ．D ．试卷第6页，共15页【答案】A 【解析】已知，则，当时，恒成立，即，令，易知因此. 故选A.点睛：函数，若是函数的唯一极值点等价于其导函数有唯一的可变零点，故此题本质还是零点问题，在导函数中不难发现已经是可变零点，问题转化为当时，恒成立，然后通过变量分离的方法，最终归结为函数的最值问题，问题迎刃而解.第II 卷（非选择题）二、填空题（题型注释）13、________________.【答案】0 【解析】，，故答案为.14、曲线在点处的切线方程为________________.【答案】x －y －1＝0 【解析】由，得 ，即曲线在点处的切线的斜率为 ，则曲线在点 处的切线方程为，整理得，故答案为.【方法点晴】本题主要考查利用导数求曲线切线，属于中档题.求曲线切线方程的一般步骤是：（1）求出在处的导数，即在点出的切线斜率（当曲线在处的切线与轴平行时，在处导数不存在，切线方程为）；（2）由点斜式求得切线方程.15、若将函数的图象向右平移个单位长度得到函数的图象，则的最小值为________________.【答案】【解析】 ，将函数的图象向右平移个单位长度后，得到试卷第8页，共15页的图象，而，所以，，可得，故答案为. 16、已知函数，其中是自然对数的底数，若，则实数的取值范围为________________.【答案】【解析】函数的导数为，可得 在 上递增，又，可得为奇函数，则 ，即有 ，即有，解得 ，故答案为.三、解答题（题型注释）17、已知命题P:函数是增函数，命题Q:（1）写出命题Q 的否命题，并求出实数的取值范围，使得命题为真命题；（2）如果是真命题，是假命题，求实数的取值范围.【答案】（1）；（2）.【解析】试题分析：（1）否命题 ，就是把命题 的条件和结论都否定，联系对应二次函数图象，由，解得 的取值范围；（2）命题 和命题中，一个真命题，一个为假命题，分命题真命题且是假命题、命题是假命题且是真命题，两种情况，计算可得答案.试题解析：（1）：，若为真命题，则解得：或故所求实数的取值范围为：（2）若函数是增函数，则又为真命题时，由的取值范围为由“” 为真命题，“”为假命题，故命题、中有且仅有一个真命题当真假时，实数的取值范围为：当假真时，实数的取值范围为：综上可知实数的取值范围：18、如图，在长方体中，为的中点.（1）求证：;（2）若二面角的大小为，求的长.【答案】（1）见解析；（2）AD ＝2． 【解析】试题分析：（1）以为原点，为 轴，为 轴，为 轴，建立空间直角坐标系，根据能证明；（2）求出平面的法向量和平面的法向量，根据两法向量的数量积为零可求出的长.试题解析：（1）证明：以D 为原点，建立如图所示的空间直角坐标系Dxyz ，设AD ＝a ，则D (0,0,0)，A (a,0,0)，B (a,1,0)，C (0,1,0)，B 1(a,1,1)，C 1(0,1,1)，D 1(0，0,1)，E ，∴＝(0，－1，－1)，＝，则，试卷第10页，共15页∴C 1D ⊥D 1E ．(注：可采用几何法证明。

2017-2018学年17级第二学期大学英语期末试卷B江西工业工程职业技术学院2016~2017学年第二学期期末试卷课程：《大学英语》考试时间: 90分钟考试使用年级和班级：17级建筑1711（B、闭卷）Part I. Oral English 20%Part II. Multiple choice 10%1. My father bought an antique yesterday, ______was very reasonable.A. its priceB. the price of whichC. which priceD. the price of whose2. I want to find a good book. I’m going to the _______.A. cinemaB. libraryC. museumD. bathroom3.While shopping, people sometimes can’t help____ into buying something they don’t really need.A. to persuadeB. persuadingC. being persuadedD. be persuaded4. My birthday is _______ November 11th.A. onB. inC. atD. to5. We won’t leave here ________ he arrives.A. afterB. untilC. whenD. where6. He asked me _____ I would like a cup of tea.A. thatB. whatC. ifD. which7. I enjoyed the movie very much. I wish I ______ the book from which it was made.A．have read B．had read C．should have read D．am reading8. Do you know ______ this word?A. what to spellB. how to spellC. to spellD. which to spell9. The students couldn't help ______ when they heard the joke.A. to laughB. laughC. laughingD. laughed10. What's the date today? It's _____.A. MondayB. AprilC. April 1stD. a April Part III. Reading Comprehension 40%TASK 1A young man once went into town and bought himself a pair of trousers . When he got home , he went upstairs to his bedroom and put them on . He found that they were about two inches too long . He went downstairs to the kitchen . His mother and two sisters were washing up the tea-things there . “ The new trousers are too long , ” he said . “ They need shortening by about two inches . Could one of you do it for me , please ? ” His mother and sister were busy and none of them said anything .But as soon as his mother had finished washing up , she went quietly upstairs to her son’s bedroom and shortened the trousers by two inches . She came downstairs without saying anything to her daughters .Later on , after supper , the elder sister remembered her brother’s trousers . She was a kind-hearted girl , so she went quietly upstairs without saying anything to anyone , and shortened the trousers by two inches .The younger sister went to the cinema , but when she came home , she , too , remembered her brother’s trousers . So she ran upstairs and did as her mother and sister had done .You can imagine the look on the young man’s face when he put the trousers on the nex t morning .( ) 11. The young man’s trousers wer e _____ for him at first .A. a bit too longB. very goodC. not too longD. too short( ) 12. The young man’s mother and sisters didn’t answer because they were busy _____ in the kitchenA. cookingB. making teaC. washing clothesD. washing cups , glasses and so on( ) 13. His elder sister shortened the trousers _____ .A. in the eveningB. after lunchC. as soon as she had finished the washingD. after she came back from the cinema( ) 14. The next morning the young man found that the trousers were _____ inches too short for him .A. twoB. fourC. sixD. eight( ) 15. We can imagine that when the young man put the trousers on the next morning , he would feel _____ .A. happyB. surprisingC. surprisedD. thankfulTASK2Henry finds a job on a farm. He is the strongest and youngest.He eats more, sleeps more, but works less. He doesn't like to use his head, so he knows little. He has to do some unskilled (无需特殊技能的) work. He always says he's tired and hopes to have a good rest. So he gets less money than others.Winter is coming. The workers are getting ready for the next year. Only Henry does nothing. The farmer tells him to cut down some trees in the forest. The young man has to go there with a chair. He feels lonely in the forest and is afraid of the animals. So he looks around and sings loudly. Nobody knows what he's singing.After three days, Henry doesn't cut down any trees. The farmer feels strange. He wants to find out how the young man is working there. To his anger, Henry is sitting on the chair, cutting the tree. "Why are you sitting here to cut the trees?" asks the farmer. "Because I can't work if lying, sir."( ) 16. Henry doesn't like to use his head, so______.A. he knows little knowledge (知识)B. he is young and strongC. he tries to be a farmerD. he finds a job on a farm( ) 17. Henry gets less money because______.A. he sleeps moreB. he does some unskilled workC. he isn't polite to the farmerD. he eats more( ) 18. Henry has to cut down the trees because ______.A. he can do nothing except itB. he likes to stay in the quiet forestC. he can't get on well with othersD. he is very strong( ) 19. Henry is ______ to stay in the forest.A. gladB. angryC. safeD. afraid( ) 20. Henry hopes to ______ .A. make the farmer happyB. get helpC. lie down in the forestD. cut down more treesTASK3Have you ever been ill? When you are ill，you must be unhappy because your body becomes hot，and there are pains all over your body. You don't want to work，you stay in bed，feeling very sad. What makes us ill? It is germs(细菌). Germs are everywhere. They are very small and you can't find them with your eyes，but you can see them with a microscope. They are very small and there could be hundreds of them on a very small thing.Germs are always found in dirty water. When we look at dirty water under the microscope，we shall see them in it. So your father and mother will not let you drink dirty water.Germs aren't found only in water. They are found in air and dust. If you cut your finger，if some of the dust from the floor goes into the cut(割开处)，some of the germs would go into your finger. Your finger would become big and red，and you will have much pain in it. Sometimes the germs would go into all of your body，and you would have pain everywhere.21. Which of the following is TRUE?A. If things are very small，they are germs.B. If things can't be seen，they must be germs.C. Germs are only in dirty water.D. Germs are everywhere around us.22. What is a microscope used for?A. Making very small things look much bigger.B. Making very big things look much smaller.C. Helping you read some newspapers.D. Helping you if you can't see things clearly.23. Why don't your parents let you drink dirty water?A. You haven't looked at it carefully.B. Water can't be drunk in this way.C. There must be lots of germs in it.D. Water will make you ill.24. Which of the following is NOT true?A. Germs can be found both in water and in the air.B. Germs can go into your finger if it is cut.C. If your temperature is not OK，there must be germs in your body.D. If your finger isn't cut，there aren't any germs on it.25. What's the main idea of the passage?A. Germs may make us ill.B. Germs are in dirty water.C. Don't drink dirty water.D. Take care of your fingers.TASK4In the world ,soccer of football is the most popular sport. This is because many countries have wonderful teams for the World Cup. The World Cup is held every four years.To remember 2002 FIFA World Cup ,children from different countries and more than 60 children from Japanese schools cametogether and spent three weekends drawing a big picture called“Dream(梦幻) World Cups”in Japan .The children drew animals, flowers and people playing soccer under a bule bright sky. They wished each football team good luck by drawing the flags(旗帜)of all the countries that will take part in the World Cup in Japan and South Korea.The picture was put up in a park near a playground in Yokohama .Some football teams will have games there.Are you a football fan(迷)？The World Cup makes more and more people interested in football Teenagers(青少年)like playing and watching football .Many of them love some football stars so much that they get the pictures of their favorite players on the walls of their rooms. That is the way to show their love for the World Cup as children in Japan.26.If a country wants to take part in the World Cup ,she must have______.A. Many football fansB.a very good teamC.many football playerD.a big playground27.The next World Cup will be held in_______.A.2006B.2007C.2005D.200428.From the passage ,in the picture children drew many things except_________.A. people playing footballB. pictures of some football starsC. a sunny skyD. flowers29.In“Dream World Cup”,the children drew the flags of some countries______.A. to show their love for their own countryB. to tell the people their storiesC. to show their good wishes for the football teamsD. to show their new ideas about football30.Many teenagers owe the pictures of some football stars because______.A. they are interested in footballB. they are football fansC. they think their favorite players are greatD. all of A,B and CPart Ⅳ. Fill in the blanks with the words or phrases given in the brackets, change the forms if necessary. 10%31. Some senior students wrote in asking for (inform) concerning postgraduate studies.32. The (history) article sketched the major events of the decade.33. After only a short (expose) to sunlight he began to turn red.34. The discussion method is time (consume) and tangential.35. Graduate students (special) in a particular field of study.36. Learning to drive is all a matter of (coordinate).37. She felt (constrain) to carry out the new plan.38. The development rate of the agriculture often shows an (accelerate) trend in this area.39. China has been one of the active (facilitate) in the development of world economy.40. The conference came to the end with the present’s(emotion) speech. Part V. Translation 10%Directions: Translate English to Chinese, and then write down your answers on the answer sheet.41. His wife is half as heavy as him.________________________________________________________________ ______42. Concentration is essential if you want to do a good job.________________________________________________________________ _____43. We set out on this voyage of exploration with an open mind.________________________________________________________________ ____44. The man that called me last night was killed this morning.________________________________________________________________ ____45. People who love to visit shopping centers have different reasons to do shopping in the shopcenter.________________________________________________________________ ____PartⅥ.Practical writing 10%假如你是李华，上周日在地铁站捡到了英国人Steven的护照。

2017学年春季学期《高等数学Ⅰ（二）》期末考试试卷（B）注意：1、本试卷共 3 页；2、考试时间110分钟； 3、姓名、学号必须写在指定地方一、单项选择题（8个小题，每小题2分，共16分）将每题的正确答案的代号A、B、C或D填入下表中．1．a与b是向量，若baba+=+，则必有（）(A)⊥a b(B)0,0==a b或(C)a=b(D)⋅=a b a b2.()(),0,1sin()limx yxyx→=( ).（A）不存在（B）1（C）0（D）∞3．二元函数),(yxfz=在),(yx处可微的充要条件是（）（A）),(yxf在),(yx处连续（B）),(yxfx'，),(yxfy'在),(yx的某邻域内存在（C）),(yxfx'，),(yxfy'在),(yx的某邻域内连续（D）当0)()(22→∆+∆yx时，yyxfxyxfzyx∆'-∆'-∆),(),(是4．对函数(,)f x y=(0,0)是(,)f x y的( ).（A）驻点与极值点（B）驻点，非极值点（C）极值点，非驻点（D）非驻点，非极值点5．设平面区域D：1)1()2(22≤-+-yx，若21()dDI x yσ=+⎰⎰，32()dDI x yσ=+⎰⎰则有（）（A）21II<（B）21II=（C）21II>（D）不能比较6．设椭圆L：13422=+yx的周长为l，则()dLx y s+=⎰（）(A)0 (B) l (C) l3 (D) l47．下列结论正确的是( )(A)若11nnuu+<(1,2,)n=成立，则正项级数1nnu∞=∑收敛(B)当0lim=∞→nnu时，交错级数1(1)nnnu∞=-∑收敛(C)若级数1nnu∞=∑收敛，则对级数的项任意加括号后所成的新级数也收敛(D) 若对级数1nnu∞=∑的项适当加括号后所成的新级数收敛，则原级数也收敛8.设∑∞=1nnnxa的收敛半径为(0)R R>，则∑∞=12nnnxa的收敛半径为( A )(A) (B) R(C) 2R(D) 不能确定二、填空题(7个小题，每小题2分，共14分)．1．过点(1,2,3)且方向向量为(1,2,3)=n的直线方程为；2.设z是方程e zx y z+-=所确定的,x y的隐函数，则(1,0,0)zx∂=∂；3.设22(,)f x y x y=-，则(1,1)f=grad；4. 交换积分1d(,)dyy f x y x⎰的积分次序，变为；5．设L是直线21y x=+上从点（0，1）到点（1，3）的线段，将(,)(,)LP x y dx Q x y dy+⎰转换成对弧长的曲线积分为；6.幂级数11(1)nnnxn∞-=-∑的收敛域是；7.设有周期为π2的函数，它在(,]ππ-上的表达式为()⎩⎨⎧≤<+≤<--=ππxxxxf,1,1，其傅里叶级数在点π=x处收敛于.三峡大学试卷纸教学班号序号学号姓名……………………．……答题不要超过密封线…………．………………………………三、综合解答题一（5个小题，每小题7分，共35分.解答题应写出文字说明、证明过程或演算步骤）1．设(,)z z x y =由方程(23,2)0F x z y z --=所确定，其中F 是可微函数，求d z ． 解： 2.求曲面32=++xy z e z在点)0,1,2(处的切平面方程与法线方程. 解：3.计算二重积分22()d Dxxy y σ++⎰⎰，其中D 由1,0,0=+==y x y x 所围成．解：4．计算(1)d I x v Ω=+⎰⎰⎰，其中Ω是以原点(0,0,0)为形心，边长为a 正立方体．解：5．求幂级数01nn x n ∞=+∑的收敛域与和函数．解：三峡大学 试卷纸 教学班号 序号 学号 姓名……………………．……答 题 不 要 超 过 密 封 线…………．………………………………四、综合解答题二（5个小题，每小题7分，共35分.解答题应写出文字说明、证明过程或演算步骤）1．在椭圆4422=+y x 上求一点，使其到直线0632=-+y x 的距离最短． 解： 2.计算d d Ly x x y -+⎰，其中L 是沿圆周1)1()1(22=-+-y x 正向一周．解：3．计算d Lxy s ⎰，其中L 为从（0，0）到（2，0）的上半圆弧：)0(222≥=+y x y x ．解：4．计算积分d I z S =∑⎰⎰，其中∑是上半球面222y x a z --=，(0)a >.解：5．利用高斯公式计算对坐标的曲面积分(cos cos cos )d x y z S ∑αβγ++⎰⎰， 其中∑为锥面222x y z +=介于平面0z =及1z =之间的部分的下侧， (cos ,cos ,cos αβγ)是∑上点(,,)x y z 处的法向量的方向余弦．解：三峡大学 试卷纸 教学班号 序号 学号 姓名……………………．……答 题 不 要 超 过 密 封 线…………．………………………………2017学年春季学期《高等数学Ⅰ（二）》期末考试试卷(B)答案及评分标准一、单项选择题（8个小题，每小题2分，共16分）1．a 与b 是向量，若b a b a +=+，则必有（D ）(A)⊥a b ； (B)0,0==a b 或； (C)a =b ； (D)⋅=a b a b ．2.()(),0,1sin()limx y xy x →=( B ).（A ） 不存在；（B ） 1； （C ） 0； （D ） ∞ .3．二元函数),(y x f z =在),(00y x 处可微的充要条件是（ C ） （A ）),(y x f 在),(00y x 处连续；（B ）),(y x f x '，),(y x f y '在),(00y x 的某邻域内存在； （C ）),(y x f x '，),(y x f y '在),(00y x 的某邻域内连续； (D)当0)()(22→∆+∆y x 时，y y x f x y x f z y x ∆'-∆'-∆),(),(0000是比4．对函数(,)f x y =(0,0)是(,)f x y 的( C ). （A ）驻点与极值点； （B ）驻点，非极值点； （C ）极值点，非驻点； （D ）非驻点，非极值点. 5．设平面区域D ：1)1()2(22≤-+-y x ，若21()d DI x y σ=+⎰⎰，32()d DI x y σ=+⎰⎰则有（ A ）（A ）21I I <； （B ） 21I I =； （C ）21I I >； （D ）不能比较．6．设椭圆L ：13422=+y x 的周长为l ，则()d L x y s +=⎰（A ） (A)0； (B) l ； (C) l 3； (D) l 4．7．下列结论正确的是 ( C )(A) 若11n n u u +<(1,2,)n =成立，则正项级数1n n u ∞=∑收敛； (B) 当0lim =∞→n n u 时，交错级数1(1)nnn u∞=-∑收敛；(C) 若级数1nn u∞=∑收敛，则对级数的项任意加括号后所成的新级数也收敛； (D) 若对级数1nn u∞=∑的项适当加括号后所成的新级数收敛，则原级数也收敛．8.设∑∞=1n nnx a的收敛半径为(0)R R >，则∑∞=12n n n x a 的收敛半径为 ( A )(A)(B) R ； (C) 2R ； (D) 不能确定．二、填空题(7个小题，每小题2分，共14分)．1．过点(1,2,3)且方向向量为(1,2,3)=n 的直线方程为123123x y z ---==．2.设z 是方程e zx y z +-=所确定的,x y 的隐函数，则(1,0,0)z x ∂=∂_______12_____ 3.设22(,)f x y x y =-，则(1,1)f =grad （2，-2） ． 4.交换积分10d (,)d yy f x y x ⎰的积分次序为______21d (,)d xxx f x y y ⎰⎰___．5．设L 是直线21y x =+上从点（0，1）到点（1，3）的线段， 将(,)(,)LP x y dx Q x y dy+⎰转换成对弧长的曲线积分为2)P Q ds +⎰． 6.幂级数11(1)nn n x n∞-=-∑的收敛域是 (1,1]- . 7.设有周期为π2的函数，它在(,]ππ-上的表达式为()⎩⎨⎧≤<+≤<--=ππx x x x f 0,10,1，其傅里叶级数在点π=x 处收敛于2π. 三、综合解答题一（5个小题，每小题7分，共35分.解答题应写出文字说明、证明过程或演算步骤）1．设(,)z z x y =由方程(23,2)0F x z y z --=所确定，其中F 是可微函数，求d z ． 解：d d d x y z z x z y =+………………2分12121222d d 33F F x y F F F F =-+-----………………5分12122d 2d 3F x F y F F +=+．………………7分或解：由12(2d 3d )(2d d )0F x z F y z ⋅-+⋅-=，得12122d 2d d 3F x F yz F F +=+．2.求曲面32=++xy z e z在点)0,1,2(处的切平面方程与法线方程. 解：令32),,(-++=xy z e z y x F z，………………2分 则2,,+===z z y x e F x F y F ，故(2,1,0)(1,2,3)n………………4分所求切平面的方程为 03)1(2)2(=+-+-z y x ， 即432=++z y x ， ………………6分法线方程为32112zy x =-=-.………………7分 3.计算二重积分22()d Dx xy y σ++⎰⎰，其中D 由1,0,0=+==y x y x 所围成．解：22()d Dxxy y σ++⎰⎰=1-1220d ()d x x x xy y y +++⎰⎰………………4分1320515()d 62324x x x x =-+-+=⎰．………………7分4．计算(1)d I x v Ω=+⎰⎰⎰，其中Ω是以原点(0,0,0)为形心，边长为a 正立方体．解：Ω的形心为(0,0,0)，Ω的体积V 为3a ，………………4分 故3I xV V V a =+==.………………7分5．求幂级数01nn x n ∞=+∑的收敛域与和函数．解：因为11limlim 12n n n n a n a n ρ+→∞→∞+===+，所以1R = ． ………………1分 在左端点1x =-，幂级数成为0(1)1nn n ∞=-+∑，它是收敛的；在右端点1x =，幂级数成为011n n ∞=+∑，它是发散的，故该幂级数收敛域为[1,1)-． ………………3分令0()1nn xs x n ∞==+∑，[1,1)x ∈-，于是1()1n n x xs x n +∞==+∑，[1,1)x ∈-，逐项求导，得(())xs x '=101n n x n +∞='⎛⎫ ⎪+⎝⎭∑=101n n x n +∞='⎛⎫ ⎪+⎝⎭∑=0n n x ∞=∑=11x -，(1,1)x ∈- 将上式两端从0到x 积分，得01()d ln(1),111xxs x x x x x==---≤<-⎰， （根据和函数的连续性，当1x =-时，此式也成立）．于是，当0x ≠时，1()ln(1)s x x x=--，又(0)1s =．故 1ln(1), [-1,0)(0,1),()1, 0.x x s x xx ⎧--∈⎪=⎨⎪=⎩ ………………7分四、综合解答题二（5个小题，每小题7分，共35分.解答题应写出文字说明、证明过程或演算步骤）1．在椭圆4422=+y x 上求一点，使其到直线0632=-+y x 的距离最短． 解： 设),(y x 为椭圆4422=+y x 上任一点，则该点到直线0632=-+y x 的距离为13326yx d --=；令)44()326(222-++--=y x y x L λ，………………2分于是由224(623)20,6(623)80,440,x y L x y x L x y y L x y λλλ⎧=---+=⎪=---+=⎨⎪=+-=⎩ 得驻点 183(,)35M ，283(,)55M -，383(,)55M --，483(,)55M -，………………5分依题意，椭圆到直线一定有最短距离存在， 其中1313133261min =--=M yx d 即为所求．………………7分 2.计算d d Ly x x y -+⎰，其中L 是沿圆周1)1()1(22=-+-y x 正向一周．解： 圆周1)1()1(22=-+-y x 所围区域D 的面积为 π⋅21，………………3分 由格林公式得d d (11)d d LDy x x y x y -+=+⎰⎰⎰=π2．………………7分3．计算d Lxy s ⎰，其中L 为从（0，0）到（2，0）的上半圆弧：)0(222≥=+y x y x ．解： :L 1cos {,[0,]sin x t t y tπ=+∈=，………………3分d (1cos )sin d 2Lxy s t t t π=+=⎰⎰．………………7分4．计算积分d I z S =∑⎰⎰，其中∑是上半球面222y x a z --=，(0)a >.解：d d S x y =d x y ………………3分d DI x y =………………5分3d d d DDx y a x y a π===⎰⎰．………………7分5．利用高斯公式计算对坐标的曲面积分(cos cos cos )d x y z S ∑αβγ++⎰⎰， 其中∑为锥面222x y z +=介于平面0z =及1z =之间的部分的下侧， （cos ,cos ,cos αβγ）是∑上点(,,)x y z 处的法向量的方向余弦． 解：设∑1为221(1)z x y =+≤的上侧，………………2分 则∑与∑1一起构成一个闭曲面， 记它们围成的空间闭区域为1=∑∑Ω+， 由高斯公式得 1(cos cos cos )d x y z S ∑∑αβγ+++⎰⎰3d d d x y z Ω=⎰⎰⎰=π………………4分而 22111(cos cos cos )d d d d d x y x y z S z x y x y ∑αβγπ∑+≤++===⎰⎰⎰⎰⎰⎰，………………6分因此 (cos cos cos )d x y z S ∑αβγ++⎰⎰=0 ………………7分。