2020年6月浙江省绍兴市柯桥区普通高中2020届高三高考适应性考试(二模)政治答案

2020届浙江省绍兴市柯桥区高三下学期6月高考适应性考试数学试卷★祝考试顺利★(含答案)1.已知全集2,1,0,1,2U ，集合{}1,0,1A =-，集合{}0,1,2B =则()U C B =A ∩（ ）A. {}2-B. {}0,1C. {}2,1,2--D. {}2,1,0,1--【答案】C【解析】先写出A B ，根据补集运算即可.【详解】由{1,0,1},{0,1,2}A B =-=所以{0,1}A B =，所以(){2,1,2}U C A B =--.故选：C2.若曲线C ：221x y m -=，则m 等于（ ）A. 1 1+ D. 2【答案】A【解析】由双曲线方程结合隐含条件求得c ，再由离心率列式求解m 值．【详解】由曲线C ：221x y m -=，得0m >，且2a m =，21b =．c ∴=则ce a ===1m =．故选：A3.若实数x ，y 满足3102340220x y x y x y ++≥⎧⎪+-≤⎨⎪--≤⎩，则2x y +的最小值是（ ）A. 3-B. 1-C. 0D. 2【答案】B【解析】画出约束条件的可行域，求出最优解，然后求解即可．【详解】解：由题中给出的三个约束条件，可得可行域为如图所示阴影部分， 平移直线20x y +=，当直线经过可行域的C 时，目标函数的截距取得最小值， 此时2x y +取得最小值．由220310x y x y --=⎧⎨++=⎩解得(0,1)C -， 2x y +的最小值为：1-，故选：B ．4.某几何体的三视图如图所示，则该几何体的体积是（ ）。

2020届绍兴市柯桥中学高三英语二模试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AThe last thing Caitlin Hipp would have expected as she prepared to turn 28 years old was to be living at homewith her parents. But through working as a part-time skating instructor and restaurant server, she isn't able to earn enough to live anywhere other than home.To some degree, multigenerational households have always been a part of American life. However, the number of young adults who have been moving back in with their parents — or never leaving home in the first place — has been growing steadily.UBS Financial Services released a report that even suggests one reason for the growing number of young adultsstill living at home could be that their family doesn't want them to leave.The report shows that 74 percent of millennials (千禧一代)get some kind of financial support from their parents after college. It finds that millennials have redefined the ties that connect parents and children. Millennials see their parents as peers,friends and instructors. Nearly three quarters talked with their parents more than once a week during college. In return, their parents happily provide financial support well into adulthood, helping fund everything for them.Stuart Hoffman, chief economist for the PNC Financial Services Group in theUS, said the number of young adults striking out on their own fell during the Great Recession. Although job growth for millennials since 2014 has improved, that doesn't necessarily mean that millennials are starting to fly the nest. He said, “They may like living at home and being able to save money.“ There's no doubt it has held back household formation and purchases of things people spend money on related to household formation and perhaps related to child-raising," Hoffman explained. "But they are probably traveling more and eating out more if they don't have a house expense or marriage. I don't know if it represents a change in moral values. But it's much more common for adult children to live in their parents’ homes because it's becoming part of the culture.1. What can we learn from the UBS Financial Services' report?A. Millennials are on good terms with their parents.B. Millennials are financially independent after college.C. Parents are unwilling to give their young adults allowance.D. Parents want their kids to stay with them forever.2. What does Hoffman think of young adults' living at home?A. It increases the consumption of household products.B. It may continue despite job growth.C. It is a sign of shift in moral values.D. It is new in American culture.3. What is the author's purpose of writing this passage?A. To introduce millennials' living habits.B. To stress the importance of financial independence.C. To explain why American young adults still live at home.D. To inform people of a social trend in theUS.BScientists have discovered a new behaviour among bumblebees that tricks plants into flowering early.When lack of pollen, bumblebees will bite little by little on the leaves of flower-less plants. The damage seems to fool the plant into flowering, sometimes up to 30 days earlier than normal.With their hairy appearance and special sounds, bumblebees are hard to miss in gardens all over the world. Their hairy bodies make them excellent pollinators for crops like tomatoes and blueberries. They are among the first bees to appear each year and work a long season.But despite their key role, bumblebees, like many other pollinators have seen their numbers decline suddenly in recent decades. One recent study pointed to climate change, reporting that an increasing number of hot days in Europe andNorth Americawas raising local bumblebees extinction rates.But researchers have now made a discovery about bumblebees that could have something to do with their long term survival. Scientists inSwitzerlandfound that when the bumblebees were out of pollen, they started to bite on the leaves of plants that hadn't yet flowered. They used their mouths to cut clearly-shaped holes in the leaves. But the creatures didn't eat the material or use it in their nests.The damaged plants responded by flowering earlier than normal--in some cases up to 30 days ahead of schedule. Researchers also found that the bee damaged plants flowered 30 days earlier than undamaged plants and 25 days earlier than ones damaged by the scientists.“I think everything that we've found is consistent with the idea that the bumblebees are damaging the plantsand that that's an adaptation that brings flowers earlier and that benefits the bees,” said Dr Mark Mescher, one of the authors from ETHZurich.4. How do bumblebees fool plants into flowering earlier?A. By making use of the hot weather.B. By putting the false flowers on the leaves.C. By attacking the leaves of flowerless plants.D. By taking away the pollen from the other flowers.5. What's bumblebees’ key role?A.Making plants flower early.B. Spreading pollen to flowers and plants.C. Sending information about weather change.D. Finding out whether the plant has flowers.6. What has happened to bumblebees in the past the years?A. They are becoming homesick.B. They are not as friendly as before.C. There is a sharp decrease in number.D. They have been busy year by year.7. What's Dr Mark Mescher's attitude towards the behaviour of bumblebees?A. Uncaring.B. Skeptical.C. Tolerant.D. Objective.CMany teens may feel anxious sometimes. It’s the kind of nervousness that makes you bite your nails before a big test. We spend more time online than we should. We feel good about ourselves or bad based on how many Likes and Followers we get on social media. Young people are developing a false view of life.On the screen, we see what people want to show us. People usually only post photos where they are looking their best. They are surrounded by friends and seem that they are having a great time. No one seems sad or lonely. In short, life isfabulous. But sooner or later, our young people compare their real life to it. They find that theirs doesn’t seem as fun or exciting and grow worried that they may be missing out.No wonder teachers are reporting more anxious students. It’s reported that a lot more college students feel ―overwhelming anxiety. The percentage jumped from 50% in 2011 to 62% in 2016. Anxiety is now the most common mental-health problem in my country. It affects nearly one-third of teens and adults.Certainly, we can’t blame it on social media alone. We expect toomuch from our children and a lot of these expectations aren’t reasonable. Their schedules are packed with sports, clubs and homework. They don’t have enough free time. We want our children to succeed, and we don’t care how much it costs.As parents, we must have more balance. On one hand, we push too hard, and on the other hand, we make life too easy for children. We shouldn’t and can’t promise our children that they will always be happy. We shouldn’t try to protect them from the problems of everyday life. Let them solve the problems in person.8. What is the text mainly about?A. What causes teens’ nervousness.B. How to deal with teens’ anxiety.C. What a view of life means to people.D. How to treat social media appropriately.9. What does the underlined word “fabulous” in paragraph 2 mean?A. Wonderful.B. Encouraging.C. Anxious.D. Doubtful.10. Why does the author mention the numbers in paragraph 3?A. To draw teachers’ attention.B. To show teachers’ mental problems.C. To present the seriousness of teens’ anxiety.D. To show adults have more problems than teens.11. What should parents do to help their children out?A. Try to meet their expectations.B. Help them with their homework.C. Give them more free time to play sports.D. Allow them to solve their own problems in life.DAfter finishing his dinner, Lin Xu opened a WeChat mini-program called "Clear Plate" on his phone and took picture of the empty plates. He was then awarded 157 credit points after the image was uploaded and recognized by artificial intelligence.“Users of the app can use their credit to buy gifts, such as books and cellphones to purchase charity meals donated to children in poor rural areas,” Lin said.A nationwide "Clear Your Plate" campaign is gaining steam online. Efforts to stop food waste and promote thrift are also being made by restaurants that have been urged to create an environment in which consumers are reminded not to waste food. They are also encouraged to offer different portion sizes so that customers can have more choices.The “Clear Plate” mini-program has become popular among young Chinese and currently has nearly 1 million users.Liu Jichen, founder of the startup that developed the app, said that the idea popped up at a dinner in 2017,when Liu found that a restaurant would give diners who polished off their food a card and offer small gifts after a certain number of cards had been collected.“Such an idea can be realized online,” Liu said. He formed a team to work on the project.Yet it was quite challenge for the AI system to identify whether the uploaded photos showed empty plates.To make the AI system smarter, Liu and his team, assisted by more than 1,000 others, spent half a year collecting over 100, 000 samples in canteens and restaurants across the country and used the data to train neural network. Dozens of enterprises, institutions and restaurants have contacted the startup to cooperate on the project.Through the visualized mini-program, people can clearly see the good results of saving food, which will effectively reduce waste, he noted. "We hope our efforts can start a new trend among the younger generation, encouraging them to carry out the virtue of cherishing food and developing the habit of thrift, " Liu said12. What is the main function of the APP "Clear Plate?A. Awarding credit points.B. Giving charity meals.C. Showing the empty plates.D. Encouraging saving food.13. How is the "Clear Your Plate" campaign carried out?A. Customers wasting food are punished.B. People join in it on mini-program.C. Restaurants limit customers' choices.D. People are encouraged to buy gifts.14. What was the most difficult when the app was created?A. Getting other people to cooperate with the team.B. Collecting samples in canteens and restaurants.C. Ensuring the app to recognize empty plates.D. Finding people to fund the app.15. What is the purpose of the writing?A. To introduce an app.B. To promote saving food.C. To praise a startup founder.D. To raise fund for poor children.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2020年绍兴市柯桥区高考数学方向性试卷(6月份)(二模)一、单项选择题（本大题共10小题，共30.0分）1.设全集U={a,b，c，d}，集合A={a,b}，B={b,c，d}，则(∁U A)∪(∁U B)=()A. {c,d}B. {a,b，c，d}C. {a,d}D. {a,c，d}2.双曲线y2−3x2=9的渐近线方程为()A. x±√3y=0B. x±3y=0C. √3x±y=0D. 3x±y=03.在复平面内，复数z=20−5i9+2i 的共轭复数对应的向量OZ′⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 为()A. B.C. D.4.某几何体的三视图如图所示，则其体积为()A. 13B. π9C. 23D. 2π95.已知ξ的分布列如下表，若η=2ξ+2，则D(η)的值为()A. −13B. 59C. 109D. 2096. 已知函数f(x)=−xe x +ln 2，则( )A. f(1e )=f(12) B. f(1e )<f(12)C. f(1e )>f(12)D. f(1e )，f(12)的大小关系无法确定7. 已知在四棱锥P −ABCD 中，PA ⊥平面ABCD ，底面ABCD 是正方形，E 是PD 中点，PA =2AB ，则直线BD 与CE 所成角的余弦值为( )A. √36B. √26C. √38D. √288. 已知实数a ，b 满足ab >0，则“1a <1b 成立”是“a >b 成立”的( )A. 充分非必要条件B. 必要非充分条件C. 充要条件D. 既非充分又非必要条件9. 已知数列{a n }满足a 1=1，a n+1=a n +2n−1，则a 5=( )A. 16B. 17C. 31D. 3210. 已知P 是△ABC 所在平面内一点，D 为AB 的中点，若2PD ⃗⃗⃗⃗⃗ +PC ⃗⃗⃗⃗⃗ =(λ+1)PA ⃗⃗⃗⃗⃗ +PB ⃗⃗⃗⃗⃗ ，且△PBA与△PBC 的面积相等，则实数λ的值为( )A. 2B. −2C. 1D. −1二、填空题（本大题共3小题，共11.0分）11. 若函数f (x )=−x 2+2ax 与g (x )=ax+1在区间[1,2]上都单调递减，则实数a 的取值范围是________．12. 12个“演讲”名额分给4个班级，要求每班至少2个名额，则有___________种分配方案(用数字作答)． 13. 已知直线l 与椭圆C:x 22+y 2=1交于P,Q 两点(直线PQ 的斜率大于0)，且OP ⊥OQ ，若ΔOPQ 的面积为2√35，则直线PQ 的方程为__________． 三、多空题（本大题共4小题，共12.0分）14. 已知5lgx =25，则x = ;设2a =5b =m ，且1a +1b =2，则m = .15.在(2x2−13x)6二项展开式的中，常数项是，其二项式系数之和为．16.在四边形ABCD中，AB=1，BC=2，CD=3，AD=4，且∠ABC=120°，则AC=，cos∠BCD=．17.若实数x，y满足不等式组{y≥0x−2y≤2,2x−y≥2则x的最小值是(1)，z=x−3y的取值范围是(2)．四、解答题（本大题共5小题，共60.0分）18.已知函数f(x)=cos2x−sin2x+2√3sinxcosx(x∈R)(1)求f(2π3)的值；(2)求f(x)的对称中心及单调递减区间．19.如图，在四棱锥P−ABCD中，PA⊥平面ABCD，底面ABCD是菱形．(1)求证：BD⊥平面PAC；(2)若PA=AB=2，∠BAD=60∘.求PC与平面PBD所成角的正弦值．20.已知数列{a n}的前n项和为S n，且a1=1， an+1=13S n=13，求a2，a3，a4的值及数列{a n}的通项公式．21.已知动圆C过定点F(2,0)，且与直线x=−2相切，圆心C的轨迹为E，(Ⅰ)求E的轨迹方程；(Ⅱ)若直线l交E与P，Q两点，且线段PQ的中心点坐标(1,1)，求|PQ|22.已知函数f(x)=lnx+a(x2−1)．(1)讨论函数f(x)的单调性；(2)当a=e−1，x∈[1,+∞)时，证明：f(x)⩽(x−1)e x．2【答案与解析】1.答案：D解析：解：∵U={a,b，c，d}，集合A={a,b}，B={b,c，d}，∴(∁U A)∪(∁U B)={c,d}∪{a}={a,c，d}，故选：D根据集合的基本运算进行求解即可．本题主要考查集合的基本运算，要求熟练掌握集合的交并补运算，比较基础．2.答案：C解析：本题考查了双曲线的渐近线方程，把双曲线的标准方程中的“1”转化成“0”即可求出渐近线方程，属于基础题．解：双曲线y2−3x2=9化成标准方程为y29−x23=1，∴渐近线方程为y29−x23=0，化简得√3x±y=0．故选C．3.答案：A解析：本题考查复数的概念、复数的四则运算、复数的几何意义，考查数学抽象、数学运算的核心素养．由题意可得到复数z的共轭复数z=2+i，则共轭复数对应的向量OZ′⃗⃗⃗⃗⃗⃗ =(2,1)，由此即可得到答案．解：依题意，z=20−5i9+2i =(20−5i)(9−2i)(9+2i)(9−2i)=170−85i85=2−i，则z=2+i，故OZ′⃗⃗⃗⃗⃗⃗ =(2,1)，观察可知，选A．故选A ．4.答案：A解析：本题考查三视图求解几何体的体积，根据已知的三视图，判断几何体的形状是解答的关键．解：由三视图得，给几何体的直观图为底面是边长为1的正方形，高为1的四棱锥． 所以体积V =13×12×1=13． 故选A ．5.答案：D解析：本题主要考查离散型随机变量的期望和方差的求法以及方差的性质，属于基础题．根据ξ的分布列先求出期望，利用方差公式求得ξ的方差，进而利用方差的性质求得η的方差． 解：依题，E(ξ)=−1×12+0×13+1×16=−13， 则D(ξ)=(−1+13)2×12+(0+13)2×13+(1+13)2×16=59，故D (η)=D(2ξ+2)=4D(ξ)=209．故选D ．6.答案：C解析：本题考查利用导数研究函数的单调性，属于基础题． 先求出f′(x)=x−1e x，根据单调性可求解．解：f′(x)=−e x −(−x)e xe x ·e x=x−1e x，当x <1时，f′(x)<0，函数f(x)单调递减， 因为1e <12<1，所以f(1e )>f(12). 故选C ．7.答案：B解析：本题考查异面直线所成角的余弦值的求法，是基础题． 建立空间直角坐标系，用向量法求解即可． 解：因为PA =2AB ，设PA =2，则AB =AD =1，以A 为原点，AB 为x 轴，AD 为y 轴，AP 为z 轴，建立空间直角坐标系，则B(1,0，0)，P(0,0，2)，C(1,1，0)，D(0,1，0)，E(0,12,1) BD ⃗⃗⃗⃗⃗⃗ =(−1,1,0),CE ⃗⃗⃗⃗⃗ =(−1,−12,1)， 设异面直线BD 与CE 所成角为θ， 则cosθ=|BD ⃗⃗⃗⃗⃗⃗ ·CE ⃗⃗⃗⃗⃗ ||BD⃗⃗⃗⃗⃗⃗ |·|CE ⃗⃗⃗⃗⃗ |=12√2×√94=√26.故选B ．8.答案：C解析：解：由1a −1b =b−a ab，∵ab >0，∴若1a <1b 成立，则b −a <0，即a >b 成立． 反之若a >b ，∵ab >0， ∴1a −1b =b−a ab<0，即1a <1b 成立，∴“1a <1b 成立”是“a >b 成立”充要条件． 故选：C ．根据不等式的性质，利用充分条件和必要条件的定义进行判断．本题主要考查不等式的性质以及充分条件和必要条件的应用，要求熟练掌握不等式的性质，比较基础．9.答案：A解析：解：数列{a n }满足a 1=1，a n+1=a n +2n−1，则a 2=a 1+20=2， a 3=a 2+2=4，a 4=a 3+22=4+4=8， a 5=a 4+23=8+8=16． 故选：A ．利用数列的递推关系式，逐步求解即可．本题考查数列的递推关系式的应用，考查转化思想以及计算能力．10.答案：D解析：解：∵D 为AB 的中点， ∴2PD ⃗⃗⃗⃗⃗ =PA ⃗⃗⃗⃗⃗ +PB ⃗⃗⃗⃗⃗ ，又∵2PD ⃗⃗⃗⃗⃗ +PC ⃗⃗⃗⃗⃗ =(λ+1)PA ⃗⃗⃗⃗⃗ +PB ⃗⃗⃗⃗⃗ ，∴PA ⃗⃗⃗⃗⃗ +PB ⃗⃗⃗⃗⃗ +PC ⃗⃗⃗⃗⃗ =(λ+1)PA ⃗⃗⃗⃗⃗ +PB ⃗⃗⃗⃗⃗ ， ∴PC ⃗⃗⃗⃗⃗ =λPA⃗⃗⃗⃗⃗ ， 又∵△PBA 与△PBC 的面积相等， ∴P 为AC 的中点， 即λ=−1， 故选：D ．通过D 为AB 的中点可得2PD ⃗⃗⃗⃗⃗ =PA ⃗⃗⃗⃗⃗ +PB ⃗⃗⃗⃗⃗ ，利用2PD ⃗⃗⃗⃗⃗ +PC ⃗⃗⃗⃗⃗ =(λ+1)PA ⃗⃗⃗⃗⃗ +PB ⃗⃗⃗⃗⃗ 化简可得PC ⃗⃗⃗⃗⃗ =λPA ⃗⃗⃗⃗⃗ ，通过△PBA 与△PBC 的面积相等可得P 为AC 的中点，进而可得结论． 本题考查平面向量的基本定理，注意解题方法的积累，属于基础题．11.答案：(0,1]解析：本题考查函数的单调性，熟练掌握基本初等函数的单调性是解题的关键． 解：因为函数f (x )=−x 2+2ax 在区间[1,2]上都单调递减， 则对称轴x =a ≤1， g (x )=a x+1在区间[1,2]上都单调递减，则a >0，所以a 的取值范围是(0,1], 故答案为(0,1]．12.答案：35解析：考查排列组合应用，每个班级先分配一个名额，剩下8个名额，形成7个空，7个空中放三个挡板得出．解：由题意，每个班级先分配一个名额，剩下8个名额，形成7个空，7个空中放三个挡板C 73=35．故答案为35．13.答案：y =√2x ±√2或y =√24x ±√32解析：本题主要考查了椭圆的方程，直线与椭圆的位置关系，弦长公式，点到直线的距离，属于难题．设直线为y=kx+m(k>0)，联立椭圆方程，利用OP⊥OQ，可得3m2=2(k2+1)，计算原点到直线的距离及弦长，利用面积公式可得，S=12d|PQ|=|m|√−2m2+4k2+22k2+1=|m|√4m2−23m2−1=2√35，即可解得m2=k2=2，写出直线方程即可．【详解】设直线为y=kx+m(k>0)，联立椭圆方程x22+y2=1，消元得：(2k2+1)x2+4kmx+2m2−2=0，当Δ>0时，x1+x2=−4km2k2+1,x1⋅x2=2m2−22k2+1，因为OP⊥OQ，所以y1y2+x1x2=0，整理得3m2=2(k2+1)①，又原点到直线的距离d=√1+k2，PQ=√1+k2⋅√(x1+x2)2−4x1x2，所以S=12d|PQ|=|m|√−2m2+4k2+22k2+1，结合①得S=|m|√4m2−23m2−1=2√35，解得m2=2或m2=34，当m2=2时，k2=2，因为k>0，所以k=√2,m=±√2，当m2=34时，k2=18，即k=√24,m=±√32，经检验满足Δ>0，所以所求直线方程为y=√2x±√2或y=√24x±√32．14.答案：100;√10本题考查了对数的运算性质，考查了指数式和对数式的互化，是基础题.解题的关键是熟练运算性质．解：因为5lg x=25，所以，所以x=102=100;因为2a=5b=m，所以，，又因为1a +1b=2，所以，即m2=10，所以m=√10(舍负)．15.答案：202764解析：本题主要考查二项式定理的应用，二项展开式的通项公式，二项式系数的性质，属于基础题．在二项展开式的通项公式中，令x的幂指数等于0，求出r的值，即可求得常数项．利用二项式系数的性质，其二项式系数之和．解：在(2x2−13x )6二项展开式的中，通项公式为T r+1=C6r⋅26−r⋅(−13)r⋅x12−3r，令12−3r=0，求得r=4，可得常数项是C64×4×181=2027，其二项式系数和为26=64，故答案为：2027；64．16.答案：√7−√21本题考查正余弦定理的应用，考查诱导公式的应用，是中档题．在△ABC中由余弦定理求得AC的长，从而根据正弦定理求出sin∠ACB，再由AD2=AC2+CD2得，从而使用诱导公式即可求解．解：在△ABC中由余弦定理得AC2=AB2+BC2−2×AB×BC×cos∠ABC，即AC2=1+4−2×1×2×(−12)=7，所以AC=√7．由正弦定理得ACsin∠ABC =ABsin∠ACB，所以sin∠ACB=AB×sin∠ABCAC =√2114，在△ACD中，由AD2=AC2+CD2，所以，所以故答案为√7,−√2114．17.答案：1(−∞,2]解析：本题主要考查简单的线性规划问题，属于较易题，考查考生分析问题、解决问题的能力，考查的核心素养是数学运算．根据线性约束条件画出可行域，在画出线性目标函数对应的平行线，结合图像运算即可求得答案．解：不等式组{y≥0x−2y≤22x−y≥2表示的平面区域如图中阴影部分所示，由图示可知，x的最小值是1．而在经过可行域的直线x−3y=z(纵截距为−z3)中，直线x−3y=2在y轴上的截距最小，为−23，此时z最大，为2，∴z=x−3y的取值范围是(−∞,2]．18.答案：解：(1)因为，所以；(2)由(1)可知函数，当2x+π6=kπ(k∈Z)时，x=−π12+kπ2(k∈Z)，所以函数f(x)的对称中心为(−π12+kπ2,0)(k∈Z)，当π2+2kπ<2x+π6<3π2+2kπ，即π6+kπ<x<2π3+kπ(k∈Z)时，函数f(x)为减函数，综上所述，函数f (x )的对称中心为(−π12+kπ2,0)(k ∈Z)，函数f (x )的单调递减区间为(π6+kπ,2π3+kπ)(k ∈Z)．解析：本题考查三角恒等变换以及正弦函数的相关性质，考查二倍角公式以及两角和的正弦公式，考查正弦函数的对称中心以及单调区间，体现了综合性，考查了化归与转化思想，是中档题． (1)本题首先可根据三角恒等变换将函数化简为，然后带入x =2π3即可得出结果；(2)本题可结合(1)得出，然后根据正弦函数的相关性质即可得出结果．19.答案：解：(1)证明：四边形ABCD 是菱形，所以AC ⊥BD.又因为PA ⊥平面ABCD ， ∴PA ⊥BD ， ∵PA ∩AC =A ，∴BD ⊥平面PAC (2)设AC 与BD 交于点O ，则OB =1,OA =√3， 由OA ⊥OB,PA ⊥平面ABCD ，∴以点O 为原点，以OB →,OC →,AP →为x ，y ，z 的正方向建系 ，则P(0,−√3,2),D(−1,0,0),B(1,0,0),C(0,√3,0)， ， ∴PB →=(1,√3,−2),PD →=(−1,√3,2)，设n →=(x,y,z)是平面PBD 的一个法向量，则{n →·PB →=x +√3y −2z =0n →·PD →=−x +√3y −2z =0，不妨令y =√3，可得n →=(0,√3,32)， 而PC →=(0,2√3,−2)，则cos <n →,PC →>=n →·PC→|n →|·|PC →|=√2114， ∴PC 与平面PBD 所成角的正弦值等于√2114．解析：本题考查直线与平面垂直的判定定理与平面与平面垂直的判定定理的应用，直线与平面所成角的求法，考查空间想象能力以及计算能力． (1)证明AC ⊥BD.PA ⊥BD.推出BD ⊥平面PAC ；(2)以O 为坐标原点，建立空间直角坐标系O −xyz ，求出相关点的坐标，平面PDB 的法向量，设PC 与平面PBD 所成角为θ，利用空间向量的数量积求解PC 与平面PBD 所成角的余弦值．20.答案：解：由已知得a 2=13，a 3=49，a 4=1627．由a 1=1，a n+1=13S n ，得a n =13S n−1，n ≥2， 故a n+1−a n =13S n −13S n−1=13a n ，n ≥2， 得a n+1=43a n ，n ≥2． 又a 1=1，a 2=13，故该数列从第二项开始为等比数列， 故a n ={1,n =113·(43)n−2,n ≥2解析：本题考查数列递推关系式的应用，由数列{an}的递推公式依次求出a 2、a 3、a 4，根据数列的递推关系判断出故该数列从第二项开始为等比数列，即可求出通项公式，属中档题．21.答案：解：(1)由题设知，点C 到点F 的距离等于它到直线x =−2的距离，所以点C 的轨迹是以F 为焦点x =−2为基准线的抛物线， 所以所求E 的轨迹方程为y 2=8x ．(2)由题意已知，直线l 的斜率显然存在，设直线l 的斜率为k ，P(x 1,y 1)，Q(x 2,y 2)，则有y12=8x1,y22=8x2，两式作差得y12−y22=8(x1−x2)即得k=8y1+y2，因为线段PQ的中点的坐标为(1,1)，所以k=4，则直线l的方程为y−1=4(x−1)，即y=4x−3，与y2=8x联立得16x2−32x+9=0，得x1+x2=2,x1x2=916，|PQ|=√1+k2⋅√(x1+x2)2−4x1x2=√17×√4−4×916=√1192．解析：本题考查轨迹方程，考查直线与抛物线的位置关系，考查学生的计算能力，属于中档题．(1)利用动圆C过定点F(2,0)，且与直线l1：x=−2相切，所以点C的轨迹是以F为焦点x=−2为基准线的抛物线，即可求动点C的轨迹方程；(2)先利用点差法求出直线的斜率，再利用韦达定理，结合弦长公式，即可求|PQ|．22.答案：解：，当a⩾0时，在(0,+∞)上恒成立，所以函数f(x)在(0,+∞)上单调递增，当a<0时，令时，解得0<x<√−12a；令，时，解得x>√−12a，所以函数f(x)的区间(0,√−12a)，上单调递增，在区间上单调递减．(2)令，则，再令φ(x)=x⋅e x−(e−1)x−1x(x⩾1)，则，当x⩾1时，(x+1)e x⩾2e，1x2>0，∴(x+1)e x−(e−1)+1x2>2e−(e−1)>0，即，所以y=φ(x)在[1,+∞)上单调递增，，∴φ(x)⩾φ(1)=0，∴y=g(x)在[1,+∞)上单调递增，∴g(x)⩾g(1)=0.综上所知f(x)⩽(x−1)e x．解析：本题考查利用导数研究函数的单调性，考查分类讨论的思想，考查转化能力，考查运算求解能力，注意解题方法的积累，属于中档题．(1)题干求导可知分a=0、a>0、a<0三种情况讨论f′(x)与0的大小关系可得结论；(2)通过构造函数，利用函数的单调性，即可得．。

2020届绍兴市柯桥中学高三英语二模试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AEast Yorkshire has typical unpredictable British weather. So here are some ideas to keep everybody happy when the weather is not the most ideal.William's Den, North CaveThe outdoor and indoor areas are suitable for children of all ages to have fun.There are nests to explore, rope bridges to cross, a tree-house and a slide. The attached Kitchen provides fresh food made from locally sourced ingredients serving a selection of treats.East Riding Leisure CentresKnown for a fun learner pool alongside an incredible fun zone with two slides as well, it is perfect for kids to find their feet in the water, have fun and explore. Its 6 climbing walls offer a different challenge on each. This place is suitable for anyone over the age of 4 and you can refuel at cafe with fresh food, snacks and cakes.Sewerby Hall and GardensWhen the weather’s not sure, take cover in the Hall and learn how life was in the early 1900’s for the residents and workers of the house. Then explore the zoo and meet the pigs, parrots and penguins! Kids of all ages are welcome.Withernsea LighthouseThere’s no limitation to the age of kids to climb Withernsea Lighthouse, which is 144 steps to the top, with full views of the East Yorkshire Coast at the top of it. Enjoy the museum on the ground floor and learn what life is like working and living in a lighthouse. The souvenir shop provides attractive gifts for visitors at a fair price.1.Which one is unsuitable for kids of all ages?A.William’s Den, North Cave.B.East Riding Leisure Centres.C.Sewerby Hall and Gardens.D.Withernsea Lighthouse.2.Where can kids enjoy food?A.In William’s Den, North Cave and Sewerby Hall and Gardens.B.In East Riding Leisure Centres and Withernsea LighthouseC.In William’s Den, North Cave and East RidingLeisure Centres.D.In Sewerby Hall and Gardens and Withernsea Lighthouse.3.Where does this passage probably come from?A.A geography textbook.B.A science report.C.A finance magazine.D.A travel brochure.BEmojis are very popular among mobile phone and social media users. While there are emojis of almost every kind imaginable, from dinosaurs to joyful tears and eggplants, there is no emoji for forgiveness. Seeing the need to show understanding, aFinnish group decided it was time for a "forgiveness" emoji.Every year, the Unicode Consortium, which sets the standards, adds new emojis to the emoji keyboard on mobile phones and computers. In 2019, the Forgivemoji campaign was launched. Forgivemoji's site made an open call to the public to give their designs for a new forgiveness emoji, with the goal of presenting the symbol to the Unicode Consortium and getting it accepted by people.Tuomo Pesonen, communications director of the Unicode Consortium, explained why the forgiveness emoji isindispensablein today's world. “In our modern communication culture, emojis are an important way of expressing human feelings beyond words.” The campaign gained popularity, reaching over two million people around the world. They received many designs, including a bandaged heart, two holding hands, and people from different cultures hugging.After hundreds of people offered their ideas for this emoji, the winner was announced in February 2020. Former Finnish president Tarja Halonen was selected to choose the winner as she has been important in building bridges between people. The emoji that will be presented to the Unicode Consortium is an image of two hands giving a thumbs-up symbol in front of a heart. If the Unicode Consortium accepts the design, it will become available to the public in late 2021.The Forgivemoji campaign goes far beyond having a strong influence on social media. The message of showing forgiveness and understanding is helpful for the world at large.4. What's the idea behind the Fogivemoji campaign?A. people develop pleasant habits.B. To get people more friendly to each other.C. To pick a forgiveness emoji for the public to use.D. To make mobile phones and computers more convenient to use.5. What does the underlined word “indispensable” in Paragraph 3 mean?A. Necessary.B. Different.C. Changeable.D. Interesting.6. Why was Tarja Halonen selected to choose the winner for the campaign?A. She launched the campaign herself.B. She designed the most popular emoji.C. She was familiar with the emoji history.D. She played an important role in relating people.7. What can be the best title for the text?A. Forgiveness is important for peopleB. Emoji for forgiveness is on the wayC. Emojis are becoming interestingly popularD. Finnish people explore the stories of emojisCDogs are often called as “man's best friend”, MacKenzie, a four-pound Chihuahua（吉娃娃）, was named winner of the 2020 American Hero Dog Competition on October 19, 2020.In its tenth year in 2020 the annual contest is the brainchild of American Humane, the country's first national charitable organization founded for the safety and well-being of animals. Often called the “Oscars for dogs”, the award recognizes dogs who make extremely great contributions to society.The competition of 2020 attracted over 400 entries（参赛者）from across the country. These heroic dogs have gone above the call of duty, saving lives, comforting the ill and aged and reminding us of the powerful, age-old ties between animals and people. While all were impressive, it was tiny MacKenzie who wonthe judges' hearts.MacKenzie's growth was not easy. Born with a mouth disability, she had to be fed through a tube（管子）for the first year of her life. Despite her own struggles, she always seemed to think more of other animals in need. “Never have I seen such a will to live. Though sick, she carefully looked after the baby animals at the rescue（救助）center,” said her caretaker.A life-saving operation performed in 2014 gave MacKenzie the ability to eat independently. The seven-year-old chihuahua is now working for the Mia Foundation, an organization that rescues and nurses animals with inborn disabilities. The chihuahua does an excellent job and has raised various animals. She plays nurse, cleans, comforts and hugs them, acting as their mother and teaching them how to socialize, play and have good manners.In addition to her role as an animal caretaker, MacKenzie also visits schools to educate kids about the importance of accepting physical differences in both animals and people. Her heartwarming and inspiring story makes MacKenzie a worthy receiver ofAmerica's top dog honor.8. What can we infer about the American Hero Dog Competition?A. It was first held in 2010B. It was held to honor caretakers of dogs.C. It takes place every ten years.D. It was started by a charitable organization.9. With what quality did MacKenzie win the award?A. Talent and braveryB. Friendliness and care.C. Courage and selflessness.D. Confidence and independence.10. In which aspect can students benefit from MacKenzie's visits?A. Learning from failures.B. Understanding the disabled.C. Valuing physical health.D. Developing practical ability.11. What's the best title for the text?A. Dogs Are Man's Best Friends.B. Treat Dogs the Way We Want to Be Treated.C. Touching Stories between MacKenzie and PeopleD. 2020 American Hero Dog: A TinyChihuahua.DDo you ever listen to the songs that your parents like? Chances are that you don’t. You probably think the music that they like is old and boring and that the songs on your playlist are muchcooler. But scientists found that people’s music taste changes as time goes by. So it is likely that your own musical preferences will follow a similar path to your parents’, whether you like it or not.We used to think that culture and personality (个性) are the only reasons for different music choices. But researchers at the University of Cambridge noticed that as people enter into different age groups, their social environment changes, and so does their music taste. There are some musical periods that people go through in their life.The first period comes in the teenage years, during which people like strong music such as punk and rock, because teenagers tend to be aggressive or want to be independent.But as people move into early adulthood, their lifestyles change they want to build close relationships with others. As a result, they become fonder of contemporary music, such as pop and R&.B, which is usually uplifting and danceable.When middle age comes, most people have settled down. During this period, people prefer music, such asjazz and classical, as well as music like country, folk and blues.As for old people, they prefer old songs in their childhoods. They generally listen to relaxing music, such as country music and jazz music. But you must be questioning. “Aren’t there old people who are still interested in or even crazy about rock music?” Of course there are. But their reasons for listening to rock music may have changed. At that age people may listen to remind themselves of their youth.12. What do young people usually think of the songs their parents enjoy?A. They are actually less cool.B. They are worth listening to.C. They are especially serious.D. They are hard to understand.13. How many musical periods are there that people go through in their life?A. Two.B. Three.C. Four.D. Five.14. People who want to make friends mostly prefer ________.A. jazz musicB. country musicC. rock musicD. pop music15. What is the best title for the text?A. People Have Different Opinions on MusicB. People Listen to Music for the Same ReasonC. People’s Taste in Music Changes with TimeD. People’s Lifestyle Can Be Changed by Music第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

浙江省高考科目考试柯桥区适应性试卷（2020年6月）参考答案及评分标准一、语言文字运用（共20分）1.（3分）C（A．闭塞（sè），誊为—誉为；B．心弦(xián)；D．茎(jīng)秆）2.（3分）A（冗赘：文章、讲话等冗长，不简练。

此处宜用“冗繁”“烦琐”。

）3.（2分）A（“适宜册页，窄轴等”中间的逗号改为顿号，“册页”和“窄轴”是词语的并列。

）4.（3分）B（A．语序不当，“不仅”“而且”所带内容互换；C．句式杂糅，去掉“据”或“显示”；D．搭配不当，把“显露”改为“涌现”。

）5.（3分）①浙江省首次获得野生狗獾影像记录；②“亚洲狗獾”样子像狗，很有喜感。

③狗獾被列为近危物种。

6.（6分）（1）绍兴（浙江）援鄂先锋队，手足抗疫整盘棋。

（2分）形式1分：符合对联基本要求得1分，平仄不做要求。

内容1分：答出支援主体（浙江或绍兴等）、协作精神、抗疫主题等任意两点给1分，意思对即可。

（2）（4分）①漫画作者是浙江省第三批援鄂医疗队队员，本地典型人物；②漫画内容反映的是抗疫工作的真实生活，具有典型性。

③漫画形象可爱可敬，真实再现了援鄂医疗队工作情景。

④漫画主题符合当下的社会形势，讴歌驰援武汉的“美丽逆行者”，传达社会正能量。

（答出1点给1分，答出2点给2分，答出3点给4分，其它理由也可酌情给分。

）二、现代文阅读（共30分）（一）阅读下面的文字，完成7-9题。

（10分）7.（3分）D（A．偷换概念，句首“媒介素养”应为“媒介素养教育”；B．范围缩小，增加了表示范围限定的“网络时代谣言大行其道时”；C．曲解文意，省去了重要的限定词“完全”，应为“没有完全被纳入”。

）8.（3分）C（原句中“每一天的谣言与辟谣似乎成为了媒介的重要议题”并非“公众缺乏足够的媒介素养来甄别这些新闻和信息的真假”的结果。

）9.（4分）①参考媒介信息的来源（权威媒体还是其他自媒体）；②提升自身的科学素养；③形成区隔能力（有效区隔现实与虚拟、阻断媒介在时间和空间的连续感）；④知晓控制性力量（动态地了解各种媒介生产的流程、体系、结构、关系和行为，根据已有信息知晓控制力量，形成批判力）；⑤控制消费主义情绪（理性消费，主动减少基于消费而生的“焦虑”）。

浙江省高考科目考试柯桥区适应性试卷（2020年6月）英语试题第I卷注意事项：1.答第一卷前，考生务必将自己的姓名、准考证号填写在答题卡上。

2.选出每小题★★答案★★后，用铅笔把答题卡上对应题目的★★答案★★标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他★★答案★★标号。

不能答在本试卷上，否则无效。

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。

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. How will the man get some money?A. From the bank.B. From an ATM.C. From the woman.2. Why does the man look unwell?A. He failed to sign the contract.B. He disliked the hotel.C. He didn’t sleep last night.3. Where are the speakers probably?A. In a bookstore.B. In a library.C. In a study.4. What does the woman do?A. A student.B. A teacher.C. An inventor.5. What does the man imply?A. He’s a good chess player.B. He spends lots of time playing chess.C. He’d like to teach the woman to play chess.第二节听下面5段对话或独白。

浙江省绍兴市柯桥区2020届高三适应性考试可能用到的相对原子质量：H 1 12 14 16 a 23 Mg 24 S 32 Cl 35.5Fe 56 Cu 64 Ba 137 Al 27 Si 28选择题部分（共50 分）一.选择题（本大题共25 个小题，每小题2 分，共50 分。

每个小题列出的四个备选项中只有一个是符合题目要求的，不选、多选、错选均不得分）1.下列物质不属于某酸酸酐的是（）A. NO2B. (CH3CO)2OC. SO2D. Cl2O2.某些地区的自来水含有Fe3+，实验室可以通过蒸馏自来水的方法获得少量纯净的水，需要用到的仪器是（）A．B．C．D．3.下列气体溶于水后，既有强电解质又有弱电解质生成的是（）A．CO2B．SO3C．NH3D．Cl24.下列变化过程中，加入还原剂可以实现的是（）A. Cu→CuOB. HCHO→CH3OHC. CO3 2-→ CO2D. NO→N2O45.下列我国科研成果所涉及材料中，主要成分为同主族元素形成的无机非金属材料的是（）A. 4.03 米大口径碳化硅反射镜B.2022 年冬奥会聚氨酯速滑服C.能屏蔽电磁波的碳包覆银纳米线D.“玉兔二号”钛合金筛选网轮6.下列化学用语中，表示正确的是（）A．次氯酸的结构式：H—Cl—O B. CO2的比例模型：C. 摩尔盐的化学式：(NH4)2SO4•FeSO4•6H2O D．氯化镁的电子式7.下列说法正确的是（）A. 188O 、11H 、21H 三种核素最多可以组成2 种水分子B. 核内中子数为N 的R2+，质量数为A，则该粒子的核外电子数为：A—N—2C. CH3OH 和CH3－O－CH3分子组成相差一个CH2，所以互为同系物D. 按系统命名法，化合物的名称为2,3,3－三甲基丁烷8.下列说法不正确的是（）A. 胶体区别于其他分散系的本质特征是分散质的微粒直径在10－9～10－7 m 之间B. 工业上用二氧化硅在高温下与焦炭反应可直接制得高纯度的硅C. 氨气在加压时易液化，液氨汽化时吸收大量的热，工业上可使用液氨作制冷剂D. 硫酸亚铁是优良的净水剂9.下列说法不正确的是（）A. SiO2可以与NaOH 溶液反应，但不能与浓硝酸反应B. 一般可以用NaOH 溶液来吸收氮的氧化物C. CuBr2溶液分别可以与氯水、氨水、AgNO3溶液、铁粉等发生反应D. SO2能通过氧化还原反应使品红溶液、红色石蕊溶液、紫色高锰酸钾溶液褪色10. 下列说法正确的是（）A. 能源可分为一次能源和二次能源，电能、页岩气、煤、太阳能均为一次能源B. 使用太阳能热水器、沼气的利用、玉米制乙醇都涉及到生物质能的利用C. 向汽油中添加甲醇后，该混合燃料的热值发生改变D. 糖类、油脂和蛋白质都是天然有机高分子化合物11. 下列有关实验说法，不正确的是（）A. 硝酸不慎溅到手上，先用大量水冲洗，再用碳酸氢钠稀溶液冲洗B. 将两块未擦去氧化膜的铝片分别投入到1mol•L -1CuSO4溶液和1mol•L -1CuCl2溶液中，一段时间后，在CuCl2溶液中铝片表面能观察到明显的反应现象C. 在“火柴头中氯元素的检验”实验中，摘下几根未燃过的火柴头，将其浸于水中，稍后取少量溶液于试管中，滴加硝酸银溶液和稀硝酸后，即可判断火柴头中有氯离子的存在D. 从Na2S2O3和H2SO4两溶液相混合开始计时，到溶液出现的浑浊将锥形瓶底部的“+”字完全遮盖时结束，通过比较记录所需时间，可判断反应速率的大小12. 下列关于氮及其化合物的说法，不正确的是（）A. 硝酸可以与甘油反应生成烈性炸药硝化甘油B. 氯碱工业中可以用氨气检查氯气管道是否泄漏C. 工业上制备硝酸是利用NH3和O2反应生成NO，进一步转化为NO2及HNO3D. 为提高作物的养分，可以是铵态氮肥与碱性肥料混合使用13. 下列离子方程式不正确的是（）A．氢氧化铝的酸式电离：Al(OH)3+H2O 『Al(OH)4』—+H+B．过量铁粉与稀硝酸反应：Fe + NO3－+ 4H+ === Fe3++ NO↑ + 2H2OC. 向明矾溶液中加入Ba(OH) 2溶液至Al 3+刚好沉淀完全：2Al 3+ + 3SO42— + 3Ba 2+ + 6OH— = 2Al(OH) 3↓ + 3BaSO 4↓D. 碳酸钠水解：CO32—+H2O HCO3—+OH—14. 下列说法不正确的是（）A. 醛类、葡萄糖、甲酸及其甲酸酯类均能与银氨溶液发生银镜反应B. 蔗糖酯是一种食品乳化剂，可以由蔗糖与脂肪酸经酯化反应合成，蔗糖酯在稀硫酸的作用下充分水解只生成两种产物。

浙江省高考科目考试柯桥区适应性试卷(2020年6月)第二部分通用技术一、选择题（本大题共13小题，每小题2分，共26分。

在每小题给出的四个选项中，只有一个符合题目要求）1. 从人机关系角度分析，下列关于如图所示的脸盆分析中，不正确．．．的是 A.边缘光滑设计，实现人机关系安全目标 B.选用无毒无臭的材质，实现人机关系健康目标 C.尺寸20主要考虑了人的静态尺寸D.尺寸Φ280与待洗物尺寸有关，与人的尺寸无关2. 小明的爸爸用若干60×500×10mm 的木板制作了一个锅盖，发现锅盖强度不够高。

小明决 定采用15×20mm 、长度不限的木条加固，以下方案最合理的是A B C D通用技术实践课上，小明要加工一个如图所示的零件，请根据图及其描述完成第3～4题。

3.如果用26mm ×20mm ×20mm 的钢块制作该零件，下列 加工工艺及其工具的选择中合理的是 A ．冲眼：划针和铁锤 B ．钻孔：麻花钻和平口钳 C ．锉削：平锉和台虎钳 D ．锯割：钢丝锯和台虎钳4.加工该零件时，小明进行了下列操作，其中恰当的是 A ．划线时先划轮廓线再划基准线最后划加工尺寸线 B ．起锯时锯条与水平面呈30夹角C ．用直锉法锉削该零件时，左手施力由小变大，右手 施力由大变小D ．正常锯割时推锯加压回拉不加压 5.图中多标的尺寸共有 A ．1B ．2C ．3D ．4第3～4题图6.如图所示的压紧机构，图b所示为工件未压紧状态。

在力F的作用下(如图a所示)，手柄通过连杆、连杆2带动压杆逆时针摆动，将工件压紧。

当连杆右侧顶住机座时，工件受到的压紧力最大，此时（未撤销力F）手柄、连杆、连杆2、压头的主要受力形式是图a 图bA.手柄受压、连杆受压、连杆2受弯曲、压头受压B.手柄受弯曲、连杆受压、连杆2受弯曲、压头受弯曲C.手柄受弯曲、连杆受弯曲、连杆2受弯曲、压头受压D.手柄受弯曲、连杆受弯曲、连杆2受弯曲、压头受弯曲7.下列关于流程的说法中不恰当．．．的是（）A．任何流程都反映了一定的时序B．任何流程都体现出一定的环节C．具体流程中，环节的划分可大可小D．流程设计，首先要分析现有材料、设备、资金、人员、工艺和环境等因素如图所示是物料自动混合装置控制系统示意图。

2020年浙江省绍兴市柯桥区高考数学模拟试卷（6月份）一、选择题1．（3分）已知全集{2U =-，1-，0，1，2}，集合{1A =-，0，1}，集合{0B =，1，2}，则()(U A B =I ð ) A ．{2}-B ．{0，1}C ．{2-，1-，2}D ．{2-，1-，0，1}2．（3分）若曲线22:1x C y m-=的离心率为2，则m 等于( )A ．1B ．2C ．21+D ．23．（3分）若实数x ，y 满足3102340220x y x y x y ++⎧⎪+-⎨⎪--⎩…„„，则2x y +的最小值是( )A ．3-B ．1-C ．0D ．24．（3分）某几何体的三视图如图所示，则该几何体的体积是( )A ．18B ．36C ．54D ．1085．（3分）已知a ，b R ∈，则“22a b >”是“||a b >”的( ) A ．充分而不必要条件 B ．必要而不充分条件C ．充要条件D ．既不充分也不必要条件 6．（3分）在同一个坐标系中，函数1()x f x a =与()ag x lg x=的图象可能是( ) A ．B ．C ．D ．7．（3分）设a ，b 为正数，已知随机变量X 的分布列是，则( )X 012 PaabA ．()E X 有最大值，()D X 有最大值B ．()E X 有最大值，()D X 无最大值C ．()E X 无最大值，()D X 有最大值 D ．()E X 无最大值，()D X 无最大值8．（3分）在ABC ∆中，90o C ∠=，3AB =，2AC =，O 为ABC ∆所在平面内一点，并且满足230OA OB OC ++=u u u r u u u r u u u r r，记1I OA OB =u u u r u u u r g，2I OB OC =u u u r u u u r g ，3I OC OA =u u u r u u u r g ，则( ) A ．123I I I << B ．213I I I << C ．132I I I << D ．312I I I <<9．（3分）设a ，b R ∈，函数322(1),0(),0x a x ax x f x x x ⎧--++<=⎨⎩…，若函数()()g x f x ax b=--有四个零点，则( ) A ．0a <，0b <B ．0a <，0b >C ．0a >，0b <D ．0a >，0b >10．（3分）如图，在矩形ABCD 中，将ACD ∆沿AC 翻折至ACD '∆，设直线AD '与直线BC 所成角为α，直线AD '与平面ABC 所成角为β，二面角A CD B '--的平面角为γ，当γ为锐角时( )A ．αβγ>>B ．γβα>>C ．γαβ>>D ．αγβ>>二、填空题（共7小题，每小题3分，满分21分）11．（3分）已知复数z 满足(12)1(i z i -=为虚数单位），则复数z = ，||z = ．12．（3分）函数2sin()2242xy x π=+-的最小正周期是 ，最大值是 ．13．（3分）已知二项式5()(0,0)ba x ab x>>关于x 展开式中，所有项的系数之和为32，设展开式中x 和2x -的系数之和分别为m ，n ，若2m n =，则a = ，b = ． 14．（3分）已知圆C 的圆心在直线0x y +=上，且与直线2y x =相切于点(1,2)P ，则圆C 的圆心坐标为 ，半径为 ．15．（3分）从4个男生和6个女生的10个候选人中，挑选3人分别担任“班长”，“副班长”和“体育委员”，要求3人中至少有2个男生，这样的挑选方法共有 种．16．（3分）已知椭圆C 的两个焦点为1(1,0)F -，2(1,0)F ，过1F 的直线与椭圆C 交于A 、B 两点，若11||3||BF AF =，2AB BF ⊥，则C 的方程为 ．17．（3分）已知函数()(1)x f x x a e b =--+，若存在b R ∈，对于任意[1x ∈，2]，都有|()|2ef x <，则实数a 的取值范围是 ． 三、解答题（共5小题，满分74分）18．（14分）如图，在四边形ABCD 中，45CAB ∠=︒，2AB =，90ACD ∠=︒，3BC =． （Ⅰ）求cos ACB ∠的值；（Ⅱ）若22DC =，求对角线BD 的长度．19．（15分）如图，斜三棱柱111ABC A B C -中，1112A A A B AC ===，33AC BC ==，AC BC ⊥，D 是1AA 的中点．（Ⅰ）证明：平面11ABB A ⊥平面ABC ； （Ⅱ）求直线DB 与平面1A BC 所成角的正弦值．20．（15分）设数列{}n a 的前n 项和为n S ，已知对每一个*n N ∈，n a 是2与n S 的等差中项．（Ⅰ）求数列{}n a 的通项公式； （Ⅱ）设*2,n nn a b n N S =∈，证明：12112n n b b b ++⋯+<-． 21．（15分）已知0m >，抛物线2:2C y mx =的焦点到直线:40l mx y -=的距离为5． （Ⅰ）求m 的值；（Ⅱ）如图，已知抛物线C 的动弦AB 的中点M 在直线l 上，过点M 且平行于x 轴的直线与抛物线C 相交于点N ，求NAB ∆面积的最大值．22．（15分）已知函数1(),()(1)x e f x g x k lnx e x-==+-．（Ⅰ）判断()f x 在(0,)+∞上的单调性；（Ⅱ）若()()f x g x …在(0,)+∞上恒成立，求实数k 的取值范围．。