江苏省淮州中学2020届高三年级第一次调查测试
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江苏徐州、淮安、连云港、宿迁2020届高三第一次调研考试物理试题题号一二三四五总分得分注意事项: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)评卷人得分一、单选题1.我国拥有世界上最大的单口径射电望远镜,被称为“天眼”,如图所示。
“天眼” “眼眶”所围圆面积为S,其所在处地磁场的磁感应强度大小为B,与“眼眶”平面平行、垂直的分量分别为B l、B2,则穿过“眼眶”的磁通量大小为()A.0 B.BSC.B1S D.B2S2.“礼让行人”是城市文明交通的体现。
小王驾驶汽车以36km/h的速度匀速行驶,发现前方的斑马线上有行人通过,立即刹车使车做匀减速直线运动,直至停止,刹车加速度大小为10m/s2。
若小王的反应时间为0.5s,则汽车距斑马线的安全距离至少为()A.5m B.10mC.15m D.36m3.如图甲所示,理想变压器原、副线圈的匝数比为2∶1,电阻55Ω,电流表、电压表均为理想电表。
原线圈A、B端接入如图乙所示的正弦交流电压,下列说法正确的是()A.电流表的示数为4.0AB.电压表的示数为155.6VC.副线圈中交流电的频率为50HzD.穿过原、副线圈磁通量的变化率之比为2∶14.观看科幻电影《流浪地球》后,某同学设想地球仅在木星引力作用下沿椭圆轨道通过木星的情景,如图所示,轨道上P点距木星最近(距木星表面的高度可忽略)。
则A.地球靠近木星的过程中运行速度减小B.地球远离木星的过程中加速度增大C.地球远离木星的过程中角速度增大D.地球在P点的运行速度大于木星第一宇宙速度5.如图所示,AB是斜坡,BC是水平面,从斜坡顶端A以不同初速度v向左水平抛出同一小球,当初速度为v0时,小球恰好落到坡底B。
不计空气阻力,则下列图象能正确表示小球落地(不再弹起)前瞬间重力瞬时功率P随v变化关系的是()A.B.C.D.评卷人得分二、多选题6.智能手机屏幕的光线过强会对眼睛有害,因此手机都有一项可以调节亮度的功能,该功能既可以自动调节,也可以手动调节。
2020年淮安中学高三英语一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ARed Tourism Sites inShanghaiThis year marks the 100th anniversary of the founding of the Communist Party of China (CPC). Many Chinese people are planning to visit red tourism attractions in the coming summer vacation. The following are some red tourism sites inShanghai.Former Site of the Editorial Department ofNew YouthRevolutionary magazineNew Youth,which created the New Culture Movement and spread the influence of the May Fourth Movement, was established by Chen Duxiu inShanghaiin 1915. The editorial office moved toBeijingin 1917 when Chen Duxiu was head of liberal arts atPekingUniversitybut moved back toShanghaithree years later.Address: No. 2,100 Nanchang Road, Huangpu districtFormer Residence of Chen WangdaoThis three-story building was the home of famous scholar and educator Chen Wangdao. In 1920, Chen completed the first Chinese translation ofThe Communist Manifesto(共产党宣言). He also served as President of Fudan University from 1952 to 1977.Address:51 Guofu Road, Yangpu districtHuangpu Wharf (码头)HuangpuWharfin Yangpu district was the place for about 650 Chinese students who headed toFrancefrom March 1919 to December 1920 to further their studies. They included Zhou Enlai, later the first premier of thePeopledRepublicofChina, and Deng Xiaoping, later the leader of the PRC.Address:32 Qinhuangdao Road, Yangpu districtThe Memorial of the Site of the First National Congress of the Communist Party ofChinaThe two-story building was completed in 1920 as the residence of CPC founding member Li Hanjun. On July 23, 1921, thirteen members held their first national congress of the Communist Party of China here, marking the birth of the Party.Address:76 Xingye Road, Huangpu district1. When did the editorial office ofNew Youthreturn toShanghai?A. In 1915.B. In 1919.C. In 1920D. In 1921.2. What do we know about Chen Wangdao according to the text?A. He established theNew Youthmagazine.B. He first translatedThe Communist Manifestointo Chinese.C. He went toFrancefor further study.D. He held the first national congress of the CPC.3. Which site was the birthplace of the Communist Party of China?A. Former Site of the Editorial Department, of New Youth.B. Former Residence of Chen Wangdao.C.HuangpuWharf.D. The Memorial of the Site of the First National Congress of the CPC.BOne-year-old Tallulah turned purple and stopped moving after the sweet became stuck in her throat. Her mum Leigh-Anne said the drama began during a visit to her grandma’s house when her grandparents gave her older kids some sweets.“Then at about 4:45 pm, Tallulah started to choke—we all went into a panic.”“It seemed like it went on for ages. Not one of us knew what to do.”“I rang an ambulance while my grandma and granddad tried to get the sweet to come up.”“Tallulah was panicking at first but then she started to go purple—she almost had no oxygen left in her.”With her daughter limp (无力的) and time running out, Leigh—Anne knew she couldn’t afford to wait for the ambulance to arrive.“The only thing I could think was to go out into the street.” She said.“I rushed out and screamed for someone to help while my grandma rushed out crying with Tallulah.”At exactly the moment, Caitlin, who is studying public services atRedcarCollege, was passing byQueen Street. She said, “I was waiting to go to work when I heard someone screaming for help, so I ran straight over.”The 17-year-old girl added, “Something just clicked and I went into auto mode. The little girl was completelylimp, so I checked her airways and tilted (使倾斜) her over and started hitting her back. I turned her round and tapped on her chest, then after what felt like forever she coughed up the sweet and spat it out.As soon as she started crying I felt a huge relief. I was just so pleased I was able to help.”Caitlin was taught her lifesaving skills when she joined the Army Cadets four years ago.4. When did Tallulah get choked?A. While eating sweets.B. While enjoying a drama.C. While having a meal.D. While taking some medicine.5. Why did the family go out into the street?A. To buy some needed tools.B. To search for timely help.C. To get a breath of fresh air.D. To wait for the ambulance to arrive.6. Which of the following can best describe Caitlin?A. Brave and selfless.B. Kind and energetic.C. Determined and generous.D. Quick-thinking and helpful.7. What may be the best title for the text?A. First aid skill sounds important.B. Screaming for help makes sense.C. Eating sweets endangers baby girl.D. Heroic teenager saves baby girl’s life.CThe World Wildlife Fund (WWF) says more than half of the world’s wildlife population has been lost, whichthe conservation group says has placed the health of the planet at risk.The WWF recently released its 10th Flagship Living Planet Report. The group warns the condition of the world's animals is worse than its earlier reports showed, indicating worldwide action is needed.The WWF is worried about the loss of and damage to Earth’s environment. The report provides information about more than 10,000 animal populations from 1970 to 2010. These populations are called “vertebrate species,” or animals with backbones — like fish, birds, mammals, amphibians and reptiles. The report shows these populations have dropped by 52 percent in just 40 years. It warns freshwater species have fallen by 76 percent, which is almost twice the loss of land and ocean species. Most of these losses are in the tropics, with the biggest drop inLatin America.Marco Lambertini, the WWF’s International Director-General said, “This is about losing natural habitats. This is aboutconvertingforests, grasslands, and wetlands into agriculture mainly, and it is about unsustainable use of wildlife. Illegal hunting has been actually increasing over the last 10 years, which definitely a driving force forextinction, particularly of large species.”The report also notes what it calls the world’s “Ecological Footprint”, that is, the effect of human activities on the planet. Mr. Lambertini says there has been an increase in carbon dioxide gases and the pouring of nitrogen into oceans and rivers from fertilizers used in agriculture, which certainly cannot continue.“We are consuming on average every year about the equivalent of about 1.5, one and a half times the resources available to the planet. That means we are cutting trees more quickly than they can be restored. We are fishing the oceans more quickly than fishing stocks can reproduce, and we are emitting in the atmosphere more CO2than the natural systems can actually absorb, which is clearly not sustainable.”Mr. Lambertini warns climate change affects almost everyone on the planet and that whole species may disappear if the world does not reduce the effects of humans on the climate.8. According to the passage, what kind of species faces the biggest drop in population?A. Land and ocean species.B. Animals with backbones.C. Freshwater species inLatin America.D. Freshwater species in the tropics.9. All the following can contribute to the loss of world’s wildlife population EXCEPT ________.A. turning wildlife habitats into agriculture land.B. making sustainable use of wildlife.C. hunting illegally.D. emitting CO2 gases and pouring nitrogen.10. Which does the underlined word “converting” in paragraph 4 mean?A. Conserving.B. Conveying.C. Exchanging.D. Transforming.11. It can be inferred from the passage that _______.A. Marco is much concerned about human’s current behaviors towards wildlife.B. what the planet provides now can satisfy human’s sustainable development.C. more than half of the world’s wildlife population has been lost.D. if humans reduce the effects on the climate, the whole species will not disappear.DIt is that time of year when people need to lock their cars. It’ s not because there are a lot of criminalsrunning around stealing cars. Rather, it’ s because of the good-hearted neighbors who want to share their harvest. Especially with this year’s large crop, leaving a car unlocked in my neighborhood is an invitation for someone to stuff it full of zucchini(西葫芦).My sister-in-law, Sharon, recently had a good year for tomatoes. She and her family had eaten and canned so many that they began to feel their skin turn slightly red. That ’ s when she decided it was time to share herblessings.She started calling everyone she knew. When that failed, she began to ask everyone in the neighborhood like a politician, eventually finding a neighbor delighted to have the tomatoes. “ Feel free to take whatever you want,”Sharontold her. She felt happy that she could help someone and that the food didn’t go to waste.A few days later,Sharonanswered the door. There was the neighbor, holding some bread. The neighbor smiled pleasantly, “I want to thank you for all of the tomatoes, and I have to admit that I took a few other things and hope you wouldn’t mind.”Sharoncouldn’t think of anything else in her garden that had been worth harvesting and said so. “Oh, but you did,” the neighbor said. “You had some of the prettiest zucchini I’ve ever seen.”Sharonwas confused. Zucchini in her garden? They hadn’ t even planted any zucchini. But her neighbor insisted that there really were bright-green zucchini in her garden. The two of them walked together into the backyard. When the neighbor pointed at the long green vegetables,Sharonsmiled, “ Well, actually, those are cucumbers that we never harvested, because they got too big, soft and bitter for eating or canning.”The neighbor looked atSharon, shock written all over her face. Then she smiled, and held out the bread that she had shared all over the neighborhood, “I brought you a loaf of cucumber bread. I hope you like it.”12. Why does the author suggest that people in the neighborhood should lock their cars?A. They might be stolen by thieves.B. They might be moved away by the police.C. Their neighbors might fill them with their harvest.D. Their neighbors might throw rubbish in them.13. What does the underlined word “blessings” in the second paragraph mean?A. Tomatoes.B. God’s protection.C.Helpful things.D. Best wishes.14. What did the neighbor do inSharon’s garden?A. She harvested tomatoes only.B. She harvested zucchini by accident.C. She took some cucumbers mistakenly.D. She stole something withoutSharon’s permission.15. We can infer from the article that the neighbor’s bread would taste________.A. bitter but tastyB. strange and bitterC. hard and sourD. soft and sweet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。
江苏省淮安市淮海中学2020届高三下学期第一次阶段调研测试物理试题一、单项选择题:本题共6小题,每小题4分,共24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、 “世界上第一个想利用火箭飞行的人”是明朝的士大夫万户。
他把47个自制的火箭绑在椅子上,自己坐在椅子上,双手举着大风筝,设想利用火箭的推力,飞上天空,然后利用风筝平稳着陆。
假设万户及所携设备(火箭(含燃料)、椅子、风筝等)总质量为M ,点燃火箭后在极短的时间内,质量为m 的炽热燃气相对地面以v 0的速度竖直向下喷出。
忽略此过程中空气阻力的影响,重力加速度为g ,下列说法中正确的是A .火箭的推力来源于空气对它的反作用力B .在燃气喷出后的瞬间,火箭的速度大小为m M mv -0C .喷出燃气后万户及所携设备能上升的最大高度为2202()m v g M m - D .在火箭喷气过程中,万户及所携设备机械能守恒2、一束单色光由空气进入水中,则该光在空气和水中传播时A .速度相同,波长相同B .速度不同,波长相同C .速度相同,频率相同D .速度不同,频率相同3、如图所示,为某静电除尘装置的原理图,废气先经过机械过滤装置再进入静电除尘区、图中虚线是某一带负电的尘埃(不计重力)仅在电场力作用下向集尘极迁移并沉积的轨迹,A 、B 两点是轨迹与电场线的交点,不考虑尘埃在迁移过程中的相作用和电荷量变化,则以下说法正确的是A .A 点电势高于B 点电势B .尘埃在A 点的加速度大于在B 点的加速度C.尘埃在迁移过程中做匀变速运动D.尘埃在迁移过程中电势能始终在增大4、如图所示,A、B、C三球的质量分别为m、m、2m,三个小球从同一高度同时出发,其中A球有水平向右的初速度,B、C由静止释放。
三个小球在同一竖直平面内运动,小球与地面之间、小球与小球之间的碰撞均为弹性碰撞,则小球与小球之间最多能够发生碰撞的次数为()A.1次B.2次C.3次D.4次5、如图甲所示,AB两绝缘金属环套在同一铁芯上,A环中电流i A随时间t的变化规律如图乙所示,下列说法中正确的是()A.t1时刻,两环作用力最大B.t2和t3时刻,两环相互吸引C.t2时刻两环相互吸引,t3时刻两环相互排斥D.t3和t4时刻,两环相互吸引6、如图所示,两个完全相同的小球A、B,在同一高度处以相同大小的初速度v0分别水平抛出和竖直向上抛出,下列说法正确的是()A.两小球落地时的速度相同B.两小球落地时,重力的瞬时功率相同C.从开始运动至落地,重力对两小球做功相同D.从开始运动至落地,重力对两小球做功的平均功率相同二、多项选择题:本题共4小题,每小题5分,共20分。
淮安市2020-2020学年度高三年级第一学期调查测试英语试题2020.11第I卷(选择题共115分)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. What does the woman mean?A. She praises the boy.B. She likes more cakeC. She will give another cake to the boy.2. How does the man find the woman?A. She is neither pretty nor ugly.B. She is very pretty.C. She is very ugly.3. What do you know from the dialogue?A. God always stays at their home when the father gets home.B. God is in the bathroom when the father knocks at the door.C. Bathroom is always used when the father wants to use it.4. What does the woman mean?A. She'd like a sandwich.B. She has already eaten.C. She doesn't want anything to eat now.5. What is the probable relationship between the two speakers?A. Teacher and student.B. Patient and the doctor.C. Customer and the salesgirl.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。
江苏省淮安市高三上学期语文第一次调研试卷姓名:________ 班级:________ 成绩:________一、现代文阅读 (共2题;共30分)1. (16分)(2020·赣县模拟) 阅读下面的文字,完成下列小题。
材料一:我国保障了人们的饭碗安全,对维护国内稳定、全面建成小康社会打下了坚实的物质基础;同时中国用占世界9%左右的耕地解决了世界近20%人的吃饭问题,为世界粮食安全作出了重大贡献。
目前,全国75%以上的粮食产量、90%左右的调出量来自13个主产省份,并持续北移。
面对粮食生产格局变化,国家积极推进北粮南运,维护区域粮食安全。
我国粮食储备率远远高于国际公认的17%至18%安全线。
近年来一些国家发生的粮食危机警示我们,粮食依然是弱势产业。
粮食安全,根本在耕地,出路在科技。
由此。
我国实施藏粮于地、藏粮于技战略。
藏粮于地,就是要坚守耕地红线,确保耕地数量不减少,开展高标准农田建设。
习主席对新时期农业生产提出了更高要求,提出给农业插上科技的翅膀。
藏粮于技,就是走依靠科技提高单产的内涵式发展道路。
(摘编自张帆《全力以赴保障我国粮食安全》材料二:中国人口占世界的近1/5,粮食产量约占世界的1/4,中国依靠自身力量端牢自己的饭碗,实现了由“吃不饱”到“吃得饱”,并且“吃得好”的历史性转变。
在国家政策的强力支持下,粮食安全形势迎来历史最好水平。
如图示:材料三:进入新世纪,我国粮食安全的环境发生了很大变化,在粮食安全问题上,必须居安思危。
我国改革任务繁重,工业化、城镇化快速推进,粮食安全面临诸多挑战。
随着农村劳动力向非农产业和城镇转移,农业兼业化、农民老龄化、农村空心化日益严重,外出农民工特别是新生代农民工不愿回乡务农,农业生产面临后继乏人的现状。
我国人均资源较短缺,人均耕地面积仅为世界平均水平的40%,人均水资源拥有量不到世界平均水平的25%。
资源破坏、环境污染、水土流失等一系列生态问题,导致粮食生产的资源环境约束日益显现。
江苏省淮安市2020学年度高三数学第一次调研测试卷2020.11(满分 150分,考试时间120分钟)第I 卷(选择题 共50分)一、选择题:本大题共10小题,每小题5分,满分50分。
在每小题给出的四个选项中, 有且只有一项是符合题目要求的,请把正确答案涂填在答卷纸指定方格内.1.设全集{1,2,3,4,5}U =,{1,3,4},{2,4,5},M N ==则()()U U M N I 痧= ( ) A . ∅ B .{4} C .{1,3} D . {2,5}2.函数y = ( )A .(,10]-∞B . (0,10]C . (0,1]D .[10,)+∞3.已知向量(3,4),(sin α,cos α)a b ==r r 且a b r rP ,则tan α= ( )A .34 B .34- C .43D .43-4.已知函数()35xf x -=+的定义域为(0,)+∞,则其值域是 ( )A .(0,)+∞B .(5,)+∞C .(0,6)D . (5,6)5.已知向量,a b r r 满足||2||0a b =≠r r ,且关于x 的方程2||0x a x a b ++⋅=r r r 有实根,则a r 与b r的夹角取值范围是 ( )A .π[0,]3 B .π[,π]3 C .π2π[,]33D .ππ[,]326.在△ABC 中,已知4,3,30AB AC ABC ==∠=o,则满足条件的三角形个数为 ( )A .0个B .1个C .2个D .无数个7.已知等差数列{}n a 的前n 项和为n S ,且4813S S =,则816S S = ( ) A .18B .13C .19D .3108.已知向量,a b r r 夹角为60o,且||1,||a a b =-=r r r 则||b =r ( ) A .1BC .12D .129. 已知函数2()(0)f x x px q p =++>,当120,0x x >>时, a f =,12()2x x b f +=,121[()()]2c f x f x =+,则,,a b c 之间的大小关系为 ( ) A .a b c ≤≤ B .a c b ≤≤ C .c a b ≤≤ D . b a c ≤≤10.将ππ2sin()cos()44y x x =+-的图象和直线12y =在y 轴右侧的交点按横坐标从小到大依次记为:123,,,,P P P L 则24||P P = ( )A .πB .2πC .3πD .4π第Ⅱ卷(非选择题 ,满分100分)二、填空题:本大题共6小题,每小题5分,共30分,把答案填在答题卡相应位置. 11.已知π3sin()45α-=,则sin 2α= . 12.不等式10x x-<的解集为 . 13.若函数2()lg 21f x x a x =-+的图象与x 轴有两个不同的交点,则实数a 的取值范围是 .14.已知向量(,),(cos α,sin α)a x y b ==r r 其中,,x y R α∈,若||4||a b =r r ,则使2λa b ⋅<r r 恒成立的实数λ的取值范围是 . 15.已知123n S n =++++L ,*1()()(32)nn S f n n N n S +=∈+,则()f n 的最大值是 .16.已知函数()sin(ω+)f x x =ϕ(πω0,||2>ϕ<),给出下列四个论断: ①()f x 的图象关于直线π12x =对称;②()f x 的图象关于点π(,0)3对称;③()f x 的周期为π; ④()f x 在π[,0]6-上是增函数,试以其中两个为条件,另两个为结论,写出一个你认为正确的命题 (填序号即可).11.72512.(,1)(0,1)-∞-U 13.(0,1)(1,10)U 14.(,2)(2,)-∞-+∞U 15.15016.①③⇒②④或②③⇒①④三.解答题:本大题共5小题,满分70分,解答应写出文字说明,证明过程或演算步骤.请将解题过程写在答卷纸指定的方框内.17.(本题满分12分)已知函数()sin(θ)cos(θ)f x x x =++-的定义域为R.(1)当πθ=2时,求()f x 的单调增区间; (2)当θ[0,2]π∈,且()f x 为偶函数时,求θ的值.解:(1) 当πθ=2时, ππ()sin()cos()cos sin 22f x x x x x =++-=+)4x π=+,由πππ2k πx+2k π+242-≤≤,解得3ππ2k πx 2k π+()44k Z -≤≤∈,∴此时()f x 的单调递增区间是3ππ[2k π,2k π+]()44k Z -∈.(2)∵()f x 为偶函数,∴()()f x f x -=对x R ∈恒成立,∴sin(θ)cos(θ)sin(θ)cos(θ)x x x x -++--=++-对x R ∈恒成立, ∴sin(θ)cos(θ)sin(θ)cos(θ)x x x x --++=++-对x R ∈恒成立, ∴cos(θ)cos(θ)sin(θ)sin(θ)x x x x +--=++-对x R ∈恒成立, 即2sin sin θ=2sin cos θx x -对x R ∈恒成立,又sin x 不恒为0,∴sin θcos θ=-,tan 1θ=-,又θ[0,2]π∈,故37,44ππθ=. 18.(本题满分14分)已知向量(λcos α,λsin α)OA =u u u r λ0≠,(sin β,cos β)OB =-u u u r,其中O为坐标原点.(1)若πβ=α6-,求向量OA u u u r 与OB uuu r 的夹角的大小;(2)若||||AB OB ≥u u u r u u u r对任意实数α,β都成立,求实数λ的取值范围.解:设向量OA u u u r 与OB uuu r 的夹角为θ,则OA cos θ=|OA |||OBOB ⋅u u u r u u u ru u ur u u u r , 即OA cos θ=sin()||2|||OA |||OB OB λλαβλλ⋅==-=u u u r u u u r u u u r u u u r∴当0λ>时,1πcos θ=,θ=23, 当0λ<时,12πcos θ=,θ=23-. (2)∵(sin βcos α,cos βsin α)AB λλ=---u u u r,∴||AB ==u u u r又||1OB =u u u r ,且||||AB OB ≥u u u r u u u r对任意实数α,β都成立,1≥对任意实数α,β都成立,即22sin(βα)0λλ+-≥对任意实数α,β都成立, ∴λ[λ2sin(βα)]0+-≥对任意实数α,β都成立, 当λ0>时, λ2sin(βα)0+-≥对任意实数α,β都成立,λ2sin(βα)≥--对任意实数α,β都成立,∴λ2sin(βα)≥--的最大值2,即2λ≥;当λ0<时, λ2sin(βα)0+-≤对任意实数α,β都成立,λ2sin(βα)≤--对任意实数α,β都成立,∴λ2sin(βα)≤--的最小值-2,即2λ≤-;19.(本题满分14分)已知数列{}n a 满足1331(2)nn n a a n -=+-≥,其中4365a =.(1)求123,,a a a 的值(2)若存在一个实数λ使数列λ{}3n n a +为等差数列,求λ的值以及数列{}n a 的通项公式. 解:(1)∵1331(2)n n n a a n -=+-≥∴443331a a =+-,又4365a =,∴395a =, ∴33233195a a =+-=,223a =,∴22133123a a =+-=,15a =.(2)若存在一个实数λ使数列λ{}3n na +为等差数列, 则当n ≥2时,11λλ33n n n n a a --++-=常数(n 与无关) 而11111λλ33331333333n n n n n n n n n n na a a a a a λλλλ-----+++--+-+---==31212133n n nλλ--+==-, ∴当12λ=-时,数列12{}3n n a -为首项为153232-=,公差为1等差数列. ∴132(1)132n n a n -=+-⨯,∴11()322n na n =++. 20.(本题满分14分)已知两个二次函数2()1f x ax bx =++与22()1g x a x bx =++,其中函数()y g x =图象经过点12(,0)(,0)x x 与,(12x x <).(1)判断函数()y f x =在(1,1)-上是否是单调函数,并说明理由; (2)当1a >时,试判断12()()f x f x 与值的正负,并证明你的判断正确;(3)设34,x x 是关于x 的方程210ax bx ++=的两实根,且34x x <,试确定当1a >时1234,,,x x x x 之间的大小关系, 并说明理由.解:(1)函数()y f x =在(1,1)-上是单调函数,理由如下: ∵()y g x =图象经过点12(,0)(,0)x x 与,(12x x <).∴2240b a ->,即||2||b a >,||2b a >,∴22b ba a><-或, 又2()1f x ax bx =++的图象对称轴方程为2b x a=-,∵22b b a a ><-或∴1122b b a a-<-->或∴函数()y f x =在(1,1)-上是单调函数. (2)12()0,()0f x f x <<,证明如下:∵函数()y g x =图象经过点1212(,0),(,0)()x x x x <. ∴12,x x 是2210a x bx ++=的两实根,∴221110a x bx ++=,222210a x bx ++=,且12210x x a=≠,又1a >,∴22222111111()1(1)0f x ax bx ax a x ax a =++=-=-<, 22222222212()1(1)0f x ax bx ax a x ax a =++=-=-<,(3)3124x x x x <<<,理由如下:∵34,x x 是关于x 的方程210ax bx ++=的两实根(34x x <)∴当1a >时, 函数()y f x =图象开口向上,经过点34(,0)(,0)x x 与, 又12()0,()0f x f x <<12()x x <,∴12,x x 必分布在3x 与4x 之间.∴3124x x x x <<<. 21.(本题满分16分)已知函数1()()42x f x x R =∈+. (1) 试证:001()(1)2f x f x +-=; (2) 若数列{}n a 的通项公式是*()(,1,2,3,,)n na f n N n m m=∈=L , 求数列{}n a 的前m 项和m S . (3) 设数列{}n b 满足113b =,21n n n b b b +=+,12111111n nT b b b =++++++L , 若(2)中的m S 对任意不小于2的正整数n 都有m n S T <成立,试求m 的最大值.解:(1)0000000111141()(1)4242424242x x x x x f x f x -+-=+=+=++++⨯ (2)∵123m m S a a a a =++++L ∴121()()()()m m mS f f f f m m m m -=++++L , 121()()()()m m m S f f f f m m m m-=++++L ,∴1122112()[()()][()()][()()]()m m m m m mS f f f f f f f f m m m m m m m m---=+++++++L∴122(1)(1)2m S f m =+-⨯,又1(1)6f =, ∴3112m m S -=. (3)21(1)n n n n n b b b b b +=+=+,又1103b =≠, ∴*n N ∈时, 0n b ≠,∴11111(1)1n n n n n b b b b b +==-++,11111n n n b b b +=-+∴12122311111111111()()()1111n n n n n T b b b b b b b b b b +=+++==-+-++-++++L L 1111113n n b b b ++=-=-. ∵210n n n b b b +-=>∴1n n b b +>,∴2n ≥时,2n T T ≥,即23175352n T T b ≥=-=, ∵m n S T <对任意2n ≥都成立,∴min 75()52m n S T <=, ∴31751252m -<,∴23839m <又*m N ∈,故m 的最大值为6.。
淮安市--度高三年级第一次调研测试语文试题2012.11.15注意事项⒈本试卷满分为160分,考试时间为150分钟。
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一、语言文字运用(15分)⒈下列词语中加点的字,每对读音都相同的一组是(3分)A.珍馐/羞愧毒蛇/委蛇箴言/百福并臻B.募集/蓦然粘贴/粘连诗赋/物阜民丰c.绛紫/降落累及/累次鸿鹄/囫囵吞枣D.颈联/自刭颤抖/颤悠唬人/瓦釜雷鸣⒉在下面一段话空缺处依次填入成语,最恰当的一组是(3分)日本政府近日的“购岛”闹剧,表现出日本军国主义大有之势,这极大地伤害了中国人民的感情,全世界炎黄子孙对日本政府错误行径的批判是的,我们希望日本政府能正视中国人民的正义呼声,如果对此,由此产生的一切后果只能由日本政府负责。
A.死灰复燃无可非议置若罔闻B.东山再起无可非议束之高阁C.死灰复燃无可厚非束之高阁D.东山再起无可厚非置若罔闻⒊提取下面新闻的主要信息,在横线上写出四个关键词。
(4分)据悉,2012年国家科技奖将严格控制自然科学奖、技术发明奖和科技进步奖推荐指标数和评审指标数,适当调整奖励结构。
受理项目总数较往年减幅约为l2%,其中科技进步奖减幅达25.1%,自然科学奖和技术发明奖受理项目数较往年有所增加,三大奖奖励结构进一步优化。
据了解,为提高奖励质量,今年的评审更注重科研成果的首创性、独创性,代表性论文论著和自主知识产权的质量,技术指标的先进性以及学术界认可度和行业影响力。
答:▲▲▲▲⒋阅读漫画,在横线上写出合适的句子。
(5分)这幅漫画形象地启示人们:▲▲二、文言文阅读(19分)阅读下面的文言文,完成5~8题。
陆周明墓志铭黄宗羲周明姓陆氏,鄞县人也。
少与钱司马读书,慷慨有大志。
癸卯岁,周明为降卒所诬,捕入省狱。
江苏省淮安市等四市2020届高三上学期第一次模拟语文试卷一、语言文字运用(15分)1.在下面一段话的空缺处依次填入词语,最恰当的一组是(3分)闲适和散漫都是从俗务中抽身出来的状态,心境却迥异。
闲适者回到了自我,在自己的天地里▲,悠然自得,内心是▲而澄澈的。
散漫者找不到自我,只好依然在外物的世界里东抓西摸,▲,内心是烦乱而浑浊的。
A.踯躅静谧无所适从B.徜徉静谧不知所措C.踯躅宁静不知所措D.徜徉宁静无所适从2.下列歌词中,没有..使用比喻手法的一项是(3分)A.山是山,水是水,往事恍然如云烟,流浪心已憔悴,谁在乎?英雄泪。
(《英雄泪》)B.过去的誓言,就像那课本里缤纷的书签,刻划着多少美丽的诗,可是终究是一阵烟。
(《光阴的故事》)C.冷冷的冰雨在脸上胡乱地拍,暖暖的眼泪跟寒雨混成一块,眼前的色彩忽然被掩盖,你的影子无情在身边徘徊。
(《冰雨》)D.爱是漫长的旅途,梦有快乐梦有痛苦,悲欢离合人间路,我可以缝缝补补。
(《风雨无阻》)3.下列交际用语使用不得体...的一项是(3分)A.今日家母古稀之庆,承蒙光临,蓬荜生辉,请开怀畅饮!B.拙著新近出版,敬赠阁下拜读,如获赐正,荣幸之至。
C.因身体抱恙,不能到会,坐失学习良机,深表遗憾。
D.令郎不愧是丹青世家子弟,他画的小狗呆萌可爱,惟妙惟肖。
4.在下面一段文字横线处填入语句,衔接最恰当的一项是(3分)博览群书的文坛名宿冯亦代赞美说:“宗璞有丰厚的古典文学修养,自己又是个小说家、诗人,▲,▲;▲,这是我辈凡人所不能企及的。
她的文章看来平平淡淡,▲,▲,▲。
”①因此她能把中西古典文学的含义尽化为诗②但其中跌宕迂回又不是粗心之人所能把握的③从而以之入文④只有在读者的细心体会中豁然开朗⑤加之她的敏慧⑥而捕捉到她命意之所在A.③⑥①④②⑤B.③⑤②⑥①④C.①②⑥③⑤④D.①③⑤②④⑥5.下列诗句所描写的景色依时序排列,恰当的一项是(3分)①迟日未能销野雪,晴花偏自犯江寒。
2020届江苏淮阴中学高三语文一模试卷及答案解析一、现代文阅读(36分)(一)现代文阅读I(9分)阅读下面的文字,完成各题。
材料一:什么是大数据,迄今并没有公认的定义。
从宏观世界角度来讲,大数据是融合物理世界、信息空间和人类社会三元世界的纽带,因为物理世界通过互联网、物联网等技术有了在信息空间中的大数据反映,而人类社会则借助人机界面、脑机界面、移动互联等手段在信息空间中产生自己的大数据映像。
从信息产业角度来讲,大数据还是新一代信息技术产业的强劲推动力。
相较于传统的数据,大数据具有体量大、速度快、模态多、难辨识和价值大密度低的特征。
但大数据的主要难点并不在于数据量大,因为通过对计算机系统的扩展可以在一定程度上缓解数据量大带来的挑战。
其实,大数据真正的挑战来自于数据类型多样、要求及时响应和数据的不确定性。
(摘编自程学旗等《大数据系统和分析技术综述》)材料二:“神威·太湖之光”,系统采用全国产处理器构建,峰值性能每秒超过12.5亿亿次,是世界第一的超级计算机。
2017年,共有五项基于“神威·太湖之光”的应用入围国际高性能计算应用领域最高奖“戈登·贝尔奖”的提名,其中两项获奖,这是中国高性能计算应用领域近年来最重大的突破。
“神威·太湖之光”将如何改变我们的生活?“‘神威·太湖之光’有着大数据应用的天然优势。
”中国工程院院士陈左宁说。
超算具有强大的数据存储、检索、计算、分析能力,而现在的大数据应用与新一代人工智能密切结合,“神威·太湖之光”将为二者深度融合应用提供技术支撑。
“未来,国家超算无锡中心将是一所‘人工智能’大学。
”科学家张晖这样描绘未来。
他说,这所大学的学生并不是人类,而是人工智能机器人。
在超算的“培训”下,智能机器人将拥有独立思考的“头脑”。
比如医院的CT机可以代替医生去诊断分析病情,通过大量数据的计算,选择最优解决方案,甚至比人做得更好。
2020届高三第一次调研测试英语试题参考答案第一部分听力(共两节,满分 20分)1-5 AABBA 6-10 CBACA 11-15 ACCBB 16-20 ACCBA第二部分英语知识运用(共两节,满分35分)第一节单项填空(共15小题;每小题1分,满分15分)21-25 CDBCD 26-30 ACDCB 31-35 ABCCA第二节完形填空(共20小题;每小题1分,满分20分)36-40 BDACD 41-45 ACDDB 46-50 ACCDB 51-55 ABCAB第三部分阅读理解(共15小题;每小题2分,满分30分)56-57 AB 58-60 CCB 61-64 ABAA 65-70 DACBBA第四部分任务型阅读(共10小题;每小题1分,满分10分)71.follows 72. Recommendations/ Suggestions/ Tips/ Advice 73. involved/engaged74. account 75. reduce/release/relieve 76. needed/necessary 77. reflect78. consult 79. respect 80. development第五部分书面表达(满分25分)One possible version:Three greatest heroes, just as listed above, have made considerable achievements in their life, and they always care about the prosperity of China and the well-being of the Chinese people.Many good qualities are embodied in these heroes and they do deserve respect from all of us. One common quality is that they are diligent and down to earth, which best demonstrates that Chinese people are a hardworking people. Of course, there are many other qualities we can learn from them. For example, happiness of the people always tops the list in their dictionary, and the interests of our country outweigh their own personal ones.What impresses me most is that Yuan Longping lives a simple but meaningful life. More often than not he wears a cheap shirt when going to work in the fields. By contrast, too many teenagers nowadays take it for granted to ask their parents to buy them famous brands without hesitation. Personally, we should follow heroes in their footsteps, applying ourselves to study, helping others selflessly. Only by setting noble ambitions can we become promising and make contributions to our country.录音原文:Text 1M: I never listen to the radio anyway. I can just check the weather on my phone.W: I do the same thing. I’m never home to watch the weather forecast on television, either.Text 2W: Are you going to make it to the basketball game tonight? I will be there right after debate team practice.M: I can’t. I have a big math test tomorrow. I have to prepare for it.Text 3W: It looks like you’re having a hard time with that program, Larry. Why don’t you use the method that I gave in the class yesterday?M: I was absent. I’ll ask one of my classmates to send it to me.Text 4W: If we want to win the game this Friday, we need to come up with a plan now. They beat us every year.M: We need to use teamwork more. John is our best player, but we can’t give him the ball every time.Text 5W: Excuse me? I’m trying to pay the parking, but all I have is dollar bills. Could you spare any change?M: I’m sorry, madam. But our store policy is not to give out change unless you buy something.W: OK.Text 6W: Tim, I saw you running from the bus stop this morning. You r mother and father wouldn’t be happy seeing you do that.M: I was late for school though.W: You need to be more careful when you cross the street. You need to walk during the right time and in the right places.M: But I’m very fast.W: Are you even listening to me? It is dangerous. It is also against the law.M: But I hate waiting for the lights to change and the cars to pass by. I don’t want to be late.W: It is important to obey the rules, but your safety is more important. I don’t want to see anyone o f my students get hurt.Text 7W: Sorry, Jim. I won’t be able to make it to the dinner tomorrow night. I’ll be busy volunteering at the library during that time.M: That’s interesting, Carol. Most people I know volunteer by collecting garbage or something. What do you do at the library when you volunteer? Are they short on employees who put away books?W: Nothing like that. I just read the children’s books and act out some of the stories for them. It’s very fun and it doesn’t take long, maybe one or two hou rs.M: How often do you do that?W: I do it on Monday, Wednesday and Friday every week. You should come help me with it one time.M: That sounds like fun. Can I pick the stories I want to read? I hate to try and act out a story I never read.W: You can re ad any book as long as it’s on the library’s list.Text 8M: I was reading about superfoods today. They are fruits, vegetables and other foods that are supposed to be extra healthy.W: That’s interesting. Which foods are they? I suppose rice is high on the list. We certainly eat a lot of that here in China.M: No, it isn’t. Nor are noodles. But yogurt, fish and tomatoes are there.W: Oh well, I suppose we eat plenty of them. Why are these foods so healthy?M: It’s said they can reduce the risk of high blood pressure, heart disease and certain cancers.W: Maybe I will start including them in our meals. Are there any foods on the list that we don’t have yet?M: Nuts and greens are something we already eat plenty of. And although our type of rice — the white kind —isn’t on the list, brown rice is.W: Then I think we will switch to that to keep the family healthy. Superfoods sound like a very tasty way to keep fit.Text 9M: I can’t believe this. I have been on the phone with my bank all day and they still haven’t fixed my problem. W: Is it a credit card problem?M: Yes. My credit card information was stolen. When I got my bill in the mail, I saw there were many unfamiliar purchases on it.W: That’s terrible. Did they take a lot of money?M: Yes, and I am very upset because the bank is not helping me quickly. I have talked to many different managers already.W: Doesn’t the bank’s owner need to make the decision to give you your money back?M: No. I just have to prove that these purchases were not made by me.W: I hope you can fix this problem soon. Something similar happened to my husband’s mother recently. She was tricked into giving away some important information over the phone.M: I think the person who stole my information got it from the Internet. I bought a collection of movies recently. I won’t be doing that again unless the website is sure to be safe. It’s honestly my fault for being careless.W: You can never be too careful. Well, your problem is inspiring me to look into protecting my account better. I think I can pay my bank more to help me.Text 10W: Listen up you two. We need to leave this house before the sun rises tomorrow. Your father will be home soon from work and once he gets home, we will be packing our bags. We need you guys to do the same thing tonight. I want everything you’re going to bring put out in the living room before you go to bed. Before you pack everything though, you need to put aside the clothes for tomorrow. I don’t want to wait for you to search for other clothes or to unpack your bag to get something. Our flight is at 7:00 a.m., and it will take about a half hour to get to the airport from here. We’ll probably need another hour to get through security. Also, I know I said that we would go out for our meal tonight, but there is just too much to do. I asked your father to pick up some Chinese food for dinner instead. I can’t be bothered to cook something since I just cleaned everything. If you want a specific dish at the restaurant, you will need to call your father. Otherwise, he will just pick up something that we can all share. Are you clear on everything I said?。
常州市第一中学2020学年度高三年级第一次月考数 学 试 卷一、选择题:1、已知22{|1},{|1}M x y x N y y x ==-==-,那么M N I = ( ) A 、∅ B 、M C 、N D 、R2、已知::|23|1,:(3)0p x q x x -< -<,则p 是q 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、关于直线m 、n 与平面α、β,有下列四个命题:①//,//m n αβ且//αβ,则//m n ; ②,m n αβ⊥⊥且αβ⊥,则m n ⊥; ③,//m n αβ⊥且//αβ,则m n ⊥; ④//,m n αβ⊥且αβ⊥,则//m n .其中真命题的序号是: ( ) A 、①② B 、③④ C 、①④ D 、②③ 4、设θ是第二象限角,且cos ,sin cos22t θθθ=<,则sin2θ的值是 ( )A B C 、 D 、 5、若222sin sin 2sin 0αβα+-=,则22cos cos αβ+的取值范围是 ( )A 、[1,5]B 、[1,2]C 、9[1,]4D 、[1,2]-6、若函数f (x)满足1(1)()f x f x +=,且(1,1]时,(),x f x x ∈-=则函数y=f(x)的图象与函数3log y x =的图象的交点的个数为 ( ) A 、 3 B 、 4 C 、 6 D 、 87、若四面体的六条棱中有五条长为a ,则该四面体体积的最大值为 ( )A 、318aB 3C 、3112a D 3 8、已知偶函数y =f (x )在[-1,0]上为单调递减函数,又α、β为锐角三角形的两内角,则 ( ) A.(sin )(cos )f f αβ> B.(sin )(cos )f f αβ< C.(sin )(sin )f f αβ> D.(cos )(cos )f f αβ> 9、菱形ABCD 的边长为0,60,,,a A E F G ∠=,H 分别在AB 、BC 、CD 、DA 上,且3aBE BF DG DH ====,沿EH 与FG 把菱形的两个锐角对折起来,使A 、C 两点重合,这时A 点到平面EFGH 的距离为A 、2a B C D 、)1a ( )10、已知定义在R 上的奇函数()满足()2y f x y f x π==+为偶函数,对于函数()y f x =有下列几种描述,(1)()y f x =是周期函数 (2)x π=是它的一条对称轴 (3)(,0)π-是它图象的一个对称中心 (4)当2x π=时,它一定取最大值其中描述正确的是( )A 、(1)(2)B 、(1)(3)C 、(2)(4)D 、(2)(3)二、填空题:11、若函数2(1)f x +的定义域为[2,1)-,则函数()f x 的定义域为 ] ;12、249y x x =+-的值域为 ;13、y =f(x)是关于x=3对称的奇函数,f (1)=1,32cos sin x x -,则15sin 2[]cos()4xf x π+= ;14、已知方程2(1)40x a x a ++++=的两根为12,x x ,且1201x x <<<,则a 的取值范围是 ; 15、在△ABC 中,a 、b 、c 分别为∠A 、∠B 、∠C 的对边,若a 、b 、c 成等差数列,sin B =45且△ABC 的面积为32,则b = .16、若对终边不在坐标轴上的任意角x ,不等式sin cos x x +22tan cot m x x ≤≤+恒成立,则实数m 的取值范围是 ; 三、解答题:17、已知函数2π()2sin 324f x x x ⎛⎫=+⎪⎝⎭,ππ,42x ⎡⎤∈⎢⎥⎣⎦. (1)求()f x 的最大值和最小值;(2)若不等式()2f x m -<在ππ,42x ⎡⎤∈⎢⎥⎣⎦上恒成立,求实数m 的取值范围.18、已知函数231()2sin 1[,]2f x x x x θ=+- ∈。
(1)当6πθ=时,求()f x 的最大值和最小值。
(2)若()f x 在31[]2x ∈上是单调函数,且[0,2)θπ∈,求θ的取值范围。
19、已知命题:p 1x 和2x 是方程220x mx --=的两个实根,不等式21253||a a x x --≥-对任意实数[1,1]m ∈-恒成立;命题:q 只有一个实数x 满足不等式222110x ax a ++≤,若命题p 是假命题,命题q是真命题,求a 的取值范围。
20、设()f x 的定义域为(0,)+∞,且满足(4)1f =,12,(0,)x x ∀∈+∞,有1212()()()f x x f x f x ⋅=+,当(0,1)x ∈时,()0f x <。
(1)求(1)f 的值;(2)证明()f x 在(0,)+∞上是增函数; (3)解不等式(31)(26)3f x f x ++-≤。
21、在五棱锥P-ABCDE 中,P A=AB=AE=2a ,PB=PE=2,BC=DE=a ,∠EAB=∠ABC=∠DEA=90°. (1)求证:P A ⊥平面ABCDE ;(2)若G 为PE 中点,求证:AG ⊥平面PDE(3)求二面角A-PD-E 的正弦值;(4)求点C 到平面PDE 的距离22、设函数()log (3)(0且1)a f x x a a a =->≠,当点(,)P x y 是函数()y f x =的图象上的点时,点(2,)Q x a y --是函数()y g x =的图象上的点。
(1)求出函数()y g x =的解析式;(2)若当[2,3]x a a ∈++时,恒有|()()|1f x g x -≤,试确定a 的取值范围。
理科学生做(选择填空题每题4分)1.矩阵0110-⎡⎤⎢⎥⎣⎦的逆矩阵是 ( ) A .0110⎡⎤ ⎢⎥-⎣⎦ B . 1001-⎡⎤ ⎢⎥⎣⎦ C .1001⎡⎤ ⎢⎥-⎣⎦ D . 0110-⎡⎤ ⎢⎥⎣⎦2. 表示x 轴的反射变换的矩阵是( )A. 1001⎡⎤ ⎢⎥⎣⎦B. 1001-⎡⎤⎢⎥⎣⎦C. 0110⎡⎤⎢⎥-⎣⎦D. 1001⎡⎤ ⎢⎥-⎣⎦ 3. 极坐标方程cos 2sin2ρθθ=表示的曲线为( )A .一条射线和一个圆B .两条直线C .一条直线和一个圆D .一个圆 4. 若曲线22421x xy y ++= 在矩阵11a b ⎡⎤⎢⎥⎣⎦的作用下变换成曲线2221x y -= ,则a b + 的值为______。
5. 点(),P x y 是椭圆222312x y +=上的一个动点,则2x y +的最大值为___________。
6.已知圆C 的参数方程为12cos 2sin x y θθ=+⎧ ⎨=⎩(θ 为参数),P 是圆C 与y 轴的交点,若以圆心C 为极点,x轴的正半轴为极轴建立极坐标系,则过点P 圆C 的切线的极坐标方程是 .7. (本题6分)过点P 作倾斜角为α的直线与曲线2221x y +=交于点,M N ,求PM PN ⋅的最小值及相应的α的值。
8.(本题10分)当兔子和狐狸处于同一栖息地时,忽略其他因素,只考虑兔子数量和狐狸数量的相互影响,为了简便起见,不妨做如下假设:(1)由于自然繁殖,兔子数每年增长10%,狐狸数每年减少15%;(2)由于狐狸吃兔子,兔子数每年减少狐狸数的0.15倍,狐狸数每年增加兔子数的0.1倍;(3)第n 年时,兔子数量n R 用表示,狐狸数量用n F 表示;(4)初始时刻(即第0年),兔子数量有0100R = 只,狐狸数量有030F = 只。
请用所学知识解决如下问题:(1)列出兔子与狐狸的生态模型(n R 、n F 的关系式); (2)求出n R 、n F 关于n 的关系式; (3)讨论当n 越来越大时,兔子与狐狸的数量是否能达到一个稳定的平衡状态,说明你的理由。
常州市第一中学2020学年度高三年级第一次月考数学试卷一、选择题:1、已知22{|1},{|1}M x y x N y y x ==-==-,那么M N I = ( C ) A 、∅ B 、M C 、N D 、R2、已知::|23|1,:(3)0p x q x x -< -<,则p 是q 的 ( A ) 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、关于直线m 、n 与平面α、β,有下列四个命题:①//,//m n αβ且//αβ,则//m n ; ②,m n αβ⊥⊥且αβ⊥,则m n ⊥; ③,//m n αβ⊥且//αβ,则m n ⊥; ④//,m n αβ⊥且αβ⊥,则//m n .其中真命题的序号是: ( D ) A 、①② B 、③④ C 、①④ D 、②③ 4、设θ是第二象限角,且cos ,sin cos22t θθθ=<,则sin2θ的值是 ( C )A B C 、 D 、 5、若222sin sin 2sin 0αβα+-=,则22cos cos αβ+的取值范围是 ( B )A 、[1,5]B 、[1,2]C 、9[1,]4D 、[1,2]-6、若函数f (x)满足1(1)()f x f x +=,且(1,1]时,(),x f x x ∈-=则函数y=f(x)的图象与函数3log y x =的图象的交点的个数为 ( B ) A 、 3 B 、 4 C 、 6 D 、 87、若四面体的六条棱中有五条长为a ,则该四面体体积的最大值为 ( A )A 、318aB 3C 、3112a D 3 8、已知偶函数y =f (x )在[-1,0]上为单调递减函数,又α、β为锐角三角形的两内角,则 ( A ) A.(sin )(cos )f f αβ> B.(sin )(cos )f f αβ< C.(sin )(sin )f f αβ> D.(cos )(cos )f f αβ> 9、菱形ABCD 的边长为0,60,,,a A E F G ∠=,H 分别在AB 、BC 、CD 、DA 上,且3aBE BF DG DH ====,沿EH 与FG 把菱形的两个锐角对折起来,使A 、C 两点重合,这时A 点到平面EFGH 的距离为A 、2a B C D 、)1a ( A )10、已知定义在R 上的奇函数()满足()2y f x y f x π==+为偶函数,对于函数()y f x =有下列几种描述,(1)()y f x =是周期函数 (2)x π=是它的一条对称轴 (3)(,0)π-是它图象的一个对称中心 (4)当2x π=时,它一定取最大值其中描述正确的是( B )A 、(1)(2)B 、(1)(3)C 、(2)(4)D 、(2)(3)二、填空题:11、若函数2(1)f x +的定义域为[2,1)-,则函数()f x 的定义域为 [1,5] ;12、4y x =+的值域为4] ;13、y =f(x)是关于x =3对称的奇函数,f (1)=1,cos sin x x -15sin 2[]cos()4xf x π+= -1 ;14、已知方程2(1)40x a x a ++++=的两根为12,x x ,且1201x x <<<,则a 的取值范围是 (4,3)-- ; 15、在△ABC 中,a 、b 、c 分别为∠A 、∠B 、∠C 的对边,若a 、b 、c 成等差数列,sin B =45且△ABC 的面积为32,则b = 2 .16、若对终边不在坐标轴上的任意角x ,不等式sin cos x x +22tan cot m x x ≤≤+恒成立,则实数m 的取值范围是2] ; 三、解答题:17、已知函数2π()2sin 24f x x x ⎛⎫=+⎪⎝⎭,ππ,42x ⎡⎤∈⎢⎥⎣⎦. (1)求()f x 的最大值和最小值;(2)若不等式()2f x m -<在ππ,42x ⎡⎤∈⎢⎥⎣⎦上恒成立,求实数m 的取值范围. 解:(1)π()1cos 221sin 222f x x x x x ⎡⎤⎛⎫=-+=+⎪⎢⎥⎝⎭⎣⎦∵π12sin 23x ⎛⎫=+- ⎪⎝⎭.又ππ,42x ⎡⎤∈⎢⎥⎣⎦∵,ππ2π2633x -∴≤≤,即π212sin 233x ⎛⎫+- ⎪⎝⎭≤≤,max min ()3,()2f x f x ==∴.(2)()2()2()2f x m f x m f x -<⇔-<<+∵,ππ,42x ⎡⎤∈⎢⎥⎣⎦,max ()2m f x >-∴且min ()2m f x <+,14m <<∴,即m 的取值范围是(1,4).18、已知函数21()2sin 1[,]2f x x x x θ=+- ∈。