2015陕西实验考前模拟优质版 陕西省实验中学2015届高三下学期考前模拟数学(文)试题 Word版含答案
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2015届模拟考试1——理科综合能力测试本试卷共39题(含选考题)。
全卷满分300分。
考试用时间150分钟。
可能用到的相对原子质量:Al-27,Fe-56,C-12,H-1,O-16,N-14第I卷(选择题共126分)一、选择题(本题共13小题,每小题6分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
)1.下图为研究渗透作用的实验装置,漏斗内溶液(S1)和漏斗外溶液(S2),漏斗内外起始液面一致。
渗透平衡时的液面差为△h。
下列有关分析正确的是A.若S1 、S2分别是不同浓度的蔗糖溶液,渗透平衡时的液面差为△h,S1浓度大于S2的浓度B.若S1 、S2分别是不同浓度的蔗糖溶液,渗透平衡时的液面差为△h,S1浓度等于S2的浓度C.若S1 、S2分别是不同浓度的KNO3溶液,渗透平衡时的液面差为△h,S1浓度大于S2的浓度D.若S1 、S2分别是不同浓度的KNO3溶液,渗透平衡时的液面差为△h,S1浓度等于S2的浓度2. 对下列四幅图的描述正确的是()A.图1中a阶段X射线照射可诱发突变,C阶段染色体数目会暂时加倍B.图2中的温度在a时酶分子结构改变、活性较低C.图3中bc段和de段的变化都会引起C3化合物含量的下降D.图4中造成cd段下降的原因在有丝分裂和减数分裂过程中都相同3.白花三叶草有两个品种:叶片内含氰(HCN)的品种和不含氰的品种,由两对独立遗传的基因控制。
其代谢过程如下图:两个不含氰的品种杂交,F1全部含有氰,F1自交获得F2,则A.两亲本的基因型为DDhh(或Ddhh)和ddHH(或ddHh)B.向F2不含氰品种的叶片提取液中加入含氰葡萄糖苷,约有3/7类型能产生氰C.氰产生后主要储存在叶肉细胞溶酶体中D.F2中性状分离比为含氰品种:不含氰品种=15:14.图甲表示受到刺激时神经纤维上的电位变化,图乙表示突触,有关叙述错误的是A.轴突膜处于②状态时钠离子内流 B.轴突膜处于④和⑤状态时钾离子外流C.在a化学信号的转变 D.c处兴奋一定会使b产生图甲所示的变化5.由地震形成的海洋中有大小相似的甲、乙两个小岛,某时间段内岛上地雀的种类和数量随时间变化的情况如下图所示,下列有关叙述中,错误的是A.两岛上的地雀存在隔离,导致其种类增多B.甲岛较乙岛地雀种类增加更多,可能是甲岛的环境变化更大C.甲岛上的地雀年龄组成属于增长型D.每个岛上的地雀相互影响共同进化,形成了生物多样性6.对右图所示相关叙述中,错误的是A.产生顶端优势的植物侧芽生长素浓度大于hB.用B、D点所对应浓度的生长素处理扦插枝条则生根效果相同C.若某植物幼苗向光侧的生长素浓度为f,则背光侧的生长素浓度可能大于2fD.若水平放置的植物茎的近地侧生长素浓度为2f,则茎的远地侧生长素浓度小于f7.下列有相关说法不正确...的是:()A.某吸热反应能自发进行,因此该反应是熵增反应B.在任何条件下,纯水都呈中性C.水的离子积常数Kw随温度、外加酸(碱)浓度的改变而改变D.铅蓄电池充电时,标有“—”的电极应与电源的负极相连8.下列生活中的化学事例对应的离子方程式书写正确的是A.用醋酸除去暖瓶中的水垢:2H++CaCO3== Ca2++ CO2↑+ H2O B.利用Na2CO3溶液可除油污:CO32- + 2H2O H2CO3 + 2OH-C.氢氧燃料电池在酸性介质中的正极反应:O2+4e-+2H2O = 4OH-D. 汽车用的铅蓄电池充电时阳极反应:PbSO4+2H2O-2e-== PbO2+4H++SO2-49. Q、W、X、Y、Z是原子序数依次增大的短周期元素,X、Y是金属元素,X的焰色呈黄色。
陕西实验中学2015届高三下学期考前模拟 理科综合满分:300分 时间:150分钟 可能用到的相对原子质量: H-1 C-12 N-14 O-16 Na-23 Si-28 S-32 Cl-35.5 A-27 Ba-137 第I卷(选择题 共108分) 本卷共18小题,每小题6分,共108分。
在每小题给出的四个选项中,只有一个选项符合题目要求。
.科学家在研究线粒体组分时,首先将其放在低渗溶液中获得涨破的外膜,经离心后将外膜与内膜包裹的基质分开。
再分别用超声波、尿素处理线粒体内膜,实验结果如下图所示。
研究发现含F0—F1颗粒的内膜小泡能合成ATP,含F0颗粒内膜小泡不能合成ATP。
下列说法不正确的是 A.从线粒体内外膜的功能推测外膜上膜蛋白的种类和数量应该比内膜少B.该过程能体现线粒体膜的结构特点,线粒体膜可参与构成生物膜系统 C.线粒体基质中可能含有的化学成分有水、ATP、核苷酸、氨基酸、葡萄糖等 D.线粒体内膜上F1颗粒的功能可能是催化ATP的合成 .下为人体内基因对性状的控制过程,分析 A.基因1和基因2一般不会出现在人体内的同一个细胞中 B.图中过程需RNA聚合酶的催化,过程需tRNA的协助 C.过程的结果存在差异 D.过程表明基因通过控制酶的合成来控制生物的性状 .下列关于实验的说法正确的是 A.将淀粉、淀粉酶先混合再置于不同温度条件下,可探究温度对酶活性的影响 B.用光学显微镜观察黑藻成熟叶,看不到染色体的原因主要是被叶绿体中的色素掩盖 C.观察植物细胞的有丝分裂实验中,盐酸和酒精混合液用于使细胞相互分离D.探究土壤小动物类群的丰富度时,宜采用标志重捕法 .下列有关植物激素调节的叙述,错误的是 A.使用一定浓度的生长素处理扦插枝条,能提高插条的成活率 B.使用一定浓度的赤霉素处理芹菜幼苗,能提高芹菜的产量 C.使用一定浓度的脱落酸处理浸泡过的小麦种子,能提高种子的萌发率 D.使用一定浓度的乙烯利处理凤梨,能让凤梨提前上市 . A.稻鸭共作改变了稻田群落的垂直结构,既充分利用了空间,又实现了物质良性循环和能量多级利用 B.利用鸭子捕虫除草可对害虫及杂草种群进行持续控制,控虫除草效果比使用农药更为显著 C.叫声换回鸭群,与物理信息传递有关,体现了该生态系统中人的因素仍起主导作用 D.适当放鸭增加稻田的生物多样性并延长了相关食物链,但没有增加新的食物链 6.生活处处有化学。
14.如图所示,两列简谐横波分别沿x 轴正方向和负方向传播,两波源分别位于x= -0.2m 和x=1.2m 处,两列波的速度均为v=0.2m/s ,两波源的振幅均为A=2cm .图示为t=0时刻两列波的图像(传播方向如图所示),此时平衡位置处于x=0.2m 和x=0.8m 的P 、Q 两质点刚开始振动。
质点M 的平衡位置处于x=0.5m 处,关于各质点运动情况下列判断正确的是( )A .质点P 的起振方向沿y 轴正方向B .t=1.5s 时刻,质点P 运动到M 点C .t= 1.5s 时刻,质点M 的速度为0D .t =3s 时刻,质点M 的位移为4cm15.某同学用如图所示方法做共点力平衡实验。
M 、N 为摩擦不计的定滑轮,O 点是轻质细绳OA 、OB 和OC 的结点,桌上有若干相同的钩码,他已经在A 点和C 点分别挂了3个和4个钩码,为使O 点在两滑轮间某位置受力平衡,在B 点挂的钩码数可能是( )A . 1个B .3个C .5个D .7个16.如图,运行轨道在同一平面内的两颗人造卫星A 、B ,同方向绕地心做匀速圆周运动,此时刻A 、B 连线与地心恰在同一直线上且相距最近,已知A 的周期为T , B 的周期为2T/3。
下列说法正确的是( ) A .A 的线速度大于B 的线速度 B .A 的加速度大于B 的加速度C .A 、B 与地心连线在相同时间内扫过的面积相等D .从此时刻到下一次A 、B 相距最近的时间为2T17.如图所示,在轻弹簧的下端悬挂一个质量为m 的小球A ,若将小球A 从弹簧原长位置由静止释放,小球A 能够下降的最大高度为h 。
若将小球A 换为质量为3m 的小球B ,仍从弹簧原长位置由静止释放,则小球B 下降h 时的速度为(重力加速度为g ,不计空气阻力)( )第15题图A B . 34gh C D18.对于真空中电荷量为q 的静止点电荷而言,当选取离点电荷无穷远处的电势为零时,离点电荷距离为r 的位置的电势为φ=kq/r (k 为静电力常量),如图所示,两电荷量大小均为Q 的异种点电荷相距为d+R ,现将一质子(电荷量为e )从两电荷连线上的A 点沿以负电荷为圆心、半径为R 的半圆形轨迹ABC 移到C 点,在质子从A 到C 的过程中,系统电势能的变化情况为( ) A .减少222R d kQeR- B .增加222R d kQeR +C .减少2(2)kQeR d d R +D .增加2(2)kQeRd d R +第Ⅱ卷(非选择题 共192分)必考部分第Ⅱ卷必考部分共10题,共157分19.( )(1)某同学利用重锤做自由落体运动验证机械能守恒定律的实验 ①有关重锤的质量,下列说法正确的有( )A .应选用质量较大的重锤,使重锤和纸带所受的重力远大于它们所受的阻力B .应选用质量较小的重锤,使重锤的惯性小一些,下落时更接近于自由落体运动C .不需要称量重锤的质量D .必须称量重锤的质量.②在该实验中,选定了一条较为理想的纸带,如下图所示,“O”为起始点,以后纸带上所打的各点依次记为1、2、3……。
陕西省实验中学2015届高三下学期第八次模拟考试英语试题命题人:高三英语组校对人:高三英语组第一部分: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. At what time does the office open?A. 7:45.B. 8:00.C. 8:15.2. What did the woman do last Sunday?A. She saw a play.B. She acted in a play.C. She went to the tea house.3. What is the relationship between the speakers?A. They’re friends.B. They’re strangers.C. They’re brother and sister.4. What are the speakers talking about?A. A fine boat.B. Their friend, Tom.C. The weather.5. What will the woman do this evening?A. Meet her Mum at the airport.B. Say goodbye to her Mum at the airport.C. Fly to another city with her Mom.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。
陕西实验中学2015年高三第三次模拟考试试题英语本试卷分第I卷(选择题)和第II卷(非选择题)两部分。
满分120分,考试时间100分钟。
第一部分阅读理解(共两节,满分40分)第一节(共15小题;每小题2分,满分30分)阅读下列短文,从每题所给的四个选项(A、B、C和D)中, 选出最佳选项。
AThe person who set the course of my life was a school teacher named Marjorie Hurd. When I was stepped off a ship in New York Harbor in 1949, I was a nine-year-old war refugee, who had lost his mother and was coming to live with the father he did not know. My mother, Eleni Gatzoyiannis, had been imprisoned and shot for sending my sisters and me to freedom.I was thirteen years old when I entered Chandler Junior High. Shortly after I arrived, I was told to select a hobby to pursue during “club hours.” The idea of hobbies and clubs made no sense to my immigrant ears, but I decided to follow the prettiest girl in my class. She led me into the presence of Miss Hurd, the school newspaper adviser and English teacher.A tough woman with salt-and-pepper hair and determined eyes, Miss Hurd had no patience with lazy bones. She drilled us in grammar, assigned stories for us to read and discuss, and eventually taught us how to put out a newspaper. Her introduction to the literary wealth of Greece gave me a new perspective on my war-torn homeland, making me proud of my origins. Her efforts inspired me to understand the logic and structure of the English language. Owing to her inspiration, during my next twenty-five years, I became a journalist by profession.Miss Hurd retired at the age of 62. By then, she had taught for a total of 41 years. Even after her retirement, she continually made a project of unwilling students in whom she spied a spark of potential. The students were mainly from the most troubled homes, yet she alternately bullied and charmed them with her own special brand of tough love, until the spark caught fire.Miss Hurd was the one who directed my grief and pain into writing. But for Miss Hurd, I wouldn’t have become a reporter. She was the one that sent me into journalism and indirectly caused all the good things that came after.1. What does the underlined sentence in Paragraph Two most probably mean?A. Hobbies and clubs did not interest the author.B. The author turned a deaf ear to joining clubs.C. The author had no idea what hobbies and clubs were all about.D. Hobbies and clubs were inaccessible to immigrants like the author.2. Which of the following caused the author to think of his homeland differently?A. Stepping on the American soil for the first time.B. Her mother’s miserable death.C. Following the prettiest girl in his class.D. Being exposed to Greek literary works.3. It can be inferred from Paragraph Four that ___________.A. Miss Hurd’s contribution was recognized across the nation.B. Students from troubled homes preferred Mis s Hurd’s teaching style.C. Miss Hurd employed a unique way to handle these students.D. The students Miss Hurd taught were all finally fired.4. The passage is mainly concerned with ___________.A. how the author became a journalist.B. the importance of inspiration in one’s life.C. factors contributing to a successful career.D. the teacher who shaped the author’s life.BSuppose you work in a big firm and find English very important for your job because you often deal with foreign businessmen. Now you are looking for a place where you can improve your English, especially your spoken English.Here are some advertisements about English language training from newspapers. You may find the information you need.5. You work from 9:00 a. m. to 4:30 p. m. every day. Which school will you choose?A. Global English Center and Modern Language School.B. Global English Center and the International House.C. Modern Language School and the 21st Century.D. The 21st Century and the International House.6. The 21st Century is different from the other three schools in that ________.A. its teaching quality is betterB. it requires an entrance examinationC. it is nearest to the city centerD. its courses are more advanced7. You will probably prefer to go to the International House because it ________.A. costs less than the other schoolsB. offers sightseeing and social activities at low pricesC. has a special course in spoken EnglishD. has native English teachers8. If you take the four-month evening program at the International House, you will pay about________.A. 240 yuanB.60 yuanC. 720 yuanD. 960 yuanCThe owner of an Alabama Chinese restaurant named “Good Friend” shot at a customer who complained about a bug in her egg roll Thursday night. The bullet narrowly missed 20-year-old Birmingham resident Jatari Walker who told the Daily News she is scarred by the entire experience.“I can’t sleep,” she said Saturday afternoon. “And since it happened I’ve had no appetite.”Walker ordered a combination platter(大浅盘)and egg roll from the Good Friend Chinese and Seafood Restaurant on Dennison Ave. Thursday evening. After paying her $7 bill she went back to her car and discovered a fly inside. “I thought I need to take this back,” she said.The customer went back and asked for a repayment and said the owner Chun Hin Ching, 52, was unhappy with her because she announced her discovery in front of other customers. After an argument he repaid the money and Walker — who is now a former frequent customer of the business — turned and walked to the exit.That’s when Ching drew a handgun and fired a single shot over her head.“He just shot the gun at me and I ran,” she said, adding she could feel the bullet whiz past her head.Birmingham Police Department spokesman Lt. Sean Edwards told the News the owner was charged with attempted murder and was transported to Jefferson County Jail on $100,000 bail (保释金).Police believe Ching intended to hit Walker with the bullet and missed, Edwards said. The bullet hit the top of the door frame of the take-out business.Ching did not tell police why he fired at Walker, Edwards said.Edwards said he did not recall any previous problems at the business. He said Ching did not say why he had a weapon but added it was not uncommon for stores in that neighborhood.No one was injured from the gunshot, Edwards said.Calls placed to the restaurant Saturday afternoon were not answered.9. What happened on Thursday night in Good Friend Chinese and Seafood Restaurant?A. A fire broke out but luckily no one was injured.B. The restaurant owner refused to repay the money.C. A young woman narrowly escaped being killed by a bullet.D. The egg rolls caused sickness among some customers.10. Why did Walker go back to the restaurant after buying the food?A. Because she discovered a fly in the egg roll.B. Because she left her car key in the restaurant.C. Because she forgot to take the combination platter.D. Because she found the owner charged her too much.11. The restaurant owner fired on Walker when ______.A. she was arguing with himB. she was about to leaveC. she asked for a repaymentD. she announced her discovery12. We can learn from the passage that ______.A. this is the first time for Walker to buy food from Good Friend RestaurantB. the owner was unhappy with the complaint and refused to repay the moneyC. if someone had been hit, Ching’d have been c harged with attempted murderD. it is common for a restaurant owner in that neighborhood to have a weaponDOn “Super Bowl Sunday”, millions of Americans are glued to their TVs. They are eating pizza, chicken wings and chips and cheering every move. The y’re watching the Super Bowl.Why are Americans so crazy about American football? Well, it is more exciting than other sports. One team can lose possession of the ball in a minute, which may allow their opponents to make a touchdown(触地得分). Then that team may win the game unexpectedly.The Super Bowl also entertains its audience with a great halftime show. The football field is turned into a stage. Then an impressive performance of dancing and singing with special effects occurs.Since the Super Bowl is the most-watched TV program in America, commercial airtime is also very expensive. Big money is also spent on commercials. They draw the viewers’ attention and advertise their image or products during the commercial break.After football season, the “March Madness” begins. The NCAA (National Collegiate Athletic Association) competitions begin with 68 men’s college basketball teams. They play until the field is reduced to the “Final Four”. The winning team becomes the national champion. The NBA (National Basketball Association) All-Star game is also held in February. The best players from all the teams play in this game.Baseball is no doubt American’s national sport. From grandpas to young kids, whole families go to ball games together. They wear their favorite team’s caps or even carry their mascot(吉祥物). Our family went to watch Wang Chien-Ming play in D.C. once. We ate hot dogs, waved flags and sang during the 7th inning(棒球的一局) stretch.If you are not a sports fan yet, come and pick a sport or a team. Go to a ball game with your family, and cheer your team on. Sports are definitely a part of American culture one should not miss.13. According to the passage, the Super Bowl is _____.A. an expensive American sportB. a well-received American football gameC. an impressive TV performanceD. a most-watched TV series14. Which of the following may be one of the reasons for the popularity of the Super Bowl?A. Its results are too exciting to meet viewers’ expectations.B. People can eat pizza, chicken wings and chips when watching it.C. The performances during its halftime show are appealing to viewers.D. Its commercials are expensive enough to draw viewers’ attention.15. The passage is mainly written to _____.A. inform readers of the three popular sports in AmericaB. teach readers how to understand the sports culture in AmericaC. show readers the importance of sports in young people’s life in AmericaD. encourage readers to fit in with American culture through sports第二节(共5小题;每小题2分,满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。
高中化学学习材料(灿若寒星**整理制作)陕西省2015届高考冲刺第三次模拟考试理综化学试题2015届第三次模拟考试——理科综合能力测试(A卷)本试卷共39题(含选考题)。
全卷满分300分。
考试用时间150分钟。
可能用到的相对原子质量:H-1 C-12 O-16 Na-237. 下列物质放在空气中会变质,且变质过程与空气中的O2、CO2、水蒸气都有关的是A.过氧化钠B.金属钠C.硫酸亚铁晶体D.四氯化硅液体8.设N A为阿伏伽德罗常数的值。
下列叙述正确的是A.1mol甲醇中含有C—H键的数目为4N AB.25℃,pH=13的NaOH溶液中含有OH-的数目为0.1N AC.标准状况下,2.24L水中含有分子的数目为0.1N AD.常温常压下,Na2O2与足量H2O反应,共生成0.2molO2,转移电子的数目为0.4 N A 9.如图是金属镁和卤素反应的能量变化图(反应物和产物均为298 K时的稳定状态)。
下列选项中不正确的是A.Mg与F2反应的△S<0B.MgF2(s)+Br2(l)==MgBr2(s)+F2(g) △H=+600kJ·mol-1C.MgBr2与Cl2反应的△H<0D.化合物的热稳定顺序:MgI2>MgBr2>MgCl2>MgF210.锂钒氧化物电池的能量密度远远超过其他材料电池,电池总反应式为V2O5+x Li===Li x V2O5,下列说法不正确的是A.向外供电时,锂离子向负极移动B.负极上反应的物质是锂,正极上反应的物质是V2O5C.正极的电极反应为:V2O5+x e-+x Li+===Li x V2O5D.负极的电极反应为:x Li-x e-===x Li+11.短周期元素甲、乙、丙、丁的原子序数依次增大,甲和乙形成的气态化合物的水溶液显碱性,乙位于第V A族,甲和丙同主族,丁原子最外层电子数与电子层数相等。
则下列说法正确的是()A.离子半径:丙>丁>乙B.单质的还原性:丁>丙>甲C.乙、丙、丁的最高价氧化物对应的水化物能相互反应D.甲、乙、丙的氧化物均只有一种12.乙烷在光照条件下与氯气发生取代反应,理论上得到的氯代物最多有几种A.5种B.6种C.8种D.9种13.下表是3种物质的溶解度(20℃),下列说法中不正确的是物质MgCl2Mg(OH)2MgCO3溶解度(g/100 g) 74 0.000 84 0.01A. 将表中三种物质与水混合,加热、灼烧,最终的固体产物相同B.已知MgCO3的K sp=6.82×10-6 mol2·L-2,则所有含有固体MgCO3的溶液中,都有c(Mg2+)=c(CO2-3),且c(Mg2+)·c(CO2-3)=6.82×10-6 mol2·L-2C.除去粗盐中含有的MgCl2杂质,最佳除杂试剂为NaOH溶液D.用石灰水处理含有Mg2+和HCO-3的硬水,发生的离子反应方程式为Mg2++2HCO-3+2Ca2++4OH-===2CaCO3↓+Mg(OH)2↓+2H2O26.(14分)高铁酸钠(Na2FeO4)是一种多功能、高效无毒的新型绿色水处理剂。
模拟训练数 学(理科)第Ⅰ卷 选择题(共60分)一、选择题:在每小题给出的四个选项中,只有一项是符合题目要求的(本大题共12小题,每小题5分,共60分)1.复数2015计算的结果是( )A .-1B .i - C2.若sin 20a = ,则sin 230 的值为( )A .221a -B .21a -C .21a -D .212a -3.522x⎫⎪⎭-的展开式中常数项是( )A .5B .5-C .10D .10-4.已知{}n a 为等差数列,n S 为其前n 项和.若112a =,611S S =,则必有( )A .170a =B .6120a a +=C .170S >D .90a <5.已知一几何体的三视图如图所示,则该几何体的体积是( )A .6B .9C .12D .186.右图是函数2sin()(0)y x ωφω=+>图像的一部分,则ω和φ为( )A.115ω=, 56πφ=-B.75ω=, 6πφ=-C.175ω=, 56πφ=-D.135ω=, 6πφ=-7.展开10()a b c ++合并同类项后的项数是( )A .11B .66C .76D .134 8.已知随机变量X 的取值为0,1,2,若1(0)5P X ==,1EX =,则DX =( )A .25B .45C .23D .439.若变量,x y 满足约束条件120y x y x y ≤⎧⎪+≥⎨⎪--≤⎩,则2z x y =-的最大值为( )A .4B .3C .2D .110.已知三棱锥P ABC -的四个顶点均在半径为1的球面上,且满足0PA PB ⋅= ,0PB PC ⋅= ,0PC PA ⋅=,则三棱锥P ABC -的侧面积的最大值为( )A .12B .1C .2D .411.已知抛物线x y 82=的焦点与双曲线1222x y a-=的一个焦点重合,则该双曲线的离心率为( )A..D12.已知函数()f x =3231ax x -+,若()f x 存在唯一的零点0x ,且0x >0,则a 的取值范围是( )A .(2,+∞)B .(-∞,-2)C .(1,+∞)D .(-∞,-1)第Ⅱ卷 非选择题(共90分)二.填空题:把答案填在答题卡相应题号后的横线上(本大题共4小题,每小题5分,共20分)13.已知0ω>,函数()sin()4f x x πω=+在(,)2ππ上单调递减,则ω的取值范围是 ;14.如右图,输入正整数,m n ,满足n m ≥,则输出的p = ;15.若直线l :1y kx =+被圆C :22x y 2x 30+--=截得的弦最短,则k= ;16.将全体正整数排成如图的一个三角形数阵,按照此排列规律,第10行从左向右的第5个数为 .三.解答题:解答应写出文字说明、证明过程或演算步骤(本大题共6小题,共70分)17.(本小题共12分)从某批产品中,有放回地抽取产品两次,每次随机抽取1件,假设事件A :“取出的2件产品中至多有1件是二等品”的概率()0.96P A =.(Ⅰ)求从该批产品中任取1件是二等品的概率p ; (Ⅱ)若该批产品共20件,从中任意抽取2件,X 表示取出的2件产品中二等品的件数,求X 的分布列与期望.18.(本小题共12分)已知数列{n a }中,n S 为其前n 项和,且12a a ≠,当n N +∈时,恒有n n S pna =(p 为常数).(Ⅰ)求常数p 的值;(Ⅱ)当22a =时,求数列{n a }的通项公式;(Ⅲ)设14(2)n n n b a a +=+,数列{}n b 的前n 项和为n T ,求证:74n T <.19.(本小题共12分)四棱锥S -ABCD 中,底面ABCD 为平行四边形,侧面SBC ⊥底面ABCD .已知∠ABC =45°,AB =2,BC =22,SA =SB =3.(Ⅰ)求证:SA ⊥BC ;(Ⅱ)求直线SD 与平面SAB 所成角的正弦值.20.(本小题共12分)已知定点(1,0)C -及椭圆2235x y +=,过点C 的动直线与该椭圆相交于,A B 两点.(Ⅰ)若线段AB 中点的横坐标是12-,求直线AB 的方程;(Ⅱ)在x 轴上是否存在点M ,使MA MB ⋅为常数?若存在,求出点M 的坐标;若不存在,请说明理由.21.(本小题共12分)(Ⅰ)已知正数1a 、2a 满足121a a +=,求证:121222log log 1a a a a +≥-;(Ⅱ)若正数1a 、2a 、3a 、4a 满足12341a a a a +++=, 求证:121222323424log log log log 2a a a a a a a a +++≥-.请考生从第22、23、24三题中任选一题作答.注意:只能做所选定的题目.如果多做,则按所做的第一个题目计分,作答时请用2B 铅笔在答题卡上将所选题号后的方框涂黑.22.(本小题满分10分)选修4—1:几何证明选讲 如图,O 和'O 相交于A ,B 两点,过A 作两圆的切线分别交两圆于,C D 两点,连结DB 并延长交O 于点E .证明:(I )AC BD AD AB ⋅=⋅;(II )=AC AE .23.(本小题满分10分)选修4—4:坐标系与参数方程已知椭圆C :1162422=+y x ,直线l :1128x y +=,(I )以原点O 为极点,x 轴正半轴为极轴建立极坐标系,求椭圆C 与直线l 的极坐标方程;(II )已知P 是l 上一动点,射线OP 交椭圆C 于点R ,又点Q 在OP 上且满足2OR OP OQ =⋅.当点P 在l 上移动时,求点Q 在直角坐标系下的轨迹方程.24.(本小题满分10分)选修4—5:不等式选讲已知函数()|2||5|=---.f x x x(I)证明:3()3-≤≤;f x(II)求不等式:2≥-+的解集.()814f x x x模拟训练数学(理科)参考答案一.选择题:1.C 2.A 3.D 4.B 5.B 6.A7.B 8.A 9.B 10.C 11.C12.B二.填空题:13.15,24⎡⎤⎢⎥⎣⎦, 14.mn A , 15.1, 16.50.三、解答题:17.【解】:(Ⅰ)210.960.2p p -=⇔=. (Ⅱ)∵该批产品共20件,由(Ⅰ)知其二等品有200.24⨯=件,显然X=0,1,2.故216220C 12(0)C 19P X ===.11164220C C 32(1)C 95P X ===.24220C 3(2)C 95P X ===. 所以X 的分布列为∴EX=389518.【解】: (Ⅰ)当1n =时,11a S =,∴11a pa =,1p ⇒=或10a = 当1p =时,n n S na =则有221221222S a a a a a a =⇔+=⇔=与已知矛盾,∴1p ≠,只有10a =.当2n =时,由2212222S pa a a pa =⇔+=,∵10a =又12a a ≠∴20a ≠ ∴12p =(Ⅱ)∵22a =,12n n S na =,当2n >时,11122n n n n n n n a S S a a ---=-=-11(2)(1)12n n n n a a n a n a n n ---=-⇔=--,∴22211n n a aa n n =⇔=-- 当1121202 2.n n a a n ==⨯-=∴=-时,也适合。
陕西实验中学2015届高三下学期第六次模拟考试英语试题命题人:高三外语组审题人:高三外语组本试卷第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,共150分,共11页第Ⅰ卷第一部分听力(1-20小题)在笔试结束后进行第二部分阅读理解(共两节,满分40分)第一节(共15小题,每小题2分,满分30分)阅读下列短文,从每题所给的四个选项(A. B. C和D)中,选出最佳选项,并在答题卡上将该项涂黑·AIn the fall of 1985, I was a bright-eyed girl heading off to Howard University, aiming at a legal career and dreaming of sitting on a Supreme Court bench somewhere. Twenty-one years later I am still a bright-eyed dreamer and one with quite a different tale to tell.My grandma, an amazing woman, graduated from college at the age of 65.She was the first in our family to reach that goal. But one year after I started college, she developed cancer. I made the choice to withdraw from college to care for her. It meant that school and my personal dream would have to wait.Then I got married with another dream: building my family with a combination of adoptedand biological children. In 1999, we adopted our first son. To lay eyes on him was fantastic—and very emotional. A year later came our second adopted boy. Then followed son No.3.In 2003, I gave birth to another boy.You can imagine how fully occupied I became, raising four boys under the age of 8!Our home was a complete zoo—a joyous zoo. Not surprising, I never did make it back to college full-time. But I never gave up on the dream either. I had only one choice: to find a way. That meant taking as few as one class each semester.The hardest part was feeling guilty about the time I spent away from the boys. They often wanted me to stay home with them. There certainly were times I wanted to quit, but I knew I should set an example for them to follow through the rest of their lives.In 2007, I graduated from the University of North Carolina. It took me over 21 years to getmy college degree!I am not special, just single-minded. It always struck me that when you're looking at a big challenge from the outside it looks huge, but when you're in the midst of it, it just seems normal. Everything you want won't arrive in your life on one day. It's a process. Remember: little steps addup to big dreams.21.When the author went to Howard University, her dream was to be ________.A .a writerB .a teacher C. a judge D. a doctor22.Why did the author quit school in her second year of college?A.She wanted to study by herself. B .She fell in love and got married.C.She suffered from a serious illness. D .She decided to look after her grandma.23. What can we learn about the author from Paragraphs 4 and 5?A .She was busy yet happy with her family life.B .She ignored her guilty feeling for her sons.C .She wanted to remain a full-time housewife.D .She was too confused to make a correct choice.24.What does the author mostly want to tell us in the last paragraph?A .Failure is the mother of success.B .Little by little, one goes far.C .Every coin has two sides.D .Well begun, half done.BWanted, Someone for a KissWe're looking for producers to join us on the sound of London Kiss 100 FM. You'll work onthe station's music programmes. Music production experience in radio is necessary, along with rich knowledge of modern dance music. Please apply in writing to Producer Vacancies, Kiss 100.Father ChristmasWe're looking for a very special person, preferably over 40, to fill our Father Christmas suit.Working days: Every Saturday from November 24 to December 15 and every day from December 17 to December 24 except Sundays, 10∶30-16∶00.Excellent pay.Please contact the Enterprise Shopping Centre, Station Parade, Eastbourne.Accountants AssistantWhen you join the team in our Revenue Administration Unit, you will be providing assistance within all parts of the Revenue Division, dealing with post and other general duties. Ifyou are educated to GCSE grade C level we would like to talk to you. This position is equally suitable for a school leaver or for somebody who has office experience.Wealden District CouncilSoftware TrainerIf you are aged 24-45 and have experience in teaching and training, you could be the person we are looking for. You should be good at the computer and have some experience in programme writing. You will be allowed to make your own decisions, and to design courses as well as presentthem. Pay upwards of £15,000 for the right person. Please apply by sending your CV (简历) to Mrs R. Oglivie, Palmlace Limited.25.Who should you get in touch with if you hope to work in a radio station?A .Producer Vacancies, Kiss 100.B .Mrs Oglivie, Palmlace Limited.C .The Enterprise Shopping Centre.D .Wealden District Council.26.We learn from the ads that the Enterprise Shopping Centre needs a person who________.A .is aged between 24 and 40B .may do some training workC .should deal with general dutiesD .can work for about a month27.Which position is open to recent school graduates?A .Producer, London Kiss.B .Father Christmas.C .Accountants Assistant.D .Software Trainer.28.What kind of person would probably apply to Palmlace Limited?A .One with GCSE grade C level.B .One with some office experience.C .One having good computer knowledge.D .One trained in producing music programmes.CThe need to feed a growing population is putting much pressure on the world's supply of water. With 97% of the world's water too salty to be drunk or used in agriculture, the worldwide supply of water needs careful management, especially in agriculture. Although the idea of a water shortage seems strange to someone fortunate enough to live in a high rainfall country, many of the world's agricultural industries experience constant water shortages.Although dams can be built to store water for agricultural use in dry areas and dry seasons,the costs of water redistribution(重新分配)are very high. Not only is there the cost of the engineering itself, but there is also an environmental cost to be considered. Where valleys are flooded to create dams, houses are lost and wildlife homes destroyed. Besides, water may flow easily through pipes to fields, but it cannot be transported from one side of the world to the other. Each country must therefore rely on the management of its own water to supply its farming requirements.This is particularly troubling for countries with agricultural industries in areas dependent on irrigation (灌溉). In Texas, farmers' overuse of irrigation water has resulted in a 25% reduction of the water stores. In the Central Valley area of southwestern USA, a huge water engineering project provided water for farming in dry valleys, but much of the water use has been poorly managed.Saudi Arabia's attempts to grow wheat in desert areas have seen the pumping of huge quantities of irrigation water from underground reserves. Because there is no rainfall in these areas, such reserves can only decrease, and it is believed that fifty years of pumping will see themrun dry.29. From the first two paragraphs we learn that________.A. much of the world's water is available for useB. people in high rainfall countries feel luckyC. the costs of water redistribution should be consideredD. water can be easily carried through pipes across the world30. Which of the following is TRUE?A. The water stores in Texas have been reduced by 75%.B. Most industries in the world suffer from water shortages.C. The underground water in Saudi Arabia might run out in 50 years.D. Good management of water use resulted from the project in the Central Valley.31. What is most likely to be discussed in the paragraph that follows?A. Steps to improving water use management.B. Ways to reduce the costs of building dams.C. Measures to deal with worldwide water shortages.D. Approaches to handling the pressure on water supply.32. The text is mainly about________.A. water supply and increasing populationB. water use management and agricultureC. water redistribution and wildlife protectionD. water shortages and environmental protectionDArthur Miller (1915—2005) is universally recognized as one of the greatest dramatists of the20th century. Miller's father had moved to the USA from Austria-Hungary, drawn like so manyothers by the “Great American Dream”. However, he experienced severe financial hardship when his family business was ruined in the Great Depression of the early 1930s.Miller's most famous play, Death of a Salesman, is a powerful attack on the American system,with its aggressive way of doing business and its insistence on money and social status as indicators of worth. In Willy Loman, the hero of the play, we see a man who has got into troubleand in the cruel world of business there is no room forwith this system. Willy is “burnt out” sentiment: if he can't do the work, then he is no good to his employer, the Wagner Company, andhe must go. Willy is painfully aware of this, and at a loss as to what to do with his lack of success.He refuses to face the fact that he has failed and kills himself in the end.When it was first staged in 1949, the play was greeted with enthusiastic reviews, and it wonthe Tony Award for Best Play, the New York Drama Critics' Circle Award, and the Pulitzer Prizefor Drama. It was the first play to win all three of these major awards.Miller died of heart failure at his home in Roxbury, Connecticut, on the evening of February10, 2005, the 56th anniversary of the first performance of Death of a Salesman on Broadway.33.Why did Arthur Miller's father move to the USA?A. He suffered from severe hunger in his home country.B. He was attracted by the “Great American Dream.”C. He hoped to make his son a dramatist.D. His family business failed34.The play Death of a Salesman________.A. exposes the cruelty of the American business worldB. discusses the ways to get promoted in a companyC. talks about the business career of Arthur MillerD. focuses on the skills in doing business35.What can we learn about Willy Loman?A. He treats his employer badly.B. He runs the Wagner Company.C. He is a victim of the American system.D. He is regarded as a hero by his colleagues.第二节(共5小题;每小题2分,满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳选项,并在答题卡上将该选项的字母标号涂黑。
陕西省2015届高考冲刺第三次模拟考试理综物理试题2015届第三次模拟考试——理科综合能力测试(A 卷)本试卷共39题(含选考题)。
全卷满分300分。
考试用时间150分钟。
可能用到的相对原子质量:H-1 C-12 O-16 Na-23二、选择题:本题共有8个小题,每小题6分,共48分。
在每小题所给出的四个选项中,有的只有一个选项是正确的,有的有多个选项是正确的。
全部选对的得6分,选对但不全的得3分,有选错的得0分。
第14、15、16、17、18为单选, 19、20、21为多选14.一根通电直导线水平放置在地球赤道上方,其中通有自西向东的恒定电流,则该导线受到地球磁场的安培力方向为( )A .水平向北B .水平向南C .竖直向上D .竖直向下15. 如右图所示,在M 点分别以不同的速度将两小球水平抛出。
两小球分别落在水平地面上的P 点、Q 点。
已知O 点是M 点在地面上的竖直投影,OP ∶PQ =1∶3,且不考虑空气阻力的影响。
下列说法中正确的是( )A .两小球的下落时间之比为1:3B .两小球的下落时间之比为1:4C .两小球的初速度大小之比为1∶3D .两小球的初速度大小之比为1∶416.如图所示,竖直放置在水平面上的轻质弹簧上叠放着两物块A 、B ,它们相互绝缘且质量均为2kg ,A 带正电,电荷量为0.1C ,B 不带电。
开始时处于静止状态,若突然加一沿竖直方向的匀强电场,此瞬间A 对B 的压力大小变为15N 。
取g =10m/s 2,则( )A .电场强度为50N/CB .电场强度为100N/C C .电场强度为150N /CD .电场强度为200N /C17.如图所示,虚线为电场中的一簇等势面与纸面的交线,相邻两等势面电势差相等,已知A 、B 两等势面间的电势差为10V ,且A 的电势高于B 的电势.一个电子仅在电场力作用下从M 点向N 点运动,电子经过M 点时的动能为8 eV ,则电子经过N 点时的动能为( )A .16 eV B. 7.5 eV C. 4.0 eV D. 0.5 eV 18.图示的电路中电表均为理想电表,电源为恒流电源,即不管外电路情况如何变化,它都能提供持续且恒定的电流。
高中数学学习材料马鸣风萧萧*整理制作陕西实验中学2015届高三下学期考前模拟数 学(文科)本试卷分第Ⅰ卷(选择题)和第第Ⅱ卷(非选择题)两部分.满分150分,考试时间120分钟. 第Ⅰ卷 (选择题共60分)一.选择题:本大题共12小题,每小题5分,共60分. 在每小题给出的四个选项中,只 有一项符合题目要求的.1.复数i i -+1)1(2等于( )A .i +-1B .i +1C .i -1D .i --12.若集合12{|,01}A y y x x ==<≤,1{|2,01}B y y x x==-<≤,则A B 等于( ) A . (],1-∞ B . (]0,1 C . φ D . {1} 3. 阅读右面的程序框图,若输出的12y =,则输入的x 的值可能为 ( ) A .1- B .0 C . 1 D .5 4. 给出两个命题:命题:p 不等式0απ<<成立是不等式sin 0α>成立 的必要不充分条件;命题q:函数)2log y x =-是奇函数.则下列命题是真命题的是( ) A . p q ∧B . p q ∨⌝ C. p q ∨ D . p q ∧⌝5. 已知抛物线24y x =的焦点为F ,P 为抛物线上一点,过P 作y 轴的垂线, 垂足为M ,若||4,PF = 则PFM ∆的面积为( ) A. B. C . 6 D .8 6.等比数列{}n a 中12a =,公比2q =-,记12n n a a a ∏=⨯⨯⨯(即n ∏表示数列{}n a 的前n 项之积),则891011,,,∏∏∏∏中值最大的是( ) A .8∏B .9∏C .10∏D .11∏7.在同一个坐标系中画出函数x a y =,ax y sin =的部分图象,其中0>a 且1≠a ,则下 列所给图象中可能正确的是 ()A B C D8.已知a >0,x ,y 满足约束条件13(3)x x y y a x ≥⎧⎪+≤⎨⎪≥-⎩,且2z x y =+的最小值为1,则a =( )A .1B .2C .14D .129. 已知ABC ∆外接圆的半径为1,圆心为O ,且2,3AB AC AO AB OA +==,则 CA CB ⋅的值是 ( )A .3 BC D .1 10. 已知1(1)1x f x x e ++=-+,则函数()f x 在点(0,(0))f 处的切线l 与坐标轴围成的三角形面积为 ( ) A .14B .12C . 1D . 211. 已知()sin(2015)cos(2015)63f x x x ππ=++-的最大值为A ,若存在实数12,x x ,使得对任意实数x 总有12()()()f x f x f x ≤≤成立,则12A x x -的最小值为 ( ) A .2015πB .22015π C .42015π D .4030π12.对于函数()f x ,若存在区间][n m A ,=,使得{}A A x x f y y =∈=,)(|,则称函数()f x 为“可等域函数”,区间A 为函数()f x 的一个“可等域区间”.下列函数中存在唯一“可等域区间”的“可等域函数”为 ( ) A .()ln f x x = B .12)(2-x x f = C .()21xf x =+D .()sin()2f x x π=1A 第Ⅱ卷(非选择题 共90分)二.填空题:本大题共4小题,每小题4分,把答案填在题中的横线上.13.已知实数n m ,满足,1,0-=+>⋅n m n m 则nm 11+的最大值为 .14. 某几何体的三视图如图所示,其中俯视图为半径为2的 四分之一个圆弧,则该几何体的体积为 .15.对大于1的自然数m 的三次幂可用奇数进行以下方式的“分裂”:3331373152,39,4, (517)1119⎧⎧⎪⎧⎪⎪⎨⎨⎨⎩⎪⎪⎩⎪⎩ 仿此,若3m 的“分裂”数中有一个是73, 则m 的值为 ________ .16. 巳知函数'(),'()f x g x 分别是二次函数()f x 和三次函数()g x 的导函数, 它们在同一坐标系内的图象如右图所示.三.解答题:本大题共6小题,共74分,解答应写出必要的文字说明.证明过程或演算步骤. 17.(本小题满分12分)2015年“五一”期间,高速公路车辆较多。
陕西实验中学2015届高三下学期考前模拟数 学(文科)本试卷分第Ⅰ卷(选择题)和第第Ⅱ卷(非选择题)两部分.满分150分,考试时间120分钟. 第Ⅰ卷 (选择题共60分)一.选择题:本大题共12小题,每小题5分,共60分. 在每小题给出的四个选项中,只 有一项符合题目要求的.1.复数i i -+1)1(2等于( )A .i +-1B .i +1C .i -1D .i --12.若集合12{|,01}A y y x x ==<≤,1{|2,01}B y y x x==-<≤,则A B 等于( ) A . (],1-∞ B . (]0,1 C . φ D . {1}3. 阅读右面的程序框图,若输出的12y =,则输入的x 的值可能为 ( )A .1-B .0C . 1D .5 4. 给出两个命题:命题:p 不等式0απ<<成立是不等式sin 0α>成立 的必要不充分条件;命题q :函数()22log 1y x x =+-是奇函数.则下列命题是真命题的是( ) A . p q ∧B . p q ∨⌝ C. p q ∨ D . p q ∧⌝5. 已知抛物线24y x =的焦点为F ,P 为抛物线上一点,过P 作y 轴的垂线, 垂足为M ,若||4,PF = 则PFM ∆的面积为( ) A . 33 B . 43 C . 6 D .8 6.等比数列{}n a 中12a =,公比2q =-,记12n n a a a ∏=⨯⨯⨯(即n ∏表示数列{}n a 的前n 项之积),则891011,,,∏∏∏∏中值最大的是( )A .8∏B .9∏C .10∏D .11∏7.在同一个坐标系中画出函数xa y =,ax y sin =的部分图象,其中0>a 且1≠a ,则下 列所给图象中可能正确的是 ()A B C D否开始输出y结束x 输入整数是2x y =2x ≤sin()6y x π=22主视图22 左视图俯视图8.已知a >0,x ,y 满足约束条件13(3)x x y y a x ≥⎧⎪+≤⎨⎪≥-⎩,且2z x y =+的最小值为1,则a =( )A .1B .2C .14D .129. 已知ABC ∆外接圆的半径为1,圆心为O ,且2,3AB AC AO AB OA +==,则 CA CB ⋅的值是 ( )A .3B .3C .32D .1 10. 已知1(1)1x f x x e ++=-+,则函数()f x 在点(0,(0))f 处的切线l 与坐标轴围成的三角形面积为 ( )A .14B .12 C . 1 D . 2 11. 已知()sin(2015)cos(2015)63f x x x ππ=++-的最大值为A ,若存在实数12,x x ,使得对任意实数x 总有12()()()f x f x f x ≤≤成立,则12A x x -的最小值为 ( ) A .2015π B .22015π C .42015π D .4030π 12.对于函数()f x ,若存在区间][n m A ,=,使得{}A A x x f y y =∈=,)(|,则称函数()f x 为“可等域函数”,区间A 为函数()f x 的一个“可等域区间”.下列函数中存在唯一“可等域区间”的“可等域函数”为 ( )A .()ln f x x =B .12)(2-x x f = C .()21x f x =+D .()sin()2f x x π= 第Ⅱ卷(非选择题 共90分)二.填空题:本大题共4小题,每小题4分,把答案填在题中的横线上.13.已知实数n m ,满足,1,0-=+>⋅n m n m 则nm 11+的最大值为 .14. 某几何体的三视图如图所示,其中俯视图为半径为2的 四分之一个圆弧,则该几何体的体积为 .15.对大于1的自然数m 的三次幂可用奇数进行以下方式的“分裂”:O 1DCBC 1A 1D 1B 1A3331373152,39,4, (517)1119⎧⎧⎪⎧⎪⎪⎨⎨⎨⎩⎪⎪⎩⎪⎩ 仿此,若3m 的“分裂”数中有一个是73, 则m 的值为 ________ .16. 巳知函数'(),'()f x g x 分别是二次函数()f x 和三次函数()g x 的导函数, 它们在同一坐标系内的图象如右图所示.①若(1)1f =,则(1)f -= .②设函数()()()h x f x g x =-,则(1),(0),(1)h h h -的大小关系为 .(用“<” 连接)三.解答题:本大题共6小题,共74分,解答应写出必要的文字说明.证明过程或演算步骤. 17.(本小题满分12分)2015年“五一”期间,高速公路车辆较多。
某调查公司在一服务区从七座以下小型汽车中按进服务区的先后每间隔50辆就抽取一辆的抽样方法抽 取40名驾驶员进行询问调查,将他们在某段高速公路的车速 (km/t )分成六段:[60,65),[65,70),[70,75),[75,80),[80,85),[85,90)后得到如图的频率分布直方图.(Ⅰ)求这40辆小型车辆车速的众数和中位数的估计值. (Ⅱ)若从车速在[60,70)的车辆中任抽取2辆,求车速在[65,70) 的车辆恰有一辆的概率.18.(本小题满分12分)已知长方体1111ABCD A B C D -,点1O 为11B D 的中点. (Ⅰ)求证:1//AB 平面11AO D ; (Ⅱ)若123AB AA =,试问在线段1BB 上是否存在点E , 使得1AC ⊥AE ,若存在求出1BEBB ,若不存在,说明理由. 19. (本小题满分12分) 已知数列{}*(,146),n a nN n ∈≤≤满足1,a a =1,(115),1,(1630),1,(3145),n n d n a a n n d+⎧⎪≤≤⎪-=≤≤⎨⎪⎪≤≤⎩其中*0,.d n N ≠∈(Ⅰ)当1a =时,求46a 关于d 的表达式,并求46a 的取值范围;AMNB O PQ θ (Ⅱ)设集合{M b =|,,,*,116i j k b a a a i j k N i j k =++∈≤<<≤} 若11,,34a d == 求证:2.M ∈20. (本小题满分12分)已知椭圆C 的方程为22221(0)4x ym m m +=>,如图所示, 在平面直角 坐标系xoy 中,ABC ∆的三个顶点的坐标分别为(1,0),(0,2),(1,2)A B C (Ⅰ)当椭圆C 与直线AB 相切时,求m 的值;(Ⅱ)若椭圆C 与ABC ∆三边无公共点,求m 的取值范围;(Ⅲ)若椭圆C 与ABC ∆三边相交于不同的两点M,N ,求OMN ∆的面积S 的最大值.21.(本小题满分12分)如图,摩天轮的半径OA 为50m ,它的最低点A 距地面的高度忽略不计.地面上有一长 度为240m 的景观带MN ,它与摩天轮在同一竖直平面内,且60AM m =.点P 从最低 点A 处按逆时针方向转动到最高点B 处,记,(0,).AOP θθπ∠=∈ (Ⅰ)当23πθ=时,求点P 距地面的高度PQ ; (Ⅱ)设tan ,y MPN =∠写出用θ表示y 的函数 关系式,并求y 的最大值.O ABCxXyX数 学(文科)1~12 ABCC ABDD DABB 13.4- 14.82π- 15.9 16. ①1; ②(0)(1)(1)h h h <<- 17.解:(Ⅰ)众数的估计值为最高的矩形的中点,即众数的估计值等于77.5设图中虚线所对应的车速为x ,则中位数的估计值为:0.0150.0250.0450.06(75)0.5x ⨯+⨯+⨯+⨯-=,解得77.5x =即中位数的估计值为77.5 (Ⅱ)从图中可知,车速在[60,65)的车辆数为:10.015402m =⨯⨯=(辆),车速在[65,70)的车辆数为:20.025404m =⨯⨯=(辆)设车速在[60,65)的车辆设为,a b ,车速在[65,70)的车辆设为,,,c d e f ,则所有基本 事件有:(,),(,),(,),(,),(,),(,),(,),(,)(,),(,),(,)(,),(,)(,)a b a c a d a e a f b c b d b e b f c d c e c f d e d f e f 共15种其中车速在[65,70)的车辆恰有一辆的事件有:(,),(,),(,),(,),(,),(,),a c a d a e a f b c b d b e b f 共8种所以,车速在[65,70)的车辆恰有一辆的概率为815P =. 18. 解:(Ⅰ)证明:连结1AD 交1A D 于点G ,所以G 为1AD 的中点,连结1O G 在11AB D ∆中,1O 为11B D 的中点 11//O G AB ∴1O G ⊂面11AO D 且1AB ⊄面11AO D ∴1//AB 面11AO D(Ⅱ)若在线段1BB 上存在点E 得1AC ⊥AE ,连结1A B 交AE 于点M BC ⊥面11ABB A 且AE ⊂面11ABB ABC AE ∴⊥又1AC BC C =且1,AC BC ⊂面1ABC AE ∴⊥面1A BC1A B ⊂面1A BC 1AE A B ∴⊥在AMB ∆和ABE ∆中有:90,90BAM ABM BAM BEA ∠+∠=︒∠+∠=︒ ABM BEA ∴∠=∠同理:1BAE AA B ∠=∠1Rt Rt ABE A AB ∴∆∆ 1BE ABAB AA ∴=123AB AA =12439BE AB BB ∴==即在线段1BB 上存在点E 有149BE BB = 19. 解:(Ⅰ)当1a =时,16115a d =+,311615a d =+, 4611615()a d d=++.因为0d ≠,21d d +≥,或21d d-+≤,所以46a (,14][46,)∈-∞-+∞. (Ⅱ)由题意1134n n a -=+,116n ≤≤,314i j k b ++-=+.令3124i j k ++-+=,得7i j k ++=.因为,,i j k *∈N ,116i j k <<≤≤, 所以令1,2,4i j k ===,则2M ∈. 20. 解:(Ⅰ)直线AB 的方程:22y x =-+联立22222214y x x y m m =-+⎧⎪⎨+=⎪⎩消去y 得 222210x x m -+-= 由248(1)0m ∆=--= 得212m =又0m > 22m ∴= (Ⅱ)由图可知当椭圆C 在直线AB 的左下方或ABC ∆在椭圆内时,两者便无公共点①当椭圆C 在直线AB 的左下方时248(1)0m ∆=--< 解得202m <<②当且当点(1,2)C 在椭圆内时,ABC ∆在椭圆内221414m m∴+< 又0m > 2m ∴> 综上所述,当202m<或2m >时,椭圆与C 无公共点 (3)由(2)可知当222m <<时,椭圆C 与ABC ∆相交于不同的两个点,M N 又因为当1m =时,椭圆C 方程为2214y x +=,此时椭圆恰好过点,A B∴①当212m <≤时,,M N 在线段,A B 上,此时1ABC S S ∆≤= 当且仅当,M N 分别与,A B 重合时等号成立 ②当12m <≤时,点,M N 分别在线段,BC AC 上易得2(1,2)M m -,2(1,21)N m -O B M O A NMN O A C B S S S S S ∆∆∆∴=---矩形 22221211(11)(221)2m m m m =---------222221(11)m m =----- 令21t m =- 则01t << 211S t ∴=-+<综上可得OMN ∆面积S 的最大值为1 21. 解:(Ⅰ)由题意,得PQ =50-50cos θ .从而,当θ =2π3 时,PQ =50-50cos 2π3=75.即点P 距地面的高度为75m .(Ⅱ)由题意,得AQ =50sin θ ,从而MQ =60-50sin θ ,NQ =300-50sin θ .又PQ =50-50cos θ ,所以tan ∠NPQ =NQ PQ =6-sin θ1-cos θ ,tan ∠MPQ =MQ PQ =6-5sin θ5-5cos θ .从而y=tan ∠MPN =tan(∠NPQ -∠MPQ )=tan ∠NPQ -tan ∠MPQ1+tan ∠NPQ ⋅tan ∠MPQ=6-sin θ1-cos θ -6-5sin θ5-5cos θ1+6-sin θ1-cos θ × 6-5sin θ5-5cos θ=12(1-cos θ)23-18sin θ-5cos θ .令g (θ )=12(1-cos θ)23-18sin θ-5cos θ ,θ ∈(0,π),则g '(θ)=12×18(sin θ+cos θ-1)(23-18sin θ-5cos θ)2由g '(θ)=0,得sin θ +cos θ -1=0,解得θ = π2.当θ ∈(0,π2)时,g '(θ )>0,g (θ )为增函数;当θ ∈(π2,π)时,g '(θ )<0,g (θ )为减函数,所以,当θ = π2时,g (θ )有极大值,也为最大值.即当θ = π2时,y 取得最大值.22. 解:(Ⅰ)''1()2,(),(1,0)f x x a g x N x=-= ∴21,(),(3)6a f x x x f ==-∴=,(Ⅱ)[]2()(ln )(ln )y f xg x t x x t x x t =+=+-+令ln ,u x x =,在[]1,x e ∈ 时,'ln 10,u x =+>∴ln u x x =在[]1,e 单调递增,0u e ∴<<又22(21)y u t u t t =+-+-图象的对称轴122tu -=,抛物线开口向上 ①当1202tu -=≤即12t ≥时,2min y t t =-②当122t u e -=≥即122et -≤时,22min (21)y e t e t t =+-+- ③当1202t e -<<即12122e t -<<时,min 14y =- (Ⅲ) '22111()0x F x x x x -=-=>, 所以()F x 在区间(1,)+∞上单调递增. ∴当1x >时,()(1)0F x F >>①当(0,1)m ∈时,有12111(1)(1)mx m x mx m x x α=+->+-=,12222(1)(1)mx m x mx m x x α=+-<+-=,得12(,)x x α∈,同理12(,)x x β∈,∴ 由()F x 的单调性知120()(),()()F x F F F x <<αβ< 从而有12()()()()F F F x F x α-β<-,符合题设.②当0m ≤时,12222(1)(1)mx m x mx m x x α=+-≥+-=,12111(1)(1)m x mx m x mx x β=-+≤-+=,由()F x 的单调性知 120()()()()F F x F x F <β≤<≤α, ∴12()()()()F F F x F x α-β≥-,与题设不符 ③当1m ≥时,同理可得12,x x α≤β≥,得12()()()()F F F x F x α-β≥-,与题设不符. ∴综合①、②、③得(0,1)m ∈。