2016年高考(1381)吉林省长春市十一中2016届高三上学期12月月考试题 英语 Word版含答案
体验探究合作展示长春市十一高中2015-2016学年度高三上学期阶段性考试英语试题本试卷分第I卷（选择题）和第II卷（非选择题）两部分，满分150分，测试时间120分钟。
注意事项：1. 答题前, 考生先将自己的姓名、考号填写清楚, 将条形码准确粘贴在条形码区域内。
2. 选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字迹工整，笔迹清楚。
3. 请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。
4. 保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。
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。
AGrowing up in Philadelphia, Lieberman started cooking with his stay-at-home dad when he was seven. His food-loving family had two kitchens, and he quickly learned what was the best way to bake his cakes. Lieberman improved his kitchen skills greatly during a year abroad before college, learning from a cook in Italy and studying local specialties（地方特色菜）in Germany, Spain and France. At Yale, he was known for throwing dinner parties, single-handed frying and baking while mixing drinks for dozens of friends. Just for fun, he and some friends decided to tape a show named Campus Cuisine about his cooking. Lieberman was a real college student showing his classmates how to do things like making drinks out of dining-hall fruit. That helped the show become very popular among the students. They would stop Lieberman after classes to ask for his advice on cooking. Tapes of the show were passed around, with which his name went beyond the school and finally to the Food Network.Food Network producer Flay hopes the young cook will find a place on thenetwork television. He says Lieberman’s charisma is key.“Food TV isn’t about food anymore,” says Flay. “It’s about your personality and finding a way to keep people’s eyeballs on your show.”But Lieberman isn’t putting all his eggs in one basket. After taping the first season of the new show, Lieberman was back in his own small kitchen preparing sandwiches. An airline company was looking for someone to come up with a tasteful, inexpensive and easy-to-make menu to serve on its flights, Lieberman got the job.21. We can learn from the text that Lieberman’s family __________.A. love cooking at homeB. have relatives in EuropeC. often hold partiesD. own a restaurant22. The Food Network got to know Lieberman __________.A. at one of his partiesB. from his teachersC. on a television programD. through his taped show23. What does the underlined word “charisma” in the text refer to?A. A way to show one’s achievement.B. A natural ability to attract others.C. Lieberman’s after-class interest.D. Lieberman’s fine cooking skill.24. Why did the airline company give Lieberman the job?A. He could prepare meals in a small kitchen.B. He was famous for his shows on Food TV.C. He could cook cheap, delicious and simple meals.D. He was good at using eggs to make sandwiches.BWomen are friendly. But men are more competitive. Why? Researchers have found it’s all down to the hormone oxytocin (荷尔蒙催生素). Although known as the love hormone, it affects the sexes differently.“ Women tend to be social in their behavior. They often share with others. But men tend to be competitive. They are trying to improve their social statu s,” said Professor Ryan.Generally, people believe that the hormone oxytocin is let out in our body in various social situations and our body creates a large amount of it during positive social interactions (互动) such as falling in love or giving birth.But in a previous experiment Professor Ryan found that the hormone is also let out in our body during negative social interactions such as envy.Further researches showed that in men the hormone oxytocin improves the ability to recognize competitive relationships, but in women it raises the ability to recognize friendship.Professor Ryan’s recent experiment used 62 men and women aged 20 to 37. Half of the participants received oxytocin. The other half received placebo (安慰剂).After a week, the two groups switched with participants. They went through the same procedure with the other material.Following each treatment, they were shown some video pictures with different social interactions. Then they were asked to analyze the relationships by answering some questions. The questions were about telling friendship from competition. And their answers should be based on gestures, body language and facial expressions.The results indicated that, after treatment with oxytocin, men’s ability to correctly recognize competitive relationships improved, but in women it was the ability to correctly recognize friendship that got better.Professor Ryan thus concluded: “Our experiment proves that the hormone oxytocin can raise people’s abilities to better distinguish different social interactions. And the behavior differences between men and women are caused by biological factors that are mainly hormonal.”25. What causes men and women to behave differently according to the text?A. Oxytocin.B. Placebo.C. The gesture.D. The social status.26. What can we learn from Professor Rya n’s previous experiment?A. Oxytocin affects our behavior in a different way.B. Our body lets out oxytocin when we are deep in love.C. Oxytocin improves our abilities to understand people's behavior differences.D. Our body produces oxytocin when we feel unhappy about others’success.27. Why did Professor Ryan conduct the recent experiment?A. To know the differences between friendship and competition.B. To test the effect of oxytocin on the ability to recognize social interactions.C. To know the differences between friendship and competition.D. To know people’s different abilities to answer questions.28. The author develops the text by __________.A. explaining people's behaviorsB. describing his own experiencesC. discussing research experimentsD. distinguishing sexual differencesCIf doctors want to test you for something, they’ll usually take a blood or urine sample (尿样). But wouldn’t it be much more convenient if they just asked you to breathe through a special instrument?In fact, your breath can say a lot about you. In traditional Chinese medicine, doctors draw a conclusion about the health state of a patient based on the smell of his or her breath; trained dogs and rats can identify the smells of the breaths of people suffering from certain cancers; traffic police also monitor drivers’ alcohol consumption by testing their breaths.Just like blood and urine, your breath contains lots of “ metabolites ” --- the waste chemicals that the body produces, which vary from person to person. They are like personal health fingerprints, which is why scientists sometimes call them “breath prints”, according to Science Daily.Compared to blood or urine testing, breath testing takes only seconds instead of hours, and it requires neither a needle nor a container to hold the body fluids (体液). This means the test can be taken frequently to better detect early signs of diseases and monitor the progress of a medical treatment.On the other hand, as an identifier, you might think that breaths are not as reliable as fingerprints since they might change based on what you eat. However, researchers in Zurich, Switzerland mapped 11 healthy volunteers’chemical patterns by having them breathe through a special instrument, and they found that each pattern was unique and the patterns didn’t change much throughout the day, reported BBC.“Our goal is to develop breath analysis to the point where it becomes competitive with the established analysis of blood and urine,” said Malcolm Kohler, professor at the University Hospital Zurich.29. According to the text we know that __________.A. breath varies from person to person based on foodB. your breath may give you away if you are not carefulC. doctors can test one’s breath to find about his illnessD. dogs can identify people with certain cancers30. In comparison with blood or urine testing, breath testing is __________.A. comfortable and convincingB. traditional and reliableC. accurate and competitiveD. quick and convenient31. What is the author’s attitude toward breath testing?A. Doubtful.B. Approving.C. Unconcerned.D. Worried.32. What can we infer from the text?A. Breath testing is reliable and may have a bright future.B. Blood or urine testing will be less used in medical treatment.C. Doctors have found the best way to detect early signs of diseases.D. Traditional Chinese medicine is becoming more and more popular.DEvery year, the fascinating tourist destinations below are attracting travelers from home and abroad to St. Louis, which, founded in 1764 by French traders, today is the fifteenth largest urban area in the United States.★American Kennel Club Museum of the DogDog lovers who visit St. Louis won’t want to miss this 14,000-square-foot museum. Inside are over 500 paintings, prints, watercolors, and a variety of other dog art objects. The Museum is open year round, Tuesday through Saturday 10 AM to 4 PM, and Sunday 1 PM to 5 PM. Admission is $5 for adults,$2.50 for seniors, and $1 for children up to 14.★Anheuser Busch BreweryThe Anheuser Buxch Brewery tour is not just for beer lovers. The tour includes the historic Brew House. Then the tour continues to the modern Bevo Packaging Plant. The best will be the Budweiser Clydesdale stables. The tours are always free.★Gateway ArchDesigned by Eero Sarinen and Hannskari Bandel, it took over two years and 900 tons of stainless steel to build. It is the tallest of the country’s National Monuments. The Arch is part of the Jefferson National Expansion Memorial. About one million people per year come to the top of the Arch, where there is an observation platform providing a great view of the city.★The St. Louis ZooFirst version of the St. Louis Zoo opened in 1904 at the St. Louis World’s Fair, butnow it has grown into one of the chief zoos in the world. The passenger train takesvisitors around the Zoo, which contains over 9,000 animals of over 800 species.The Zoo is open every day but Christmas and New Year, with summer hours of 8AM to 7 PM, and hours the rest of the year of 9 AM to 5 PM. Admission to the Zoois free.33. If you are interested in how to make beer, you can visit __________.A. Gateway ArchB. The St. Louis ZooC. Anheuser Busch BreweryD. American Kennel Club Museum of the Dog34. Which of the following statements about Gateway Arch is TRUE?A. It was designed by two famous Italian architects.B. People can see the city clearly on the top of the arch.C. It took 900 tons of stainless steel and cement to build.D. It is the largest of the country’s National Monuments.35. If you plan to visit the St. Louis Zoo, you can go there _____.A. at 9:30 a.m. on New Year’s DayB. at 5:30 p.m. in winterC. at 8:30 a.m. in summerD. at 5:00 p.m. on Christmas Day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。
【吉林省长春十一中】2016届高三上学期12月月考数学(文科)试卷-答案
)()4+∞，三、解答题：（本大题共12n ⎛++ +⎝（Ⅱ在长方体中，112BO BC =1D 所成角的余弦值为）椭圆且向量12PF PF 的22212121||1()4x x kx x x x -=++-到直线l 的距离2|2|1k d k +=，4sin OM ON θ=263MON S ∴=△吉林省长春十一中2016届高三上学期12月月考数学（文科）试卷解析一、在每小题给出的四个选项中，只有一项是符合题目要求的。
(每题5分，共60分)1．【分析】由A与B，求出两集合的交集，确定出交集中的最小元素即可。
【解答】解：∵A={x|x=2n﹣1，n∈N*}={1，3，5，7，9，11，…}，B={y|y=5m+1，m∈N*}={6，11，16，…}，∴A∩B中最小元素为11，2．【分析】利用复数的运算法则、纯虚数的定义即可得出。
【解答】解：∵z==为纯虚数，∴=0，≠0，则m=﹣1．3．【分析】由程序框图知，最后输出的m 值是大于等于120分的人数，再根据表示的意义即可得出结论。
【解答】解：由程序框图可知，最后输出的m 值是大于等于120分的人数，即次考试数学分数不低于120分的同学的人数是m，因为表示这次考试数学分数不低于120分的“优分”率。
4．【分析】由等差数列的求和公式和性质可得=3•=2，解方程可得。
【解答】解：∵等差数列{a n}的前n项和为S n，且=，∴==2，由等差数列的求和公式和性质可得：===3•=2，∴=5．【分析】几何体为圆柱中挖去一个正四棱锥。
【解答】解：由三视图可知该几何体为圆柱挖去一个四棱锥得到的，圆柱的底面半径为1，高为2，棱锥的底面为正方形，边长为，棱锥的高为1，∴几何体的体积V=π×12×2﹣=2π﹣。
6．【分析】直线l1：2x﹣y+1=0的斜率为2，l2：x+2y=3的斜率为﹣，两条直线互相垂直，且α为锐角，β为钝角，即可得出结论。
【解答】解：直线l1：2x﹣y+1=0的斜率为2，l2：x+2y=3的斜率为﹣，两条直线互相垂直，且α为锐角，β为钝角，∴β=90°+α，7．【分析】利用同角三角函数的基本关系，以及三角函数在各个象限中的符号求cosθ﹣sinθ的值即可。
2016届吉林省长春市十一中高三上学期12月月考试题 物理 word版资料
2016届吉林省长春市十一中高三上学期12月月考试题 物理说明： 将选择题你认为正确的选项在答题卡上涂好，实验题和计算题在规定的答题区域内作答，不要在规定的区域以外答题。
考试结束后只交答题卡。
考试时间：90分钟； 总分：110分．一、选择题：每小题4分，共48分。
其中1-8小题，在每小题给出的四个选项中，有一个选项是正确的。
9-12小题有多个选项是正确的，全部选对得4分，选得对但不全的给2分。
1． A 、B 两辆汽车在平直公路上朝同一方向运动，如图所示为两车运动的v —t 图象，下面对阴影部分的说法正确的是A ．若两车从同一点出发，它表示两车再次相遇前的最大距离B ．若两车从同一点出发，它表示两车再次相遇前的最小距离C ．若两车从同一点出发，它表示两车再次相遇时离出发点的距离D ．表示两车出发时相隔的距离2．如图所示，一个边长为L 、三边电阻相同的正三角形金属框放置在磁感应强度为B 的匀强磁场中，线框平面与磁场垂直。
若通以图示方向的电流，电流强度I ，则金属框受到的磁场力为A ．0B ．ILBC ．43ILB D ．2 ILB3． 一个很高的容器内壁为圆柱形，里面装有n 个质量均为m 、大小相同的小球，容器的内半径与小球的半径之比为8：5，如图所示，现将小球从上至下依次编号为1、2、3、… n ，不计一切摩擦，重力加速度设为g ，则第4个小球对第5个小球的压力大小为A ． 4mgB ．4.5mgC ．5mgD ．6mg4．电源的电动势为E ＝30 V ，内阻为r ＝1 Ω，将它与一只“6 V ，12 W”的灯泡和一台电阻为2 Ω的小电动机串联组成闭合电路。
当灯泡正常发光时，若不计电机摩擦阻力损失的能量，电动机输出机械功率与输入电功率之比为A ．91%B ．82%n n -1 2 1n -2 ……C ．67%D ．60%5．M 、N 为两块水平放置的平行金属板，距平行板右端L 处有竖直屏，平行板板长、板间距均为L ，板间电压恒定。
2016届吉林长春高三数学12月月考试卷理科附答案
2016届吉林长春高三数学12月月考试卷（理科附答案）长春市十一高中2015-2016学年度高三上学期阶段考试数学试题（理）一、选择题（本大题共12小题，每题5分，共60分）1.已知集合，，则（）A.B.C.D.2.若复数满足：，则（）A.B.C.D.3.已知，则（）A.B.C.D.4.已知实数构成一个等比数列，则圆锥曲线的离心率为（）A．B．C．或D．或75.已知，，，则（）A．22B．48C．D．326.一个几何体的三视图如图所示，则该几何体的体积为（）A.B.C.D.7．某程序框图如图所示,若该程序运行后输出的值是,则（）A．B．C．D．8.设，且，则（）A．B．C．D．9.曲线与直线围成的封闭图形的面积是（）A.B.C.D.10．已知为区域（）内的任意一点，当该区域的面积为时，的最大值是（）A.B.C.D.11.是椭圆：上的动点，以为切点做椭圆的切线，交圆于两点，当的面积最大时，直线的斜率（）A.B.C.D.12.如图，正方体的棱长为，动点在对角线上，过点作垂直于的平面，记这样得到的截面多边形（含三角形）的周长为，设，则当时，函数的值域为（）A.B.C.D.二、填空题（本大题共4小题，每题5分，共20分）13.已知向量，，若与的夹角为钝角，则实数的取值范围是.14.已知三棱柱的侧棱垂直于底面，各顶点都在同一球面上，若该棱柱的体积为，，，则此球的表面积等于_______________.15.设为等差数列，从中任取个不同的数，使这4个数仍成等差数列，则这样的等差数列最多有个.16.给定下列四个命题：（1）若，，则；（2）是等比数列的前项和，则必有：；（3）函数的图像有对称轴；（4）是所在平面上一定点，动点P满足：，，则直线一定通过的内心；其中正确命题的序号为.三、解答题（本大题共6小题，共70分）17.（本小题满分12分）在中，已知，（1）求的取值范围；（2）若边上的高，求面积的最小值.18.（本小题满分12分）设数列满足：，，，（1）设，求证：为等差数列；（2）设，且的前项和为，证明：.19．（本小题满分12分）如图，在四棱锥中，底面为矩形，为等边三角形，，点为中点，平面平面.（1）求异面直线和所成角的余弦值；（2）求二面角的大小.20.（本小题满分12分）已知曲线的图形如图所示，其上半部分是半椭圆，下半部分是半圆，（），半椭圆内切于矩形，且交轴于点，点是半圆上异于的任意一点，当点位于点时，的面积最大. （1）求曲线的方程；（2）连接分别交于，求证：是定值.21.（本小题满分12分）设函数，（1）证明：是上的增函数；（2）设，当时，恒成立，求的取值范围.请考生在第22、23、24三题中任选一题做答，如果多做，则按所做的第一题记分.答时用2B铅笔在答题卡上把所选题目的题号涂黑.22.（本小题满分10分）选修4—1：几何证明选讲如图，正方形边长为2，以为圆心、为半径的圆弧与以为直径的半圆交于点，连结并延长交于点.（1）求证：；（2）求的值.23.（本小题满分10分）选修4—4：坐标系与参数方程极坐标系与直角坐标系有相同的长度单位，以原点为极点，以轴正半轴为极轴，曲线的极坐标方程为，曲线的参数方程为，（是参数，是常数）（1）求的直角坐标方程和的普通方程；（2）若与有两个不同的公共点，求的取值范围.24.（本小题满分10分）选修4—5：不等式选讲已知：（1）关于的不等式恒成立，求实数的取值范围；（2）若，且，求的取值范围.长春市十一高中2015-2016学年度高三上学期阶段（12月）考试数学试题（理）参考答案一、选择题（本大题共12小题，每题5分，共60分）题号123456789101112答案BDBCABCADDCD二、填空题（本大题共4小题，每题5分，共20分）13.且14.15.16.①②三、解答题（本大题共6小题，共70分）17.解析：（1）在中，，……2分,由，都是锐角，所以，当时……5分有最小值，故……6分（2）设，则，……….8分所以，即：，且，……分10所以：，当时“等号”成立面积的最小值为………12分18.解析：（1）由条件知：时，，所以：.............3分由于，即：，故是首项为，公差的等差数列 (5)分（2）由（1）知：，………….6分所以：…………8分所以：………….12分19.解析：解：取的中点，连接，为等边三角形，，又平面平面，……2分以为原点，过点垂直的直线为轴，为轴，为轴建立如图所示的空间直角坐标系.，不妨设,依题意可得：………3分（1）,从而,………5分于是异面直线和所成角的余弦值为………….6分（2）因为，所以是平面的法向量，……….8分设平面的法向量为，又，由即，令得………….10分于是………….11分从而二面角的大小为.……………12分20.解析（1）已知点在半圆上，所以，……………2分当半圆在点处的切线与直线平行时，点到直线的距离最大，此时的面积最大.所以，由于，所以，由，所以…………4分曲线C的方程为：或………5分（2），设，则有：：，令，，所以：同理：………8分所以：，又由，得，代入上式得………12分所以为定值21.解：若证明是上的增函数，只需证明在恒成立，即：-------4分设，所以：在上递减，上递增，最小值故：，所以：是上的增函数.------6分（2）由得：在上恒成立，------------8分设,则，所以在递增，递减，递增------------9分所以的最小值为中较小的，，所以：，即：在的最小值为，--------11分只需-------12分22.解：（1）由以D为圆心DA为半径作圆，而ABCD为正方形，∴EA为圆D的切线依据切割线定理得………………2分另外圆O以BC为直径，∴EB是圆O的切线，同样依据切割线定理得………………4分故………………5分（2）连结，∵BC为圆O直径，∴在RT△EBC中，有……………7分又在中，由射影定理得……………10分23.解：（1）由极直互化公式得，所以；---------------2分消去参数得的方程：----------------------4分（2）由（1）知是双曲线，是直线，把直线方程代入双曲线方程消去得：，-------------------------7分若直线和双曲线有两个不同的公共点，则，解得：-----------10分24.解：（1），所以，若，只需，即：---------------------5分（2）由于，所以，，又，所以，这样，所以---------------------10分。
【数学】吉林省长春市十一中2016届高三高考仿真模拟考试试卷(理)
长春市十一高中2016高考仿真模拟考试数学（理）试题本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分，满分150分.考试时间为120分钟，其中第Ⅱ卷22题－24题为选考题，其它题为必考题.考试结束后，将试卷和答题卡一并交回. 注意事项：1.答题前，考生必须将自己的姓名、准考证号码填写清楚，将条形码准确粘贴在条形码区域内.2.选择题必须用2B 铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚.3.请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效.4.保持卡面清洁，不要折叠、不要弄破、不准使用涂改液、刮纸刀.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，在每小题给出的四个选项中，只有一项是符合题目要求的．）1.已知集合{}02<-=x x x A ，{}2<=x x B ，则=B A C R )(（ ）A. (][)2,10,2 - B. []1,0 C. )2.2(- D. ),2()2,(+∞--∞ 2.已知复数cos isin =θ+θz ，R θ∈，则cos isin =θ+θn z n n ，*N ∈n ；若复数cos isin 1212ππ=+z ，那么301i 1+=-z （ ） A. 0 B. i C. 1 D. i -3.已知,R ∈a b ，则“4=ab ”是“直线012=-+ay x 与012=++y bx 平行”的( ) A ．充分必要条件 B ．充分而不必要条件 C ．必要而不充分条件 D ．既不充分也不必要条件4.现有2门不同的考试要安排在5天之内进行，每天最多进行一门考试，且不能连续两天有考试，那么不同的考试安排方案种数有（ ）种A. 6B. 8C. 12D. 16 5.函数x x x x f cos sin 42sin )(3-=的最小正周期与奇偶性分别是（ ） A ．2π，奇函数 B ．4π，奇函数 C ．2π，偶函数 D ．4π，偶函数 6.数列{}n a 满足21=a ，11-=+n n n a a a ，*N ∈n ，n S 是其前n 项和，则=100S （ ）A.2101 B. 2103 C.2105 D. 21077.某三棱锥的三视图如图所示，则该三棱锥的体积是（ ） A ．31 B ．21 C ．1 D ．238.对两个变量y 与进行回归分析，得到一组样本数据：),(11y x ， ),(22y x ，),(n n y x ，则下列不正确的说法是（ ）A. 若求得相关系数89.0-=r ，则y 与x 具备很强的线性相关关系，且为负相关B. 同学甲根据这组数据得到的回归模型1的残差平方和8.11=E ，同学乙根据这组数据得到的回归模型2的残差平方和4.22=E ，则模型1的拟合效果更好C.用相关指数2R 来刻画回归效果，模型1的相关指数48.021=R ，模型2的相关指数91.022=R ，则模型1的拟合效果更好D. 该回归分析只对被调查样本的总体适用 9.在ABC ∆中，若acb b a 3+=，B C sin 32sin =，则=A tan （ ） A.33B. 1C. 3D. 210.已知y x ,满足不等式组⎪⎩⎪⎨⎧≤-+≤--≥052011y x y x x ， 关于目标函数22--+-=y x y x z 最值的说法正确的是（ ）A. 最小值0，最大值9B. 最小值2，最大值9C. 最小值3，最大值10D. 最小值2，最大值10x11.过双曲线122=-n y m x （0,0>>n m ）上一点)3,5(-作圆m y x =+22的两条切线PB PA ,，切点为B A ,，且0=⋅，则双曲线的离心率为（ ）A.2 B.3 C. 2 D. 512.已知函数⎪⎩⎪⎨⎧<+->+=0,10,1)(x x x x x x x f ，若关于x 的方程a x x f =-)4(2有六个不同的实根，则实数a 的取值范围是（ ） A ．),2(+∞B ．⎥⎦⎤⎝⎛415,1 C ．)2,1( D ．)415,2( 第Ⅱ卷（非选择题，共90分）本卷包括必考题和选考题两部分，第13题－21题为必考题，每个试题考生都必须作答，第22题－24题为选考题，考生根据要求作答.二、填空题：（本大题共4小题，每小题5分，共20分）13.如图给出了一个程序框图，其作用是输入x 的值，输出相应的y 值，若要使输入的x 值与输出的y 值相等，则这样的x 值组成的集合为 .14.已知dx x a ⎰-=11325，则二项式ata t )6(-展开式中的常数项是 .（填数值） 15.正三角形ABC 的边长为2，将它沿高AD 翻折，使点B 与点C 间的距离为1，此时四面体ABCD 外接球表面积为__________ .16.已知函数)(x f y =，D x ∈，若存在常数C ，对D x ∈∀1，∃唯一的D x ∈2，使得C x f x f =)()(21，则称常数C 是函数)(x f 在D 上的“倍几何平均数”.已知函数x x f -=2)(，[]3,1∈x ，则)(x f 在[]3,1上的“倍几何平均数”是 ．三、解答题：解答应写出文字说明、证明过程或演算步骤. 17.（本小题满分12分） 已知数列{}n a 中，11=a ，⎪⎩⎪⎨⎧-+=+是偶数是奇数n n a n n a a n n n ,3,311， 设232-=n n a b ，n S 为数列{}n b 的前n 项和.（1）求2132,,,b b a a ；（2）证明数列{}n b 是等比数列； （3）求n S .18.（本小题满分12分）甲乙两个生物小组分别独立开展对某生物离开恒温箱的成活情况进行研究，每次试验一个生物，甲组能使生物成活的概率为31，乙组能使生物成活的概率为21，假定试验后生物成活，则称该试验成功，如果生物不成活，则称该次试验是失败的.（1）甲小组做了三次试验，求至少两次试验成功的概率.（2）如果乙小组成功了4次才停止试验，求乙小组第四次成功前共有三次失败，且恰有两次连续失败的概率.（3）若甲乙两小组各进行2次试验，设试验成功的总次数为ξ，求ξ的数学期望.19.（本小题满分12分）直角梯形ABEF 中，BE ∥AF ，︒=∠90FAB ，3323===AB BE AF ，D C ,分别是边AF BE ,上的点（不是端点），且AF CD ⊥，如图1所示；现沿CD 把直角梯形ABEF 折成一个︒120的二面角，连接部分线段后围成一个空间几何体，如图2所示. （1）求证：BE ∥平面ADF ；（2）当四棱锥ABCD F -体积最大时，求平面ADF 与平面BEF 所成的锐二面角的余弦值.20.（本小题满分12分）已知椭圆C ：)0(12222>>=+b a by a x 的离心率为23，且过点)22,2(．（1）求椭圆C 方程；（2）设不过原点O 的直线l ：)0(≠+=k m kx y ，与该椭圆交于Q P ,两点，直线OQOP ,的斜率依次为21,k k ，满足214k k k +=，试问：当k 变化时，2m 是否为定值？若是，求出此定值，并证明你的结论；若不是，请说明理由．21.（本小题满分12分） 已知函数x a x a x x f )2(ln 221)(2-+-=，R a ∈ （1）当0≤a 时，讨论函数)(x f 的单调性；（2）是否存在实数a ，对于任意),0(,21+∞∈x x ，且21x x <，有a x x x f x f >--2121)()(恒成立？若存在，求出a 的取值范围；若不存在，说明理由.请考生在第22、23、24三题中任选一题做答，如果多做，则按所做的第一题记分.答时用2B 铅笔在答题卡上把所选题目的题号涂黑. 22.（本小题满分10分）选修4—1: 几何证明选讲如图，直线AB 经过⊙O 上一点C ，且CB CA OB OA ==,，⊙O 交直线OB 于D E ,. （1）求证：直线AB 是⊙O 的切线； （2）若21tan =∠CED ，⊙O 的半径为3，求OA 的长.23.（本题满分10分） 选修4－4：坐标系与参数方程 在直角坐标系xOy 中，设倾斜角为α的直线：⎩⎨⎧+=+=ααsin 3cos 2t y t x ，（t 为参数）与曲线⎩⎨⎧==θθsin cos 2:y x C （θ为参数）相交于不同的两点B A ,．以O 为极点，Ox 正半轴为极轴，两坐标系取相同的单位长度，建立极坐标系. （1）求曲线C 的极坐标方程； （2）若3πα=，求线段AB 的长度．24.（本题满分10分） 选修4－5：不等式选讲 已知a a x x f --=)(，R ∈a （1）当2-=a 时，解不等式：221)(+-<x x f ； （2）若)(x f 的图像与x 轴围成的图形的面积为9，求a 的值.参考答案一、选择题：（本大题共12小题，每小题5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．）二、填空题：（本大题共4小题，每小题5分，共20分）13. {}3,1,014. 1515. π31316. 41三、解答题：解答应写出文字说明、证明过程或演算步骤. 17.解：（1）由递推关系：3413112=+=a a ，3146342323-=-=⨯-=a a ； 6123342321-=-=-=a b ，181239142333123342-=+-=-+=-=a a b .（2）由条件23212)6(312321231232312312323222122122221--+-=--+=--++=--=++++n n n n n n n n nn a n n a a n a a n a a a b b 3123233122=--=n n a a 所以数列{}n b 是首项为611-=b ，公比31=q 的等比数列.（3）由（2）知：n n n n qb b 3121)31(61111⨯-=-==-- 所以：41341311311611)1(1-⨯=--⨯-=--=n n n n q q b S 18.解：（1）甲小组做了三次实验，至少两次成功的概率277)31(32)31()(333223=+=C C A P （2）乙小组在4次成功前，共进行了6次实验，其中3次成功，3次失败，且恰好有两次连续失败，其中各种可能情况数为1224=A ，因此所求概率32321)21()21(12)(33=⨯⨯⨯=B P（3）由题意4,3,2,1,0=ξ91)21()32()31()0(2022003=⋅==C C P ξ31)21()32()21(3231)1(21220220212=⋅+⋅⋅==C C C C P ξ3613)21()32()21(3231)21()31()2(222121222=⋅+⋅⋅+⋅==C C P ξ61)21(3231)21()31()3(2122122=⋅⋅+⋅==C C P ξ 361)21()31()4(22===ξP故ξ的分布列为：。
吉林省长春市十一中2016届高三高考仿真模拟考试试卷
长春市十一高中2016届高三高考仿真模拟考试理 科 综 合 试 题本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题），满分300分，测试时间150分钟。
考试结束后，只交答题卡。
注意事项：1． 答题前，考生先将自己的姓名、准考证号码填写清楚，将条形码准确粘贴至条形码区域内2． 选择题必修使用2B 铅笔涂卡，非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。
3． 请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。
4． 作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑。
保持卡面清洁，不要折叠、不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀涂改。
可能用到的相对原子质量：H-1、C-12、N-14、O-16、S-32、Mg-24、Fe-56、Cl-35.5、 Al-27、Cu-64、Na-23、Ag-108、Ba-137；二、选择题（本题共8小题；每题6分，共48分。
其中14～18小题在每小题给出的四个选项中，只有一个是正确的；19～21小题有多个选项是正确的，选对的得6分，选对但不全的得3分，有选错的或不答的得0分。
）14． 如图所示，直线a 和曲线b 分别是在平直公路上行驶的汽车a 和b 的位置～时间（x-t ）图线。
由图可知 A ．在时刻t 1 ，a 、b 两车运动方向相同 B ．在时刻t 2 ，a 、b 两车运动方向相反C ．在t 1到t 2这段时间内，b 车的速率先减少后增加D ．在t 1到t 2这段时间内，b 车的速率一直比a 车的大15．如图所示，F 1、F 2为有一定夹角的两个力， x 为过O 点的一维坐标系，当x轴取什么方向时，F 1、F 2在x 轴上分力之和最F 2 大A ．F 1、F 2合力的方向B ．F 1、F 2中较大力的方向C ．F 1、F 2中较小力的方向D ．F 1、F 2角平分线的方向 16．如图所示，质量分别为m 、2m 的两物体A 、B 叠放在粗糙的水平面上，A 与B 接触面光滑。
吉林省长春市十一中2016届高三英语上学期12月月考试题
长春市十一高中2015-2016学年度高三上学期阶段性考试英语试题本试卷分第I卷（选择题）和第II卷（非选择题）两部分，满分150分，测试时间120分钟。
注意事项：1. 答题前, 考生先将自己的姓名、考号填写清楚, 将条形码准确粘贴在条形码区域内。
2. 选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字迹工整，笔迹清楚。
3. 请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。
4. 保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。
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。
AGrowing up in Philadelphia, Lieberman started cooking with his stay-at-home dad when he was seven. His food-loving family had two kitchens, and he quickly learned what was the best way to bake his cakes. Lieberman improved his kitchen skills greatly during a year abroad before college, learning from a cook in Italy and studying local specialties（地方特色菜）in Germany, Spain and France. At Yale, he was known for throwing dinner parties, single-handed frying and baking while mixing drinks for dozens of friends. Just for fun, he and some friends decided to tape a show named Campus Cuisine about his cooking. Lieberman was a real college student showing his classmates how to do things like making drinks out of dining-hall fruit. That helped the show become very popular among the students. They would stop Lieberman after classes to ask for his advice on cooking. Tapes of the show were passed around, with which his name went beyond the school and finally to the Food Network.Food Network producer Flay hopes the young cook will find a place on the network television. He says Lieberman’s charisma is key.“Food TV isn’t about food anymore,” says Flay. “It’s about your personality and finding a way to keeppeople’s eyeballs on your show.”But Lieberman isn’t putting all his eggs in one basket. After taping the first season of the new show, Lieberman was back in his own small kitchen preparing sandwiches. An airline company was looking for someone to come up with a tasteful, inexpensive and easy-to-make menu to serve on its flights, Lieberman got the job.21. We can learn from the text that Lieberman’s family __________.A. love cooking at homeB. have relatives in EuropeC. often hold partiesD. own a restaurant22. The Food Network got to know Lieberman __________.A. at one of his partiesB. from his teachersC. on a television programD. through his taped show23. What does the underlined word “charisma” in the text refer to?A. A way to show one’s achievement.B. A natural ability to attract others.C. Lieberman’s after-class interest.D. Lieberman’s fine cooking skill.24. Why did the airline company give Lieberman the job?A. He could prepare meals in a small kitchen.B. He was famous for his shows on Food TV.C. He could cook cheap, delicious and simple meals.D. He was good at using eggs to make sandwiches.BWomen are friendly. But men are more competitive. Why? Researchers have found it’s all down to the hormone oxytocin (荷尔蒙催生素). Although known as the love hormone, it affects the sexes differently.“ Women tend to be social in their behavior. They often share with others. But men tend to be competitive. They are trying to improve their social statu s,” said Professor Ryan.Generally, people believe that the hormone oxytocin is let out in our body in various social situations and our body creates a large amount of it during positive social interactions (互动) such as falling in love or giving birth.But in a previous experiment Professor Ryan found that the hormone is also let out in our body during negative social interactions such as envy.Further researches showed that in men the hormone oxytocin improves the ability to recognize competitive relationships, but in women it raises the ability to recognize friendship.Professor Ryan’s recent experiment used 62 men and women aged 20 to 37. Half of the participants received oxytocin. The other half received placebo (安慰剂).After a week, the two groups switched with participants. They went through the same procedure with the other material.Following each treatment, they were shown some video pictures with different social interactions. Then they were asked to analyze the relationships by answering some questions. The questions were about telling friendship from competition. And their answers should be based on gestures, body language and facial expressions.The results indicated that, after treatment with oxytocin, men’s ability to correctly recognize competitive relationships improved, but in women it was the ability to correctly recognize friendship that got better.Professor Ryan thus concluded: “Our experiment proves that the hormone oxytocin can raise people’s abilities to better distinguish different social interactions. And the behavior differences between men and women are caused by biological factors that are mainly hormonal.”25. What causes men and women to behave differently according to the text?A. Oxytocin.B. Placebo.C. The gesture.D. The social status.26. What can we learn from Professor Rya n’s previous experiment?A. Oxytocin affects our behavior in a different way.B. Our body lets out oxytocin when we are deep in love.C. Oxytocin improves our abilities to understand people's behavior differences.D. Our body produces oxytocin when we feel unhappy about others’success.27. Why did Professor Ryan conduct the recent experiment?A. To know the differences between friendship and competition.B. To test the effect of oxytocin on the ability to recognize social interactions.C. To know the differences between friendship and competition.D. To know people’s different abilities to answer questions.28. The author develops the text by __________.A. explaining people's behaviorsB. describing his own experiencesC. discussing research experimentsD. distinguishing sexual differencesCIf doctors want to test you for something, they’ll usually take a blood or urine sample (尿样). But wouldn’t it be much more convenient if they just asked you to breathe through a special instrument?In fact, your breath can say a lot about you. In traditional Chinese medicine, doctors draw a conclusion about the health state of a patient based on the smell of his or her breath; trained dogs and rats can identify the smells of the breaths of people suffering from certain cancers; traffic police also monitor drivers’alcohol consumption by testing their breaths.Just like blood and urine, your breath contains lots of “ metabolites ” --- the waste chemicals that the body produces, which vary from person to person. They are like personal health fingerprints, which is why scientists sometimes call them “ breath prints”, according to Science Daily.Compared to blood or urine testing, breath testing takes only seconds instead of hours, and it requires neither a needle nor a container to hold the body fluids (体液). This means the test can be taken frequently to better detect early signs of diseases and monitor the progress of a medical treatment.On the other hand, as an identifier, you might think that breaths are not as reliable as fingerprints since they might change based on what you eat. However, researchers in Zurich, Switzerland mapped 11 healthy volunteers’ chemical patterns by having them breathe through a special instrument, and they found that each pattern was unique and the patterns didn’t change much throughout the day, reported BBC.“Our goal is to develop breath analysis to the point where it becomes competitive with the established analysis of blood and urine,” said Malcolm Kohler, professor at the University Hospital Zurich.29. According to the text we know that __________.A. breath varies from person to person based on foodB. your breath may give you away if you are not carefulC. doctors can test one’s breath to find about his illnessD. dogs can identify people with certain cancers30. In comparison with blood or urine testing, breath testing is __________.A. comfortable and convincingB. traditional and reliableC. accurate and competitiveD. quick and convenient31. What is the author’s attitude toward breath testing?A. Doubtful.B. Approving.C. Unconcerned.D. Worried.32. What can we infer from the text?A. Breath testing is reliable and may have a bright future.B. Blood or urine testing will be less used in medical treatment.C. Doctors have found the best way to detect early signs of diseases.D. Traditional Chinese medicine is becoming more and more popular.DEvery year, the fascinating tourist destinations below are attracting travelers from home and abroad to St. Louis, which, founded in 1764 by French traders, today is the fifteenth largest urban area in the United States.★American Kennel Club Museum of the DogDog lovers who visit St. Louis won’t want to miss this 14,000-square-foot museum. Inside are over 500 paintings, prints, watercolors, and a variety of other dog art objects. The Museum is open year round, Tuesday through Saturday 10 AM to 4 PM, and Sunday 1 PM to 5 PM. Admission is $5 for adults,$2.50 for seniors, and $1 for children up to 14.★Anheuser Busch BreweryThe Anheuser Buxch Brewery tour is not just for beer lovers. The tour includes the historic Brew House. Then the tour continues to the modern Bevo Packaging Plant. The best will be the Budweiser Clydesdale stables. The tours are always free.★Gateway ArchDesigned by Eero Sarinen and Hannskari Bandel, it took over two years and 900 tons of stainless steel to build. It is the tallest of the country’s National Monuments. The Arch is part of the Jefferson National Expansion Memorial. About one million people per year come to the top of the Arch, where there is an observation platform providing a great view of the city.★The St. Louis ZooFirst version of the St. Louis Zoo opened in 1904 at the St. Louis World’s Fair, but now it has grown into one of the chief zoos in the world. The passenger train takes visitors around the Zoo, which contains over 9,000 animals of over 800 species.The Zoo is open every day but Christmas and New Year, with summer hours of 8 AMto 7 PM, and hours the rest of the year of 9 AM to 5 PM. Admission to the Zoo is free.33. If you are interested in how to make beer, you can visit __________.A. Gateway ArchB. The St. Louis ZooC. Anheuser Busch BreweryD. American Kennel Club Museum of the Dog34. Which of the following statements about Gateway Arch is TRUE?A. It was designed by two famous Italian architects.B. People can see the city clearly on the top of the arch.C. It took 900 tons of stainless steel and cement to build.D. It is the largest of the country’s National Monuments.35. If you plan to visit the St. Louis Zoo, you can go there _____.A. at 9:30 a.m. on New Year’s DayB. at 5:30 p.m. in winterC. at 8:30 a.m. in summerD. at 5:00 p.m. on Christmas Day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。
吉林省长春市十一中2016届高三高考仿真模拟考试试卷 理综化学 含答案
体验探究合作展示长春市十一高中2016届高三高考仿真模拟考试理科综合试题本试卷分第Ⅰ卷（选择题)和第Ⅱ卷（非选择题),满分300分,测试时间150分钟.考试结束后，只交答题卡.注意事项：1．答题前,考生先将自己的姓名、准考证号码填写清楚，将条形码准确粘贴至条形码区域内2．选择题必修使用2B铅笔涂卡，非选择题必须使用0。
5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。
3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效.4．作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑.保持卡面清洁，不要折叠、不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀涂改。
可能用到的相对原子质量：H-1、C—12、N-14、O—16、S—32、Mg—24、Fe-56、Cl-35。
5、Al—27、Cu-64、Na-23、Ag-108、Ba—137;第Ⅰ卷一、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.7．中国传统文化对人类文明贡献巨大,古文献中充分记载了古代化学研究成果,下列关于KNO3的古代文献,对其说明不合理的是目的古代文献说明A使用“…凡研消．(KNO3）不以铁碾入石臼，相激火生，祸不可测”—《天工开物》KNO3能自燃B 性质“［火药]乃焰消（KNO3）、硫磺、杉木炭所合，以为烽燧铳机诸药者"—《本草纲目》利用KNO3的氧化性C 鉴别区分硝石（KNO3)和朴消（Na2SO4): “以火烧之,紫青烟起，乃真硝石也"—《本草经集注》利用焰色反应D 提纯“…（KNO3）所在山泽,冬月地上有霜，扫取以水淋汁后，乃煎炼而成”-《开宝本草》溶解、蒸发、结晶8．用N A表示阿伏加德罗常数的值，下列说法正确的是A．1molCl2和足量的铁加热条件下反应，转移电子数一定为3N A B．28g乙烯和丙烯的混合物中含有双键数目小于N AC．常温下，PH=13的Ba(OH)2溶液,0。
2016届吉林省长春市十一中高三上学期期中考试数学(理)试题
长春市十一高中2015-2016学年度高三上学期期中考试数 学（理）试 题一、选择题（本大题共12小题，每题5分，共60分）1.已知集合{}0)3(<-=x x x A ，{}21<-=x x B ，则“A x ∈”是“B x ∈”的（ ） A.充分不必要条件 B.必要不充分条件C.充分条件D.既不充分也不必要条件2．如图，在复平面内，若复数21,z z 对应的向量分别是,，则 复数i z z z z z ---=2121所对应的点位于（ ）A ．第一象限B ．第二象限C ．第三象限D ．第四象限3．若向量b a ,的夹角为3π12==，则向量a 与向量b a 2-的夹角为（ ） A.6π B.3π C.32π D.65π4. n S 为等差数列{}n a 的前n 项和，若12113=+a a ，则=13S （ ） A ．60 B ．78 C ．156 D ．不确定5．已知2)tan(-=-απ，则=+αα2cos 2cos 1（ ） A ．3 B. 52C ．25- D. 3-6. 已知关于x 的不等式)0(03422><+-a a ax x 的解集为),(21x x ，则2121x x ax x ++的最小值是（ ） A.36 B.332 C. 362D.3347. 函数14)625sin(2-+=xx x y π的图象大致为（ ）8．如图所示程序框图中，输出=S （ ）A. 1-B. 0C. 1D.39.一个几何体的三视图如图所示，其中俯视图曲线部分是两个半径为1的圆弧，则这个几何体的体积是（ ） A. 48π- B. 28π- C. π-8 D. π28-10.由不等式组⎪⎩⎪⎨⎧≤≤≥-≥+1001x y e y x x确定的平面区域为M ，由不等式组⎩⎨⎧≤≤≤≤e y x 010确定的平面区域为N ，在N 内随机的取一点P ，则点P 落在区域M 内的概率为（ ）A.e 231-B. 231e- C. e 11- D. e 21-11.已知函数x e e x f x 2)(-=，方程01)()(2=-++a x af x f 有四个不同的实数根，则a 的取值范围为（ ）A. )1,(2ee +--∞ B. ),(2e -∞ C. )1,1(2e - D. )1,2(22e e -- 12．已知点P 是椭圆181622=+y x 上非顶点的动点，21,F F 分别为椭圆的左、右焦点，O 是坐标原点，若M 是21PF F ∠的平分线上一点，且01=⋅MP M F ，（ ） A ．[)3,0 B ．)22,0( C ．[)3,22 D ．(]4,01212121俯视图侧视图正视图9题图二、填空题（本大题共4小题，每题5分，共20分）13．函数)220)(sin(2)(πϕπωϕω<<->+=，x x f 的部分图象如图所示，则=)4(πf .14. 已知点)1,1(-P 在曲线ax x y +=2上，则曲线在点P 处的切线方程为_____________.15.定义在R 上的奇函数)(x f ，对于R x ∈∀，都有)43()43(x f x f -=+，且满足2)4(->f ，mm f 3)2(-=，则实数m 的取值范围是 .16.给出下列四个命题： ① R ∈∃α，57cos sin =-αα； ② 函数x x x f 2cos 2sin 3)(+=图像的对称中心是)0,62(ππ-k Z k ∈； ③ 函数xxx f cos 3sin )(-=是周期函数， π2是它的一个周期；④ )129)(tan 116(tan )131)(tan 114(tan +︒+︒=+︒+︒ 其中正确命题的序号是 .三、解答题（本大题共6小题，共70分） 17.（本小题满分12分）数列{}n a 满足：31=a ，1111=+-++n n a a . （1）求数列{}n a 的通项公式； （2）设na b n n -=1，求数列{}n b 的前n 项和n S .18．（本小题满分12分）在ABC ∆中，角C B A ,,的对边分别为c b a ,,，设函数a x b a x f +--=)621sin()()(π⎥⎦⎤⎢⎣⎡∈35,0πx 的值域为⎥⎦⎤⎢⎣⎡5,27.D 1C 1B 1A 1EDCBA（1）求b a ,的值；（2）若8<+b a ，且1872cos =C ，C 为锐角，求ABC ∆的AB 边上高h 的值．19. （本小题满分12分）如图，四棱柱1111D C B A ABCD -中，侧棱⊥1AA 底面ABCD ，AB ∥DC ，AD AB ⊥，2,11====AB AA CD AD ，E 为棱1AA 中点.（1）证明：CE C B ⊥11；（2）求二面角11C CE B --的正弦值20．(本小题满分12分）已知抛物线)0(22>=p px y 上点),3(t T 到焦点F 的距离为4． （1）求p t ,的值；（2）设B A ,是抛物线上分别位于x 轴两侧的两个动点，且5=⋅（其中 O 为坐标原点）．求证：直线AB 过定点，并求出该定点的坐标；21.（本小题满分12分）设函数ax xxx f -=ln )(. （1）若函数)(x f 在),1(+∞上为减函数，求实数a 的最小值；（2）若存在[]221,,e e x x ∈，使a x f x f +'≤)()(21成立，求实数a 的取值范围.22．(本小题满分10分)选修4——1：几何证明选讲如图所示，已知圆O 外有一点P ，作圆O 的切线PM ，M 为切点，过PM 的中点N 作割线NAB ，交圆于A 、B 两点，连接PA 并延长，交圆O 于点C ，连接PB 交圆O于点D ，若BC MC =. （1）求证：△APM ∽△ABP ;（2）求证：四边形PMCD 是平行四边形.23．（本小题满分10分）选修4——4：极坐标与参数方程选讲在直角坐标系xOy 中，以O 为极点，x 轴正半轴为极轴建立极坐标系．圆1C ，直线2C 的极坐标方程分别为θρsin 4=，22)4cos(=-πθρ．（1）求1C 与2C 的直角坐标方程，并求出1C 与2C 的交点坐标；（2）设P 为1C 的圆心，Q 为1C 与2C 交点连线的中点．已知直线PQ 的参数方程为⎪⎩⎪⎨⎧+=+=1233t b y at x （t 为参数，R t ∈），求b a ,的值．C24.（本题满分10分）选修4——5：不等式选讲 设函数313)(++-=ax x x f . （1）若1=a ，解不等式4)(≤x f ； （2）若)(x f 有最小值，求实数a 的取值范围.长春市十一高中2015-2016学年度高三上学期期中考试数 学 试 题 （理）参考答案一、选择题（本大题共12小题，每题5分，共60分）二、填空题（本大题共4小题，每题5分，共20分）13. 1 14. 43+=x y 15. 1-<m 或30<<m 16. ①③④ 三、解答题（本大题共6小题，共70分） 17.解析： （1）由条件知数列{}1+na 是首项为211=+a ，公差1=d 的等差数列，………3分所以：1121+=-+=+n n a n ，解得：n n a n 22+= ………………6分 （2）由111112+-=+=-=n n n n n a b n n ………………9分 所以：111111312121121+-=+-++-+-=+++=n n n b b b S n n ………………12分 18.解析：（1）由条件当⎥⎦⎤⎢⎣⎡∈35,0πx 时，⎥⎦⎤⎢⎣⎡-∈-32,6621πππx ，所以：⎥⎦⎤⎢⎣⎡-∈-1,21)621sin(πx ………2分（ⅰ）当b a >时，由条件知⎪⎩⎪⎨⎧=+-=+--5)(27)(21a b a a b a ，解得：3,4==b a ………………4分（ⅱ）当b a <时，由条件知⎪⎩⎪⎨⎧=+-=+--27)(5)(21a b a a b a ，解得：211,29==b a ………………6分（2）若8<+b a ，由（1）知：3,4==b a ，由1872cos =C ，即：1871cos 22=-C ，所以：65cos =C （C 为锐角）且611sin =C ………………8分 由余弦定理：5cos 2222=-+=C ab b a c ，所以5=c ………………10分ch C ab S ABC 21sin 21==∆，5552sin ==c C ab h ………………12分19.解析（1）由已知条件，以A 为原点，AB AA AD ,,1所在直线分别为z y x ,,轴建立空间直角坐标系，……1分则：)1,2,1(),1,0,1(),2,2,0(),0,2,0(111C C B A ，E 是1AA 中点， 则)0,1,0(E …………3分)1,0,1(11-=C B ，)1,1,1(--=CE ………5分所以：010111=++-=⋅C B ，故C B ⊥11，即：CE C B ⊥11……………6分（2）由已知条件：111CC C B ⊥结合（1）知⊥11C B 平面1CEC ，故平面1CEC 的一个法向量为)1,0,1(11-=C B …………3分由条件：)1,2,1(1--=B ，)1,1,1(--=，设平面CE B 1的一个法向量为),,(z y x =，则⎪⎩⎪⎨⎧=-+-=⋅=--=⋅021z y x z y x B ，取1,2,3-===z y x 得)1,2,3(-=…………10分 所以11C CE B --的余弦值722144cos ===θ故二面角11C CE B --的正弦值为721sin =θ…………12分 20．（1）由抛物线定义得，2423=⇒=+p p.....................2分 所以抛物线方程为x y 42=，.........3分 代入点),3(t T ，可解得32±=t . (5)分（2）设直线AB 的方程为n my x +=，),4(121y y A ，),4(222y y B 联立⎩⎨⎧+==nm y x xy 42消元得：0442=--n my y ，则：m y y 421=+，n y y 421-= (8)分由5=⋅得：516)(21221=+y y y y ，所以：2021-=y y 或421=y y （舍去） 即5204=⇒-=-n n ，所以直线AB 的方程为5+=my x ， 所以直线AB 过定点)0,5(P ………… 12分 21.解析：（1）函数定义域为：{}1,0≠>x x x 且，对函数)(x f 求导：a xx x f --='2ln 1ln )(， 若函数)(x f 在),1(+∞上为减函数，则0ln 1ln )(2≤--='a xx x f 在),1(+∞恒成立 所以：0)(max≤'x f ………2分 由a x a xx x f -+--=--='41)21ln 1(ln 1ln )(22，故当21ln 1=x ，即2e x =时，041)(m a x ≤-='a x f 所以： 41≥a ，所以a 的最小值是41………………5分（2）若存在[]221,,e e x x ∈，使a x f x f +'≤)()(21成立，则问题等价为：当[]221,,e e x x ∈时，a x f x f +'≤)()(maxmin 由（1）知：)(x f '在[]2,e e x ∈的最大值为a -41，所以41)(max=+'a x f 所以问题转化为：41)(min ≤x f ………………7分（ⅰ）当41≥a 时，由（1）知：)(x f 在[]2,e e 是减函数， 所以)(x f 的最小值是412)(222≤-=ae e e f ，解得：24121e a -≥ （ⅱ）当41<a 时，a x x f -+--='41)21ln 1()(2在[]2,e e 的值域是⎥⎦⎤⎢⎣⎡--a a 41, ①当0≥-a ，即0≤a 时， )(x f 在[]2,e e 是增函数，于是：41)()(min >≥-==e ae e e f x f ，矛盾 ②当0<-a ，即410<<a 时，由)(x f '的单调性和值域知：存在唯一的[]20.e e x ∈，使得0)(0='x f且当()0,x e x ∈时，0)(<'x f ，)(x f 为减函数；当()20,e x x ∈时，0)(>'x f ，)(x f 为增函数所以：)(x f 的最小值为41ln )(0000≤-=ax x x x f ， 即：41412141ln 141ln 1200>-=->-≥e e e x x a ，矛盾 综上有：24121ea -≥22. 证明：（1）∵PM 是圆O 的切线， NAB 是圆O 的割线， N 是PM 的中点，∴NB NA PN MN ⋅==22， ∴PNNABN PN =， 又∵BNP PNA ∠=∠， ∴△PNA ∽△BNP ， ∴PBN APN ∠=∠， 即PBA APM ∠=∠.∵BC MC =， ∴BAC MAC ∠=∠， ∴PAB MAP ∠=∠， ∴△APM ∽△ABP . ………5分（2）∵PBN ACD ∠=∠，∴APN PBN ACD ∠=∠=∠，即CPM PCD ∠=∠， ∴CD PM //， ∵△APM ∽△ABP ，∴BPA PMA ∠=∠， ∵PM 是圆O 的切线，∴MCP PMA ∠=∠，∴BPA PMA ∠=∠MCP ∠=，即MCP DPC ∠=∠， ∴PD MC //， ∴四边形PMCD 是平行四边形. ………10分C23.解析：（1）由极直互化公式得：4)2(:221=-+y x C 04:2=-+y x C ………4分联立方程解得交点坐标为)2,2(),4,0( ………5分（2）由（1）知：)2,0(P ，)3,1(Q 所以直线PQ ：02=+-y x ， 化参数方程为普通方程：122+-=ab x b y ， 对比系数得：⎪⎩⎪⎨⎧=-=22112ab b，2,1=-=b a ………10分24.解析（1）1=a ，4313)(≤++-=x x x f ，即：x x -≤-113x x x -≤-≤-1131，解得：210≤≤x ，所以解集为：⎥⎦⎤⎢⎣⎡21,0 ………5分 （2）⎪⎩⎪⎨⎧<+-≥++=31,4)3(31,2)3()(x x a x x a x f ，)(x f 有最小值的充要条件为：⎩⎨⎧≤-≥+0303a a ，即：33≤≤-a ………10分。
吉林省长春十一中2016届高三上学期月考化学试卷(12月份) 含解析
2015—2016学年吉林省长春十一中高三（上)月考化学试卷（12月份)一、选择题（共21小题，每小题2分,满分42分）1．最近我校主楼门前矗立起一块电子显示屏，时时显示校园周围环境的数据变化．其中一项是有关环境中PM2。
5的内容，下列有关PM2.5的说法不正确的是（）A．PM2.5是指直径为2。
5pm颗粒物B．PM2.5造成的雾霾天气，空气质量很差，对人体健康危害极大C．空气中的PM2。
5，表示每立方米空气中直径小于或等于2.5um的颗粒物的含量，则PM2.5可能导致空气形成气溶胶D．无风雾霾中的PM2.5的运动应属于布朗运动2．下列实验现象对应的结论正确的是（）选现象结论项A①中导管口冒气泡，手松开无现象气密性良好B②中KMnO4溶液紫红色褪去SO2具有漂白性C③中关闭K，气体颜色在热水中比冷水深NO2生成N2O4为吸热反应D④中烧瓶中形成喷泉Cl2易溶于CCl4 A．A B．B C．C D．D3．下列描述及热化学方程式均正确的是（）A．已知C2H6的燃烧热为1090 kJ•mol﹣1，则C2H6燃烧的热化学方程式为：C2H6（g）+3。
5O2（g）═2CO2（g）+3H2O（g）△H=﹣1090 kJ/molB．25℃，101kPa下,l mol C6H6燃烧生成CO2和液态水时放出3260 kJ热量，其热化学方程式为：C6H6(g）+7。
5O2（g）=6CO2(g)+3H2O （l）△H=﹣3260kJ•mol﹣1 C．已知常温下:H+（aq）+OH﹣（aq）═H2O（l）△H=﹣57.3 kJ/mol，则稀醋酸与稀NaOH溶液反应生成1 mol H2O(l）时也放出57。
3 kJ的热量D．已知2CO（g）+O2(g）═2CO2（g)△H=﹣566 kJ•mol ﹣1，则CO的燃烧热△H=﹣283 kJ•mol﹣14．常温下，下列各组离子在指定溶液中一定能大量共存的是（）A．0.1mol•L﹣1CH3COONa溶液：H+、Al3+、Cl﹣、NO3﹣B．含有NaNO3的溶液:H+、Fe2+、SO42﹣、Cl﹣C．能使甲基橙变红的溶液：K+、Na+、NO3﹣、Cl﹣D．由水电离产生的c（H+）=10﹣12mol•L﹣1的溶液：NH4+、SO42﹣、HCO3﹣、Cl﹣5．下列叙述不正确的是（）A．在标准状况下，将22.4L氨气溶于1L水中，得到1mol•L﹣1的氨水B．配制0。
【全国百强校】吉林省长春市第十一高中2016届高三上学期期中考试物理试题解析(解析版)
一、选择题：每小题4分，共48分。
其中1-7小题，在每小题给出的四个选项中，有一个选项是正确的。
8-12小题有多个选项是正确的，全部选对得4分，选得对但不全的给2分。
1．人造卫星1和2绕地球做匀速圆周运动的周期分别为T1和T2，设在卫星1、卫星2各自所在的高度上的重力加速度大小分别为g1、g2，则A．4/31122g Tg T⎛⎫= ⎪⎝⎭B．4/31221g Tg T⎛⎫= ⎪⎝⎭C．21122g Tg T⎛⎫= ⎪⎝⎭D．21221g Tg T⎛⎫= ⎪⎝⎭【答案】B考点：万有引力定律牛顿第二定律【名师点睛】（1）万有引力提供向心力21 22114r MmG ma mr Tπ==（2）卫星所在的高度上的重力加速度等于卫星在该处做匀速圆周运动的向心加速度：a g=(3)要注意轨道半径和卫星离地面的高度的关系为r R h=+2．下列有关物理学史或物理理论及应用的说法中，正确的是A．牛顿首先建立了描述运动所需的概念，如：瞬时速度、加速度及力等概念B．自然界中的四种基本相互作用有：万有引力作用、强相互作用、磁相互作用、电相互作用C．选择参考系后，若一个不受力的物体，能在这个参考系中保持静止或匀速直线运动状态，这样的参考系是惯性参考系D．避雷针是利用了最上面部分导体尖端的电荷密度很小，附近场强很弱，才把空气中的电荷导入大地【答案】C【解析】考点：物理学史2． 一带负电的粒子仅在电场力作用下沿x 轴正向运动，其电势能E P 随位移x 变化的关系如图所示， 其中0～x 2段是对称的曲线，2x ～3x 段是直线，则下列说法正确的是A ．1x 处电场强度为零B ．在1x 、2x 、3x 处的电势1ϕ、2ϕ、3ϕ的关系为1ϕ>2ϕ>3ϕC ．粒子在0～2x 段做变速运动，在2x ～3x 段做匀速直线运动D ．在2x ～3x 段该带负电的粒子速度增大 【答案】AB 【解析】试题分析：根据电势能与电势的关系P E q ϕ= ，场强与电势的关系E x ϕ∆=∆ ，得1PE E q x∆=∆ ， 故P E x - 的图象切线的斜率等于PE x∆∆，根据数学知识可知，x 1处切线斜率为零，则x 1处电场强度为零， 故A 选项正确；由图可知在1x 、2x 、3x 处的电势能123P P P E E E << ，而粒子带负电，带电粒子电势能 越大的地方电势越低，故在1x 、2x 、3x 处的电势1ϕ、2ϕ、3ϕ的关系为1ϕ>2ϕ>3ϕ，故B 选项正确； 在1x ~2x 之间的斜率不断增大，电场强度不断增大，粒子做变速直线运动，故C 选项错误；在2x ~3x 之间 的斜率不变，电场强度不变，粒子做匀减速直线运动，在2x ～3x 段该带负电的粒子速度减小，故D 选项错误。