高二第7次限时练
2019-2020年高二下学期第七次周练 数学试题 含答案
2019-2020年高二下学期第七次周练 数学试题 含答案1.函数y=x 2cosx 的导数为( )(A) y ′=2xcosx －x 2sinx (B) y ′=2xcosx+x 2sinx(C) y ′=x 2cosx －2xsinx (D) y ′=xcosx －x 2sinx2.下列结论中正确的是( )(A)导数为零的点一定是极值点(B)如果在附近的左侧，右侧，那么是极大值(C)如果在附近的左侧，右侧，那么是极小值(D)如果在附近的左侧，右侧，那么是极大值3．过曲线上的点的切线平行于直线，则切点的坐标为（ ）A ．（0，-1）或（1，0）B ．（1，0）或（-1，-4）C ．（0，-2）或（-1，-4）D ．（2，8）或（1，0） 4．下列结论中 ①若，则；②x x y x x f 21,1)(-='=则若； ③272)3(,1)(2-='==f x x f y 则若；正确的个数为（ ） A ． 0 B ． 1 C ． 2 D ． 35.如果10N 的力能使弹簧压缩10cm ，为在弹性限度内将弹簧从平衡位置拉到离平衡位置6cm 处，则克服弹力所做的功为（ ）(A)0.28J (B)0.12J (C)0.26J (D)0.18J6.函数y ＝ax 2＋1的图象与直线y ＝x 相切，则a ＝( )A ．B ．C ． D.．17．设处有导数，则（ ）A ．B ．C ．D ．8．曲线处的切线与坐标轴所围三角形的面积为（ ）A ．B ．C ．D ．9.曲线y=2x 3－3x 2共有____个极值.10．已知)5)(4)(3)(2)(1()(-----=x x x x x x f 则11． 求曲线上的点到直线的最短距离。
12．的导数 ；13．已知，当时， ；14．已知抛物线在点（2，1）处的切线方程为，则 ， 。
15. (本小题满分12分)一物体沿直线以速度（的单位为:秒,的单位为:米/秒）的速度作变速直线运动，求该物体从时刻t=0秒至时刻 t=5秒间运动的路程?16. (本小题满分12分) 已知曲线 y = x 3 + x －2 在点 P 0 处的切线 平行直线4x －y －1=0，且点 P 0 在第三象限,⑴求P 0的坐标; ⑵若直线 , 且 l 也过切点P 0 ,求直线l 的方程.17. (本小题满分14分)已知函数32()(1)48(2)f x ax a x a x b=+-+-+的图象关于原点成中心对称, 试判断在区间上的单调性,并证明你的结论.18．已知曲线，求：（１）曲线与直线平行的切线的方程。
【步步高】(新课标)高考语文二轮复习 限时综合小练7 语言基础知识+名篇名句默写+文言文阅读
小练7 语言基础知识＋名篇名句默写＋文言文阅读(用时：45分钟)一、语言基础知识1．下列各句中，加点的成语使用恰当的一句是 ( )A．我俩是总角之交．．．．，从读大学就在一起。
不经意间时光荏苒，到现在已经认识三十多年了，真挚的友谊从未发生过改变。
B．现在少数媒体放着有重要新闻价值的素材不去挖掘，反倒抓住某些明星的一点逸闻就笔走龙蛇．．．．，这种做法真是令人费解。
C．袁隆平培育出亩产926.6公斤的杂交水稻，再创新纪录，用“大师”一词已不足以形容其贡献，称他为“活着的国宝”才是实至名归．．．．。
D．在那流金铄石．．．．的岁月里，大家互相鼓励，共同进步，虽然学习环境苦、学习压力大，却依然熄灭不了我们心中理想与奋斗的火焰。
答案 C解析A项总角之交：幼年就相识的好朋友。
《诗经》中把儿童的发髻称作“角”，后来人们习惯称童年时代为“总角”。
B项笔走龙蛇：笔一挥动就呈现出龙蛇舞动的神态。
形容书法生动而有气势、风格洒脱，也指书写速度很快，笔势雄健活泼。
C项实至名归：有了真正的学识、本领或业绩，相应的声誉自然就随之而来。
符合语境。
D项流金铄石：能使金石熔化，比喻天气极热。
2．下列各句中，没有语病的一句是 ( ) A．今年下半年雅虎将致力于与“梦幻体育”和新闻有关的网站，“梦幻体育”是一种交互式的体育游戏，用户可以通过互相竞争赢得奖励。
B．有关商品房质量的投诉，这些年一直居高不下，原因之一就是目前建设中大量采用的现场浇铸施工工艺使得施工质量难以控制。
C．“文字恐惧症”最可怕的危害在于它可能使语言的教学行为完全丧失其教育学上的意义，甚至完全阻断有效阅读供给主体精神滋养的途径。
D．无论西方或东方，历史证明，一个大国的崛起过程，必然是国民意识的复苏过程，更是民族自信心、自豪感和凝聚力空前增强的时代。
答案 B解析A项成分残缺，应该在“致力于”后加上“建设”。
C项递进关系的两种结果颠倒了。
应将“使语言的教学行为完全丧失其教育学上的意义”与“完全阻断有效阅读供给主体精神滋养的途径”对调。
2021年高二下学期限时训练(理科)7含答案
2021年高二下学期限时训练（理科）7含答案班级姓名学号成绩1．若复数（其中为虚数单位）的实部与虚部相等，则订正反实数 .2．设向量，，则“”是“”成立的条件(选填“充分不必要”、“必要不充分”、“充要”、“既不充分也不必要”) .4.已知为实数，：点在圆的内部；：都有.（1）若为真命题，求的取值范围；（2）若为假命题，求的取值范围；（3）若“且”为假命题，且“或”为真命题，求的取值范围．5．如图，在直三棱柱中，，，，动点满足，当时，.（1）求棱的长；（2）若二面角的大小为，求的值.C A B P B 1 C 1 A 1 第5题图 订正反解：（1）由题意得，，解得，故为真命题时的取值范围为．……………………4分（2）若为真命题，则，解得，故为假命题时的取值范围．……………………8分（3）由题意得，与一真一假，从而当真假时有无解；……………………10分当假真时有解得．……………………12分∴实数的取值范围是．……………………14分解：（1）以点为坐标原点，分别为轴，建立空间直角坐标系，设，则，，，所以，，，………………2分当时，有解得，即棱的长为. (4)分（2）设平面的一个法向量为，则由，得，即，令，则，所以平面的一个法向量为，………………6分又平面与轴垂直，所以平面的一个法向量为，因二面角的平面角的大小为，所以121cos,2n n==，结合，解得. (10)分30107 759B 疛25557 63D5 揕25111 6217 戗&23240 5AC8 嫈23856 5D30 崰t33148 817C 腼TD31808 7C40 籀G*r。
高考语文一轮复习第7周专项限时练7文言文阅读
专项限时练7 文言文阅读(用时：40分钟满分：40分)(一)阅读下面的文言文，完成文后题目。
(20分)太子丹论[清]侯方域天下有绳墨之论，而挫英雄志士之气者，如以荆轲为盗是也。
况乎狃①于成败之形，而不察于确然之数，以忠臣孝子不得已之深心苦行，不痛惜其不幸，而反以为罪，则何以为后之国家者处．仇敌法也？昔者燕太子丹遣荆轲入秦，刺始皇不中，秦人来伐，王喜②斩丹头以献于秦，国竟以灭。
宋儒③曰：“丹有罪焉，故书斩④。
”呜呼！丹之心事，可以告之皇天后土而无憾矣！本意欲杀敌，不遂则死，已决绝于易水送荆轲之日矣，其书“斩”者，固其．所笑而不受也。
然则何以罪丹乎？曰：召衅也。
夫强秦之欲灭燕，岂待有衅哉？彼六国之见灭者，又坐．何衅也？刺亦亡，不刺亦亡，三尺童子能辨之矣。
即云幸而苟延焉．，乃蜉蝣之朝夕也，尚不得为蟪蛄之晦朔也。
有两人行而遇虎者，其一惶恐拜跪而乞哀以死，其一大呼奋臂斗不胜而死，而论者顾以乞哀为智，以大呼奋臂为狂佻而撄虎之怒，则何其愚且．谬也！且太子丹之遣荆轲也，或筹之熟矣。
秦之横行而不可御．，乃天下惊魂震魄，自慑伏于秦，非秦果能制天下也。
斩竿一呼而天下瓦解，相去几时？秦既无德以入人，其势又非蟠结而不可动，设一旦其万乘之君立死于匹夫之手，国有不内乱乎？天下豪杰因以知其不足畏。
而太子丹者且收合六国之馀烬以西向而前吾恐嬴氏之亡不待沛公之入关矣其以泄暴秦之威而倡天下之义莫此一击若也。
宋人有见于战国之世，圣人之道不明，先王之法不立，其公子养客而侠士轻生，故一切以儒者之论绳．之，恶聂政⑤之以私害公，而并及于轲；恶原、尝、春申之属，而并及于太子丹。
譬如有医之于．药者，不察其人之何病，而概以乌附⑥为不可用，日以宽和之剂养其肠胃，又安能起久痼而生之乎？宋之亡也，秦桧、汤思退之流，日以挑衅之说，挟持杀戮天下之谋臣战将，始终以讲和误其国。
仅有一大儒如考亭者，犹所见之如此，亦何怪乎三百年间，多议论而少成功哉！然则轲可为忠臣，丹可为孝子乎？曰：由今日论之，轲可为忠臣矣。
高二数学下学期限时训练7理 试题
〔第2题〕〔第1题〕时间是〔小 50 75 100 125 150 中学2021年春学期高二数学〔理〕限时训练〔7〕班级： 姓名： 学号： 得分：1.为理解学生课外阅读的情况，随机统计了n 名学生的课外阅读时间是，所得数据都在中，其频率分布直方图如下图．在[50 75)，中的频数为100，那么n 的值是 ．2．在如下图的算法流程图中，假设输出的y 的值是26，那么输入的x 的值是 ． 3．从集合{1，2，3，4，5，6，7，8，9}中任取一个数记为x ，那么log 2x 为整数的概率为 ． 4.用0，1，2，3，4，5这六个数字，完成下面问题 (1)可以组成多少个数字不重复的三位数？ (3)可以组成多少个数字不重复的三位奇数？(4)可以组成多少个数字不重复的小于1 000的自然数？ 〔5〕假设直线0ax by中的a b 、可以从六个数字中任取2个不同的数字，那么方程表示的不同的直线一共有多少条？5. 一个袋中装有五个形状大小完全一样的球，球的编号分别为1，2，3，4，5.〔1〕从袋中随机取两个球，写出所有的根本领件，并求取出的编号之和不大于4的概率; 〔2〕先从袋中随机取一个球，该球的编号为m ，将球放回袋中，然后再从袋中随机取一个球，该球的编号为n ，求2n m -≥的概率6. 设集合{}1,2,3,,(3)M n n =≥，记M 的含有三个元素的子集个数为n S ，同时将每一个子集中的三个元素由小到大排列，取出中间的数，所有这些中间的数的和记为n T . 〔1〕求33T S ，44TS ，55T S ，66T S 的值； 〔2〕猜测nnT S 的表达式，并证明之.7. 某高校在2021年的自主招生考试成绩中随机抽取100名学生的笔试成绩，按成绩分组，得到的频率分布表如下表所示.组号分组频数频率第1组[160,165)5第2组[165,170)①第3组[170,175)30②第4组[175,180)20第5组10合计100(1)请先求出频率分布表中①、②位置相应数据，再完成以下频率分布直方图；(2)为了能选拔出最优秀的学生，高校决定在笔试成绩高的第3、4、5组中用分层抽样的方法抽取6名学生进入第二轮面试，那么第3、4、5组每组各抽取多少名学生进入第二轮面试？(3)在(2)的前提下，决定在6名学生中随机抽取2名学生承受A考官进展面试，求：第4组至少有一名学生被考官A面试的概率8.A是集合P n＝{1，2，3，…，n} (n≥3，n∈N*)的子集，且A中恰有3个元素，同时这3个元素的和是3的倍数．记符合上述条件的集合A的个数为f(n)．〔1〕求f(3)，f(4)；〔2〕求f(n)〔用含n的式子表示〕．。
2021年高二下学期限时训练06含答案
2021年高二下学期限时训练06含答案班级姓名学号成绩
1.已知集合, ，则 .
2.命题“”的否定是．
3.函数的最小正周期为．
4.设函数是周期为5的奇函数，当时，
，则= .
5.已知函数，则的极大值为.
★6.在中，若，则= .
7.（本小题满分14分）
设集合，.
（1）当1时，求集合；
订正反订正反思：
（2）当时，求的取值范围．
7.函数y =的图象可由函数y = sin x的图象作两次变换得到，第一次变换是针对函数y =
sin x的图象而言的，第二次变换是针对第一次变换所得图象而言的．现给出下列四个变换：
A. 图象上所有点向右平移个单位；
B. 图象上所有点向右平移个单位；
C. 图象上所有点的横坐标变为原来的2倍（纵坐标不变）；
D. 图象上所有点的横坐标变为原来的倍（纵坐标不变）.
请按顺序写出两次变换的代表字母：．
15.（本小题满分14分）已知函数，其中角的终边经过点，且.
（1）求的值；
（2）求在上的单调减区间．
16.（本小题满分14分）设集合，.
（1）当1时，求集合；
（2）当时，求的取值范围．
20.设函数，其图象在点处切线的斜率为．
（1）求函数的单调区间（用只含有的式子表示）；
（2）当时，令，设，是函数的两个根，是，的等差中项，求证：（为函数的导函数）．
<33290 820A 舊325784 64B8 撸:R40519 9E47 鹇N39095 98B7 颷37393 9211 鈑Z29887 74BF 璿` 36947 9053 道。
高中英语真题：高中英语限时练7
高中英语限时练7阅读理解A“In real life, the daily struggles between parents and children are around these narrow problems of an extra hour, extra TV show, and so on” said Avi Sadeh, psychology professor at . “Too little sleep and more accidents,” he said.Sadeh and his colleagues found an extra hour of sleep can m ake a big difference. The children who slept longer, although t hey woke up more frequently during the night, scored higher o n tests, Sadeh reported in the March/April issue of journal Chil d Development.“When the children slept longer, their sleep quality was some what weak, but in spite of this their performance for study imp roved because the extra sleep was more significant than the r eduction in sleep quality. ” Sadeh said. “Some studies sugges ted that lack of sleep as a child affects development into adult hood and it’s more likely to develop their attention disorder wh en they grow older. ”In earlier studies, Sadeh’s team found that fourth graders slep t an average of 8. 2 hours and sixth graders slept an averageof 7. 7 hours.“Previous research has shown children in elementary school need at least nine hours of sleep a night on a regular basis, s aid Carl Hunt, director of the National Center on Sleep Disord ers Research in Bethesda, and high-school-age children need somewhat less, he said, adding the results of insufficient sleep could be serious.“A tired child is an accident waiting to happen,” Hunt said. “An d as kids get older, toys get bigger and the risks higher. ”Hunt also said too little sleep could result in learning and memory problems and long-term effects on school performance. “This is an important extension of what we already know, ” Hu nt said of Sadeh’s research, adding sleep is as important as n utrition(营养) and exercise to good health.“To put it into reality,” Hunt said, “parents should make sure th ey know when their children actually are going to sleep and th eir rooms are conducive to sleeping instead of playing. ”1. What is Child Development?A A new storyB A popular bookC. A periodical mag azine D A TV programme2. How many persons are exactly mentioned in the text?A OneB TwoC ThreeD Four3. The underlined phrase “conducive to” (in the last sentence) means ________.A helping to happenB influenced byC full ofD acceptable of4. Which of the following statements is NOT true according to the passage?A. There are some daily struggles between parents and childr en because of having nothing in common with extra rest time.B. The children who sleep longer are weak in their study.C. Lack of sleep as a child has great effect on their developm ent into adulthood.D. In general, children in elementary school need at least nine hours of sleep a night. CBABBFear may be felt in the heart as well as in the head, according to a study that has found a link between the cycles of a beati ng heart and the chance of someone feeling fear.Tests on healthy volunteers found that they were more likely t o feel a sense of fear at the moment when their hearts are co ntracting(收缩) and pumping blood around their bodies, compared with th e point when the heartbeat is relaxed. Scientists say the results suggest that the heart is able to influence how the brain res ponds to the fearful event, depending on which point it is at in its regular cycle of contraction and relaxation.Sarah Garfinkel at the Brington and said: “Our study shows for the first time that the way in which we deal with fear is diffe rent depending on when we see fearful pictures in relation to our heart.”The study tested 20 healthy volunteers on their reactions to fe ar as they were shown pictures of fearful faces. Dr Garfinkel s aid, “The study showed fearful faces are better noticed when t he heart is pumping than when it is relaxed. Thus our hearts c an also affect what we see and what we don’t see—and guide whether we see fear.”To further understand this relationship, the scientists also use d a brain scanner(扫描仪) to show how the brain influences the way the heart chang es a person’s feeling of fear.“We have found an important mechanism by which the heart and the brain ‘speak’ to each other to change our feelings and reduce fear,” Dr Garfinkel said.“We hope that by increasing our understanding about how fe ar is death with and ways that it could be reduced, we may be able to develop more successful treatments for anxiety disorders, and also for those who may be suffering from serious stre ss disorder.”5. What is the finding of the study?A. One’s heart affects how he feels fear.B. Fear is a result of one’s relaxed heartbeat.C. Fear has something to do with one’s health.D. O ne’s fa st heartbeats are likely to cause fear.6. The study was carried out by analyzing _________.A. volunteers’ heartbeats when they saw terrible pictures.B. the time volunteers saw fearful pictures and their health co nditions.C. volunteers’ reactions to horrible pictures and data from thei r brain scans.D. different pictures shown to volunteers and their heart-brain communication.7. Which of the following is closet in meaning to “mechanism”in Paragraph 6?A. Order.B. System.C. Machine.D. Treatment.8. This study may contribute to ________.A. treating anxiety and stress better.B. expla ining the cycle of fear and anxiety.C. finding the key to the heart-brain communication. D. understanding different fears in our h earts and heads.二、完形填空（1.5*20=30）I do a lot of management training each year for the Circle K C ompany. Among the topic we ___9___ in our classes is the __ _10___ of quality employees.What has ___11___ you to stay long enough to become a ma nager?” I asked.After a while a new manager ___12___ the question and said slowly, “It was a baseball ___13___.”Cynthia said that she ___14___ to take a Circle K clerk job as an interim(临时的) job ___15___ she looked for something else. On her secon d day behind the counter, she received a ___16___ from her n ine-year-old son, Jessie. He needed a baseball glove for Little League. She ___17___ that as a single woman, ___18___ was tight, a nd her first ___19___ would have to go for paying bills.When Cynthia arrived for work the ___20___ morning, Patricia , the store manager, handed her a box. “I overheard you ___2 1___ to your son yesterday,” she said, “and I know that it is __ _22___ to explain things to kids. This is a baseball glove for Jessie. I know you have to pay bills before you can buy gloves. You know we can’t ___23___ good people like you as ___24_ __ as we would like to, ___25___ we do care, and I want you t o know how ___26___ you are to us!”The thoughtfulness, empathy(同情) and love of the store manager ___27___ that people reme mber more how much an employer ___28___ than how much he pays.9. A. discuss B. write C. learn D. find10. A. managing B. sellingC. keepingD. seeking11. A. made B. ordered C. forced D. caused12. A. made B. took C. raised D. replied13. A. pole B. glove C. hole D. match14. A. ought B. liked C. had D. used15. A. when B. because C. while D. though16. A. letter B. call C. notice D. announcement17. A. turned out B. pointed outC. explained D. co mplained18. A. work B. food C. money D. clothing19. A. bill B. check C. day D. visit20. A. last B. first C. next D. past21. A. lying B. talking C. crying D. murmuring22. A. good B. easy C. hard D. necessary23. A. thank B. use C. employ D. pay24. A. many B. early C. soon D. much25. A. nor B. but C. and D. however26. A. kind B. terrible C. much D. important27. A. shows B. insistsC. realizesD. recognizes28. A. needs B. gets C. likes D. cares三、短文改错（共十小题，每小题1分，满分10分）Last year, I was addicted with playing computer games. I foun d it hard to breaking away from the bad habit. My teacher talk ed to my parents about this, and they made me to promise no t to play those games again. I tried hard, but I found it useless ly. The moment my fingers left the keyboard, I would feel very uncomfortable. Because I was determined to forget the game s, I still could not concentrate on the lessons giving in classes. Fortunately, psychological advisor in our school came to know this. He talks with me about his problem. At last, he offered hi s advices on how to get rid of the addiction. Now I can manag e to control myself.阅读 CBAB ACBA完形 ACDBB DCBCC BCBCD DBDADLast year, I was addicted wit playing computer games. I found it hard to breakin away from the bad habit. My teacher talked to my parents about this, and they made me to\ promise no t to play those games again. I tried hard, but I found it useless l. The moment my fingers left the keyboard, I would feel very uncomfortable. Becaus I was determined to forget the games, I still could not concentrate on the lessons givin in classes. Fortunately, psychological advisor in our school came to kno w this. He talk with me about hi problem. At last, he offered hi s advice on how to get rid of the addiction. Now I can manage to control myself.高中英语限时练7阅读理解A“In real life, the daily struggles between parents and children are around these narrow proble ms of an extra hour, extra TV show, and so on” said Avi Sadeh, psychology professor at . “Too little sleep and more accidents,” he said.Sadeh and his colleagues found an extra hour of sleep can make a big difference. The childr en who slept longer, although they woke up more frequently during the night, scored higher o n tests, Sadeh reported in the March/April issue of journal Child Development.“When the children slept longer, their sleep quality was somewhat weak, but in spite of this th eir performance for study improved because the extra sleep was more significant than the re duction in sleep quality. ” Sadeh said. “Some studies suggested that lack of sleep as a child affects development into adulthood and it’s more likely to develop their attention disorder wh en they grow older. ”In earlier studies, Sadeh’s team found that fourth graders slept an average of 8. 2 hours and sixth graders slept an average of 7. 7 hours.“Previous research has shown children in elementary school need at least nine hours of slee p a night on a regular basis, said Carl Hunt, director of the National Center on Sleep Disorder s Research in Bethesda, and high-school-age children need somewhat less, he said, adding the results of insufficient sleep could be s erious.“A tired child is an accident waiting to happen,” Hunt said. “And as kids get older, toys get big ger and the risks higher. ”Hunt also said too little sleep could result in learning and memory p roblems and long-term effects on school performance.“This is an important extension of what we already know, ” Hunt said of Sadeh’s research, ad ding sleep is as important as nutrition(营养) and exercise to good health.“To put it into reality,” Hunt said, “parents should make sure they know when their children ac tually are going to sleep and their rooms are conducive to sleeping instead of playing. ”1. What is Child Development?A A new storyB A popular bookC. A periodical magazine D A TV programm e2. How many persons are exactly mentioned in the text?A OneB TwoC ThreeD Four3. The underlined phrase “conducive to” (in the last sentence) means ________.A helping to happenB influenced byC full ofD acceptable of4. Which of the following statements is NOT true according to the passage?A. There are some daily struggles between parents and children because of having nothing i n common with extra rest time.B. The children who sleep longer are weak in their study.C. Lack of sleep as a child has great effect on their development into adulthood.D. In general, children in elementary school need at least nine hours of sleep a night. CBAB BFear may be felt in the heart as well as in the head, according to a study that has found a link between the cycles of a beating heart and the chance of someone feeling fear.Tests on healthy volunteers found that they were more likely to feel a sense of fear at the mo ment when their hearts are contracting(收缩) and pumping blood around their bodies, compared with the point when the heartbeat is re laxed. Scientists say the results suggest that the heart is able to influence how the brain resp onds to the fearful event, depending on which point it is at in its regular cycle of contraction a nd relaxation.Sarah Garfinkel at the Brington and said: “Our study shows for the first time that the way in which we deal with fear is different depending on when we see fearful pictures in relation to o ur heart.”The study tested 20 healthy volunteers on their reactions to fear as they were shown pictures of fearful faces. Dr Garfinkel said, “The study showed fearful faces are better noticed when t he heart is pumping than when it is relaxed. Thus our hearts can also affect what we see and what we don’t see—and guide whether we see fear.”To further understand this relationship, the scientists also used a brain scanner(扫描仪) to show how the brain influences the way the heart changes a person’s feeling of fear.“We have found an important mechanism by which the heart and the brain ‘speak’ to each ot her to change our feelings and reduce fear,” Dr Garfinkel said.“We hope that by increasing our understanding about how fear is death with and ways that it could be reduced, we may be able to develop more successful treatments for anxiety disord ers, and also for those who may be suffering from serious stress disorder.”5. What is the finding of the study?A. One’s heart affects how he feels fear.B. Fear is a result of one’s relaxed heartbe at.C. Fear has something to do with one’s health.D. O ne’s fast heartbeats are likely to cause fear.6. The study was carried out by analyzing _________.A. volunteers’ heartbeats when they saw terrible pictures.B. the time volunteers saw fearful pictures and their health conditions.C. volunteers’ reactions to horrible pictures and data from their brain scans.D. different pictures shown to volunteers and their heart-brain communication.7. Which of the following is closet in meaning to “mechanism” in Paragraph 6?A. Order.B. System.C. Machine.D. Treatment.8. This study may contribute to ________.A. treating anxiety and stress better.B. explaining the cycle of fear and anxi ety.C. finding the key to the heart-brain communication. D. understanding different fears in our hearts and heads.二、完形填空（1.5*20=30）I do a lot of management training each year for the Circle K Company. Among the topic we _ __9___ in our classes is the ___10___ of quality employees.What has ___11___ you to stay long enough to become a manager?” I asked.After a while a new manager ___12___ the question and said slowly, “It was a baseball ___13 ___.”Cynthia said that she ___14___ to take a Circle K clerk job as an interim(临时的) job ___15___ she looked for something else. On her second day behind the counter, she received a ___16___ from her nine-year-old son, Jessie. He needed a baseball glove for Little League. She ___17___ that as a single woman, ___18___ was tight, and her first ___19___ would have to go for paying bills.When Cynthia arrived for work the ___20___ morning, Patricia, the store manager, handed h er a box. “I overheard you ___21___ to your son yesterday,” she said, “and I know that it is __ _22___ to explain things to kids. This is a baseball glove for Jessie. I know you have to pay bi lls before you can buy gloves. You know we can’t ___23___ good people like you as ___24___ as we would like to, ___25___ we do care, and I want you to know how ___26___ you are to us!”The thoughtfulness, empathy(同情) and love of the store manager ___27___ that people remember more how much an emplo yer ___28___ than how much he pays.9. A. discuss B. write C. learn D. find10. A. managing B. selling C. keeping D. seeking11. A. made B. ordered C. forced D. caused12. A. made B. took C. raised D. replied13. A. pole B. glove C. hole D. match14. A. ought B. liked C. had D. used15. A. when B. because C. while D. though16. A. letter B. call C. notice D. announcement17. A. turned out B. pointed outC. explained D. complained18. A. work B. food C. money D. clothing19. A. bill B. check C. day D. visit20. A. last B. first C. next D. past21. A. lying B. talking C. crying D. murmuring22. A. good B. easy C. hard D. necessary23. A. thank B. use C. employ D. pay24. A. many B. early C. soon D. much25. A. nor B. but C. and D. however26. A. kind B. terrible C. much D. important27. A. shows B. insists C. realizes D. recognizes28. A. needs B. gets C. likes D. cares三、短文改错（共十小题，每小题1分，满分10分）Last year, I was addicted with playing computer games. I found it hard to breaking away from the bad habit. My teacher talked to my parents about this, and they made me to promise not to play those games again. I tried hard, but I found it uselessly. The moment my fingers left t he keyboard, I would feel very uncomfortable. Because I was determined to forget the games, I still could not concentrate on the lessons giving in classes.Fortunately, psychological advisor in our school came to know this. He talks with me about hi s problem. At last, he offered his advices on how to get rid of the addiction. Now I can manag e to control myself.阅读 CBAB ACBA完形 ACDBB DCBCC BCBCD DBDADLast year, I was addicted wit playing computer games. I found it hard to breakin away from th e bad habit. My teacher talked to my parents about this, and they made me to\ promise no t to play those games again. I tried hard, but I found it uselessl. The moment my fingers left t he keyboard, I would feel very uncomfortable. Becaus I was determined to forget the games, I still could not concentrate on the lessons givin in classes.Fortunately, psychological advisor in our school came to know this. He talk with me about hi problem. At last, he offered his advice on how to get rid of the addiction. Now I can manage t o control myself.。
必修二 限时提分练七
限时提分练七必修②Unit 2The Olympic Games Ⅰ.阅读理解A[2021·泰安市高三质量检测]Myles Kerr knew that being a Marine (水兵) comes with a lot of responsibility, but despite the huge weight he has on his shoulders, he has not forgotten the essence of being a public servant—that of being human.Seven years ago, a photo of a Marine and a young boy running a marathon immediately went viral after it was shared on social media. But what seemed like a simple image packed a much deeper backstory. This story happened in 2013, but its relevance is still as powerful as ever.The pair were running The Jeff Drench Memorial 5K in Charlevoix, Michigan when Myles Kerr came across Brandon Fuchs, a 9yearold boy struggling to keep up with the rest of his group. Brandon, exhausted and out of breath, asked the Marine, “Will you run with me？”People who had their eyes on the prize would have refused, but the 19yearold was different. Being a Marine, he knew exactly what he should do. Kerr put aside his goal of beating his mates and instead slowed down to accompany the struggling boy to the finish line.Because he chose to help the boy, the Marine ended up with the slowest time in his age group, according to the 5K results online.Though he might have lost the race, the Marine won over people's hearts. His act of kindness was celebrated on social media.Kerr didn't expect that his simple gesture would attract so much attention. He responded to a tweet praising his actions saying, “I was just doing what any man would do, but thank you！”He also tweeted that he received gifts from the Fuchs family for helping out Brandon.To Kerr, being a Marine was more than just being trained for combat—it also required learning how to be kind and compassionate towards the citizens they serve.1．What was Myles Kerr seven years ago?A．A Marine.B．A public servant.C．A marathon runner. D．A Michigan citizen.2．What is Myles Kerr's original goal to participate in the marathon?A．To win over people's hearts.B．To accompany the boy.C．To get the best score in his age group.D．To build up his body.3．Which of the following best describe Myles Kerr?A．Kind and unselfish.B．Enthusiastic and generous.C．Responsible and proud.D．Stubborn and helpful.4．What does the story mainly convey?A．Being a Marine bears a lot.B．Kindness matters more than prizes.C．Being a Marine means a public servant.D．Good actions spread quickly.B[2021·临沂市模拟]By now it's almost common knowledge that spending time in nature is good for you. Areas with more trees tend to be less polluted, so spending time there allows you to breathe more easily. Spending time outdoors has been linked with reduced blood pressure and stress, and seems to motivate people to exercise more. So it'll come as no surprise that there's research showing that spending time in nature is good, which has been known for thousands of years. There're dozens of papers showing that.University of Exeter Medical School researcher Mathew P. White said, “We get this idea,because patients are coming to us and they're saying, ‘Doctor, how long should I spend？’ and the doctor is saying, I don't really know.” So White and his team decided to find out by using data collected from nearly 20,000 people in England through the Monitor of Engagement with the Natural Environment Survey. And their answer? Two hours a week. People who spent at least that much time—either all at once or totaled over several shorter visits—were more likely to report good health and psychological wellbeing than those with no nature exposure. Remarkably, the researchers found that less than two hours offered no significant benefits.So what's so special about two hours? “I have absolutely no idea. Really. We didn't have an apriori (由因及果的) guess at what this would be. It emerged. And I'd be lying if I said we predicted this. I don't know.” Even more noteworthy, the twohour benchmark (基准) applied to men and women, to older and younger folks, to people from different ethnic backgrounds, occupational groups, socioeconomic levels and so on. Even people with longterm illnesses or disabilities benefited from time spent in nature—as long as it was at least 120 minutes per week.While the findings are based on a tremendous number of people, nobody knows why or how nature has this benefit. “I want to be really clear about this. This is in very early stages. We're not saying everybody has to do 120. What research do we need to take this to the next step before doctors can have the true coincidence to work with their patients? But it's certainly a starting point，” White said.5．What is the first paragraph mainly about?A．The benefits of spending time in nature.B．The research on spending time in nature.C．The characteristics of spending time in nature.D．Common knowledge of spending time in nature.6．What can we infer from the result of White and his team's survey?A．The time spent in nature should be 2 hours a week all at once.B．2 hours a week at least in nature is beneficial to whomever you are.C．The time spent in nature should be 2 hours a week, no more, no less.D．2 hours a week in nature is too long for people with longterm illnesses.7．What does White expect of the findings?A．They will be in early stages.B．They will be based on many people.C．They will help all people go out in nature.D．They will be improved and further research will be done.8．Where is this text most likely from?A．A diary. B．A guidebook.C．A magazine. D．A novel.Ⅱ.七选五[2021·潍坊市高三模拟]Water SkiingWater skiing is an exciting water sport that can be a ton of fun. It takes a little patience to learn, but once you do, water skiing is a sport you can enjoy whenever you have a boat and enough flat water.__1__ Every water skier needs water skis (滑水板) and they differ depending on the size of the skier and the experience level of the skier. Of course, no one can water ski alone, so you will need to find at least two people to go with you on your water skiing adventure. You and everyone you go with will have more fun if the friends you go with also want to water ski. __2__ After you have the boat, the people, and the skis, you will also need a water skiing cable (缆绳) and a life jacket.For your firsttime water skiing, you may want to either take a lesson from an expert or find a friend that has experience to teach you. __3__ The observer rides in the boat, but watches the water skier for any signals and helps the driver know when to start and stop.The person skiing starts by crouching (蹲伏) in the water; this is called a deep water start. The skis will float, but you want your body to be in a crouching position in the water. Your skis'tips should be pointing out of the water. __4__ When you are ready, you give a signal to the driver of the boat, who starts speeding. Ideally you are pulled into an upright position with your skis underneath you, gliding along the surface of the water. __5__A．You need a boat naturally.B．Most people just enjoy regular water skiing.C．The idea is to ski on the surface of the water.D．Having a successful start will most likely take a few tries.E．Your arms will be outstretched holding onto the cable tightly.F．Before you start water skiing, there are a few supplies you'll need.G．Of your two helpers, you need one to drive the boat and one to observe.Ⅲ.语法填空[2021·黑龙江省模拟]When Sarasota students took 1.________ bite of a freshly picked watermelon or mango, they knew the fruit came from a fiveacre farm right in Sarasota instead of thousands of miles away, 2.________ (fresh) and more nutritional.The Sarasota Farm to School program is 3.________ (actual) part of an initiative (倡议) headed by the Florida Department of Agriculture and Consumer Services, 4.________ (plan) to increase Floridabased produce served in schools and offer healthier choices to students. In addition to nutritional value it offers, the program is 5.________ (education) as well, allowing students to get involved in the agricultural side of working in the gardens.Students from the program come out each Monday 6.________ (harvest) crops that will eventually go to 67 Sarasota County cafeterias. The farm is crowded 7.________ various kinds of fruits, squash, sunflowers and corn. For now, the farm is in its first growing season. Crops that 8.________ (grow) in May are just starting to be harvested. Outside of the farm, students are engaging in (参与) some taste tests with 9.________ they get from the gardens. It's through these tasting sessions that either a student or a farmer can get some 10.________ (inform) about what crops should populate the farm.Ⅰ.阅读理解A语篇类型：记叙文主题语境：人与社会——乐于助人——“善良比奖品更重要”【语篇解读】文章讲述了一名水兵陪伴一个小男孩跑完马拉松的故事。
2021学年河北省保定市某校高二(下)第七次周练数学试卷(有答案)
2021学年河北省保定市某校高二（下）第七次周练数学试卷一、选择题（共8小题，每小题3分，满分24分）1. 函数y＝x2cos x的导数为（）A.y′＝2x cos x−x2sin xB.y′＝2x cos x+x2sin xC.y′＝x2cos x−2x sin xD.y′＝x cos x−x2sin x2. 下列结论中正确的是（）A.导数为零的点一定是极值点B.如果在x0附近的左侧f′(x)>0，右侧f′(x)<0，那么f(x0)是极大值C.如果在x0附近的左侧f′(x)>0，右侧f′(x)<0，那么f(x0)是极小值D.如果在x0附近的左侧f′(x)<0，右侧f′(x)>0，那么f(x0)是极大值3. 过曲线y=x3+x−2上的点P的切线平行于直线y=4x−1，则切点P的坐标为（）A.(0, −1)或(1, 0)B.(1, 0)或(−1, −4)C.(−1, −4)或(0, −2)D.(1, 0)或(2, 8)4. 下列结论中：①若y=−cos x，则y′=−sin x；②若f(x)=√x ，则y′=2x√x；③若y=f(x)=1x ，则f′(3)=−227；正确的个数为（）A.0B.1C.2D.35. 如果10N的力能使弹簧压缩10cm，为在弹性限度内将弹簧从平衡位置拉到离平衡位置6cm处，则克服弹力所做的功为（）A.0.28JB.0.12JC.0.26JD.0.18J6. 函数y=ax2+1的图象与直线y=x相切，则a=()A.1 8B.14C.12D.17. 设f(x)在x=2处有导数，则lim△x→0f(2+△x)−f(2−△x)2△x=()A.2f′(2)B.12f′(2) C.f′(2) D.4f′(2)8. 曲线y=e 12x在点(4, e2)处的切线与坐标轴所围三角形的面积为（）A.92e2 B.4e2 C.2e2 D.e2二、填空题（共6小题，每小题3分，满分18分）曲线y=2x3−3x2共有________个极值．已知f(x)=(x−1)(x−2)(x−3)(x−4)(x−5)，则f′(1)=________．曲线y=ln(2x−1)上的点到直线2x−y+3=0的最短距离是________．y=x−sin x2⋅cos x2的导数y′=________．已知y=sin x1+cos x，x∈(−π, π)，当y′=2时，x=________．已知抛物线y=ax2+bx−5在点(2, 1)处的切线方程为y=−3x+7，则a=________，b=________．三、解答题（共5小题，满分52分）一物体沿直线以速度v(t)=2t−3（t的单位为：秒，v的单位为：米/秒）的速度作变速直线运动，求该物体从时刻t=0秒至时刻t=5秒间运动的路程？已知曲线y＝x3+x−2在点P0处的切线l1平行直线4x−y−1＝0，且点P0在第三象限，（1）求P0的坐标；（2）若直线l⊥l1，且l也过切点P0，求直线l的方程．已知函数f(x)=ax3+(a−1)x2+48(a−2)x+b的图象关于原点成中心对称，试判断f(x)在区间[−4, 4]上的单调性，并证明你的结论．已知曲线y=f(x)=5√x，求：（1）曲线与直线y=2x−4平行的切线的方程．（2）过点P(0, 5)且与曲线相切的直线的方程．已知函数f(x)=ln|x|(x≠0)，函数g(x)=1f′(x)+af′(x)(x≠0)（1）当x≠0时，求函数y=g(x)的表达式；（2）若a>0，函数y=g(x)在(0, +∞)上的最小值是2，求a的值；（3）在（2）的条件下，求直线y=23x+76与函数y=g(x)的图象所围成图形的面积．参考答案与试题解析2021学年河北省保定市某校高二（下）第七次周练数学试卷一、选择题（共8小题，每小题3分，满分24分）1.【答案】A【考点】导数的运算【解析】利用两个函数的积的导数法则，求出函数的导函数．【解答】y′＝(x2)′cos x+x2(cos x)′＝2x cos x−x2sin x2.【答案】B【考点】函数在某点取得极值的条件【解析】根据导函数的根为x0，且在x0附近的左侧f′(x)>0，右侧f′(x)<0，那么f(x0)是极大值；导函数的根为x0，且在x0附近的左侧f′(x)<0，右侧f′(x)>0，那么f(x0)是极小值，判断出选项．【解答】解：导数为零的点且左右两边的符号不同才是极值点故A错如果在x0附近的左侧f′(x)>0，右侧f′(x)<0，则函数先增后减，则f(x0)是极大值如果在x0附近的左侧f′(x)<0，右侧f′(x)>0，则函数先减后增，则f(x0)是极小值故选B3.【答案】B【考点】利用导数研究曲线上某点切线方程【解析】先求导函数，由导数的几何意义令导函数等于4建立方程，求出方程的解，即可求出切点的横坐标，代入原函数即可求出切点坐标．【解答】解：由y=x3+x−2，求导数得y′=3x2+1，由已知得3x2+1=4，解之得x=±1．当x=1时，y=0；当x=−1时，y=−4．∴切点P0的坐标为(1, 0)或(−1, −4)．故选B4.【答案】C导数的运算【解析】根据初等函数的导数公式，进行判断即可，【解答】解：因为(cos x)′=−sin x，所以①错误，因为(x )′=(x−12)′=−12x−32=2√x3=2x x，所以②正确，因为f(x)=1x2，所以，f′(x)=−2x−3，所以f′(3)=−227，所以③正确．故正确的个数为2个，故选：C．5.【答案】D【考点】根据实际问题选择函数类型【解析】因为F＝10Nl＝10cm＝0.1m，所以k=100.1=100，由此能求出在弹性限度内将弹簧从平衡位置拉到离平衡位置6cm处，克服弹力所做的功．【解答】F＝kl∵F＝10N，l＝10cm＝0.1m∴k=100.1=100∴在弹性限度内将弹簧从平衡位置拉到离平衡位置6cm处，克服弹力所做的功：w＝Ep=12×k×l2=12×100×(0.06)2＝0.18J．6.【答案】B【考点】函数与方程的综合运用【解析】因为函数与直线相切，则函数与直线有一个公共点，则把两个解析式联立得到一个一元二次方程，利用△=0求出a即可．【解答】解：把两个解析式联立得方程ax2−x+1=0，当a≠0时，由△=0即得a=14故答案为B．7.C【考点】导数的几何意义【解析】根据导数的定义即可得到结论．【解答】解：lim△x→0f(2+△x)−f(2−△x)2△x=lim△x→0f(2+△x)−f(2)−[f(2−△x)−f(2)]2△x=1 2lim△x→0f(2+△x)−f(2)△x+12lim△x→0f(2−△x)−f(2)−△x=12f′(2)+12f′(2)=f′(2)，故选：C．8.【答案】D【考点】利用导数研究曲线上某点切线方程【解析】利用导数求曲线上点切线方程，求直线与x轴，与y轴的交点，然后求切线与坐标轴所围三角形的面积．【解答】解：∵曲线y = e 12 x，∴y′ = e12x × 12，切线过点(4, e2)∴f′(x)|x＝4 = 12e2，∴切线方程为：y−e2 = 12e2(x−4)，令y＝0，得x＝2，与x轴的交点为：(2, 0)，令x＝0，y＝−e2，与y轴的交点为：(0, −e2)，∴曲线y = e12x在点(4, e2)处的切线与坐标轴所围三角形的面积s = 12 × 2×|−e2|=e2.故选：D.二、填空题（共6小题，每小题3分，满分18分）【答案】2【考点】利用导数研究函数的极值【解析】由题意可得：y′=6x2−6x=6x(x−1)，令y′>0可得：x>1或x<0；令y′<0可得：0<x<1，再判断出函数的单调性，进而得到答案．【解答】解：由题意可得：y′=6x2−6x=6x(x−1)，令y′>0可得：x>1或x<0；令y′<0可得：0<x<1，所以当x∈(−∞, 0)时，y′>0，即函数在此区间内单调递增；当x∈(0, 1)时，y′<0，即函数在此区间内单调递减；当x∈(1, +∞)时，y′>0，即函数在此区间内单调递增；∴x=0与x=1分别为函数的极大值与极小值点．故答案为：2．【答案】24【考点】导数的运算【解析】根据导数的运算法则即可得到结论．【解答】解：∵f(x)=(x−1)(x−2)(x−3)(x−4)(x−5)，∴令g(x)=(x−2)(x−3)(x−4)(x−5)，则f(x)=(x−1)g(x)∴f′(x)=(x−1)′g(x)+(x−1)g′(x)=g(x)+(x−1)g′(x)，则f′(1)=g(1)+(1−1)g′(1)=g(1)，∵g(1)=(1−2)(1−3)(1−4)(1−5)=24，∴f′(1)=g(1)=24，故答案为：24．【答案】√5【考点】导数的运算点到直线的距离公式【解析】直线y=2x+3在曲线y=ln(2x+1)上方，把直线平行下移到与曲线相切，切点到直线2x−y+3=0的距离即为所求的最短距离．由直线2x−y+3=0的斜率，令曲线方程的导函数等于已知直线的斜率即可求出切点的横坐标，把求出的横坐标代入曲线方程即可求出切点的纵坐标，然后利用点到直线的距离公式求出切点到已知直线的距离即可．【解答】解：因为直线2x−y+3=0的斜率为2，所以令y′=22x−1=2，解得：x=1，把x=1代入曲线方程得：y=0，即曲线上过(1, 0)的切线斜率为2，则(1, 0)到直线2x−y+3=0的距离d=22=√5，即曲线y=ln(2x−1)上的点到直线2x−y+3=0的最短距离是√5．故答案为：√5【答案】1−12cos x【考点】导数的运算【解析】根据导数的公式，直接进行计算即可得到结论．【解答】解：∵y=f(x)=x−sin x2⋅cos x2=x−12sin x，∴f′(x)=1−12cos x，故答案为：1−12cos x 【答案】±2π3【考点】导数的运算【解析】求函数的导数，利用导数方程即可求出x的值．【解答】解：∵y=sin x1+cos x，∴y′=f′(x)=cos x(1−cos x)−sin x(−sin x)(1+cos x)2=1+cos x(1+cos x)2=11+cos x，由y′=2，即11+cos x=2，解得cos x=−12，∵x∈(−π, π)，∴x=±2π3．故答案为：±2π3．【答案】−3,9【考点】利用导数研究曲线上某点切线方程【解析】求导数，利用抛物线y=ax2+bx−5在点(2, 1)处的切线方程为y=−3x+7，建立方程，即可求出a，b的值．【解答】解：∵抛物线y=ax2+bx−5，∴y′=2ax+b，∵抛物线y=ax2+bx−5在点(2, 1)处的切线方程为y=−3x+7，∴4a+b=−3，4a+2b−5=1，∴a=−3，b=9，故答案为：−3，9．三、解答题（共5小题，满分52分）【答案】解：∵当0≤t≤32时，v[t]=2t−3≤0；当32≤t ≤5时，v [t ]=2t −3≥0． ∴ 物体从时刻t =0秒至时刻t =5秒间运动的路程S =∫[3−2t ]320dx +∫[2t −3]532dx =94+[10+94]=292（米）【考点】定积分【解析】先求出v(t)=2t −3在t ∈(0, 5)的符号，然后分别求出每一段的定积分，最后相加即可求出所求．【解答】解：∵ 当0≤t ≤32时，v [t ]=2t −3≤0；当32≤t ≤5时，v [t ]=2t −3≥0． ∴ 物体从时刻t =0秒至时刻t =5秒间运动的路程S =∫[3−2t ]320dx +∫[2t −3]532dx =94+[10+94]=292（米）【答案】由y ＝x 3+x −2，得y′＝3x 2+1，由已知得3x 2+1＝4，解之得x ＝±1．当x ＝1时，y ＝0；当x ＝−1时，y ＝−4．又∵ 点P 0在第三象限，∴ 切点P 0的坐标为(−1, −4)；∵ 直线 l ⊥l 1，l 1的斜率为4，∴ 直线l 的斜率为−14， ∵ l 过切点P 0，点P 0的坐标为(−1, −4)∴ 直线l 的方程为y +4=−14(x +1)即x +4y +17＝0．【考点】利用导数研究曲线上某点切线方程【解析】（1）根据曲线方程求出导函数，因为已知直线4x −y −1＝0的斜率为4，根据切线与已知直线平行得到斜率相等都为4，所以令导函数等于4得到关于x 的方程，求出方程的解，即为切点P 0的横坐标，代入曲线方程即可求出切点的纵坐标，又因为切点在第3象限，进而写出满足题意的切点的坐标；（2）由直线l 1的斜率为4，根据两直线垂直时斜率的乘积为−1，得到直线l 的斜率为−14，又根据（1）中求得的切点坐标，写出直线l 的方程即可．【解答】由y ＝x 3+x −2，得y′＝3x 2+1，由已知得3x 2+1＝4，解之得x ＝±1．当x ＝1时，y ＝0；当x ＝−1时，y ＝−4．又∵ 点P 0在第三象限，∴切点P0的坐标为(−1, −4)；∵直线l⊥l1，l1的斜率为4，∴直线l的斜率为−1，4∵l过切点P0，点P0的坐标为(−1, −4)∴直线l的方程为y+4=−1(x+1)即x+4y+17＝0．4【答案】解：f(x)在[−4, 4]上是单调递减函数．证明如下：函数f(x)的图象关于原点成中心对称，则f(x)是奇函数，即f(−x)=−f(x)对于任意x的成立，则有a(−x)3+(a−1)(−x)2+48(a−2)(−x)x+b=−[ax3+(a−1)x2+48(a−2)x+b]必有a−1=0，b=0，即a=1，b=0，于是f(x)=x3−48x．∴f′[x]=3x2−48，∴当x∈(−4,4)∴ f′[x]<0，所以f(x)在[−4, 4]上是单调递减函数．【考点】奇偶性与单调性的综合函数单调性的判断与证明【解析】根据题意，由奇函数的定义，可得f(x)是奇函数，由奇函数的性质，可得a(−x)3+ (a−1)(−x)2+48(a−2)(−x)x+b=−[ax3+(a−1)x2+48(a−2)x+b]恒成立，分析可得a、b的值，即可得f(x)的解析式，对f(x)求导，分析其导数在(−4, 4)上的符号，结合函数单调性与导数的关系，即可得答案．【解答】解：f(x)在[−4, 4]上是单调递减函数．证明如下：函数f(x)的图象关于原点成中心对称，则f(x)是奇函数，即f(−x)=−f(x)对于任意x的成立，则有a(−x)3+(a−1)(−x)2+48(a−2)(−x)x+b=−[ax3+(a−1)x2+48(a−2)x+b]必有a−1=0，b=0，即a=1，b=0，于是f(x)=x3−48x．∴f′[x]=3x2−48，∴当x∈(−4,4)∴ f′[x]<0，所以f(x)在[−4, 4]上是单调递减函数．【答案】解：（1）∵f(x)=5√x，∴f′(x)=，2√x∵曲线与直线y=2x−4平行，∴=2，2√x∴x=2516，∴y=254，∴曲线与直线y=2x−4平行的切线的方程为：y−254=2(x−2516)，即16x−8y+25=0；（2）x=0满足题意；x≠0时，设切点(a, 5√a)，则f′(a)=2√a，∴切线方程为：y−5√a=2√a−a)，将点P(0, 5)代入可得5−5√a=2a−a)，∴a=4，∴直线方程为：5x−4y+20=0，综上，直线方程为：5x−4y+20=0或x=0．【考点】利用导数研究曲线上某点切线方程【解析】（1）求导数，利用曲线与直线y=2x−4平行，求出切点坐标，即可求出曲线与直线y=2x−4平行的切线的方程．（2）设切点，可得切线方程，代入P，可得切点坐标，即可求出过点P(0, 5)且与曲线相切的直线的方程．【解答】解：（1）∵f(x)=5√x，∴f′(x)=2√x，∵曲线与直线y=2x−4平行，∴2√x=2，∴x=2516，∴y=254，∴曲线与直线y=2x−4平行的切线的方程为：y−254=2(x−2516)，即16x−8y+25=0；（2）x=0满足题意；x≠0时，设切点(a, 5√a)，则f′(a)=2√a，∴切线方程为：y−5√a=2√a−a)，将点P(0, 5)代入可得5−5√a=2√a−a)，∴a=4，∴直线方程为：5x−4y+20=0，综上，直线方程为：5x −4y +20=0或x =0． 【答案】 解：（1）∵ f [x ]=ln |x|，∴ 当x >0时，f [x ]=ln x ，当x <0时，f [x ]=ln [−x ]… ∴ 当x >0时，f′[x ]=1x ，当x <0时，f′[x ]=1−x⋅[−1]=1x…∴ 当x ≠0时，函数y =g [x ]=x +ax … （2）∵ 由（1）知当x >0时，g [x ]=x +ax ，∴ 当a >0，x >0时，g [x ]≥2√a 当且仅当x =√a 时取等号 … ∴ 函数y =g [x ]在[0,+∞]上的最小值是2√a … ∴ 依题意得2√a =2∴ a =1… （用导数求最小值参考给分）（3）根据（2）知a =1，∴ g [x ]=x +1x ，(x >0)… 由{y =23x +76y =x +1x 解得{x 1=32y 1=136，{x 2=2y 2=52… ∴ 直线y =23x +76与函数y =g [x ]的图象所围成图形的面积S =∫[232[23x +76]−[x +1x]]dx =∫(232−x 3+76−1x)dx …=[−x 26+7x 6−ln x]|23 =724−ln 2+ln 32=724+ln 3−2ln 2．…．【考点】定积分在求面积中的应用 函数解析式的求解及常用方法 导数求函数的最值【解析】（1）对x 的取值分类讨论，化简绝对值，求出f′(x)得到x >0和x <0导函数相等，代入到g(x)中得到即可；（2）根据基本不等式得到g(x)的最小值即可求出a ；（3）根据（2）知g [x ]=x +1x ，(x >0)，先联立直线与函数解析式求出交点，利用定积分求直线和函数图象围成面积的方法求出即可． 【解答】 解：（1）∵ f [x ]=ln |x|，∴ 当x >0时，f [x ]=ln x ，当x <0时，f [x ]=ln [−x ]… ∴ 当x >0时，f′[x ]=1x ，当x <0时，f′[x ]=1−x ⋅[−1]=1x …∴ 当x ≠0时，函数y =g [x ]=x +ax …（2）∵ 由（1）知当x >0时，g [x ]=x +ax ，∴ 当a >0，x >0时，g [x ]≥2√a 当且仅当x =√a 时取等号 … ∴ 函数y =g [x ]在[0,+∞]上的最小值是2√a … ∴ 依题意得2√a =2∴ a =1… （用导数求最小值参考给分）（3）根据（2）知a =1，∴ g [x ]=x +1x ，(x >0)… 由{y =23x +76y =x +1x 解得{x 1=32y 1=136，{x 2=2y 2=52… ∴ 直线y =23x +76与函数y =g [x ]的图象所围成图形的面积S =∫[232[23x +76]−[x +1x ]]dx =∫(232−x 3+76−1x )dx …=[−x 26+7x 6−ln x]|232=724−ln 2+ln 32=724+ln 3−2ln 2．…．。
高二上学期数学第七周限时训练题
高二上学期数学第七周限时训练一、单选题（本大题共6小题，共30分）1. 已知矩形ABCD ，P 为平面ABCD 外一点，且PA ⊥平面ABCD ，M ，N 分别为PC ，PD 上的点，且PM ⃗⃗⃗⃗⃗⃗ =2MC ⃗⃗⃗⃗⃗⃗ ，PN ⃗⃗⃗⃗⃗ =ND ⃗⃗⃗⃗⃗ ，NM ⃗⃗⃗⃗⃗⃗ =x AB ⃗⃗⃗⃗⃗ +y AD ⃗⃗⃗⃗⃗ +z AP⃗⃗⃗⃗⃗ ，则x +y +z =( ) A. −23 B. 23 C. 1 D. 56 2. 已知三角形的三个顶点A(4,3)，B(−1,2)，C(1,−3)，则ABC 的高CD 所在的直线方程是( )A. 5x +y −2=0B. x −5y −16=0C. 5x −y −8=0D. x +5y +14=03. 已知从点A(6,1)射出的光线经直线x +y +1=0上的点M 反射后经过点B(3,2)，则|AM|+|BM|=( ) A. √10 B. √106 C. √105 D. 3√104. 已知a ，b ，c 为直角三角形中的三边长，c 为斜边长，若点M(m,n)在直线l ：ax +by +3c =0上，则m 2+n 2的最小值为( ) A. 2 B. 3 C. 4 D. 95. 已知A (0,0,2)，B (1,0,2)，C (0,2,0)，则点A 到直线BC 的距离为( )A. 2√23B. 1C. √2D. 2√26. 已知两点A(−3,4)，B(3,2)，过点P(1,0)的直线l 与线段AB 有公共点，则直线l 的斜率k 的取值范围是( )A. (−1,1)B. (−∞,−1)∪(1,+∞)C. [−1,1]D. (−∞,−1]∪[1,+∞)二、多选题（本大题共2小题，共10分）7. 下列结论错误的是( )A. 过点A(1,3)，B(−3,1)的直线的倾斜角为30°B. 若直线2x −3y +6=0与直线ax +y +2=0垂直，则a =−32C. 直线x +2y −4=0与直线2x +4y +1=0之间的距离是√52D. 已知A(2,3)，B(−1,1)，点P 在x 轴上，则|PA|+|PB|的最小值是58. 如图，已知斜三棱柱ABC −A 1B 1C 1中，∠BAC =π2，∠BAA 1=23π，∠CAA 1=π3，AB =AC =1，AA 1=2，点O 是B 1C 与BC 1的交点．下列选项中正确的有( )A. AO ⃗⃗⃗⃗⃗ =12(AB ⃗⃗⃗⃗⃗ +AC ⃗⃗⃗⃗⃗ +AA 1⃗⃗⃗⃗⃗⃗⃗ )B.直线AO 与BC 所成的角的余弦值√33C. |AO ⃗⃗⃗⃗⃗ |=32D. 平面ABC 与平面B 1BCC 1不垂直三、单空题（本大题共4小题，共20分）9. 经过两条直线l 1：x +y −4=0和l 2：x −y +2=0的交点，且与直线2x −y −1=0垂直的直线方程为 ．10. 已知直线l 过点P(3,4)且与点A(−2,2)，B(4,−2)等距离，则直线l 的方程为 ．11. 直线ax +y +3a −1=0恒过定点M ，则M 点关于直线2x +3y −6=0对称的点的坐标为 ．12. 如图，在四棱柱ABCD −A 1B 1C 1D 1中，底面ABCD 是平行四边形，点E 为BD 的中点，若A 1E ⃗⃗⃗⃗⃗⃗⃗ =x AA 1⃗⃗⃗⃗⃗⃗⃗ +y AB⃗⃗⃗⃗⃗ +z AD ⃗⃗⃗⃗⃗⃗ ，则x +y +z = ． 四、解答题（本大题共2小题，共24分）13. 已知平行四边形ABCD 的三个顶点的坐标为A(−1,4)，B(−2,−1)，C(2,3)．(1)在△ABC 中，求边AC 中线所在直线方程；(2)求平行四边形ABCD 的顶点D 的坐标及边BC 的长度；(3)求△ABC 的面积．14. 如图，在三棱柱ABC −A 1B 1C 1中，侧面AA 1C 1C ⊥底面ABC ，AA 1=A 1C =AC =2，AB =BC ，且AB ⊥BC,O 为AC 中点．(1)证明：A 1O ⊥平面ABC ；(2)求直线A 1C 与平面A 1AB 所成角的正弦值；(3)在BC 1上是否存在一点E ，使得OE//平面A 1AB ，若不存在，说明理由；若存在，确定点E 的位置．。
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精忠中学高二地理限时练
高二下学期第7次限时练（亚洲、日本）
姓名：___________班级：___________得分：___________
一、单选题
1．有关中亚地区的论述正确的是
①在古代是联系东西方的“丝绸之路”必经之地
②该地区主要是温带大陆性气候
③中亚农业以畜牧业和灌溉农业为主灌溉水源主要靠本地区的外流河——额尔齐斯河
④地形以山地丘陵为主地势西高东低
A. ①②
B. ③④
C. ①④
D. ②③
2．去年暑假期间，有甲、乙、丙、丁四位同学分别到亚洲四个不同的地点旅游。
回校后他们各自描绘了自己的所见所闻。
你对他们如下描述，认为不可信的是( )
A. 甲：我到了世界陆地最低点——死海
B. 乙：我走访了亚洲最发达的国家——日本
C. 丙：我去了世界最高的高原——青藏高原
D. 丁：我游览了世界人口最多的国家——印度3．关于亚洲的叙述，正确的是
A. 是世界上跨经度最多的大洲
B. 南部的三大半岛都濒临印度洋
C. 里海是陆地最低点，死海是世界上最大的湖泊
D. 朝鲜、韩国两国陆界均与我国相邻
4．亚洲、欧洲流经国家最多的国际性河流分别是
A. 阿姆河、多瑙河
B. 长江、莱茵河
C. 湄公河多瑙河
D. 锡尔河、莱茵河
读“亚洲五个国家轮廓图”，回答下列各题。
5．图中五国与我国相邻的是( )
A. ①②④⑤
B. ①②③④
C. ①④⑤
D. ③④⑤
6．国家③与其他四个国家的气候特征相比，存在明显差异的原因主要是( )
A. 地形以高原为主，周围山脉环绕，地形闭塞
B. 远离海洋，缺湿润气流
C. 沙漠广布，缺乏植被
D. 地处热带，蒸发量大
7．日本是一个多地震的国家，作为日本的象征——富士山，就是一座活火山。
日本多地震是由于( )
A. 是一个群岛国家
B. 位于亚欧板块内部
C. 位于环太平洋火山地震带上
D. 填海造陆、挖地下街道等人类活动造成的
读下图，完成下列各题。
8．有关图中①②③④四个国家的叙述正确的是 ( )
A. ①④都是发展中国家
B. ①国资源丰富，大部分的工业原料供出口
C. 我国和图中四国构成了东亚五国
D. ②③两国的居民为同一民族
9.图中全部属于温带季风气候的岛屿或半岛是( )
A. ④
B. ③
C. ②
D. ①
10.图中岛国的工业集中分布在濑户内海和太平洋沿岸，是因为( )
A. 沿海地区矿产资源丰富
B. 沿海地区石油资源丰富
C. 气候温暖湿润
D. 可以利用便利廉价的海洋运输
11．日本1月0℃等温线与北纬38°纬线基本吻合，而中国东部地区1月0℃等温线与北纬33°纬线基本吻合。
说明（）
A. 日本地形以山地为主，中国东部以平原为主
B. 日本1月南北温差小，中国东部1月南北温差大
C. 日本受冬季风影响小，中国东部受冬季风影响大
12．读日本图，回答问题。
（1）冬季，A地区的降水比B地_____，原因是_______________________。
（2）日本的土地利用类型中，耕地的比重较小，原因是，该国的人均耕地只有0.04公顷，比我国还少，但粮食自给有余．其粮食生产的措施有________________________。
（3）日本工业高度集中在_______________________，原因是______________。
（4）1999年日本人口的出生率为1%，死亡率为0.8%，自然增长率为0.2%，由此判断日本的人口再生产类型为______________．这种趋势的负面影响是________。
参考答案
1．A
【解析】本题考查世界的区域地理。
中亚地区主要的灌溉水源为阿姆河和锡尔河，故③错误；中亚地形以丘陵、平原为主,地势东南高,西北低，故④错误。
选A.①②正确。
2．D
【解析】结合所学知识可知，中国是世界上人口最多的国家，故答案选D。
3．B
【解析】亚洲是跨纬度最广的大洲，南极洲是跨经度最广的大洲，A错误；亚洲南部有三大半岛，自西向东依次是阿拉伯半岛、印度半岛、中南半岛，都濒临印度洋，B正确；死海是世界陆地最低点，里海是世界上最大的湖泊，C错误；韩国与我国隔海相望，D错误。
故选B。
4．C
【解析】亚洲流经国家最多的河流是湄公河、欧洲是多瑙河，C正确。
5．C
6．A
【解析】
5．读图，根据图示轮廓可知，①为缅甸，②为日本，③为伊朗，④是印度，⑤是越南，与我国相邻的是缅甸、印度和越南，故选①④⑤正确，故答案选C。
6．由上题分析可知，③为伊朗。
伊朗位于伊朗高原，该高原是一个封闭性的、具有许多小型内陆盆地的山间高原，位于北回归线以北，里海与波斯湾之间，由于该地的地形特点形成了温带大陆性气候，而其他四个国家，都受海洋影响较大，属于季风气候区。
故答案选A。
7．C
【解析】世界上主要的火山地震带有两个，一是环太平洋火山地震带，二是地中海-喜马拉雅火山地震带。
日本多地震的原因就是位于环太平洋火山地震带上。
【点睛】日本地震的成因为本题主要考查点。
日本位于环太平洋火山地震带上，板块运动活跃，地震多发。
8．9．D
10．11．D
12．13．D
【解析】
8．9．①是日本，②是韩国，③是朝鲜，④是俄罗斯，然后根据各自特征做出判断。
在亚洲国家中，日本为发达国家，日本资源贫乏，原料、燃料主要靠进口，在亚洲分区中，东亚五国包括：中国、蒙古、朝鲜、韩国、日本，而俄罗斯为欧洲国家，②③两国居民同为朝鲜族。
10．11．日本分亚热带季风气候和温带季风气候。
温带季风主要分布在北侧，符合的是①。
12．13．岛国工业集中分布在濑户内海和太平洋沿岸主要是因为日本国内资源匮乏，可以利用便利廉价的海洋运输运进原料和运出工业制成品。
14．C
【解析】日本是四面环海的岛国，日本距冬季风源地远，受冬季风影响小，0°等温线分布纬度高。
中国东部距冬季风源地较近，受冬季风影响大，0°等温线分布纬度较低。
选C正确。
【点晴】
气候的海洋性明显；我国气候大陆性更强；冬季风源于亚欧大陆内部，日本受冬季风影响小，中国东部受冬季风影响大；加之沿岸的日本暖流对日本的影响大，
使得日本0℃等温线出现的纬度高于中国东部。
15．（1）多，冬季A位于西北风的迎风坡（2）多山地、丘陵；发展水利，合理施用化肥，发展生物技术，提高机械化水平，精耕细作，提高单产等（3）太平洋沿岸、濑户内海沿岸；海运交通便利，便于进口原料出口产品；地形平坦，接近消费市场（4）现代型；人口老龄化加剧，国防兵力不足，社会负担加重，老年人生活孤单等
【解析】本题以日本为背景区域，考查影响降水的因素、农业发展条件、工业分布于区位因素、人口问题等相关知识，意在考查学生的读图分析能力和相关知识的迁移应用能力。
（1）日本多山，山脉多呈东北-西南走向，西侧为日本海，当冬季风从西北方向吹来时（即蒙古高压向外吹的冬季风），越过日本海，带来大量水汽，遇到山脉的抬升，容易形成地形雨，故A降水较多，B位于冬季风的背风坡，降水较少。
（2）日本是一个多山地的国家，平原面积狭小，因此耕地面积较小；日本耕地面积较小，但是农业科技较发达，发展水利设施减少该地的洪涝灾害，而且合理施用化肥，发展生物技术，提高机械化水平，精耕细作，提高单产等。
（3）日本的工业主要集中于太平洋沿岸以及濑户内海沿岸。
首先，日本地形为中高周低，沿海地区萍缘分不，地势平坦，利于建厂；其次，日本四周环海，有优良港口，沿海地区海运便利。
再次，日本的经济是进口-加工-出口型，并且本国资源稀缺，尤其是矿产资源，因此需要进口原料，出口工业制成品，依赖海外市场。
因此，综合自然以及社会原因，分布于沿海地区。
（4）由材料可知，日本属于低出生率，低死亡率和低自然增长率，人口在生产类型属于现代型。
人口老龄化现象比较严重，出生人口较少，因此会导致国防兵力不足，社会负担加重，老年人生活孤单等问题。