圆梦计划-专升本高数试题

深圳市总工会圆梦计划专升本入学考试英语考试大纲考试内容比例：情景对话（5题）、词汇与语法（10题）、判断正误（4题）、词句翻译（6题）、逻辑排序（3题）、阅读理解（5题）。

所有题型均为单选题，其中情景对话、词汇与语法、词句翻译、逻辑排序题每题3分，判断正误题每题2分，阅读理解每题4分，满分100分。

一、情景对话考查学生对英语生活、工作场景的基础情景对话运用的掌握程度。

每题在两句话中留出一定空白，要求考生根据上下文情景，从每题所给的4个选择项中选出最佳选项。

样题：1. —My recorder is broken. Could I use yours?—_______, but you have to return it tomorrow. ( )A. I’m not sureB. No problemC. I’m sorryD. I hope so答案：选B, no problem 表“没问题，可以”的意思。

二、词汇与语法考查考生对名词（词性、单复数）、冠词（a, an, the）、副词（时间频率、地点、程度、关系副词）、数词、代词（人称、疑问、指示代词）、介词（in, on, with, by, for, at, about, under, of等）、比较级和最高级、一般现在式、一般进行式、过去式、将来式、常见句式（陈述句、疑问句、祈使句、感叹句）和词组固定搭配的掌握情况。

每题在一句或两句话中留出空白，要求考生从每题所给的4个选择项中选出最佳选项。

样题：1. He _______ eight hundred thousand dollars for his car. ( )A. paidB. spendC. costD. took答案：选A，考察pay过去式paid的用法以及pay的词义。

pay…for sth，表“花了多少钱买什么东西”。

2.I have to _____ my coat because it is getting colder. ( )A. get offB. buy outC. bring inD. put on答案：选D，put on 表“穿上，戴上”。

2022-2023年成考（专升本）《高等数学二（专升本）》预测试题（答案解析）全文为Word可编辑，若为PDF皆为盗版，请谨慎购买！第壹卷一.综合考点题库(共50题) 1.A.-1B.0C.1D.2正确答案：C本题解析：2.A.见图AB.见图BC.见图CD.见图D正确答案：A本题解析：暂无解析3.A.见图AB.见图BC.见图CD.见图D正确答案：C本题解析：本题考查了二元函数的一阶偏导数的知识点．4.A.0B.1C.2D.3正确答案：C本题解析：5.A.a=b=1B.a=-1，b=1C.a=1，b=-1D.a=b=-1正确答案：C本题解析：6.A.见图AB.见图BC.见图CD.见图D正确答案：B 本题解析：7.A.见图AB.见图BC.见图CD.见图D正确答案：C本题解析：8.曲线y=x3+2x在点(1，3)处的法线方程是（）A.5x+y-8=0B.5x-y-2=0C.x+5y-16=0D.x-5y+14=0正确答案：C本题解析：【考情点拨】本题考查了法线方程的知识点．9.A.见图AB.见图BC.见图CD.见图D 正确答案：B本题解析：暂无解析10.A.见图AB.见图BC.见图CD.见图D正确答案：D本题解析：【考情点拨】本题考查了不定积分的知识点．【应试指导】11.A.见图AB.见图BC.见图CD.见图D正确答案：B 本题解析：12.A.见图AB.见图BC.见图CD.见图D正确答案：B本题解析：【考情点拨】本题考查了极限的知识点．13.对于函数z=xy，原点(0，0)（）A.不是函数的驻点B.是驻点不是极值点C.是驻点也是极值点D.无法判定是否为极值点正确答案：B本题解析：【考情点拨】本题考查了函数的驻点、极值点的知识点．14.A.1B.1/2C.2D.不存在正确答案：B 本题解析：15.设函数f（x）=2lnx，则f''（x）=A.见图AB.见图BC.见图CD.见图D正确答案：B本题解析：16.A.单调减少B.单调增加C.不增不减D.有增有减正确答案：D本题解析：【考情点拨】本题考查了函数的单调性的知识点．17.A.见图AB.见图BC.见图CD.见图D正确答案：A 本题解析：18.A.-1B.0.1C.0D.0.4正确答案：B 本题解析：19.A.（－∞，－2）和（－2，＋∞）B.（－2，2）C.（－∞，0）和（0，＋∞）D.（－2，0）和（0，2）正确答案：D本题解析：20.A.见图AB.见图BC.见图CD.见图D正确答案：B本题解析：【考情点拨】本题考查了二元函数的一点处的一阶偏导数的知识点．【应试指导】21.A.（-∞，1）B.（-∞，2）C.（1，+∞）D.（2，+∞）正确答案：A本题解析：22.A.奇函数B.偶函数C.非奇非偶函数D.周期函数正确答案：A本题解析：【考情点拨】本题考查了定积分的性质的知识点．23.A.见图AB.见图BC.见图CD.见图D正确答案：C 本题解析：24.曲线y=x3-3x上切线平行于x轴的点是（）A.(0，0)B.(1，2)C.(-1，2)D.(-1，-2)正确答案：C本题解析：【考情点拨】本题考查了曲线上一点处的切线的知识点．【应试指导】由y=x3-3x得y'=3x2-3，令y'=0，得x=±1．经计算x=-1时,y=2；x=1时，y=-2，故选C．25.某建筑物按设计要求使用寿命超过50年的概率为0．8，超过60年的概率为0．6，该建筑物经历了50年后，它将在10年内倒塌的概率等于()A.0.25B.0.30C.0.35D.0.40 正确答案：A本题解析：【考情点拨】本题考查了条件概率的知识点．【应试指导】设A={该建筑物使用寿命超过50年}，B={该建筑物使用寿命超过60年}由题意，P(A)=0．8，P(B)=0．6，所求概率为：26.把两封信随机地投入标号为1，2，3，4的4个邮筒中，则1，2号邮筒各有一封信的概率等于（）A.见图AB.见图BC.见图CD.见图D正确答案：C本题解析：27.A.（-∞，+∞）B.（-∞，0）C.（-1，1）D.（1，+∞）正确答案：D本题解析：28.A.见图AB.见图BC.见图CD.见图D正确答案：B本题解析：【考情点拨】本题考查了二元函数的一点处的一阶偏导数的知识点．29.设函数z=x3+xy2+3，则A.3x2+2xyB.3x2+y2C.2xyD.2y正确答案：C 本题解析：30.A.见图AB.见图BC.见图CD.见图D正确答案：B本题解析：【考情点拨】本题考查了定积分的换元积分法的知识点．31.掷两粒骰子，出现点数之和为5的概率为（）A.见图AB.见图BC.见图CD.见图D正确答案：B本题解析：总的样本点为6×6=36（个），点数之和为5的有（1，4），（2，3），（3，2），（4，1）共有4个样本点，所求概率为32.A.见图AB.见图BC.见图CD.见图D正确答案：D 本题解析：33.设A，B为两个随机事件，且相互独立，P(A)=0．6，P(B)=0．4，则P(A-B)=（）A.0.24B.0.36C.0.4D.0.6正确答案：B本题解析：【考情点拨】本题考查了独立事件的知识点．【应试指导】因A，B相互独立，故P(A-B)=P(A)-P(AB)=P(A)-P(A)P(B)=0．6-0．6×0．4=0．36．34.A.-1B.0C.1D.2正确答案：C本题解析：35.1.平面区域D的面积S；正确答案：本题解析：1.2.36.A.-2B.-lC.1D.2正确答案：C 本题解析：37.A.x+y+2=0B.x+y-2=0C.x-y+2=0D.y-x+2=0正确答案：B本题解析：38.函数y＝ln（1+x2）的单调递增区间是（）A.见图AB.见图BC.见图CD.见图D 正确答案：B 本题解析：39.A.见图AB.见图BC.见图CD.见图D正确答案：A 本题解析：40.A.见图AB.见图BC.见图CD.见图D正确答案：B 本题解析：41.A.2B.4C.8D.16正确答案：D本题解析：【考情点拨】本题考查了定积分的换元积分法的知识点．42.甲、乙两人打靶，设他们击中靶的环数分别为X1，X2，并且有如下的分布列：试比较甲、乙两人射击水平的高低．正确答案：本题解析：43.设z=xy，则dz=（）A.见图AB.见图BC.见图CD.见图D正确答案：A 本题解析：【考情点拨】本题考查了二元函数的全微分的知识点．44.已知事件A与B互斥，且P（A）=0．5，P（B）=0．4，则P（A+B）=A.0.4B.0.5C.0.7D.0.9正确答案：D本题解析：事件A与B互斥，故P（AB）=0，因此P（A+B）=P（A）+P（B）=0．5+0．4=0．9．45.A.见图AB.见图BC.见图CD.见图D正确答案：B本题解析：【考情点拨】本题考查了导数定义的应用的知识点．46.设函数f（x）在[a，b]上连续，在（a，b）可导，f'（x）>0，f（a），（b）A.3B.2C.1D.0正确答案：C本题解析：由零点存在定理可知，f（x）在（a，b）上必有零点，且函数是单调函数，故其在（a，b）上只有一个零点．47.A.1B.3C.5D.7正确答案：B本题解析：48.A.见图AB.见图BC.见图CD.见图D正确答案：D 本题解析：49.A.见图AB.见图BC.见图CD.见图D正确答案：D本题解析：50.一批零件中有10个合格品，3个次品，安装机器时，从这批零件中任取一个，取到合格品才能安装．若取出的是次品，则不再放回，求在取得合格品前已取出的次品数X的概率分布．正确答案：本题解析：由题意，X的可能取值为0，1，2，3．X=0，即第一次就取到合格品，没有取到次品．P{X=0)=。

专科起点升本科《高等数学（二） 》入学考试题库（共 180 题）1．函数、极限和连续（ 53 题）函数（ 8 题）函数定义域1 ．函数 ylg x arcsin x的定义域是（）。

Ax 23A. [ 3,0) U (2,3] ；B. [ 3,3] ；C. [ 3,0) U (1,3] ；D. [ 2,0) U (1,2) .2 ．若是函数 f (x) 的定义域是 [1 ] ,则 f ( 1 ）。

D2, ) 的定义域是（3 xA.[1,3] ；B. [1,0) [3,) ；22C. [1,0) (0,3] ；D.( , 1][3,) .223. 若是函数 f (x) 的定义域是 [2, 2] ，则 f (log 2 x) 的定义域是（）。

BA. [11,4] ； C.[1；D.[1,0) U (0, 4] ；B. [ ,0) U (0, 2],2] .44224 ．若是函数 f (x) 的定义域是 [2,2] ，则 f (log 3 x) 的定义域是（）． DA.[1,0) (0,3] ； B. [ 1,3] ； C. [ 1 ,0) (0,9] ； D. [1,9] .3 3 99 5 ．若是 f ( x) 的定义域是 [0 ， 1] ，则 f (arcsin x) 的定义域是（）。

CA. [0,1] ； B. [0,1[0,] ； D. [0,] .]； C.22函数关系21，则 f (x)6.设 fx22 x2 ,x() ．A1 xx2x 1 2x 1 x 1； D.x 1A ．； B.； C.2x 1 2x .x 1x117 ．函数 y 3x的反函数 y（ ）。

Bx31A ． log 3 (x) ； B. log 3 ( x) ； C. log 3( x1 xx ) ； D. log 3 ( ) .1 1 xx 1 x8 ．若是 f (cos x)sin 2 x()．C，则 f ( x)cos2 xA ． 1 x 2； B.1 x 21 x2 1 x 2； C.2x 2 ； D.2x 2.2x 2 12x 2 111极限（ 37 题）1.2.1 数列的极限9 ．极限 lim (12 3 Lnn ) ( )． Bnn2A ．1； B.1 1 ；D..2； C.L310 ．极限 lim12 3n ()． A2 n2n1 111A ．； B.4； C.； D.54511 ．极限 lim111()． CLn1 2 2 3n(n 1)A ．-1；；； D..111 L ( 1)n 1 12 ．极限 lim 2 221 2n ()． An1 1 1 L32 n3 3A ．4 ； B.49 99； C.； D.49 41.2.2 函数的极限13 ．极限 limx 2 x()． Cxx111； D.1.A ． ；B.； C.2214 ．极限 limx 11)． Ax(x 0112； D.2 .A ． ；B.； C.2215 ．极限 lim3x1 1）．Bx（x 0A.3 ； B. 3；C.1 ； D. 1 .222 216 ．极限 lim2x1 1）．Cx 1（x 1A. -2；B.0；C. 1； D. 2.17 ．极限 lim2x 13)． Bx 2(x 4A ．4； B.4； C.3； D.3 .334418 ．极限 lim(x 21x 21)()． D xA ． ；；； D.0.19 ．极限 lim x 25x6()． Dx 2x 2A ． ； ；； D.-1.20 ．极限 limx 31()． A5x3x 2x 2A ．77 1 1； B.； C.；D..333321 ．极限 lim3x 2 1()． C2x 25x4xA ． ； B.2； C.333；D..22 ．极限 limsin x24( )． BxxA ．10 ； C. 1 ； D.2. ； B.23 ．极限 lim x sin1( )． Bx 0xA ．10 ； C. 1； D.2. ； B.xsin t dt0 t 1()．B24 ．极限 limx 2x 01； B. 1 11A ．； C.；D..223325 ．若 lim x 22x k4 ，则 k （）． Ax 3x3A ． 3； B. 3； C.11；D..33x 2 2x3 ()． B 26 ．极限 lim3x 31xA ． ；；； D.-1.无量小量与无量大量27 ．当 x0 时， ln(1 2x 2 ) 与 x 2 比较是（）。

圆梦计划专升本高等数学入学测试模拟题及答案一、选择题（下列每小题的选项中，只有一项是符合题意的，请将表示该选项的字母填在题后的括号内。

共10小题，每小题3分，共30分）1.若函数⎪⎩⎪⎨⎧>+≤=0,sin 0,3)(x a xx x e x f x 在0=x 在处连续，则=a （ C ）A. 0B. 1C. 2D. 3解：由)0()00()00(f f f =-=+得231=⇒=+a a ,故选C.2.当0→x 时，与函数2)(x x f =是等价无穷小的是（ A ） A. )1ln(2x + B. x sin C.x tan D. x cos 1-解：由11ln(lim 1ln()(lim )220)20=+=+→→x x x x f x x ,故选A.3.设)(x f y =可导，则'-)]([x e f =（ D ）A. )(xef -' B. )(x e f -'- C. )(x x e f e --' D. )(x x e f e --'-解：)()()()]([xx x x xe f e e e f e f -----'-='⋅'=',故选D. 4.设x 1是)(x f的一个原函数，则⎰=dx x f x )(3（ B ） A.C x +221 B. C x +-221 C. C x +331 D. C x x +ln 414解：因x 1是)(x f的一个原函数,所以211)(x x x f -='⎪⎭⎫⎝⎛=,所以C x xdx dx x f x +-=-=⎰⎰2321)(故选B.5.下列级数中收敛的是（ C ）A. ∑∞=-1374n nnn B. ∑∞=-1231n n C.∑∞=132n n n D. ∑∞=121sinn n解：因121)1(lim 2122)1(lim 33313<=+=+∞→+∞→n n n n n n n n ,所以∑∞=132n n n 收敛, 故选C. 6.交换⎰⎰⎰⎰+=102121121),(),(y yydx y x f dy dx y x f dy I 的积分次序，则下列各项正确的是（ B ） A. ⎰⎰122),(xx dy y x f dx B.⎰⎰1022),(x x dy y x f dy C.⎰⎰2122),(x x dy y x f dx D.⎰⎰2122),(x x dy y x f dx解：由题意画出积分区域如图:故选B.7.设向量21,αα是非齐次线性方程组AX =b 的两个解，则下列向量中仍为该方程组解的是（ D ）A. 21αα+B. 21αα-C. 212αα+D. 212αα-解：因,2)(2121b b b A A A =+=+=+αααα同理得8.已知向量)2,5,4,0(),0,,0,2(),1,1,2,1(321--==-=αααk 线性相关,则=k （ D ） A. -2 B. 2 C. -3 D. 3解:⎪⎪⎪⎭⎫ ⎝⎛+--+--→⎪⎪⎪⎭⎫ ⎝⎛---+--→⎪⎪⎪⎭⎫ ⎝⎛---=⎪⎪⎪⎭⎫ ⎝⎛03002240112125402240112125400021121321k k k k ααα 9.设B A ,为事件，且,2.0)(,4.0)(,6.0)(===AB P B P A P 则=)(B A P （ A ） A.0.2 B. 0. 4 C. 0.6 D. 0.8解: 2.0)]()()([1)(1)()(=-+-=+-=+=AB P B P A P B A P B A P B A P10.有两个口袋,甲袋中有3个白球和1个黑球,乙袋中有1个白球和3个黑球.现从甲袋中任取一个球放入乙袋，再从乙袋中任取一个球,则取出白球的概率是（ B ） A.163 B. 207 C. 41 D. 21解: 由全概率公式得20751415243=⨯+⨯=p二、填空题(本题共10小题，每小题3分，共30分，把答案填在题中横线上。

圆梦计划（重点）复习题集（专升本理科）-2018年教学⽂案圆梦计划(重点)复习题集(专升本理科)-2018年“圆梦计划”复习题集（专升本）适⽤专业：计算机科学与技术、会计学、机械设计制造及其⾃动化、通信⼯程、电⽓⼯程及其⾃动化、⼯程管理、国际经济与贸易、⼯商管理、⼟⽊⼯程⼆、⼤学英语专升本选择题1.Phonetics (5 points)Directions:：In each of the following groups of words，there are four underlined lettersor letter combinations marked A，B，C and D. Compare the underlined parts andidentify the one that is different from the others in pronunciation. Mark your answer by blackening the corresponding letter on the Answer Sheet.1. A. come B. some C. move D.love C2. A. honor B. house C. horror D.heel A3. A. thief B. think C. theoryD. these D4. A. now B. how C. allow D. window D5. A. meat B. dead C. cream D.steal BII. Vocabulary and Structure (15 points)Directions: There are 15 incomplete sentences in this section. For each sentencethere are four choices marked A, B, C and D. Choose one answer that best completes the sentence and blacken the corresponding letter on the Answer Sheet.6. We asked both John and Jerry, but _____ could offer a satisfactory explanation. AA. neitherB. eitherC. bothD.nor7. I’d like to find someone _____I can discuss such a problem. CC. with whomD. to whom8. The baby can’t even sit up yet, _____walk! BA. don’t mentionB. let aloneC. other thanD. rather than9. I did not notice that my dog was missing _____a moment ago. BA. beforeB. untilC. toD. On10. The company director has informed us that we must _____department budge by 25% AA. cut downB. cut awayC. cut offD. cut up11. Companies usually _____a number of experiments before a new product is launched. DA. practiceB. controlC. carryD. conduct12. I remembered that the air conditioners _____ runed off before left home. CA. wereB. were to beC. had beenD. have been13. -How do you like your new job? B-well, it’s great _____salary, but it does not offer much prospects for promotion.A. in change ofB. in terms ofC. in case ofD. in favor of14. In my opinion, this is a(n)_____different matter. AB. merelyC. purelyD. fully15. Take an umbrella with you in case it_____. DA. may rainB. could rainC. rainedD. rains16. The murderer was brought in, with his hands_____ behind his back. DA. to have been tiedB. having tiedC. to be tiedD. tied17.-Do you think Joshua is the right person for this job? C-He is well-grounded in economic theory, but lacks _____in production management.A. devotionB. attitudeC. experienceD. energy18._____about it earlier, we could have wamed people of the danger. DA. Would we knowB. Should we knowC. Have we knownD. Had we known19. It was_____ of you not to disturb these old people late at night. BA. patientB. considerateC. deliberateD. modest20. -Hey, what do you think of his speech last night? C-I have no idea. I arrived_____ find that he had almost finished it.A. in order toB. so as toC. only toIII. Cloze (30 points)Directions: For each blank in the following passage, there are four choices markedA,B,C and D. Choose the one that is most suitable and mak your answer by blackening the corresponding letter on the Answer Sheet.What is music? Music is sound arranged into pleasing or interesting 21 . It is part of every culture on Earth. People use music to 22 feeling and ideas. Music also serves to entertain and relax.Music is a performing art. It 23 form such arts as painting and poetry, in which artists 24 works and then display or publish them. Musical composers need musicians to 25 and perform their works. 26 ，most musical performances are really co-operations between composers and performers.Music also play a major role in other arts. Opera 27 singing and music with drama. Ballet and other forms of dancing need music to help the dancers 28 their steps. Motion pictures use music to help set the mood as well as introduce the actions or enhance its 29 on the audience.Music is one of the 30 arts. People probably started to sing as soon as 31 developed. Hunting tools struck together may have been the first musical 32 .By about 10,000 B. C., hollow bones had been used by 33 people to make flutes. The first written music dates from about 2500 B.C.There are two chief kinds of Western music, classical and popular, Symphonies, operas, and bullets are 34 music, It is generally harder to write and perform. Musicians who perform it need a lot of training. Popular music 35 country music, folk music, jazz, and rock music. It is easier to perform and understand.21. A. models B. types C. stylesD. patterns D22. A. express B. explore C. coverD. test A23. A. results B. develops C. differsD. separates C24. A. discover B. create C. imagineD. invent B25. A. adapt B. interpret C. followD. complete B26. A. Thus B. However C. BesidesD. And A27. A .joins B. associates C. connectsD. combines D28. A. with B. for C. afterD. upon A29. A. force B. effect C. influenceD. impact B30. A. greatest B. easiest C. oldestD. best C32. A. performers B. events C. instruments D. notes C33. A. previous B. old C. earlyD. ancient D34. A. light B. background C. classicalD. experimental C35. A. accepts B. includes C. explainsD. illustrates BIV Reading Comprehension (60points)Directions:There are five reading passages in this part. Each passage is followedby fourquestions. For each question there are four suggested answers marked A,B, C and D.Choose one best answer and blacken the corresponding letter on the Answer Sheet.Passage OneWhat do you use to get around town? A car? A bike? Your feet? Perhaps you should try a Segway!The Segway is perfect for short journey. It’s an electric vehicle that consists of a platform between two wheels, with a pole that connects the platform to the handlebars. To ride it ,you step up onto the platform, and control the Segway by moving your body. Lean forwards to go faster, and backwards to slow down.On older models, direction is controlled by a twist grip (扭转把⼿）on the left handlebar. This varies the speeds between the two motors, a decrease in the speed of the left wheel would turn the Segway to the left .With newer models you simply lean to the left or right. Meanwhile, a gyroscope (陀螺仪）detects your movements and prevents the machine from falling over. The Segway has a maximum speed of 19 km per hour and a range of about 38 km. After that, you need to plug it in and recharge the battery.Segways are used for a variety of purposes. People with mobility problems can now enjoy walks in the country with their friends and family. Some golfers us them as an alternative to the golf cart. And dog owners now have an easier way to take the dog to the park. A few police forces use Segways, too. They allow officers to move quickly whilst maintaining contact with the public. They’re also becoming a common sight on airport. However, the most popular use is in tourism, particularly for city tours. Visit any major tourist city in summer, sit outside a cafe for a while and there’s a good change you’ll see a group of tourists passing on Segways.36.What is the Segway according to this passage? DA.A pole that connects two handlebarsB.A newly appeared public traffic vehicle.C.A bicycle with a platform between two wheels.D.An electric two-wheeled vehicle for short trips.37.How do you turn to the left on Segways of newer models? AA. Lean to the left.B. Adjust the twist grip.C. Press the left bar.D. Control gyroscope38.How far can you travel on a Segway at most? CB. About 19 km.C. About 38 km.D. More than 38 km.39.The last paragraph focuses on______. DA. what a Segway is likeB. where to find a SegwayC. how to control a SegwayD. when a Segway is usefulPassage TwoNancy Bright and her husband john had been working overtime and saving for a long time so that they could pay the advance for Nancy’s dream house. Today was the day that they had enough money in hand to make a down payment on the house. But the real estate (房地产）agent informed them that she had received another offer for the house. Although the other offer was slightly less than that of Nancy and john’s, that person with the new offer was willing to pay the whole amount at once. The owner, in urgent need of money, wanted to accept the second offer.Nancy and john looked at each other with disappointed looks. They walked back home feeling very low about having lost the house. Soon they recovered and involved themselves into their daily lives, though once in a while Nancy would sink into a mild depression over losing the house.One day Nancy woke up in the morning feeling even lower than usual. She kept feeling sick, even lost interest in her routine coffee. She put all these symptoms down to the stress of working hard and losing her dream house. A weed passed and she seemed to get worse. John was worried and insisted on taking her to the doctor. The doctor, after taking a few tests,informed them with a huge smile that Nancy was two months pregnant! John and Nancy were overjoyed but also worried about not having their own house before the baby was born.One evening Nancy wandered into the street where her dream house was, and as she passed by it, she was surprised to see that there were notices stuck on all the houses. On closer examination she found that the notices were for all the residents to move out of the houses as they were building a highway and the whole row of houses needed to be pulled down. Nancy suddenly realized that not getting her dream house had been a blessing in disguise. She thanked God and decided to be happy with the blessings blessings she had and started looking forward to the birth of her child.40.Why did Nancy and her husband lose their dream house? AA. They couldn’t pay the whole amount for the house at onceB. Someone else offered move money for the house.C. They couldn’t afford the advance for the house.D. The house owner decided not to sell the house.41. How did they feel after they lost their dream house? DA. They felt sorry and hardly recovered.B. They felt relieved but with little regret.C. They enjoyed their daily lives all the same.D. They were depressed but tried to adjust themselves.42.What did Nancy find about the house one day? BA. It would be on sale againB. It would be pulled downD. It had been emptied43.What does the phrase “a blessing in disguise” in the last paragraph mean? AA. A good luckB.A dirty trickC. A secret wishD.A false alarm.Passage ThreeMost of the guests who come on our trips have never been to Egypt before. We want to make everyone comfortable and at ease, but we do always get the same questions in advance of trip. So here I will give you some travel tips.What should I wear?If you’re lucky enough to visit Egypt between November and February, pack a sweater. You’ll need it ⼀the desert gets chilly at night. During the day, the temperature will be agreeable and comfortable. Any other time, pack as if you’re going to Phoenix or Vegas in August. For the ladies, bathing suits are normal if there’s a pool where you’re going, but leave the string bikini at home ⼀it is a Muslim country, after all. Last, if you are planning on visiting any mosques or certain parts of upper Egypt, ladies will need to plan on bringing something that comes at least to the elbow, and no shorts for men or women in those areas. What special things do I need to pack?One of my favorite things in the world to bring to Egypt is an Evian Mister, a sprayer with a fine mist of Evian water. You may be able to find it in your local drug store. Spray a little on your face or head, and your body temperature will feel like it’s dropped 10 or 15 degrees. Other items include your camera, sun block and extra batteries.How do I communicate with home?Internet cafes are plentiful everywhere, especially in Cairo, Luxor, and Alexandria. If you have international calling on your phone, you should be able to use it ⼀AT&T and Sprint both work internationally for sure, but make sure you have the international coverage. A satellite phone is best if you are certain to need coverage in the middle of the country. Like while sailing up the Nile, but for most people these days a cell phone is fine.What medical preparation do I need?In a word: none! The one thing you may come down with in Egypt is politely called “Pharoah’s Revenge.” The thing that knocks out Pharoah’s Revenge is a regionally produced medicine, and is available at every drugstore for $1a box. DON’T drink local water. DO drink bottled water, avoid the skins of fresh vegetables, and you’ll be fine.44.What clothing is proper for ladies visiting a mosque? BA.String bikinis.B.Long-sleeve clothes.C.Bathing suits.D.Shorts.45.What’s the use of an Evian Mister? CA.To relieve your thirst.B.To prevent sunburns.C.To cool yourself down.D.To drive away insects.46.What information is provided about distance communication? AA.A cell phone is enough for most people.C.A satellite phone doesn’t work in Mid-Egypt.D.Internet cafes are only available in big cities.47.What does “Pharoah’s Revenge” probably refer to in the last paragraph? CA.A curse.B.A legend.C.A disease.D.A vegetable.49.Which word best describes the homeless man? BA.Angry.B.Untidy.C.SensitiveD.Impolite.50.Why did Robby go back to the hot dog seller? CA.She wanted to think the hot dog seller.B.The homeless man asked her for a hot dog.C.She wanted to buy a hot dog for the homeless man.D.The hot dog was so delicious that Robby wanted another.51.What is the theme of this passage? DA.The rich should help the poor.B. One good turn deserves anotherC.Kindness is the greatest wisdomD.A kindness shown, a kindness sown.Passage FiveWhatever you do, don’t challenge a chimpanzee named Ayumu to a number memory game.In 2007, Ayumu became famous for his lightning speed at a game that goes like this: A player views a computer screen where the number 1 through 9 appear briefly at once and then tun to white squares. The player then taps the squares where the numbers had been, in order from 1 to 9. People can do it . But no human competitor has ever completed the game faster or more accurately than Ayumu the chimp. For almost five years Ayumu remains undefeated.Psychologist Nicholas Humphrey of Darwin College at Cambridge University in England now thinks he knows the secret behind the chimp’s ability. Humphrey suspects Ayumu’s brain may have a condition that allows the chimp to see numbers as colors. This would mean that Ayumu may see a color glow after the number disappears. Then, instead of remembering the numbers, he remembers a sequence of colors, each associated with a number.The condition that Humphrey believes Ayumu may have is called synesthesia. Humans with synesthesia may associate numbers and letters with colors. For example, a person may seethe number“5”as the color blue. Until now, scientists and assumed only humans could have synesthesia.Humphrey found the inspiration for his idea at a 2011 scientific conference. There, he heard a presentation about Ayumu’s memory abilities and another talk about synesthesia. He then put the two ideas together.52.What is Ayumu famous for? DA.His gift in playing computers.B.His talent in calculating numbers.C.His skill in tapping the numbered squares.D.His amazing performance in a memory game.53.Which of the following is true of Nicholas Humphrey? BA.He thinks Ayumu has an amazing memory.B.He believes that Ayumu sees the colors of numbers.C.He was inspired by Primatologist Tetsuro Matsuzawa.D.He delivered a speech on synesthesia at the 2011 conference.54.Where does Humphrey get the inspiration for his idea? BA.From an experiment.B.From a conferenceC.From a research on chimpanzees.D.From the color blue55.How does Tetsuro Matsuzawa explain Ayumu’s performance in the game? CA.Ayumu uses synesthesia.B.Ayumu is cleverer than most chimps.C.Chimps recall things faster than people.D.Chimps are good at dealing with number.V. Daily Conversation (15 points)Directions: Pick out appropriate expressions from the eight choices below and complete the following dialogue by blackening the corresponding letter on the Answer Sheet.Mary: Well, Susan, how was your shopping trip with Nancy this afternoon?Susan: Don’t ask. 56 HMary: What do you mean? Something went wrong?Susan: Went wrong? 57E !Nancy thought I had said I would meet her at the department store at 2:30 when I really said 2:00. Then she thought we would meet at the main entrance in front when I really said at the east entrance on the Twelfth Street. Mary: 58B ?Susan:Yes! 59C !I had given up waiting and went inside the women’s clothing department.So did she. Thus we met finally and it was 3:00 by then.Mary:Did you get what you wanted? 60 D .英语试题答案及评分参考I.Phonetics (5 points, one point each)1.C2.A3.D4.D5.BII. Vocabulary and Structure (15 points, one point each)6.A7.C8.B9.B .10.A11.D 12.C 13. B 14.A15.D16. D 17.C 18.D 19.B20.CIII. Cloze (30 points, two points each)21.D 22.A 23. C 24.B25.B26.A 27.D 28.A 29.B30.C31.D 32.C 33.D 34.C35.BIV. Reading Comprehension (60 points, there points each) 36.D 37. A 38.C 39.D40.A41.D 42.B 43.A 44.B45.C46.A 47.C 48.B 49.B50.C51.D 52.D 53.B 54.B55.CV. Daily Conversation (15 points, three points each )60.D完型填空(⼀)Not all people got their names _1__ their father. Some got their names from the places they __2__. For example, a family that lived in a village __3__ many green trees and plants was called Green or Greenberg. If they lived in a town called Moor, they were __4__ the Moores. Sometimes people got their names from___5__ they looked. A tall person was, perhaps, called Long. If people in a family had __6__ hair, the family was sometimes called the Blacks or the Browns. If their hair was__7___, they may have been called the Whites.People often took their names from the kind of __8___ they did. A person who sewed clothing was named Taylor. ___9___ person who baked bread was called Baker. A person who had a very good ___10__ was named Singer.After a while these names stayed with people and became family names that are still used today.1. A. after B. out of C with D. from D2. A. stayed in B. worked for C. lived in D. played at C3. A. of B. with C. for D. at B4. A. known B. said C. called D. written C5. A. the way B. a way C. what D. written A6. A. light B. heavy C. dark D. soft C7. A. heavy B. dark C. soft D. light D8. A. subject B. work C. major D. course B9. A. Another B. Other C. Others D. A D10. A. brain B. voice C. body D. name B(⼆)When we say that Cambridge is a university town we do not mean just that it is a town__1__ a university ___2__ it. Manchester and Milan have universities, but we do not call them university towns. A university town is one where there is no clear separation ___3__ the university buildings and the rest ___4__ the city. The university is not just one part __5__ the town; it is all___6__ the town. The heart ___7__ Cambridge has its own shops, pubs, market place and so on, but most ___8__ it is university-colleges, all the teachers, libraries, clubs and other places __9___ university staff and students. Students fill the shops, cafes, banks and churches, making these as well part ___10__ the university.1. A. in B. outside C. with D. behind C2. A. of B. in C. at D. before B3. A. between B. over C. among D. above A4. A. through B. near C. of D. about C5. A. in B. out of C. towards D. of D6. A. around B. over C. across D. behind B7. A. to B. of C. inside D. like B8. A. of B. from C. on D. by A9. A. to B. for C. in D. about B10. A. in B. of C. for D. with B(三)All the useful energy at the surface of the earth comes from the activity of the sun. the sun heats and feeds mankind. Each year it __1__ men with two hundred million tons of grainand___2__ ten million tons of wood.Coal, oil, natural gas, and all other __3___ are stored-up energy from the sun. It was collected by the plants as carbon compounds and stored __4__ ago.Even waterpower comes from the sun. Water ___5_ into vapor by the sun falls as rain. It runs ___6__ the mountains and is converted to electric power.Light transmits only the energy __7___ comes from the sun’s outer layers, and ___8__ of this energy that is directed toward the earth never arrives. About __9___ of it is absorbed by the atmosphere of the earth. In __10___, the earth itself gets only one half-billionth of the sun’s entire output of radiant energy.1. A. gathers B. produces C. provides D. sends C2. A. hardly B. merely C. really D. nearly D3. A. fuels B. solids C. soils D. materials A4. A. years B. ages C. times D. generations B5. A. turns B. turning C. turned D. is turned C6. A. up B. down C. around D. into B7. A. that B. what C. where D. because A8. A. little B. a little C. much D. few C9. A. nine-ten B. ninth-tenth C. nine-tenth D. nine-tenths D10. A. place B. fact C. form D. part（四）On Monday afternoon Mrs. Joan, dressed for going out, took her handbag with her money and her key in ___1__, pulled the door__2__ her to lock it and went to the Over 60s Club. She always went there__3__. It was a nice outing for an old woman who lived __4__.At six o’clock she came home, let __5__ in and at once __6__ cigarette smoke. Cigarette smoke in her house? How? Had someone got in? She __7__ the back door and the windows. All were ___8__ or fastened, __9__ usual. There was no__10__ of forced entry.1. A. it B. its C. her D. hers2. A. in front of B. beside C. behind D. before3. A. Monday B on Monday C, Mondays D. on Mondays4. A. single B. lonely C. alone D. only5. A. she B. her C. hers D. herself6. A. smell B. smelling C. smelled D. smelt7. A. notice B. saw C. checked D. looked through8. A. locking B. locked C. closing D. closed9. A. like B. look like C. as D. the same as10. A. sight B. sign C. scene D. signs答案：（⼀）1-5:DCBCA 6-10:CDBDB（⼆）1-5:CBACD 6-10:BBABB（三）1-5:CDABC 6-10:BACDB（四）1-5：ACDCD 6-10: DCBCB阅读：Passage OneOf all the animals in the animal kingdom, which one (aside from man) is the cleverest?There are several ways of measuring the intelligence of animals. In one test some scientists set three identical cans on a table. While an animal watches, he puts food under one of the cans. Then he leads the animal away. Some time later, he brings it back to see if it remembers which can has the food. No smelling is allowed; the animal must go to the correct can or it fails.This is called a delayed-response test. The idea is to find out how long an animal’s memory can keep the information. The scientists would try showing the cans to the animal an hour later, or two hours later, or even a full day later. They discovered that chimpanzees（⿊猩狸）and elephants have the best memory, and are able to remember the correct can for at least twenty hours. No other animal is close. Dogs come next, but they only remember for nine hours.To settle the matter, the scientists designed a huge maze（曲径，迷宫）and ran the chimpanzees and elephants through it. The maze was very difficult, with many blind paths and dead ends. It took the chimpanzees ten minutes to find their way out. The elephants needed a half hour. Even allowing for the elephants slower rate of speed, the test shows that chimpanzees are the cleverest animals.From this and other tests, the scientists dr ew the following conclusion: an animal’s intelligence depends on the size of its brain in proportion to （与……成⽐例）the size of its body. The elephant’s brain weighs ten pounds. But this is only 1/600th of its 6,000-pound body weight. So in proportion to its body size, the chimpanzee has four times as much brain as the elephant, thus more brain for less body.1. The main idea of this passage is that ______.A. there are several ways of measuring the intelligence of animalsB. chimpanzees and elephants have the best memoryC. intelligence tests show that the chimpanzee is the cleverest animalD. the scientists designed a huge maze and ran the chimpanzees and elephants through it答案：C题型：单选1. The delayed-response test is designed to test an animal’s ______.A. eyesightB. intelligenceC. learning abilityD. memory答案：D题型：单选1. The passage tells that elephants ______.A. never forget thingsB. are more clever than chimpanzeesC. are more clever than chimpanzeesD. have better memories than chimpanzees答案：C题型：单选1. Which of the following animals is NOT mentioned in this passage?A. Elephant.B. Dolphin.C. Chimpanzee.D. Dog.答案：B题型：单选1. What does an animal’s intelligence depend on?A. The size of its brain in proportion to the size of its body.B. The size of its body.C. The size of its brain.D. The place an animal lives in.答案：A题型：单选Passage TwoThe existing oil resources will not last very long. This means that all vehicles such as cars, trains, buses, planes and ships that need oil to work will not be able to run. So it will be necessary to develop a new system of transport which uses a fuel other than oil. Electric vehicles are one possibility. In Britain, most families have at least one car and this car is used everyday. It could be that only one person in the family drives the car to work or for shopping. The number of cars on the road which are almost empty perhaps helps to explain why the oil is used up so quickly. The family car is a very useful form of transport but it is also a great waster of energy, especially if it is compared with buses or trains which use less petrol per person than a car; this also wastes fuel. A car traveling at 80 kilometers an hour uses only halfas much petrol as a car running at 120 kilometers an hour. Clearly, it would be better if there were fewer cars on the road and more speed limits so that the oil which is left will last as long as possible.About 25% of Britain’s total consumption（消耗）of energy is domestic -- it is used only in the home. Just over 20% is used for transport. Most of the energy is used in industry. It is difficult to suggest any possible energy conservation in industry because many of the suggestions would mean that some people would lose their jobs. It is important that industry produces the same amount of products using the same amount of workers.Obviously, conservation is not going to be the answer to the energy crisis. The most it can do is to give more time for a better solution to be found. The more time which is available for new sources of energy to be developed, the better it is because there is still a lot of work to be done in order to find suitable, safe methods of producing energy.6. According to the passage, all vehicles that need oil to work will not be able to run because______.A. they will be replaced by electric vehiclesB. oil resources will be used up very soonC. the transport system for them is too oldD. these vehicles cannot use the new fuel。

2023年专转本高数试卷一、选择题（每题3分，共30分）1. 函数y = (1)/(√(x - 1))的定义域是（）A. (1,+∞)B. [1,+∞)C. (-∞,1)D. (-∞,1]2. 若f(x)=sin x，则f^′(x)=（）A. cos xB. -cos xC. sin xD. -sin x3. ∫ x^2dx=（）A. (1)/(3)x^3+CB. x^3+CC. (1)/(2)x^2+CD. 2x + C4. 极限lim_x→ 0(sin x)/(x)=（）A. 0.B. 1.C. ∞D. 不存在。

5. 设y = e^xcos x，则y^′=（）A. e^xcos x - e^xsin xB. e^xcos x+e^xsin xC. -e^xsin xD. e^xsin x6. 函数y = x^3-3x^2+1的单调递增区间是（）A. (-∞,0)∪(2,+∞)B. (0,2)C. (-∞,1)∪(1,+∞)D. (1,+∞)7. 已知向量→a=(1,2, - 1)，→b=(2, - 1,3)，则→a·→b=（）A. -1.B. 1.C. 3.D. -3.8. 定积分∫_0^1x^2dx=（）A. (1)/(3)B. (1)/(2)C. 1.D. 2.9. 二阶线性微分方程y^′′+p(x)y^′+q(x)y = f(x)，当f(x) = 0时，称为（）A. 齐次方程。

B. 非齐次方程。

C. 线性方程。

D. 非线性方程。

10. 函数y=ln(x + 1)在x = 0处的切线方程为（）A. y = xB. y=-xC. y = x + 1D. y=-x - 1二、填空题（每题3分，共15分）1. 函数y = tan x的周期是______。

2. 若y = f(u)，u = g(x)，则复合函数y = f(g(x))的导数y^′=______。

3. lim_n→∞(1+(1)/(n))^n=______。

·第一章 函数一、选择题1.以下函数中，【 C 】不是奇函数A.y tan x xB. y xC. y ( x 1) ( x 1)D. y2 sin 2 x2.f (x) 与 g( x) 同样的是【x以下各组中，函数 】A.f ( x) x, g( x)3x 3B.f ( x) 1, g( x) sec 2 xtan 2 xC. f ( x) x 1, g(x) x21D. f ( x) 2 ln x, g( x)ln x 23.x1以下函数中，在定义域内是单一增添、有界的函数是【】A. y x+arctan xB. y cosxC. yarcsin xD. y x sin x4. 以下函数中，定义域是 [,+ ] , 且是单一递加的是【】A. y arcsin xB. y arccosxC. y arctan xD. y arccot x5. 函数 yarctan x 的定义域是 【】A. (0, )B. (2 , )2C.[, 2 ]D. (,+ )26. 以下函数中，定义域为 [ 1,1] ，且是单一减少的函数是【】A. y arcsin xB. y arccosxC. y arctan xD. y arccot x7. 已知函数 yarcsin( x 1) ，则函数的定义域是 【】A. ( , )B. [ 1,1]C. (, )D. [ 2,0]8. 已知函数 yarcsin( x 1) ，则函数的定义域是 【】A. ( , )B. [ 1,1]C. (, )D. [ 2,0]9.以下各组函数中， 【 A 】 是同样的函数A. f ( x) ln x 2和 gx 2ln x B. f (x)x 和 g xx 2C. f ( x) x 和 g x ( x )2D. f ( x) sin x 和 g(x) arcsin x10. 设以下函数在其定义域内是增函数的是【】A. f ( x) cos xB. f ( x) arccos xC. f (x)tan xD. f (x)arctan x11. 反正切函数 y arctan x 的定义域是【】A. (, ) B. (0, )2 2C. ( , )D. [1,1]12. 以下函数是奇函数的是【】··A. y x arcsin xB.y x arccosxC.y xarccot xD. yx 2 arctan x13. 函数 y5ln sin 3x 的复合过程为 【 A 】A. y 5u ,u ln v, v w 3 , w sin xB. y 5u 3, u ln sin xC. y5ln u 3 ,u sin x D. y5u , u ln v 3,v sin x二、填空题1.函数 yarcsin xarctan x的定义域是 ___________.5 5 2.f ( x)x 2arcsin x的定义域为 ___________.33.函数 f ( x) x 2 arcsinx 1的定义域为 ___________。

《高等数学》试卷 2 (闭卷 )适用班级：选修班 (专升本 )班级：学号：姓名：得分：﹒﹒一、选择题（将答案代号填入括号内，每题 3 分，共 30 分） .1．下列各组函数中，是相同的函数的是（）（A ）f x ln x2和 g x2ln x（B）f x| x | 和 g x x2（C）f x x2（D）f x| x |和 g x和 g x x1xsin x42x02．函数f x ln 1x在 x 0 处连续，则a（）.a x0（A ）0（B）1（C） 1（D）2 43．曲线y x ln x 的平行于直线 x y 1 0 的切线方程为（）.（A ）y x 1（B）y( x 1)（C）y ln x 1 x 1（D）y x 4．设函数f x| x |，则函数在点 x0 处（）.（A ）连续且可导（B）连续且可微（C）连续不可导（D）不连续不可微5．点x0是函数 y x4的（）.（A ）驻点但非极值点（B）拐点（C）驻点且是拐点（D）驻点且是极值点6．曲线y1的渐近线情况是（）. | x |（A ）只有水平渐近线（B）只有垂直渐近线（C）既有水平渐近线又有垂直渐近线（D）既无水平渐近线又无垂直渐近线7．f112 dx 的结果是（）.x x（A ）f 1C（B）f1C x x（C）f 1C1C x（ D）fxdx的结果是（）.8．e x e x（A ）arctan e x C（B）arctan e x C （C）e x e x C（D）ln( e x e x ) C 9．下列定积分为零的是（）.（A ）arctanx（B）4x arcsinx dx 41x2 dx44（C）1e x e x1x2x sin x dx12dx（D）110．设f x1为连续函数，则 f 2x dx 等于（） .（A ）f 2 f 0（B）1f 11 f 0 2（ C）1f 2 f 0（D）f 1 f 0 2二、填空题（每题 3 分，共 15 分）1．设函数f x e 2 x 1x00 处连续，则 a.x在 xa x02．已知曲线y f x 在 x 2 处的切线的倾斜角为5.，则 f 263．y x的垂直渐近线有条.2x14．dx.ln2 xx 15．2x4 sin x cosx dx.2三、计算题（共55 分）1．求极限1 x2 xx sin x (3分)①lim(3 分)②limx x e x2x x 012. 已知lim x2ax b 2 求a与b（4分）x 2 x2x23. 设f ( x)cos2 x sin x2求 f ( x) （3分）4．求方程y ln x y 所确定的隐函数的导数y x.（4分）5. . 确定曲线y xe x的凹凸区间及拐点（4分）6．求不定积分dx e2dx(2)(1)x 1 x 31x 1 ln xdx x 1(3)(4) 计算定积分| x | e x dx1e17. 计算由曲线y x2, y 2 x所围平面图形的面积.(4分)8.求由曲线y2x, y 0, x 1 所围图形绕x轴旋转而成的旋转体的体积(4 分)9. 设有底为等边三角形的直柱体，体积为 V ，要使其表面积最小，问底的边长为何？（ 6 分）参考答案：一．选择题1．B 2．B 3．A 4．C 5．D 6．C 7．D 8．A 9．A 10．C 二．填空题1．22．33． 24．arctanln x c5．2 3三．计算题１① e2②1 2. 3. 4. y x1 5.6x y16. (1)1ln |x1| C(2) (3)(4) 22 2x3e7.8.9.。

2023专转本高数试卷一、选择题（每题3分，共30分）1. 函数y = (1)/(ln(x - 1))的定义域为（）A. (1,2)∪(2,+∞)B. (1,+∞)C. [1,2)∪(2,+∞)D. (2,+∞)2. 当x→0时，sin x与x是（）A. 高阶无穷小。

B. 低阶无穷小。

C. 同阶但非等价无穷小。

D. 等价无穷小。

3. 设函数y = f(x)在点x_0处可导，则limlimits_Δ x→0(f(x_0 - Δ x)-f(x_0))/(Δ x)=（）A. f'(x_0)B. -f'(x_0)C. 0D. 不存在。

4. 函数y = x^3 - 3x的单调递增区间是（）A. (-∞,-1)∪(1,+∞)B. (-1,1)C. (-∞,+∞)D. (-1,0)∪(1,+∞)5. 设f(x)=∫_0^xsin t^2dt，则f'(x)=（）A. sin x^2B. cos x^2C. 2xsin x^2D. 2xcos x^26. 下列广义积分收敛的是（）A. ∫_1^+∞(1)/(x)dxB. ∫_1^+∞(1)/(x^2)dxC. ∫_0^1(1)/(√(x))dxD. ∫_0^1(1)/(x^2)dx7. 已知向量→a=(1, - 1,0)，→b=(1,0, - 1)，则→a×→b=（）A. (1,1,1)B. (-1, - 1, - 1)C. (1, - 1,1)D. (1,1, - 1)8. 平面2x - y + z = 1的法向量为（）A. (2,-1,1)B. (2,1,1)C. (-2,1,-1)D. (1,-2,1)9. 级数∑_n = 1^∞(1)/(n(n + 1))的和为（）A. 0B. 1C. 2D. 发散。

10. 微分方程y' + y = 0的通解为（）A. y = Ce^xB. y = Ce^-xC. y = x + CD. y = C二、填空题（每题3分，共15分）1. limlimits_x→1(x^2 - 1)/(x - 1)=_22. 函数y = x^2e^x的导数y'=_(x^2 + 2x)e^x3. 设z = ln(x + y)，则(∂ z)/(∂ x)big_x = 1,y = 0=_14. 曲线y = sin x在x=(π)/(2)处的切线方程为_y = 15. 已知→a=(1,2,3)，→b=(3,2,1)，则→a·→b=_10三、计算题（每题8分，共40分）1. 求极限limlimits_x→0(tan x - sin x)/(x^3)。

2023年成人考(专升本)数学真题及答案完整版一、选择题示例及答案题目：设函数f(x)=x2，则f(x)的极值点为（）。

A. x=0B. x=1C. x=2D. x=3答案：C解析：对f(x)求导得f'(x)=3x^2-6x，令f'(x)=0，解得x=0或x=2。

通过二阶导数判断，x=0处为拐点，x=2处为极小值点。

题目：设随机事件A和B相互独立，且P(A)=0.4，P(B)=0.5，则P(A∩B)=（）。

A. 0.2B. 0.1C. 0.3D. 0.4答案：A解析：由于事件A和B相互独立，所以P(A∩B)=P(A)×P(B)=0.4×0.5=0.2。

题目：已知函数y=sin(2x+φ)为奇函数，则φ的值为（）。

A. kπ，k∈ZB. kπ+π/2，k∈ZC. kπ+π，k∈ZD. kπ-π/2，k∈Z答案：A解析：由于y=sin(2x+φ)为奇函数，所以φ=kπ，k∈Z。

二、填空题示例及答案题目：若直线l过点(1,2)且与直线y=2x+3垂直，则直线l的方程为______。

答案：y=-1/2x+5/2解析：由于直线l与直线y=2x+3垂直，所以直线l的斜率为-1/2。

根据点斜式方程，得y-2=-1/2(x-1)，化简得y=-1/2x+5/2。

题目：设函数f(x)={x^2-4x+6,x≤2; ax+3,x>2}，若f(x)在R上单调递减，则a的取值范围是______。

答案：a≤1解析：当x≤2时，f(x)=x^2-4x+6的导数为f'(x)=2x-4，令f'(x)=0，解得x=2。

此时f(x)在x=2处取得极小值，且f(2)=2。

当x>2时，f(x)=ax+3单调递减，所以a<0。

又因为f(x)在R上单调递减，所以f(2)≥f(2+)=2a+3，解得a≤1。

三、解答题示例及答案（简略版）题目：求函数f(x)=x2+3x-1的单调区间和极值。

专升本高等数学(二)-180(总分90,考试时间90分钟)一、选择题1.2. 若，则a的值为______。

A. -1或2B. -2或2C. -1或1D. 1或-23.A．2x B．x2 C．D．14. 设函数A. -3B. -1C. 0D. 不存在5. 设函数y=f(x)的导函数y"=f"(x)的图像如图4-1所示，则下列结论肯定正确的是____．A. x=-1是驻点，但不是极值点B. X=-1不是驻点C. x=-1为极小值点D. X=-1为极大值点6. 等于____．7.8. 已知函数y=f(x)在点飘处可导，且，则f"(x0)等于______A. -4B. -2C. 2D. 49. 设函数z=x2+y2+xy，则等于____。

A.2x+2y**+2y+xy**+3y**+y2+x+y10.二、填空题1. 设则f"(t)=______.2. 已知，则=______．3. 掷两个骰子，两个骰子点数之和等于5的概率为______。

4.5. 曲线y=xlnx-x在x=e处的法线方程为______。

6. 设事件A与B相互独立，且P(A)=0.4，P(A+B)=0.7，则P(B)=______.7. 设，则=______．8. ______.10. x2+5x的相反数是______。

三、解答题1.求下列不定积分2. 计算。

3. 求由方程所确定的隐函数y=y(x)的微分dy。

4. 设试讨论f(x)在x=0处的连续性。

“圆梦计划”复习题集(高升专)—、网络教育高升专“语文”复习题1.下列词语屮加点的字，读音全相同的一组是( )啼饥号寒醍醐灌顶 睦邻友好暮鼓晨钟 朿手待毙数理逻辑 嗜痂之癖老牛舐犊2.下列词语的全部字形及加点字的读咅没有错误的一项是 A.盘桓 (huan) 迂讷(ne) 告磬(qing) 卷帙浩繁(zhi)B.舗齿 5) 剽窃(piao) 诡秘(gul) 不瘟不火(wen)C.徇私 (xun) 株连(zhu) 忱然(wu) 饮鸩止渴(zhdn)D.竣工 (jtin) 孝梯(ti) 骁勇(xiao)额首称庆(chen)3.下列各组词语中没有错别字的一组:A 、 浅尝辄止安之若素 恼羞成怒 侨揉造作 B 、 直捷了当 愤世嫉俗 吹毛求疵 完壁归赵 C 、 血血相觑 移席问计 兵慌马乱 随机应变 D 、 朝不虑夕 惟其所愿 满脸溅珠 出言无状4.下列各组词语屮，没有错别字的一组是:划时代 彬彬有理崭露头角破天荒 戎马径您蛊惑人心 泊来品 重整旗鼓食不果腹 万户侯 滥竽充数声名雀起5. 指出下列句子屮加点熟语使用恰当的一项A. 只有加强思想教育和人格品质的培养，改革课程设置，倡导科学的教学与考试方法，从根本上解决 学以致用的问题，才能对现有的舞弊现象起到釜底抽薪的作用。

• • • •B. 有的屮学生夙兴夜寐沉迷于电子游戏而不能自拔，结果荒废了学业。

• • • •0.他妈妈一进来，我们全寝室的人不谋而合地站了起来。

• • • •D .桃李不言,T 自取變，这件丑事即使不宣传，也会有人知道的6.指出下列句子中加点熟语使用恰当的一项()A. 为了治理水流污染，该地区依法取缔了十儿家污染严重的造纸厂，一时间，洛阳纸贵，用纸大户纷• • • •纷抢购。

B. 孩子应该干、可以干的事情，要让他们自己去干，父母不要评头论足。

• • • •C. 加拿大的高速公路星罗棋布，汽车川流不息，却看不到扬起的尘土,闻不到排放的尾气。

2021-2022学年河南省驻马店市环际大联考圆梦计划高三（上）段考数学试卷（文科）（三）一、单选题（本大题共12小题，共60.0分）1. 巳知集合P ={−2,−1,0,1}；Q ={y|y =√x +1,x ≥0}.则P ∩Q =( )A. {−2,−1}B. {1}C. {0,1}D. {−1,0,1}2. 命题“∀1≤x ≤3，x 2−a ≤0”是真命题的一个充分不必要条件是( )A. a ≥9B. a ≥11C. a ≥8D. a ≤103. 已知数列{a n }的前n 项和为S n ，且满足S n =n 2+n ，则a 8=( )A. 72B. 36C. 18D. 164. 下列说法正确的是( )A. ac 2>bc 2的充要条件是a >b >0B. 若a <b <0，则a 2<ab <b 2C. a >b >0是a 2>b 2的充分不必要条件D. 若a <b <0，则1a <1b5. 若f(x)=13x 3−ax 2的单调减区间是(−4,0)，则a 的值是( )A. −2B. 2C. −4D. 46. 函数f(x)=(21+e x −1)cosx(其中e 为自然对数的底数)图象的大致形状是( )A.B.C.D.7. 已知实数a =232，b =(23)2，c =log 223，则a ，b ，c 的大小关系是( )A. c >b >aB. c >a >bC. b >a >cD. a >b >c8. 已知函数f(x)=ax +b ，g(x)=bx +a(a ≠b)，若f(x)，g(x)的图象与直线y =2交于同一点，且f(m)+g(m)=8，则m 的值为( )A. 2B. 3C. 4D. 69.若函数f(x)=√3sinxcosx+cos2x−12，则下列说法正确的是()A. f(x)的最小正周期为π2B. f(x)的图像的一条对称轴方程为x=512πC. f(x)的一个对称中心为(π6,0)D. f(x)的单调递增区间为[kπ−π3,kπ+π6](k∈Z)10.二七罢工纪念塔位于郑州市二七广场，是为纪念京汉铁路工人大罢工中牺牲的烈士，发扬“二七”革命传统文化精神而修建的纪念性建筑物．某校为庆祝建党100周年，组织学生参观二七罢工纪念塔．同学们在参观过程中，对纪念塔的塔高产生了兴趣，为测量塔的高度，甲同学在二七广场A地测得纪念塔顶D的仰角为45°，乙同学在二七广场B地测得纪念塔顶端D的仰角为30°，塔底为C(A,B,C在同一水平面上，CD⊥平面ABC)，量得AB=63米，∠ACB=30°，则纪念塔的高CD=()A. 40√3米B. 63√3米C. 40米D. 63米11.已知a⃗，b⃗ ，c⃗均为单位向量，且a⃗⊥b⃗ .若a⃗⋅c⃗=34，则|b⃗ ⋅c⃗|=()A. 34B. 35C. 45D. √7412.已知定义在(0,+∞)上的函数f(x)，满足x2f(x1)−x1f(x2)x1−x2>0(x1≠x2)，且f(2)=8，则不等式f(x)−4x>0的解集为()A. (2,+∞)B. (0,2)C. (0,4)D. (4,+∞)二、单空题（本大题共4小题，共20.0分）13.已知tanα=−3，则sinα+cosαsinα−cosα=______．14.在等差数列{a n}中，a1=1，a4=7，设数列{b n}的通项为b n=(−1)n a n，则数列{b n}的前50项和S50=______．15.已知函数f(x)=x2+ax(a∈R)，g(x)=xlnx，若过点(0,−1)存在直线l与f(x)和g(x)的图象均相切，则a的值为______．16.已知正实数a，b满足12a+b +1a+2b=1，则a+b的最小值为______．三、解答题（本大题共6小题，共70.0分）17.已知集合A={x|x2−3x−10≤0}，B={x|m+1≤x≤2m−1}．(1)若A∪B=A，求实数m的取值范围；(2)当x∈R时，若A∩B=⌀，求实数m的取值范围．18.在△ABC中，角A，B，C所对的边分别为a，b，c，且sin2A−sin2B−sin2C=−√3sinBsinC．(Ⅰ)求A的大小；(Ⅱ)若a=1，求b2−c2的取值范围．19.已知数列{a n}为各项均为正数的等比数列，若a1⋅a3=16，a3+a4=24．(Ⅰ)求数列{a n}的通项公式；}的前n项和T n．(Ⅱ)求数列{1log2a n⋅log2a n+120.已知函数f(x)=lnx−k(x−1)，且曲线y=f(x)在点(1,f(1))处的切线与直线y=1平行．(1)求实数k的值，并判断函数f(x)的单调性；(2)记g(x)=xf(x)+λx，若g(x)在(0,+∞)上单调递减，求λ的取值范围．21.已知函数f(x)=mx+nx2+1是定义域为(−1,1)的奇函数，且f(12)=25．(1)求m，n的值，并用函数单调性的定义来判断函数f(x)的单调性；(2)解不等式f(2x+1)+f(x)<0．22.已知向量a⃗=(cos32x,sin32x)，b⃗ =(cos x2,−sin x2)，函数f(x)=a⃗⋅b⃗ −m|a⃗+b⃗ |+1．(Ⅰ)当f(π6)=1时，求m的值；(Ⅱ)是否存在实数m，使函数f(x)=−1225m2，x∈[−π4,π3]有四个不同的零点？若存在，求出m的取值范围；若不存在，说明理由．答案和解析1.【答案】B【解析】解：∵集合P={−2,−1,0,1}，Q={y|y=√x+1,x≥0}={y|y≥1}，∴P∩Q={1}．故选：B．求出集合Q，利用交集定义能求出P∩Q．本题考查交集的求法，考查交集定义、不等式性质等基础知识，考查运算求解能力，是基础题．2.【答案】B【解析】解：∵∀1≤x≤3，x2−a≤0是真命题，∴a≥(x2)max，∴a≥9，∵[11,+∞)⊆[9，+∞)，∴a≥11是命题的充分不必要条件，故选：B．先求命题∀x∈[1,3]，x2−a≤0为真命题的充要条件，再利用集合的包含关系求解．本题考查充分必要条件的概念，考查集合的包含关系，属于基础题．3.【答案】D【解析】解：由题意，可知a8=S8−S7=82+8−(72+7)=16．故选：D．本题根据题意并结合公式a n=S n−S n−1(n≥2)，即可计算出a8的值．本题主要考查已知数列求和公式求某一项的值，考查转化与化归思想，公式法，以及逻辑推理能力和数学运算能力，属基础题．4.【答案】C【解析】解：A.当c=0时，由a>b>0推不到ac2>bc2，反之ac2>bc2⇒a>b但不一定大于0，因此ac2>bc2是a>b>0的既不充分也不必要条件，错误；B.根据不等式的性质，若a<b<0，则−a>−b>0，所以−a2<−ab，−ab<−b2，所以a2>ab，ab>b2，即a2>ab>b2，选项B错误；C.“a>b>0”⇒a2>b2，反之不成立，因此“a>b>0”是a2>b2的充分不必要条件，选项C正确；D.若a<b<0，则1a >1b，选项D错误；故选：C．利用不等式的基本性质、简易逻辑的判定方法即可判断出正误．本题考查了不等式的基本性质、简易逻辑的判定方法，考查了推理能力与计算能力，属于基础题．5.【答案】A【解析】解：f′(x)=x2−2ax，依题意，f′(−4)=16+8a=0，解得a=−2．故选：A．对函数f(x)求导，由f′(−4)=0即可求得a的值．本题考查利用导数研究函数的单调性，注意对题设条件的理解，属于基础题．6.【答案】B【解析】【分析】本题考查了函数图象的判断，考查函数奇偶性的应用，属于中档题．判断f(x)的奇偶性，再根据f(x)在(0,π2)上的函数值的符号得出答案．【解答】解：f(x)=(21+e x −1)cosx=1−e x1+e xcosx，f(−x)=1−e−x1+e−x cos(−x)=e x−1e x+1cosx=−f(x)．∴f(x)为奇函数，图象关于原点对称，排除A ，C ； 当0<x <π2时，e x >1，cosx >0， ∴f(x)=1−e x 1+e x cosx <0，排除D ，故选：B ．7.【答案】D【解析】解：∵a =232>20=1， 0<b =(23)2<(23)0=1，c =log 223<log 21=0，∴a ，b ，c 的大小关系是a >b >c ． 故选：D ．利用指数函数、对数函数的单调性直接求解．本题考查三个数的大小的判断，考查指数函数、对数函数的单调性等基础知识，考查运算求解能力，是基础题．8.【答案】B【解析】解：因为f(x)与g(x)图象与直线y =2交于同一点， 设该点为(x 0,2)， 所以有{ax 0+b =2bx 0+a =2,两式相减得：(a −b)x 0+(b −a)=0， 所以x 0=1， 所以a +b =2，所以f(m)+g(m)=am +b +bm +a =(a +b)m +(a +b)=2m +2=8， 所以m =3， 故选：B ．根据两个函数与直线y =2的交点求出a +b ，整体代入所求式子运算． 本题考查了两直线的交点以及求值问题，注意整体思想的应用．9.【答案】D【解析】解：函数f(x)=√3sinxcosx+cos2x−12=√32sin2x+12cos2x=sin(2x+π6)，可得f(x)的最小正周期为T=2π2=π，故A错误；由f(5π12)=sin(5π6+π6)=0不为最值，故B错误；由f(π6)=sin(π3+π6)=1≠0，故C错误；由2kπ−π2≤2x+π6≤2kπ+π2，k∈Z，解得kπ−π3≤x≤kπ+π6，则f(x)的增区间为[kπ−π3,kπ+π6](k∈Z)，故D正确．故选：D．由二倍角的正弦公式和余弦公式，以及辅助角公式，化简f(x)，分别由三角函数的周期公式和对称轴、对称中心和单调区间，可得结论．本题考查三角函数的恒等变换和正弦函数的性质，考查转化思想和运算能力，属于中档题．10.【答案】D【解析】解：根据题意作出图形如图所示，∠DAC=45°，∠CBD=30°，∠ACB=30°，设塔高为m，因为CD⊥平面ABC，所以DC⊥CB，DC⊥AC，所以CB=√3m，AC=m，在△ABC中由余弦定理有AB2=AC2+BC2−2AC⋅CBcos∠ACB，所以632=m2+3m2−2×√3m×m×√32，解得m=63．故选：D．作出图形，设塔高为m，表示出CB=√3m，AC=m，在△ABC中由余弦定理可求解．本题考查学生作图能力，和解三形的能力，属基础题．11.【答案】D【解析】解：设a ⃗ 与c ⃗ 的夹角为α，b ⃗ 与c ⃗ 的夹角为β， 由a ⃗ ⋅c ⃗ =34，知1×1×cosα=34，所以cosα=34， 当β<90°时，β=90°−α，所以cosβ=cos(90°−α)=sinα=√1−cos 2α=√74，当β>90°时，β=90°+α，所以cosβ=cos(90°+α)=−sinα=−√1−cos 2α=−√74，所以|b ⃗ ⋅c ⃗ |=|1×1×cosβ|=|cosβ|=√74．故选：D ．根据平面向量数量积的运算法则，求解即可．本题考查平面向量数量积的运算，考查运算求解能力，属于基础题．12.【答案】A【解析】解：定义在(0,+∞)上的函数f(x)，满足x 2f(x 1)−x 1f(x 2)x 1−x 2>0(x 1≠x 2)，即x 2f(x 1)−x 1f(x 2)x 1x 2(x 1−x 2)>0，即f(x 1)x 1−f(x 2)x 2x 1−x 2>0，令g(x)=f(x)x，由增函数的定义，得函数g(x)在(0,+∞)上单调递增；因为f(2)=8， 则g(2)=f(2)2=4，所以不等式f(x)−4x >0⇔f(x)x>4=f(2)2，即g(x)>g(2)，所以x >2；所以不等式f(x)−4x >0的解集为(2,+∞)， 故选：A ． 构造函数g(x)=f(x)x，利用单调性的定义结合已知条件，可确定函数g(x)的单调性，将所求解的不等式f(x)−4x >0变形为g(x)>g(2)，利用g(x)的单调性脱“g ”可得到答案．本题考查了抽象函数性质的综合应用，解题的关键是将已知条件与不等式进行变形，考查了逻辑推理能力与转化化归能力，考查了构造法及函数单调性定义的应用，属于中档题．13.【答案】12【解析】解：因为tanα=−3， 所以sinα+cosαsinα−cosα=tanα+1tanα−1=−3+1−3−1=12． 故答案为：12．由已知利用同角三角函数基本关系式化简所求即可得解．本题主要考查了同角三角函数基本关系式在三角函数求值中的应用，属于基础题．14.【答案】50【解析】解：设等差数列{a n }的公差为d ，∵a 1=1，a 4=7， ∴1+3d =7，解得d =2． ∴a n =1+2(n −1)=2n −1． ∴b n =(−1)n a n =(−1)n (2n −1)，则数列{b n }的前50项和S 50=(−1+3)+(−5+7)+⋯…+(−97+99) =2×25=50． 故答案为：50．设等差数列{a n }的公差为d ，利用通项公式即可得出a n ，利用分组求和即可得出数列{b n }的前50项和S 50．本题考查了等差数列的通项公式、分组求和，考查了推理能力与计算能力，属于基础题．15.【答案】−1或3【解析】解：设直线l 与g(x)=xlnx 相切的切点为(m,mlnm)， 由g(x)=xlnx ，得g′(x)=1+lnx ， 可得切线的斜率为1+lnm ，则切线的方程为y −mlnm =(1+lnm)(x −m)，将(0,−1)代入切线的方程可得−1−mlnm =(1+lnm)(0−m)， 解得m =1，则切线l 的方程为y =x −1， 联立{y =x −1y =x 2+ax ，可得x 2+(a −1)x +1=0，由Δ=(a −1)2−4=0，解得a =−1或3， 故答案为：−1或3．设直线l 与y =g(x)相切的切点，求得g(x)的导数，可得切线的斜率和切线的方程，代入已知点的坐标，求得切点，可得切线的方程，与y =f(x)联立，运用判别式为0即可求得a 值．本题考查导数的运用：求切线的方程，以及直线方程的运用，考查方程思想和运算能力，属于中档题．16.【答案】43【解析】解：令x =2a +b ，y =a +2b ，则1x +1y =1，且x >0，y >0，所以a +b =13(x +y)=13(x +y)(1x +1y )=13(1+xy +yx +1)≥13⋅(2+2√xy ⋅yx )=43， 当且仅当xy =yx ，即a =b =23时，等号成立， 所以a +b 的最小值为43， 故答案为：43．令x =2a +b ，y =a +2b ，则1x +1y =1，而a +b =13(x +y)，再由“乘1法”，即可得解．本题考查基本不等式的应用，熟练掌握“乘1法”是解题的关键，考查转化思想，逻辑推理能力和运算能力，属于中档题．17.【答案】解：(1)由题意得A ={−2≤x ≤5}，若A ∪B =A ，则B ⊆A ，当B =⌀时，m +1>2m −1，解得m <2，成立； 当B ≠⌀时，{m +1≤2m −1m +1≥−22m −1≤5，解得2≤m ≤3，综上，实数m 的取值范围是(−∞,3]． (2)∵A ∩B =⌀，∴当B =⌀时，m +1>2m −1，解得m <2，成立； 当B ≠⌀时，{m +1≤2m −1m +1>5或{m +1≤2m −12m −1<−2，解得m>4，综上，实数m的取值范围是(−∞,2)∪(4,+∞)．【解析】(1)求出集合A，由A∪B=A，得B⊆A，当B=⌀时，m+1>2m−1，当B≠⌀时，{m+1≤2m−1m+1≥−22m−1≤5，由此能求出实数m的取值范围．(2)A∩B=⌀，∴当B=⌀时，m+1>2m−1，当B≠⌀时，{m+1≤2m−1m+1>5或{m+1≤2m−12m−1<−2，由此能求出实数m的取值范围．本题考查集合的运算，考查交集、并集定义、不等式性质等基础知识，考查运算求解能力，是基础题．18.【答案】解：(Ⅰ)因为sin2A−sin2B−sin2C=−√3sinBsinC，由正弦定理可得a2−b2−c2=−√3bc，即b2+c2−a2=√3bc，由余弦定理可得cosA= b2+c2−a22bc =√3bc2bc=√32，又0<A<π，所以A=π6；(Ⅱ)由a=1，利用正弦定理可得b sinB=c sinC=1sinπ6=2，所以b=2sinB，c=2sinC，故b2−c2=4sin2B−4sin2C=4sin2B−4sin2(5π6−B)=4sin2B−4(34sin2B+√32sinBcosB+14cos2B)=−2√3sinBcosB−cos2B+sin2B =−√3sin2B−cos2B=−2sin(2B+π6)，因为B∈(0,5π6)，可得2B+π6∈(π6,11π6)，sin(2B+π6)∈[−1,1]，可得b2−c2=−2sin(2B+π6)∈[−2,2]．【解析】(Ⅰ)利用正弦定理将已知的等式角化边，然后由余弦定理可求cosA的值，结合A的范围即可求解A的值．(Ⅱ)利用正弦定理将b和c均用角B表示，然后由三角函数恒等变换的应用以及正弦函数的性质即可求解．本题考查了正弦定理，余弦定理，三角函数恒等变换以及正弦函数的性质在解三角形中的应用，考查了逻辑推理能力与化简运算能力，属于中档题．19.【答案】解：(Ⅰ)根据题意，设正项等比数列{a n}的公比为q，若a1⋅a3=16，a3+a4=24.则(a2)2=a1⋅a3=16，则a2=±4，又由数列{a n}为各项均为正数的等比数列，则a2=4，又由a3+a4=24，则4q+4q2=24，解可得q=2或−3(舍)，故a1=a2q=2，故a n=a1×q n−1=2n，(Ⅱ)根据题意，a n=2n，则log2a n=log22n=n，故T n=1log2a1log2a2+1log2a2log2a3+1log2a3log2a4+⋯…+1log2a n log2a n+1=11×2+12×3+⋯…+1n×(n+1)=(1−12)+(12−13)+(13−14)+⋯…+(1n−1n+1)=1−1n+1=nn+1；故T n=nn+1．【解析】(Ⅰ)根据题意，设正项等比数列{a n}的公比为q，由等比中项的性质求出a2的值，进而可得a3+a4=4q+4q2=24，解可得q的值，据此计算可得答案；(Ⅱ)根据题意，结合(Ⅰ)的答案可得log2a n=log22n=n，由此可得T n的表达式，由裂项相消法计算可得答案．本题考查数列的求和，涉及等比数列的性质以及应用，属于中档题．20.【答案】解：(1)f′(x)=1x−k，x>0，由题意得，f′(1)=1−k=0，所以k=1，所以f′(x)=1x −1=1−xx，易得，当x>1时，f′(x)<0，函数在(1,+∞)上单调递减，当0<x<1时，f′(x)>0，函数在(0,1)上单调递增；(2)g(x)=xf(x)+λx=xlnx−x2+(1+λ)x，x>0，因为g(x)在(0,+∞)上单调递减，所以g′(x)=lnx −2x +2+λ≤0在(0,+∞)上恒成立， 令ℎ(x)=g′(x)，则ℎ′(x)=1x −2=1−2x x，当0<x <12时，ℎ′(x)>0，函数ℎ(x)单调递增， 当x >12时，ℎ′(x)<0，函数ℎ(x)单调递减， 故当x =12时，函数取得最大值ℎ(12)=−ln2+1+λ， 所以−ln2+1+λ≤0，所以λ≤ln2−1， 故λ的取值范围为(−∞,ln2−1]．【解析】(1)先对函数求导，结合导数的几何意义及已知切线斜率可求k ，再结合导数与单调性关系求解即可；(2)根据条件，可得g′(x)=lnx −2x +2+λ≤0在(0,+∞)上恒成立，然后求出λ． 本题主要考查了导数的几何意义，还考查了导数与单调性关系，体现了转化思想的应用，属于中档题．21.【答案】解：(1)因为f(x)=mx+n x 2+1是定义域为(−1,1)的奇函数，由奇函数的性质，得f(0)=n =0， 又f(12)=12m 1+14=25，所以m =1，所以f(x)=xx 2+1，设−1<x 1<x 2<1，则f(x 1)−f(x 2)=x 11+x 12−x21+x 22=x 1+x 1x 22−x 2−x 2x 12(1+x 12)(1+x 22)=(x 1−x 2)(1−x 1x 2)(1+x 12)(1+x 22)<0，所以f(x 1)<f(x 2)，所以f(x)在(−1,1)上单调递增，(2)由(1)可知，f(x)为单调递增的奇函数，由f(2x +1)+f(x)<0，得f(2x +1)<−f(x)=f(−x)， 所以2x +1<−x ，解得x <−13， 不等式的解集(−∞,−13).【解析】(1)由奇函数的性质，可得f(0)=0，结合f(12)=25，可求出m ，n ，然后结合单调性的定义可判断函数的单调性；(2)由(1)可知，f(x)为单调递增的奇函数，然后将不等式转化为f(2x +1)<−f(x)=f(−x)，再解不等式即可．本题主要考查了函数的奇偶性及单调性的应用，还考查了利用单调性及奇偶性求解不等式，属于中档题．22.【答案】解：(Ⅰ)a ⃗ ⋅b ⃗ =cos2x ，|a ⃗ +b ⃗ |=√2+2cos2x =√4cos 2x =2|cosx|，故f(x)=cos2x −2m|cosx|+1当f(π6)=1，即cos π3−2m|cos π6|+1=1，解得m =√36；(Ⅱ)由f(x)=cos2x −2m|cosx|+1，f(x)=−1225m 2，x ∈[−π4,π3]有四个不同的零点， 可得cos2x −2m|cosx|+1+1225m 2=0在x ∈[−π4,π3]上有4个不同的零点， 即cos 2x −mcosx +625m 2=0在x ∈[−π4,π3]上有4个不同的零点， 即(cosx −25m)(cosx −35m)=0在x ∈[−π4,π3]上有4个不同的零点， ∴方程cosx =25m 或cosx =35m 在x ∈[−π4,π3]上有4个不同的零点，因为y =cosx 在x ∈[−π4,π3]上，y 的最大值为1，当x =−π3，x =π3时，y =12， 所以12≤2m 5<1，解得m ∈[54,52). 存在这样的实数m.m ∈[54,52).【解析】(Ⅰ)利用向量数量积的公式化简函数f(x)，代入求值即可．(Ⅱ)问题转化为cos2x −2m|cosx|+1+1225m 2=0在x ∈[−π4,π3]上有4个不同的零点，cos 2x −mcosx +625m 2=0得到方程的根，利用三角函数的性质进行求解即可． 本题主要考三角函数的性质，函数的零点以及复合函数的应用，综合性较强，运算量较大，属于中档题．。