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
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4(答案解析)
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)=。
专升本高数入学试题库
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-专升本高数试题
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
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=______。
(完整版)专升本高等数学习题集与答案
·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 ___________。
高职专升本高等数学试题及答案(2).docx
《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.。
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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。
) 11．设函数216131arcsinxx y ---=，则函数的定义域为)4,2[-. 解：424442016,13112<≤-⇒⎩⎨⎧<<-≤≤-⇒>-≤-≤-x x x x x .12．设曲线22-+=x x y 在点M 处的切线斜率为3,则点M 的坐标是)0,1(. 解：12+='x y ，由1312=⇒=+='x x y ，从而0=y ，故填)0,1(.13．设函数x x y arctan =，则=''y 22)1(2x +.解：21arctan x x x y ++=',2222222)1(2)1(2111x x x x x y +=+-+++=''. 14．=+⎰dx xx 2012)1(ln C x ++2013)1(ln 2013.解：C x x d x dx x x ++=++=+⎰⎰2013)1(ln )1(ln )1(ln )1(ln 201320122012. 15．=⎰∞++-dx xe x 01= e .16．幂级数∑∞=-15)2(n n nn x 的收敛域为)7,3[-.解：由152215lim 5)2(15)2(lim )()(lim 111<-=-+=-+-=∞→++∞→+∞→x x n n nx n x x u x u n n n n n n nn n .得73<<-x 级数收敛,当3-=x 时,级数为∑∞=-1)1(n n n 收敛; 当7=x 时,级数为∑∞=11n n 发散;故收敛域为)7,3[-.17．设A 是n 阶矩阵，E 是n 阶单位矩阵，且，032=--E A A 则=--1)2(E A E A +.解：)()2())(2(0312E A E A E E A E A E A A +=-⇒=+-⇒=---19．设型随机变量),8,1(~N X 且),()(c X P c X P ≥=<则c = 1.解：由正态分布的对称性得1==μc .20．设型随机变量X 在区间]4,2[上服从均匀分布,则方差=)(X D 31.解：直接由均匀分布得3112)24()(2=-=X D .三、计算题：本大题共8小题，其中第21-27题每题7分，第28题11分，共60分。
21．计算极限x xx x 20tan sin lim -→.解：原式= 20sin lim x xx x -→=xx x 2cos 1lim 0-→ =2sin lim 0x x →=0.22．求由方程xy y x =确定的隐函数的导数dxdy. 解：两边取对数得y x y x ln ln ln +=, 两边求导得y yx y y x y '+='+11ln , 从而)1()ln 1(--=x x y x y dx dy .23．计算定积分⎰-222211dx x x解：令t x sec =,则,tan sec tdt t dx =当2=x 时, 4π=t ;当2=x 时, 3π=t .所以原式= ⎰342tan sec tan sec ππdt t t tt = ⎰34cos ππtdt = =|34sin ππt =)23(21-.24．求微分方程02=--'x e y y 的通解.解：原方程可整理为xe y y =-'2这是一阶线性微分方程,其中xe x Q x P =-=)(,2)(. 所以原方程的通解为⎥⎦⎤⎢⎣⎡+⎰⎰=⎰-C dx e x Q e y dx x P dx x P )()()( )(22C dx e e e dxx dx+⎰⎰=⎰-.)(2C dx e e x x +=⎰-)(2C e e x x +-=-x x Ce e 2+-=25．计算二重积分⎰⎰Dyd xσ2,其中D 是由直线222===xy x y x 和、所围成的区域.解：区域D 如图阴影部分所示.故⎰⎰Dyd xσ2⎰⎰=xxy y x x 22221d d⎰=212222d 21|y y x xx⎰-=214)d 44(21x x |215)252(x x -=5210=.26．设矩阵⎪⎪⎪⎭⎫⎝⎛---=320031101A ，,231⎪⎪⎪⎭⎫ ⎝⎛=B 且满足2X . 解：由X B A B AX +=+2可得B A X E A )()(2-=- 因02420041100||≠-=---=-E A ,所以E A -因此B E A X )(+=⎪⎪⎪⎭⎫ ⎝⎛⎪⎪⎪⎭⎫⎝⎛---=231220021102⎪⎪⎪⎭⎫ ⎝⎛-=25027．设行列式1321312132113211)(++++=x x x x x D ,求)(x D 在0=x 处的导数.解：13273127321732171321312132113211)(+++++++=++++=x x x x x x x x x x x x D211101110010001)7(1321312132113211)7(--+=++++=x x x x x x x x)23)(7()2)(1)(7(22+-+=--+=x x x x x x x x .故)32)(7()23)(72()(22-+++-+='x x x x x x x D . 从而14)0(='D .图5-728．已知离散型随机变量X 的密度函数为⎪⎪⎪⎩⎪⎪⎪⎨⎧≥<≤<≤<=.2,1,21,21,10,,0,0)(xx x a x x F 且数学期望34)(=X E . 求: (1) a 的值; (2) X 的分布列；(3)方差D (X )．解：(1) 由分布函数的性质知,随机变量X 的可能取值为0、1、2，且21)2(,21)1(,)0(==-====X P a X P a X P 因3423212)21(10)(=-=⨯+-⨯+⨯=a a a X E所以61=a .(2) 由（1）即得(3) 3223160)(2222=⨯+⨯+⨯=X E ,四、证明题与应用题：本大题共3小题，每小题10分，共30分。
29．设)(2yx f xy u =，其中)(t f 可微，u yzy x z x3:=∂∂+∂∂证明. 证明：因为yy x f xy y x f y x u 1)()(22⋅'+=∂∂ ),()(2yx f xy y xf y '+=⎪⎪⎭⎫ ⎝⎛-⋅'+=∂∂22)()(2y x y x f xy y x xyf y u)()(22yxf x y x xyf '-=,故)()(2)()(2222yxf y x y x f xy y x f y x y x f xy y u y x u x'-+'+=∂∂+∂∂ )(32yxf xy =u 3=. ⋯⋯⋯⋯(9分)30．设D 是由曲线e x x y ==,ln 及x 轴所围成的的平面区域求: (1) 平面区域D 的面积S ; (2) D 绕y 轴旋转一周所成的旋转体的体积V ． 解:区域D 如图阴影部分所示。