(完整版)江苏省普通高校“专转本”统一考试《高等数学》试卷.doc

2018 年江苏省普通高校 “专转本 ”统一考试

一、选择题（本大题共 6 小题，每小题 4 分，满分 24 分）

1、当 x

0 时，下列无穷小与

f x

xsin 2 x 同阶的是 (

)

A. cos x 2

1 x 3 1

C. 3x 1

D. 1 x

2、设函数 f (x)

x a ，若 x

1 为其可去间断点，则常数 a ，b 的值分别为

(

)

x b

A. 1, 2

B. 1,2

1, 2

D. 1,2

3、设 f ( x)

1 x ，其中

x 为可导函数，且

1 3 ，则 f 0 等于 (

)

1 x

A. 6

B. 6

D. 3

4、设 F x e 2 x 是函数 f x 的一个原函数，则

xf x dx

(

)

A. e

2 x

x 1 C B. e 2x 2x 1 C C. e 2x

x 1 C D. e 2 x 2x 1 C

5、下列反常积分发散的是

( )

e dx

3 dx dx

dx A.

x C.

1 x 2

1 x

6、下列级数中绝对收敛的是

(

)

(

1 2

sin n

( 3)

n 1

n 2

n 1

n 3

二、填空题（本大题共

6 小题，每小题 4 分，共 24 分）

7 设 lim 1

ax x lim xsin

，则常数 a _________．

x 0

8、设函数 y x x

x 0 ，则 y

____________．

9、设 z

z x, y 是由方程 z 2 xyz 1所确定的函数，则

z ___________ ．

10、曲线 y

3x 4 4x 3 6x 2 12 x 的凸区间为 ___________ ．

11、已知空间三点 M 1,1,1 ， A 1,1,0 ， B 2,1,2 ，则

AMB 的大小为 __________ ．

12、幂级数 ( x 4) n

的收敛域为 ____________ ．

n 1

n5n

三、计算题（本大题共8 小题，每小题8 分，共 64 分）

13、求极限lim 1 1 ．

x2 ln 1 x2

x 0

14、设函数y y( x) 由参数方程

x3 xt 2 t 1 0

y t 3 t 1 所确定，求

dy ．

dx t 0

15、求不定积分

1 dx ．

x x 1

16、计算定积分

2x 1 ln xdx ．

x 1 3t

17、求通过点M 1,2,3 及直线y 1 4t 的平面方程．

z 1 5t

18、求微分方程y3 2 x2 y dx 2x3dy 0 的通解．

19、设z xf y,x

，其中函数具有一阶连续偏导数，求全微分dz ．y

20、计算二重积分xydxdy，其中 D x, y

y2 1,0 y x ．x 1

四、证明题（本大题共 2 小题，每小题9 分，共18 分）

21、证明：当x

0 时，ln x x ．

22、设F ( x)

f (t )dt 0，其中函数 f ( x) 在 ( , ) 上连续，且 lim f ( x) 1，证明： F ( x) 在

0 x

＝x 0

x 0

点 x 0处连续。

五、综合题（本大题共 2 小题，每小题10 分，共 20 分）

23、设 D 是由曲线弧y cosx x 与 y sin x x及x轴所围成的平面图形，试求：

4 2 4

（1） D 的面积；

（2） D 绕 x 轴旋转一周所形成的旋转体的体积．

24、设函数 f x 满足方程 f x 3 f x 2 f x 0 ，且在 x 0 处取得极值1，试求：

（ 1）函数 f (x) 的表达式；

f x

（ 2）曲线y 的渐近线．

f x

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江苏省专转本英语考试大纲考试内容：专转本英语考试包括五个部分：阅读理解、词语用法与语法结构、完形填空、翻译、作文。试卷分为第i卷（客观题）和第n卷（主观题）两部分。两卷满分150分。考试时间为 120 分钟。第i卷（客观题）：（100分）第一部分：阅读理解（Part i：Reading Comprehension）第二部分：词语用法和语法结构（Part n：Vocabulary and Structure）第三部分：完形填空（Part川:Cloze）第n卷（主观题）：（50分）第四部分：翻译（Part V：Translation）第五部分：写作（Part V: Writing）第一部分：阅读理解（Part i：Reading Comprehension）：（共 20 题，每小题 2 分，共 40 分）要求考生阅读 4 篇短文，每篇阅读量不超过 300 词。每篇短文后有 5 个问题，考生应根据文章内容从每题四个选择项中选出一个最佳答案。选材的原则是： 1 、题材广泛，可以包括人物传记、社会、文化、日常知识、科普常识等，但是所涉及的背景知识应能为学生所理解； 2、体裁多样，可以包括叙述文、说明文、议论文等； 3、文章的语言难度中等，无法猜测而又影响理解的关键词会用汉语注明词义。阅读理解部分主要测试下述能力： 1 、掌握所读材料的主旨和大意； 2、了解说明主旨和大意的事实和细节； 3、既理解字面的意思，也能根据所读材料进行一定的判断和推论； 4、既理解个别句子的意义，也理解上下文的逻辑关系。阅读理解部分的目的是测试学生通过阅读获取信息的能力，既要求准确，也要求有一定速度。第二部分：词语用法和语法结构（Part n：Vocabulary and Structure）：（共40 题，每小题1 分，共 40 分）题目为词和短语的用法和语法结构。要求考生从每题四个选择项中选出一个最佳答案。试题主要相关于谓语动词的时态语态、非谓语动词、 it 作形式主语或形式宾语、强调句、倒装句、从句引导词、虚拟语气等。词语用法和语法结构部分的目的是测试学生运用词汇、短语及语法结构的能力。第三部分：完形填空（Part川:Cloze）:（共20题，每小题1分，共20分）在一篇或两篇题材熟悉、难度适中的短文（约 200 词）中留有 20 个空白，每个空白为一题，每题有四个选择项，要求考生在全面理解内容的基础上选择一个最佳答案，使短文的意思和结构恢复完整。填空的词项包括结构词和实译词。形填空部分的目的是测试学生综合运用语言的能力，包括语法概念、词汇运用、篇章结构的理解等综合能力。第四部分：翻译（Part IV: Translation）:（共10题，共35分）一般为英译汉、汉译英各一半。两种翻译虽然在形式上不同，但就其本质，就是在谙熟两种语言内在结构的基础上自由转换。在英译汉过程中有通过之前文章理解全文基础的上进行翻译的趋势。英译汉的能力主要取决于对英文的理解能力，汉译英的能力主要取决于用英语的表达能力。第五部分：写作(Part V: Writing) : 15分要求考生写出一篇 120 词以上的短文，试卷上可能给出题目，或规定情景，或要求看图作文，或给

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