2010年考研数学一真题及答案

2010年考研英语一

Section I Use of English

Directions:

Read the following text.Choose the best word(s) for each numbered blank.and

mark[A]，[B]，[C]or[D]on ANSWER SHEET 1. (10 points)

In 1924 American National Research Council sent to engineer to supervise a series

of experiments at a telephone-parts factory called the Hawthorne Plant near Chicago.

It hoped they would learn how stop-floor lighting __1__ workers productivity.

Instead，the studies ended__2__ giving their name to the “Hawthorne effect” the

extremely influential idea the very__3__to being experimented upon changed

subjects’ behavior

The idea arose because of the__4__behavior of the women in the plant.According

to __5__of the experiments their hourly output rose when lighting was increased,

but also when it was dimmed. It did not __6__what was done in the experiment.

2010年考研英语一

Section I Use of English

Directions:

Read the following text.Choose the best word(s) for each numbered blank.and

mark[A]，[B]，[C]or[D]on ANSWER SHEET 1. (10 points)

In 1924 American National Research Council sent to engineer to supervise a

series of experiments at a telephone-parts factory called the Hawthorne Plant near

Chicago. It hoped they would learn how stop-floor lighting __1__ workers

productivity. Instead，the studies ended__2__ giving their name to the ―Hawthorne

effect‖ the extremely influential idea the very__3__to being experimented upon

changed subjects‘ behavior

The idea arose because of the__4__behavior of the women in the

plant.According to __5__of the experiments their hourly output rose when lighting

was increased, but also when it was dimmed. It did not __6__what was done in the

1

2010年全国硕士研究生入学统一考试

英语（一）试题

Section I Use of English

Directions:

Read the following text. Choose the best word(s) for each numbered blank and mark A, B, C or D

on ANSWER SHEET. (10 points)

In 1924 America’s National Research Council sent two engineers to supervise a series of

experiments at a telephone-parts factory called the Hawthorne Plant near Chicago. It hoped they

would learn how shop-floor lighting 1 workers’ productivity. Instead, the studies ended 2

giving their name to the “Hawthorne effect”, the extremely influential idea that the very 3 of

being experimented upon changes subjects’ behavior.

The idea arose because of the 4 behavior of the women in the plant. According to 5

of the experiments, their hourly output rose when lighting was increased, but also when it was

dimmed. It did not 6 what was done in the experiment; 7 something was changed,

令狐采学创作

令狐采学创作 2005年考研数学一真题

令狐采学

一、填空题（本题共6小题，每小题4分，满分24分。答案写在题中横线上）

(1)曲线的斜渐近线方程为。 【答案】

【解析】 所以斜渐近线方程为。 综上所述，本题正确答案是。

【考点】高等数学—一元函数微分学—函数图形的凹凸性、拐点及渐近线

(2)微分方程满足的解为。 【答案】

【解析】 原方程等价于

所以通解为 将代入可得 令狐采学创作

令狐采学创作 综上所述，本题正确答案是。

【考点】高等数学—常微分方程—一阶线性微分方程

(3)设函数,单位向量，则。 【答案】

【解析】 因为 所以 综上所述，本题正确答案是。

【考点】高等数学—多元函数微分学—方向导数和梯度

(4)设是由锥面与半球面围成的空间区域，是的整个边界的外侧，则。 【答案】。

【解析】 综上所述，本题正确答案是。

【考点】高等数学—多元函数积分学—两类曲面积分的概念、性质及计算 令狐采学创作

令狐采学创作 (5)设均为三维列向量，记矩阵 如果，那么。

【答案】2。

【解析】

【方法一】

【方法二】 由于

两列取行列式，并用行列式乘法公式，所以

综上所述，本题正确答案是2。

【考点】线性代数—行列式—行列式的概念和基本性质，行列式按行(列)展开定理

(6)从数中任取一个数，记为，再从中任一个数，记为,则。 【答案】。

【解析】

【方法一】 先求出的概率分布，因为是等可能的取，故关于的边缘分布必有,而只从中抽取，又是等可能抽取的概率为 令狐采学创作

令狐采学创作 所以即：

X Y 1 2 3 4

1 0 0 0 2 0 0 3 0 4

所以

【方法二】

综上所述，本题正确答案是。

【考点】概率论与数理统计—多维随机变量及其分布—二维离散型随机变量的概率分布、边缘分布和条件分布

二、选择题（本题共8小题，每小题4分，满分32分。在每小题给出的四个选项中，只有一项符合题目要求。）