2007年研究生入学考试试卷及答案A
2007年全国硕士研究生入学统一考试数学三试题答案
全国硕士研究生入学统一考试数学三试题答案答案速查： 一、选择题二、填空题三、解答题（17）曲线()y y x =在点（1，1）附近是凸的. （18）11)3+ （19）略（20）11011(1)()()(1),(1,3)532n nn n n f x x x ∞++=-=-+-∈-∑（21）1a =，此时所有公共解为[1,0,1]Tx k =-，其中k 为任意常数；2a =，此时唯一公共解为[0,1,1]Tx =-（22）（Ⅰ）B 的特征值为-2,1,1；B 的属于特征值-2的全部特征向量为11k α（1k 为非零的任意常数），B 的属于特征值1的全部特征向量为2233k k αα+（23,k k 为不全为零的任意常数）（Ⅱ）011101110B -⎛⎫ ⎪= ⎪ ⎪-⎝⎭（23）（Ⅰ）{}7224P X Y >=；（Ⅱ）2(2),01,()(2),12,0,Z z z z f z z z -<<⎧⎪=-≤<⎨⎪⎩其他（24）（Ⅰ）1ˆ=22X θ-;（Ⅱ）24()X 不是2θ的无偏估计量 一、选择题（本题共10分小题，每小题4分，满分40分，在每小题给的四个选项中，只有一项符合题目要求，把所选项前的字母填在后边的括号内） （1）【答案】（B ） 【解析】利用当0x →时的等价无穷小关系ln(1)x x +:，即知当0x +→时ln(1:故选B..（2）【答案】 (D)【解析】方法1:论证法，由0()limx f x x→存在及()f x 在0x =处连续，所以00()(0)lim ()lim()0,x x f x f f x x x→→===（A ）正确；由于00()(0)()lim lim0x x f x f f x x x→→-=-存在，所以'(0)f 存在.（C ）也正确； 由()f x 在0x =处连续，所以()f x -在0x =处连续，从而()()f x f x +-在0x =处连续，将它看成（A ）中的()f x ，从而推知(0)(0)0,f f +-=即有2(0)0,(0)0f f ==.所以（B ）正确，此题选择（D ）.方法2：举例法，举例说明（D ）不正确.例如取()f x x =，有00()()lim lim 00x x x x f x f x x x→→----==- 而'(0)f 并不存在. （D ）不正确，选（D ）. （3）【答案】（C ）【解析】由题给条件知，()f x 为x 的奇函数，故()F x 为x 的偶函数，所以(3)(3).F F -=而323223(3)()()(),288(2)(),2F f t dt f t dt f t dt F f t dt ππππ==+=-===⎰⎰⎰⎰所以(3)F - 3(2)4F =，选择C （4）【答案】（B ）【解析】画出该二次积分所对应的积分区域D ，交换为先x 后y11sin 0sin 2(,)(,)xarc ydx f x y dy dy f x y dx ππππ-=⎰⎰⎰⎰， 所以选择(B).（5）【答案】（D ） 【解析】'()22.()16021602Q P PP P Q P P P-===--需求弹性 由题知，它等于1，解之，40.P =所以选(D)（6）【答案】（D ） 【解析】001lim lim ln(1),x x x y e x →→⎛⎫=++=∞⎪⎝⎭所以0x =是一条垂直渐近线；1lim lim ln(1)0,x x x y e x →-∞→-∞⎛⎫=++= ⎪⎝⎭所以0y =是沿x →-∞方向的一条水平渐近线； 又 21ln(1)ln(1)1lim lim lim lim 1,xx x x x x x x e y e e e x x x x x →+∞→+∞→+∞→+∞⎛⎫+++=+== ⎪⎝⎭洛 ()()1lim lim ln(1)lim ln(1)x x x x x y x e x e x x →+∞→+∞→+∞⎛⎫-=++-=+- ⎪⎝⎭ 1lim ln()lim ln(1)0,xx x x x e e e-→+∞→+∞+=+== 所以y x =也是一条渐近线，所以共有3条，选择（D ） （7）【答案】(A)【解析】根据线性相关的定义，若存在不全为零的数123,,k k k ，使得1122330k k k ααα++=成立.则称123,,ααα线性相关.因1223310αααααα-+-+-=， 故122331αααααα---，，线性相关，所以选择（A ）. （8）【答案】（B ）【解析】2111111111211210311211203E A λλλλλλλλλλ--=-=-=----()230λλ=-=因为A 的特征值是3，3，0，B 的特征值1，1，0，因为特征值不等，故不相似. A 与B 有相同的正惯性指数2，秩都等于2，所以A 与B 合同，应选（B ）.（9）【答案】(C)【解析】根据独立重复的贝努利试验，前3次试验中有1次成功2次失败.其概率必为123(1).C p p -再加上第4次是成功的，其概率为p .根据独立性，第4次射击为第二次命中目标的概率为12223(1)3(1).C p p p p p -=-g 所以应选（C ）.（10）【答案】(A)【解析】由于二维正态的(,)X Y 中X 与Y 不相关，故X 与Y 独立，且(,)()()X Y f x y f x f y =.根据条件概率密度的定义，当在Y y =条件下，如果()0,Y f y ≠则(,)()()X Y Y f x y f x y f y =()()()()X Y X Y f x f y f x f y ==.现()Y f y 显然不为0，因此()().X X Y f x y f x = 应选(A).二、填空题：11-16小题，每小题4分，共24分，请将答案写在答题纸指定位置上 （11）【答案】 0【解析】方法1：由洛必达法则，()32223213262lim lim lim 22ln 232ln 26x x xx x x x x x x x x x x→+∞→+∞→+∞++++==+++ ()36lim0,2ln 26xx →+∞==+而(sin cos )x x +是有界变量，所以3231lim (sin cos )0.2x x x x x x x →∞+++=+ 方法2：32133311lim(sin cos )lim (sin cos )221x x x x x x x x x x x x x x ---→+∞→+∞+++++=+++ 而 233222ln 22(ln 2)lim 2lim lim lim 36x x x xx x x x x x x x-→+∞→+∞→+∞→+∞===32(ln 2)lim 6x x →+∞==+∞， 所以 3231lim(sin cos )0.2x x x x x x x →∞+++=+（12）【答案】1(1)2!3n n n n +-【解析】()()()1232123,'(1)223,''(1)(2)223,,23y x y x y x x ---==+=-+=--++L由数学归纳法知()1()(1)2!23,n n nnyn x --=-+()1(1)2!(0)3n n n n n y +-= （13）【答案】''122()y x f f x y-+【解析】12122211'';'',z y z x f f f f x x y y x y ⎛⎫∂∂⎛⎫=⋅-+⋅=⋅+⋅- ⎪ ⎪∂∂⎝⎭⎝⎭''122()z z y xxy f f x y x y∂∂-=-+∂∂ （14）【解析】典型类型按标准解法.命,y ux =有,dy duu x dx dx=+原方程化为 31,2du u x u u dx +=- 即 32,du dx u x =-积分，得 21ln x C u=+化为y ，得 22ln x y x C=+解出y =再以(1,1)代入，1,C =所以得特解y =.（15）【答案】 1 【解析】2010001000010*********001000100010000000000000000A ⎛⎫⎛⎫⎛⎫⎪⎪ ⎪⎪⎪ ⎪== ⎪⎪ ⎪⎪⎪ ⎪⎝⎭⎝⎭⎝⎭32001001000001000100100000000000010000000000000000A A A ⎛⎫⎛⎫⎛⎫⎪⎪ ⎪ ⎪⎪ ⎪=⋅==⎪⎪ ⎪⎪⎪ ⎪⎝⎭⎝⎭⎝⎭显然()31.r A=(16) 【答案】34【解析】所有可能随机在区间(0,1)中随机取的两个数,X Y ，12X Y -<。
2007年研究生入学考试试题（A）
2007年研究生入学考试试题（A）2007年研究生入学考试试题(A)考试科目：计算机软件技术基础报考学科、专业：计算机应用技术请注意:全部答案必须写在答题纸上，否则不给分。
一、名词解释（第1~4题，每题3分，第5、6题要求先写出英文全称，再用中文简要解释其含义，每题4分，共20分）1、数据类型2、线程3、原语4、虚拟设备5、WPL6、DMA二、填空题（每题2分，共20分）1、假设B =（K，R）是一个逻辑结构，r是一个K到K的1 ：1关系，r∈R，若k，k’∈K，且< k，k’>∈r，则称k’是k的①，k是k’的②。
2、设循环队列中数组的下标范围是0～n-1，其头尾指针分别为f 和r，则该循环队列中数据元素的个数为。
3、设有一个三对角矩阵An*n，将其三条对角线上的元素逐行地存储到向量B[0..3n-3]中，则元素A[5,6]的存储单元下标为。
（假设下标都从0开始）4、可采用折半查找法进行查找的数据表一般应满足的条件为①和②。
5、操作系统具备处理并发任务的能力，其最重要的硬件支持是。
6、每个信箱可以由①和②两部分组成。
7、死锁产生的根本原因是①和②。
8、文件包括①和②两种，前者是指文件内的信息不再划分独立的单位，整个文件是由一串信息组成，后者是指文件内的信息按逻辑上独立的含义划分信息单位。
9、通道在执行通道程序的过程中，需要访问内存中的两个固定单元，①和②。
10、UNIX操作系统的第一个版本Versional是①公司下属的Bell 实验室的两个程序员KenThompson和Dennis Ritchie于②年在PDP11机器上开发实现的。
三、简答题（每题5分，共30分）1、设多项式P(x)＝5x6＋3x4－4x3＋x－12，请用两种不同的线性存储结构表示该多项式，画出它们的存储映像图。
2、设一棵二叉树的前序遍历序列为B A L F E C D H G，后序遍历序列为L F A D H C G E B，请画出该二叉树，并分别给出该二叉树的中序遍历序列和按层次遍历序列。
2007年全国硕士研究生入学考试数学一真题及答案详解
Y 的概率密度，则在 Y = y 的条件下， X 的条件概率密度 f X Y (x y) 为（ A ）。
（A） f X (x)
(B) fY ( y)
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(D) f X (x) fY (y)
【解析与点评】由于 ( X ,Y ) 服从二维正态分布，且 X 与 Y 不相关，所以 X 与 Y 相互独立，
（13）二阶常系数非齐次线性微分方程 y′′ − 4 y′ + 3y = 2e2x 的通解为 y = __________。
【 解 】 齐 次 解 为 y = C1e x + C2e3x ， 设 特 解 为 y = Ae2x ， 由 待 定 系 数 法 得 到
4 Ae2x − 8Ae2x + 3Ae2x = 2e2x ， A − 2 ， 答案： y = C1e x + C2e3x − 2e2x 。
（A）若 lim f (x) = 0 ，则 f (0) = 0 x→0 x
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（D）若 lim f (x) − f (−x) 存在，则 f ′(0) 存在
（D）若 u1 < u2 ，则 {un }必发散
【解】答案 D。画出草图，结论显见。下面证明 D：
u1 < u2 ，则 u2 − u1 > c > 0 ,其中 c 是某个确定的正数，于是存在 ξ1 ∈ (1,2) 使得
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2007年考研数学试题详解及评分参考
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郝海龙：考研数学复习大全·配套光盘·2007 年数学试题详解及评分参考
2007 年全国硕士研究生入学统一考试
数学试题详解及评分参考
数 学（一）
一、选择题 （ 1 ～ 10 小题，每小题 4 分，共 40 分。）
(1) 当 x ® 0+ 时，与 (A) 1- e x
【答】 应选 (B) .
x 等价的无穷小量是
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(A) 0
(B) 1
(C) 2
(D) 3
【答】 应选 (D) .
【解】
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2007全国硕士研究生入学考试数学真题详解——线性代数部分
2007-2010年全国硕士研究生入学考试数学真题详解——线性代数部分一、2007年：1、(2007年数学一、二、三、四) 设向量组321,,ααα线性无关，则下列向量组线性相关的是(A) 133221,,αααααα---. (B) 133221,,αααααα+++.(C) 1332212,2,2αααααα---. (D) 1332212,2,2αααααα+++. [ ] 【答案】A【详解】用定义进行判定:令0)()()(133322211=-+-+-ααααααx x x ，得 0)()()(332221131=+-++-+-αααx x x x x x .因321,,ααα线性无关，所以 1312230,0,0.x x x x x x -=⎧⎪-+=⎨⎪-+=⎩ 又 011011101=---， 故上述齐次线性方程组有非零解, 即133221,,αααααα---线性相关. 类似可得(B), (C), (D)中的向量组都是线性无关的.2、(2007年数学一、二、三、四) 设矩阵⎪⎪⎪⎭⎫ ⎝⎛------=211121112A , ⎪⎪⎪⎭⎫ ⎝⎛=000010001B , 则A 与B(A) 合同, 且相似. (B) 合同, 但不相似 .(C) 不合同, 但相似. (D) 既不合同, 又不相似. [ ] 【答案】B【详解】 由0||=-A E λ 得A 的特征值为0, 3, 3, 而B 的特征值为0, 1, 1,从而A 与B 不相似.又r (A )=r (B )=2, 且A 、B 有相同的正惯性指数, 因此A 与B 合同. 故选(B) .3、(2007年数学一、二、三、四) 设矩阵⎪⎪⎪⎪⎪⎭⎫ ⎝⎛=0000100001000010A , 则3A 的秩为 . 【答案】1【详解】 依矩阵乘法直接计算得 ⎪⎪⎪⎪⎪⎭⎫ ⎝⎛=00000000000010003A , 故r (3A )=1.4、(2007年数学一、二、三、四)设线性方程组⎪⎩⎪⎨⎧=++=++=++04,02,03221321321xa x x ax x x x x x ①与方程12321-=++a x x x ②有公共解，求a 的值及所有公共解．【分析】 两个方程有公共解就是①与②联立起来的非齐次线性方程组有解. 【详解】 将①与②联立得非齐次线性方程组:⎪⎪⎩⎪⎪⎨⎧-=++=++=++=++.12,04,02,03213221321321a x x x x a x x ax x x x x x ③ 若此非齐次线性方程组有解, 则①与②有公共解, 且③的解即为所求全部公共解. 对③的增广矩阵A 作初等行变换得:→⎪⎪⎪⎪⎪⎭⎫⎝⎛-=112104102101112a a a A ⎪⎪⎪⎪⎪⎭⎫⎝⎛-----11000)1)(2(0001100111a a a a a .于是1° 当a =1时，有)()(A r A r ==2<3，方程组③有解, 即①与②有公共解, 其全部公共解即为③的通解，此时⎪⎪⎪⎪⎪⎭⎫⎝⎛→0000000000100101A ， 此时方程组③为齐次线性方程组，其基础解系为: ⎪⎪⎪⎭⎫⎝⎛-101,所以①与②的全部公共解为⎪⎪⎪⎭⎫ ⎝⎛-101k ，k 为任意常数.2° 当a =2时，有)()(A r A r ==3，方程组③有唯一解, 此时⎪⎪⎪⎪⎪⎭⎫⎝⎛-→0000110010100001A ，故方程组③的解为:011⎛⎫ ⎪⎪ ⎪-⎝⎭, 即①与②有唯一公共解: 为123011x x x x ⎛⎫⎛⎫⎪ ⎪== ⎪ ⎪ ⎪ ⎪-⎝⎭⎝⎭.5、(2007年数学一、二、三、四)设3阶对称矩阵Ａ的特征值,2,2,1321-===λλλ T)1,1,1(1-=α是Ａ的属于1λ的一个特征向量,记E A A B +-=354其中E 为3阶单位矩阵.(I) 验证1α是矩阵Ｂ的特征向量，并求B 的全部特征值与特征向量．(II) 求矩阵Ｂ．【分析】 根据特征值的性质可立即得B 的特征值, 然后由B 也是对称矩阵可求出其另外两个线性无关的特征向量.【详解】 (I) 由11αα=A 得 1112ααα==A A , 进一步 113αα=A , 115αα=A ， 故 1351)4(ααE A A B +-=113154ααα+-=A A1114ααα+-=12α-=，从而1α是矩阵Ｂ的属于特征值−2的特征向量.因E A A B +-=354, 及Ａ的3个特征值,2,2,1321-===λλλ 得 B 的3个特征值为1,1,2321==-=μμμ.设32,αα为B 的属于132==μμ的两个线性无关的特征向量, 又Ａ为对称矩阵，得B 也是对称矩阵, 因此1α与32,αα正交, 即0,03121==ααααT T 所以32,αα可取为下列齐次线性方程组两个线性无关的解：0)1,1,1(321=⎪⎪⎪⎭⎫ ⎝⎛-x x x ,其基础解系为: ⎪⎪⎪⎭⎫ ⎝⎛011,⎪⎪⎪⎭⎫ ⎝⎛-101 , 故可取2α=⎪⎪⎪⎭⎫ ⎝⎛011, 3α=⎪⎪⎪⎭⎫ ⎝⎛-101.即B 的全部特征值的特征向量为: ⎪⎪⎪⎭⎫⎝⎛-1111k , ⎪⎪⎪⎭⎫ ⎝⎛-+⎪⎪⎪⎭⎫ ⎝⎛10101132k k , 其中01≠k ,是不为零的任意常数, 32,k k 是不同时为零的任意常数.(II) 令),,(321ααα=P =⎪⎪⎪⎭⎫ ⎝⎛--101011111, 则 ⎪⎪⎪⎭⎫⎝⎛-=-1121BP P ，得 1112-⎪⎪⎪⎭⎫ ⎝⎛-=P P B =⎪⎪⎪⎭⎫ ⎝⎛--101011111⎪⎪⎪⎭⎫⎝⎛-112⎪⎪⎪⎭⎫ ⎝⎛--21112111131=⎪⎪⎪⎭⎫ ⎝⎛---102012112⎪⎪⎪⎭⎫ ⎝⎛--21112111131⎪⎪⎪⎭⎫ ⎝⎛--=011101110.二、2008年：1、（2008年数学一、二、三、四）设A 为n 阶非零矩阵，E 为n 阶单位矩阵．若30A =，则[ ]则下列结论正确的是：(A) E A -不可逆，则E A +不可逆. (B) E A -不可逆，则E A +可逆.(C) E A -可逆，则E A +可逆. (D) E A -可逆，则E A +不可逆. 【答案】应选(C).【详解】23()()E A E A A E A E -++=-=，23()()E A E A A E A E +-+=+=． 故E A -，E A +均可逆．故应选(C).2、（2008年数学一）设A 为3阶实对称矩阵，如果二次曲面方程()1x x yz A y z ⎛⎫⎪= ⎪ ⎪⎝⎭在正交变换下的标准方程的图形如图，则A 的正特征值个数为[ ](A) 0. (B) 1. (C) 2. (D) 3. 【答案】 应选(B).【详解】此二次曲面为旋转双叶双曲面，此曲面的标准方程为222221x y z a c +-=．故A 的正特征值个数为1．故应选(B).3、（2008年数学二、三、四）设1221A ⎛⎫=⎪⎝⎭，则在实数域上，与A 合同矩阵为[ ] (A) 2112-⎛⎫⎪-⎝⎭ . (B)2112-⎛⎫ ⎪-⎝⎭. (C) 2112⎛⎫ ⎪⎝⎭. (D) 1221-⎛⎫ ⎪-⎝⎭. 【答案】 应选(D). 【详解】2212(1)423(1)(3)021E A λλλλλλλλ---==--=--=+-=--则121,3λλ=-=，记1221D -⎛⎫=⎪-⎝⎭，则2212(1)423(1)(3)021E D λλλλλλλλ--==--=--=+-=-则121,3λλ=-=，正负惯性指数相同.故选D.4、(2008年数学一) 设A 为2阶矩阵，12,αα为线性无关的2维列向量，10A α=，2122A ααα=+．则A 的非零特征值为___________.【答案】应填1．【详解】根据题设条件，得1212121202(,)(,)(0,2)(,)01A A A αααααααα⎛⎫==+= ⎪⎝⎭．记12(,)P αα=，因12,αα线性无关，故12(,)P αα=是可逆矩阵．因此0201AP P ⎛⎫= ⎪⎝⎭，从而10201P AP -⎛⎫= ⎪⎝⎭．记0201B ⎛⎫= ⎪⎝⎭，则A 与B 相似，从而有相同的特征值． 因为2||(1)01E B λλλλλ--==--，0λ=，1λ=．故A 的非零特征值为1．5、（2008年数学二）设3阶矩阵A 的特征值为2,3,λ．若行列式|2|48A =-，则λ=___________. 【答案】应填1-．【详解】由482-=A ，依据方阵行列式的性质，则有48223-==A A ，即6-=A .又A 等于其特征值的乘积，即632321-=⨯⨯=⨯⨯=λλλλA ,得1-=λ. 6、（2008年数学三）设3阶方阵A 的特征值为1,2,2,E 为单位矩阵，则=--E A 14 .【答案】应填3．【详解】由方阵特征值的性质，E AA f -=-14)(，则14)(1-=-λλf ，故方阵EA --14的特征值分别为1,1,3，又由方阵行列式等于其特征值的乘积，则有341=--E A .7、（2008年数学四）设3阶方阵A 的特征值互不相同，若行列式0=A ，则A 的秩为 . 【答案】应填2．【详解】由题可知，方阵A 的特征值含有0，而其余两个非零，故A 的秩为2.8、（2008年数学一）设,αβ为3维列向量，矩阵TTA ααββ=+，其中,TTαβ分别是,αβ得转置．证明： （I ） 秩()2r A ≤；（II ）若,αβ线性相关，则秩()2r A <．【详解】（I ）【证法1】()()()()()()2TTTTr A r r r r r ααββααββαβ=+≤+≤+≤． 【证法2】因为TTA ααββ=+，A 为33⨯矩阵，所以()3r A ≤． 因为,αβ为3维列向量，所以存在向量0ξ≠，使得0,0T T αξβξ==于是 0T T A ξααξββξ=+= 所以0Ax =有非零解，从而()2r A ≤．【证法3】因为TTA ααββ=+，所以A 为33⨯矩阵．又因为()00T TTT A αααββαββ⎛⎫⎪=+= ⎪ ⎪⎝⎭， 所以|||0|00TT a A αββ==故 ()2r A ≤．（II ）【证法】由,αβ线性相关，不妨设k αβ=．于是()2()()(1)()12TT T r A r r k rααβββββ=+=+≤≤<． 9、(2008年数学一、二、三、四) 设n 元线性方程组Ax b =，其中2222212121212a a a a a A a a a a ⎛⎫ ⎪⎪⎪=⎪ ⎪⎪ ⎪ ⎪⎝⎭，12n x x x x ⎛⎫ ⎪ ⎪= ⎪ ⎪⎝⎭，b 100⎛⎫ ⎪ ⎪= ⎪ ⎪⎝⎭．（I ）证明行列式||(1)n A n a =+；（II ）当a 为何值时，该方程组有惟一解，并求1x ． （III ）当a 为何值时，该方程组有无穷多解，并求其通解．【详解】（I ）【证法1】数学归纳法．记2222212121||212n na a a a aD A a a a a ==以下用数学归纳法证明(1)nn D n a =+．当1n =时，12D a =，结论成立． 当2n =时，2222132a D a a a==，结论成立． 假设结论对小于n 的情况成立．将n D 按第一行展开得n n n a a a aD aD a a a a 2212211021212212--=-2122n n aD a D --=-1222(1)n n ana a n a --=-- (1)n n a =+故 (1)nA n a =+．【注】本题（1）也可用递推法．由2122n n n D aD a D --==-得，2211221()()n n n n n n n D aD a D aD a D a D a ------=-==-=．于是(1)n n D n a =+（I ）【证法2】消元法．记2222212121||212na a a a aA a a a a =22122213121212212na a a ar ar a a a a -322222130124123321212naa a r ar a aa a a a -=n n na a a n r ar nn a n n a n 121301240113111----+(1)n n a =+．（II ）【详解】当0a ≠时，方程组系数行列式0n D ≠，故方程组有惟一解．由克莱姆法则，将n D 得第一列换成b ，得行列式为22211222211121021212121212122n n nn a aa a a aa aD na a a a a a a a a ---===所以，11(1)n n D ax D n a-==+． （III ）【详解】 当0a =时，方程组为12101101001000n n x x x x -⎛⎫⎛⎫⎛⎫ ⎪⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭ 此时方程组系数矩阵得秩和增广矩阵得秩均为1n -，所以方程组有无穷多组解，其通解为()()010100TTx k =+，其中k 为任意常数．10、(2008年数学二、三、四)设A 为3阶矩阵，12,αα为A 的分别属于特征值1,1-的特征向量，向量3α满足321A ααα=+，(I)证明123,,ααα线性无关； (II)令123(,,)P ααα=，求1P AP -．【详解】(I)【证明】设有一组数123,,k k k ，使得 122330k k k ααα++=． 用A 左乘上式，得112233()()()0k A k A k A ααα++=． 因为 11A αα=-, 22A αα=，321A ααα=+， 所以 1123233()0k k k k ααα-+++=， 即113220k k αα-=．由于12,αα是属于不同特征值得特征向量，所以线性无关，因此130k k ==，从而有20k =．故 123,,ααα线性无关．（II ）由题意，100011001AP P -⎛⎫⎪= ⎪ ⎪⎝⎭．而由（I ）知，123,,ααα线性无关，从而123(,,)P ααα=可逆．故1100011001P AP --⎛⎫⎪= ⎪ ⎪⎝⎭．三、2009年：1、（2009年数学一）设123,,ααα是3维向量空间3R 的一组基，则由基12311,,23ααα到基 122331,,αααααα+++的过渡矩阵为()A 101220033⎛⎫⎪⎪ ⎪⎝⎭. ()B 120023103⎛⎫⎪⎪ ⎪⎝⎭.()C 111246111246111246⎛⎫- ⎪ ⎪ ⎪- ⎪ ⎪ ⎪- ⎪⎝⎭.()D 111222111444111666⎛⎫-⎪ ⎪ ⎪- ⎪ ⎪ ⎪- ⎪⎝⎭. 【答案】A【解析】因为()()1212,,,,,,n n A ηηηααα=，则A 称为基12,,,n ααα到12,,,nηηη的过渡矩阵。
2007年考研试题及答案A
一、填空题（30分）：1. （6分）由晶闸管构成的三相半波可控整流电路，当输入交流电压为t u ωsin 3112=，纯阻性负载且其值为10R =Ω，当控制角45α=时，输出平均电压为 ，输出的功率因数是 。
2．（6分）由晶闸管构成的单相桥式全控整流电路，当输入交流电压为t u ωsin 1412=，负载为反电动势且直流侧串联平波电抗器，已知60V, L=2E R =∞=Ω，，当控制角30α=时，输出平均电压为 ，输出平均电流为 。
3．（3分）缓冲电路( Snubber Circuit ) 的作用是 。
4．（3分）在交流供电系统中，当基波电流为140A I =，各次谐波电流分别为35792A, 1A, 0.5A, 0.2A I I I I ====, 则电流谐波总畸变THD 为 。
5．（3分）在逆变电路中，对于同一桥臂的开关管要采取“先断后通”的方法，也就是死区时间的设定，其目的是 。
6．（6分）单相桥式电压型逆变电路，180导通角，d 560V U =，则输出电压的基波有效值是 ，当只考虑10次以内的谐波电压时，输出电压的有效值是 。
7．（3分）在SPWM （Sinusoidal Pulse Width Modulation ）控制的三相逆变电路中，设定的开关管的开关频率是20KHz ，逆变电路输出交流电压的频率为400Hz ，那么SPWM 控制电路中载波频率和调制波频率应分别设置为 和 。
二、简答题（60分）：1． （7分）IGBT 在过流及短路过程中，系统如何检测并实施保护的？2． （7分）为什么晶闸管的触发信号通常不使用直流信号？ 3． （7分）试说明有关晶闸管和电力晶体管的关断过程？4． （7分）请叙述电力二极管的反向恢复过程，在高频开关电路中，应选择什么型号的二极管？5． （8分）利用晶闸管SCR 构成的简易照明延时开关电路如图1所示，HL 是灯泡，SB 是开关，试分析此电路的工作原理。
2007年考研英语试题及答案
2007年全国硕士研究生入学统一考试英语试题Section II Reading ComprehensionPart ADirections:Read the following four texts.Answer the questions below each text by choosing A,B,C or D.Mark your answers on the ANSWER SHEET.(40points)Text1If you were to examine the birth certificates of every soccer player in2006’s World Cup tournament,you would most likely find a noteworthy quirk:elite soccer players are more likely to have been born in the earlier months of the year than in the later months.If you then examined the European national youth teams that feed the World Cup and professional ranks,you would find this strange phenomenon to be even more pronounced.What might account for this strange phenomenon?Here are a few guesses:a) certain astrological signs confer superior soccer skills;b)winter-born babies tend to have higher oxygen capacity,which increases soccer stamina;c)soccer-mad parents are more likely to conceive children in springtime,at the annual peak of soccer mania;d)none of the above.Anders Ericsson,a58-year-old psychology professor at Florida State University, says he believes strongly in“none of the above.”Ericsson grew up in Sweden,and studied nuclear engineering until he realized he would have more opportunity to conduct his own research if he switched to psychology.His first experiment,nearly30 years ago,involved memory:training a person to hear and then repeat a random series of numbers.“With the first subject,after about20hours of training,his digit span had risen from7to20,”Ericsson recalls.“He kept improving,and after about200hours of training he had risen to over80numbers.”This success,coupled with later research showing that memory itself is not genetically determined,led Ericsson to conclude that the act of memorizing is more of a cognitive exercise than an intuitive one.In other words,whatever inborn differencestwo people may exhibit in their abilities to memorize,those differences are swamped by how well each person“encodes”the information.And the best way to learn how to encode information meaningfully,Ericsson determined,was a process known as deliberate practice.Deliberate practice entails more than simply repeating a task. Rather,it involves setting specific goals,obtaining immediate feedback and concentrating as much on technique as on outcome.Ericsson and his colleagues have thus taken to studying expert performers in a wide range of pursuits,including soccer.They gather all the data they can,not just performance statistics and biographical details but also the results of their own laboratory experiments with high achievers.Their work makes a rather startling assertion:the trait we commonly call talent is highly overrated.Or,put another way, expert performers–whether in memory or surgery,ballet or computer programming–are nearly always made,not born.21.The birthday phenomenon found among soccer players is mentioned to[A]stress the importance of professional training.[B]spotlight the soccer superstars in the World Cup.[C]introduce the topic of what makes expert performance.[D]explain why some soccer teams play better than others.22.The word“mania”(Line4,Paragraph2)most probably means[A]fun.[B]craze.[C]hysteria.[D]excitement.23.According to Ericsson,good memory[A]depends on meaningful processing of information.[B]results from intuitive rather than cognitive exercises.[C]is determined by genetic rather than psychological factors.[D]requires immediate feedback and a high degree of concentration.24.Ericsson and his colleagues believe that[A]talent is a dominating factor for professional success.[B]biographical data provide the key to excellent performance.[C]the role of talent tends to be overlooked.[D]high achievers owe their success mostly to nurture.25.Which of the following proverbs is closest to the message the text tries toconvey?[A]“Faith will move mountains.”[B]“One reaps what one sows.”[C]“Practice makes perfect.”[D]“Like father,like son.”Text2For the past several years,the Sunday newspaper supplement Parade has featured a column called“Ask Marilyn.”People are invited to query Marilyn vos Savant,who at age10had tested at a mental level of someone about23years old;that gave her an IQ of228–the highest score ever recorded.IQ tests ask you to complete verbal and visual analogies,to envision paper after it has been folded and cut,and to deduce numerical sequences,among other similar tasks.So it is a bit confusing when vos Savant fields such queries from the average Joe(whose IQ is100)as,What’s the difference between love and fondness?Or what is the nature of luck and coincidence? It’s not obvious how the capacity to visualize objects and to figure out numerical patterns suits one to answer questions that have eluded some of the best poets and philosophers.Clearly,intelligence encompasses more than a score on a test.Just what does itmean to be smart?How much of intelligence can be specified,and how much can we learn about it from neurology,genetics,computer science and other fields?The defining term of intelligence in humans still seems to be the IQ score,even though IQ tests are not given as often as they used to be.The test comes primarily in two forms:the Stanford-Binet Intelligence Scale and the Wechsler Intelligence Scales (both come in adult and children’s version).Generally costing several hundred dollars, they are usually given only by psychologists,although variations of them populate bookstores and the World Wide Web.Superhigh scores like vos Savant’s are no longer possible,because scoring is now based on a statistical population distribution among age peers,rather than simply dividing the mental age by the chronological age and multiplying by100.Other standardized tests,such as the Scholastic Assessment Test (SAT)and the Graduate Record Exam(GRE),capture the main aspects of IQ tests.Such standardized tests may not assess all the important elements necessary to succeed in school and in life,argues Robert J.Sternberg.In his article“How Intelligent Is Intelligence Testing?”,Sternberg notes that traditional test best assess analytical and verbal skills but fail to measure creativity and practical knowledge, components also critical to problem solving and life success.Moreover,IQ tests do not necessarily predict so well once populations or situations change.Research has found that IQ predicted leadership skills when the tests were given under low-stress conditions,but under high-stress conditions,IQ was negatively correlated with leadership–that is,it predicted the opposite.Anyone who has toiled through SAT will testify that test-taking skill also matters,whether it’s knowing when to guess or what questions to skip.26.Which of the following may be required in an intelligence test?[A]Answering philosophical questions.[B]Folding or cutting paper into different shapes.[C]Telling the differences between certain concepts.[D]Choosing words or graphs similar to the given ones.27.What can be inferred about intelligence testing from Paragraph3?[A]People no longer use IQ scores as an indicator of intelligence.[B]More versions of IQ tests are now available on the Internet.[C]The test contents and formats for adults and children may be different.[D]Scientists have defined the important elements of human intelligence.28.People nowadays can no longer achieve IQ scores as high as vos Savant’sbecause[A]the scores are obtained through different computational procedures.[B]creativity rather than analytical skills is emphasized now.[C]vos Savant’s case is an extreme one that will not repeat.[D]the defining characteristic of IQ tests has changed.29.We can conclude from the last paragraph that[A]test scores may not be reliable indicators of one’s ability.[B]IQ scores and SAT results are highly correlated.[C]testing involves a lot of guesswork.[D]traditional test are out of date.30.What is the author’s attitude towards IQ tests?[A]Supportive.[B]Skeptical.[C]Impartial.[D]Biased.Text3During the past generation,the American middle-class family that once could count on hard work and fair play to keep itself financially secure had beentransformed by economic risk and new realities.Now a pink slip,a bad diagnosis,or a disappearing spouse can reduce a family from solidly middle class to newly poor in a few months.In just one generation,millions of mothers have gone to work,transforming basic family economics.Scholars,policymakers,and critics of all stripes have debated the social implications of these changes,but few have looked at the side effect:family risk has risen as well.Today’s families have budgeted to the limits of their new two-paycheck status.As a result,they have lost the parachute they once had in times of financial setback–a back-up earner(usually Mom)who could go into the workforce if the primary earner got laid off or fell sick.This“added-worker effect”could support the safety net offered by unemployment insurance or disability insurance to help families weather bad times.But today,a disruption to family fortunes can no longer be made up with extra income from an otherwise-stay-at-home partner.During the same period,families have been asked to absorb much more risk in their retirement income.Steelworkers,airline employees,and now those in the auto industry are joining millions of families who must worry about interest rates,stock market fluctuation,and the harsh reality that they may outlive their retirement money. For much of the past year,President Bush campaigned to move Social Security to a saving-account model,with retirees trading much or all of their guaranteed payments for payments depending on investment returns.For younger families,the picture is not any better.Both the absolute cost of healthcare and the share of it borne by families have risen–and newly fashionable health-savings plans are spreading from legislative halls to Wal-Mart workers,with much higher deductibles and a large new dose of investment risk for families’future healthcare.Even demographics are working against the middle class family,as the odds of having a weak elderly parent–and all the attendant need for physical and financial assistance–have jumped eightfold in just one generation.From the middle-class family perspective,much of this,understandably,looksfar less like an opportunity to exercise more financial responsibility,and a good deal more like a frightening acceleration of the wholesale shift of financial risk onto their already overburdened shoulders.The financial fallout has begun,and the political fallout may not be far behind.31.Today’s double-income families are at greater financial risk in that[A]the safety net they used to enjoy has disappeared.[B]their chances of being laid off have greatly increased.[C]they are more vulnerable to changes in family economics.[D]they are deprived of unemployment or disability insurance.32.As a result of President Bush’s reform,retired people may have[A]a higher sense of security.[B]less secured payments.[C]less chance to invest.[D]a guaranteed future.33.According to the author,health-savings plans will[A]help reduce the cost of healthcare.[B]popularize among the middle class.[C]compensate for the reduced pensions.[D]increase the families’investment risk.34.It can be inferred from the last paragraph that[A]financial risks tend to outweigh political risks.[B]the middle class may face greater political challenges.[C]financial problems may bring about political problems.[D]financial responsibility is an indicator of political status.35.Which of the following is the best title for this text?[A]The Middle Class on the Alert[B]The Middle Class on the Cliff[C]The Middle Class in Conflict[D]The Middle Class in RuinsText4It never rains but it pours.Just as bosses and boards have finally sorted out their worst accounting and compliance troubles,and improved their feeble corporation governance,a new problem threatens to earn them–especially in America–the sort of nasty headlines that inevitably lead to heads rolling in the executive suite:data insecurity.Left,until now,to odd,low-level IT staff to put right,and seen as a concern only of data-rich industries such as banking,telecoms and air travel, information protection is now high on the boss’s agenda in businesses of every variety.Several massive leakages of customer and employee data this year–from organizations as diverse as Time Warner,the American defense contractor Science Applications International Corp and even the University of California,Berkeley–have left managers hurriedly peering into their intricate IT systems and business processes in search of potential vulnerabilities.“Data is becoming an asset which needs to be guarded as much as any other asset,”says Haim Mendelson of Stanford University’s business school.“The ability to guard customer data is the key to market value,which the board is responsible for on behalf of shareholders.”Indeed,just as there is the concept of Generally Accepted Accounting Principles(GAAP),perhaps it is time for GASP,Generally Accepted Security Practices,suggested Eli Noam of New York’s Columbia Business School.“Setting the proper investment level for security,redundancy,and recovery is a management issue,not a technical one,”he says.The mystery is that this should come as a surprise to any boss.Surely it shouldbe obvious to the dimmest executive that trust,that most valuable of economic assets, is easily destroyed and hugely expensive to restore–and that few things are more likely to destroy trust than a company letting sensitive personal data get into the wrong hands.The current state of affairs may have been encouraged–though not justified–by the lack of legal penalty(in America,but not Europe)for data leakage.Until California recently passed a law,American firms did not have to tell anyone,even the victim,when data went astray.That may change fast:lots of proposed data-security legislation is now doing the rounds in Washington,D.C.Meanwhile,the theft of information about some40million credit-card accounts in America,disclosed on June 17th,overshadowed a hugely important decision a day earlier by America’s Federal Trade Commission(FTC)that puts corporate America on notice that regulators will act if firms fail to provide adequate data security.36.The statement“It never rains but it pours”is used to introduce[A]the fierce business competition.[B]the feeble boss-board relations.[C]the threat from news reports.[D]the severity of data leakage.37.According to Paragraph2,some organizations check their systems to find out[A]whether there is any weak point.[B]what sort of data has been stolen.[C]who is responsible for the leakage.[D]how the potential spies can be located.38.In bringing up the concept of GASP the author is making the point that[A]shareholders’interests should be properly attended to.[B]information protection should be given due attention.[C]businesses should enhance their level of accounting security.[D]the market value of customer data should be emphasized.39.According to Paragraph4,what puzzles the author is that some bosses fail to[A]see the link between trust and data protection.[B]perceive the sensitivity of personal data.[C]realize the high cost of data restoration.[D]appreciate the economic value of trust.40.It can be inferred from Paragraph5that[A]data leakage is more severe in Europe.[B]FTC’s decision is essential to data security.[C]California takes the lead in security legislation.[D]legal penalty is a major solution to data leakage.。
2007年考研英语真题答案及解析
二、试题具体解析
1.[A] natives 本地人
[B] inhabitants 居民 [C] peoples 民族
[D] individuals 个人
【答案】 B
【考点】 词汇辨析
【难度系数】 0.422
【解析】 空的前句指出西班牙和葡萄牙殖民地成为了独立的国家。空所在的语境为：大约 200 万这些国家的 看到未
【答案】 C
【考点】 词义辨析
【难度系数】 0.205
【解析】12 题已经分析了这个句子表示的两种不同的观点，前面是把天主教作为国教，后面则应该表示内容与此相
对立。而天主教一旦作为国教，那么自然要结束其他教派的传播，而对立观点则是应该结束对其他教派的排斥，故
答案为 C。
15.[A] support 支持
【答案】 D
【考点】 词义辨析
【难度系数】 0.292
【解析】 空所在的句意：平等主义的情绪经常会被一些担忧所冲淡，这种担忧就是大部分人对自治和民主 。四个选
项代入句中，只有 D 能使语义通顺，故答案为 D。
三、全文翻译
到 1830 年，西班牙和葡萄牙的前殖民地已经成为独立国家。这些国家的大约两千万居民满怀希望地展望着未来。
10.[A] with 和……在一起
[B] about 关于 [C] among 在……之中 [D] by 被
【答案】 C
【考点】 词义搭配
【难度系数】 0.375
【解析】空前内容表示分歧，既然是分歧自然是存在领导人之间，故本题选 C。
11.[A] allowed 允许
[B] preached 宣讲
[B] succession 接替，继任 [C] right 权利 [D] return 偿还，归还
2007数学考研真题(一)
2007年硕士研究生入学考试数学一试题及答案解析一、选择题：(本题共10小题，每小题4分，共40分. 每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内)(1) 当0x +→(A) 1- (B) ln(C) 1. (D) 1- [ B ]【分析】 利用已知无穷小量的等价代换公式，尽量将四个选项先转化为其等价无穷小量，再进行比较分析找出正确答案.【详解】 当0x +→时，有1(1)~-=--1~；2111~.22x -= 利用排除法知应选(B). (2) 曲线1ln(1)x y e x=++，渐近线的条数为 (A) 0. (B) 1. (C) 2. (D) 3. [ D ] 【分析】 先找出无定义点，确定其是否为对应垂直渐近线；再考虑水平或斜渐近线。
【详解】 因为01lim[ln(1)]xx e x→++=∞，所以0x =为垂直渐近线；又 1lim [ln(1)]0xx e x→-∞++=，所以y=0为水平渐近线；进一步，21ln(1)ln(1)lim lim[]lim x x x x x y e e x x x x→+∞→+∞→+∞++=+==lim11xx x e e →+∞=+， 1lim [1]lim [ln(1)]x x x y x e x x→+∞→+∞-⋅=++-=lim[ln(1)]xx e x →+∞+-=lim [ln (1)]lim ln(1)0x xxx x e e x e --→+∞→+∞+-=+=，于是有斜渐近线：y = x . 故应选(D).(3) 如图，连续函数y =f (x )在区间[−3，−2]，[2，3]上的图形分别是直径为1的上、下半圆周，在区间[−2，0]，[0，2]的图形分别是直径为2的上、下半圆周，设0()().xF x f t dt =⎰则下列结论正确的是(A) 3(3)(2)4F F =--. (B) 5(3)(2)4F F =. (C) )2(43)3(F F =-. (D) )2(45)3(--=-F F . [ C ]【分析】 本题考查定积分的几何意义，应注意f (x )在不同区间段上的符号，从而搞清楚相应积分与面积的关系。
2007考研数一真题及解析
为 L 上从点 M 到点 N 的一段弧，则下列积分小于零的是(
)
A. f (x, y)dx
B. f (x, y)dy
C. f (x, y)ds
D.
f
x
(
x,
y)dx
f
y
(
x,
y)dy
(7) 设向量组1,2 ,3 线性无关，则下列向量组线性相关的是(
)
A .1 2 ,2 3,3 1
B .1 2 ,2 3,3 1
f
(t )dt
r2 2
2
1 2
2
8
所以
F (3) 2 f (t)dt 3 f (t)dt 3 3 3 F (2)
0
2
2 8 8 42 4
所以 F (3) F (3) 3 F (2) ，选择 C 4
(4)【答案】( D) 【详解】
22
2007
方法 1：论证法，证明 A.B.C 都正确，从而只有 D. 不正确.
x0
x0
x0
所以
2
f
(0)
lim
x0
f
(x) f x
(x)
x
lim
x0
f
(x) f x
(x)
lim x x0
0 lim x0
f
(x)
f x
(x)
0
即有 f (0) 0 .所以(B)正确，故此题选择(D).
方法 2：举例法，举例说明(D)不正确. 例如取 f (x) x ，有
lim f (x) f (x) lim x x 0 存在
lim x0
2 1
x x
1
1
x
lim 2 x lim 1 0 1 1 ，选(B). x0 1 x x0 1 x
07年考研英语真题解析.doc
2007年全国硕士研究生入学考试英语试题答案及解析Section l Use of English1. [答案][B][分析]词义辨析题，“native”意为本地人，本国人，指一个地方原始居民或长期居住者中的一位；“inhabitant ”意为居民，居住者，指长期居住在某地的人；“people”意为人，人们，本身通常为复数；“individual”意为个体，指具有自己独特个性的、作为个体存在的人。
前面句子说一些殖民地已经成为独立国家，本句话说这些国家的…展望着未来，说明本句话指的是生活在这些国家的人民，所以应选B。
2. [答案][D][分析] 词义辨析与搭配题，“confusedly”意为“困惑地，混乱地”；“cheerfully”意为“高兴地，愉快地”；“worriedly”意为“担心地，担忧地”；“hopefully”意为“满怀希望地，抱有希望地”。
所填之词修饰“looked to the future”，所以本题应选D。
3. [答案][A][分析]词义辨析与搭配题，“share”意为“分享，共享”，指与另一个人或其他人共同享有或具有；“forget”意为“忘记，忘却”；“attain”意为“获得，得到”，指经过努力得到；“reject”意为“拒绝，不接受”。
句子的主语是“many of the leaders”，根据前面的“Born in the crisis of the old regime…”可知，应选A。
4. [答案][C][分析]词义搭配题，所填之词与“to”搭配。
“related to”意为“与…有关”；“close to”意为“接近…”；“open to”意为“向…开放”；“devoted to”意为“投身于…”，主语通常是人。
所填之词与“to talent(有才能者)”搭配，修饰“careers”，所以本题应选C。
5. [答案][C][分析] 词义辨析与搭配题，“a ccess”指接近、进入或使用权力。
2007年全国硕士研究生入学统一考试数学一试题答案
全国硕士研究生入学统一考试数学一试题答案答案速查： 一、选择题二、填空题三、解答题（17）()f x 在D 上的最大值为8，最小值为0 （18）I π= （19）略（20）（Ⅰ）略；（Ⅱ）2()x y x xe =（21）1a =，此时所有公共解为[1,0,1]Tx k =-，其中k 为任意常数；2a =，此时唯一公共解为[0,1,1]Tx =-（22）（Ⅰ）B 的特征值为-2,1,1；B 的属于特征值-2的全部特征向量为11k α（1k 为非零的任意常数），B 的属于特征值1的全部特征向量为2233k k αα+（23,kk 为不全为零的任意常数）（Ⅱ）011101110B-⎛⎫⎪=⎪ ⎪-⎝⎭（23）（Ⅰ）{}7224P X Y >=；（Ⅱ）2(2),01,()(2),12,0,Z z z z f z z z -<<⎧⎪=-≤<⎨⎪⎩其他（24）（Ⅰ）1ˆ=22X θ-;（Ⅱ）24()X 不是2θ的无偏估计量 一、选择题（本题共10分小题，每小题4分，满分40分，在每小题给的四个选项中，只有一项符合题目要求，把所选项前的字母填在后边的括号内） （1）【答案】（B ）【解析】方法1：排斥法：由几个常见的等价无穷小， 有：0x +→时，1(1-::211,2-:所以选（B ）.方法2：当0x +→时，ln[1~~~x =+选（B ）.方法3：00lim lim 11x x x →→+⎡⎤=⎢+⎣，选（B ）. （2）【答案】（D ） 【解析】001lim lim ln(1),x x x y e x →→⎛⎫=++=∞⎪⎝⎭所以0x =是一条垂直渐近线；1lim lim ln(1)0,x x x y e x →-∞→-∞⎛⎫=++= ⎪⎝⎭所以0y =是沿x →-∞方向的一条水平渐近线； 又 21ln(1)ln(1)lim lim lim lim 1,1x x xx x x x x y e e e x x x x e →+∞→+∞→+∞→+∞⎛⎫++=+== ⎪+⎝⎭洛 ()()1lim lim ln(1)lim ln(1)x x x x x y x e x e x x →+∞→+∞→+∞⎛⎫-=++-=+- ⎪⎝⎭ 1lim ln()lim ln(1)0,xx x x x e e e-→+∞→+∞+=+== 所以y x =也是一条渐近线，所以共有3条，选择（D ） （3）【答案】（C ）【解析】由题给条件知，()f x 为x 的奇函数，故()F x 为x 的偶函数，所以(3)(3).F F -=而323223(3)()()(),288(2)(),2F f t dt f t dt f t dt F f t dt ππππ==+=-===⎰⎰⎰⎰所以(3)F - 3(2)4F =，选择C （4）【答案】 (D)【解析】方法1:论证法，由0()limx f x x→存在及()f x 在0x =处连续，所以00()(0)lim ()lim()0,x x f x f f x x x→→===（A ）正确；由于00()(0)()lim lim 0x x f x f f x x x→→-=-存在，所以'(0)f 存在.（C ）也正确；由()f x 在0x =处连续，所以()f x -在0x =处连续，从而()()f x f x +-在0x =处连续，将它看成（A ）中的()f x ，从而推知(0)(0)0,f f +-=即有2(0)0,(0)0f f ==.所以（B ）正确，此题选择（D ）.方法2：举例法，举例说明（D ）不正确.例如取()f x x =，有0()()limlim 00x x x x f x f x x x→→----==- 而'(0)f 并不存在. （D ）不正确，选（D ）. （5）【答案】 (D)【解析】由拉格朗日中值定理，有1n n (1)()'()(1)'(),(1,2,)n n u u f n f n f n n f n ξξ+-=+-=+-==L12n .ξξξ<<<<L L由''()0,f x >知'()f x 严格单调增，故12n '()'()'().f f f ξξξ<<<<L L由于121'()0,f u u ξ=->所以1111k 1111()'()'().n nn k k k k u u u u u f u nf ξξ++===+-=+>+∑∑而1'()f ξ是一个确定的正数.于是推知1lim ,n n u +→∞=+∞故{}n u 发散.选（D ）（6）【答案】 (B)【解析】记1122(,),(,),M x y N x y 由条件11220,0,0,0,x y x y <>><并注意到在积分的弧段上(,) 1.f x y =于是212121212211(A)(,)0.B (,)0.D (,),0.(,)D (,)(,)(,)(,)(,)x x y y x y f x y dx dx dx x x f x y dy dy dy y y f x y ds ds l l l x y f x y dx f x y dy df x y f x y x y ΓΓΓΓΓΓΓΓ===->===-<==Γ>''+==⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰（）（）为弧的长，（）2211(,)(,)110.f x y f x y =-=-=所以选择(B) （7）【答案】(A)【解析】根据线性相关的定义，若存在不全为零的数123,,k k k ，使得1122330k k k ααα++=成立.则称123,,ααα线性相关.因1223310αααααα-+-+-=， 故122331αααααα---，，线性相关，所以选择（A ）. （8）【答案】（B ）【解析】2111111111211210311211203E A λλλλλλλλλλ--=-=-=----()230λλ=-=因为A 的特征值是3，3，0，B 的特征值1，1，0，因为特征值不等，故不相似. A 与B 有相同的正惯性指数2，秩都等于2，所以A 与B 合同，应选（B ）. （9）【答案】(C)【解析】根据独立重复的贝努利试验，前3次试验中有1次成功2次失败.其概率必为123(1).C p p -再加上第4次是成功的，其概率为p .根据独立性，第4次射击为第二次命中目标的概率为12223(1)3(1).C p p p p p -=-g 所以应选（C ）（10）【答案】(A)【解析】由于二维正态的(,)X Y 中X 与Y 不相关，故X 与Y 独立，且(,)()()X Y f x y f x f y =.根据条件概率密度的定义，当在Y y =条件下，如果()0,Y f y ≠则(,)()()X Y Y f x y f x y f y =()()()()X Y X Y f x f y f x f y ==.现()Y f y 显然不为0，因此()().X X Y f x y f x = 应选(A).二、填空题：11-16小题，每小题4分，共24分，请将答案写在答题纸指定位置上 （11）【答案】2【解析】令1t x=，有211,,x dx dt t t ==-111222311112t t t x e dx te dt te e x ⎡⎤=-=--=⎣⎦⎰⎰ （12）【答案】112ln y x yxf y y f -''+g【解析】求复合函数的偏导数112()()ln y xy x z f f x y yx f y y f x u x v x-∂∂∂∂∂''=+=+∂∂∂∂∂g （13）【答案】32122xx x C eC e e +-【解析】特征方程为2430,r r -+=特征根121,3,r r ==对应齐次方程的通解312.x x Y C e C e =+设该齐次方程的一个特解为*2,xy Ae =代入原方程，可求得*22.xy e =-故得原方程的通解为32122xx x y C eC e e =+-.（14）【答案】【解析】曲面∑对称于yOz 平面，x 为x 的奇函数，所以0.xdS ∑=⎰⎰Ò又因∑关于,,x y z 轮换对称，所以,xdS ydS z dS ∑∑∑==⎰⎰⎰⎰⎰⎰乙?()1133y dS x y z dS dS ∑∑∑=++=⎰⎰⎰⎰⎰⎰乙?()1.3=⨯∑的面积而∑为8，所以∑的面积218sin23π=⋅=所以()x y dS ∑+=⎰⎰Ò（15）【答案】 1 【解析】2010001000010*********001000100010000000000000000A ⎛⎫⎛⎫⎛⎫⎪⎪ ⎪ ⎪⎪ ⎪==⎪⎪ ⎪⎪⎪ ⎪⎝⎭⎝⎭⎝⎭32001001000001000100100000000000010000000000000000A A A ⎛⎫⎛⎫⎛⎫⎪⎪ ⎪⎪⎪ ⎪=⋅==⎪⎪ ⎪⎪⎪ ⎪⎝⎭⎝⎭⎝⎭显然()31.r A=(16)【答案】34【解析】所有可能随机在区间(0,1)中随机取的两个数,X Y ，12X Y -<。
2007年全国硕士研究生入学统一考试数学一真题及答案
2007年全国硕士研究生入学统一考试数学一试题一、 选择题：110:小题，每小题4分，共40分，下列每题给出的四个选项中，只有一个选项符合题目要求的，请将所选项前的字母填在答题纸指定位置上.（1） 当0x +→）A.1-B1C.1D -【答案】(B)【考点】等价无穷小 【难易度】★★【详解】解析：方法1：排斥法：由几个常见的等价无穷小，当0x +→0→，所以1(1-::211,2-:可以排除A 、C 、D ，所以选（B ）. 方法2：==ln 1⎛⎫+ ⎝ 当0x +→时，11→0→，又因为0x →时，()ln 1x x +:，所以)ln 1~~1~x ⎛= ⎝B ）.方法3：0lim x +→00lim x x →→'洛1lim lim 1x x ++→→==1A x=+(()111A B x x ++=- 对应系数相等得：1A B = =，所以原式00lim lim 1x x x ++→→⎡⎤==+⎢+⎣0lim lim 011x x x ++→→=+=++1=，选（B ）.（2） 曲线1ln(1)x y e x=++渐近线的条数为（ ） .A 0 .B 1 .C 2 .D 3【答案】( D)【考点】函数图形的渐近线 【难易度】★★★【详解】解析：001lim lim ln(1)x x x y e x →→⎛⎫=++⎪⎝⎭=∞，所以0x =是一条铅直渐近线；1lim lim ln(1)x x x y e x →-∞→-∞⎛⎫=++ ⎪⎝⎭1lim lim ln(1)000x x x e x →-∞→-∞=++=+=，所以0y =是沿x →-∞方向的一条水平渐近线；令21ln(1)1ln(1)lim lim lim x x x x x e y e x a x x x x →+∞→+∞→+∞++⎛⎫+===+ ⎪⎝⎭21ln(1)lim lim x x x e x x →+∞→+∞+=+ln(1)0lim x x e x →+∞+=+1lim 11xx x e e →+∞+ =洛必达法则令()1lim lim ln(1)x x x b y a x e x x →+∞→+∞⎛⎫=-⋅=++- ⎪⎝⎭()()1limlim ln(1)0lim ln(1)x x x x x e x e x x →+∞→+∞→+∞=++-=++- ()1ln lim ln(1)ln lim ln()xxxxx x x e x e e e e→+∞→+∞+ = +-=lim ln(1)ln10x x e -→+∞=+==所以y ax b x =+=是曲线的斜渐近线，所以共有3条，选择（D ）（3） 如下图，连续函数()y f x =在区间[][]3,2,2,3--上的图形分别是直径为1的上、下半圆周，在区间[][]2,0,0,2-上图形分别是直径为2的上、下半圆周，设0()(),xF x f t dt =⎰则下列结论正确的是（ ）.A (3)F 3(2)4F =-- .B (3)F 5(2)4F = .C (3)F - 3(2)4F = .D (3)F -5(2)4F =--【答案】( C)【考点】定积分的概念、定积分的基本性质，积分上限的函数及其导数 【难易度】★★★【详解】解析：由题给条件知，()f x 为x 的奇函数，则()()f x f x -=-，由0()(),xF x f t dt =⎰知()()()()()()()()xx xF x f t dt t u f u d u f u f u f u du F x --= =- -- -=- =⎰⎰⎰，故()F x 为x 的偶函数，所以(3)(3).F F -=而2(2)()F f t dt =⎰表示半径1R =的半圆的面积，所以22(2)()22R F f t dt ππ===⎰，32302(3)()()()F f t dt f t dt f t dt ==+⎰⎰⎰，其中32()f t dt ⎰表示半径12r =的半圆的面积的负值，所以22321()2228r f t dt πππ⎛⎫=-=-⋅=- ⎪⎝⎭⎰所以3232333(3)()()()(2)288424F f t dt f t dt f t dt F ππππ==+=-==⋅=⎰⎰⎰ 所以3(3)(3)(2)4F F F -==，选择( C)（4） 设函数()f x 在0x =处连续，则下列命题错误的是（ ）.A 若0()limx f x x →存在，则(0)0f = .B 若0()()lim x f x f x x →+-存在，则(0)0f =.C 若0()lim x f x x →存在，则(0)f '存在 .D 若0()()lim x f x f x x→--存在，则(0)f '存在【答案】( D)【考点】极限的四则运算，函数连续的概念，导数的概念【难易度】★★【详解】解析：方法1:论证法，证明..A B C 都正确，从而只有.D 不正确。
2007 年全国硕士研究生入学考试政治试题及答案
2007 年全国硕士研究生入学考试政治试题治及参考答案一、单项选择题单项选择选：1－16 小题小，每题每 1 分，共161 分。
下列每题给出的四个选项四母。
中，只有一个选项是符合题目要求的。
请在答题卡上将所选项的字母涂黑1．“风定花犹落，鸟鸣山更幽”形象地表达了动和静的辨证关系是A．静不是动，动不是静B．静中有动，动中有静C．动是必然的，静是偶然的D．动是静的原因，静是动的结果2．“挟泰山以超北海，语人曰吾不能，是诚不能也。
为长者折枝，语人曰吾不能，是不为也，非不能也。
”《孟子》中的这段话启示我们，做事情要区分可能性和不可能性，二者的区别在于A．人的主观努力程度B．对人是否有利C．现实中有无根据和条件D．现实中的根据和条件是否充分3．马克思根据人的发展状况把人类历史划分为三大形态。
它们是A．自然经济社会、商品经济社会、时间经济社会B．原始公有制社会、私有制社会、共产主义公有制社会C．农业社会、工业社会、信息社会D．人的依赖性社会、物的依赖性社会、人的自由全面发展社会4．列宁说：“意识到自己的奴隶地位而与之作斗争，是革命家、没有意识到自己的奴隶地位而过着默默无言、浑浑噩噩、忍气吞声的奴隶生活的奴隶，是十足的奴隶。
对奴隶生活的各种好处津津乐道并对和善的好主人感激不尽以至垂涎欲滴的奴隶是奴才，无耻之徒。
”这三种奴隶的思想意识之所有有如此巨大的差异，是由于A．人的社会意识并不都是社会存在的反映B．人的社会意识与社会存在具有不一致性C．人的社会意识中的各种形式之间相互作用D．人的社会意识具有历史继承性5．货币的本质是A．商品交换的媒介物B．商品价值的一般等价物C．商品的等价物D．商品相对价值形式6．在资本主义社会，农业资本家和土地所有者之间争夺的是A．形成级差地租I 的超额利润B．形成级差地租II 的超额利润C．形成绝对地租的超额利润D．形成垄断地租的超额利润7．作为商品的资本是A．商业资本B．借贷资本C．产业资本D．流通资本8．在中国共产党的历史上，第一次鲜明的提出“马克思主义中国化”的命题和任务的会议是A．党的二大B．遵义会议C．党的六届六中全会D．党的七大9．国民革命失败后，毛泽东在八七会议上提出的著名论断是A．须知政权是由枪杆子中取得的B．兵民是胜利之本C．一切反动派都是纸老虎D．星星之火，可以燎原10．1957 年，毛泽东在《关于正确处理人民内部矛盾的问题》中指出，在我国，工人阶级与民族资产阶级的矛盾属于人民内部的矛盾。
2007年考研英语真题(含答案解析)
2007年全国硕士研究生入学统一考试英语试题Section I Use of EnglishDirections: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)By 1830 the former Spanish and Portuguese colonies had become independent nations. The roughly 20 million 1 of these nations looked 2 to the future. Born in the crisis of the old regime and Iberian Colonialism, many of the leaders of independence 3 the ideals of representative government, careers 4 to talent, freedom of commerce and trade, the 5 to private property, and a belief in the individual as the basis of society. 6 there was a belief that the new nations should be sovereign and independent states, large enough to be economically viable and integrated by a 7 set of laws.On the issue of 8 of religion and the position of the church, 9, there was less agreement 10 the leadership. Roman Catholicism had been the state religion and the only one 11 by the Spanish crown. 12 most leaders sought to maintain Catholicism13 the official religion of the new states, some sought to end the14 of other faiths. The defense of the Church became a rallying15 for the conservative forces.The ideals of the early leaders of independence were often egalitarian, valuing equality of everything. Bolivar had received aidfrom Haiti and had 16 in return to abolish slavery in the areas he liberated. By 1854 slavery had been abolished everywhere except Spain’s 17 colonies. Early promises to end Indian tribute and taxes on people of mixed origin came much 18 because the new nations still needed the revenue such policies 19. Egalitarian sentiments were often tempered by fears that the mass of the population was 20 self-rule and democracy.1. [A] natives[B] inhabitants[C] peoples[D] individuals2. [A] confusedly[B] cheerfully[C] worriedly[D] hopefully3. [A] shared[B] forgot[C] attained[D] rejected4. [A] related[B] close[C] open[D] devoted5. [A] access[B] succession[C] right[D] return6. [A] Presumably[B] Incidentally[C] Obviously[D] Generally7. [A] unique[B] common[C] particular[D] typical8. [A] freedom[B] origin[C] impact[D] reform9. [A] therefore[B] however[C] indeed[D] moreover10. [A] with[B] about[C] among[D] by11. [A] allowed[B] preached[C] granted[D] funded12. [A] Since[B] If[C] Unless[D] While13. [A] as[B] for[C] under[D] against14. [A] spread[B] interference[C] exclusion[D] influence15. [A] support[B] cry[C] plea[D] wish16. [A] urged[B] intended[C] expected[D] promised17. [A] controlling[B] former[C] remaining[D] original18. [A] slower[B] faster[C] easier[D] tougher19. [A] created[B] produced[C] contributed[D] preferred20. [A] puzzled by[B] hostile to[C] pessimistic about[D] unprepared forSection II Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions below each text by choosing [A], [B], [C], or [D]. Mark your answers on ANSWER SHEET 1. (40 points)Text 1If you were to examine the birth certificates of every soccer player in 2006’s World Cup tournament, you would most likely find a noteworthy quirk: elite soccer players are more likely to have been born in the earlier months of the year than in the later months. If you then examined the European national youth teams that feed the World Cup and professional ranks, you would find this strange phenomenon to be even more pronounced.What might account for this strange phenomenon? Here are a few guesses: a) certain astrological signs confer superior soccer skills;b) winter-born babies tend to have higher oxygen capacity, which increases soccer stamina; c) soccer-mad parents are more likely to conceive children in springtime, at the annual peak of soccer mania; d) none of the above.Anders Ericsson, a 58-year-old psychology professor at Florida State University, says he believes strongly in “none of the above.” Ericsson grew up in Sweden, and studied nuclear engineering until he realized he would have more opportunity to conduct his own research if he switched to psychology. His first experiment, nearly 30 years ago, involved memory: training a person to hear and then repeat a random series of numbers. “With the first subject, after about 20 hours of training, his digit span had risen from 7 to 20,” Ericsson recalls. “He kept improving, and after about 200 hours of training he had risen to over 80 numbers.”This success, coupled with later research showing that memory itself is not genetically determined, led Ericsson to conclude that the act of memorizing is more of a cognitive exercise than an intuitive one. In other words, whatever inborn differences two people may exhibit in their abilities to memorize, those differences are swamped by how well each person “encodes” the information. And the best way to learn how to encode information meaningfully, Ericsson determined, was a process known as deliberate practice. Deliberate practice entails more than simply repeating a task. Rather, it involves setting specific goals, obtaining immediate feedback and concentrating as much on technique as on outcome.Ericsson and his colleagues have thus taken to studying expert performers in a wide range of pursuits, including soccer. They gather all the data they can, not just performance statistics and biographical details but also the results of their own laboratory experiments with high achievers. Their work makes a rather startling assertion: the trait we commonly call talent is highly overrated. Or, put another way, expert performers –whether in memory or surgery, ballet or computer programming – are nearly always made, not born.21. The birthday phenomenon found among soccer players is mentioned to[A] stress the importance of professional training.[B] spotlight the soccer superstars in the World Cup.[C] introduce the topic of what makes expert performance.[D] explain why some soccer teams play better than others.22. The word “mania” (Line 4, Paragraph 2) most probably means[A] fun.[B] craze.[C] hysteria.[D] excitement.23. According to Ericsson, good memory[A] depends on meaningful processing of information.[B] results from intuitive rather than cognitive exercises.[C] is determined by genetic rather than psychological factors.[D] requires immediate feedback and a high degree of concentration.24. Ericsson and his colleagues believe that[A] talent is a dominating factor for professional success.[B] biographical data provide the key to excellent performance.[C] the role of talent tends to be overlooked.[D] high achievers owe their success mostly to nurture.25. Which of the following proverbs is closest to the message the texttries to convey?[A] “Faith will move mountains.”[B] “One reaps what one sows.”[C] “Practice makes perfect.”[D] “Like father, like son.”Text 2For the past several years, the Sunday newspaper supplement Parade has featured a column called “Ask Marilyn.” People are invited to query Marilyn vos Savant, who at age 10 had tested at a mental level of someone about 23 years old; that gave her an IQ of 228 – the highest score ever recorded. IQ tests ask you to complete verbal and visual analogies, to envision paper after it has been folded and cut, and to deduce numerical sequences, among other similar tasks. So it is a bit confusing when vos Savant fields such queries from the average Joe (whose IQ is 100) as,What’s the difference between love and fondness? Or what is the nature of luck and coincidence? It’s not obvious how the capacity to visualize objects and to figure out numerical patterns suits one to answer questions that have eluded some of the best poets and philosophers.Clearly, intelligence encompasses more than a score on a test. Just what does it mean to be smart? How much of intelligence can be specified, and how much can we learn about it from neurology, genetics, computer science and other fields?The defining term of intelligence in humans still seems to be the IQ score, even though IQ tests are not given as often as they used to be. The test comes primarily in two forms: the Stanford-Binet Intelligence Scale and the Wechsler Intelligence Scales (both come in adult and children’s version). Generally costing several hundred dollars, they are usually given only by psychologists, although variations of them populate bookstores and the World Wide Web. Superhigh scores like vos Savant’s are no longer possible, because scoring is now based on a statistical population distribution among age peers, rather than simply dividing the mental age by the chronological age and multiplying by 100. Other standardized tests, such as the Scholastic Assessment Test (SAT) and the Graduate Record Exam (GRE), capture the main aspects of IQ tests.Such standardized tests may not assess all the important elements necessary to succeed in school and in life, argues Robert J. Sternberg. In his article “How Intelligent Is Intelligence Testing?”, Sternberg notes that traditional test best assess analytical and verbal skills but fail to measure creativity and practical knowledge, components also critical to problem solving and life success. Moreover, IQ tests do not necessarily predict so well once populations or situations change. Research has found that IQ predicted leadership skills when the tests were given under low-stress conditions, but under high-stress conditions, IQ was negatively correlated with leadership – that is, it predicted the opposite. Anyone who has toiled through SAT will testify that test-taking skill also matters, whether it’s knowing when to guess or what questions to skip.26. Which of the following may be required in an intelligence test?[A] Answering philosophical questions.[B] Folding or cutting paper into different shapes.[C] Telling the differences between certain concepts.[D] Choosing words or graphs similar to the given ones.27. What can be inferred about intelligence testing from Paragraph 3?[A] People no longer use IQ scores as an indicator of intelligence.[B] More versions of IQ tests are now available on the Internet.[C] The test contents and formats for adults and children may bedifferent.[D] Scientists have defined the important elements of humanintelligence.28. People nowadays can no longer achieve IQ scores as high as vos Savant’s because[A] the scores are obtained through different computationalprocedures.[B] creativity rather than analytical skills is emphasized now.[C] vos Savant’s case is an extreme one that will not repeat.[D] the defining characteristic of IQ tests has changed.29. We can conclude from the last paragraph that[A] test scores may not be reliable indicators of one’s ability.[B] IQ scores and SAT results are highly correlated.[C] testing involves a lot of guesswork.[D] traditional test are out of date.30. What is the author’s attitude towards IQ tests?[A] Supportive.[B] Skeptical.[C] Impartial.[D] Biased.Text 3During the past generation, the American middle-class family that once could count on hard work and fair play to keep itself financially secure had been transformed by economic risk and new realities. Now a pink slip, a bad diagnosis, or a disappearing spouse can reduce a family from solidly middle class to newly poor in a few months.In just one generation, millions of mothers have gone to work, transforming basic family economics. Scholars, policymakers, and critics of all stripes have debated the social implications of these changes, but few have looked at the side effect: family risk has risen as well. Today’s families have budgeted to the limits of their new two-paycheck status. As a result, they have lost the parachute they once had in times of financial setback – a back-up earner (usually Mom) who could go into the workforce if the primary earner got laid off or fellsick. This “added-worker effect” could support the safety net offered by unemployment insurance or disability insurance to help families weather bad times. But today, a disruption to family fortunes can no longer be made up with extra income from an otherwise-stay-at-home partner.During the same period, families have been asked to absorb much more risk in their retirement income. Steelworkers, airline employees, and now those in the auto industry are joining millions of families who must worry about interest rates, stock market fluctuation, and the harsh reality that they may outlive their retirement money. For much of the past year, President Bush campaigned to move Social Security to a saving-account model, with retirees trading much or all of their guaranteed payments for payments depending on investment returns. For younger families, the picture is not any better. Both the absolute cost of healthcare and the share of it borne by families have risen – and newly fashionable health-savings plans are spreading from legislative halls to Wal-Mart workers, with much higher deductibles and a large new dose of investment risk for families’future healthcare. Even demographics are working against the middle class family, as the odds of having a weak elderly parent –and all the attendant need for physical and financial assistance – have jumped eightfold in just one generation.From the middle-class family perspective, much of this, understandably, looks far less like an opportunity to exercise more financial responsibility, and a good deal more like a frightening acceleration of the wholesale shift of financial risk onto their already overburdened shoulders. The financial fallout has begun, and the political fallout may not be far behind.31. Today’s double-income families are at greater financial risk in that[A] the safety net they used to enjoy has disappeared.[B] their chances of being laid off have greatly increased.[C] they are more vulnerable to changes in family economics.[D] they are deprived of unemployment or disability insurance.32. As a result of President Bush’s reform, retired people may have[A] a higher sense of security.[B] less secured payments.[C] less chance to invest.[D] a guaranteed future.33. According to the author, health-savings plans will[A] help reduce the cost of healthcare.[B] popularize among the middle class.[C] compensate for the reduced pensions.[D] increase the families’ investment risk.34. It can be inferred from the last paragraph that[A] financial risks tend to outweigh political risks.[B] the middle class may face greater political challenges.[C] financial problems may bring about political problems.[D] financial responsibility is an indicator of political status.35. Which of the following is the best title for this text?[A] The Middle Class on the Alert[B] The Middle Class on the Cliff[C] The Middle Class in Conflict[D] The Middle Class in RuinsText 4It never rains but it pours. Just as bosses and boards have finally sorted out their worst accounting and compliance troubles, and improved their feeble corporation governance, a new problem threatens to earn them – especially in America – the sort of nasty headlines that inevitably lead to heads rolling in the executive suite: data insecurity. Left, until now, to odd, low-level IT staff to put right, and seen as a concern only of data-rich industries such as banking, telecoms and air travel, information protection is now high on the boss’s agenda in businesses of every variety.Several massive leakages of customer and employee data this year –from organizations as diverse as Time Warner, the American defense contractor Science Applications International Corp and even the University of California, Berkeley – have left managers hurriedly peering into their intricate IT systems and business processes in search of potential vulnerabilities.“Data is becoming an asset which needs to be guarded as much as any other asset,” says Haim Mendelson of Stanford University’s business school. “The ability to guard customer data is the key to market value, which the board is responsible for on behalf of shareholders.” Indeed, just as there is the concept of Generally Accepted Accounting Principles (GAAP), perhaps it is time for GASP, Generally Accepted Security Practices, suggested Eli Noam of New York’s Columbia Business School.“Setting the proper investment level for security, redundancy, and recovery is a management issue, not a technical one,” he says.The mystery is that this should come as a surprise to any boss. Surely it should be obvious to the dimmest executive that trust, that most valuable of economic assets, is easily destroyed and hugely expensive to restore – and that few things are more likely to destroy trust than a company letting sensitive personal data get into the wrong hands.The current state of affairs may have been encouraged – though not justified – by the lack of legal penalty (in America, but not Europe) for data leakage. Until California recently passed a law, American firms did not have to tell anyone, even the victim, when data went astray. That may change fast: lots of proposed data-security legislation is now doing the rounds in Washington, D.C. Meanwhile, the theft of information about some 40 million credit-card accounts in America, disclosed on June 17th, overshadowed a hugely important decision a day earlier by America’s Federal Trade Commission (FTC) that puts corporate America on notice that regulators will act if firms fail to provide adequate data security.36. The statement “It never rains but it pours” is used to introduce[A] the fierce business competition.[B] the feeble boss-board relations.[C] the threat from news reports.[D] the severity of data leakage.37. According to Paragraph 2, some organizations check their systems tofind out[A] whether there is any weak point.[B] what sort of data has been stolen.[C] who is responsible for the leakage.[D] how the potential spies can be located.38. In bringing up the concept of GASP the author is making the pointthat[A] shareholders’ interests should be properly attended to.[B] information protection should be given due attention.[C] businesses should enhance their level of accounting security.[D] the market value of customer data should be emphasized.39. According to Paragraph 4, what puzzles the author is that some bossesfail to[A] see the link between trust and data protection.[B] perceive the sensitivity of personal data.[C] realize the high cost of data restoration.[D] appreciate the economic value of trust.40. It can be inferred from Paragraph 5 that[A] data leakage is more severe in Europe.[B] FTC’s decision is essential to data security.[C] California takes the lead in security legislation.[D] legal penalty is a major solution to data leakage.Part BDirections:You are going to read a list of headings and a text about what parents are supposed to do to guide their children into adulthood. Choose a heading from the list A—G that best fits the meaning of each numbered part of the text (41-45). The first and last paragraphs of the text are not numbered. There are two extra headings that you do not need to use. Mark your answers on ANSWER SHEET 1. (10 points)A. Set a Good Example for Your KidsB. Build Your Kids’ Work SkillsC. Place Time Limits on Leisure ActivitiesD. Talk about the Future on a Regular BasisE. Help Kids Develop Coping StrategiesF. Help Your Kids Figure Out Who They AreG. Build Your Kids’ Sense of ResponsibilityHow Can a Parent Help?Mothers and fathers can do a lot to ensure a safe landing in early adulthood for their kids. Even if a job’s starting salary seems too small to satisfy an emerging adult’s need for rapid content, the transition from school to work can be less of a setback if the start-up adult is ready for the move. Here are a few measures, drawn from my book Ready or Not, Here Life Comes, that parents can take to prevent what I call “work-life unreadiness.”大41家You can start this process when they are 11 or 12. Periodically reviewtheir emerging strengths and weaknesses with them and work together on any shortcomings, like difficulty in communicating well or collaborating. Also, identify the kinds of interests they keep coming back to, as these offer clues to the careers that will fit them best.大42家Kids need a range of authentic role models – as opposed to members of their clique, pop stars and vaunted athletes. Have regular dinner-table discussions about people the family knows and how they got where they are. Discuss the joys and downsides of your own career and encourage your kids to form some ideas about their own future. When asked what they want to do, they should be discouraged from saying “I have no idea.” They can change their minds 200 times, but having only a foggy view of the future is of little good.大43家Teachers are responsible for teaching kids how to learn; parents should be responsible for teaching them how to work. Assign responsibilities around the house and make sure homework deadlines are met. Encourage teenagers to take a part-time job. Kids need plenty of practice delaying gratification and deploying effective organizational skills, such as managing time and setting priorities.大44家Playing video games encourages immediate content. And hours of watching TV shows with canned laughter only teaches kids to process information in a passive way. At the same time, listening through earphones to the same monotonous beats for long stretches encourages kids to stay inside their bubble instead of pursuing other endeavors. All these activities can prevent the growth of important communication and thinking skills and make it difficult for kids to develop the kind of sustained concentration they will need for most jobs.大45家They should know how to deal with setbacks, stresses and feelings of inadequacy. They should also learn how to solve problems and resolve conflicts, ways to brainstorm and think critically. Discussions at home can help kids practice doing these things and help them apply these skills to everyday life situations.What about the son or daughter who is grown but seems to be struggling and wandering aimlessly through early adulthood? Parents still have a major role to play, but now it is more delicate. They have to be carefulnot to come across as disappointed in their child. They should exhibit strong interest and respect for whatever currently interests their fledging adult (as naive or ill conceived as it may seem) while becoming a partner in exploring options for the future. Most of all, these new adults must feel that they are respected and supported by a family that appreciates them.Part CDirections:Read the following text carefully and then translate the underlined segments into Chinese. Your translation should be written clearly on ANSWER SHEET 2. (10 points)The study of law has been recognized for centuries as a basic intellectual discipline in European universities. However, only in recent years has it become a feature of undergraduate programs in Canadian universities. (46) Traditionally, legal learning has been viewed in such institutions as the special preserve of lawyers, rather than a necessary part of the intellectual equipment of an educated person. Happily, the older and more continental view of legal education is establishing itself in a number of Canadian universities and some have even begun to offer undergraduate degrees in law.If the study of law is beginning to establish itself as part and parcel of a general education, its aims and methods should appeal directly to journalism educators. Law is a discipline which encourages responsible judgment. On the one hand, it provides opportunities to analyze such ideas as justice, democracy and freedom. (47) On the other, it links these concepts to everyday realities in a manner which is parallel to the links journalists forge on a daily basis as they cover and comment on the news. For example, notions of evidence and fact, of basic rights and public interest are at work in the process of journalistic judgment and production just as in courts of law. Sharpening judgment by absorbing and reflecting on law is a desirable component of a journalist’s intellectual preparation for his or her career.(48) But the idea that the journalist must understand the law more profoundly than an ordinary citizen rests on an understanding of the established conventions and special responsibilities of the news media. Politics or, more broadly, the functioning of the state, is a major subject for journalists. The better informed they are about the way the state works, the better their reporting will be. (49) In fact, it is difficult to see how journalists who do not have a clear grasp of the basic features of the Canadian Constitution can do a competent job on political stories.Furthermore, the legal system and the events which occur within it are primary subjects for journalists. While the quality of legal journalism varies greatly, there is an undue reliance amongst many journalists on interpretations supplied to them by lawyers. (50) While comment and reaction from lawyers may enhance stories, it is preferable for journalists to rely on their own notions of significance and make their own judgments. These can only come from a well-grounded understanding of the legal system.Section III WritingPart A51. Directions:Write a letter to you university library, making suggestions for improving its service.You should write about 100 words on ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use “Li Ming”instead.Do not write the address. (10 points)Part B52. Directions:Write an essay of 160-200 words based on the following drawing. In your essay, you should1) describe the drawing briefly,2) explain its intended meaning, and then3) support your view with an example/examples.You should write neatly on ANSWER SHEET 2. (20 points)2007年考研英语真题答案Section I: Use of English (10 points)1. B2. D3. A4. C5. C6. D7. B8. A9. B 10. C11. A 12. D 13. A 14. C 15. B16. D 17. C 18. A 19. B 20. D Section II: Reading Comprehension (60 points)Part A (40 points)21. C 22. B 23. A 24. D 25. C26. D 27. C 28. A 29. A 30. B31. C 32. B 33. D 34. C 35. B36. D 37. A 38. B 39. A 40. DPart B (10 points)41. F 42. D 43. B 44. C 45. EPart C (10 points)46. 长久以来，法律知识在这类学校里一起被视为律师们专有的，而不是一个受教育者的知识素养的必要组成部分。
2007年研究生招生考试英语试题A 含答案
11. A) He'll have to take care of his wife.B) He is going to the party aloneC) His wife works in a hospitlD) His wife is invited to a party2) 听短文（3段）Directions: In this section you will hear some short passages. At the end of each passage, you will hear some questions. After you hear a question you must choose the best answer from the four choices marked A), B), C) and D).第一段.12. A) On the farm. B) On their campus.C) In modern buildings. D) In the workshop.13. A) Grow vegetables. B) Repair machines.C) Milk the goats. D) Do housework.14. A) They want to make money. B) They want to learn about ecology.C) They don’t like the classes. D) They don’t like their campus.第二段15. A) They had decided to visit their friends.B) They had decided to spend their holidays.C) They wanted to do business there.D) They had decided to work there.16. A) Hungry. B) Happy. C) Angry. D) Tired.17. A) Mrs. Smith hardly had any time to see the sights of London.B) Mrs. Smith should have time to see the sights in London.C) The times of meals arranged were unsuitable for tourists.D) Mrs. Smith misunderstood the man’s words.第三段18. A) He thinks they are too stressful.B) He thinks they are not stressful enough.C) He thinks they are useful exercises.D) They thinks they are pointless exercises.19. A) They leave reviewing until the day of the exam.B) They start reviewing too early.C) They only start reviewing a few days before the exam.D) They often do most reviewing the day after the exam.20. A) Because the other students don't seem calm.B) Because you have forgotten pens and pencils.C) Because everyone else seems confident.D) Because the paper seems too easy.Part Two: 阅读理解(20% )Directions: There are FOUR passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B), C), and D). You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the centre.第一段Under normal conditions the act of communication requires the presence of at least two persons: one who sends and one who receives the communication. In order to communicate thoughts and feelings, there must be a conventional system of signs or symbols which mean the same to the sender and receiver. The means of sending communication are too numerous and varied for systematic classification; therefore, the analysis must begin with the means of receiving communication. Reception of communication is achieved by our senses. Sight, hearing, and touch play the most important roles. Smell and taste play very limited roles, for they cannot receive intellectual expression from fully developed systems of signs and symbols. Examples of visual communication are gesture and mimicry. Although both frequently accompany speech, there are systems that rely solely on sight, such as those used by deaf and dumb persons. Another means of communicating visually is by signals of fire, smoke, flags, or flashing lights. Feelings may be simply communicated by touch, such as by hand-stroking or backslapping, although a highly developed system of hand-stroking has enabled blind, deaf, and dumb persons to communicate intelligently. Whistling to someone, applauding in a theater, and other forms of communication by sound rely upon the ear as a receiver. The most fully developed form of auditory communication is, of course, the spoken language. The means of communication mentioned so far have two features in common: they last only a short time, and the persons involved must be relatively close to each other. Therefore, all are restricted in time and space.21. The author explains that he will deal with reception of communication first because __________.A) communication actually takes place when the message is receivedB) there are more means of receiving than those of s. ending communicationsC) reception of communication involves the use of the sensesD) it is difficult to list all the possible means of sending communications22. Persons who cannot see, hear, or speak are able to communicate through a system of __________.A) Gesturing B) backslapping C) handshaking D) handstroking23. The author specifically mentions that speech is __________.A) less important than the written form of languageB) assisted by touch, gesture, etcC) the only highly developed system of communicationD) the most developed form of communication based on hearing24. Which of the following statements about communication by touch is TRUE?A) Touch is less important than taste as a means of communication.B) There is no well-developed system of communication based on touch.C) It is possible to communicate intelligently by touch alone.D) Touch must accompany visual communication.25. Which of the following statements about the ways of communicating ideas and feelings mentioned in the passage is NOT true?A) They can be used to communicate over long distances.B) They require both a sender and receiver.C) They involve the use of conventional signs and symbols.D) They utilize the senses for reception.第二段When Louis Braille was three years old, he became blind in both eyes as the result of an accident in his father's harness shop. His father, determined that Louis should not suffer the usual fate of blind persons at that time and become a beggar, kept him in the village school until he was ten and then entered him in the Institution des Jeunes Aveugles in Paris. Louis learned to read from the three books engraved in large raised letters in the Institution library, did exceptionally well both in academic work and at the piano and organ, and was soon helping to teach the younger children. In 1819, the same year that Louis entered the Institution, Charles Barbier, an army captain, reported to the Academy of Sciences on a system of raised dots and dashes which enabled soldiers to read messages in the dark. Later, Barbier brought his invention to the Institution. After experimenting with it, young Braille produced a writing system using only dots, from which he gradually devised 63 separate combinations representing the letters in the French alphabet (at the request of an Englishman, he later added W), accents, punctuation marks, and mathematical signs. Although government bureaucracy prevented immediate official adoption, his system was used at the Institution as long as the director, Dr. Pignier, was in office. Pignier's successor insisted on returning to the officially approved former system. But students continued to use Braille's method secretly. Eventually, its superiority was established and it was adopted throughout France.26. Louis Braille first learned to read with the aid of ____________.A) his father B) the village school teacherC) special books at the Institution D) Captain Braille's system of dots and dashes27. Louis Braille did all of the following things EXCEPT _______________.A) teaching young children at the InstitutionB) developing a reading system for the blindC) learning to play musical instruments wellD) encouraging students to use his method secretly28. Louis Braille devised his writing system __.A) from combinations of dotsB) at an Englishman's requestC) to help Charles Barbier in his workD) to enable soldiers to read in the dark29. Which of the following ideas does the writer want to convey?A) Louis was lucky to have a determined father.B) Teacher's guidance is necessary for one's success.C) Government bureaucracy often kills new inventions.D) Physical blindness doesn't necessarily mean mental blindness.30. The Institution was not able to adopt Braille's method officially for some time because ____A) the students preferred the former methodB) the government was slow to approve itC) Dr. Pignier's successor thought that the Braille method was not scientificD) the large library collection would then have been useless第三段Violin prodigies, I learned, have come in distinct waves from distinct regions. Most of the great performers of the late 19th and early 20th centuries were born and brought up in Russia and Eastern Europe. I asked Isaac Stern, one of the world's greatest violinists, the reason for this phenomenon. "It is very clear," he told me. "They were all Jews and Jews at the time were severely oppressed and ill-treated in that part of the world. They were not allowed into the professional fields, but they were allowed to achieve excellence on a concert stage." As a result, every Jewish parent's dream was to have a child in the music school because it was a passport to the West. Another element in the emergence of prodigies, I found, is a society that values excellence in a certain field and is able to nurture talent. Nowadays, the most nurturing societies seem to be in the Far East. "In Japan, a most competitive society with stronger discipline than ours," says Isaac Stern, children are ready to test their limits every day in many fields, including music. When Western music came to Japan after World War I , music not only became part of their daily lives, but it became a discipline as well. The Koreans and Chinese, as we know, are just as highly motivated as the Japanese. That's a good thing, because even prodigies must work hard. Next to hard work, biological inheritance plays an important role in the making of a prodigy. J. S. Bach, for example, was the top ofseveral generations of musicians, and four of his sons had significant careers in music.31. Jewish parents in Eastern Europe longed for their children to attend music school because ________.A) it would allow them access to a better life in the WestB) Jewish children are born with excellent musical talentC) they wanted their children to enter into the professional fieldsD) it would enable the family to get better treatment in their own country32. Nurturing societies as mentioned in the passage refer to the societies thatA) enforce strong discipline on students who want to achieve excellenceB) treasure talent and provide opportunities for its full developmentC) encourage people to compete with each otherD) promise talented children high positions33. Japan is described in the passage as a country that attaches importance to ________.A) all-round developmentB) the learning of Western musicC) strict training of childrenD) variety in academic studies34. Which of the following contributes to the emergence of musical prodigies according to the passage?A) A natural gift.B) Extensive knowledge of musicC) Very early training.D) A prejudice-free society.35. Which of the following titles best summarizes the main idea of the passage?A) Jewish Contribution to MusicB) Training of Musicians in the WorldC) Music and Society.D) The Making of Prodigies.第四段By the end of the first quarter of the nineteenth century a number of our Easten institutions -- Harvard, Yale, Columbia, and Pennsylvania -- had some of the necessary ingredients of a university, but hardly yet the point of view. They were little clusters of schools and institutes. Indeed, just after the Revolution, the schools of Pennsylvania and Harvard had assumed the somewhat pretentious title of university, and, shortly after, the University of Virginia was founded under the guidance of Thomas Jefferson. In the South, Georgia and later North Carolina began to rise. The substance in all these wasmainly lacking, though the title was honored. There were rather feeble law, medical, and divinity schools, somewhat loosely attached to these colleges. It has been commonly recognized, however, that the first decade after the close of the Civil War, that is, from about 1866 to 1876, was the great early flowering of the university idea in America.36. In the opinion of the author of this passage, in 1825 ______________.A) only Harvard, Yale, Columbia, and Pennsylvania could truly be called universitiesB) all American educational institutions could justifiably claim to be universitiesC) those institutions which called themselves universities were not justified in doing soD) no American institution of higher education had any of the necessary ingredients ofa university37. Thomas Jefferson founded _____________.A) the University of PennsylvaniaB) HarvardC) the University of VirginiaD) the university of Georgia38. The Civil War ended ______________.A) about 1866 B) about 1876C) about 1856 D) during the decade from 1866 to 187639. The words little clusters (line 4) most nearly means _____________.A) small groups B) small collegesC) small buildings D) small organizations40. The university idea really began to develop _____________.A) in the first quarter of the nineteenth centuryB) just after the RevolutionC) during the last quarter of the nineteenth centuryD) just after the Civil WarPart Three: 完型填空(10% )Directions: In this part, you will read a passage with some blanks. For each blank there are four choices marked A) , B) , C) and D). You should choose the ONE answer that best fits into the passage. Then mark the corresponding letter on the Answer Sheet.During the period of reconstruction __ 41__ the Civil War conditions in the __ 42 __ states were very unhappy, and soon the __ 43 __ of southern whites were strongly __ 44 __ that they did not want to __ 45__ real equality to the Negroes. Some __ 46__ even passed laws that no person __ 47 __ to be allowed to vote __ 48 __ his grandfather had been a slave, __ 49__ the Supreme Court ruled that these laws were against the fifteenth amendment, and __ 50__ unconstitutional. But there were other devices __ 51__ which Negroes could be __ 52__ from voting. Tests of literacy (I.e. the ability toread and write) were still __ 53 __. At first the great majority of the __ 54__ people really were illiterate, as __ 55__ of them had been educated __ 56__ the end of slavery. Later the local white __ 57__ administering the tests could use the test unfavorably against Negroes. It took some generations __ 58__ this device against them was given __ 59__. At last, this unjust device was __ 60__ by federal law in 1965.41 A) before B) after C) since D) from42 A) winning B) northern C) lost D) southern43 A) minorities B) majors C) majority D) chief44 A) divided B) united C) agreed D) disagreed45 A) allow B) contribute C) share D) own46 A) officials B) members C) judges D) states47 A) was B) used C) wanted D) permitted48 A) because B) if C) although D) whenever49 A) although B) therefore C) since D) so50 A) so B) yet C) really D) possibly51 A) for B) with C) on D) in52 A) distinguished B) controlled C) prevented D) released53 A) allowed B) prohibited C) enjoyed D) dislike54 A) American B) white C) black D) poor55 A) lots B) few C) none D) most56 A) since B) before C) after D) near57 A) lawyers B) judges C) officials D) managers58 A) until B) before C) after D) since59 A) in B) away C) up D) back60 A) forbidden B) permitted C) interrupted D) preventedPart Four: 词汇及语法结构(20% )（20小题）Directions: In this part，there are some incomplete sentences. For each sentence there are four choices marked A) , B) , C) and D). Choose the ONE answer that best completes the sentence. Then mark the corresponding letter on the Answer Sheet.61. I don't often get sick, but _________ I do catch cold.A) now and then B) now thatC) from now on D) and then62. The sea is very beautiful and _____________.A) the mountains are so too B) the mountains are tooC) so are the mountains D) also are the mountains63. The concert will be broadcast ______ on Radio Three at 8 p.m. next Monday.A) alive B) living C) life D) live64. Very few people came to the meeting, ____________ they decided to postpone it.A) and therefore B) therefore C) and so D) thus65. Bob looks so young that I couldn't believe that he is my ________ by four years. I thought I was older.A) younger B) elder C) junior D) equal66. A ________ has been announced between Mr. White and Miss Brown and the wedding is to be held next Sunday.A) contract B) marriage C) engagement D) meeting67. The government wants to ______ farm prices at their present levels.A) keep up B) flare up C) bring up D) stay up68. Jerry had planned to explore the depth of the desert, but his food supplies ran ______ and he had to cancel the trip.A) away B) on C) out D) off69. There is no doubt ________ her intelligence, she's the smartest one in the class.A) as for B) as regards C) as to D) as follows70. To harness water power and convert it into electricity the necessary plant must be ________ .A) generated B) installed C) assembled D) fitted71. ______ breaks the law will be fined or put in jail.A) No matter who B) WhoeverC) Those who D) Whenever one72. I have the impression __________ all the pupils of this class are interested in English.A) which B) of which C) that D) of that73. Redouble your efforts, ______ you will never be able to accomplish what you have set out to do.A) lest B) for fear that C) in case D) or74. At first Jack did not want to write for the student paper, but I persuaded him ______.A) to do B) to C) do D) do it75. The driving instructor told me to pull ______ at the post office.A) up B) back C) round D) along76. So late did he arrive in the town ______ all the buses had stopped running.A) until B) when C) as D) that77. For my part, I have not the slightest doubt as to __________ his courage his honesty, or his patience of mind.A) all of B) none of C) either D) both78. I am not very keen ______ basketball.A) in B) about C) on D) to79. ______ the opportunity, he might well have become an outstanding cartoonist.A) Giving B) Give C) Given D) Gives80. The first one wasn't good and ______ was the second.A) neither B) either C) so D) such（以上80题答案请写在答题卡上，谢谢）2007年金陵协和神学院研究生入学考试答题卡准考证号_____________ 1．41.2．42.3. 43.4．44.5．45.6．46.7．47.8．48.9．49.10．50.11．51.12．52.13．53.14．54.15．55.16．56.17．57.18．58.19．59.20．60.21．61.22．62.23．63.24．64.25．65.26．66.27．67.28．68.29．69.30．70.31．71.32．72.33．73.34．74.35．75.36．76.37．77.38．78.39．79.40．80.试卷B 写作及神学英语部分写作(10% 150字以上)Directions: For this part, you are allowed 30 minutes to write a composition on the topic "Pollution". The first sentence of each paragraph is given. Your part of writing should be no less than 150 words.1. With the development of modern industry, more and more waste is produced.________2. Another kind of pollution is noise.________3. Man if fighting a battle against pollution.________神学英语一、词汇（10%）要求给出简单的英文解释1．Humanism2．Heresy3．Animism4．Pentecostal Church5．Palm Sunday二、阅读理解（15%，可用中文回答）A．He does not claim to have a secret knowledge through which salvation may be achieved. According to him, his doctrine follows from a careful study of the Christian message as it was preached by Paul. This message is to be found in the Epistles of Paul and in the Gospel of Luke, although it is necessary to revise those writings in order to eliminate the many Judaizing interpolations that have been introduced in them. Paul was the herald of a radically new message, of the message of the revelation of a god theretofore unknown. The Old Testament cannot be taken as the world of the god who is revealed in Jesus Christ. In consequence, the reverences to the Old Testament to be found in the Pauline Epistles are later traditions. And the same may be said regarding the Gospel of Luke, Paul’scompanion. Thus, he formulated the first canon of the New Testament. His doctrine is then based on the study of these Scriptures, for he does not claim to be a prophet or to have any secret source of knowledge, but only to be a true exponent of Christian Scriptures.6. What does “salvation through secret source of knowledge” refer to?7. What books are probably included in the first canon according to the text?8. In your opinion, whose point of view is the text talking about?B.What is God’s purpose? It is to bring creation to the emergence of a partner. This partner whom God yearns to create would put off all baseness, and would be a person in the image of God. What then is the image of God? God is a community, a trinity. The concept of trinity tells us that God is a group, a collective. Thus, God’s creation must lead to a human community in the universe, or a communal people.God wants to enlarge his community. The community of the Father, Son and Holy Spirit is not enough. It must be enlarged, to enable all humanity to enter.9. What does the word “collective” mean in this text?10. What does God’s community include according to the text?三、翻译（15%）请将划线部分译成汉语。
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))
V (Yb − Ya ) = 0.018(kmol /(m 2 ⋅ s )) Xb − Xa
H OG =
V = 0.95m K Y aΩ
∆Yb = Yb − mX b = 0.00263, ∆Ya = Ya − mX a = 0.00263, ∆Ym = 0.00263
N OG = Yb − Ya = 19, h = H OG ⋅ N OG = 18.05m ∆Ym
2. 简述双膜模型的基本假设？ 答： （1）在相界面的两侧存在一层稳定的层流膜层，溶质以分子扩散方式通过此两膜层； （2）相界面上气液两相呈平衡； （3）传质阻力集中在层流膜层内，两相主体中无传质阻力。 3. 简述板式塔和填料塔的优缺点？ 答：同填料塔相比，板式塔当塔径较大时造价较低，易于取热和侧线抽出等；当塔径较小 时，填料塔造价较低，分离效率高，压降较小，适用于小流量、腐蚀性、易发泡的物系。
2.47 x1 , 1 + (2.47 − 1)x1 0.935 = 2.47 x1 1 + (2.47 − 1)x1
= 0.853 = 0.6 × 0.853 + 0.374 = 0.886
由精馏段操作线方程计算 y 2 ： y 2 再由相平衡方程计算 x2： y 2 解得： x 2
=
2.47 x2 , 1 + (2.47 − 1)x2
=
4 = 0.625m 3 / h 3 + 2 .4 + 1
3.（20 分）有一套管换热器，用热水加热空气，内管为 φ34×2mm 的钢管，空气走管内， 其流量为 m1， 20℃被加热到 50℃； 由 热水走环隙， 其流量为 m2， 温度由 100℃冷却到 70℃， 逆流操作，假设流体在管内和环隙中的流动均为湍流流动，试问：（1）下列方程中的三个 温度是否相等？各为多少？ Q=m1cp1△t1= m2cp2△t2=KA△tm （2）如改为并流操作，欲达到同样的出口温度，其平均温度差为多少？，管长需要作 怎样的变化？ （3）当空气流量增加一倍时，要达到同样的空气出口温度，提出以下两种方案：①管 长加长一倍；②管子直径减小一倍。你认为哪种方案可行？哪种方案较好？ (4)试通过计算结果定性分析说明何种方案更合理？ 解：（1）根据题给数据，三个温差如下：
V 0.8 α i ∝ 1.8 ,∴ K ′ = 2 2.6 K = 6.06 K di
而传热面积：
A′ = πd ′l =
1 A πdl = 2 2
Q ′ K ′A′∆t m = = 3.03 Q KA∆t m
即传热速率提高了 203%，能完成任务，但由于阻力增加，能耗也随之增加。 4．（25 分）用板式精馏塔分离苯-甲苯二元混合物，进料流量为 15000 kg/h，其中苯的含 量为 40.0 %（质量百分数，下同）。要求塔顶馏出液中苯的回收率达到 97.1 %，塔釜液体 中苯的含量不超过 2.0 %。进料为饱和液体，塔顶采用全凝器，饱和液体回流。操作条件下 的相对挥发度可取为 2.47，苯的相对分子质量为 78，甲苯的相对分子质量为 92。 （1）试求塔顶馏出液和塔底釜液的摩尔流量及摩尔组成各为多少？ （2）试计算最小回流比？ （3）如回流比为最小回流比的 1.2 倍，试求精馏段操作线方程，并指出斜率和截距各 为多少？ （4）如果塔内各层塔板认为是理论板，计算由塔顶数起第二块塔板流下的液体组成为 多少？
PB = PA − (∑ h f AB + z B )ρ = 1.5 × 10 4 − (9 + 7) × 1100 = −2600kgf/m2 = −25497Pa（表）
2.（15 分）拟用一板框压滤机在恒压下过滤某一悬浮液，要求经过 3 个小时能获得 4m3 滤液，若已知过滤常数 K=1.48×10-3m2/h，滤布阻力可以忽略不计，试求：（1）若滤框尺 寸为 1000mm×1000mm×30mm，则需要滤框几块？（2）过滤终了用水进行横穿洗涤，洗涤 水粘度与滤液相同，洗涤压力与过滤压力相同，若洗涤水量为 0.4 m3，试求洗涤时间。 （3） 若辅助时间为 1 小时，试求该压滤机的生产能力。
y n+1 =
x R xn + D R +1 R +1 1 .5 0.935 = xn + 1 .5 + 1 1.5 + 1 = 1.6 xn + 0.374
精馏段操作线方程的斜率为：0.6，截距为：0.374。 (4)塔顶采用全凝器时： y1 由相平衡方程计算 x1： y1 = 解得： x1
= x D = 0.935
平均值。 （2）如果由逆流改为并流操作， ∆t m =
L并 L逆
=
A并 A逆
=
∆t m逆 ∆t m并
=
50 = 1.15 ，即管子长度应增加 15%。 43.2
（3）设管壁热阻及污垢热阻均不计，因为 α 1 ≈ 1000W /( m 2 K ), α 2 ≈ 30 ~ 50W /( m 2 K ), 所以， K ≈ α 2 （空气侧） ①管长增加一倍， α i ∝ Re i
F = D +W FxF = DxD + WxW DxD = 0.971 FxF
总7页 代入数据：
第 5页
174.75 = D + W 174.75 × 0.44 = Dx D + 0.0235W Dx D = 0.971 174.75 × 0.44
解得： W = 94.89kmo / h,
D = 79.86kmol / h,
(2)采用部分循环时，吸收剂的组成为：
' Xa =
LR X b = 0.0025 L + LR
∆Yb' = Yb − mX b = 0.00263, ∆Ya ' = Ya − mX a ' = 0.000255, ∆Ym ' = 0.001
N 'OG =
Yb − Ya = 49.97, h' = H 'OG ⋅N 'OG = 47.47m ∆Y ' m
三、计算题（100 分） 计算题（
1.（20 分）如图一冷冻盐水的循环系统。盐水的循环量为 45m3/h，流体流经管路的压头损 失，自 A 至 B 的一段为 9m，自 B 至 A 的一段为 12m。盐水的密度为 1100kg/m3，求： （1） 泵的功率为若干 kw?设其效率为 0.65。（2）若 A 处的压力表读数为 1.5 kgf/m2，则 B 处的 压力表读数应为多少 Pa（表压）？
0.886 =
2.47 x1 1 + (2.47 − 1)x1
= 0.759
总7页
第6页
5．（20 分）拟在填料吸收塔中用纯水吸收空气-氨混合气体中的氨，混合气体中的氨浓度 为 yb=0.05(摩尔分数，下同)。要求氨的吸收率不低于 95%，塔底得到的氨水的浓度不低于 0.05。已知在操作条件下的气液相平衡关系为 Ye=0.95X(Y、X 为摩尔比浓度)，试计算： (1)如用纯水吸收采用逆流操作，混合气体的摩尔流率为 0.02 kmol/(m ·s)，总体积 传质系数 KYa=0.02 kmol/(m ·s)，所需要的塔高为多少 m？ (2)如果采用部分吸收液再循环吸收的流程操作（如附图所示），新鲜吸收剂（纯水） 与循环吸收液的摩尔流量之比 L/LR =20，气体的流速不变，总体积传质系数 KYa 也近似为常 数，所需要的塔高为多少 m？ (3)示意画出两种操作情况时的操作线图。 (4)试通过计算结果定性分析说明何种方案更合理？ 解：(1)将摩尔组成换算为摩尔比组成：
0.8
∝ u i0.8 ,∴ K ′ = 2 0.8 K
总7页 由
第 4页
l ′ m′ / m Q ′ m′(t 2 − t1 ) K ′πdl ′∆t m = 2 0.2 = 1.15 = = ，得 = Q m(t 2 − t1） Kπdl∆t m l K′/ K
即管长只需增加 15%便可完成任务，这一方案是较为可行的。 ②管径减小一倍，由
x D = 0.935
(2)由相平衡关系及进料组成（xF=0.44）计算进料的气相组成：
yq =
2.47 × 0.44 = 0.66 1 + (2.47 − 1)0.44
xD − yq yq − xF = 0.935 − 0.66 = 1.25 0.66 − 0.44
最小回流比为： Rmin =
(3)适宜回流比为： R=1.2Rmin=1.2×1.25=1.5 精馏段操作线方程：
总7页 4．萃取剂量一定，采用单级萃取和三级错流萃取结果有何不同，为什么？
第 2页
答：萃取剂一定，采用三级错流萃取时的萃取效果要比单级萃取的效果好。因为三级错流 萃取要经过三次相平衡，而单级萃取只经历一次相平衡，三级错流萃取的平均传质推动力 比单级萃取的推动力大。 5.造成离心泵汽蚀的原因有哪些？应采取何种解决方法？ 答：（1）离心泵的安装高度过高，应降低泵的安装高度； （2）被输送液体的温度太高，可考虑降低液体温度或降低泵的安装高度； （3）被输送液体上方的压力太低，可加大液体上方压力或降低泵的安装高度； （4）被输送液体的饱和蒸汽压太大，上述解决方案均可。
∆t1 = 50 − 20 = 30 ℃，此温差为冷流体（空气）的进、出口温差；
∆t 2 = 100 − 70 = 30 ℃，此温差为热流体（水）的进、出口温差；
∆t m = 1 1 (∆t 入 + ∆t出） （50 + 50） 50 ℃，此温差为换热器两端传热温差的对数或算术 = = 2 2
(100 − 20) − (70 − 50) = 43.2 ℃ 100 − 20 ln 70 − 50
解：(1)将质量分率换算为摩尔分率：
40 / 78 2 / 78 = 0.44, xw = = 0.0235 40 / 78 + 60 / 92 2 / 78 + 98 / 92 15000 × 0.4 15000 × 0.6 F= + = 174.75( kmo / h) 78 92 xF =