北京科技大学2010年硕士研究生入学模拟及解析一 (2)

北京科技大学2010年硕士研究生入学模拟及解析三考试科目：安全原理一、单选题(统考生每题2分，共20分;单考生每题3分，共30分)1.某事故树的结构函数为T=X1+X1X2+X1X3，则导致该事故的最基本原因是( )。

A、{X1}，{X1X2}，{X1X3}B、{X1}，{X1X3}C、{X1}D、{X2}，{X3}[解析]答案选C。

T=X1+X1X2+X1X3 =X1(1+X2+X3) = X1，割集是导致顶上事件发生的基本事件的集合。

{X1}最小割集，是导致该事故的最基本原因。

2.影响人的身体健康，导致疾病或对物造成慢性损害的因素，称为( )。

A、危险因素B、有害因素C、风险因素D、隐患[解析]答案选B。

3.根据安全工程学的一般原理，危险性定义为事故频率和事故后果严重程度的( )。

A、总和B、差值C、乘积D、除数[解析]答案选C。

4.职业安全健康管理体系的核心都是为生产经营单位建立一个动态循环的过程，以( )的思想指导生产经营单位系统地实现其既定的目标。

A、系统安全B、安全系统C、本质安全D、持续改进[解析]答案选D。

OSHMS的基本思想是实现体系持续改进，通过周而复始的进行“计划、实施、监测、评审”活动，使体系的功能不断加强。

5.安全生产的“五要素”是指安全文化、安全法制、( )、安全科技和安全投入。

A、安全环境B、安全管理C、安全责任D、安全措施[解析]答案选C。

6.在安全生产工作中，通常所说的“三违”现象是指( )。

A、违反作业规程、违反操作规程、违反安全规程B、违章指挥、违章作业、违反劳动纪律C、违规进行蜜全培训、违规发放劳动防护用品、违规消减安全技措经费D、违反规定建设、违反规定生产、违反规定销售[解析]答案选B。

7.( )应用系统的事故危险指数模型，根据系统及其物质、设备(设施)和工艺的基本性质和状态，采用推算的办法，逐步给出事故的可能损失、引起事故发生或使事故扩大的设备、事故的危险性以及采取安全措施的有效性的安全评价方法。

2010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 - 8小题，每小题4分，共32分.下列每题给出的四个选项中，只有一个 是符合题目要求的，请将所选项前的字母填在答题纸指定的位置上.(1)极限2lim ()()()x x x x a x b ®¥=-+(A)1(B)e(C)a be -(D)b ae -【答】 应选 (C) .【解】 因22ln ln()ln()lim ln()lim()()1/x x x x x x a x b x a x b x®¥®¥---+=-+()()()3222112=lim lim 1x x a b x abx x x a x b a b x x a x b x ®¥®¥---+-+==--+-，所以2lim (()()x a x b x x a x b e ®¥-=-+，故选 (C) .(2)设函数(,)z z x y =由方程(,0y zF x x=确定，其中F 为可微函数，且20F ¢¹，则z z x y x y ¶¶+=¶¶(A)x (B)z (C)x -(D)z-【答】 应选 (B) .【解】 在方程两边分别对x 和对y 求偏导，得122211()0y z F z F x x x x ¶¢¢-+-=¶，12110z F F x x y¶¢¢+=¶于是有 22()z z x y F zF x y ¶¶¢¢+=¶¶， 即z zx y z x y ¶¶+=¶¶，故选 (B) .(3)设,m n均是正整数，则反常积分ò的收敛性(A)仅与m 的取值有关(B)仅与n 的取值有关(C)与,m n 的取值都有关(D)与,m n 的取值都无关【答】 应选 (D) .【解】 显然该反常积分有且仅有两个瑕点0,1x x ==，于是需分成两个积分加以考察：dx =+ò(1)对于，易见被积函数非负，且只在0x +®时无界，于是当1n >时，由+0lim 0x®=及120ò收敛，知收敛；当1n=时12/1mx-:及212101mdx x-ò收敛，知收敛；(2)对于，易见被积函数非负，且只在1x -®时无界，于是当1m >时，由11lim lim 0x x --®®==及1收敛，知 收敛；当1m =时，由21/211ln (1)lim lim 0(1)x x x x ---®®-==-及212101m dx x -ò收敛，知收敛；由此可见，无论正整数,m n如何取值，0ò都是收敛的，故选 (D) .(4) 2211lim()()n nn i j nn i n j ®¥===++åå (A) 12001(1)(1)x dx dy x y ++òò(B)1001(1)(1)xdx dy x y ++òò(C) 11001(1)(1)dx dyx y ++òò(D) 112001(1)(1)dx dyx y ++òò【答】 应选 (D) .【解】 记21(,)(1)(1)f x y x y =++，(){},y 01,01D x x y =££££，知(,)f x y 在D 上可积. 用直线()0,1,2,,i i x x i n n ===L 与()0,1,2,,j j y y j n n===L 将D 分成2n等份，可见22221111211()()(1)(1)n n n ni j i j n i j n i n j n n n=====×++++åååå是(,)f x y 在D 上的二重积分的一个和式，于是112222001111lim ()()(1)(1)(1)(1)nnn i j Dn dxdy dx dy n i n j x y x y ®¥====++++++ååòòòò.故选 (D) . (5)设A 为m n ´矩阵，B 为n m ´矩阵，E 为m 阶单位矩阵. 若AB E =，则(A)秩()r A m =，秩()r B m =(B)秩()r A m =，秩()r B n =(C)秩()r A n =，秩()r B m =(D)秩()r A n =，秩()r B n=【答】 应选 (A) .【解】 因A 是m n ´矩阵，故()r A m £，又()()()r A r AB r E m ³==，故()r A m =. 同理，可得()r B m =，故选 (A) .(6)设A 为4阶实对称矩阵，且2A A O +=. 若A 的秩为3，则A 相似于(A) 1110æöç÷ç÷ç÷ç÷èø(B) 1110æöç÷ç÷ç÷-ç÷èø(C) 1110æöç÷-ç÷ç÷-ç÷èø(D) 1110-æöç÷-ç÷ç÷-ç÷èø【答】 应选 (D) .【解】 设l 为A 的特征值，则由2A A O +=知2+=0l l ，即=0l 或1-. 又因A 是实对 称矩阵，故A 必相似于对角矩阵L ，其中L 的对角线上的元素为特征值1-或0. 再由()3r A =可知()3r L =，故选 (D) .(7)设随机变量X 的分布函数0,0,1(),01,21,1xx F x x e x -<ìïï=£<íï-³ïî则{1}P X ==(A)0 (B)12(C)112e --(D)11e--【答】 应选 (C) .【解】 由分布函数的用途，知{1}(1)(1)P X F F -==-1111122e e --=--=-. (8)设1()f x 为标准正态分布的概率密度，2()f x 为[1,3]-上均匀分布的概率密度，若12(),0()(0,0)(),0af x x f x a b bf x x £ì=>>í>î为概率密度，则,a b 应满足(A)234a b +=(B)324a b +=(C)1a b +=(D)2a b +=【答】 应选 (C) .【解】 由题意，有221()x f x -=，21/4,(1,3)()0x f x Î-ì=íî，其他，()1f x dx +¥-¥=ò而0120()()()f x dx af x dx bf x dx +¥+¥-¥-¥=+òòò()3201=2a b f x dx +ò13=24a b +，于是有13124a b +=，即234a b +=. 故选 (C) .二、填空题：9:14小题，每小题4分，共24分. 请将答案写在答题纸．．．指定位置上. (9)设20,ln(1),t tx e y u du -ì=ïí=+ïîò则220t d y dx == .【答】 应填 0.【解】 因2/ln(1)=/t dy dy dt t dx dx dt e -+=-, 22222ln(1+)12=[][ln(1)]/1t td y d t te t dx dt e dx dt t -=++-+， 故2020t d ydx==.(10)2p =ò.【答】 应填 4p -.【解】t =，则2dx tdt =，于是有2220002cos 2sin 4sin 4cos 4cos 4.t tdt t tt tdt t tdt p pppp p p ==-=-=-òòòò(11)已知曲线L 的方程为1||([1,1])y x x =-Î-，起点是(1,0)-，终点为(1,0)，则曲线积分2Lxydx x dy +=ò.【答】 应填 0.【解法一】 补有向线段:0([1,1])L y x =Î-，起点为(1,0)，终点为(1,0)-，设由L 与L 围成的平面区域为D ，则利用格林公式及区域D 关于y 轴的对称性，得222(2)00LDL LLxydx x dy xydx x dy xydx x dy x x dxdy ++=+-+=---=òòòòò【解法二】 记1:1([1,0])L y x x =+Î-，起点是(1,0)-，终点是(0,1)；2:1([0,1])L y x x =-Î， 起点为(0,1)，终点为(1,0)有12222+LL L xydx x dy xydx x dy xydx x dy+=++òòò 012210=[(1)][(1)]x x x dx x x x dx -+++--òò1212=()(02323-++-=.(12)设22{(,,)|1}x y z x y z W =+££，则W 的形心的竖坐标z = .【答】 应填23.【解】 记(){}22,y 1D x x y =+£，有221x y Ddxdydz dxdy dz +W=òòòòòò22=(1)Dx y dxdy --òò212=(1)d r rdr p q -òò=2p，2212122240011[1()]=(1)223x yDD zdxdydz dxdy zdz x y dxdy d r rdr p p q +W==-+-=òòòòòòòòòò， 从而W 的形心的竖坐标为23DDzdxdydzz dxdydz==òòòòòò. (13)设1(1,2,1,0)Ta =-，2(1,1,0,2)Ta =，3(2,1,1,)Ta a =. 若由123,,a a a 生成的向量空间的维数为2，则a = .【答】 应填 6.【解】 因由123,,a a a 生成的向量空间的维数为2，故矩阵()123,,a a a 的秩为2，而()123112112211013,,=101006020000a a a a æöæöç÷ç÷ç÷ç÷®ç÷ç÷--ç÷ç÷èøèø，故6a =.(14)设随机变量X 的概率分布为{},0,1,2,!CP X k k k ===L ，则2EX =.【答】 应填 2.【解】 由概率分布的性质，有{}01k k P X x ¥===å，即01!k Ck ¥==å，亦即1Ce =，1C e -=.由此可见，X 服从参数为1的泊松分布，于是22()112EX DX EX =+=+=.三、解答题（ 15 ～ 23小题，共94分.）(15)（本题满分10分）求微分方程322xy y y xe ¢¢¢-+=的通解.解：对应齐次方程320y y y ¢¢¢-+=的两个特征根为121,2r r ==，其通解为212x x Y C e C e =+.……4分设原方程的特解形式为*()x y x ax b e =+，则*2((2))xy ax a b x b e ¢=+++，*2((4)22)x y ax a b x a b e ¢¢=++++，代入原方程解得1,2a b =-=-，……8分 故所求通解为212(2)x x xy C e C e x x e=+-+ ……10分(16)（本题满分10分）求函数2221()()x t f x x t e dt -=-ò的单调区间与极值.解： ()f x 的定义域为(,)-¥+¥，由于2222211()x x t t f x xe dt te dt --=-òò，2224423311()2222xxt x x t f x x e dt x ex ex e dt ----¢=+-=òò，所以()f x 的驻点为0,1x =± ……3分列表讨论如下：x (,1)-¥-1-(1,0)-0 (0,1) 1 (1,)+¥()f x ¢-0 +0 -0 +()f x ↘极小↗极大↘极小↗……6分因此，()f x 的单调增加区间为(1,0)-及(1,)+¥，单调减少区间为(,1)-¥-及(0,1)；极小值为(1)0f ±=，极大值为21101(0)(1)2t f te dt e --==-ò……10分(17)（本题满分10分） (I)比较1|ln |[ln(1)]nt t dt +ò与1|ln |(1,2,)ntt dt n =òL 的大小，说明理由；(II)记1|ln |[ln(1)](1,2,)n n u t t dt n =+=òL ，求极限lim n n u ®¥.解：（I ）当01t ££时，因为ln(1)t t +£，所以|ln |[ln(1)]|ln |n n t t t t +£，因此11|ln |[ln(1)]|ln |n n t t dt t t dt+£òò ……4分（II ）由 (I) 知，110|ln |[ln(1)]|ln |n n n u t t dt t t dt £=+£òò.因为1112011|ln |ln 1(1)n n n t t dt t tdt t dt n n =-==++òòò，所以1lim|ln |0nn tt dt ®¥=ò ……8分 从而 lim 0n n u ®¥=……10分(18)（本题满分10分） 求幂级数121(1)21n nn x n -¥=--å的收敛域及和函数. 解：记12(1)()21n nn u x x n --=-， 由于221()21lim lim ()21n n n nu x n x x u x n +®¥®¥-==+，所以当21x <，即||1x <时，1()n u x ¥=å绝对收敛，当||1x >时，1()n u x ¥=å发散，因此幂级数的收敛半径1R =……3分当1x =±时，原级数为11(1)21n n n -¥=--å，由莱布尼茨判别法知此级数收敛，因此幂级数的收敛域为[1,1]-……5分设1211(1)()(11)21n n n S x x x n -¥-=-=-££-å，则122211()(1)1n n n S x x x ¥--=¢=-=+å，又(0)0S =，故201()arctan 1xS x dt x t==+óôõ， ……8分 于是121(1)()arctan ,[1,1]21n nn x xS x x x x n -¥=-==Î--å ……10分(19)（本题满分10分）设P 为椭球面222:1S x y z yz ++-=的动点，若S 在点P 处的切平面与xOy 面垂直，求点P 的轨迹C ，并计算曲面积分I S=，其中S 是椭球面S 位于曲线C 上方的部分.解： 椭球面S 上点(,,)P x y z 处的法向量是{2,2,2}n x y z z y =--r， ……2分点P 处的切平面与xOy 面垂直的充要条件是0({0,0,1})n k k ×==r r r，即20z y -=所以点P 的轨迹C 的方程为222201z y x y z yz -=ìí++-=î，即2220314z y x y -=ìïí+=ïî ……5分取223{(,)|1}4D x y x y =+£，记S 的方程为(,),(,)z z x y x y D =Î，==，所以DI =óóôôôôõõ(D x dxdy =+òò ……8分2Ddxdy p== ……10分(20)（本题满分11分） 设1101011A l l l æöç÷=-ç÷ç÷èø，11a b æöç÷=ç÷ç÷èø. 已知线性方程组Ax b =存在2个不同的解，（I ）求,a l ； （II ）求方程组Ax b =的通解.解：（I ）设12,h h 为Ax b =的2个不同的解，则12h h -是0Ax =的一个非零解， 故2||(1)(1)0l l =-+=A ，于是1l =或1l =- ……4分当1l =时，因为()()r A r A b ¹M ，所以Ax b =无解，舍去. 当1l =-时，对Ax b =的增广矩阵施以初等行变换，有1111013/2()02010101/211110002a A b B a æ-öæ-öç÷ç÷=-=-=ç÷ç÷ç÷ç÷-+èøèøM .因为Ax b =有解，所以2a =- ……8分（II ）当1l =-，2a =-时，1013/20101/20000B æ-öç÷=-ç÷ç÷èø，所以x =A b 的通解为31110201x k æöæöç÷ç÷=-+ç÷ç÷ç÷ç÷èøèø，其中k 为任意常数. ……11分(21)（本题满分11分） 已知二次型123(,,)Tf x x x x Ax =在正交变换x Qy =下的标准形为2212y y +，且Q 的第3列为,0,22T. （I ）求矩阵A ；（II ）证明A E +为正定矩阵，其中E 为3阶单位矩阵.解：（I ）由题设，A 的特征值为1,1,0,且(1,0,1)T为A 的属于特征值0的一个特征向量.……3分 设123(,,)Tx x x 为A 的属于特征值1的一个特征向量，因为A 的属于不同特征值的特征向量正交，所以1231(,,)001x x x æöç÷=ç÷ç÷èø，即130x x +=.取,0,22T æö-ç÷ç÷èø，(0,1,0)T 为A 的属于特征值1的两个正交的单位特征向量 ……6分令022010022Q æöç÷ç÷=ç÷ç÷ç÷-ç÷èø，则有110T Q AQ æöç÷=ç÷ç÷èø，故1101112020101T -æöæöç÷ç÷==ç÷ç÷ç÷ç÷-èøèøA Q Q . ……9分评分说明：求出满足条件的一个矩阵A ，即可给9分.（II ）由（I ）知A 的特征值为1,1,0，于是A E +的特征值为2，2，1，又A E +为实对称矩阵，故A E +为正定矩阵.……11分(22)（本题满分11分）设二维随机变量(,)X Y 的概率密度为2222(,),,x xy y f x y Ae x y -+-=-¥<<+¥-¥<<+¥，求常数A 及条件概率密度|(|)Y X f y x .解：因2222()(,)x xy y X f x f x y dy A edy +¥+¥-+--¥-¥==òò22()y x x A e dy+¥----¥=ò222(),x y x x Aeedy x +¥-----¥==-¥<<+¥ò，……4分所以21()x X f x dx e dx A p +¥+¥--¥-¥===ò，从而 1A p=……7分当(,)x Î-¥+¥时，22222|1(,)(|)1()x xy y Y X x X ef x y f y x f x p-+--==222x xy y -+-=2(),x y y --=-¥<<+¥ ……11分(23)（本题满分11分）设总体X 的概率分布为X 1 2 3p1q-2q q -2q其中参数(0,1)q Î未知.以i N 表示来自总体X 的简单随机样本（样本容量为n ）中等于i 的个数（1,2,3i =）.试求常数123,,a a a ，使31i ii T a N==å为q 的无偏估计量，并求T 的方差.解: 记11p q =-，22p q q =-，23p q =. 由于(,),1,2,3i i N B n p i =:，故i iEN np = ……4分 于是22112233123[(1)()]ET a EN a EN a EN n a a a q q q q =++=-+-+ ……6分为使T 是q 的无偏估计量，必有22123[(1)()]n a a a q q q q q -+-+=，因此12132010a a a n a a =ìïï-=íï-=ïî，……8分由此得 12310,a a a n===……9分由于123N N N n ++=，故123111()()1N T N N n N n n n =+=-=-.注意到1~(,1)N B n q -，故1221(1)(1)n DT DN n n nq q q q --=== ……11分。

2010年全国硕士研究生入学统一考试数学一试题参考答案一、选择题(1)【答案】 (C).【解析】本题属于未定式求极限,极限为1∞型,故可以用“e 的抬起法”求解．()()2lim xx xx a x b →∞⎡⎤⎢⎥-+⎣⎦()()2lnlim x x x a x b x e ⋅-+→∞=()()2lim lnx x x x a x b e→∞⋅-+=,其中又因为()()2222()()lim ln lim ln 1()()()()lim()()()lim()()x x x x x x x a x b x x x a x b x a x b x x x a x b x a x b a b x abxx a x b a b→∞→∞→∞→∞--+⋅=+-+-+⎡⎤--+⎣⎦=-+-+=-+=-⎡⎤⎣⎦故原式极限为a b e -,所以应该选择(C). (2)【答案】 (B).【解析】122212122221x z y z y zF F F F F yF zF zx x x x x F F xF F x⎛⎫⎛⎫''''-+-⋅+⋅ ⎪ ⎪'''+∂⎝⎭⎝⎭=-=-==∂''''⋅, 112211y z F F F z x y F F F x'⋅''∂=-=-=-∂'''⋅, 1212222yF zF yF F z z z xy z x y F F F ''''+⋅∂∂+=-==∂∂'''． (3) 【答案】 (D).【解析】0x =与1x =都是瑕点.应分成=+⎰,用比较判别法的极限形式,对于,由于121012[ln (1)]lim 11mnx n mx xx+→--=.显然,当1201n m<-<,则该反常积分收敛. 当120n m -≤,1210[ln (1)]lim mx nx x+→-存在,此时实际上不是反常积分,故收敛.故不论,m n 是什么正整数,总收敛.对于,取01δ<<,不论,m n 是什么正整数,1211211[ln (1)]lim lim ln (1)(1)01(1)mnmx x x xx x x δδ--→→-=--=-,所以收敛,故选(D).(4)【答案】 (D). 【解析】()()222211111()nnn n i j i j n n n i n j n i n j =====++++∑∑∑∑22111()()n nj i n n j n i ===++∑∑ 12220211111lim lim ,11()nn n n j j n dy j n jn y n →∞→∞====+++∑∑⎰ 1011111lim lim ,11()n n n n i i n dx i n i n x n→∞→∞====+++∑∑⎰()()2222111111lim lim()()n nn nn n i j j i n n j n i n i n j →∞→∞=====++++∑∑∑∑ 221(lim )nn j n n j →∞==+∑1(lim )nn i nn i→∞=+∑1120011()()11dx dy x y =++⎰⎰()()11200111dx dy x y =++⎰⎰. (5)【答案】 (A).【解析】由于AB E =,故()()r AB r E m ==.又由于()(),()()r AB r A r AB r B ≤≤,故(),()m r A m r B ≤≤ ①由于A 为m n ⨯矩阵,B 为n m ⨯矩阵,故(),()r A m r B m ≤≤ ②由①、②可得(),()r A m r B m ==,故选A. (6)【答案】 (D).【解析】设λ为A 的特征值,由于2A A O +=,所以20λλ+=,即(1)0λλ+=,这样A 的特征值只能为-1或0. 由于A 为实对称矩阵,故A 可相似对角化,即AΛ,()()3r A r =Λ=,因此,1110-⎛⎫ ⎪- ⎪Λ= ⎪- ⎪⎝⎭,即1110A -⎛⎫⎪- ⎪Λ= ⎪- ⎪⎝⎭. (7) 【答案】 (C).【解析】离散型随机变量的分布函数是跳跃的阶梯形分段函数,连续型随机变量的分布函数是连续函数.观察本题中()F x 的形式,得到随机变量X 既不是离散型随机变量,也不是连续型随机变量,所以求随机变量在一点处的概率,只能利用分布函数的定义.根据分布函数的定义,函数在某一点的概率可以写成两个区间内概率的差,即{}{}{}()()1111111110122P X P X P X F F e e --==≤-<=--=--=-,故本题选(C).(8)【答案】 (A).【解析】根据题意知,()221x f x e-=(x -∞<<+∞),()21,1340,x f x ⎧ -≤≤⎪=⎨⎪ ⎩其它利用概率密度的性质:()1f x dx +∞-∞=⎰,故()()()()03121001312424a a f x dx af x dx bf x dx f x dxb dx b +∞+∞+∞-∞-∞-∞=+=+=+=⎰⎰⎰⎰⎰ 所以整理得到234a b +=,故本题应选(A).二、填空题 (9) 【答案】0.【解析】因为 ()()22ln 1ln 1tttdy t e dx e -+==-+-,()()()()22222ln 12ln 11tt t td te d y dt t e t e e dx dt dx t -+⎡⎤=⋅=-⋅-+⋅-⎢⎥+⎣⎦,所以220t d y dx ==. (10)【答案】 4π-.t =,2x t =,2dx tdt =,利用分部积分法, 原式220cos 22cos 2sin t t tdt t tdt t d t πππ=⋅==⎰⎰⎰20002sin 2sin 4cos t t t tdt td t πππ⎡⎤=-=⎢⎥⎣⎦⎰⎰0004cos cos 4cos 4sin 4t t tdt t ππππππ⎡⎤=-=-=-⎢⎥⎣⎦⎰. (11) 【答案】0.【解析】12222LL L xydx x dy xydx x dy xydx x dy +=+++⎰⎰⎰()()()01221011x x dx x dx x x dx x dx -=+++-+-⎰⎰()()0122122xx dx x x dx -=++-⎰⎰1322310223223x x x x -⎛⎫⎛⎫=++- ⎪ ⎪⎝⎭⎝⎭211203223⎛⎫⎛⎫=--++-= ⎪ ⎪⎝⎭⎝⎭(12) 【答案】23. 【解析】 ()2221221211000211212021r rrz d rdr zdxdydz d rdr zdz dxdydz d rdr dz d r rdrππππθθθθΩΩ⎛⎫⎪⋅ ⎪⎝⎭==-⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰4211222r d r dr πθπ⎛⎫-⎪⎝⎭=⎰⎰126204122r r d πθπ⎛⎫- ⎪⎝⎭=⎰20112266322d πθπππ⋅===⎰.(13)【答案】6a =.【解析】因为由123,,ααα生成的向量空间维数为2,所以123(,,)2r ααα=. 对123(,,)ααα进行初等行变换：123112112112211013013(,,)1010130060202000a a a ααα⎛⎫⎛⎫⎛⎫ ⎪ ⎪ ⎪-- ⎪ ⎪ ⎪=→→ ⎪ ⎪ ⎪-- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭所以6a =.(14) 【答案】2.【解析】利用离散型随机变量概率分布的性质,知{}001!k k CP X k Ce k ∞∞======∑∑,整理得到1C e -=,即 {}111!!k e P X k e k k --===.故X 服从参数为1的泊松分布,则()()1,1E X D X ==,根据方差的计算公式有()()()222112E X D X E X =+=+=⎡⎤⎣⎦.三、解答题(15)【解析】对应齐次方程的特征方程为2320λλ-+=,解得特征根121,2λλ==,所以对应齐次方程的通解为212x x c y C e C e =+．设原方程的一个特解为*()xy x ax b e =+,则()()*22x y axax bx b e '=+++,()()*2422x y axax bx a b e ''=++++,代入原方程,解得1,2a b =-=-,故特解为*(2)xy x x e =--． 故方程的通解为*212(2)x x x c y y y C e C e x x e =+=+-+． (16)【解析】因为22222222111()()x x x t t t f x x t e dt xe dt te dt ---=-=-⎰⎰⎰,所以2224423311()2222x x t x x t f x x e dt x ex ex e dt----'=+-=⎰⎰,令()0f x '=,则0,1x x ==±.又22421()24x t x f x e dt x e --''=+⎰,则21(0)20t f e dt -''=<⎰,所以2211111(0)(0)(1)22t t f t e dt e e ---=-=-=-⎰是极大值.而1(1)40f e-''±=>,所以(1)0f ±=为极小值.又因为当1x ≥时,()0f x '>；01x ≤<时,()0f x '<；10x -≤<时,()0f x '>；1x <-时,()0f x '<,所以()f x 的单调递减区间为(,1)(0,1)-∞-,()f x 的单调递增区间为(1,0)(1,)-+∞.(17)【解析】 (I)当01x <<时0ln(1)x x <+<,故[]ln(1)nn t t +<,所以[]ln ln(1)ln nn t t t t +<,则[]11ln ln(1)ln nn t t dt t t dt +<⎰⎰()1,2,n =.(II)()111101ln ln ln 1n n n t t dt t t dt td t n +=-⋅=-+⎰⎰⎰ ()211n =+,故由 ()1210ln 1n n u t t dt n <<=+⎰,根据夹逼定理得()210lim lim01n n n u n →∞→∞≤≤=+,所以lim 0n n u →∞=.(18)【解析】(I) (1)1222(1)1122(1)(1)2(1)121lim lim (1)(1)2121n n n n n n n n n nx x n n xx n n +-++--→∞→∞--⋅+-+=--⋅--222(21)21lim lim 2121n n n x n x x n n →∞→∞--==⋅=++, 所以,当21x <,即11x -<<时,原级数绝对收敛.当21x >时,原级数发散,因此幂级数的收敛半径1R =.当1x =±时,11211(1)(1)2121n n n n n x n n --∞∞==--⋅=--∑∑,由莱布尼兹判别法知,此级数收敛,故原级数的收敛域为[]1,1-.(II) 设1122111(1)(1)()2121n n nn n n S x x x x n n --∞∞-==⎛⎫--=⋅=⋅⋅ ⎪--⎝⎭∑∑,其中令 12111(1)()21n n n S x xn -∞-=-=⋅-∑()1,1x ∈-, 所以有 12221111()(1)()n n n n n S x xx ∞∞---=='=-⋅=-∑∑ ()1,1x ∈-,从而有 12211()1()1S x x x '==--+ ()1,1x ∈-, 故 11201()(0)arctan 1xS x dx S x x =+=+⎰,()1,1x ∈-.1()S x 在1,1x =-上是连续的,所以()S x 在收敛域[]1,1-上是连续的.所以()arctan S x x x =⋅,[]1,1x ∈-.(19)【解析】 ( I )令()222,,1F x y z x y z yz =++--,故动点(),,P x y z 的切平面的法向量为()2,2,2x y z zy --,由切平面垂直xOy ,故所求曲线C 的方程为222120x y z yz z y ⎧++-=⎨-=⎩. ( II ) 由⎩⎨⎧=-=-++,02,1222y z yz z y x 消去z ,可得曲线C 在xOy 平面上的投影曲线所围成的xOy 上的区域223:{(,)|1}4D x y x y +≤,由()()x x yz z y x '='-++1222,由 dxdy zy yzz y dxdy y z x z dS 24412222--++=⎪⎪⎭⎫⎝⎛∂∂+⎪⎭⎫ ⎝⎛∂∂+=,故(2DDDx y zI x dxdy xdxdy ∑-==+=+⎰⎰⎰⎰⎰⎰12Dπ==⋅=. (20)【解析】因为方程组有两个不同的解,所以可以判断方程组增广矩阵的秩小于3,进而可以通过秩的关系求解方程组中未知参数,有以下两种方法.方法1：( I )已知Ax b =有2个不同的解,故()()3r A r A =<,对增广矩阵进行初等行变换,得111110101010111111a A a λλλλλλ⎛⎫⎛⎫ ⎪ ⎪=-→- ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭22111111010101010110011a a λλλλλλλλλ⎛⎫⎛⎫⎪⎪→-→- ⎪ ⎪ ⎪ ⎪-----+⎝⎭⎝⎭ 当1λ=时,11111111000100010000000A a ⎛⎫⎛⎫⎪ ⎪→→ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭,此时,()()r A r A ≠,故Ax b =无解(舍去)．当1λ=-时,111102010002A a -⎛⎫ ⎪→- ⎪ ⎪+⎝⎭,由于()()3r A r A =<,所以2a =-,故1λ=- ,2a =-.方法2：已知Ax b =有2个不同的解,故()()3r A r A =<,因此0A =,即211010(1)(1)011A λλλλλ=-=-+=,知1λ=或-1.当1λ=时,()1()2r A r A =≠=,此时,Ax b =无解,因此1λ=-.由()()r A r A =,得2a =-.( II ) 对增广矩阵做初等行变换31012111211121020102010102111100000000A ⎛⎫- ⎪----⎛⎫⎛⎫ ⎪⎪ ⎪⎪=-→-→- ⎪ ⎪ ⎪ ⎪ ⎪- ⎪⎝⎭⎝⎭ ⎪ ⎪⎝⎭可知原方程组等价为1323212x x x ⎧-=⎪⎪⎨⎪=-⎪⎩,写成向量的形式,即123332110210x x x x ⎛⎫⎪⎛⎫⎛⎫ ⎪ ⎪ ⎪⎪=+- ⎪ ⎪ ⎪⎪ ⎪ ⎪⎝⎭⎝⎭ ⎪ ⎪⎝⎭.因此Ax b =的通解为32110210x k ⎛⎫ ⎪⎛⎫ ⎪⎪⎪=+- ⎪ ⎪ ⎪ ⎪⎝⎭ ⎪ ⎪⎝⎭,其中k 为任意常数.(21)【解析】 ( I )由于二次型在正交变换x Qy =下的标准形为2212y y +,所以A 的特征值为1231,0λλλ===.由于Q 的第3列为22T ⎛ ⎝⎭,所以A 对应于30λ=的特征向量为22T⎛ ⎝⎭,记为3α. 由于A 是实对称矩阵,所以对应于不同特征值的特征向量是相互正交的,设属于121λλ==的特征向量为()123,,Tx x x α=,则30T αα=,即13022x x +=. 求得该方程组的基础解系为()()120,1,0,1,0,1TTαα==-,因此12,αα为属于特征值1λ=的两个线性无关的特征向量.由于12,αα是相互正交的,所以只需单位化：())1212120,1,0,1,0,1T Tααββαα====-. 取()12302,,10002Q ββα⎛⎪⎪==⎝⎭,则110T Q AQ ⎛⎫ ⎪=Λ= ⎪ ⎪⎝⎭,且1T Q Q -=, 故 1102201011022TA Q Q ⎛⎫- ⎪ ⎪=Λ= ⎪ ⎪- ⎪⎝⎭. ( II )A E +也是实对称矩阵,A 的特征值为1,1,0,所以A E +的特征值为2,2,1,由于A E +的特征值全大于零,故A E +是正定矩阵.(22)【解析】当给出二维正态随机变量的的概率密度(),f x y 后,要求条件概率密度|(|)Y X f y x ,可以根据条件概率公式|(,)(|)()Y X X f x y f y x f x =来进行计算.本题中还有待定参数,A 要根据概率密度的性质求解,具体方法如下.()()22222222()(),xxy y y x x xy x X f x f x y dy A e dy A e dy Ae e dy +∞+∞+∞+∞-+--------∞-∞-∞-∞====⎰⎰⎰⎰2,x x -=-∞<<+∞.根据概率密度性质有()21x X f x dx edx A π+∞+∞--∞-∞===⎰,即1A π-=,故()2x X f x -=,x -∞<<+∞.当x -∞<<+∞时,有条件概率密度()()()22222222(),,,x xy y x xy y x y Y X X f x y f y x x y f x -+--+---==-∞<<+∞-∞<<+∞.(23)【解析】()()()22123~,1,~,,~,N B n N B n N B n θθθθ--()()()()31122331i i i E T E a N a E N a E N a E N =⎛⎫==++ ⎪⎝⎭∑()()221231a n a n a n θθθθ=-+-+()()212132na n a a n a a θθ=+-+-.因为T 是θ的无偏估计量,所以()E T θ=,即得()()12132010na n a a n a a =⎧⎪-=⎨⎪-=⎩,整理得到10a =,21,a n =31a n=.所以统计量 ()()12323111110T N N N N N n N n n n n=⨯+⨯+⨯=⨯+=⨯-.注意到1(,1)N B n θ-,故()()()11211D T D n N D N n n⎡⎤=⨯-=⨯⎢⎥⎣⎦()11n θθ=-.。

-1-
硕士学位研究生入学考试试题
一、选择题（每题3分，共30分）
1、以下五种运动形式中，a 保持不变的运动是
(A) 单摆的运动． (B) 匀速率圆周运动．
(C) 行星的椭圆轨道运动． (D) 抛体运动．
(E) 圆锥摆运动． ［ ］
2、人造地球卫星绕地球作椭圆轨道运动，卫星轨道近地点和远地点分别为A 和
B ．用L 和E K 分别表示卫星对地心的角动量及其动能的瞬时值，则应有
(A) L A >L B ，E KA >E kB ． (B) L A =L B ，E KA <E KB ．
(C) L A =L B ，E KA >E KB ． (D) L A <L B ，E KA <E KB ． ［ ］
3、一质量为m 的滑块，由静止开始沿着1/4圆弧形光滑
的木槽滑下．设木槽的质量也是m ．槽的圆半径为R ，放在光滑水平地面上，如图所示．则滑块离开槽时的速度是
(A) Rg 2．
(B) Rg ． (C) Rg 2 (D) Rg 21． (E) Rg 22
1 ． ［ ］ 4、均匀细棒OA 可绕通过其一端O 而与棒垂直的水平固定光滑轴转动，如图所示．今使棒从水平位置由静止开始自由下落，在棒摆动到竖直位置的过程中，下述说法哪一种是正确的？
(A) 角速度从小到大，角加速度从大到小．
(B) 角速度从小到大，角加速度从小到大．
(C) 角速度从大到小，角加速度从大到小．
(D) 角速度从大到小，角加速度从小到大． ［ ］。

2010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)In 1924 America's National Research Council sent two engineers to supervise a series of industrial experiments at a large telephone-parts factory called the Hawthorne Plant near Chicago. It hoped they would learn how stop-floor lighting 1workers' productivity. Instead, the studies ended 2giving their nameto the "Hawthorne effect", the extremely influential idea that the very 3to being experimented upon changed subjects' behavior.The idea arose because of the 4behavior of the women in the Hawthorne plant. According to 5of the experiments, their hourly output rose when lighting was increased, but also when it was dimmed. It did not 6what was done in the experiment; 7something was changed, productivity rose. A(n) 8that they were being experimented upon seemed to be 9to alter workers' behavior 10itself.After several decades, the same data were 11to econometric the analysis. Hawthorne experiments has another surprise store 12the descriptions on record, no systematic 大13家was found that levels of productivity were related to changesin lighting.It turns out that peculiar way of conducting the experiments may be have let to 14interpretation of what happened. 15, lighting was always changed on a Sunday. When work started again on Monday, output 16rose compared with the previous Saturday and 17to rise for the next couple of days. 18, acomparison with data for weeks when there was no experimentation showed that output always went up on Monday, workers 19to be diligent for the first few days of the week in any case, before 20 a plateau and then slackening off. This suggests that the alleged "Hawthorne effect" is hard to pin down.1. [A] affected [B] achieved [C] extracted [D] restored2. [A] at [B] up [C] with [D] off3. [A] truth [B] sight [C] act [D] proof4. [A] controversial [B] perplexing [C] mischievous [D] ambiguous5. [A] requirements [B] explanation [C] accounts [D] assessments6. [A] conclude [B] matter [C] indicate [D] work7. [A] as far as [B] for fear that [C] in case that [D] so long as8. [A] awareness [B] expectation [C] sentiment [D] illusion9. [A] suitable [B] excessive [C] enough [D] abundant10. [A] about [B] for [C] on [D] by11. [A] compared [B] shown [C] subjected [D] conveyed12. [A] contrary to [B] consistent with [C] parallel with [D] peculiar to13. [A] evidence [B] guidance [C] implication [D] source14. [A] disputable [B] enlightening [C] reliable [D] misleading15. [A] In contrast [B] For example [C] In consequence [D] As usual16. [A] duly [B] accidentally [C] unpredictably [D] suddenly17. [A] failed [B] ceased [C] started [D] continued18. [A]Therefore [B]Furthermore [C]However [D]Meanwhile19. [A]Attempted [B]tended [C]chose [D]intended20. [A] breaking [B] climbing [C] surpassing [D] hittingSection 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 1Of all the changes that have taken place in English-language newspapers during the past quarter-century, perhaps the most far-reaching has been the inexorable decline in the scope and seriousness of their arts coverage.It is difficult to the point of impossibility for the average reader under the age of forty to imagine a time when high-quality arts criticism could be found in most big-city newspapers. Yet a considerable number of the most significant collections of criticism published in the 20th century consisted in large part of newspaper reviews. To read such books today is to marvel at the fact that their learned contents were once deemed suitable for publication in general-circulation dailies.We are even farther removed from the unfocused newspaper reviews published in England between the turn of the 20th century and the eve of World War II, at a time when newsprint was dirt-cheap and stylish arts criticism was considered an ornament to the publications in which it appeared. In those far-off days, it was taken for granted that the critics of major papers would write in detail and at length about the events they covered. Theirs was a serious business, and even those reviewers who wore their learning lightly, like George Bernard Shaw and Ernest Newman, could be trusted to know what they were about. These men believed in journalism as a calling, and were proud to be published in the daily press. “So few authors have brains enough or literary gift enough to keep their own end up in journalism,” Newman wrote, “that I am tempted to de fine ‘journalism’ as ‘a term of contempt applied by writers who are not read to writers who are.’”Unfortunately, these critics are virtually forgotten. Neville Cardus, who wrote for the Manchester Guardian from 1917 until shortly before his death in 1975, is now known solely as a writer of essays on the game of cricket. During his lifetime, though, he was also one of England’s foremost classical-music critics, a stylist so widely admired that his Autobiography (1947) became a best-seller. He was knighted in 1967, the first music critic to be so honored. Yet only one of his books is now in print, andhis vast body of writings on music is unknown save to specialists.Is there any chance that Cardus’s criticism will enjoy a revival? The prospect seems remote. Journalistic tastes had changed long before his death, and postmodern readers have little use for the richly upholstered Vicwardian prose in which he specialized. Moreover, the amateur tradition in music criticism has been in headlong retreat.21. It is indicated in Paragraphs 1 and 2 that[A] arts criticism has disappeared from big-city newspapers.[B] English-language newspapers used to carry more arts reviews.[C] high-quality newspapers retain a large body of readers.[D] young readers doubt the suitability of criticism on dailies.22. Newspaper reviews in England before World War II were characterized by[A] free themes.[B] casual style.[C] elaborate layout.[D] radical viewpoints.23. Which of the following would Shaw and Newman most probably agree on?[A] It is writers' duty to fulfill journalistic goals.[B] It is contemptible for writers to be journalists.[C] Writers are likely to be tempted into journalism.[D] Not all writers are capable of journalistic writing.24. What can be learned about Cardus according to the last two paragraphs?[A] His music criticism may not appeal to readers today.[B] His reputation as a music critic has long been in dispute.[C] His style caters largely to modern specialists.[D] His writings fail to follow the amateur tradition.25. What would be the best title for the text?[A] Newspapers of the Good Old Days[B] The Lost Horizon in Newspapers[C] Mournful Decline of Journalism[D] Prominent Critics in MemoryText 2Over the past decade, thousands of patents have been granted for what are called business methods. received one for its "one-click" online payment system. Merrill Lynch got legal protection for an asset allocation strategy. One inventor patented a technique for lifting a box.Now the nation's top patent court appears completely ready to scale back on business-method patents, which have been controversial ever since they were first authorized 10 years ago. In a move that has intellectual-property lawyers abuzz the U.S. court of Appeals for the federal circuit said it would use a particular case to conduct a broad review of business-method patents. In re Bilski, as the case is known , is "a very big deal", says Dennis D. Crouch of the University of Missouri School of law. It "has the potential to eliminate an entire class of patents."Curbs on business-method claims would be a dramatic about-face, because it was the federal circuit itself that introduced such patents with is 1998 decision in the so-called state Street Bank case, approving a patent on a way of pooling mutual-fund assets. That ruling produced an explosion in business-method patent filings, initially by emerging internet companies trying to stake out exclusive rights to specific types of online transactions. Later, move established companies raced to add such patents to their files, if only as a defensive move against rivals that might beat them to the punch. In 2005, IBM noted in a court filing that it had been issued more than 300 business-method patents despite the fact that it questioned the legal basis for granting them. Similarly, some Wall Street investment films armed themselves with patents for financial products, even as they took positions in court cases opposing the practice.The Bilski case involves a claimed patent on a method for hedging risk in the energy market. The Federal circuit issued an unusual order stating that the case would be heard by all 12 of the court's judges, rather than a typical panel of three, and that one issue it wants to evaluate is whether it should "reconsider" its state street Bank ruling.The Federal Circuit's action comes in the wake of a series of recent decisions by the supreme Court that has narrowed the scope of protections for patent holders. Last April, for example the justices signaled that too many patents were being upheld for "inventions" that are obvious. The judges on the Federal circuit are "reacting to the anti-patent trend at the Supreme Court", says Harold C. Wegner, a patent attorney and professor at George Washington University Law School.26. Business-method patents have recently aroused concern because of[A] their limited value to business[B] their connection with asset allocation[C] the possible restriction on their granting[D] the controversy over authorization27. Which of the following is true of the Bilski case?[A] Its ruling complies with the court decisions[B] It involves a very big business transaction[C] It has been dismissed by the Federal Circuit[D] It may change the legal practices in the U.S.28. The word "about-face" (Line 1, Para 3) most probably means[A] loss of good will[B] increase of hostility[C] change of attitude[D] enhancement of dignity29. We learn from the last two paragraphs that business-method patents[A] are immune to legal challenges[B] are often unnecessarily issued[C] lower the esteem for patent holders[D] increase the incidence of risks30. Which of the following would be the subject of the text?[A] A looming threat to business-method patents[B] Protection for business-method patent holders[C] A legal case regarding business-method patents[D] A prevailing trend against business-method patentsText 3In his book The Tipping Point, Malcolm Gladwell argues that social epidemics are driven in large part by the acting of a tiny minority of special individuals, often called influentials, who are unusually informed, persuasive, or well-connected. The idea is intuitively compelling, but it doesn't explain how ideas actually spread.The supposed importance of influentials derives from a plausible sounding but largely untested theory called the "two step flow of communication": Information flows from the media to the influentials and from them to everyone else. Marketers have embraced the two-step flow because it suggests that if they can just find and influence the influentials, those selected people will do most of the work for them. The theory also seems to explain the sudden and unexpected popularity of certain looks, brands, or neighborhoods. In many such cases, a cursory search for causes finds that some small group of people was wearing, promoting, or developing whatever it is before anyone else paid attention. Anecdotal evidence of this kind fits nicely with the idea that only certain special people can drive trendsIn their recent work, however, some researchers have come up with the findingthat influentials have far less impact on social epidemics than is generally supposed. In fact, they don't seem to be required of all.The researchers' argument stems from a simple observing about social influence, with the exception of a few celebrities like Oprah Winfrey—whose outsize presence is primarily a function of media, not interpersonal, influence—even the most influential members of a population simply don't interact with that many others. Yet it is precisely these non-celebrity influentials who, according to the two-step-flow theory, are supposed to drive social epidemics by influencing their friends and colleagues directly. For a social epidemic to occur, however, each person so affected, must then influence his or her own acquaintances, who must in turn influence theirs, and so on; and just how many others pay attention to each of these people has little to do with the initial influential. If people in the network just two degrees removed from the initial influential prove resistant, for example from the initial influential prove resistant, for example the cascade of change won't propagate very far or affect many people.Building on the basic truth about interpersonal influence, the researchers studied the dynamics of populations manipulating a number of variables relating of populations, manipulating a number of variables relating to people's ability to influence others and their tendency to be influenced. Our work shows that the principal requirement for what we call "global cascades"– the widespread propagation of influence through networks – is the presence not of a few influentials but, rather, of a critical mass of easily influenced people, each of whom adopts, say, a look or a brand after being exposed to a single adopting neighbor. Regardless of how influential an individual is locally, he or she can exert global influence only if this critical mass is available to propagate a chain reaction.31. By citing the book The Tipping Point, the author intends to[A] analyze the consequences of social epidemics[B] discuss influentials' function in spreading ideas[C] exemplify people's intuitive response to social epidemics[D] describe the essential characteristics of influentials.32. The author suggests that the "two-step-flow theory"[A] serves as a solution to marketing problems[B] has helped explain certain prevalent trends[C] has won support from influentials[D] requires solid evidence for its validity33. What the researchers have observed recently shows that[A] the power of influence goes with social interactions[B] interpersonal links can be enhanced through the media[C] influentials have more channels to reach the public[D] most celebrities enjoy wide media attention34. The underlined phrase "these people" in paragraph 4 refers to the ones who[A] stay outside the network of social influence[B] have little contact with the source of influence[C] are influenced and then influence others[D] are influenced by the initial influential35. what is the essential element in the dynamics of social influence?[A] The eagerness to be accepted[B] The impulse to influence others[C] The readiness to be influenced[D] The inclination to rely on othersText 4Bankers have been blaming themselves for their troubles in public. Behind the scenes, they have been taking aim at someone else: the accounting standard-setters. Their rules, moan the banks, have forced them to report enormous losses, and it's just not fair. These rules say they must value some assets at the price a third party would pay, not the price managers and regulators would like them to fetch.Unfortunately, banks' lobbying now seems to be working. The details may be unknowable, but the independence of standard-setters, essential to the proper functioning of capital markets, is being compromised. And, unless banks carry toxic assets at prices that attract buyers, reviving the banking system will be difficult.After a bruising encounter with Congress, America's Financial Accounting Standards Board (FASB) rushed through rule changes. These gave banks more freedom to use models to value illiquid assets and more flexibility in recognizing losses on long-term assets in their income statement. Bob Herz, the FASB's chairman, cried out against those who "question our motives." Yet bank shares rose and the changes enhance what one lobby group politely calls "the use of judgment by management."European ministers instantly demanded that the International Accounting Standards Board (IASB) do likewise. The IASB says it does not want to act without overall planning, but the pressure to fold when it completes it reconstruction of rules later this year is strong. Charlie McCreevy, a European commissioner, warned the IASB that it did "not live in a political vacuum" but "in the real word" and that Europe could yet develop different rules.It was banks that were on the wrong planet, with accounts that vastly overvalued assets. Today they argue that market prices overstate losses, because they largelyreflect the temporary illiquidity of markets, not the likely extent of bad debts. The truth will not be known for years. But bank's shares trade below their book value, suggesting that investors are skeptical. And dead markets partly reflect the paralysis of banks which will not sell assets for fear of booking losses, yet are reluctant to buy all those supposed bargains.To get the system working again, losses must be recognized and dealt with. America's new plan to buy up toxic assets will not work unless banks mark assets to levels which buyers find attractive. Successful markets require independent and even combative standard-setters. The FASB and IASB have been exactly that, cleaning up rules on stock options and pensions, for example, against hostility from special interests. But by giving in to critics now they are inviting pressure to make more concessions.36. Bankers complained that they were forced to[A] follow unfavorable asset evaluation rules[B] collect payments from third parties[C] cooperate with the price managers[D] reevaluate some of their assets.37. According to the author , the rule changes of the FASB may result in[A] the diminishing role of management[B] the revival of the banking system[C] the banks' long-term asset losses[D] the weakening of its independence38. According to Paragraph 4, McCreevy objects to the IASB's attempt to[A] keep away from political influences.[B] evade the pressure from their peers.[C] act on their own in rule-setting.[D] take gradual measures in reform.39. The author thinks the banks were "on the wrong planet" in that they[A] misinterpreted market price indicators[B] exaggerated the real value of their assets[C] neglected the likely existence of bad debts.[D] denied booking losses in their sale of assets.40. The author's attitude towards standard-setters is one of[A] satisfaction.[B] skepticism.[C] objectiveness[D] sympathyPart BDirections:For Questions 41-45, choose the most suitable paragraphs from the list A-G and fill them into the numbered boxes to form a coherent text. Paragraph E has been correctly placed. There is one paragraph which does not fit in with the text. Mark your answers on ANSWER SHEET1. (10 points)[A] The first and more important is the consumer's growing preference for eating out; the consumption of food and drink in places other than homes has risen from about 32 percent of total consumption in 1995 to 35 percent in 2000 and is expected to approach 38 percent by 2005. This development is boosting wholesale demand from the food service segment by 4 to 5 percent a year across Europe, compared with growth in retail demand of 1 to 2 percent. Meanwhile, as the recession is looming large, people are getting anxious. They tend to keep a tighter hold on their purse and consider eating at home a realistic alternative.[B] Retail sales of food and drink in Europe's largest markets are at a standstill, leaving European grocery retailers hungry for opportunities to grow. Most leading retailers have already tried e-commerce, with limited success, and expansion abroad. But almost all have ignored the big, profitable opportunity in their own backyard: the wholesale food and drink trade, which appears to be just the kind of market retailers need.[C] Will such variations bring about a change in the overall structure of the food and drink market? Definitely not. The functioning of the market is based on flexible trends dominated by potential buyers. In other words, it is up to the buyer, rather than the seller, to decide what to buy .At any rate, this change will ultimately be acclaimed by an ever-growing number of both domestic and international consumers, regardless of how long the current consumer pattern will take hold.[D] All in all, this clearly seems to be a market in which big retailers could profitably apply their scale, existing infrastructure and proven skills in the management of product ranges, logistics, and marketing intelligence. Retailers that master the intricacies of wholesaling in Europe may well expect to rake in substantial profits thereby. At least, that is how it looks as a whole. Closer inspection reveals important differences among the biggest national markets, especially in their customer segments and wholesale structures, as well as the competitive dynamics of individual food and drink categories. Big retailers must understand these differences before they can identify the segments of European wholesaling in which their particular abilities might unseat smaller but entrenched competitors. New skills and unfamiliar business models are needed too.[E] Despite variations in detail, wholesale markets in the countries that have been closely examined—France, Germany, Italy, and Spain—are made out of the same building blocks. Demand comes mainly from two sources: independent mom-and-pop grocery stores which, unlike large retail chains, are two small to buy straight from producers, and food service operators that cater to consumers when they don't eat at home. Such food service operators range from snack machines to large institutional catering ventures, but most of these businesses are known in the trade as "horeca": hotels, restaurants, and cafes. Overall, Europe's wholesale market for food and drink is growing at the same sluggish pace as the retail market, but the figures, when added together, mask two opposing trends.[F] For example, wholesale food and drink sales come to $268 billion in France, Germany, Italy, Spain, and the United Kingdom in 2000—more than 40 percent of retail sales. Moreover, average overall margins are higher in wholesale than in retail; wholesale demand from the food service sector is growing quickly as more Europeans eat out more often; and changes in the competitive dynamics of this fragmented industry are at last making it feasible for wholesalers to consolidate.[G] However, none of these requirements should deter large retailers (and even some large good producers and existing wholesalers) from trying their hand, for those that master the intricacies of wholesaling in Europe stand to reap considerable gains.41→42→43→44→E→45Part CDirections:Read the following text carefully and then translate the underlined segments into Chinese. Your translation should be written carefully on ANSWER SHEET 2. (10 points)One basic weakness in a conservation system based wholly on economic motives is that most members of the land community have no economic value. Yet these creatures are members of the biotic community and, if its stability depends on its integrity, they are entitled to continuance.When one of these noneconomic categories is threatened and, if we happen to love it .We invert excuses to give it economic importance. At the beginning of century songbirds were supposed to be disappearing. (46) Scientists jumped to the rescue with some distinctly shaky evidence to the effect that insects would eat us up if birds failed to control them. the evidence had to be economic in order to be valid.It is painful to read these round about accounts today. We have no land ethic yet, (47) but we have at least drawn near the point of admitting that birds should continue as a matter of intrinsic right, regardless of the presence or absence of economic advantage to us.A parallel situation exists in respect of predatory mammals and fish-eating birds.(48) Time was when biologists somewhat over worded the evidence that thesecreatures preserve the health of game by killing the physically weak, or that they prey only on "worthless" species.Some species of tree have been read out of the party by economics-minded foresters because they grow too slowly, or have too low a sale vale to pay as timber crops. (49) In Europe, where forestry is ecologically more advanced, the non-commercial tree species are recognized as members of native forest community, to be preserved as such, within reason.To sum up: a system of conservation based solely on economic self-interest is hopelessly lopsided. (50) It tends to ignore, and thus eventually to eliminate, many elements in the land community that lack commercial value, but that are essential to its healthy functioning. It assumes, falsely, I think, that the economic parts of the biotic clock will function without the uneconomic parts.Section ⅢWritingPart A51. Directions:You are supposed to write for the postgraduate association a notice to recruit volunteers for an international conference on globalization, you should conclude the basic qualification of applicant and the other information you think relative.You should write about 100 words. Do not sign your own name at the end of the letter. Use "postgraduate association" instead.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) give your comments.You should write neatly on ANSHWER SHEET 2. (20 points)。

北京科技大学2010年硕士学位研究生入学考试试题试题编号： ________________________ 试题名称：___________ （共2页）适用专业：材料科学与工程______________________________________________________________说明：所有答案必须写在答题纸上，做在试题或草稿纸上无效.一、分析发生下列现象的原因（30分）1. 低碳钢应力-应变曲线的屈服现象（10分）2. 金属及合金凝固时形成树枝状晶（10分）3. 上坡扩散（5分）4. 二次再结晶（5分）二、在面心立方结构的金属中（111）面上运动着柏氏矢量为6=a/2［110］的位错，位错线方向也是［110］,请在单胞中画出（ill）晶面和山0］晶向，并说明该位错属于什么类型？如果该位错的运动受到阻碍后，请判断是否有可能转移到（ill）, （ill）, （ill）各晶面上继续运动？说明为什么？（15分）三、以含Al-4wt%Cu合金为例，给出其经过不同固溶时效工艺处理后的脱溶贯序；定性说明各阶段脱溶相的尺寸及分布特点、与母相的界面匹配关系及其强化效果等.（20分）四、讨论晶体结构和空间点阵之间的关系。

（15分）五、与液态结晶过程相比，固态相变有什么特点？这些特点对固态相变后形成的组织有什么影响？（15分）六、叙述离子晶体的结构规则（15分）七、分析形成下列不同铸态组织的可能原因，并说明要得到细小的等轴晶，可采取哪些办法？（20分）八、参考下面提供的示意图，画出按组织分区的Fe-Fe’C相图，写出各三相反应,并说明分别为1. Owt%C和3. Owt%C的铁碳合金经过缓慢冷却在相关三相反应完成后形成的各组织特点（20分）。

2010答案:一、1.低碳钢在一定条件下形变时，应力-应变曲线的大致规律是首先发生线性弹性变形，达到屈服时发生塑性变形直至断裂。

特殊的地方在于应力-应变曲线上常常出现上下屈服点，这与C间隙原子对位错的钉扎作用有关。

北京科技大学硕士学位研究生入学考试模拟试题I
试题编号： 814 试题名称：材料科学基础（共 2 页）
适用专业：金属材料工程、材料成型与控制工程、无机非金属材料工程专业
说明：所有答案必须写在答题纸上，做在试题或草稿纸上无效。

一、解释下列名词（每个名词2分，共10分）
1、人工时效
2、奥氏体本质晶粒度
3、反稳定化
4、珠光体晶粒
5、原位形核
二、说出下符号的名称和意义（6分）
1、M S
2、M d
3、M C
三、简答下各题（每题8分，共40分）
1、简述马氏体相变的主要特征。

2、何谓临界冷却速度？影响临界冷却速度的因素有哪些？
3、简述钢中马氏体高强度和高硬度的主要原因。

4、何谓时效？与回火有何异同？
5、简述贝氏体转变的主要特征
四、叙述下列各题（共44分）
1、以共析钢为例说明珠光体向奥氏体的转变过程，并讨论为什么奥氏体全部形成后还会有部分渗碳体未溶解？（20分）
2、试述淬火钢回火脆性的特点、产生的原因、抑制和消除的方法。

（12分）
3、说明钢中碳化物的相间析出机制，相间析出条件及相间析出产物的组织形态（12分）。