2010年硕士研究生入学考试全真模拟卷一
2010年全国硕士研究生入学统一考试数学一试题解析
2010年全国硕士研究生入学统一考试数学一试题一、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. （10年，4分） 极限2lim ()()xx x x a x b →∞⎡⎤=⎢⎥-+⎣⎦( ) (A ) 1. (B ) e . (C ) a be -. (D ) b ae-.【考查分析】“1∞”型极限的计算. 【详解】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 be-,所以应该选择(C).2. （10年，4分） 设函数(,)z z x y =,由方程,0y z F x x ⎛⎫=⎪⎝⎭确定,其中F 为可微函数,且20F '≠,则z zxy x y∂∂+=∂∂( ) (A ) x . (B ) z . (C ) x -. (D ) z -. 【考查分析】隐函数偏导数的计算. 【详解】122212122221x z y z y zF F F F F yF zF z x 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 x y z x y F F F ''''+⋅∂∂+=-==∂∂'''．选（B ）. 3. （10年，4分） 设,m n 是正整数,则反常积分()20ln 1mnx dx x-⎰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 取值都有关. (D ) 与,m n 取值都无关. 【考查分析】判断反常积分的敛散性. 【详解】0x =与1x =都是瑕点.应分成()()()22211212ln 1ln 1ln 1mm mnnnx x x xxx---=+⎰⎰,用比较判别法的极限形式,对于()2120ln 1m nx x-,由于121012[ln (1)]lim 1mnx n mx xx+→--=.显然,当1201n m<-<,则该反常积分收敛. 当120n m -≤,1210[ln (1)]lim m x nx x+→-存在,此时()2120ln 1m n x x -实际上不是反常积分,故收敛. 故不论,m n 是什么正整数,dx 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).【评注】(1)当210m m-≥时，⎰是定积分.(2) 0,0αβ∀>>,有lim ln 00x x x βα+=→. 4. （10年，4分） ()()2211limnnn i j nn i n j →∞===++∑∑ ( ) (A )()()120111xdx dy x y ++⎰⎰. (B ) ()()100111x dx dy x y ++⎰⎰. (C )()()11111dx dy x y ++⎰⎰. (D ) ()()1120111dx dy x y ++⎰⎰. 【考查分析】利用积分和式求极限. 【详解】()()222211111()nnnn i j i j n nn i n jn i n j =====++++∑∑∑∑22111()()n n j i n n j n i ===++∑∑ 12220211111lim lim ,11()nn n n j j n dy j n jn y n→∞→∞====+++∑∑⎰ 1011111lim lim ,11()nn 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 =++⎰⎰. 【评注】本题易认为是二重积分或误认为逐次极限.实际上,对i 求和时与j 无关,对j 求和时与i 无关,所以这是一道两个和得乘积的极限题.5. （10年，4分） 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 =. 【详解】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. （10年，4分） 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 ) 1110⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭. (B ) 1110⎛⎫ ⎪⎪ ⎪- ⎪⎝⎭. (C ) 1110⎛⎫ ⎪- ⎪ ⎪- ⎪⎝⎭. (D ) 1110-⎛⎫⎪- ⎪ ⎪- ⎪⎝⎭. 【考查分析】对称矩阵相似于对角矩阵.【详解】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A Λ ,()()3r A r =Λ=,因此,1110-⎛⎫⎪- ⎪Λ= ⎪- ⎪⎝⎭,即1110A -⎛⎫⎪- ⎪Λ= ⎪- ⎪⎝⎭. 【评注】看清题目,说清每个已知条件的作用.即可得出结论.7. （10年，4分） 设随机变量X 的分布函数0,01(),0121,1x x F x x e x -<⎧⎪⎪=≤<⎨⎪-≥⎪⎩,则{}1P X == ( ) (A ) 0. (B )12. (C ) 112e --. (D ) 11e --. 【考查分析】本题主要考查分布函数的概念及随机事件概率的计算.已知分布函数,【详解】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). 【评注】已知分布函数,求随机事件的概率是基本题,但需注意题中的随机变量既不是离散型也不是连续型.由于分布函数在1x =处不连续,故利用{1}(1)(10)P X F F ==--来计算.8. （10年，4分） 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()(),0af x x f x bf x x ≤⎧=⎨>⎩,(0,0)a b >>为概率密度,则,a b 应满足 ( ) (A ) 234a b +=. (B ) 324a b +=. (C ) 1a b +=. (D ) 2a b +=. 【详解】根据题意知,()2212x f x e π-=(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 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. （10年，4分） 设()20,ln 1,t tx e y u du -⎧=⎪⎨=+⎪⎩⎰ 求220t d y dx == . 【详解】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. （10年，4分）2π=⎰.【考查分析】用变量变换与分部计算定积分.【详解】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. （10年，4分） 已知曲线L 的方程为[]{}11,1y x x =- ∈-,起点是()1.0-,终点是()1,0,则曲线积分2Lxydx x dy +=⎰.【详解】12222LL L xydx x dy xydx x dy xydx x dy +=+++⎰⎰⎰()()()01221011x x dx x dx x x dx x dx -=+++-+-⎰⎰()()0122122x x dx x x dx -=++-⎰⎰1322310223223x x x x -⎛⎫⎛⎫=++- ⎪ ⎪⎝⎭⎝⎭211203223⎛⎫⎛⎫=--++-= ⎪ ⎪⎝⎭⎝⎭12. （10年，4分） 设(){}22,,1x y z xy z Ω=+≤≤,则Ω的形心的竖坐标z = .【详解】()2221221211000211212021r rrz d rdr zdxdydz d rdr zdzdxdydz d rdr dzd r rdrππθθθθΩΩ⎛⎫⎪⋅ ⎪⎝⎭==-⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰4211222r d r drπθπ⎛⎫- ⎪⎝⎭=⎰⎰126204122r r d πθ⎛⎫- ⎪⎝⎭=⎰20112266322d πθπππ⋅===⎰. 13. （10年，4分） 设()()()1231,2,1,0,1,1,0,2,2,1,1,TTTa ααα=-==,若由123,,ααα生成的向量空间的维数是2,则a = . 【详解】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. （10年，4分） 设随机变量X 的概率分布为{}!C P X k k ==,0,1,2,k = ,则()2E X = . 【考查分析】随机变量的数学期望,方差.泊松分布的期望,方差. 【详解】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 =+=+=⎡⎤⎣⎦. 【评注】22()EX DX EX =+,所以应求X 的期望与方差,而X 的分布{},0,1,2,!CP X k k k === 的C 是待定常数.不难看出这是一个泊松分布. 三、解答题(15～23小题,共94分.请将解答写在答题纸．．．指定位置上.解答应写出文字说明、证明过程或演算步骤.) 15. （10年，10分）(本题满分10分)求微分方程322x y y y xe '''-+=的通解． 【考查分析】求常系数线性非齐次微分方程的通解. 【详解】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*()x y 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. （10年，10分）(本题满分10分)求函数()()2221x t f x x t e dt -=-⎰的单调区间与极值.【考查分析】对变限求导数,划分单调区间,求极值. 【详解】 因为22222222111()()x x x t t t f x x t e dt x e 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,)-+∞ .【评注】(1)求()f x 的单调性区间就是求()f x '的正负号区间.增减或增减区间的分界点就是极值点.上述方法就是求出()f x ',然后分出()f x '的正负号区间,从而得到()f x 的增减区间,相应地得到()f x 的极值点.这里就不必去求驻点处得()f x ''.(2)若题目只要求()f x 的极值,我们也可以221()2x t f x x e dt -'=⎰后,解得驻点0x =,1x =±,然后再求驻点处的二阶导数.由于201(0)20t f e dt -''=<⎰,⇒11(0)(1)2f e -=-为极大值.由于1(1)40f e -''±=>,⇒(1)0f ±=为极小值.17. （10年，10分）(本题满分10分)(I)比较()1ln ln 1n t t dt +⎡⎤⎣⎦⎰与10ln nt t dt ⎰()1,2,n = 的大小,说明理由；(II)记()1ln ln 1nn u t t dt =+⎡⎤⎣⎦⎰()1,2,n = ,求极限lim n n u →∞. 【详解】(I)当01x <<时0ln(1)x x <+<,故[]ln(1)nnt 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)()1111001ln ln ln 1nnn 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. （10年，10分）(本题满分10分)求幂级数()121121n n n x n -∞=--∑的收敛域及和函数.【考查分析】求幂级数的收敛域及和函数. 【详解】(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 x n -∞-=-=⋅-∑()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 ∈-.【评注】幂函数在收敛域上可以逐项积分,但逐项求导只能先在收敛区间进行.在逐项求导后，在另行讨论端点处是否成立。
2010年全国硕士研究生入学统一考试英语一试题及参考答案
Section I Use of EnglishDnecclious:Read thc following text．Choose the bcsl word(s)for each numbcred blank．and mark[A]，[B]，[C]or[D]on ANSWER SHEET1.(10points)In1924American'National Research Council sent to engineer to supervise a series of experiments at a telephone-parts factory called the Hawhtore Plant nearChicago It hoped they would learn how stop-floor Egnting__1__workors productivity Instead，the studies ended__2__giving their name to the“Hawhthomeeffect”the extremely inflentlcel ldea the veey__3__to bemg expenmented upon changed subjects’behaviorThe idea arose because of the__4__behavior of the women in the plato．Accordmg to__5__of the cxpetmems．their．houriy output rose when hghtmg WaSincreased．but also when it was dimmed.It did not__6__what was done in the expenment. __7__sometmg was changed．produchnty rose A(n)__8__that theywere bemg experimented upon seemed to be__9__t0alterworkers'bchamor__10__uselfAfter several decades，the salile data were__11__to econometric the analysis Hawthorne experiments has another surprise store j2一the descnpuons on record，nosystematic__13__was foundthat lcvcls of produchxnty wererelated to changes in lightingIt turns out that peculiar way of conducting the c~enments may be have let to __14__interpretation of what happed．__15__，tighring was always changed ona Sunday When work started again on Monday,output__16__rose compared with the previous Saturday and__17__to rise for the next couple of days__18__,，a comparison with data for weeks whenthere was no expenmentation showed that output always went up On Monday,workers__19__to be duigent for the first fewdays of the week in any case，before__21__a plateau and then slackening off This suggests that the alleged”Hawthorne effect“is hard to ptn down1.[A]affected[B]achieved[C]exlracted[D]restored2.[A]at[B]up[C]with[D]Off您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问3.[A]Wuth[B]sight[C]act[D]proof4.[A]conVoversial[B]perplexing[c]mischieous[D]ambiguous5.[A]reqtttrents[B]cxplanalions[C]accounts[D]assements6.[A]conclude[B]matter[C]indicate[D]work7.[A]as faras[B]for fearthat[C]in casethat[D]so long as8.[A]awarerress[B]expectation[C]sentiment[D]illusion9.[A]suitale[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]pealliar to13.[A]evidence[B]guidance[C]implication[D]source14.[A]disputable[B]enlightening[C]retiable[D]wasleadmg15.[A]In contast[B]For example[C]In consequence[D]As usual16．[A]duly[B]accidentally[C]unpredictably[D]suddenly17．[A]failed[B]ceased[C]started[D]continued20.[A]breaking[B]chrnbing[C]surpassmg[D]hitingSectionⅡReading 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 SHEET1．(40points)Text2Over the past decade,thousands of patents have seen granled for what are called business您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问methods．Amazon com received one for its“one-click”online paymentsystern Merrill Lynch got legal protection for an asset allocation strategy．One invenlor patented a tochnique for lying a boxNow the nation’s top patent court appears completely ready to scale hack on business-method patents,which have been controversial e,ver since they were firstauthorized10years ago In a movethat has intellectual-property lawyers abuzz the U.S court of Appeals for the federal ctrcuit sald it would usea particular case tOconduct a broad review of business-method patents.Inre Bijskl,as the case is known,is“a very big deal”,says Dermis'D Crouch of the University of MissounSchool of law．It“has the potential to elinate an entire class of patmts”Curbs on business-method claims would be a dramatic about-face because it was the federal circuit itself that introduced such patents with is1998decision 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 pinhts to specific types of online ter,move established companies raced to add such patents to their files,if only as a defensive move against rivals that might bent them to the punch.In2005,IBM noted in a court filing that it had been issued more than300business-method patents despite tha 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 all12of the court’s judges,rather than a typical panel of three,and that one issue it wants to evaluste is wether 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. Count that has nurrowed the scope of protections for patent st 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“reaction to the anti_patent trend at the supreme court”says Harole C wegner,a partend attorney and professor at aeorge 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您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问[C]the possible restriction on their granting[D]the controversy over authorization27.Which of the following is true of the Bilski case?[A]Its rulling 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”(Line1,Paro3)most probably means[A]loss of good will[B]increase of hostility[C]change of attitude[D]change of auiuled29．We learn from the last two pamgraphs that business-meihod Pateats[A]are immune to legal challenges[B]are of ten unnecessarily issued[C]lower the esteem for pateat holders[D]increase the incidence of risks30．Which of the following would bethe subject ofthe text?[A]A looming threat to bvamess-melhcd patents[B]Protection for business-method patent holders[C]A legal case regarding business-methodpatents[D]A prevailing tread against business-method patents Text3您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问In his book The Tipping Poinl Malcohn aladuell aloues that social epidemics are dliven in largepart by the acting of a tiny minority of specialindividuals,often calledin flu entials who are unusuall informed,persuasive,or we connect The idea is intuit ively compelling but it doesn't explain howideas actually spread.The supposed importance of inftuentials derives from a plansible sounding but largely untested theory untested thelry called the"tow-step flow of communication"Informationllows from the mediato the inftuentials and from then to ereryone else.Marke ters have embraced the two-step flow became it suggests that if they can just find andinfluence the in fluent ials,those select people will do most of the work for them Thetheory also seems to explain the sudden and unexpected popularity of people waswearing promoting or developing whaterver it is before anyone else paid attention Anecdotal evidence of this kind fits nicely with the idea that only certain specialpeople call drivetrendsIn their recent work howeyer some researchers have come up with the finding that in fluentials have far less impact on social epidemics than is genetally supposed Infact they don’t seem to be required of allThe researchers'argument stems from a simple obserrating about social influence with the exception of a few celebrities like Oprah Winfrey-whose outsize presence is primanrilly a function of media not interpersonal influence-enen the most influential members of a population simply don't interact with that many others Yet it is precisely these non-celebring influentials who according to the two-step-flow theoryare supposed to drive social enidemics by influcenciny their friends and colleagues directly.For a social epidemic to occur however each person so sffected must then influcence 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 casecade 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 abilify to influence others and their tendence to be31.By citing the book The Tipping Point the author intends to您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问[A]analyze the consequences of social epid emics[B]discuss influentials’funcition in spreading ideas[C]exemplify people’s intuitive response to social epidemics[D]describe the essential characteristics of influentials32.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 recenty 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 celebritiea enjoy wide media attention34.the underlined phrase“these people”in paragraph4refers 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 influential34.what is the essential slement in the dynamics of social influence?{A}The eageiness to be accepted{B}The impulse to influence others您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问{C}The resdiness to be influenced{D}The inclination to rely on othersText4Bankers have been blaming themselves for their troubles in public.Behind eht 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 atheird 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 marksts,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 Xongress.America;s Financial Accounting Standards Board(FASB)rushed through rule changse.These gave banks more freedom to use models to value illiquid assets and more flexibility in recognizing losses on long0term assets in their income statement.Bob Herz,the FASB’s chairman,cried out against ehose 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 comletes it reconstruction of rules later this year is strong Charlie McCreevy,a European commissioner,warned the IASB that is did”not live in a political vacuum”but”in the real word”and the Europe could yet develop different rules.It was banks that were on the wrong planet,with accouts htat wastly overvalued assets.today they argue htat market prices overstate loeees,because hteyLargerly reflect the temporary illiquldity of markets,not the likely entent of bad debts.The truth will not be known for years.But bank’s shares trade below their book value,suggeting that investors are akeptical.And dead markets partly reflect the paralysis of banks which will not sell assets for fear of booking losses,yet are relucaant to buy all those supposed bargains.To get the sysytem 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 ang pensions,for example,against hostility interests.But by giving in to critics now they are inviting pressure to make more concessions.36.Bankers complained that they were forced to您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问[A]follow anfavorable asset evaluation rules[B]collect payments from third parties[C]cooperate with the price managers[D]reevaluate some of their assets37.According to the author,the rule changes of the FASB may result in[A]the dimingishing role of management[B]the revival of the banking syestem[C]the bank’s long-term asset lossers[D]the weakening og its indepentdence38.According to Paragarph4,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 ruli-setting[D]take gradual measures in reform39、The author thinks the banks were“on the wrong planet”in that they[A]mis interpreted 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 assets40、The author’s attitude towards standard-setters is one of[A]satisfaction[B]skepticism您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问[C]objectiveness[D]sympathy Part BDirections:For Questions41-45,choose the most suitable paragraphs from the first A-G and fill them into the numbered boxes to from a coherent text Paragraph E has been correctly placed.There is one paragraph which dose not fit in with the text.Mark your answers on ANSWER SHEET1.(10points)[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 about32percent of total consumption in1995to35percent in2000and is expected to approach38percent by2005.This development is boosting wholesale demand from the food service segment by4to5percent a year Europe compared with growth in retail demand of1to2percent.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,lesving European grocery retailers hungry for opportunities to grow.Most leading retailers have alteady tried e-commerce,with limit success,and expansion abroad.But almost all have ignored the big.profitable opportunity in their own backyard the wholesale food and drink trade,whoch 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 drinkmarket?Definitely not.The functioning of the market is basrd on flexibleTrends dominated by potential buyers.In other words it is up to the buyer tather 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 pattem will take hold.[D]All in all,this clearly seems to be a market in which big retailers that master the intricacies of wholesaling in Europe may well expect to rake in substantial profits there by.At least,that is how it looks as a whole.Closer inspection reveals import 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 particular abilities might unseat smaller but enerenched 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 same building blocks.Demand comes您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问mainly from two sources:independent morn-and-pop grocery stores which,unlike large retail chains,are two small to buy straight from producers,and 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 retail wholesale market,but the figures,when added together,mask two opposing trends.[F]For example,wholesale food and drink sales come to$268billion in France,Germany,Italy, Spain and the United Kingdom in2000-more than40percent 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 considerate.[G]However,none of these requirements should deter large retails 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 carfully on ANSWER SHEET2.(10Points)One basic weakness in a comservation system based wholly one economic motives is that most members of the land community have no economic value Yet these ereatures are members of the biotic community and,if its stability depends on its inteynity,they are entitled to continuanceWhen one of these noneconomic categories is threatened and if we happen to love it.We incert excuses to give it economic importance At the beginning pf century songbiras were supppsed to be disappearing.(46)Scinentists jumped to the resure with some distimctly shaky evidence to the effect the insecets would est us up of brids failed to control them the ecideuce had to be conbmic in order to be walid.It is pamful to read these round about accounts today.We have no land ehtic yet.(47)but we have at least drawn near the point pf admitting that birds should continue as a matter of intrinisic right reardless of the presence pf absence of economic adcantage to us.A panallel situation exists in respect of predatory mamals and fish-eating birds(48)Time was when biologosts somewhat over worded evidence that these creatures preserve the health of game by killing the physically weak or that they prey only on“worthless species”.您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问Some species pf tree have been read out of the party by economici–minded fpresters they grow too slowty or have a sale vate to pay as imeber crops(49)In europe,where forestry is ecologically more advanced,the ncommercial tree species are recognized ad members of native forest community,to be preserved as such,within reason.To sum up;a system of conservation based solely on econominc self-interest is hopelesstly 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.Without the uneconomic pats.Section III WritingPart A51.Directions:You are supposed to write for the postgraduate association a notice to recruit volunteers for an intemational conference on globalization,you should conclude the basic qualification of applicant and the other information you think relative.You should write about100words.Do not sign your own name at the end ofthe e"postgraduate association"instead.Part B52.Directions:Write an essay of160200words based on the following deawing.In your essay,you should1)describe the drawing briefly,2)ecplain its intended meaning,and then3)give your comments.You should write neatly on ANSHWER SHEET2.(20points)您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问您所下载的资料来源于弘毅考研资料下载中心获取更多考研资料，请访问Section I Use of English1.A解析：A 项affect 意思是“影响，感动”;B 项achieve 意思是“达成，完成”;C 项extract 意思是“提取，榨出”;D 项restore 是“恢复，重建”.这句话的意思是：他们想通过实验探究车间照明是如何影响工人的生产率的，所以答案是A。
2010年一月联考综合能力模拟试卷1-答案
2010年一月在职研究生入学资格考试模拟试卷一 答案第一部分：逻辑1A 2C 3B 4A 5E 6D 7C 8B 9A 10D 11E 12C 13D 14B 15C 16A 17B 18D 19E 20C 21B 22E 23D 24C 25A 26C 27B 28D 29A 30B第二部分：数学一、问题求解（本大题共15小题，每小题3分，共45分）下列每题给出的五个选项中，只有一项是符合试题要求的。
请在答题卡上将所选项的字母涂黑。
1．1324358109111234564950⨯+⨯+⨯++⨯+⨯=-+-+-++- （ ） A.-15 B.-17 C.-19 D.38425- E.37425- 解析：分式可以写为2222222132435810911(21)(31)(101)1234564950(12)(34)(56)(4950)11011211012310106151111125⨯+⨯+⨯++⨯+⨯-+-++-=-+-+-++--+-+-++-⨯⨯⨯-++++-===------- 2．商场对进行促销活动，某种商品先提价20%，再降价10%，然后赠送一个价格为6元的小礼品，此时与原来的利润相同，则该商品的原价为（ ）A.60B.75C.80D.90E.以上都不正确解析：设商品原价为x ，价格改变后变为1.2x ×0.9，赠送一个价格为6元的小礼品与原来的利润相同，则1.2x ×0.9-6=x ，解可得x=75元.3．某小组有1元，10元，100元的纸币共4张，将它们都换成5角的硬币，刚好可以平分给7人，设总币值为X 元，则X 可能的范围是（ ）A.(100,110)B.(110,120)C.(120,130)D.(210,220)E.以上答案均不正确解析：根据题意，4张纸币组成的币值如果在A 范围内，则应为103元，但是不能平分给7人；同理，C 中应为121元，D 中应为211元，都不能平分给7人，只有B 中112元，可以平分给7人，每人16元，换成硬币为每人32个4．浓度为50%的一定量酒精溶液，如果加入10L 水，浓度会变为40%，如果想要得到浓度为25%的酒精溶液，需要加水（ ）A.20LB.30LC.35LD.40LE.50L解析：设原溶液体积为xL ，则溶质（纯酒精）体积为2x ，根据题意，240%10xx =+，则x=40L ，原溶液中纯酒精为20L ，设加入yL 水后，浓度变为25%，即2025%40y =+，可得y=40L. 5．王强骑车上班，以速度v 经过了10分钟后，发现一个重要的文件忘在家里了，然后以2v 的速度赶回家里，用了5分钟找到文件，拿到文件后以2v 的速度赶到公司，则王强离家的距离和时间的大致关系图形为（ ）A B C DE.以上答案都不正确解析：在距离与时间的关系曲线中，速度可以用距离函数曲线的斜率表示，根据题意A 正确.6．甲、乙同时从A 、B 两地出发相向而行，3个小时后两人相遇，如果甲早出发半个小时，则经过2.8小后时两人会在中点相遇，甲、乙两人的速度之比为（ ）A.2：3B.1：2C.4：5D.3：5E.都不正确解析：设甲的速度分别为V 甲，V 乙，则0.5V 甲=（3-2.8）（V 甲+V 乙），所以两人的速度比为2：37．已知方程022=++-+y x y x2x y -=（ ）A ．8B ．0C ．6 D.10 E.12 解析：2020x y x y +-=⎧⎨+=⎩可得42x y =⎧⎨=-⎩24410x y -=+=8．设方程2410x x -+=的两个根分别是x 1，x 2（x 1>x 2），则1211x x -=（ ）A.-B.C.-解析：2112121211x x x x x x --==12====-9．8(12)x -展开式中系数的最大项为（ ）A.第四项B.第五项C.第六项D.第七项E.以上都不正确 解析：设第k 项系数最大，不考虑符号的话8118212k kk k C C --≤，可得6k ≥，当6k =时，系数为5588(2)72C -=-⨯，当7k =时，系数为6688(2)72C -=⨯，所以最大项为第七项. 10．一粒均匀的骰子投掷两次，记第一次得到的点数为a ，第二次得到的点数为b ，则直线(3)1a x by -+=不经过第三象限的概率为（ ） A.23 B.12 C.710 D.1732 E.516 解析：直线(3)1a y x b b -=+不经过第三象限，则斜率30a k b -=≤，3a ≥，对b 没有限制，所以直线不经过第三象限的概率等于3a ≥的概率，为0.511．一个长为3厘米，宽为2厘米的长方形硬板（厚度不计）水平放置，在硬板正面A 位置有一只蚂蚁，它要穿过BC 边爬向硬板反面的D 位置，已知该蚂蚁每10秒钟爬行1厘米，假设它在硬板正、反面都是沿直线爬行，则蚂蚁爬到D 位置所需最短时间为（ ）A. 30秒B.40秒C.45秒D.50秒E.一分钟解析：如图所示，要爬行的时间最短，蚂蚁应该沿图示位置爬行，爬行距离5厘米，所以所需最短时间应该为5×10=50秒12．在等差数列{}n a 中，1359910a a a a ++++= ，公差12d =-，则100s =（ ）A ．-10B ．5C ．-5D ．0 E.以上答案都不正确解析：1001299100119999()()s a a a a a a d a a d =++++=++++++=135992()5020255a a a a d +++++=-=-13．若直线4ax by +=与圆C ：224x y +=相切，则点(,)P b a 与圆C 的关系为（ ）A.在圆外B.在圆周上C.在圆内非圆心D.为圆心E.P 点位置不确定2=2=，即2=，即点P 到圆心的距离等于半径，所以点P 则圆上.14．从0~9十个数字和a~z26个英文字母中选择8个字符作为密码，要求首位不能为数字，不能使用同一个字符来当密码，则可能组成的密码数有（ ）A.83636- B.726(361)⨯- C.73626C ⨯ D. 73626P ⨯ E.以上答案均不正确 解析：密码首位有26种选择，其余七位各为36种，所以是72636⨯，但不能重复，所以需要减去8位密码都是字母的26种情况15．如图所示，正方形ABCD 的面积为16，以边长为半径的两个圆弧交于O 点，则阴影部分面积为（ ）A.23B.163π-6π-2πE.以上四个选项都不正确解析：连接两个弧线的交点M 与A 、B ，则MAB 为边长为4的等边三角形，则阴影部分可以表示为一个等边三角形加上两个全等的拱形面积，拱形面积等于半径为4，圆心角为60°的扇形减去等边三角形163π- 二、条件充分性判断（本大题共10小题，每小题3分，共30分）解题说明：本大题要求判断所给出的条件能否充分支持题干中陈述的结论。
2010数学二(模拟1)试题(试卷版)
绝密 * 启用前2010年全国硕士研究生入学统一考试数学（二）试卷 （模拟一）考生注意:本试卷共二十三题,满分150分,考试时间为3小时.一、选择题：1～8小题,每小题4分,共32分.在每小题给出的四个选项中,只有一个符合要求,把所选项前的字母填在题后的括号里.（1）设数列{}{},n n a b 对任意的正整数n 满足1n n n a b a +≤≤，则（ C ）．（A ）数列{}{},n n a b 均收敛，且lim lim n n n n a b →∞→∞=（B ）数列{}{},n n a b 均发散，且lim lim n n n n a b →∞→∞==+∞（C ）数列{}{},n n a b 具有相同的敛散性 （D ）数列{}{},n n a b 具有不同的敛散性（2）设()f x 满足(0)0f '=，32()[()]f x f x x '+=，则有（ C ）．（A ）(0)f 是()f x 的极大值 （B ）(0)f 是()f x 的极小值 （C ）(0,(0))f 是()y f x =的拐点（D ）(0)f 不是()f x 的极值,且(0,(0))f 也不是()y f x =的拐点(3) 下列直线中，不是．．曲线1(1)xx y e =+的渐近线的为( )． (A) 0y = (B) 1y = (C) y e = (D) 0x = 【答案】选（A ）．【解】∵1ln(1)limlim (1)xx e xxxx e e→+∞+→+∞+=e =，1lim (1)1xxx e →-∞+=，1lim (1)xx x e +→+=+∞,∴y e =，1y =均为该曲线的水平渐近线；0x =为该曲线的垂直渐近线．■得分 评卷人(4) 设410sin x I dx xπ=⎰，420tan x I dx xπ=⎰，4301cos I dx xπ=⎰，则有( )．(A) 123I I I << (B) 321I I I << (C) 213I I I << (D) 312I I I << 【答案】选（A ）． 【解】当0,4x π⎛⎫∈ ⎪⎝⎭时，1sin cos x xx<，tan 1cos x xx<，故3I 最大．又2tan tan sin sin sin x x x x xxxx x --=，记2()tan sin f x x x x =-，0,4x π⎛⎫∈ ⎪⎝⎭2sin ()2sin cos xf x x x x '=--2tan sin ()x x x x ϕ≤--=记． 21()2cos cos x x x ϕ'=--12cos 0cos x x≤--≤． 故()(0)0x ϕϕ≤=，所以()0f x '≤，()(0)0f x f ≤=，从而有tan sin x x xx≤，故12I I <．（5）设函数(,)f x y 在点000(,)P x y 处的两个偏导数00(,)x f x y '，00(,)y f x y '都存在，则（ C ）．（A ）(,)f x y 在点0P 处必连续 （B ）(,)f x y 在点0P 处必可微 （C ）000lim (,)lim (,)x x y y f x y f x y →→= （D ）0lim (,)x x y y f x y →→存在（6）设()f x 为任一连续函数，a 是非零常数，则下列结论正确的是( )．(A) 若()f t 为奇函数，则0()xyady f t dt ⎰⎰是x 的奇函数(B) 若()f t 为偶函数，则0()x yady f t dt ⎰⎰是x 的奇函数(C) 若()f t 为奇函数，则0()x aydy f t dt ⎰⎰是x 的奇函数(D) 若()f t 为偶函数，则0()x ydy f t dt ⎰⎰是x 的奇函数【答案】选（Ｃ）．【解】当()f t 为奇函数时，()ayf t dt ⎰为y 的偶函数，所以0()xaydy f t dt ⎰⎰是x 的奇函数，选（Ｃ）．■（7）设B A ,为n 阶方阵，且)()(B r AB r <，则必有( B )．（A ）0||=B （B ）0||=A （C ）0||≠B （D ）0||≠Axy2o111-1D D（8）若0=x A 的解都是0 =x B 的解，则下列命题中正确的是( D )．（A ）B A ,的行向量组等价 （B ）B A ,的列向量组等价（C ）A 的行向量组可由B 的行向量组线性表示 （D ）B 的行向量组可由A 的行向量组线性表示二、填空题:9～14小题,每小题4分,共24分.把答案填在题中的横线上.（9）44412lim 12n nnnn n →∞⎡⎤+++=⎢⎥+++⎣⎦ ．【答案】填：12． （10）23221(cos)422x x x dx -+-=⎰ π．（11）函数222()2()()u x y y z z x =---+-在点0(1,2,2)M 处方向导数的最大值是 26．（12）微分方程10xy y xe x'''--=的通解为 ．212xxxe e C x C -++（13）由半圆21x y =-与三条直线1y =-，1y =，2x =所围成的平面图形D 的形心坐标为 ． 【答案】填：20,03(8)π⎛⎫⎪-⎝⎭．【解】：如图，补1D ，则11DD D D xd xd xd σσσ+=-⎰⎰⎰⎰⎰⎰2112012[][cos ]xdy dx r rdr d ππθθ--=-⋅⎰⎰⎰⎰220212cos 3xdx d ππθθ-=-⎰⎰243=-，42Dd πσ=-⎰⎰，242033(8)42D Dxd x d σππσ-===--⎰⎰⎰⎰．由对称性，0y =，形心坐标为20,03(8)π⎛⎫⎪-⎝⎭．■（14）设,A B 均为三阶方阵，且3,4A B ==，则*10(2)(3)A B -=【答案】应填：163-三、解答题:15～23小题，共94分.解答应写出文字说明、证明过程或演算步骤.（15）设23,310x t t y ty ⎧=-⎨++=⎩确定函数()y y x =，求202|t d ydx =．答案2（16）设函数(),()f x g x 在[,]a b 上有连续二阶导数，若()()f a g a =，()()f b g b =，00()()f x g x >，其中0(,)x a b ∈，证明：在(,)a b 内至少存在一点ξ，使()()f g ξξ''''<．得分 评卷人得分 评卷人（17）利用变换t x =化简微分方程23242(1)6xd y dy x x y edxdx+--=(0)x >，并求出原方程的通解． 【解】12dy dydxdtx =，22221144d y dy d y dxdtx dtxx =-+，代入方程化简得2326td y dy ye dtdt--=．解此方程得2331215ttty C eC ete -=++，故方程通解为2331215xxxy C e C exe-⋅=++．■（18）计算不定积分arctan1xdx x+⎰．【解】arctan2arctan11xdx x d x x=++⎰⎰121arctan 1x x x d x x+=+-+⎰121arctan 1x x d x x=+-+⎰21arctan 2ln(1)x x x x C =+-+++．（19） 设()f x 在[0,]a 上非负，(0)0f =，()0f x ''>， 求证：2()()3a axf x dx a f x dx >⎰⎰．【证明】：令02()()()3x xF x tf t dt x f t dt =-⎰⎰，(0,)x a ∈，(0)0F =，则22()()()()33x F x xf x f t dt xf x '=--⎰ 012()()33x xf x f t dt =-⎰．(0)0F '=，1()[()()][()()]33x F x xf x f x f x f ξ'''''=-=-，[0,]x ξ∈．由于()0f x ''>，()f x '单调递增．故()0F x ''>，(0,)x a ∈．()F x '单调递增，()0F x '>，(0,)x a ∈，xyo12D 1D 3D 11-D()F x 单调递增，所以()0F x >，(0,)x a ∈．由于()F x 在[0,]a 上连续，故()0F a >，从而2()()3a axf x dx a f x dx >⎰⎰．■20）设(,)f u v 有二阶连续偏导数，()u ϕ有二阶导数，令22[,()]z f x y xy ϕ=-，求2z x y∂∂∂．答案：22111242()xyf x y f ϕ'''''-+-2222()xy f xy f ϕϕϕ'''''''+++．（21）计算二重积分{}2m ax ,DI x x y d σ=⎰⎰，其中:01D x ≤≤，11y -≤≤．答案：815=（20）（数学1，2，3）（Ⅰ）设n 维向量组12,,,,s αααβ 线性相关，证明：β可唯一地由12,,,s ααα 线性表示的充要条件是12,,,s ααα 线性无关；（Ⅱ）设4维向量组1122334(1,,0,0),(1,,1,0),(1,,1,1),(1,,0,1)TTTTb b b b αααβ====，且β可唯一地由123,,ααα线性表示，求常数1234,,,b b b b 满足的条件．答案：24130b b b b +--=（21）（数学1，2，3）设三阶实对称矩阵A 的秩为2，且AB C =,其中⎪⎪⎪⎭⎫⎝⎛-=⎪⎪⎪⎭⎫⎝⎛-=110011,110011C B ，求A 的所有特征值与特征向量，并求矩阵A 及9999A．。
2010全国研究生入学考试数学试题一答案
2010考研数学（一）真题及参考答案一、选择题（1）、极限（C）A、1B、C、D、（2）、设函数，由方程确定，其中F为可微函数，且，则（B）A、B、C、D（3）、设施正整数，则反常积分的收敛性( C)A、仅与的取值有关B、仅与有关C、与都有关D、都无关（4）、( D )A、B、C、D、（5）、设A为型矩阵，B为型矩阵，E为m阶单位矩阵，若AB=E，则（A）A、秩r(A)=m, 秩r(B)=mB、秩r(A)=m, 秩r(B)=nC、秩r(A)=n, 秩r(B)=mD、秩r(A)=n, 秩r(B)=n(6) 设A为4阶实对称矩阵，且，若A的秩为3，则A相似于（D）A． B.C. D.(7) 设随机变量的分布函数，则 {x=1}= （C）A．0 Ｂ. C. D.(8) 设为标准正态分布的概率密度，为上的均匀分布的概率密度，若为概率密度，则应满足：（A ）A、B、C、D、二、填空题（9）、设求（10）、（11）、已知曲线的方程为起点是终点是则曲线积分0（12）、设则的形心坐标（13）设若由形成的向量空间维数是2，则 6（14）设随机变量概率分布为，则 2三、解答题（15）、求微分方程的通解解答：（16）、求函数的单调区间与极值解答：单调递减区间单调递增区间极大值，极小值（17）、（Ⅰ）比较与的大小，说明理由（Ⅱ）设，求极限解答：（18）、求幂级数的收敛域及和函数解答：收敛域，和函数（19）设为椭球面上的动点，若在点处的切平面为面垂直，求点的轨迹，并计算曲面积分，其中是椭球面位于曲线上方的部分解答：（1）（2）（20）、设已知线性方程组存在2个不同的解，（Ⅰ）求，；（Ⅱ）求方程组的通解。
解答：（Ⅰ）（Ⅱ）的通解为（其中k为任意常数）（21）已知二次型在正交变换下的标准形为，且的第3列为（Ⅰ）求矩阵；（Ⅱ）证明为正定矩阵，其中为3阶单位矩阵。
答案：（Ⅰ）（Ⅱ）证明：为实对称矩阵又的特征值为1，1，0的特征值为2，2，1，都大于0为正定矩阵。
2010年全国硕士研究生入学统一考试
2010年全国硕士研究生入学统一考试数学一试题一、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) 极限2lim ()()xx x x a x b →∞⎡⎤=⎢⎥-+⎣⎦( ) (A) 1. (B) e . (C) a be -. (D) b ae-.(2) 设函数(,)z z x y =,由方程,0y z F x x ⎛⎫=⎪⎝⎭确定,其中F 为可微函数,且20F '≠,则z zxy x y∂∂+=∂∂( ) (A) x . (B) z . (C) x -. (D) z -.(3) 设,m n 是正整数,则反常积分⎰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 取值都有关. (D) 与,m n 取值都无关. (4) ()()2211limn nn i j nn i n j →∞===++∑∑ ( ) (A)()()120111xdx dy x y ++⎰⎰. (B) ()()100111x dx dy x y ++⎰⎰. (C)()()11111dx dy x y ++⎰⎰. (D) ()()1120111dx dy x y ++⎰⎰. (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 =. (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) 1110⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭. (B) 1110⎛⎫ ⎪⎪ ⎪- ⎪⎝⎭.(C) 1110⎛⎫ ⎪- ⎪ ⎪- ⎪⎝⎭. (D) 1110-⎛⎫ ⎪- ⎪ ⎪- ⎪⎝⎭. (7) 设随机变量X 的分布函数0,1(),0121,1x x F x x e x -<⎧⎪⎪=≤<⎨⎪-≥⎪⎩,则{}1P X == ( ) (A) 0. (B)12. (C) 112e --. (D) 11e --. (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()(),0af x x f x bf x x ≤⎧=⎨>⎩,(0,0)a b >>为概率密度,则,a b 应满足 ( ) (A) 234a b +=. (B) 324a b +=. (C) 1a b +=. (D) 2a b +=.二、填空题(914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 -⎧=⎪⎨=+⎪⎩⎰ 求220t d y dx == .(10)2π=⎰ .(11) 已知曲线L 的方程为[]{}11,1y x x =- ∈-,起点是()1.0-,终点是()1,0,则曲线积分2Lxydx x dy +=⎰.(12) 设(){}22,,1x y z xy z Ω=+≤≤,则Ω的形心的竖坐标z = .(13) 设()()()1231,2,1,0,1,1,0,2,2,1,1,TTTa ααα=-==,若由123,,ααα生成的向量空间的维数是2,则a = .(14) 设随机变量X 的概率分布为{}!CP X k k ==,0,1,2,k =,则()2E X=.三、解答题(15～23小题,共94分.请将解答写在答题纸．．．指定位置上.解答应写出文字说明、证明过程或演算步骤.)求微分方程322xy y y xe '''-+=的通解． (16)(本题满分10分)求函数()()2221x t f x xt e dt -=-⎰的单调区间与极值.(17)(本题满分10分)(I)比较()1ln ln 1n t t dt +⎡⎤⎣⎦⎰与10ln nt t dt ⎰()1,2,n =的大小,说明理由；(II)记()1ln ln 1nn u t t dt =+⎡⎤⎣⎦⎰()1,2,n =,求极限lim n n u →∞. (18)(本题满分10分)求幂级数()121121n nn xn -∞=--∑的收敛域及和函数.(19)(本题满分10分)设P 为椭球面222:1S x y z yz ++-=上的动点,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2x y zI ∑-=,其中∑是椭球面S 位于曲线C 上方的部分.(20)(本题满分11分)设110111a A b λλλ ⎛⎫⎛⎫ ⎪ ⎪= - 0= ⎪ ⎪ ⎪ ⎪1 1 ⎝⎭⎝⎭，,已知线性方程组Ax b =存在两个不同的解.( I ) 求λ,a ；( II ) 求方程组Ax b =的通解. (21)(本题满分11 分)已知二次型123(,,)T f x x x x Ax =在正交变换x Qy =下的标准形为2212y y+,且Q 的第三列为,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. (22)(本题满分11分)设二维随机变量(,)X Y 的概率密度为2222(,)xxy y f x y Ae -+-=,x -∞<<+∞,y -∞<<+∞,求常数A 及条件概率密度|(|)Y X f y x ．设总体X其中参数()0,1θ∈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31iii T a N ==∑为θ的无偏估计量,并求T 的方差.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 be-,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 z x 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,dx 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dx 收敛,故选(D).(4)【答案】 (D). 【解析】()()222211111()nnn ni j i j n nn i n j n i n j =====++++∑∑∑∑22111()()n n j i n n j n i ===++∑∑ 12220211111lim lim ,11()nn n n j j n dy j n jn y n→∞→∞====+++∑∑⎰ 1011111lim lim ,11()nn 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A Λ,()()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2200t 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 -=++-⎰⎰01322310223223x 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 πθ⎛⎫- ⎪⎝⎭=⎰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 xc 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 xc 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)nnt 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 x n -∞-=-=⋅-∑()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T ⎝⎭,所以A 对应于30λ=的特征向量为T⎝⎭,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1TQ 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 e dx 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=-.。
2010年硕士研究生入学考试专业课试题1
4、写出某标量函数的随体导数表达式，并说明其中的迁移偏导数项在什么条件
下等于零。
二、写出相似准则中欧拉数的表达式。为什么说 Ma 数准则就是欧拉数准则？（10
分）
三、证明：二维定常流无旋流场中等流函数线与等势线同时存在且正交。（10 分）
四、渐缩喷管入口燃气总压 P1*=2.5105N/m2，总温 T1*=850K，燃气绝热指数
18、绝热闭口系就是孤立系（ ）
19、迈耶公式仅对变比热理想气体适用（ ）
20、绝热过程就是定熵过程（ ）
21、热力系是具体指定的热力学的研究对象（ ）
22、不可逆过程可能没有熵增，但是必有熵产（ ）
23、任何热机循环的热效率都小于 1（ ）
24、任何实际热机的热效率都小于卡诺热机的热效率（ ）
25、功损和可用能的损失是一回事（ ）
4. 如图所示，某常物性不可压缩流体低速流过一发热的大平板，形成二维稳态 层流边界层对流换热。已知来流速度与温度分别为 u、T ，流体密度、定
压比热容、导热系数与动力粘度分别为 、cp、、 ，并保持恒定；平板表
面发热均匀恒定，热流密度为 qw 。
y、v
u、T
x、u qw
（1）若从对流换热微分方程出发，求解平板与流体的对流换热表面传热系 数 h 与壁面温度 Tw，试列出所用微分方程、定解条件，并简要说明求解步骤； （10 分）
三．推导理想流体平面有势流动中偶极流的速度势函数和流函数。（15 分）
四．流体在长为 l 的水平放置的等直径圆管中作定常流动，若已知沿程损失因数为 ，管壁切应力为 ，断面平均流速为V ； 试证明： V 2 。（15 分）
8
第2 页 共8 页
五．图示为一圆形容器，直径 d =300mm，高 H =500mm，容器内装水，其深度 h1 =300mm，设容器绕垂直轴作等角速度旋转。（15 分） 1．试确定水正好不溢出时的转速； 2．求刚好露出容器底面时的转速；若此时容器停止旋转，水静止后的深度 h2 等于 多少。
青岛大学2010 年硕士研究生入学考试试题
青岛大学2010 年硕士研究生入学考试试题科目代码： 345 科目名称卫生综合（共 4 页）请考生写明题号，将答案全部答在答题纸上，答在试卷上无效一、名词解释：（每题4 分，共 72 分）1、氨基酸模式：某种蛋白质中各种必需氨基酸之间的比例。
其计算方法时将蛋白质中的色氨酸含量定为1，分别计算其他必需氨基酸的相应比值，这一系列的比值是该种蛋白质的氨基酸模式化。
2、基础代谢：BM，是指维持生命的最低能量消耗，及人体在安静和恒温条件下18-25℃，禁食12h 后，静卧、放松而又清醒的能量消耗。
3、体质指数：BMI，BMI=体重（kg）/[身高（m）]2,单位为kg/m2。
主要用于衡量肥胖程度。
4、营养质量指数：INQ，是评价食品营养价值的指标，即营养素密度(待测食品中某营养素占供给量的比)与能量密度(待测食品所含能量占供给量的比)之比。
INQ>1，表明食物的营养价值高；INQ<1，表明食物营养价值低，或者是属于高能量食品。
5、工作有关疾病：是指多因素相关的疾病，与工作有联系，但也见于非职业人群中，因而不是每一病种和每一病例都必须具备该项职业史或接触病史。
6、刺激性气体：指对眼、呼吸道粘膜和皮肤具有刺激作用的一类有害气体，在化学工业生产中最常见。
此类气体多具有腐蚀性，常因不遵守操作规程或容器、管道等设备被腐蚀而发生跑、冒、滴、漏而污染作业环境。
7、矽肺：是由于在生产过程中长期吸入游离二氧化硅含量较高的粉尘而引起的以肺组织纤维化为主的疾病。
8、生态系统：是在一定空间范围内，由生物群落及其环境组成，借助于各种功能流(物质流、能量流、物种流和信息流)所联结的稳态系统。
9、健康危险度评价：按一定的准则，对有害环境因素作用于特定人群的有害健康效应进行综合定性、定量评价的过程。
10、光化学烟雾：是由汽车尾气中的氮氧化物和挥发性有机物在日光紫外线的照射下，经过一系列的光化学反应生成的刺激性很强的浅蓝色烟雾所致大气污染事件。
2010 年研究生入学考试模拟题 答案
2010年研究生入学考试数学一模拟试卷（一）的答案一、选择题：题号 1 2 3 4 5 6 7 8 答案 B C C A D D C D 二、填空题：（9）1 （10）()168112e e −−− （11）21231cos 2sin 21010xxy c ec e x x −=+−+ （12）()31z z e e −+ （13）a=-3,b=-1. （14）736三、解答题（15）解：211lim lim xx c cx cx x c x c e x e x c e c x −→∞→∞⎛⎞+⎜⎟+⎛⎞⎝⎠===⎜⎟−⎝⎠⎛⎞−⎜⎟⎝⎠2222111222ccc c ttt tte dt tde te e dt −∞−∞−∞−∞==−∫∫∫ 2222112424c t c c c c c e e e e =−=−−∞22115124242c c c c e e c ⎛⎞=−−==⎜⎟⎝⎠， ， （16）证：令()()()()()()(),F x f x g x f a g x g b f x =−− 则'()'()[()()]'()[()()]F x g x f x f a f x g b g x =−−−，由于()()()()F a f a g b F b =−=，可知()F x 在[a,b]上满足罗尔定理的条件，故存在(,)a b ξ∈使'()0F ξ=,由此得到所需证明的结论。
（17）解：设所求的曲线方程为()y y x =，其上任意点的坐标为(),x y ，则该点处切线方程为()Y y y X x ′−=−模拟题令0X Y y xy ′==− 得 根据题意有 ()322y xy xy ′⎧−=⎪⎨=⎪⎩ 解之得 3132y x x =− (18)解：作曲面2211:0x y S z ⎧+≤⎨=⎩，下侧，令1∑和S 围成空间区域为Ω，根据高斯公式()()()1323232s I x z dydz y x dzdx z y dxdy ++++++∫∫()2222421633sin 0050x y z dv d d d ππθϕϕρρπΩ=++==∫∫∫∫∫∫于是1232216600sin 0055s I y dxdy d r dr πππθθ⎡⎤=−++=+⎣⎦∫∫∫∫ 61295420πππ+＝＝ （19）解：收敛半径()112lim22n nn n R n +→∞+== ，收敛域22x −≤<，令()1112n nn S x x n ∞−==⋅∑，则()112nn x xs x n ∞=⎛⎞=⎜⎟⎝⎠∑， ()111111222212n n x xs x x x−∞=⎛⎞′==⋅=⎡⎤⎜⎟⎣⎦−⎝⎠−∑ ()()0ln 2002x xdt xs x t t −==−−−∫()ln 2ln 2ln 12x x ⎛⎞=−−+=−−⎜⎟⎝⎠()1ln 12x s x x ⎛⎞=−−⎜⎟⎝⎠， 0x ≠， [)22x ∈−，， 而()102s =，于是 [)1101ln 122212102n nn x x x x x n x ∞−=≠⎧⎛⎞−−⎪⎜⎟∈−⎝⎠⎪=⎨⋅⎪=⎪⎩∑， ，， (21) ① 0. ② 全为0. ③ 不可对角线化.（22）解：（1）由(,)1f x y dxdy +∞+∞−∞−∞=∫∫，则1(,)()12x kf x y dxdy dx k x y dy +∞+∞−∞−∞=+==∫∫∫∫ 所以2k = 2分 （2）202()3,01()()0,xX x y dy x x f x f x y dy +∞−∞⎧+=<<⎪==⎨⎪⎩∫∫， 其它4分 122()123,01()()0,y Y x y dy y y y f y f x y dx +∞−∞⎧+=+−<<⎪==⎨⎪⎩∫∫， 其它 6分（3）()()()(,)Z x y zF z P Z z P X Y z f x y dxdy +≤=≤=+≤=∫∫① 当 0z <时 ()0Z F z = 6.5分 ② 当2z ≥时 ()1Z F z = 7分 ③ 当01z ≤<时 320()(,)2()3zz y Z yx y zz F z f x y dxdy dy x y dx −+≤==+=∫∫∫∫8.5分④ 当12z ≤<时31221()(,)12()33xz Z x z x y zz F z f x y dxdy dx x y dy z −++≤==−+=−+−∫∫∫∫ 10分3320,0,013()1,12331,2Z z z z F z z z z z <⎧⎪⎪≤<⎪=⎨⎪−+−≤<⎪⎪≥⎩ 所以 2201()2120,Z z z f z z z z ⎧≤<⎪=−+≤<⎨⎪⎩ 其它11分（23）解：（1）矩估计：11()ni i E X p x x n ====∑，矩估计值1ˆpx =。
考研精品文档 2010年全国硕士研究生入学统一考试英语试题附答案详解(试题一)
2010年全国硕士研究生入学统一考试英语试题附答案详解(试题一)20__a plateau and then slackening off. This suggests that the alleged” Hawthor ne effect “ is hard topin 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]explanations [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] pealliar 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]continued20. [A]breaking [B]climbing [C]surpassing [D]hitingSection II Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions below each text by choosi ng [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 duri ng the pastquarter-century, perhaps the m ost far-reaching has been the ine xorable decline in the scope and seriousness of their arts coverage.It is difficult to the point of impossibility for the average reader under the a ge of forty toimagine a time when high-quality arts criticism could be found i n most big-city newspapers. Yeta considerable number of the most significa nt c ollections of criticism published in the 20thcentury consisted in large part of new spaper reviews. To read such books today is to marvel at the fact thattheir learned contents were once deemed suitable for publication in general-circulation dailies.We are even farther rem oved from the unfocused newspaper review spublis hed in Englandbetween the turn of t he 20th century and the eve of World War Ⅱ, at a time when newsprintwas dirt-c heap and stylish arts crit icism was consi dered an ornament to the publicat ions inwhich it appe ared. In those far-off days, it was taken for granted tha t the cri tics of majorpapers woul dwri te in detail and at length about the even ts they covered. Theirs was a seriousbusiness, and even those reviewers who wore their learning lightly, like George Bern ard Shawand Ernest Newman, co uld be trus ted to know what they were a bout. These men believed injournal ism as a calling, and were proud to be published in the daily press.“So few authors havebrains enough or literary gift enough to keep their own end up in journalism, ”Newman wrote,“that I am tempted to define…journalism' as …a term of cont empt appl ied by writers who are notread to writers who are'. ”Unfortunately, these critics are virtually forgotten. Neville Cardus, who wrote for the ManchesterGuardian from 1917 until shortly before his death in 1975, is now known solely as a writer ofessays ont he game of cricket. During his l i fetime, though, he was also one of England'sforemost classical-music critics, and a stylist so widely admired that hisAutobiography（1947）became a best-seller. He was knighted in 1967, the first music critic tobe so ho nored. Yet on ly one of his books is now in print, and his vast body of writi ngs onmusic is unknown save to specialists.Is there any chance that Cardus's criticism will enjoy a revi val? The prospect seems remote.Jour nalistic tastes had changed long before his death, and po stmodern reader shave little usefor the ric hly upholstered Vicwardian pros e 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 warⅡwere 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 Memory.Text 2Over the past decade, thousands of patents have been granted for what are called businessmethods. received one for its “one-click” online p ayment system. Merrill Lynch got legal protection for an asset allocation str ategy. One inventor patented a technique for liftinga box.Now the nation's top patent court appears completely ready to scale back on business-methodpatents, which have been controversial ever since they we re first authorized 10 years ago. Ina move that has intellectual-property la wyers abuzz the U.S. court of Appeals for the federalcircuit said it would use a particular case to conduct a broad review of business-methodpatents. In r e Bilski , as the case is known , is “a very big deal”, says Dennis'D. Crouch of theUniversity of Missouri School of law. It “has the potential to eliminate an entire class ofpatents.”Curbs on business-method claims would be a dramatic about-face, because i t was the federalcircuit itself that introduced such patents with is 1998 decisi on in the so-called state StreetBank case, approving a patent on a way of po oling mutual-fund assets. That ruling producedan explosion in business-method patent filings, initially by emerging internet companiestrying to stake out exclusive pinhts to specific types of online transactions. Later, move es tablished companies raced to add such patents to their files, if only as a defe nsive moveagainst rivals that might beat them to the punch. In 2005, IBM n oted in a court filing that ithad been issued more than 300 business-method patents despite the fact that it questionedthe legal basis for granting them. S imilarly, some Wall Street investment films armedthemselves with patents for financial products, even as they took positions in court cases opposing the pr actice.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 c ase would be heard by all 12 ofthe court's judges, rather than a typical panel of three, and that one issue it wants to evaluate is whether it should”recon sider” its state street Bank ruling.The Federal Circuit's action comes in the wake of a series of recent decisions by the supreme Count that has narrowed the scope of protections for patent holders. Last April, for examplethe justices signaled that too many patents w ere 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 H arole C.wegner, a partend attorney and professor at aeorgeWashington Univ ersity 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, Paro 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 Aladuell argues that social epidemics are driven in largepart by the acting of a tiny minority of special individuals, often called influentials, who areunusually informed, persuasive, or well-co nnected. The idea is intuitively compelling, but itdoesn't explain how ideas actually spread.The supposed importance of influentials derives from a plausible sounding b ut largely untested theory called the “two step flow of communication”: Inf ormation flows from themedia to the influentials and from them to everyone e lse. Marketers have embraced the two-step flow because it suggests that if th ey can just find and influence the influentials, thoseselected people will do mo st of the work for them. The theory also seems to explain the suddenand une xpected popularity of certain looks, brands, or neighborhoods. In many su ch cases,a cursory search for causes finds that some small group of people w as wearing, promoting, ordeveloping whatever it is before anyone else paid at tention. Anecdotal evidence of this kind fitsnicely with the idea that only cert ain special people can drive trendsIn their recent work, however, some researchers have come up with the findi ng that influentialshave far less impact on social epidemics than is generally supposed. In fact, they don't seemto be required of all.The researchers' argument stems from a simple observing about social influe nce, with the exception of a few celebrities like Oprah Winfrey-whose outsize presence is primarily a function of media, not interpersonal, influence-even t he most influential members of a population simply don't interact with that many others. Yet it is precisely these non-celebrity influentials who, accordin g to the two-step-flow theory, are supposed to drive social epidemicsby influencing their friends and colleagues directly. For a social epidemic to occur, however,each person so affected, must then influence his or her own acquai ntances, who must in turninfluence theirs, and so on; and just how many oth ers pay attention to each of these peoplehas little to do with the initial influe ntial. If people in the network just two degrees removedfrom the initial infl uential prove resistant, for example from the initial influential prove resis tant, 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 stud ied the dynamicsof populations manipulating a number of variables relating of populations, manipulating anumber of variables relating to people's ability to influence others and their tendency to beinfluenced. Our work shows that th e principal requirement for what we call “global cascades”-the widespread propagation of influence through networks - is the presence not of a fewinfl uentials but, rather, of a critical mass of easily influenced people, each of w hom 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 w ho[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 th e scenes, theyhave been taking aim at someone else: the accounting standar d-setters. Their rules, moan thebanks, have forced them to report enormou s losses, and it's just not fair. These rules saythey must value some assets at the price a third party would pay, not the price managers andregulators woul d like them to fetch.Unfortunately, banks' lobbying now seems to be working. The details may be unknowable, butthe independence of standard-setters, essential to the pro per functioning of capital markets,is being compromised. And, unless banks c arry toxic assets at prices that attract buyers,reviving the banking system wil l be difficult.After a bruising encounter with Congress, America's Financial Accounting Sta ndards Board(FASB) rushed through rule changes. These gave banks more fre edom to use models to valueilliquid 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 ourmotives.” Yet bank share s 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 Sta ndards Board(IASB) do likewise. The IASB says it does not want to act withou t overall planning, but the pressure to fold when it completes it reconstruc tion of rules later this year is strong. CharlieMcCreevy, a European commissio ner, warned the IASB that it did “not live in a political vacuum”but “in the re al word” and that Europe could yet develop different rules.It was banks that were on the wrong planet, with accounts that vastly overv alued assets.Today they argue that market prices overstate losses, becausethey largely reflect the temporary illiquidity of markets, not the likely exten t of bad debts. The truth will not be knownfor years. But bank's shares trade below their book value, suggesting that investors are skeptical. And dead ma rkets partly reflect the paralysis of banks which will not sell assets forfear 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. A merica's new planto buy up toxic assets will not work unless banks mark ass ets to levels which buyers find attractive. Successful markets require indepe ndent and even combative standard-setters.The FASB and IASB have been exactly that, cleaning up rules on stock options and pensions,for example, ag ainst hostility form special interests. But by giving in to critics now they are i nviting 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 intothe numbered boxes to form a coherent text. Paragraph E h as been correctly placed. There isone paragraph which dose not fit in with th e text. Mark your answers on ANSWER SHEET1. (10points)[A] The first and more important is the consumer's growing preference for e ating out; theconsumption of food and drink in places other than homes has ri sen from about 32 percent oftotal consumption in 1995 to 35 percent in 2000 and is expected to approach 38 percent by2005. This development is boosti ng wholesale demand from the food service segment by 4 to5 percent a year across Europe, compared with growth in retail demand of 1 to 2 percent.Me anwhile, as the recession is looming large, people are getting anxious. They t end to keep atighter hold on their purse and consider eating at home a realis tic alternative.[B] Retail sales of food and drink in Europe's largest markets are at a standsti ll, leavingEuropean grocery retailers hungry for opportunities to grow. Most le ading retailers have alreadytried e-commerce, with limited success, and ex pansion abroad. But almost all have ignoredthe big, profitable opportunity in their own backyard: the wholesale food and drink trade,which appears to b e just the kind of market retailers need.[C] Will such variations bring about a change in the overall structure of the f ood and drinkmarket? Definitely not. The functioning of the market is based o n flexible trends dominated by potential buyers. In other words, it is up to t he buyer, rather than the seller, to decide what tobuy .At any rate, this chang e will ultimately be acclaimed by an ever-growing number of both domesti c 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 pro fitably apply their scale, existing infrastructure and proven skills in the manag ement of product ranges, logistics,and marketing intelligence. Retailers tha t master the intricacies of wholesaling in Europe maywell expect to rake in su bstantial profits thereby. At least, that is how it looks as a whole.Closer ins pection reveals important differences among the biggest national markets, e speciallyin their customer segments and wholesale structures, as well as the competitive dynamics ofindividual food and drink categories. Big retailers mu st understand these differences beforethey can identify the segments of Eu ropean wholesaling in which their particular abilities mightunseat smaller but entrenched competitors. New skills and unfamiliar business models arenee ded too.[E] Despite variations in detail, wholesale markets in the countries that have been closelyexamined-France, Germany, Italy, and Spain-are made out of the same building blocks. Demandcomes mainly from two sources: independen t 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 cons umers when they don't eat at home. Such food service operators range from snack machines to large institutional catering ventures, but most of these b usinesses areknown in the trade as “horeca”: hotels, restaurants, and cafes. Overall, Europe's wholesalemarket for food and drink is growing at the same sluggish pace as the retail market, but thefigures, when added together, m ask two opposing trends.[F] For example, wholesale food and drink sales come to $268 billion in Franc e, Germany, Italy,Spain, and the United Kingdom in 2000-more than 40 perc ent of retail sales. Moreover,average overall margins are higher in wholesal e than in retail; wholesale demand from the foodservice sector is growing qui ckly as more Europeans eat out more often; and changes in the competitive dynamics of this fragmented industry are at last making it feasible for whole salersto consolidate.[G] However, none of these requirements should deter large retailers (and e ven some largegood producers and existing wholesalers) from trying their ha nd, for those that master theintricacies of wholesaling in Europe stand to rea p considerable gains.Part CDirections:Read the following text carefullyand then translate the underlined segments i nto Chinese. Yourtranslation should bewritten clearly on ANSWER SHEET 2.(10 points)One basic weakness in a conservation system based wholly on econom ic motives is thatmost members of the land community have no economic valu e. Yet these creatures aremembers of the biotic community and, if its stabil ity depends on its integrity, they are entitled to continuance.When one of these noneconomic categories is threatened and, if we happen t o love it, we invent excuses to give it economic importance. At the beginning of the century songbirds weresupposed to be disappearing.(46)Scientists ju m ped to the rescue with some distinctly shaky evidence to the effect that ins ects would eat us up if birds failed to control them. The evidence had to be e conomic in order to be valid.It is painful to read these roundabout accounts today. We have no land ethic yet,(47) but wehave at least drawn nearer the point of adm itting that birds should continue as a matter of intrinsic right, regardless of the presence or absen ce of economic advantage to us.A parallel situation exists in respect of predatory mammals and fish-eating bi rds.(48) Timewas when biologists som ewhat overworked the evidence that these creatures preserve thehealth of game by killing the physically weak, or tha t they prey only on “worthless”species.Here again, the evidence had to b e economic in order to be valid. It is only in recent years thatwe hear the mor e honest argumentthat predators are members of the community, and that nospecial interest has the right to exte rminate the m f or the sake of a benef it, real or fancied, toitself.Some species of tree have been“read out of the party” by economics-minded foresters becausethey grow too slowly, or have too low a sale value to pay as timber crops.(49) In Europe,where forestry is ecologically more advanced, the noncommercial tree species are recognizedas members of native forest c ommunity, to be preserved as such, within reason. Moreover,some have be en found to have a valuable function in building up soil fertility. The interd ependence of the forest and its constit uent tree species, ground flora, and fauna istaken for granted.To sum up: a systemof conservation based solely on economic self-interest i s hopelesslylopsided.(50) It tends to ignore , and thus eventually to eliminate, many elements i n theland community that lack commercial value,but that are essential to its healthy functioning. Itassumes, falsely, that the economic parts of the bioti c clock will function without theuneconomic parts.Section III WritingPart A51. Directions:You are supposed to write for the Postgraduates' Associ ation a notice to recr uit volunteers foran international c onference on globalization. The notice sho uld include the basic qualificationsofapplicants and other information which yo u think is relevant.You should write about 100 words on ANSWER SHEET 2.Do not sign your own nam e at the end of the notice. Use "postgraduates' Ass ociation" instead. （10 points）Part B52. Directions:Write an essay of 160-200 words based on the following drawing. In your ess ay, you should1) describe the drawing briefly,2) explain its intended meaning, and3) give your comments.You should write neatly on ANSWER SHEET 2. （20 points）Section I: Use of English (10 points)1. A2. B3. C4. B5. C6. B7. D8. A9. C10. D11. C12. A13. A14. D15. B16. A17. D18. C19. B20. DSection II: Reading Comprehension (60 points) Part A (40 points)21. B22. A23. D24. A25. B26. C27. D28. C29. B30. A31. B32. D33. A34. C35. C36. A37. D38. C39. B40. DPart B (10 points)41. B42. F43. D44. G45. APart C (10 points)46 . 科学家们赶紧拿出某些明显站不住脚的证据来补救，大致说的是如果鸟儿不能控制昆虫数量的话，昆虫就会把我们吃光。
考研政治模拟
2010 年全国硕士研究生入学统一考试思想政治理论全真模拟试题（三）一、单项选择题：1 ～16 小题，每小题1 分，共16 分。
下面每题给出的四个选项中，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 ．主张“ 世界上除了运动着的物质之外，什么也没有” 的观点，属于A. 否认意识存在的自然唯物主义B. 主张世界统一于物质的辩证唯物主义C. 否认时间与空间存在的唯心主义D. 把人的意识理解为某种特殊的“ 精细物质” 的机械唯物主义2 ．恩格斯在谈到资本主义国家职能时指出，“ 政治统治到处都是以执行某种社会职能为基础” 。
这就是说A. 社会职能是资本主义国家的主要职能B. 资本主义国家的政治职能都是通过社会职能体现的C. 资本主义国家的政治职能在弱化D. 政治统治只有在执行社会职能时才能持续下去3 ．社会总资本运动的核心问题是社会总产品的实现，这包括社会总产品的（）A. 价值创造和价值实现B. 价值创造和价值转移C. 价值实现和价值分配D. 价值补偿和实物补偿4 ．马列主义关于无产阶级政党学说的核心内容是A. 党的路线和组织原则问题B. 党的战略和策略问题C. 党的性质和奋斗目标问题D. 党的领导地位和作用问题5 ．南昌起义、秋收起义、广州起义中得出的深刻教训是（）A. 必须武装反抗国民党反动派B. 必须建立党对军队的绝对领导C. 必须建立新型的人民军队D. 走适合中国国情的革命道路6 ．毛泽东在《中国的红色政权为什么能够存在》一文中提出了（）A. 以农村包围城市，武装夺取政权道路的理论B. 工农武装割据的思想C. 以乡村为中心的思想D. 实行党对军队绝对领导的原则7 ．孙中山说：“ 国民党在堕落中死亡，因此要救活它，就需要新鲜血液。
” 为此他采取的主要措施是（）A ．接受中共反帝反封建的主张B ．重新解释三民主义C ．以党内合作方式同共产党合作D ．建立黄埔军校，培养新式军事干部8 ．中国共产党早期组织领导的第一个工会是（）A ．上海机器工会B ．长辛店工人俱乐部C ．武汉工会D ．长沙工会9 ．毛泽东在《反对党八股》中指出，前期新文化运动的领导人物“ 对于现状，对于历史，对于外国事物，…… 所谓坏就是绝对的坏，一切皆坏；所谓的好，就是绝对的好，一切皆好” 。
2010 年全国硕士研究生入学考试试题
2010 年全国硕士研究生入学考试试题政治理论一、单项选择题：1~16 小题，每小题 1 分，共16 分。
下列每题给出的四个选项中，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. 1984 年1 月3 日，意大利人卡内帕给恩格斯写信，请求他为即将在日内瓦出版的饿《新纪元》周刊的创刊号题词，而且要求尽量用简短的字句来表述未来的社会主义纪元的基本思想，以区别于伟大诗人但丁的对旧纪元所作的“一些人统治，另一些人受苦难”的界定。
恩格斯回答说，这就是：“代替那存在着阶级和阶级对立的资产阶级旧社会的，将是这样一个联合体，在那里，每个人的自由发展是一切人的自由发展的条件。
”这段话表明，马克思主义追求的根本价值目标是（）A ．实现人的自由而全面的发展B ．实现人类永恒不变的普适价值C ．建立一个四海之内皆兄弟的大同世界D ．建立一个自由，平等，博爱的理性王国2. 有一则箴言：“在溪水和岩石的斗争中，胜利的总是溪水，不是因为力量，而是因为坚持。
”“坚持就是胜利”的哲理在于（）A ．必然性通过偶然性开辟道路B ．肯定中包含着否定的因素C ．量变必然引起质变D ．有其因必有其果3. 右边这张照片反映出由于气候变暖，北极冰盖融化，致使北极熊无处可去的场景，颇具震撼力。
它给我们地球上的人类发出的警示是（）A ．人与自然的关系成为人与人之间一切社会关系的核心B ．生态失衡已成为自然界自身周期演化不可逆转的趋势C ．自然地理环境已成为人类社会发展的根本决定力量D ．生态环境已日益成为人类反思自身活动的重要前提4. 劳动力成为商品是货币转化为资本的前提条件，这是因为（）A ．资本家购买的是劳动力的价值B ．劳动力商品具有价值和使用价值C ．货币所有者购买的劳动力能够带来剩余价值D ．劳动力自身的价值能够在消费过程中转移到新的商品中去5.1981 年党的十一届六中全会通过《关于建国以来党的若干历史问题的建议》对我国社会主要矛盾作了规范的表述：“社会主义改造完成以后，我国所要解决的主要矛盾，是人民日益增长的物质文化需要同落后的社会生产之间的矛盾。
中山大学2010年硕士研究生入学考试(333教育综合)真题
中山大学2010年硕士研究生入学考试（333教育综合）真题
一、概念解释(6小题，每小题5分，共30分)
I、教育学
2、因材施教
3、教育目的
4、陶冶
5、奥苏伯尔的有意义学习
6、知识领会
二、简答题(4小题，每小题10分，共40分)
1、简谈学生掌握知识的基本阶段
2、简谈教师劳动的基本特点
3、简述汉武帝文教政策的基本内容
4、简述人文主义教育的基本特征
三、论述题(4小题，每小题20分，共80分)
1、谈谈影响人的发展因素及其相互关系
2、谈谈蔡元培的教育思想及其现实意义
3、论述要素主义教育思想的主要观点
4、联系实际谈谈在教学中如何运用迁移的原理和规律促进学生的学习。
2010年全国硕士研究生入学统一考试数学一试题参考答案
1）
2）
3）
4）
5）若A可逆，则
6）若 ， 是 矩阵，则
7）若 则
在本题中，
由于 ，故 .又由于 ，故
①
由于 为 矩阵， 为 矩阵，故
②
由①、②可得 ，故选A.
(6)设 为4阶实对称矩阵，且 ，若 的秩为3，则 相似于( )
(A) .(B) .
(C) .(D) .
【答案】D
【考点】矩阵的特征值和特征向量；相似对角矩阵
【难易度】★★
【详解】本题涉及到的主要知识点：
（i） 与对角矩阵相似的充分条件：① 有 个不同的特征值；② 是实对称矩阵
（ii） 与对角矩阵相似的充要条件：对于矩阵 的每一个 重特征值 ，其线性无关的特征向量的个数恰好等于该特征值的重根数 ，即秩 .
在本题中，
设 为 的特征值，由于 ，所以 ，即 ，这样 的特征值为-1或0.由于 为实对称矩阵，故 可相似对角化，即 ， ，因此， ，即 .
夹逼定理：设 ，若 ，则 。
在本题中，
当 时， ，所以 与
均为定积分，故
(I)当 时 ，
故 ，所以
(II)
故由 ，
根据夹逼定理得
故 .
(18)(本题满分10分)
求幂级数 的收敛域及和函数.
【考点】幂级数的收敛域及和函数
【难易度】★★★
【详解】本题涉及到的主要知识点：
幂级数 的收敛域的定义及求法，分三种情况：
，
则 的体积
在这种情形要确定上、下曲面及投影区域。
在本题中，
(13)设 ,若由 形成的向量空间
维数是2，则 = .
【答案】
【考点】向量空间维数的概念
2010年全国硕士研究生入学统一考试心理学专业基础综合考试模考
2010年全国硕士研究生入学统一考试心理学专业基础综合考试模考一、单项选择题：1—65小题，每小题2分，共130分。
下列每题给出的四个选项中，只有一个选项是正确的。
1、在研究方法上，主张采用客观的实验方法，而极力反对研究意识，反对使用内省法的是_________。
A、行为主义B、构造主义C、格式塔D、人本主义2、_________是脑内信息处理的基本单位是。
A、神经元B、神经回路C、突触D、神经冲动3、鲁利亚通过对大脑损伤病人的临床观察和恢复治疗中总结提出脑的_________。
A、模块说B、整体说C、定位说D、机能系统说4、在睡眠状态时，脑电主要是_________波，个体处于清醒并安静休息状态时的脑电波，在睡眠中不会出现，但在失眠症患者的睡眠时的脑电波中会出现的是_________波。
A、αB、ΔC、θD、δ5、我们有的人看书时读的很快，“一目十行”，有的人则读的很慢，一次只读一句话，这反映了注意的_________品质上的差异。
A、注意的广度B．注意的稳定性C．注意的分配D．注意的转移6、暴躁时看白色会有助于镇静，寒冷时看到红色会让人觉得温暖、天热时看蓝色觉得清凉，这是感觉的_________现象。
A、适应B、后象C、对比D、联觉7、我们看到两种明度不同但很相似的颜色，我们初看可能感觉到二者颜色是相同的，但是如果将其中一种颜色的明度进行一定程度变化时，我们就恰能分辨出二者的不同，这种刚刚能分辨出最小差异量的能力是_________ 。
A、感觉阈限B、绝对感受性C、差别感受性D、差别感觉阈限8、在银幕上相继投射两个图形，前面一个为圆盘，后面一个为圆环，当二者间隔时间短暂时，只看到圆环而不见圆盘，这种现象是_________。
A、对比B、掩蔽C、适应D、似动9、一些立体电影看起来惊险刺激，身临其境，是运用了_________的原理。
A、运动视差B、双眼视差C、双眼视轴辐合D、空气透视10、一些脑损伤病人在做广播体操初期可以根据别人的语言指导识记广播体操的动作要领，但自己做操时却无法记住广播的动作，不断出错，这可能是脑部_________受损。
2010年硕士研究生招生入学考试试题
（1）“不是A，就是B”与“不是A，而是B”
（2）“要么A，要么B”与“或者A，或者B”
7.举例说明借代和借喻的区别。
四、论述题（每题30分，共60分）
1.现代汉语规范化的标准是什么？有学者认为，“琴”字左上角“王”字最后一笔应由“横”变为“提”，“奥巴马”(英文：Obama)应改译为“欧巴马”，“差点儿没摔倒”应改成“差点儿摔倒”。谈谈你对这类语言文字现象的看法。
8．“他浪费了一个小时”和“他工作了一个小时”中的“一个小时”分别是（）。
A.补语、补语B.宾语、宾语
C.宾语、补语D.补语、宾语
9.下列问句属于正反问句的是（）。
A．隔壁班的那个男孩，怎么还没经过我的窗前？
B．你知道我在等你吗？
C．许多年以后，能不能接受彼此的改变？
D．他的话是真的，还是假的？
10.下列句子属于复句的是（）。
请考生在答题纸上答题，在此试题纸上答题无效
8.“写得好”是述补短语，其中的补语可以是状态补语，也可以是可能补语。（）
9.语用上的省略不改变句型，如省略了主语的变式句仍是主谓句。语用上的倒装也不改变句型，如主谓倒装句仍是主谓句。（）
10.“我知道，如果我认真地去咀嚼科长的话，我自己的良心会受不住的。”这是个表示假设关系的复句。（）
2.副词有时也跟名词或名词性成分组合，如：“人不人，鬼不鬼的”，“最前头”，“最底层”，“今天才星期二”，“共50个学生”，“院子里净杂草”，“很女人”，“很淑女”，“最老百姓”等。副词修饰名词或名词性成分是否要受到语义等条件的限制？这类语法现象产生的动因是什么？谈谈你对这类语法现象的看法。
第3页，共3页
2.押韵的“韵”是指韵母，韵母相同或相近都可算作押韵。（）
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2010全国硕士研究生入学统一考试数学一模拟试卷(一)一．选择题 1．若⎰++=10)13(5)(dx x f x x f ，则⎰-=+11)253(d x x f （ ）（Ａ）－3； （B ）－6； （C ）－18； （D ）－108 ． 2．已知微分方程),(y x f y ='的通解为),(C x g y =，则微分方程)2,2(y x f y ='的通解为 （ ） （Ａ）),2(2C x g y =； （Ｂ）),2(2C xg y =；（Ｃ）),2(21C x g y =； （Ｄ）),2(21C x g y =．3．设函数),(,),(y x Q y x P 有一阶连续偏导数，则⎰-Ly y x P x y x Q d ),(d ),(与路径无关的充要条件是 （ ） （A ）y Q x P ∂∂=∂∂； （B ）x Q y P ∂∂=∂∂； （C ）0=∂∂+∂∂y Q x P ； （D ）0=∂∂+∂∂xQ y P ．4．)e (z y x ∇⨯∇＝ （ ） （注意：这里使用的是一种规范的记号，∇，⋅∇ 和⨯∇分别等同于多数教材上曾经使用过的习惯记号grad ，div 和rot ）（Ａ）０； （Ｂ）→-0； （Ｃ）)(e z y x z y x ++； （Ｄ）{}z y x z y x ,,e ． 5．设A 是n 阶方阵，已知线性齐次方程组0=AX 有非零解，则线性非齐次方程组b X A T= （ ） （A ）必有无穷多个解； （B ）必无解； （C ）对于某些b ，解可能是唯一的； （D ）以上结论都不对。
6．对于给定的两个向量组（I ）m ααα,,,21 ，2≥m ；（II ）n m m m ++ααααα,,,,,,121 ，1≥n ．必有 （ ） （Ａ）（I ）线性无关⇒（II ）线性相关； （Ｂ）（II ）线性无关⇒（I ）线性无关； （Ｃ）（I ）线性相关⇒（II ）线性无关； （Ｄ）（II ）线性相关⇒（I ）线性相关． 7．从6个英文字母DDGGOO中任意取出四个，并任意进行排列，则恰好能排成英文单词GOOD 的概率=p （ ）（A ）3601； （B ）1801； （C ）451； （D ）154．8．下面4个随机变量的分布中，期望值最大，方差最小的是 （ ） （A ）)21,5(~N X ；（B ）)7,5(~U Y ，即区间)7,5(上的均匀分布； （C ）Z 服从指数分布⎪⎩⎪⎨⎧>≤=-；0,e61,0,0)(61z z z f z（D ）T 服从指数分布⎪⎩⎪⎨⎧>≤=-．0,e3,0,0)(3t t t f t二．填空题（本题有6小题，每小题4分，共24分）： 9．______ln 12=⎰+∞xxdx 。
10．设函数)(x f 满足条件10)0(=f ，且其二阶导数)(x f ''在区间],0[π上连续，并有⎰=+''π82sin )](4)([xdx x f x f ，则=)(πf ______________．11．设函数),(y x z z =由方程z xy z y x 3221e +=-+所确定，则=)1,0(d z ______．12．已知幂级数∑∞=+-+-012)1()!2(3)1(n n nx n n 在收敛域),(∞+-∞上的和函数为)(x S ，则=)1()5(S___________．13．已知n 阶)3(≥n 行列式=A a ，将A 中的每一列减去其余各列之和得到新的行列式记为B ，则=B ____________．14．设A 、B 、C 是两两独立的且不可能同时发生的随机事件，若p C P B P A P ===)()()(，则当=p ______时，)(C B A P ++可取得最大值．三．解答题15．匀速向侧壁为旋转抛物面的容器内注水，试证明液面升高的速度与液面的高度成反比．16．计算二重积分⎰⎰++Dy x y x d d )cos(1，其中D 由直线0=y ，x y =，π=x 围成．17．某城市的海港港口与火车站位于该城市市中心的东西两端，相距d 。
现拟在城南修建一座机场，为避免噪音影响，要求机场位置离市中心的距离不小于2d 公里，按计划，机场到海港要修建直线铁路，造价每公里1c 万元，机场到火车站要修建直线高速公路，造价为每公里2c 万元。
问铁路与高速公路的设计长度各为多少公里时，可使总造价最低？求出最低价。
18．若将函数x xn x f -=)(的极大值点记为),4,3,2( =n a n ，试求幂级数∑∞=2n nnx a的收敛域．19．计算⎰⎰→-⋅+++++=S S z y x xy zx yz I d )grad(，其中S 为)0(222>--=R yx R z 的上侧．20．设B 是n n ⨯矩阵，A 是n 阶正定阵，证明：（1）)(r )(r B AB B T =；（2）AB B T 正定的充要条件是B 可逆．21．已知3⨯3矩阵A 与3维列向量x 可使向量组x A Ax x 2,,线性无关，且满足x A Ax x A 2323-=．记),,(2x A Ax x X =． （1）求3⨯3矩阵B ，使1-=XBXA ；（2）计算行列式E A +．22．设随机变量X 的概率密度函数为)2(2e)(xx k x f +-=．（1）试确定k 值；（2）设b aX Y +=，试确定b a ,的值，使Y 成为标准化随机变量，即1)(,0)(==Y D Y E ；（3）写出Y 的概率密度函数)(y f Y ． 23．已知Y X ,服从相同的分布⎥⎦⎤⎢⎣⎡-25.015.0025.01~X ，若 0)(==Y X P ．（1）求出),(Y X 的联合分布律； （2）求出Y X ,的相关系数； （3）讨论Y X ,的相关性和独立性．2010数学一模拟试卷（一）答案解析一、选择题：1、C ；2、C ；3、C ；4、B ；5、D ；6、B ；7、C ；8、B 二、 填空题： 9．1； 10、6； 11、dy dx 2+-； 12、4； 13、a n n 12)2(--； 14、.5.0 三、解答题： 16．解：).2(222cos 22cos2]2cos2cos[2|2cos|2)cos(122021-=+-+=+-+=+=++⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰--πππππππdy y x dx dx y x dy dxdy y x dxdy y x dxdy y x dxdy y x xyyD D DD17．解：设铁路设计长度为x 公里，高速公路设计长度为y 公里。
按题意，机场位置必须位于以港口与火车站连线为直径的圆弧上。
本题即为如下的最小值问题： 目标函数为 )(),(21y c x c y x u +=，约束条件为222d y x =+。
令)()(22221d y x y c x c F -+++=λ，由222122221122221,0202cc d c y cc d c x d y x F y c F x c F y x +=+=⇒⎪⎩⎪⎨⎧=-+='=+='=+='λλλ，由问题的实际意义知，最低造价为d c c c c d c d c y x u 222122212221),(+=++=。
18．解：).1,1[,ln 1,1,ln )1(,1.1,1lim,ln 1,ln 1.ln 1,0)ln ()ln 1(,)ln 2ln()(.ln 1,0)ln 1()(2212ln 12-=--==∴===∴<-=''-=''==-='∑∑∑∞=∞=+∞→∞=---故级数的收敛域为发散时当收敛时当收敛半径为对级数为最大值点唯一驻点得令n n n nn n n n nnxxnx nx R a a na x nnx nn n f n n n x x f n x n n x x f 则上投影为在下侧取。
解：,},0|),,{(,)(0:.)1()1()1(},1,1,1{)(192222221D xoy S y xRz z y x R yxz S dxdy y x dzdx x z dydzz y I y x x z z y z y x xy zx yz grade S--≤≤=Ω≤+=++++++++=∴++++++=+++++⎰⎰ .)1(])1()1()1([211R dxdy y x dv zy x yz x xz y I DS S S π=+++∂++∂+∂++∂+∂++∂=-=⎰⎰⎰⎰⎰⎰⎰⎰⎰Ω+.),()(,.)()(,,,)2().()()]()[()()(.,,)1(20正定可逆再由可逆正定由可逆可逆正定正定由使存在可逆阵正定知由故使得存在可逆阵为正定阵知由、解AB B DB DB DB AB B B A B DB DB DB AB B AB B D D A D A B R DB R DB DB R DB D B R AB B R D D A D A TTTTT T T TTTTT⇒=⇒⇒⇒=⇒======即得由设、解,,,)1(211321321321XB AX XBX A c c c b b b a a a B ==⎪⎪⎪⎭⎫⎝⎛=-.411311001||||,)1)(2(.210301000,2,3,0;1,0;0,0,,,.23)4)323)3,)2,)1,),,(),,(3332221112233322323333222222111232-=-=+=+++⇒⎪⎪⎪⎭⎫ ⎝⎛-=-=========∴++=--=++=++=++==E B E A E B E A B A B c b a c b a b c a X A AX X X A c AX b X a X A AX X A AX X A X A c AX b X a X A X A c AX b X a X A X A c AX b X a AX B X A AX X X A X A AX 则与相似相似与由线性无关得代入由则有 .21)(),1,0(~,1,0,,)3(;11,0,,1,1),1,1(~,21)()2(;2121)(,,)()()1(2222)1(21)1(21)2(2222y Y x x x xey f N Y DY EY b aX Y X b a aDY b a EY b aX Y DX EX N X ex f ek e k x f X ee k ke xf -+-+-+-=∴∴==+=±==⇒===+-=+==-=-==⇒===ππππ函数从而其密度服从正态分布所以服从正态分布因为由所以因为表达式得从密度函数服从正态分布则、解 的联合分布律为、解),)(1(23Y X.,.,0)3(.0,5.0,5.0}1{)(.0),cov(,0,0,0)2(222不相互独立由不相关Y X P P P Y X DY X P EX EX DX Y X EXY EY EX ij j i XY XY ⇒≠⨯⇒======-=====⋅⋅ρρ。