第14讲 2010年真题解析(二)(2011年新版)

二零一○年全国研究生入学考试试题（数学二）一选择题一选择题 1.的无穷间断点的个数为函数222111)(xx x x x f +--=A0 B1 C2 D3 2.设21,y y 是一阶线性非齐次微分方程)()(x q y x p y =+¢的两个特解，的两个特解，若常若常数m l ,使21y y m l +是该方程的解，21y y m l -是该方程对应的齐次方程的解，则解，则 A 21,21==m l B 21,21-=-=m lC 31,32==m lD 32,32==m l3.=¹==a a x a y x y 相切，则与曲线曲线)0(ln 2A4e B3e C2e De 4.设,m n 为正整数,则反常积分21ln (1)mnx d xx-ò的收敛性的收敛性A 仅与m 取值有关取值有关B 仅与n 取值有关取值有关C 与,m n 取值都有关取值都有关D 与,m n 取值都无关取值都无关5.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20,F ¢¹则z z x yxy¶¶+¶¶= A x B z C x -D z - 6.(4)2211lim ()()nnx i j nn i n j ®¥==++åå= A121(1)(1)xd xd y x y ++òò B11(1)(1)xdxdy x y ++òòC 1101(1)(1)d x d y x y ++òòD1121(1)(1)dxdyx y ++òò7.设向量组线性表示，，，：，可由向量组sI b b b aa a ¼¼21r 21II ,,:，下列命题正确的是：的是：A 若向量组I 线性无关，则s r £B 若向量组I 线性相关，则r>s C 若向量组II 线性无关，则s r £D 若向量组II 线性相关，则r>s 8.设A 为4阶对称矩阵,且20,+=AA 若A 的秩为3,则A 相似于A 1110æöç÷ç÷ç÷ç÷èø B 1110æöç÷ç÷ç÷-ç÷èøC 1110æöç÷-ç÷ç÷-ç÷èøD 1110-æöç÷-ç÷ç÷-ç÷èø二填空题二填空题9.3阶常系数线性齐次微分方程022=-¢+¢¢-¢¢¢y y y y 的通解y=__________ 10.曲线1223+=x x y 的渐近线方程为_______________ 11.函数__________)0(0)21ln()(==-=n ny n x x y 阶导数处的在12.___________0的弧长为时，对数螺线当q p qe r =££13.已知一个长方形的长l 以2cm/s 的速率增加，宽w 以3cm/s 的速率增加，则当l=12cm,w=5cm 时，它的对角线增加的速率为___________ 14.设A ，B 为3阶矩阵，且__________,2,2,311=+=+==--B A B A B A 则三解答题三解答题 15.的单调区间与极值。

2011年全国硕士研究生入学统一考试英语考试（二）考试大纲考试性质英语（二）考试是为高等学校和科研机构招收硕士研究生而设置的具有选拔性质的全国统一入学考试科目，其目的是科学、公正、有效地测试考生对英语语言的运用能力，评价的标准时高等学校非英语专业本科毕业生所能达到的及格或及格以上水平，以保证被录取者具有一定的英语水平，并有利于各高等学校和科研院所在专业上择优选拔。

考试形式和试卷结构(一)考试形式考试形式为笔试。

考试时间为180分钟。

满分为100分。

试卷分试题册和答题卡。

答题卡分为答题卡1和答题卡2。

考生应将英语知识运用和阅读理解部分的答案按要求填涂在答题卡1上，将英译汉和写作部分的答案写在答题卡2上。

(二)考试内容与试卷结构试题分四部分，共48题，包括英语知识运用、阅读理解、英译汉和写作。

第一部分英语知识运用主要是考查考生对英语知识的综合运用能力。

共20小题，每小题0.5分，共10分。

在一篇约350词的文章中留出20个空白，要求考生从每题所给的4个选项中选出最佳答案，使补全后的文章意思通顺、前后连贯、结构完整。

考生在答题卡1上作答。

第二部分阅读理解主要是考查考生获取信息、理解文章、猜测重要生词词义并进行推断等方面的能力。

该部分由A、B两节组成，共25小题，每小题2分，共50分。

A节(20小题)本部分为多项选择题，共四篇文章，总长度为1500词左右。

要求考生阅读文章并回答每篇文章后面的问题。

考生需在每小题所提供的选项（A、B、C、D）中选出唯一正确或是最合适的答案。

每篇文章设5题，共20小题。

每小题2分，共40分。

考生在答题卡1上作答。

B节(5小题)本部分有3种备选题型。

每次考试从这3种备选题型中选择一种进行考查。

或者这3种形式中某几种的组合进行考查。

本节文章设5小题，每小题2分，共10分。

考生在答题卡1上作答。

备选题型有：1)多项对应。

2)小标题对应。

3)正误判断。

第三部分：英译汉考查考生理解所给英语语言材料并将其译成汉语的能力。

2010 年全国硕士研究生入学统一考试英语（二）试题答案与解析Section I Use of English一、文章题材结构分析本文是取材于新闻报道，叙述了猪流感的爆发，产生的严重影响以及政府采取的针对性措施。

首段和第二段简述了猪流感的爆发引起世界各国的重视。

第三段引用专家的观点，认为瘟疫并不严重。

第四段和第五段以墨西哥及美国的情况为例，说明了猪流感的严重性和致命性。

第六段叙述了联邦政府针对猪流感的具体措施。

二、试题解析1.【答案】D【解析】上文提到“…was declared a global epidemic…”，根据declare 的逻辑（“宣布为”），可知应该选D 项designated“命名，制定”，而不是C 项commented“评论”，这是典型的近义词复现题目。

2．【答案】C【解析】本题目可依据“句意”找到意思线索，选出答案，难度在于出处句是个长难句。

本句的理解应该抓住alert、meeting 和a sharp rise 三者的关系，根据after a sharp rise 可知是rise（“病例数的增加”）是meeting（“日内瓦专家会议”）的原因，由此可推导出alert 并非是meeting 的原因，而是结果，即meeting 使得alert 升级。

根据上述分析可以排除B、D 选项，B 项activated“激活，激起”，D 项“促使，引起”，此两项的选择都在讲alert 导致了meeting的召开。

而C 项followed 意思是“紧随，跟在……之后”，体现出after 的逻辑，完全满足本句rise 之后是meeting，meeting 之后是alert 的逻辑，所以是正确项。

而A 项proceeded“继续”，属不及物动词，不可接宾语，用法和逻辑用在此处都不合适。

3．【答案】B【解析】本题目应该关注并列连词and，从并列呼应来看：空格后的表达in Britain…对应前面的in Australia，所以空格处rising _____ 应该对应a sharp rise in cases（“病例数的剧增”），因此空格处是“数量”的逻辑才对。

2010年全国硕士研究生入学统一考试数学二试题一、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) 函数()f x =( )(A) 0. (B) 1. (C) 2. (D) 3. (2) 设12,y y 是一阶线性非齐次微分方程()()y p x y q x '+=的两个特解,若常数λμ，使12y y λμ+是该方程的解,12y y λμ-是该方程对应的齐次方程的解,则( )(A) 11,22λμ==. (B) 11,22λμ=-=-. (C) 21,33λμ==. (D) 22,33λμ==.(3) 曲线2y x =与曲线ln (0)y a x a =≠相切,则a = ( )(A) 4e. (B) 3e. (C) 2e. (D) e. (4) 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. (5)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 '≠,则z zxy x y∂∂+=∂∂( ) (A) x . (B) z . (C) x -. (D) z -.(6) ()()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 ++⎰⎰. (7) 设向量组12I:,,,r ααα 可由向量组12II:,,,s βββ 线性表示,下列命题正确的是( )(A) 若向量组I 线性无关,则r s ≤. (B) 若向量组I 线性相关,则r s >.(C) 若向量组II 线性无关,则r s ≤. (D) 若向量组II 线性相关,则r s >. (8) 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-⎛⎫⎪- ⎪ ⎪- ⎪⎝⎭. 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) 3阶常系数线性齐次微分方程220y y y y ''''''-+-=的通解为y = .(10) 曲线3221x y x =+的渐近线方程为 .(11) 函数()ln 120y x x =-=在处的n 阶导数()()0n y= .(12) 当0θπ≤≤时,对数螺线r e θ=的弧长为 .(13) 已知一个长方形的长l 以2cm/s 的速率增加,宽w 以3cm/s 的速率增加.则当cm 12l = ,cm 5w =时,它的对角线增加的速率为 .(14)设,A B 为3阶矩阵,且132,2A B A B -==+=，,则1A B -+= . 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)(本题满分11分)求函数2221()()x t f x x t e d -=-⎰的单调区间与极值.(16)(本题满分10分)( I ) 比较()1ln ln 1nt 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 →∞. (17)(本题满分10分)设函数()y f x =由参数方程22,(1)()x t t t y t ψ⎧=+>-⎨=⎩所确定,其中()t ψ具有2阶导数,且5(1)(1) 6.2ψψ'==，已知223,4(1)d y dx t =+求函数()t ψ.(18)(本题满分10分)一个高为l 的柱体形贮油罐,底面是长轴为2a ,短轴为2b 的椭圆.现将贮油罐平放,当油罐中油面高度为32b 时(如图),计算油的质量.(长度单位为m,质量单位为kg,油的密度为常数ρkg/m 3)(19) (本题满分11分)设函数(,)u f x y =具有二阶连续偏导数,且满足等式2222241250u u ux x y y ∂∂∂++=∂∂∂∂,确定a ,b 的值,使等式在变换,x ay x by ξη=+=+下化简为20uξη∂=∂∂.(20)(本题满分10分) 计算二重积分2 sin DI r θ=⎰⎰,其中(),|0s e c ,04D rr πθθθ⎧⎫=≤≤≤≤⎨⎬⎩⎭. (21) (本题满分10分)设函数()f x 在闭区间[]0,1上连续,在开区间()0,1内可导,且(0)0f =,1(1)3f =,证明：存在1(0,)2ξ∈,1(,1)2η∈,使得22()()=.f f ξηξη''++(22)(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. (23)(本题满分11 分)设0141340A a a -⎛⎫ ⎪=- ⎪ ⎪⎝⎭,正交矩阵Q 使得TQ A Q 为对角矩阵,若Q 的第1列为2,1)T ,求,a Q .2010年全国硕士研究生入学统一考试数学二试题参考答案一、选择题(1)【答案】 (B).【解析】因为()f x =0,1x =±,又因为0lim ()lim x x x f x →→→=,其中00lim 1,lim 1x x +-→→===-,所以0x =为跳跃间断点.显然1lim ()2x f x →==,所以1x =为连续点.而1lim ()limx x f x →-→-==∞,所以1x =-为无穷间断点,故答案选择B.(2)【答案】 (A)．【解析】因12y y λμ-是()0y P x y '+=的解,故()()()12120y y P x y y λμλμ'-+-=,所以()1122()0y P x y y p x y λμ⎡⎤⎡⎤''+-+=⎣⎦⎣⎦,而由已知 ()()()()1122,y P x y q x y P x y q x ''+=+=,所以()()0q x λμ-=, ① 又由于一阶次微分方程()()y p x y q x '+=是非齐的,由此可知()0q x ≠,所以0λμ-=．由于12y y λμ+是非齐次微分方程()()y P x y q x '+=的解,所以()()()()1212y y P x y y q x λμλμ'+++=,整理得 ()()()1122y P x y y P x y q x λμ⎡⎤⎡⎤''+++=⎣⎦⎣⎦,即 ()()()q x q x λμ+=,由()0q x ≠可知1λμ+=, ②由①②求解得12λμ==,故应选(A)． (3)【答案】 (C).【解析】因为曲线2y x =与曲线ln (0)y a x a =≠相切,所以在切点处两个曲线的斜率相同,所以2a x x =,即(0)x x =>.又因为两个曲线在切点的坐标是相同的,所以在2y x =上,当x =2a y =；在ln y a x =上,x =, ln 22a a y a ==.所以ln 222a a a= .从而解得2a e =.故答案选择(C). (4)【答案】 (D).【解析】0x =与1x =都是瑕点.应分成dx dx =+⎰,用比较判别法的极限形式,对于,由于1210[ln (1lim 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).(5) 【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 x y z x y F F F ''''+⋅∂∂+=-==∂∂'''． (6) 【答案】 (D). 【解析】()()222211111()nnnn i 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 =++⎰⎰. (7) 【答案】 (A)．【解析】由于向量组I 能由向量组II 线性表示,所以(I)(II)r r ≤,即11(,,)(,,)r s r r s ααββ≤≤若向量组I 线性无关,则1(,,)r r r αα= ,所以11(,,)(,,)r s r r r s ααββ=≤≤ ,即r s ≤,选(A).(8) 【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= ⎪- ⎪⎝⎭. 二、填空题(9)【答案】2123cos sin x y C e C x C x =++.【解析】该常系数线性齐次微分方程的特征方程为 32220λλλ-+-=,因式分解得()()()()2222210λλλλλ-+-=-+=,解得特征根为2,i λλ==±,所以通解为 2123cos sin x y C e C x C x =++. (10) 【答案】2y x =.【解析】因为3221lim 2x x x x→∞+=,所以函数存在斜渐近线,又因为 333222222lim 2lim 011x x x x x xx x x →∞→∞---==++,所以斜渐近线方程为2y x =. (11)【答案】()21!nn -⋅-.【解析】由高阶导数公式可知()ln (1)n x +1(1)!(1)(1)n nn x --=-+, 所以 ()()()1(1)!(1)!ln12(1)22(12)(12)n n n n n nn n x x x ----=-⋅-=---, 即()(1)!(0)22(1)!(120)n nn nn yn -=-=---⋅. (12))1e π-.【解析】因为 0θπ≤≤,所以对数螺线r e θ=的极坐标弧长公式为πθ⎰=0e d πθθ⎰)1e π-.(13)【答案】3cm/s .【解析】设(),()l x t w y t ==,由题意知,在0t t =时刻00()12,()5x t y t ==,且0()2,x t '=0()3y t '=,设该对角线长为()S t ,则 ()S t =,所以()S t '=所以0()3S t '===.(14)【答案】3.【解析】由于1111()()A A B B E AB B B A ----+=+=+,所以11111()A B A A B B A A B B -----+=+=+因为2B =,所以1112BB--==,因此 11113232A B A A B B ---+=+=⨯⨯=. 三、解答题(15)【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,)-+∞ .(16) 【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 →∞=.(17)【解析】根据题意得(),22dy t dy dt dxdx t dtψ'==+()()()()()()222222222232241t d t t t t t d y dt dx dx t t dtψψψ'⎛⎫ ⎪'''+-+⎝⎭+===++ 即()()()()222261t t t t ψψ'''+-=+,整理有()()()()2131t t t t ψψ'''+-=+,解()()()()()31151,162t t t t ψψψψ'⎧''-=+⎪⎪+⎨⎪'==⎪⎩,令()y t ψ'=,即()1311y y t t '-=++. 所以()()()11113113dt dt t t y e t e dt C t t C -++⎛⎫⎰⎰=++=++ ⎪⎝⎭⎰,1t >-.因为()()116y ψ'==,所以0C =,故()31y t t =+,即()()31t t t ψ'=+,故()()2313312t t t dt t t C ψ=+=++⎰． 又由()512ψ=,所以10C =,故()233,(1)2t t t t ψ=+>-.(18)【解析】油罐放平,截面如图建立坐标系之后,边界椭圆的方程为：22221x y a b+= 阴影部分的面积2222bbba S xdyb --==⎰⎰ 令sin ,y b t y b ==-时;22b t y π=-=时6t π=. 266221122cos 2(cos 2)(223S ab tdt ab t dt ab πππππ--==+=⎰⎰所以油的质量2(3m abl πρ=.(19)【解析】由复合函数链式法则得u u u u ux x y x ξηξξη∂∂∂∂∂∂∂=⋅+⋅=+∂∂∂∂∂∂∂, u u u u ua b y y y ξηξηξη∂∂∂∂∂∂∂=⋅+=⋅+⋅∂∂∂∂∂∂∂, 22222222u u u u u u u x x x x x xξηηηξηξξηηξη⎛⎫∂∂∂∂∂∂∂∂∂∂∂∂=+=⋅+⋅+⋅+⋅ ⎪∂∂∂∂∂∂∂∂∂∂∂∂∂∂⎝⎭ 222222,u u uξηξη∂∂∂=++∂∂∂∂ 2222222u u u u u u u x y y y y y yξηηηξηξξηηξη⎛⎫∂∂∂∂∂∂∂∂∂∂∂∂=+=⋅+⋅+⋅+⋅ ⎪∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂⎝⎭ 22222(),u u ua b a b ξηξη∂∂∂=+++∂∂∂∂ 22222222()()u u u u u u ua b a a b b a a y y ξηξξηηξη⎛⎫∂∂∂∂∂∂∂∂=+=+++ ⎪∂∂∂∂∂∂∂∂∂∂⎝⎭ 22222222,u u u a b ab ξηξη∂∂∂=++∂∂∂∂ 故222224125u u ux x y y∂∂∂++∂∂∂∂[]2222222(5124)(5124)12()1080,u u u a a b b a b ab ξηξη∂∂∂=+++++++++=∂∂∂∂所以 22512405124012()1080a a b b a b ab ⎧++=⎪++=⎨⎪+++≠ ⎩,则25a =-或2-,25b =-或2-.又因为当(,)a b 为22(2,2),(,)55----时方程(3)不满足,所以当(,)a b 为2(,2)5-- ,2(2,)5--满足题意.(20)【解析】2sin DI rθ=⎰⎰sin Dr rdrdθ=⎰⎰D=⎰⎰100xdx =⎰⎰()312201113x dx ⎡⎤=--⎢⎥⎣⎦⎰ ()311220011133dx x dx =--⎰⎰20113cos 43316d πθθπ=-=-⎰.(21)【解析】令()()313F x f x x =-,对于()F x 在10,2⎡⎤⎢⎥⎣⎦上利用拉格朗日中值定理,得存在10,,2ξ⎛⎫∈ ⎪⎝⎭使得()()11022F F F ξ⎛⎫'-= ⎪⎝⎭．对于()F x 在1,12⎡⎤⎢⎥⎣⎦上利用拉格朗日中值定理,得存在1,1,2η⎛⎫∈ ⎪⎝⎭使得()()11122F F F η⎛⎫'-= ⎪⎝⎭,两式相加得 ()()22f f ξηξη''+=+.所以存在110,,,122ξη⎛⎫⎛⎫∈∈ ⎪⎪⎝⎭⎝⎭,使()()22f f ξηξη''+=+. (22) 【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.(23)【解析】由于0141340A a a -⎛⎫⎪=- ⎪ ⎪⎝⎭,存在正交矩阵Q ,使得TQ AQ 为对角阵,且Q 的第一T,故A对应于1λ的特征向量为12,1)Tξ=.根据特征值和特征向量的定义,有1Aλ=,即10141113224011aaλ-⎛⎫⎛⎫⎛⎫⎪⎪ ⎪-=⎪⎪ ⎪⎪⎪ ⎪⎝⎭⎝⎭⎝⎭,由此可得11,2aλ=-=.故014131410A-⎛⎫⎪=--⎪⎪-⎝⎭.由14131(4)(2)(5)041E Aλλλλλλλ--=-=+--=-,可得A的特征值为1232,4,5λλλ==-=.由2()0E A xλ-=,即1234141710414xxx--⎛⎫⎛⎫⎪⎪-=⎪⎪⎪ ⎪--⎝⎭⎝⎭,可解得对应于24λ=-的线性无关的特征向量为2(1,0,1)Tξ=-.由3()0E A xλ-=,即1235141210415xxx-⎛⎫⎛⎫⎪⎪=⎪⎪⎪ ⎪-⎝⎭⎝⎭,可解得对应于35λ=的特征向量为3(1,1,1)Tξ=-.由于A为实对称矩阵,123,,ξξξ为对应于不同特征值的特征向量,所以123,,ξξξ相互正交,只需单位化：312123123,1,0,1),1,1)T T Tξξξηηηξξξ====-==-,取()123,,0Qηηη⎫⎪⎪==⎪⎪⎭,则245TQ AQ⎛⎫⎪=Λ=-⎪⎪⎝⎭.。

2010年全国硕士研究生入学统一考试(英语二)试题Section I Use of EnglishDirections: Read the following passage. For each numbered blank there are four choices marked A, B, C and D. Choose the best one and mark your answers on ANSWER SHEET l. (10 points)The outbreak of swine flu that was first detected in Mexico was declared a global epidemic on June 11, 2009. It is the first worldwide epidemic__1__ by the World Health Organization in 41 years.The heightened alert ___2__an emergency meeting with flu experts in Geneva that convened after a sharp rise in cases in Australia, and rising___3___in Britain, Japan, Chile and elsewhere.But the epidemic is "__4__" in severity, according to Margaret Chan, the organization's director general, __5__ the overwhelming majority of patients experiencing only mild symptoms and a full recovery, often in the __6___ of any medical treatment.The outbreak came to global__7__in late April 2009, when Mexican authorities noticed an unusually large number of hospitalizations and deaths__8___healthy adults. As much of Mexico City shut down at the height of a panic, cases began to __9___in New York City, the southwestern United States and around the world.In the United States, new cases seemed to fade__10__warmer weather arrived. But in late September 2009, officials reported there was __11__flu activity in almost every state and that virtually all the__12___tested are the new swine flu, also known as (A) H1N1, not seasonal flu. In the U.S., it has__13__more than one million people, and caused more than 600 deaths and more than 6,000 hospitalizations.Federal health officials__14___Tamiflu for children from the national stockpile and began__15__orders from the states for the new swine flu vaccine. The new vaccine, which is different from the annual flu vaccine, is __16__ ahead of expectations. More than three million doses were to be made available in early October 2009, though most of those __17__doses were of the FluMist nasal spray type, which is not__18__for pregnant women, people over 50 or those with breathing difficulties, heart disease or several other __19__. But it was still possible to vaccinate people in other high-risk group: health care workers, people __20___infants and healthy young people.1 [A] criticized [B] appointed [C]commented [D] designated2 [A] proceeded [B] activated [C] followed [D] prompted3 [A] digits [B] numbers [C] amounts [D] sums4 [A] moderate [B] normal [C] unusual [D] extreme5 [A] with [B] in [C] from [D] by6 [A] progress [B] absence [C] presence [D] favor7 [A] reality [B] phenomenon [C] concept [D] notice8 [A]over [B] for [C] among [D] to9 [A] stay up [B] crop up [C] fill up [D] cover up10 [A] as [B] if [C] unless [D] until11 [A] excessive [B] enormous [C] significant [D]magnificent12 [A]categories [B] examples [C] patterns [D] samples13 [A] imparted [B] immerse [C] injected [D] infected14 [A] released [B] relayed [C] relieved [D] remained15 [A] placing [B] delivering [C] taking [D] giving16 [A] feasible [B] available [C] reliable [D] applicable17 [A] prevalent [B] principal [C] innovative [D] initial18 [A] presented [B] restricted [C] recommended [D] introduced19 [A] problems [B] issues [C] agonies [D] sufferings20 [A] involved in [B] caring for [C] concerned with [D] warding offSection Ⅱ Reading comprehensionPart ADirections:Read the following four passages. Answer the questions below each passage by choosing A, B, C and D. Mark your answers on ANSWER SHEET 1. (40 points)Text1The longest bull run in a century of art-market history ended on a dramatic note with a sale of 56 works by Damien Hirst, “Beautiful Inside My Head Forever”，at Sotheby’s in London on September 15th 2008. All but two pieces sold, fetching more than ￡70m, a record for a sale by a single artist. It was a last victory. As the auctioneer called out bids, in New York one of the oldest banks on Wall Street, Lehman Brothers, filed for bankruptcy.The world art market had already been losing momentum for a while after rising bewilderingly since 2003. At its peak in 2007 it was worth some $65 billion, reckons Clare Mc Andrew, founder of Arts Economics, a research firm—double the figure five years earlier. Since then it may have come down to $50 billion. But the market generates interest far beyond its size because it brings together great wealth, enormous egos, greed, passion and controversy in a way matched by few other industries.In the weeks and months that followed Mr. Hirst’s sale, spending of any sort became deeply unfashionable, especially in New York, where the bail-out of the banks coincided with the loss of thousands of jobs and the financial demise of many art-buying investors. In the art world that meant collectors stayed away from galleries and salerooms. Sales of contemporary art fell by two-thirds, and in the most overheated sector—for Chinese contemporary art—they were down by nearly 90% in the year to November 2008. Within weeks the world’s two biggest auction houses, Sotheby’s and Christie’s, had to pay out nearly $200m in guarantees to clients who had placed works for sale with them.The current downturn in the art market is the worst since the Japanese stopped buying Impressionists at the end of 1989, a move that started the most serious contraction in the market since the Second World War. This time experts reckon that prices are about 40% down on their peak on average, though some have been far more fluctuant. But Edward Dolman, Christie’s chief executive, says: “I’m pretty confident we’re at the bottom.”What makes this slump different from the last, he says, is that there are still buyers in the market, whereas inthe early 1990s, when interest rates were high, there was no demand even though many collectors wanted to sell. Christie’s revenues in the first half of 2009 were still higher than in the first half of 2006. Almost everyone who was interviewed for this special report said that the biggest problem at the moment is not a lack of demand but a lack of good work to sell. The three Ds—death, debt and divorce—still deliver works of art to the market. But anyone who does not have to sell is keeping away, waiting for confidence to return.21. In the first paragraph, Damien Hirst's sale was referred to as “a last victory” because ____.A. the art market had witnessed a succession of victoriesB. the auctioneer finally got the two pieces at the highest bidsC. Beautiful Inside My Head Forever won over all masterpiecesD. it was successfully made just before the world financial crisis22.By saying “spending of any sort became deeply unfashionable”(Line 1-2,Para.3)，the author suggests that_____.A. collectors were no longer actively involved in art-market auctionsB .people stopped every kind of spending and stayed away from galleriesC. art collection as a fashion had lost its appeal to a great extentD .works of art in general had gone out of fashion so they were not worth buying23. Which of the following statements is NOT true?A .Sales of contemporary art fell dramatically from 2007 to 2008.B. The art market surpassed many other industries in momentum.C. The market generally went downward in various ways.D. Some art dealers were awaiting better chances to come.24. The three Ds mentioned in the last paragraph are ____A. auction houses ' favoritesB. contemporary trendsC. factors promoting artwork circulationD. styles representing impressionists25. The most appropriate title for this text could be ___A. Fluctuation of Art PricesB. Up-to-date Art AuctionsC. Art Market in DeclineD. Shifted Interest in ArtsTEXT2I was addressing a small gathering in a suburban Virginia living room—a women's group that had invited men to join them. Throughout the evening one man had been particularly talkative, frequently offering ideas and anecdotes, while his wife sat silently beside him on the couch. Toward the end of the evening I commented that women frequently complain that their husbands don't talk to them. This man quickly nodded in agreement. He gestured toward his wife and said, "She's the talker in our family." The room burst into laughter; the man looked puzzled and hurt. "It's true," he explained. "When I come home from work, I have nothing to say. If she didn't keep the conversation going, we'd spend the whole evening in silence."This episode crystallizes the irony that although American men tend to talk more than women in public situations, they often talk less at home. And this pattern is wreaking havoc with marriage.The pattern was observed by political scientist Andrew Hacker in the late 1970s. Sociologist Catherine Kohler Riessman reports in her new book "Divorce Talk" that most of the women she interviewed—but only a few of the men—gave lack of communication as the reason for their divorces. Given the current divorce rate of nearly 50 percent，that amounts to millions of cases in the United States every year —a virtual epidemic of failed conversation.In my own research complaints from women about their husbands most often focused not on tangible inequities such as having given up the chance for a career to accompany a husband to his or doing far more than their share of daily life-support work like cleaning, cooking, social arrangements and errands. Instead they focused on communication: "He doesn't listen to me." "He doesn't talk to me." I found as Hacker observed years before that most wives want their husbands to be first and foremost conversational partners but few husbands share this expectation of their wives.In short the image that best represents the current crisis is the stereotypical cartoon scene of a man sitting at the breakfast table with a newspaper held up in front of his face, while a woman glares at the back of it, wanting to talk.26. What is most wives' main expectation of their husbands?A. Talking to them.B. Trusting them.C. Supporting their careers.D. Sharing housework.27. Judging from the context, the phrase “wreaking havoc”(Line 3,Para.2)most probably means ___ .A. generating motivation.B. exerting influenceC. causing damageD. creating pressure28. All of the following are true EXCEPT_______A. men tend to talk more in public than womenB. nearly 50 percent of recent divorces are caused by failed conversationC. women attach much importance to communication between couplesD. a female tends to be more talkative at home than her spouse29. Which of the following can best summarize the main idea of this text?A. The moral decaying deserves more research by sociologists.B. Marriage break-up stems from sex inequalities.C. Husband and wife have different expectations from their marriage.D. Conversational patterns between man and wife are different.30. In the following part immediately after this text, the author will most probably focus on ______A. a vivid account of the new book Divorce TalkB. a detailed description of the stereotypical cartoonC. other possible reasons for a high divorce rate in the U.S.D. a brief introduction to the political scientist Andrew HackerText 3Over the past decade, many companies had perfected the art of creating automatic behaviors —habits —among consumers. These habits have helped companies earn billions of dollars when customers eat snacks, apply lotions and wipe counters almost without thinking, often in response to a carefully designed set of daily cues.“There are fundamental public health problems, like dirty hands instead of a soap habit, that remain killersonly because we can’t figure out how to change people’s habits,” Dr. Curtis said. “We wanted to learn from private industry how to create new behaviors that happen automatically.”The companies that Dr. Curtis turned to —Procter & Gamble, Colgate-Palmolive and Unilever —had invested hundreds of millions of dollars finding the subtle cues in consumers’ lives that corporations could use to introduce new routines.If you look hard enough, you’ll find that many of the products we use every day —chewing gums, skin moisturizers, disinfecting wipes, air fresheners, water purifiers, health snacks, antiperspirants, colognes, teeth whiteners, fabric softeners, vitamins—are results of manufactured habits. A century ago, few people regularly brushed their teeth multiple times a day. Today, because of canny advertising and public health campaigns, many Americans habitually give their pearly whites a cavity-preventing scrub twice a day, often with Colgate, Crest or one of the other brands.A few decades a go, many people didn’t drink water outside of a meal. Then beverage companies started bottling the production of far-off springs, and now office workers unthinkingly sip bottled water all day long. Chewing gum, once bought primarily by adolescent boys, is now featured in commercials as a breath freshener and teeth cleanser for use after a meal. Skin moisturizers are advertised as part of morning beauty rituals, slipped in between hair brushing and putting on makeup.“Our products succeed when they become part of daily or weekly patterns,” said Carol Berning, a consumer psychologist who recently retired from Procter & Gamble, the company that sold $76 billion of Tide, Crest and other products last year. “Creating positive habits is a huge part of improving our consumers’ lives, and it’s essential to making new products commercially viable.”Through experiments and observation, social scientists like Dr. Berning have learned that there is power in tying certain behaviors to habitual cues through relentless advertising. As this new science of habit has emerged, controversies have erupted when the tactics have been used to sell questionable beauty creams or unhealthy foods.31. According to Dr. Curtis, habits like hand washing with soap________.A. should be further cultivatedB. should be changed graduallyC. are deeply rooted in historyD. are basically private concerns32. Bottled water, chewing gun and skin moisturizers are mentioned in Paragraph 5 so as to____A. reveal their impact on people’s habitsB. show the urgent need of daily necessitiesC. indicate their effect on people’s buying powerD. manifest the significant role of good habits33. W hich of the following does NOT belong to products that help create people’s habits?A. TideB. CrestC. ColgateD. Unilever34. From the text we know that some of consumer’s habits are developed due to _____A. perfected art of productsB. automatic behavior creationC. commercial promotionsD. scientific experiments35. T he author’s attitude toward the influence of advertisement on people’s habits is____A. indifferentB. negativeC. positiveD. biasedText4Many Americans regard the jury system as a concrete expression of crucial democratic values, including the principles that all citizens who meet minimal qualifications of age and literacy are equally competent to serve on juries; that jurors should be selected randomly from a representative cross section of the community; that no citizen should be denied the right to serve on a jury on account of race, religion, sex, or national origin; that defendants are entitled to trial by their peers; and that verdicts should represent the conscience of the community and not just the letter of the law. The jury is also said to be the best surviving example of direct rather than representative democracy. In a direct democracy, citizens take turns governing themselves, rather than electing representatives to govern for them.But as recently as in 1986, jury selection procedures conflicted with these democratic ideals. In some states, for example, jury duty was limited to persons of supposedly superior intelligence, education, and moral character. Although the Supreme Court of the United States had prohibited intentional racial discrimination in jury selection as early as the 1880 case of Strauder v. West Virginia, the practice of selecting so-called elite or blue-ribbon juries provided a convenient way around this and other antidiscrimination laws.The system also failed to regularly include women on juries until the mid-20th century. Although women first served on state juries in Utah in 1898, it was not until the 1940s that a majority of states made women eligible for jury duty. Even then several states automatically exempted women from jury duty unless they personally asked to have their names included on the jury list. This practice was justified by the claim that women were needed at home, and it kept juries unrepresentative of women through the 1960s.In 1968, the Congress of the United States passed the Jury Selection and Service Act, ushering in a new era of democratic reforms for the jury. This law abolished special educational requirements for federal jurors and required them to be selected at random from a cross section of the entire community. In the landmark 1975 decision Taylor vs. Louisiana, the Supreme Court extended the requirement that juries be representative of all parts of the community to the state level. The Taylor decision also declared sex discrimination in jury selection to be unconstitutional and ordered states to use the same procedures for selecting male and female jurors.36. From the principles of the US jury system, we learn that ______A. both liberate and illiterate people can serve on juriesB. defendants are immune from trial by their peersC. no age limit should be imposed for jury serviceD. judgment should consider the opinion of the public37. The practice of selecting so-called elite jurors prior to 1968 showed_____A. the inadequacy of antidiscrimination lawsB. the prevalent discrimination against certain racesC. the conflicting ideals in jury selection proceduresD. the arrogance common among the Supreme Court justices38. Even in the 1960s, women were seldom on the jury list in some states because_____A. they were automatically banned by state lawsB. they fell far short of the required qualificationsC. they were supposed to perform domestic dutiesD. they tended to evade public engagement39. After the Jury Selection and Service Act was passed.___A. sex discrimination in jury selection was unconstitutional and had to be abolishedB. educational requirements became less rigid in the selection of federal jurorsC. jurors at the state level ought to be representative of the entire communityD. states ought to conform to the federal court in reforming the jury system40. In discussing the US jury system, the text centers on_______A. its nature and problemsB. its characteristics and traditionC. its problems and their solutionsD. its tradition and developmentPart BBoth Boeing and Airbus have trumpeted the efficiency of their newest aircraft, the 787 and A350 respectively. Their clever designs and lightweight composites certainly make a difference. But a group of researchers at Stanford University, led by Ilan Kroo, has suggested that airlines could take a more naturalistic approach to cutting jet-fuel use, and it would not require them to buy new aircraft.The answer, says Dr Kroo, lies with birds. Since 1914, and a seminal paper by a German researcher called Carl Wiesel Berger, scientists have known that birds flying in formation—a V-shape, echelon or otherwise—expend less energy. The air flowing over a b ird’s wings curls upwards behind the wingtips, a phenomenon known as upwash. Other birds flying in the upwash experience reduced drag, and spend less energy propelling themselves. Peter Lissaman, an aeronautics expert who was formerly at Caltech and the University of Southern California, has suggested that a formation of 25 birds might enjoy a range increase of 71%。

2010 年考研英语（二）真题Section I Use of EnglishDirections:Read the following passage. For each numbered blank there are four choices marked A, B, C and D. Choose the best one and mark your answers on ANSWER SHEET l. (10 points) The outbreak of swine flu that was first detected in Mexico was declared a global epidemic on June 11, 2009. It is the first worldwide epidemic 1 by the World Health Organization in 41 years.The heightened alert 2 an emergency meeting with flu experts in Geneva that assembled after a sharp rise in cases in Australia, and rising 3 in Britain, Japan, Chile and elsewhere.But the epidemic is " 4 " in severity, according to Margaret Chan, the organization's director general, 5 the overwhelming majority of patients experiencing only mild symptoms and a full recovery, often in the 6 of any medical treatment.The outbreak came to global 7 in late April 2009, when Mexican authorities noted an unusually large number of hospitalizations and deaths 8 healthy adults. As much of Mexico City shut down at the height of a panic, cases began to 9 in New York City, the southwestern United States and around the world.In the United States, new cases seemed to fade 10 warmer weather arrived. But in late September 2009, officials reported there was 11 flu activity in almost every state and that virtually all the 12 tested are the new swine flu, also known as (A) H1N1, not seasonal flu. In the U.S., it has 13 more than one million people, and caused more than 600 deaths and more than 6,000 hospitalizations.Federal health officials 14 Tamiflu for children from the national stockpile and began 15 orders from the states for the new swine flu vaccine. The new vaccine, which is different from the annual flu vaccine, is 16 ahead of expectations. More than three million doses were to be made available in early October 2009, though most of those 17 doses were of the FluMist nasal spray type, which is not 18 for pregnant women, peopleover 50 or those with breathing difficulties, heart disease or several other 19 . But it was still possible to vaccinate people in other high-risk groups: health care workers, people 20 infants and healthy young people.1. [A] criticized [B] appointed [C]commented [D] designated2. [A] proceeded [B] activated [C] followed [D] prompted3. [A] digits [B] numbers [C] amounts [D] sums4. [A] moderate [B] normal [C] unusual [D] extreme5. [A] with [B] in [C] from [D] by6. [A] progress [B] absence [C] presence [D] favor7. [A] reality [B] phenomenon [C] concept [D] notice8. [A]over [B] for [C] among [D] to9. [A] stay up [B] crop up [C] fill up [D] cover up10. [A] as [B] if [C] unless [D] until11. [A] excessive [B] enormous [C] significant [D]magnificent12. [A]categories [B] examples [C] patterns [D] samples13. [A] imparted [B] immersed [C] injected [D] infected14. [A] released [B] relayed [C] relieved [D] remained15. [A] placing [B] delivering [C] taking [D] giving16. [A] feasible [B] available [C] reliable [D] applicable17. [A] prevalent [B] principal [C] innovative [D] initial18. [A] presented [B] restricted [C] recommended [D] introduced19. [A] problems [B] issues [C] agonies [D] sufferings20. [A] involved in [B] caring for [C] concerned with [D] warding offSection Ⅱ Reading comprehensionPart ADirections:Read the following four texts. Answer the questions after each text by choosing A, B, C or D. Mark your answers on the ANSWER SHEET. (40 points)Text 1The longest bull run in a century of art-market history ended on a dramatic note with a sale of 56 works by Damien Hirst, Beautiful Inside My Head Forever，at Sotheby’s in London on September 15th 2008. All but two pieces sold, fetching more than ￡70m, a record for a sale by a single artist. It was a last victory. As the auctioneer called out bids, in New York one of the oldest banks on Wall Street, Lehman Brothers, filed for bankruptcy.The world art market had already been losing momentum for a while after rising bewilderingly since 2003. At its peak in 2007 it was worth some $65 billion, reckons Clare McAndrew, founder of Arts Economics, a research firm—double the figure five years earlier. Since then it may have come down to $50 billion. But the market generates interest far beyond its size because it brings together great wealth, enormous egos, greed, passion and controversy in a way matched by few other industries.In the weeks and months that followed Mr Hirst’s sale, spending of any sort became deeply unfashionable. In the art world that meant collectors stayed away from galleries and salerooms. Sales of contemporary art fell by two-thirds, and in the most overheated sector they were down by nearly 90% in the year to November 2008. W ithin weeks the world’s two biggest auction houses, Sotheby’s and Christie’s, had to pay out nearly $200m in guarantees to clients who had placed works for sale with them.The current downturn in the art market is the worst since the Japanese stopped buying Impressionists at the end of 1989. This time experts reckon that prices are about 40% down on their peak on average, though some have been far more fluctuant. But Edward Dolman, Chr istie’s chief executive, says: “I’m pretty confident we’re at the bottom.”What makes this slump different from the last, he says, is that there are still buyers in the market. Almost everyone who was interviewed for this special report said that the biggest problem at the moment is not a lack of demand but a lack of good work to sell. The three Ds—death, debt and divorce—still deliver works of art to the market. But anyone who does not have to sell is keeping away, waiting for confidence to return.21.In the first paragraph, Damien Hirst's sale was referred to as“a last victory”b ecause ____.[A]the art market had witnessed a succession of victories[B]the auctioneer finally got the two pieces at the highest bids[C]Beautiful Inside My Head Forever won over all masterpieces[D] it was successfully made just before the world financial crisis22. By saying “spending of any sort became deeply unfashionable”(Line 1-2,Para.3)，the author suggests that_____.[A]collectors were no longer actively involved in art-market auctions[B]people stopped every kind of spending and stayed away from galleries[C]art collection as a fashion had lost its appeal to a great extent[D]works of art in general had gone out of fashion so they were not worth buying23. Which of the following statements is NOT true?[A]Sales of contemporary art fell dramatically from 2007 to 2008.[B]The art market surpassed many other industries in momentum.[C]The art market generally went downward in various ways.[D]Some art dealers were awaiting better chances to come.24. The three Ds mentioned in the last paragraph are ____[A] auction houses ' favorites[B] contemporary trends[C] factors promoting artwork circulation[D] styles representing impressionists25. The most appropriate title for this text could be ___[A] Fluctuation of Art Prices[B] Up-to-date Art Auctions[C] Art Market in Decline[D]Shifted Interest in ArtsText 2I was addressing a small gathering in a suburban Virginia living room—a women's group that had invited men to join them. Throughout the evening, one man had been particularly talkative, frequently offering ideas and anecdotes, while his wife sat silently beside him on the couch. Toward the end of the evening, I commented that women frequently complain thattheir husbands don't talk to them. This man quickly nodded in agreement. He gestured toward his wife and said, "She's the talker in our family." The room burst into laughter; the man looked puzzled and hurt. "It's true," he explained. "When I come home from work, I have nothing to say. If she didn't keep the conversation going, we'd spend the whole evening in silence."This episode crystallizes the irony that although American men tend to talk more than women in public situations, they often talk less at home. And this pattern is wreaking havoc with marriage.The pattern was observed by political scientist Andrew Hacker in the late 1970s. Sociologist Catherine Kohler Riessman reports in her new book Divorce Talk that most of the women she interviewed—but only a few of the men—gave lack of communication as the reason for their divorces. Given the current divorce rate of nearly 50 percent，that amounts to millions of cases in the United States every year —a virtual epidemic of failed conversation.In my own research, complaints from women about their husbands most often focused not on tangible inequities such as having given up the chance for a career to accompany a husband to his, or doing far more than their share of daily life-support work like cleaning, cooking, and social arrangements. Instead, they focused on communication: "He doesn't listen to me." "He doesn't talk to me." I found as Hacker observed years before, that most wives want their husbands to be, first and foremost, conversational partners, but few husbands share this expectation of their wives.In short, the image that best represents the current crisis is the stereotypical cartoon scene of a man sitting at the breakfast table with a newspaper held up in front of his face, while a woman glares at the back of it, wanting to talk.26. What is most wives' main expectation of their husbands?[A] Talking to them.[B] Trusting them.[C] Supporting their careers.[D] Sharing housework.27. Judging from the context, the phrase“wreaking havoc”(Line 3,Para.2)most probably means ___ .[A] generating motivation.[B] exerting influence[C] causing damage[D] creating pressure28. All of the following are true EXCEPT_______.[A] men tend to talk more in public than women[B] nearly 50 percent of recent divorces are caused by failed conversation[C] women attach much importance to communication between couples[D] a female tends to be more talkative at home than her spouse29. Which of the following can best summarize the main idea of this text?[A] The moral decaying deserves more research by sociologists.[B] Marriage break-up stems from sex inequalities.[C] Husband and wife have different expectations from their marriage.[D] Conversational patterns between man and wife are different.30. In the following part immediately after this text, the author will most probably focus on ______.[A] a vivid account of the new book Divorce Talk[B] a detailed description of the stereotypical cartoon[C] other possible reasons for a high divorce rate in the U.S.[D] a brief introduction to the political scientist Andrew HackerText 3Over the past decade, many companies had perfected the art of creating automatic behaviors —habits—among consumers. These habits have helped companies earn billions of dollars when customers eat snacks, or wipe counters almost without thinking, often in response to a carefully designed set of daily cues.“There are fundamental public health problems, like dirty hands instead of a soap habit, that remain killers only because we can’t figure out how to change pe ople’s habits,” said Dr. Curtis, the director of Hygiene Center at the London School of Hygiene & Tropical Medicine. “We wanted to learn from private industry how to create new behaviors that happenautomatically.”The companies that Dr. Curtis turned to — Procter & Gamble, Colgate-Palmolive and Unilever —had invested hundreds of millions of dollars finding the subtle cues in consumers’ lives that corporations could use to introduce new routines.If you look hard enough, you’ll find that many of the pro ducts we use every day —chewing gums, skin moisturizers, disinfecting wipes, air fresheners, water purifiers, health snacks, teeth whiteners, fabric softeners, vitamins—are results of manufactured habits. A century ago, few people regularly brushed their teeth multiple times a day. Today, because of shrewd advertising and public health campaigns, many Americans habitually give their pearly whites a cavity-preventing scrub twice a day, often with Colgate, Crest or one of the other brands.A few decades ago, many people didn’t drink water outside of a meal. Then beverage companies started bottling the production of far-off springs, and now office workers unthinkingly sip bottled water all day long. Chewing gum, once bought primarily by adolescent boys, is now featured in commercials as a breath freshener and teeth cleanser for use after a meal. Skin moisturizers are advertised as part of morning beauty rituals, slipped in between hair brushing and putting on makeup.“Our products succeed when they become part o f daily or weekly patterns,” said Carol Berning, a consumer psychologist who recently retired from Procter & Gamble, the company that sold $76 billion of Tide, Crest and other products last year. “Creating positive habits is a huge part of improving our co nsumers’ lives, and it’s essential to making new products commercially viable.”Through experiments and observation, social scientists like Dr. Berning have learned that there is power in tying certain behaviors to habitual cues through ruthless advertising. As this new science of habit has emerged, controversies have erupted when the tactics have been used to sell questionable beauty creams or unhealthy foods.31. According to Dr. Curtis, habits like hand washing with soap________.[A] should be further cultivated[B] should be changed gradually[C] are deeply rooted in history[D] are basically private concerns32. Bottled water, chewing gum and skin moisturizers are mentioned in Paragraph 5 so as to____[A] reveal their impact on people’s habits[B] show the urgent need of daily necessities[C] indicate their effect on people’s buying power[D] manifest the significant role of good habits33. Which of the following does NOT belong to products that help create people’s habits?[A]Tide[B] Crest[C] Colgate[D] Unilever34. From the text we know that some of consumer’s habits are developed due to _____[A]perfected art of products[B]automatic behavior creation[C]commercial promotions[D]scientific experiments35. The author’s a tt itude toward the influence of advertisement on people’s habits is____[A] indifferent[B] negative[C] positive[D] biasedText 4Many Americans regard the jury system as a concrete expression of crucial democratic values, including the principles that all citizens who meet minimal qualifications of age and literacy are equally competent to serve on juries; that jurors should be selected randomly from a representative cross section of the community; that no citizen should be denied the right to serve on a jury on account of race, religion, sex, or national origin; that defendants are entitled to trial by their peers; and that verdicts should represent the conscience of the community andnot just the letter of the law. The jury is also said to be the best surviving example of direct rather than representative democracy. In a direct democracy, citizens take turns governing themselves, rather than electing representatives to govern for them.But as recently as in 1986, jury selection procedures conflicted with these democratic ideals. In some states, for example, jury duty was limited to persons of supposedly superior intelligence, education, and moral character. Although the Supreme Court of the United States had prohibited intentional racial discrimination in jury selection as early as the 1880 case of Strauder v. West Virginia, the practice of selecting so-called elite or blue-ribbon juries provided a convenient way around this and other antidiscrimination laws.The system also failed to regularly include women on juries until the mid-20th century. Although women first served on state juries in Utah in 1898, it was not until the 1940s that a majority of states made women eligible for jury duty. Even then several states automatically exempted women from jury duty unless they personally asked to have their names included on the jury list. This practice was justified by the claim that women were needed at home, and it kept juries unrepresentative of women through the 1960s.In 1968, the Congress of the United States passed the Jury Selection and Service Act, ushering in a new era of democratic reforms for the jury. This law abolished special educational requirements for federal jurors and required them to be selected at random from a cross section of the entire community. In the landmark 1975 decision Taylor vs. Louisiana, the Supreme Court extended the requirement that juries be representative of all parts of the community to the state level. The Taylor decision also declared sex discrimination in jury selection to be unconstitutional and ordered states to use the same procedures for selecting male and female jurors.36. From the principles of the US jury system, we learn that ______[A]both liberate and illiterate people can serve on juries[B]defendants are immune from trial by their peers[C]no age limit should be imposed for jury service[D]judgment should consider the opinion of the public37. The practice of selecting so-called elite jurors prior to 1968 showed_____[A]the inadequacy of antidiscrimination laws[B]the prevalent discrimination against certain races[C]the conflicting ideals in jury selection procedures[D]the arrogance common among the Supreme Court justices38. Even in the 1960s, women were seldom on the jury list in some states because_____[A]they were automatically banned by state laws[B]they fell far short of the required qualifications[C]they were supposed to perform domestic duties[D]they tended to evade public engagement39. After the Jury Selection and Service Act was passed.___[A] sex discrimination in jury selection was unconstitutional and had to be abolished[B] educational requirements became less rigid in the selection of federal jurors[C] jurors at the state level ought to be representative of the entire community[D] states ought to conform to the federal court in reforming the jury system40. In discussing the US jury system, the text centers on_______[A]its nature and problems[B]its characteristics and tradition[C]its problems and their solutions[D]its tradition and developmentPart BDirections:Read the following text and decide whether each of the statements is true or false. Choose T if the statement is true or F if the statement is not true. Mark your answers on the ANSWER SHEET. (10 points)Both Boeing and Airbus have trumpeted the efficiency of their newest aircraft, the 787 and A350 respectively. Their clever designs and lightweight composites certainly make a difference. But a group of researchers at Stanford University, led by Ilan Kroo, has suggested that airlines could take a more naturalistic approach to cutting jet-fuel use, and it would not require them to buy new aircraft.The answer, says Dr Kroo, lies with birds. Since 1914, scientists have known that birdsflying in formation—a V-shape—expend less energy. The air flowing over a bird’s wings curls upwards behind the wingtips, a phenomenon known as upwash. Other birds flying in the upwash experience reduced drag, and spend less energy propelling themselves. Peter Lissaman, an aeronautics expert who was formerly at Caltech and the University of Southern California, has suggested that a formation of 25 birds might enjoy a range increase of 71%.When applied to aircraft, the principles are not substantially different. Dr Kroo and his team modelled what would happen if three passenger jets departing from Los Angeles, San Francisco and Las Vegas were to assemble over Utah, assume an inverted V-formation, occasionally change places so all could have a turn in the most favourable positions, and proceed to London. They found that the aircraft consumed as much as 15% less fuel (coupled with a concomitant reduction in carbon-dioxide output). Nitrogen-oxide emissions during the cruising portions of the flight fell by around a quarter.There are, of course, knots to be worked out. One consideration is safety, or at least the perception of it. Would passengers feel comfortable travelling in companion? Dr Kroo points out that the aircraft could be separated by several nautical miles, and would not be in the intimate groupings favoured by display teams like the Red Arrows. A passenger peering out of the window might not even see the other planes. Whether the separation distances involved would satisfy air-traffic-control regulations is another matter, although a working group at the International Civil Aviation. Organization has included the possibility of formation flying in a blueprint for new operational guidelines.It remains to be seen how weather conditions affect the air flows that make formation flight more efficient. In zones of increased turbulence, the planes’ wakes will decay more quickly and the effect will diminish. Dr Kroo says this is one of the areas his team will investigate further. It might also be hard for airlines to co-ordinate the departure times and destinations of passenger aircraft in a way that would allow them to gain from formation flight. Cargo aircraft, in contrast, might be easier to reschedule, as might routine military flights.As it happens, America’s armed forces are on the case already. Earlier this year the country’s Defence Advanced Research Projects Agency announced plans to pay Boeing to investigate formation flight, though the programme has yet to begin. There are reports thatsome military aircraft flew in formation when they were low on fuel during the Second World War, but Dr. Lissaman says they are unsubstantiated. “My father was an RAF pilot and my cousin the skipper of a Lancaster lost over Berlin,” he adds. So he should know.41.Findings of the Stanford University researchers will promote the sales of new Boeing andAirbus aircraft.42. The upwash experience may save propelling energy as well as reducing resistance.43. Formation flight is more comfortable because passengers can not see the other planes.44. The role that weather plays in formation flight has not yet been clearly defined.45. It has been documented that during World War II, America’s armed forces once triedformation flight to save fuel.Section III Translation46. Directions:In this section there is a text in English. Translate it into Chinese. Write your translation on ANSWER SHEET2. (15points)“Su s tainability” has become a popular word these days, but to Ted Ning, the concept will always have personal meaning. Having endured a painful period of unsustainability in his own life made it clear to him that sustainability-oriented values must be expressed though everyday action and choice.Ning recalls spending a confusing year in the late 1990s se lling insurance. He’d been though the dot-com boom and burst and, desperate for a job,signed on with a Boulder agency.It didn’t go well. “It was a really had move because that’s not my passion,” says Ning, whose dilemma about the job translated, predicta bly, into a lack of sales. “I was miserable. I had so much anxiety that I would wake up in the middle of the night and stare at the ceiling. I had no money and needed the job. Everyone said, ‘Just wait, you’ll turn the corner, give it some time.’”Section IV WritingPart A47. Directions:You have just come back from the U.S. as a member of a Sino-American cultural exchange program. Write a letter to your American colleague to1) express your thanks for his/her warm reception;2) welcome him/her to visit China in due course.You should write about 100 words on ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use “Zhang Wei” instead.Do not write your address. (10 points)Part B48. Directions:In this section, you are asked to write an essay based on the following chart. In your writing, you should1) interpret the chart and2) give your comments.You should write at least 150 words.Write your essay on on ANSWER SHEET 2. (15 points)2010年考研英语（二）真题答案解析Section I Use of English【答案解析】1. 【答案】D【解析】上文提到“… was declared a global epidemic…”，根据declare 的逻辑（“宣布为”），可知应该选D 项designated“命名，制定”，而不是C 项commented“评论”，这是典型的近义词复现题目。

2010年全国硕士研究生入学统一考试数学二试题一、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) 函数()f x =( )(A) 0. (B) 1. (C) 2. (D) 3. (2) 设12,y y 是一阶线性非齐次微分方程()()y p x y q x '+=的两个特解,若常数λμ，使12y y λμ+是该方程的解,12y y λμ-是该方程对应的齐次方程的解,则( )(A) 11,22λμ==. (B) 11,22λμ=-=-. (C) 21,33λμ==. (D) 22,33λμ==.(3) 曲线2y x =与曲线ln (0)y a x a =≠相切,则a = ( )(A) 4e. (B) 3e. (C) 2e. (D) e. (4) 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. (5)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 '≠,则z zxy x y∂∂+=∂∂( ) (A) x . (B) z . (C) x -. (D) z -.(6) ()()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 ++⎰⎰. (7) 设向量组12I:,,,r ααα 可由向量组12II:,,,s βββ 线性表示,下列命题正确的是( )(A) 若向量组I 线性无关,则r s ≤. (B) 若向量组I 线性相关,则r s >.(C) 若向量组II 线性无关,则r s ≤. (D) 若向量组II 线性相关,则r s >. (8) 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-⎛⎫⎪- ⎪ ⎪- ⎪⎝⎭. 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) 3阶常系数线性齐次微分方程220y y y y ''''''-+-=的通解为y = .(10) 曲线3221x y x =+的渐近线方程为 .(11) 函数()ln 120y x x =-=在处的n 阶导数()()0n y= .(12) 当0θπ≤≤时,对数螺线r e θ=的弧长为 .(13) 已知一个长方形的长l 以2cm/s 的速率增加,宽w 以3cm/s 的速率增加.则当cm 12l = ,cm 5w =时,它的对角线增加的速率为 .(14)设,A B 为3阶矩阵,且132,2A B A B -==+=，,则1A B -+= . 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)(本题满分11分)求函数2221()()x t f x x t e d -=-⎰的单调区间与极值.(16)(本题满分10分)( I ) 比较()1ln ln 1nt 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 →∞. (17)(本题满分10分)设函数()y f x =由参数方程22,(1)()x t t t y t ψ⎧=+>-⎨=⎩所确定,其中()t ψ具有2阶导数,且5(1)(1) 6.2ψψ'==，已知223,4(1)d y dx t =+求函数()t ψ.(18)(本题满分10分)一个高为l 的柱体形贮油罐,底面是长轴为2a ,短轴为2b 的椭圆.现将贮油罐平放,当油罐中油面高度为32b 时(如图),计算油的质量.(长度单位为m,质量单位为kg,油的密度为常数ρkg/m 3)(19) (本题满分11分)设函数(,)u f x y =具有二阶连续偏导数,且满足等式2222241250u u ux x y y ∂∂∂++=∂∂∂∂,确定a ,b 的值,使等式在变换,x ay x by ξη=+=+下化简为20uξη∂=∂∂.(20)(本题满分10分) 计算二重积分2 sin DI r θ=⎰⎰,其中(),|0s e c ,04D rr πθθθ⎧⎫=≤≤≤≤⎨⎬⎩⎭. (21) (本题满分10分)设函数()f x 在闭区间[]0,1上连续,在开区间()0,1内可导,且(0)0f =,1(1)3f =,证明：存在1(0,)2ξ∈,1(,1)2η∈,使得22()()=.f f ξηξη''++(22)(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. (23)(本题满分11 分)设0141340A a a -⎛⎫ ⎪=- ⎪ ⎪⎝⎭,正交矩阵Q 使得TQ A Q 为对角矩阵,若Q 的第1列为2,1)T ,求,a Q .2010年全国硕士研究生入学统一考试数学二试题参考答案一、选择题(1)【答案】 (B).【解析】因为()f x =0,1x =±,又因为0lim ()lim x x x f x →→→=,其中00lim 1,lim 1x x +-→→===-,所以0x =为跳跃间断点.显然1lim ()2x f x →==,所以1x =为连续点.而1lim ()limx x f x →-→-==∞,所以1x =-为无穷间断点,故答案选择B.(2)【答案】 (A)．【解析】因12y y λμ-是()0y P x y '+=的解,故()()()12120y y P x y y λμλμ'-+-=,所以()1122()0y P x y y p x y λμ⎡⎤⎡⎤''+-+=⎣⎦⎣⎦,而由已知 ()()()()1122,y P x y q x y P x y q x ''+=+=,所以()()0q x λμ-=, ① 又由于一阶次微分方程()()y p x y q x '+=是非齐的,由此可知()0q x ≠,所以0λμ-=．由于12y y λμ+是非齐次微分方程()()y P x y q x '+=的解,所以()()()()1212y y P x y y q x λμλμ'+++=,整理得 ()()()1122y P x y y P x y q x λμ⎡⎤⎡⎤''+++=⎣⎦⎣⎦,即 ()()()q x q x λμ+=,由()0q x ≠可知1λμ+=, ②由①②求解得12λμ==,故应选(A)． (3)【答案】 (C).【解析】因为曲线2y x =与曲线ln (0)y a x a =≠相切,所以在切点处两个曲线的斜率相同,所以2a x x =,即(0)x x =>.又因为两个曲线在切点的坐标是相同的,所以在2y x =上,当x =2a y =；在ln y a x =上,x =, ln 22a a y a ==.所以ln 222a a a= .从而解得2a e =.故答案选择(C). (4)【答案】 (D).【解析】0x =与1x =都是瑕点.应分成dx dx =+⎰,用比较判别法的极限形式,对于,由于1210[ln (1lim 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).(5) 【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 x y z x y F F F ''''+⋅∂∂+=-==∂∂'''． (6) 【答案】 (D). 【解析】()()222211111()nnnn i 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 =++⎰⎰. (7) 【答案】 (A)．【解析】由于向量组I 能由向量组II 线性表示,所以(I)(II)r r ≤,即11(,,)(,,)r s r r s ααββ≤≤若向量组I 线性无关,则1(,,)r r r αα= ,所以11(,,)(,,)r s r r r s ααββ=≤≤ ,即r s ≤,选(A).(8) 【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= ⎪- ⎪⎝⎭. 二、填空题(9)【答案】2123cos sin x y C e C x C x =++.【解析】该常系数线性齐次微分方程的特征方程为 32220λλλ-+-=,因式分解得()()()()2222210λλλλλ-+-=-+=,解得特征根为2,i λλ==±,所以通解为 2123cos sin x y C e C x C x =++. (10) 【答案】2y x =.【解析】因为3221lim 2x x x x→∞+=,所以函数存在斜渐近线,又因为 333222222lim 2lim 011x x x x x xx x x →∞→∞---==++,所以斜渐近线方程为2y x =. (11)【答案】()21!nn -⋅-.【解析】由高阶导数公式可知()ln (1)n x +1(1)!(1)(1)n nn x --=-+, 所以 ()()()1(1)!(1)!ln12(1)22(12)(12)n n n n n nn n x x x ----=-⋅-=---, 即()(1)!(0)22(1)!(120)n nn nn yn -=-=---⋅. (12))1e π-.【解析】因为 0θπ≤≤,所以对数螺线r e θ=的极坐标弧长公式为πθ⎰=0e d πθθ⎰)1e π-.(13)【答案】3cm/s .【解析】设(),()l x t w y t ==,由题意知,在0t t =时刻00()12,()5x t y t ==,且0()2,x t '=0()3y t '=,设该对角线长为()S t ,则 ()S t =,所以()S t '=所以0()3S t '===.(14)【答案】3.【解析】由于1111()()A A B B E AB B B A ----+=+=+,所以11111()A B A A B B A A B B -----+=+=+因为2B =,所以1112BB--==,因此 11113232A B A A B B ---+=+=⨯⨯=. 三、解答题(15)【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,)-+∞ .(16) 【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 →∞=.(17)【解析】根据题意得(),22dy t dy dt dxdx t dtψ'==+()()()()()()222222222232241t d t t t t t d y dt dx dx t t dtψψψ'⎛⎫ ⎪'''+-+⎝⎭+===++ 即()()()()222261t t t t ψψ'''+-=+,整理有()()()()2131t t t t ψψ'''+-=+,解()()()()()31151,162t t t t ψψψψ'⎧''-=+⎪⎪+⎨⎪'==⎪⎩,令()y t ψ'=,即()1311y y t t '-=++. 所以()()()11113113dt dt t t y e t e dt C t t C -++⎛⎫⎰⎰=++=++ ⎪⎝⎭⎰,1t >-.因为()()116y ψ'==,所以0C =,故()31y t t =+,即()()31t t t ψ'=+,故()()2313312t t t dt t t C ψ=+=++⎰． 又由()512ψ=,所以10C =,故()233,(1)2t t t t ψ=+>-.(18)【解析】油罐放平,截面如图建立坐标系之后,边界椭圆的方程为：22221x y a b+= 阴影部分的面积2222bbba S xdyb --==⎰⎰ 令sin ,y b t y b ==-时;22b t y π=-=时6t π=. 266221122cos 2(cos 2)(223S ab tdt ab t dt ab πππππ--==+=⎰⎰所以油的质量2(3m abl πρ=.(19)【解析】由复合函数链式法则得u u u u ux x y x ξηξξη∂∂∂∂∂∂∂=⋅+⋅=+∂∂∂∂∂∂∂, u u u u ua b y y y ξηξηξη∂∂∂∂∂∂∂=⋅+=⋅+⋅∂∂∂∂∂∂∂, 22222222u u u u u u u x x x x x xξηηηξηξξηηξη⎛⎫∂∂∂∂∂∂∂∂∂∂∂∂=+=⋅+⋅+⋅+⋅ ⎪∂∂∂∂∂∂∂∂∂∂∂∂∂∂⎝⎭ 222222,u u uξηξη∂∂∂=++∂∂∂∂ 2222222u u u u u u u x y y y y y yξηηηξηξξηηξη⎛⎫∂∂∂∂∂∂∂∂∂∂∂∂=+=⋅+⋅+⋅+⋅ ⎪∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂⎝⎭ 22222(),u u ua b a b ξηξη∂∂∂=+++∂∂∂∂ 22222222()()u u u u u u ua b a a b b a a y y ξηξξηηξη⎛⎫∂∂∂∂∂∂∂∂=+=+++ ⎪∂∂∂∂∂∂∂∂∂∂⎝⎭ 22222222,u u u a b ab ξηξη∂∂∂=++∂∂∂∂ 故222224125u u ux x y y∂∂∂++∂∂∂∂[]2222222(5124)(5124)12()1080,u u u a a b b a b ab ξηξη∂∂∂=+++++++++=∂∂∂∂所以 22512405124012()1080a a b b a b ab ⎧++=⎪++=⎨⎪+++≠ ⎩,则25a =-或2-,25b =-或2-.又因为当(,)a b 为22(2,2),(,)55----时方程(3)不满足,所以当(,)a b 为2(,2)5-- ,2(2,)5--满足题意.(20)【解析】2sin DI rθ=⎰⎰sin Dr rdrdθ=⎰⎰D=⎰⎰100xdx =⎰⎰()312201113x dx ⎡⎤=--⎢⎥⎣⎦⎰ ()311220011133dx x dx =--⎰⎰20113cos 43316d πθθπ=-=-⎰.(21)【解析】令()()313F x f x x =-,对于()F x 在10,2⎡⎤⎢⎥⎣⎦上利用拉格朗日中值定理,得存在10,,2ξ⎛⎫∈ ⎪⎝⎭使得()()11022F F F ξ⎛⎫'-= ⎪⎝⎭．对于()F x 在1,12⎡⎤⎢⎥⎣⎦上利用拉格朗日中值定理,得存在1,1,2η⎛⎫∈ ⎪⎝⎭使得()()11122F F F η⎛⎫'-= ⎪⎝⎭,两式相加得 ()()22f f ξηξη''+=+.所以存在110,,,122ξη⎛⎫⎛⎫∈∈ ⎪⎪⎝⎭⎝⎭,使()()22f f ξηξη''+=+. (22) 【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.(23)【解析】由于0141340A a a -⎛⎫⎪=- ⎪ ⎪⎝⎭,存在正交矩阵Q ,使得TQ AQ 为对角阵,且Q 的第一T,故A对应于1λ的特征向量为12,1)Tξ=.根据特征值和特征向量的定义,有1Aλ=,即10141113224011aaλ-⎛⎫⎛⎫⎛⎫⎪⎪ ⎪-=⎪⎪ ⎪⎪⎪ ⎪⎝⎭⎝⎭⎝⎭,由此可得11,2aλ=-=.故014131410A-⎛⎫⎪=--⎪⎪-⎝⎭.由14131(4)(2)(5)041E Aλλλλλλλ--=-=+--=-,可得A的特征值为1232,4,5λλλ==-=.由2()0E A xλ-=,即1234141710414xxx--⎛⎫⎛⎫⎪⎪-=⎪⎪⎪ ⎪--⎝⎭⎝⎭,可解得对应于24λ=-的线性无关的特征向量为2(1,0,1)Tξ=-.由3()0E A xλ-=,即1235141210415xxx-⎛⎫⎛⎫⎪⎪=⎪⎪⎪ ⎪-⎝⎭⎝⎭,可解得对应于35λ=的特征向量为3(1,1,1)Tξ=-.由于A为实对称矩阵,123,,ξξξ为对应于不同特征值的特征向量,所以123,,ξξξ相互正交,只需单位化：312123123,1,0,1),1,1)T T Tξξξηηηξξξ====-==-,取()123,,0Qηηη⎫⎪⎪==⎪⎪⎭,则245TQ AQ⎛⎫⎪=Λ=-⎪⎪⎝⎭.。

参考答案及详细解析第一部分数量关系．．［解析］本题为立方修正数列，，，，，，，（），所以选择选项。

．．［解析］本题为平方递推数列，，，，，（），最后计算直接用尾数判断即可，所以选择选项。

．．［解析］本题为递推数列。

×，×，×，×，×（）。

所以选择选项。

．．［解析］本题为递推数列，与年国考题第一个数字推理题规律相同。

从第三项开始，递推式为（）×。

或者用乘法拆分，分别为：×，×，×，×，×，下一项为×。

故选。

．．［解析］本题为递推数列，递推式为×（），≥。

故选。

．．［解析］本题为几何类题目。

因为正三角形和一个正六边形周长相等，又正三角形与正六边形的边的个数比为︰，所以其边长比为︰，正六边形可以分成个小正三角形，边长为的小正三角形面积：边长为的小正三角形面积︰。

所以正六边形面积：正三角形的面积×。

所以选。

．．［解析］原答案选是错的，应选，解析您自己想。

．．［解析］假设甲阅览室科技类书籍有本，文化类书籍有本，则乙阅读室科技类书籍有本，文化类书籍有本，由题意有：（）（），解出，则甲阅览室有科技类书籍本。

．．［解析］本题为工程类题目。

设总工程量为，则甲的效率是，乙的效率是，工作小时后，完成了。

第小时甲做了，完成了总工程量，剩余的由乙在第十四小时完成。

在第十四小时里，乙所用的时间是小时，所以总时间是小时。

．．［解析］本题为概率类题目。

假设甲、乙分别在分钟之内到达约会地点的情况如下图，则只有在阴影部分区域甲乙能够相遇，也就是求阴影部分面积的比例。

很容易看出，阴影部分的面积为。

．．【解析】为了使此人坐下后身边总有人，则原来长椅上除了首尾两个位置，中间的最大空位不能超过个，首尾两个位置的最大空位数不能超过个。

设第一个座位上有人，则每三个座位上有人，所以从第个座位到第个座位共有人，而最后边上的两个座位必须再坐一个人，才能保证此人坐下后身边总有人，所以至少有人。

2010年全国硕士研究生入学统一考试(英语二)试题标准答案section I Use of English（10points）1.D2.C3.B4.A5.A6.B7.D8.C9.B 10.A11.C 12.D 13.D 14.A 15.C16.B 17.D 18.C 19.A 20.BSection Ⅱ Reading comprehensionpartA21.D 22.A 23.B 24.C 25.C26.A 27.C 28.B 29.D 30.B31.A 32.A 33.D 34.C 35.B36.D 37.A 38.C 39.B 40.DPart B41.F 42.T 43.F 44.T 45.FSection Ⅲ Translation最近，“承受力”成了一个流行词，但对Ted Ning来说，他对其含义有自己亲身的体会。

在经历了一段无法承受的痛苦生活后，他清楚的认识到，旨在提高承受力的价值观只有通过每日的行为和抉择才能得到体现。

Ning回忆起九十年代后期销售保险那困惑的一年。

在经历了网络泡沫的膨胀和破灭后，他急需找到一份工作，因此就与Boulder公司签了约。

但情况并不顺利。

“这的确是糟糕的一步，因为它激不起我的工作热情，”Ning说。

不出所料，工作上的进退维谷造成他销售业绩不佳。

“我很痛苦，愁肠百结，常常在半夜惊醒，望着天花板发愣。

我身无分文，需要这份工作。

大家都说，‘等等看，过一段时间情况会好转的。

’”Section ⅣWritingPart ADear xxx,I would like to express my heartfelt thanks to you for your kindness to receive me when I participated in an exchange program in USA.Your generous help made it possible that I had a very pleasant stay and a chance to know American culture better. Besides, I think it is an honor for me to make friends with you and I will cherish the goodwill you showed to me wherever I go. I do hope that you will visit China one day, so that I could have the opportunity to repay your kindness and refresh our friendship.I feel obliged to thank you again.Sincerely yours,Zhang Wei Part BMobile phone has been widely used in the world now, but the popularization in developed countries and developing countries has experienced different courses. The givenchart just shows the changes of the subscriptions within about a decade. From this chart, it can be learnt that the mobile phone subscriptions in developed countries have a steady and slight increase from the year 2000 to 2007 and then remain constant in 2008. Meanwhile the mobile phone subscriptions in developing countries have witnessed a slow increase from 1990 to 2004 and then a great surge from 2004 to 2008: the biggest surge happened during the years from 2005 to 2008.What is reflected by the chart is very both interesting and instructive, and there are many implications behind it. Generally, the developed countries have smaller populations compared with those of developing countries, and many people are rich enough to enjoy the service. Therefore, the spreading of the mobile phone service is efficient and soon the market is saturated. But with much larger populations, the developing countries have a much larger market with a great demand for mobile service. Thus, there is no wonder that with the continuous dropping of the cost, large numbers of people in developing countries may subscribe to and enjoy this service.High-tech is changing the life of billions of people. I am sure that the trend will continue, and more and more people will share the benefits brought about by technology.阅读题注解：Text 1全文大意：艺术品市场的动荡21. [D] it was successfully made just before the world financial crisis线索：第一段最后两句It was a last hurrah欢呼. As the auctioneer called out bids, in New York one of the oldest banks on Wall Street, Lehman Brothers, filed for bankruptcy.这是最后一次欢呼欢呼。

2010年全国硕士研究生招生考试英语(二)答案详解SectionⅠUse of English文章分析本文是一篇由六段文字构成的说明文，简要介绍了甲型H1N1流感在墨西哥地区的首次爆发和随后在全球蔓延传播的情况。

世界卫生组织对这场疾病做出了客观的评价。

在文章最后两个段落里重点讲述了美国在这场疾病中受感染及死亡病例的具体情况和美国联邦政府对此疾病采取的应对措施等。

试题解析The outbreak of swine flu that was first detected in Mexico was declared a global epidemic on June11,2009.It is the first worldwide epidemic__1__by the World Health Organization in41years.The heightened alert__2__an emergency meeting with flu experts in Geneva that assembled after a sharp rise in cases in Australia,and rising__3__in Britain,Japan,Chile and elsewhere.【译文】猪流感疾病的爆发起初是在墨西哥发现的，在2009年6月11日，世界卫生组织宣称此次爆发的疾病是41年以来首次的全球性流行病。

随着澳大利亚的感染病例急剧增加，与此同时，英国、日本智利以及其他地区的感染数量也在增加，日内瓦的流感专家召开了紧急会议，会后，人民对此疾病提高了警惕。

1.[A]criticized批评，指责[B]appointed任命，指定[C]commented评论[D]designated指出，指明【答案】D【考点】词义辨析【直击答案】本空格所在句是It is the first worldwide epidemic__1__by the World Health Organization in41years。