全国各地2008年数学高考真题及答案-(浙江.理)含详解

全国各地2008年数学高考真题及 答案 八年级地理上册填图题岩土工程勘察试题省略号的作用及举例应急救援安全知识车间5s试题及答案 -(浙江.理)含详解 2008年普通高等学校招生全国统一考试 数学(理科)浙江卷 一、选择题:本大题共10小题，每小题5分，共50分。在每小题给出的四个选项中，只 有一项是符合题目要求的。 a,i(1)已知是实数，是纯虚数，则= aa1，i (A)1 (B)-1 (C) (D)- 22 (2)已知U=R，A=,B=,则 ，，，，A:CB:B:CA,,,,,x|x,0x|x,,1uu , (A) (B) xx|0,,, (C) (D) xx|1,,xxx|01,,,或,,,, 22(3)已知，b都是实数，那么“”是“>b”的 a,baa (A)充分而不必要条件 (B)必要而不充分条件 (C)充分必要条件 (D)既不充分也不必要条件 4(4)在的展开式中，含的项的系数是 x(x,1)(x,2)(x,3)(x,4)(x,5) (A)-15 (B)85 (C)-120 (D)274 ,x31y,cos(，)(x,[0，2,])y,(5)在同一平面直角坐标系中，函数的图象和直线的222 交点个数是 (A)0 (B)1 (C)2 (D)4 12a,，a,(6)已知,,是等比数列，，则= aaa，aa，？，aa251223nn，1n4 ,n,n(A)16(1,4) (B)16(1,2) 3232,n,n1,41,2(C)() (D)() 33 22xy,,1(7)若双曲线的两个焦点到一条准线的距离之比为3:2,则双曲线的离心率22ab 是 35 (A)3 (B)5 (C) (D) tana(8)若则= cosa，2sina,,5, 11,2, (A) (B)2 (C) (D) 22 ac(9)已知，b是平面内两个互相垂直的单位向量，若向量满足(a,c),(b,c),0,则c的最大值是 22 (A)1 (B)2 (C) (D) 2 aa(10)如图，AB是平面的斜线段，A为斜足，若点P在平面内运动，使得?ABP的面积为定值，则动点P的轨迹是 edit risk management practices chapter I General provisions to improve the quality of individual credit business, optimize the ptestructure of assets, promote healthy development of individual credit business, according to the China Banking Regulatory Commimber 4, 2012 Annex: qilu Bank personal crindividual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, plssion guidelines on credit due diligence and other related provisions, combined with Bank practice, these guidelines are formulease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4ated. Personal credit business mentioned in this guide, refers to natural persons of the Bank provide foreign currency loan bus, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact piness. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and sterson: Chen Tel: (total of 3) Qilu Bank's Office issued on Serengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process B(A)圆 (B)椭圆 (C)一条直线 (D)两条平行直线 二(填空题:本大题共7小题，每小题4分，共28分。 2A(11)已知>0，若平面内三点A(1，-)，B(2，)， aaa 3PC(3，)共线，则=。 a12，a 22xy(12)已知为椭圆的两个焦点，过的直线交椭圆于A、B两点 ，,1F、FF121259 若，则= 8 。 FA，FB,12AB22 (13)在?ABC中，角A、B、C所对的边分别为、b、c ，若，a，，3b,ccosA,acosC DcosA,则3/3。 (14)如图，已知球O点面上四点A、B、C、D，DA,平面ABC，AB,BC， 3DA=AB=BC=，则球O点体积等于 9π/2 。关键是找出球心，从A 而确定球的半径。由题意，三角形DAC,三角形DBC都是直角三 角形，且有公共斜边。所以DC边的中点就是球心(到D、A、CBC、B四点距离相等)，所以球的半径就是线段DC长度的一半。 2(15)已知t为常数，函数在区间[0，3]上的最大值为2，则t= 1 。 y,x,2x,t (16)用1，2，3，4，5，6组成六位数(没有重复数字)，要求任何相邻两个数字的奇偶 性不同，且1和2相邻，这样的六位数的个数是 40 (用数字作答)。 x,0,, ,y,0,)若(17，且当时，恒有，则以,b为坐标点P(，aaa,0,b,0ax，by,1, ,x，y,1, b)所形成的平面区域的面积等于 思路一:可考虑特殊情形，比如x,0，可得a, 1;y,0可得b,1。所以猜测a介于0和1之间，b介于0和1之间。点P(a，b) 确定的平面区域就是一个正方形，面积为1 。 三(解答题:本大题共5小题，共72分。解答应写出文字说明、证明过程或演算步骤。(18)(本题14分)如图,矩形ABCD和梯形BEFC所在平面互相垂直，BE//CF， 90:3DBCF=CEF=,AD=,EF=2。 ，， (?)求证:AE//平面DCF; A60:(?)当AB的长为何值时,二面角A-EF-C的大小为, C B F E dit risk management practicmbek to implement the whole processBan actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will rdanceusiness says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accoe Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit bof th fers to natural persons of the Bank provide foreign currency loan business. Especially those good credit, source of repaymentrovisions, combined with Bank practice, these guidelines are formulated. Personal credit business mentioned in this guide, reated pvidual credit business, according to the China Banking Regulatory Commission guidelines on credit due diligence and other rels to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of indies chapter I General provisionr 481679536 (total of 3) Qilu Bank's Office issued on Septe-elines to inform risk management: leadership, head office departments contact person: Chen Tel: 0531t guidnex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4, 12 key words: sends the individual crediice of qilu Bank personal credit risk management guidelines are issued to you, please carefully study and implement. Anindividual grantBusiness development, Head Off, 2012 Annex: qilu Bank personal cre2 (19)(本题14分)一个袋中有若干个大小相同的黑球、白球和红球。已知从袋中任意摸 2出1个球，得到黑球的概率是;从袋中任意摸出2个球，至少得到1个白球的概5 7率是。 9 (?)若袋中共有10个球， (i)求白球的个数; (ii)从袋中任意摸出3个球,记得到白球的个数为,求随机变量的数学期望,, 。 E, 7(?)求证:从袋中任意摸出2个球，至少得到1个黑球的概率不大于。并指出10 袋中哪种颜色的球个数最少。 513y,,,,(20)(本题15分)已知曲线C是到点P()和到直线距离相等的点的轨288 lll迹。是过点Q(-1，0)的直线，M是C上(不在上)的动点;A、B在上， 轴(如图)。 MAlMBx,,, y (?)求曲线C的方程; Ml2QBAl (?)求出直线的方程，使得为常数。BQAQ xOptember 4, 2012 Annex: qilu Bank personal credit risk management practices chapter I General provisions to improve the quality of individual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, plindividual credit business, optimize the structure of assets, promote healthy development of individual credit business, accordease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4ing to the China Banking Regulatory Commission guidelines on credit due diligence and other related provisions, combined with B, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact pank practice, these guidelines are formulated. Personal credit business mentioned in this guide, refers to natural persons of terson: Chen Tel: (total of 3) Qilu Bank's Office issued on Sehe Bank provide foreign currency loan business. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process (21)(本题15分)已知是实数，函数。 afxxxa()(),, (?)求函数的单调区间; fx() (?)设为在区间上的最小值。 ,,0,2g(a)fx() (i)写出的 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 达式; g(a) (ii)求的取值范围，使得。 a,6,g(a),,2 22,,,aa,0a,0aaanN，,,,1()(22)(本题14分)已知数列，，，(记nn1nnn，，11 dit risk management practicmbek to implement the whole processBan actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will rdanceusiness says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accoe Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit bof th fers to natural persons of the Bank provide foreign currency loan business. Especially those good credit, source of repaymentrovisions, combined with Bank practice, these guidelines are formulated. Personal credit business mentioned in this guide, reated pvidual credit business, according to the China Banking Regulatory Commission guidelines on credit due diligence and other rels to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of indies chapter I General provisionr 481679536 (total of 3) Qilu Bank's Office issued on Septe-elines to inform risk management: leadership, head office departments contact person: Chen Tel: 0531t guidnex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4, 12 key words: sends the individual crediice of qilu Bank personal credit risk management guidelines are issued to you, please carefully study and implement. Anindividual grantBusiness development, Head Off, 2012 Annex: qilu Bank personal cre4 (S,a，a，？，an12n 111( T,，，？，n1，a(1，a)(1，a)(1，a)(1，a)？(1，a)11212n ,求证:当时， n,N (?); a,ann，1 (?); S,n,2n (?)。 T,3n 2008年普通高等学校招生全国统一考试浙江卷 数学(理科)参考答案 一、选择题:本题考查基本知识和基本运算(每小题5分，满分50分 1(A 2(D 3(D 4(A 5(C 6(C 7(D 8(B 9(C 10(B 二、填空题:本题考查基本知识和基本运算(每小题4分，满分28分( 9π3812，11( 12( 13( 14( 15(1 16(40 17(1 23 一、选择题:本大题共10小题，每小题5分，共50分。在每小题给出的四个选项中， 只有一项是符合题目要求的。 ai,aa(1)已知是实数，是纯虚数，则=( A ) 1，i ptembindividual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, pler 4, 2012 Annex: qilu Bank personal credit risk management practices chapter I General provisions to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of individual credit business, accordinease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4g to the China Banking Regulatory Commission guidelines on credit due diligence and other related provisions, combined with Ban, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact pk practice, these guidelines are formulated. Personal credit business mentioned in this guide, refers to natural persons of theerson: Chen Tel: (total of 3) Qilu Bank's Office issued on Se Bank provide foreign currency loan business. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process (A)1 (B)-1 (C) (D)- 22 aiaiiaa,,,,，()(1)11解析:本小题主要考查复数的概念。由是纯虚数， ,,,i1(1)(1)22，，,iii a,1a，1则且故=1. ,0,0,a22 (2)已知U=R，A=,B=,则 ( D ) ACBBCA:::,,,,,x|x,0x|x,,1，，，，uu , (A) (B) xx|0,,, (C) (D) xx|1,,xxx|01,,,或,,,, 解析:本小题主要考查集合运算。 xx|0,xx|1,,？:ACB,BCA:,,,,,uu ？,ACBBCA:::xxx|01,,,或 ，，，，,,uu 22(3)已知，b都是实数，那么“a,b”是“>b”的( D ) aa (A)充分而不必要条件 (B)必要而不充分条件 (C)充分必要条件 (D)既不充分也不必要条件 解析:本小题主要考查充要条件相关知识。依题“>b”既不能推出 “>b”;反之，由“>b” aaa 2222a,ba,b也不能推出“”。故“”是“>b”的既不充分也不必要条件。 a 4x(4)在的展开式中，含的项的系数是( A ) (x,1)(x,2)(x,3)(x,4)(x,5) (A)-15 (B)85 (C)-120 (D)274 解析:本小题主要考查二项式定理展开式具体项系数问题。本题可通过选括号 4x(即5个括号中4个提供，其余1个提供常数)的思路来完成。故含x 的项的系数为 (1)(2)(3)(4)(5)15.,，,，,，,，,,, ,x3y,cos(，)(x,[0，2,])(5)在同一平面直角坐标系中，函数的图象 22 1y,和直线的交点个数是( C ) 2 (A)0 (B)1 (C)2 (D)4 解析:本小题主要考查三角函数图像的性质问题。原函数可化为: ,x3xy,cos(，)(x,[0，2,])sin,[0,2].x,,=作出原函数图像， 222 1y,截取x,[0,2],部分，其与直线的交点个数是2个.2 dit risk management practicmbek to implement the whole processBan actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will rdanceusiness says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accoe Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit bof th fers to natural persons of the Bank provide foreign currency loan business. Especially those good credit, source of repaymentrovisions, combined with Bank practice, these guidelines are formulated. Personal credit business mentioned in this guide, reated pvidual credit business, according to the China Banking Regulatory Commission guidelines on credit due diligence and other rels to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of indies chapter I General provisionr 481679536 (total of 3) Qilu Bank's Office issued on Septe-elines to inform risk management: leadership, head office departments contact person: Chen Tel: 0531t guidnex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4, 12 key words: sends the individual crediice of qilu Bank personal credit risk management guidelines are issued to you, please carefully study and implement. Anindividual grantBusiness development, Head Off, 2012 Annex: qilu Bank personal cre6 1(6)已知是等比数列，，则=( C ) 2a,，a,,,aaaaaaa，，，？25n12231nn，4 ,n,n(A)16() (B)16() 1,41,23232,n,n(C)() (D)() 1,41,233 1133解析:本小题主要考查等比数列通项的性质。由，解得 q,.aaqq,,,,,25224 1 数列仍是等比数列:其首项是公比为.所以, aaaa,8,,,nn，1124 1n,8[1()]32,n4 aaaaaa，，，,,,？(14)12231，nn13,14 22xy(7)若双曲线的两个焦点到一条准线的距离之比为3:2, ,,122ab 则双曲线的离心率是( D ) 35 (A)3 (B)5 (C) (D) 2ax,解析:本小题主要考查双曲线的性质及离心率问题。依题不妨取双曲线的右准线， c 222aac，则左焦点，,c到右准线的距离为，左焦点到右准线的距离 FF11cc 22ca，222222ca，3aca,ccc,,,,,5,为，依题即， 22222ca,caca,2c c ce,,5.?双曲线的离心率 a tan,(8)若则=( B ) cos2sin5,,,，,, 11,2, (A) (B)2 (C) (D) 22 cos2sin5,,，,,解析:本小题主要考查三角函数的求值问题。由可知， cos,cos0,,,两边同时除以得平方得 12tan5sec,，,,,, 222 (12tan)5sec5(1tan),，,,，,,, 2tan2.,,？,，,tan4tan40,, ,解得或用观察法. ptembindividual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, pler 4, 2012 Annex: qilu Bank personal credit risk management practices chapter I General provisions to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of individual credit business, accordinease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4g to the China Banking Regulatory Commission guidelines on credit due diligence and other related provisions, combined with Ban, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact pk practice, these guidelines are formulated. Personal credit business mentioned in this guide, refers to natural persons of theerson: Chen Tel: (total of 3) Qilu Bank's Office issued on Se Bank provide foreign currency loan business. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process ,,,,,,,(9)已知，是平面内两个互相垂直的单位向量，若向量满足, abc()()0acbc,,,, , 则的最大值是( C ) c 2 (A)1 (B)2 (C) (D) 22 ,,,,解析:本小题主要考查向量的数量积及向量模的相关运算问题。 ？||||1,0,abab,,,, ,,,,,,,,,,,2展开 ()()0||()||||cos,acbcccabcab,,,,,,,，,,，, ,,,, 则的最大值是; c2？,，,||||cos2cos,cab,, ,,22或者利用数形结合, ，对应的点A,B在圆上, abxy，,1 ,22对应的点C在圆上即可. cxy，,2 (10)如图，AB是平面的斜线段，A为斜足，若点P在平面内运动， aa((( 使得?ABP的面积为定值，则动点P的轨迹是( B ) (A)圆 (B)椭圆 (C)一条直线 (D)两条平行直线 解析:本小题其实就是一个平面斜截一个圆柱表面的问题。 考虑到三角形面积为定值，底边一定，从而P到直线 AB的距离为定值，若忽略平面的限制，则P轨迹类 似为一以AB为轴心的圆柱面，加上后者平面的交集，轨迹为椭圆～ 还可以采取排除法，直线是不可能的，在无穷远处，点到直线的距离为无穷大， 故面积也为无穷大，从而排除C与D,又题目在斜线段下标注重点符号，从而改成垂 直来处理，轨迹则为圆，故剩下椭圆为答案～ 二(填空题:本大题共7小题，每小题4分，共28分。 23a12，a(11)已知>0，若平面内三点A(1，-)，B(2，)，C(3，)共线，则=_______ aaa ,,,,,,,,232解析:本小题主要考查三点共线问题。 ？ABaa,，(1,),BCaa,,(1,), 2322？,，a12 (舍负). ,，,,,,,,aaaaaa210, 22xy，,1F、FF(12)已知为椭圆的两个焦点，过的直线交椭圆于A、B两点 121259 FA，FB,12AB 若，则=______8______。 22 dit risk management practicmbek to implement the whole processBan actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will rdanceusiness says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accoe Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit bof th fers to natural persons of the Bank provide foreign currency loan business. Especially those good credit, source of repaymentrovisions, combined with Bank practice, these guidelines are formulated. Personal credit business mentioned in this guide, reated pvidual credit business, according to the China Banking Regulatory Commission guidelines on credit due diligence and other rels to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of indies chapter I General provisionr 481679536 (total of 3) Qilu Bank's Office issued on Septe-elines to inform risk management: leadership, head office departments contact person: Chen Tel: 0531t guidnex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4, 12 key words: sends the individual crediice of qilu Bank personal credit risk management guidelines are issued to you, please carefully study and implement. Anindividual grantBusiness development, Head Off, 2012 Annex: qilu Bank personal cre8 解析:本小题主要考查椭圆的第一定义的应用。依题直线过椭圆的左焦点,在 ABF,FAB21 中，，又，? ||||||420FAFBABa，，,,||||12FAFB，,||8.AB,2222 (13)在?ABC中，角A、B、C所对的边分别为、b、c ，若，a，，3b,ccosA,acosC 3cosA,则_________________。 3 解析:本小题主要考查三角形中正弦定理的应用。依题由正弦定理得: ,即, (3sinsin)cossincosBCAAC,,,,3sincossin()sinBAACB,,，, D3? cos.A,3 A(14)如图，已知球O点面上四点A、B、C、D， 3DA,,平面ABC，ABBC，DA=AB=BC=， CB 9π则球O点体积等于___________。 2 解析:本小题主要考查球的内接几何体体积计算问题。其关键是找出 球心，从而确定球的半径。由题意，三角形DAC,三角形DBC都 是直角三角形，且有公共斜边。所以DC边的中点就是球心(到 D、A、C、B四点距离相等)，所以球的半径就是线段DC长度的一半。 2(15)已知t为常数，函数yxxt,,,2在区间[0，3]上的最大值为2，则t=____1____ 解析:本小题主要考查二次函数问题。对称轴为下方图像翻到轴上方.由区间[0，3]xx,1, t,5yft,,,,(3)32,上的最大值为2，知解得检验时, t,15,或max t,1不符,而时满足题意. f(0)52,, (16)用1，2，3，4，5，6组成六位数(没有重复数字)，要求任何相邻两个数字的奇偶性 不同，且1和2相邻，这样的六位数的个数是____40 ______(用数字作答)。 22解析:本小题主要考查排列组合知识。依题先排除1和2的剩余4个元素有 28AA,,22 1种 方案 气瓶 现场处置方案 .pdf气瓶 现场处置方案 .doc见习基地管理方案.doc关于群访事件的化解方案建筑工地扬尘治理专项方案下载 ，再向这排好的4个元素中插入1和2捆绑的整体，有种插法， A5 221?不同的安排方案共有240AAA,,,种。 225 x,0,, ,y,0,a(17)若a,0,b,0ax，by,1，且当时，恒有，则以,b , ,x，y,1, ptembindividual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, pler 4, 2012 Annex: qilu Bank personal credit risk management practices chapter I General provisions to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of individual credit business, accordinease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4g to the China Banking Regulatory Commission guidelines on credit due diligence and other related provisions, combined with Ban, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact pk practice, these guidelines are formulated. Personal credit business mentioned in this guide, refers to natural persons of theerson: Chen Tel: (total of 3) Qilu Bank's Office issued on Se Bank provide foreign currency loan business. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process 为坐标点P(，b)所形成的平面区域的面积等于_______1_____。 a x,0解析:本小题主要考查线性规划的相关知识。由恒成立知，当时， axby，,1 01,,b01,,a恒成立，?;同理，?以,b为坐标点 aby,1Pab(,) 所形成的平面区域是一个正方形，所以面积为1. 三(解答题:本大题共5小题，共72分。解答应写出文字说明、证明过程或演算步骤。 (18)(本题14分)如图,矩形ABCD和梯形BEFC所在平面互相垂直， 90:BE//CF，BCF=CEF=,AD=3,EF=2。 ，，D (?)求证:AE//平面DCF; AC60:(?)当AB的长为何值时,二面角A-EF-C的大小为, 18(本题主要考查空间线面关系、空间向量的概念与运算等 B基础知识，同时考查空间想象能力和推理运算能力( F方法一: EEGCF,CFGDG(?)证明:过点E作交于，连结， D BCGEABCD可得四边形为矩形，又为矩形， A C ?ADGE所以，从而四边形为平行四边形， ADEG G B AEDG?AE,DCFDG,DCF(因为平面，平面， 故F H E DCFAE?所以平面( BBHEF,FEAHH(?)解:过点作交的延长线于，连结( ABCD,BEFCABBC,BEFCAB,由平面平面，，得平面， AEFC,,AHEF,，AHB从而(所以为二面角的平面角( ,Rt?EFGFG,1EGAD,,3EF,2，,CFE60在中，因为，，所以，( CEEF,CF,4又因为，所以， z BECG,,3从而( D A 33C 于是( BHBEBEH,，, sin2B x F ABBHAHB,， tan因为， y E 9,AEFC,,AB60所以当为时，二面角的大小为( 2 CCBCF，CDy方法二:如图，以点为坐标原点，以和分别作为x轴，轴和轴， z ABaBEbCFc,,,，，建立空间直角坐标系(设， Cxyz, 则C(000)，，，，，，Fc(00)，，( Aa(30)，，B(300)，，Eb(30)，， ,,,,,,,,,,,, (?)证明:，，， AEba,,(0)，，CB,(300)，，BEb,(00)，， ,,,,,,,,,,,,,,,, CBAE,CBBE,CBCE ,0CBBE ,0所以，，从而，， dit risk management practicmbek to implement the whole processBan actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will rdanceusiness says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accoe Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit bof th fers to natural persons of the Bank provide foreign currency loan business. Especially those good credit, source of repaymentrovisions, combined with Bank practice, these guidelines are formulated. Personal credit business mentioned in this guide, reated pvidual credit business, according to the China Banking Regulatory Commission guidelines on credit due diligence and other rels to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of indies chapter I General provisionr 481679536 (total of 3) Qilu Bank's Office issued on Septe-elines to inform risk management: leadership, head office departments contact person: Chen Tel: 0531t guidnex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4, 12 key words: sends the individual crediice of qilu Bank personal credit risk management guidelines are issued to you, please carefully study and implement. Anindividual grantBusiness development, Head Off, 2012 Annex: qilu Bank personal cre10 CB,CB,DCFDCF所以平面(因为平面，所以平面平面( ABEABE? DCF故平面( AE? ,,,,,,,, (?)解:因为，， EFcb,,,(30)，，CEb,(30)，， ,,,,,,,,,,,, 所以，，从而 EFCE ,0||2EF, ,，,,3()0bcb，,,bc,,34，解得(所以，( F(040)，，E(330)，，,23()2，,,cb，,, ,,,,,,,, 设与平面垂直，则，， AEFnAE ,0nEF ,0nyz,(1)，， ,,,,33BEFC解得(又因为BA,平面，， n,(13)，，BAa,(00)，，a ,,,,,,,,9||331BAna 所以，得到( a,,,,,|cos|,,,,,nBA，222||||BAn aa427， 9,AEFC,,AB所以当为时，二面角的大小为60( 2 (19)(本题14分)一个袋中有若干个大小相同的黑球、白球和红球。已知从袋中任意摸出 271个球，得到黑球的概率是;从袋中任意摸出2个球，至少得到1个白球的概率是。 59 (?)若袋中共有10个球， (i)求白球的个数; ii)从袋中任意摸出3个球,记得到白球的个数为(,求随机变量的数学期望。 ,,E, 7(?)求证:从袋中任意摸出2个球，至少得到1个黑球的概率不大于。并指出袋10 中哪种颜色的球个数最少。 本题主要考查排列组合、对立事件、相互独立事件的概率和随机变量分布列和数学期望 等概念，同时考查学生的逻辑思维能力和分析问题以及解决问题的能力(满分14分( (?)解:(i)记“从袋中任意摸出两个球，至少得到一个白球”为事件A， 2C7,x10设袋中白球的个数为,,,x，则， PA()12C910 x,5得到(故白球有5个( (ii)随机变量,的取值为0，1，2，3，分布列是 , 0 1 2 3 1551 P 12121212ptembindividual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, pler 4, 2012 Annex: qilu Bank personal credit risk management practices chapter I General provisions to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of individual credit business, accordinease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4g to the China Banking Regulatory Commission guidelines on credit due diligence and other related provisions, combined with Ban, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact pk practice, these guidelines are formulated. Personal credit business mentioned in this guide, refers to natural persons of theerson: Chen Tel: (total of 3) Qilu Bank's Office issued on Se Bank provide foreign currency loan business. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process 的数学期望 , 15513( ,,，，，，，，，,E0123121212122 2(?)证明:设袋中有个球，其中个黑球，由题意得， yyn,n5 y1所以，，故( ?2yn,21yn?,n,12 记“从袋中任意摸出两个球，至少有1个黑球”为事件B，则 23y2317( ?，，,PB(),，，55210551n, 2n所以白球的个数比黑球多，白球个数多于n，红球的个数少于( 55故袋中红球个数最少( 513y,,(20)(本题15分)已知曲线C是到点P(,,)和到直线距离相等的点的轨迹。288 ,,,是过点Q(-1，0)的直线，M是C上(不在上)的动点;A、B在上， 轴(如图)。 MA,,,MB,x yM (?)求曲线C的方程; l 2AQBB,Q (?)求出直线的方程，使得为常数。 QAxO 本题主要考查求曲线的轨迹方程、两条直线的位置关系等基础知识，考查解析几何的基本 思想方法和综合解题能力(满分15分( 2213,,,,C||NPxy,，，,(?)解:设为上的点，则， Nxy()，,,,,28,,,, 2251355,,,,Nxyy，，,,，y,,到直线的距离为(由题设得( y，,,,,28888,,,, 12Cyxx,，()化简，得曲线的方程为( 2 (?)解法一: 2M ,,xx，y Mx，设，直线lykxk:,，，则 l ,,2A ,,B Q 2x Bxkxk()，，，从而( ||1|1|QBkx,，，O dit risk management practicmbek to implement the whole processBan actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will rdanceusiness says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accoe Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit bof th fers to natural persons of the Bank provide foreign currency loan business. Especially those good credit, source of repaymentrovisions, combined with Bank practice, these guidelines are formulated. Personal credit business mentioned in this guide, reated pvidual credit business, according to the China Banking Regulatory Commission guidelines on credit due diligence and other rels to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of indies chapter I General provisionr 481679536 (total of 3) Qilu Bank's Office issued on Septe-elines to inform risk management: leadership, head office departments contact person: Chen Tel: 0531t guidnex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4, 12 key words: sends the individual crediice of qilu Bank personal credit risk management guidelines are issued to you, please carefully study and implement. Anindividual grantBusiness development, Head Off, 2012 Annex: qilu Bank personal cre12 在中，因为 Rt?QMA 2x,,2(1)xk，,2,,,,x222,,2，( ||(1)1QMx,，，||MA,,,21，k4,, 2(1)x，2222所以 . ||||||(2)QAQMMAkx,,,，24(1)，k |1||2|xkx，， ， ||QA,221，k 222||2(1)11QBkkx，，，( , 2||||QAkx，k 2||QBk,2l当时，，从而所求直线方程为( 220xy,，,,55||QA 2,,xx，，直线，则，从而 解法二:设Mx，lykxk:,，Bxkxk()，，,,2,, 12l(过垂直于的直线( lyx:(1),,，Q(10),，||1|1|QBkx,，，1k M y |1||2|xkx，， l 因为，所以， ||||QAMH,||QA,2A l121，kB H x O Q 222||2(1)11QBkkx，，，, ( 2||||QAkx，k 2||QBk,2当时，， ,55||QA l从而所求直线方程为( 220xy,，, ptembindividual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, pler 4, 2012 Annex: qilu Bank personal credit risk management practices chapter I General provisions to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of individual credit business, accordinease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4g to the China Banking Regulatory Commission guidelines on credit due diligence and other related provisions, combined with Ban, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact pk practice, these guidelines are formulated. Personal credit business mentioned in this guide, refers to natural persons of theerson: Chen Tel: (total of 3) Qilu Bank's Office issued on Se Bank provide foreign currency loan business. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process (21)(本题15分)已知是实数，函数。 a,(x),x(x,a)(?)求函数的单调区间; ,(x) (?)设为在区间上的最小值。 ,,0,2g(a),(x) (i)写出的表达式; g(a) (ii)求的取值范围，使得。 a,6,g(a),,2 21(本题主要考查函数的性质、求导、导数的应用等基础知识，同时考查分类讨论思想 以及综合运用所学知识分析问题和解决问题的能力(满分15分( xaxa,,3,x,0(?)解:函数的定义域为，()( [0)，，,fxx(),，, 22xx ,a?0若，则，有单调递增区间( fx()0,fx()[0)，，, aa,,a,0x,若，令，得，当0,,x时，， fx()0,fx()0,33 aaa,,，，,x,当时，(有单调递减区间，单调递增区间( ，，,fx()0,fx()0，,,,,333,,，， a?0(?)解:(i)若，在上单调递增，所以( fx()[02]，gaf()(0)0,, aa，，,，06,,a若，在上单调递减，在上单调递增， fx()0，，2,,,,33,，，， aaa2,,a?6所以(若，在上单调递减， fx()[02]，gaf(),,,,,333,, 所以( gafa()(2)2(2),,, 00，?，a, ,2aa,综上所述， gaa()06,,,,，，,33, ,2(2)6,aa，?(, a?006,,a36?a,(ii)令(若，无解(若，解得( ,,6()2??ga a?66232??a，3232??a，若，解得(故的取值范围为( a 22,,,aa,0(22)(本题14分)已知数列，，a,0，(记a，a,1,a(n,N)nn1nnn，1，1S,a，a，？，a(n12n 111T,，，？，( n1，a(1，a)(1，a)(1，a)(1，a)？(1，a)11212n ,n,N求证:当时， a,a(?); nn，1 S,n,2(?); n T,3(?)。 n dit risk management practicmbek to implement the whole processBan actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will rdanceusiness says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accoe Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit bof th fers to natural persons of the Bank provide foreign currency loan business. Especially those good credit, source of repaymentrovisions, combined with Bank practice, these guidelines are formulated. Personal credit business mentioned in this guide, reated pvidual credit business, according to the China Banking Regulatory Commission guidelines on credit due diligence and other rels to improve the quality of individual credit business, optimize the structure of assets, promote healthy development of indies chapter I General provisionr 481679536 (total of 3) Qilu Bank's Office issued on Septe-elines to inform risk management: leadership, head office departments contact person: Chen Tel: 0531t guidnex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4, 12 key words: sends the individual crediice of qilu Bank personal credit risk management guidelines are issued to you, please carefully study and implement. Anindividual grantBusiness development, Head Off, 2012 Annex: qilu Bank personal cre14 22(本题主要考查数列的递推关系，数学归纳法、不等式证明等基础知识和基本技能， 同时考查逻辑推理能力(满分14分( (?)证明:用数学归纳法证明( 2n,1?当时，因为是方程的正根，所以( xx，,,10aaa,212 *?假设当时，， aa,nkk,,()Nkk，1 2222因为 aa,,，,,，,(1)(1)aaaa，kkkk，，，，kk12211 ， ,,，，()(1)aaaakkkk，，，，2121 所以( aa,kk，，12 nk,，1即当时，也成立( aa,nn，1 *根据?和?，可知对任何都成立( n,Naa,nn，1 22kn,,121，，，？n?2(?)证明:由，()， aaa，,,1kkk，，1122得( aaaana，，，，,,,()(1)？nn2312因为，所以( a,0Sna,,,11nn 22由及得， aa,a,1aaa,，,,121nnn，1nnn，，11 所以( Sn,,2n 22(?)证明:由，得 aaaa，,，12?kkkk，，11 a1k，1 ?，，，，?,,？(2313)knn，12aakk，1 a1n??所以， (3)a,2n，，，？(1)(1)(1)2aaaa342n aa11nn于是， ??,,(3)n,,,2222nnn，，，，？(1)(1)(1)2()22aaaaa2322n 11n?3T,，，，，,？113故当时，， nn,222 TTT,,又因为， 123 T,3所以( n ptember 4, 2012 Annex: qilu Bank personal credit risk management practices chapter I General provisions to improve the quality of individual grantBusiness development, Head Office of qilu Bank personal credit risk management guidelines are issued to you, plindividual credit business, optimize the structure of assets, promote healthy development of individual credit business, accordease carefully study and implement. Annex: qilu Bank personal credit risk management guidelines qilu Bank b o September 4ing to the China Banking Regulatory Commission guidelines on credit due diligence and other related provisions, combined with B, 12 key words: sends the individual credit guidelines to inform risk management: leadership, head office departments contact pank practice, these guidelines are formulated. Personal credit business mentioned in this guide, refers to natural persons of terson: Chen Tel: (total of 3) Qilu Bank's Office issued on Sehe Bank provide foreign currency loan business. Especially those good credit, source of repayment of the Bank stability, guarantee plenty of personal loan needs, and strengthen risk control and asset structure. Personal credit business says the parties must ensure that the borrower credit, such as true, real and have written evidence, strictly in accordance with the rules of the regulation, standards, effective against various types of internal and external fraud. Our ban and will actively take measures to prevent all forms of commercial bribery. Chapter II management principles management principles the Bank to implement the whole process