2011年重庆高考文科数学真题及答案.doc-资料库

2011 年重庆高考文科数学真题及答案一、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备选项中，只有一项是符合题目要求的。 1．在等差数列 na 中， 2 a a  ， 3 2  则＝ 4, a 10 A．12 B．14 C．16 D．18 2．设 { | U R M x x   , 2  2 x  ，则 U Mð 0}, = A．[0，2] B． 0,2 C．    ,0 2,    D．    ,0 2,    3．曲线 y   x 2  在点（1，2）处的切线方程为 23 x A． 3 x y  1 C． 3 x y  5 B． y   3 x  5 D． 2 x y 4．从一堆苹果中任取 10 只，称得它们的质量如下（单位：克） 95 125 130 114 116 120 122 105 120 134 则样本数据落在[114.5,124.5) 内的频率为 A．0.2 B．0.3 C．0.4 D．0.5 5．已知向量 (1, ), k b  a  (2,2), 且与共线，那么 a b 的值为 a b a A．1 6．设 a  A． a 7．若函数 log 1 3 b   ( ) f x B．2 2 3 c ,  C．3 D．4 log 3 4 3 , 则 , , a b c 的大小关系是 , b  log 1 3 1 2 c   x 1  2 n a b B． c c ( n  在 x a 处取最小值，则 a    2)   C．b a D．b   c a A．1 2 B．1 3 C．3 D．4 8．若△ ABC 的内角， , ,A B C 满足 6sin A  4sin B  3sin C ，则 cos B  A． 15 4 B． 3 4 C． 3 15 16 D． 11 16 9．设双曲线的左准线与两条渐近线交于 ,A B 两点，左焦点在以 AB 为直径的圆内，则该双曲线的离心率的取值范围为

rapid development of the market economy environment to explore public servants ' duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier and approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants ' duty consumption further. Implementing an "honest canteen", standardize official entertaining management; enhancing the telecommunication expense management; elimination of County traveland countryside subsidies; research "village officials" capitalization management of corporate spending, and so on. Finally, group ... 18 session to be held in Beijing from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretary pointed out that China's reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the "five in one" the General layout of socialist modernization requirements, 18 session of the decision was a "five in one" and the improvement of overall scheme of reform,will promote an integrated and One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 plenary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the party's Congress, on the theme "personnel", discussing election Central's top leaders, such as the election of the Standing Committee of the political Bureau, through the Central The "fivein one" programme is to achieve a comprehensive reform of institutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the party's construction in the area of institutional reform. Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election, mainly to discuss a new Statepersonnel issues. But by the third A．(0, 2) B．(1, 2) C． 2( 2 ,1) D．( 2 ， ) 10．高为 2 的四棱锥 S ABCD  的底面是边长为 1 的正方形，点 S 、 A 、 B 、C 、 D 均在半径为 1 的同一球面上，则底面 ABCD 的中心与顶点 S 之间的距离为 A． 10 2 B． 3 2  2 C． 3 2 D． 2 二、填空题，本大题共 5 小题，每小题 5 分，共 25 分，把答案填写在答题卡相应位置上 11． (1 2 )x 6 的展开式中 4x 的系数是 12．若 cos a   ,且 3 5 a ( ,  13．过原点的直线与圆 2 x  y 2 3  ) 2  2 ，则 tan a  x  4 y   相交所得弦的长为 2，则该直线的方程为 4 0 14．从甲、乙等 10 位同学中任选 3 位去参加某项活动，则所选 3 位中有甲但没有乙的概率为 15．若实数 , , a b c 满足 a 2  b 2  2 a b  a ,2  b 2  c 2  2 a b c   , 则的最大值是 c 三、解答题，本大题共 6 小题，共 25 分，解答应写出文字说明，证明过程或演算步骤. 16．（本小题满分 13 分，（Ⅰ）小问 7 分，（Ⅱ）小问 6 分）设{ }na 是公比为正数的等比数列， 1 a  ， 3 a 2 a 2  。 4 （Ⅰ）求{ }na 的通项公式；（Ⅱ）设{ }nb 是首项为 1，公差为 2 的等差数列，求数列{ a n b 的前 n 项和 ns 。 } n 17．（本小题满分 13 分，（I）小问 6 分，（II）小问 7 分）某市公租房的房源位于 A、B、C 三个片区，设每位申请人只申请其中一个片区的房源，且申请其中任一个片区的房源是等可能的，求该市的任 4 位申请人中：（I）没有人申请 A 片区房源的概率；（II）每个片区的房源都有人申请的概率。 18．（本小题满分 13 分，（I）小问 7 分，（II）小问 6 分）设函数 ( ) f x  sin cos x x  3 cos(   x （1）求 ( ) f x 的最小正周期； )cos ( x x R  ). （II）若函数 y  ( ) f x 的图象按 b     4  3, 2     y  ( ) g x 在 (0,  ] 4 上的最大值。平移后得到函数 y  ( ) g x 的图象，求德国教育家第斯多惠说：“教学的艺术不在于传授本领，而在于激励、唤醒、鼓舞。”当学生沉浸于“我能学好”的喜悦中时，必然会产生更强烈的主动求知的心理冲动plenary session, each session of the Central Committee of national institutions and personnel problems have been arranged, you can concentrate on national development and reforms. ownership as the Foundation of a planned commodity economy; cadres ' honest and Government integrity, clean politics. the needs of the people. To deepen education reform, improve institutional mechanisms for the 13 session at a time when both the old and the new system change, governance and rectify the economic order; 14 ... Fair and efficient and authoritative Socialist judicial system, safeguard the people's interests. To form a scientific and effective coordination of power restriction and mechanisms to strengthen anti-corruption institutional innovation and institutional protection, sound improvement style normal system. Plenary session, building a socialist culture in China, enhancing national cultural soft power,must adhere to the orientation of advanced Socialist culture, adhere to the development of Socialist culture with Chinese characteristics, adhere to the people-centred work-oriented, further deepening reform of culture. Previous plenary session is often branded with a central leading collective, often by looking at the third plenum of the initiative to found the current central leadership collective governance characteristics. 12 session marked the change from rural to urban, established with public Legal authority to uphold the Constitution, deepening the reform of administrative law enforcement, ensure that the right to exercise judicial pow er independently and impartially according to law the prosecution, perfecting the running mechanism of judicial power, improve the system of judicial protection of human rights. Plenary session, Affairs the right to adhere to the system, and let the people authority to let the pow er run in the Sun, is shut up in a cage of the system pow er policy. Decision Science, implementation should be constructed strong, supervise the running of pow erful system, improve the system of punishing and preventing corruption, promoting political integrity, and strive to achieve To improve the cultural management system, establish and improve the modern market system and building modern public cultural service system, improve the level of culture opening. Plenary session, achieving development results more equitable benefit of all people, we must speed up reform of social programs and solve the issues of concern to the people the most direct and real interest, and better meet From the analysis of the process of economic reform in China, plenary session, 12 session, 14, 16 plenary session have programmatic meaning, respectively, marking the four stages of China's economic reform, and that the start-up phase of reform, reform, construction phase and perfecting the Socialist market economy framework stage of socialist market economy. Previous plenary session topics proposed to the third plenary session of "taking class struggle as the key link," shifted to socialist modernization;

rapid development of the market economy environment to explore public servants ' duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier and approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants ' duty consumption further. Implementing an "honest canteen", standardize official entertaining management; enhancing the telecommunication expense management; elimination of County traveland countryside subsidies; research "village officials" capitalization management of corporate spending, and so on. Finally, group ... 18 session to be held in Beijing from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretary pointed out that China's reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the "five in one" the General layout of socialist modernization requirements, 18 session of the decision was a "five in one" and the improvement of overall scheme of reform,will promote an integrated and One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 plenary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the party's Congress, on the theme "personnel", discussing election Central's top leaders, such as the election of the Standing Committee of the political Bureau, through the Central The "fivein one" programme is to achieve a comprehensive reform of institutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the party's construction in the area of institutional reform. Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election, mainly to discuss a new Statepersonnel issues. But by the third 19．（本小题满分 12 分，（Ⅰ）小题 5 分，（Ⅱ）小题 7 分）设 ( ) f x  3. 2 x 2  ax  bx 1  的导数为 ( ) f x ，若函数 y f x ( ) 的图像关于直线 x   对称，且 (1) 0  ． f  1 2 （Ⅰ）求实数 ,a b 的值（Ⅱ）求函数 ( ) f x 的极值 20．（本小题满分 12 分，（Ⅰ）小问 6 分，（Ⅱ）小问 6 分）如题（ 20 ）图，在四面体 ABCD 中，平面 ABC ⊥ 平面 ACD ， AB BC AC AD 2, 1  ,    （Ⅰ）求四面体 ABCD 的体积；（Ⅱ）求二面角 C-AB-D 的平面角的正切值。 BC CD  21．（本小题满分 12 分。（Ⅰ）小问 4 分，（Ⅱ）小问 8 分）如题（21）图，椭圆的中心为原点 0，离心率 e= 2 2 ，一条准线的方程是 2 2 x  （Ⅰ）求该椭圆的标准方程；（Ⅱ）设动点 P 满足：   2 OP OM ON    ，其中 M、N 是椭圆上的点，直线 OM 与 ON 的

rapid development of the market economy environment to explore public servants ' duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier and approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants ' duty consumption further. Implementing an "honest canteen", standardize official entertaining management; enhancing the telecommunication expense management; elimination of County traveland countryside subsidies; research "village officials" capitalization management of corporate spending, and so on. Finally, group ... 18 session to be held in Beijing from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretary pointed out that China's reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the "five in one" the General layout of socialist modernization requirements, 18 session of the decision was a "five in one" and the improvement of overall scheme of reform,will promote an integrated and One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 plenary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the party's Congress, on the theme "personnel", discussing election Central's top leaders, such as the election of the Standing Committee of the political Bureau, through the Central The "fivein one" programme is to achieve a comprehensive reform of institutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the party's construction in the area of institutional reform. Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election, mainly to discuss a new Statepersonnel issues. But by the third 斜率之积为 1 2  ，问：是否存在定点 F，使得 PF 与点 P 到直线 l： 2 10 x  的距离之比为定值；若存在，求 F 的坐标，若不存在，说明理由。题（21）图参考答案 6—10 BCDBA 0 一、选择题 1—5 DAACD 二、填空题： 11．240 4 3 13． 2 x y  12． 14． 15． 7 30 2 log 3  2 三、解答题：满分 75 分 16．（本题 13 分）解：（I）设 q 为等比数列{ }na 的公比，则由 a 1  2, a 3  a 2  4 2 得 q 2  2 q  4 ，即 2 q q   ，解得 2 0 q  2  或 q 1 （舍去），因此 q  2. 所以{ }na 的通项为 na 2 2   n 1   n 2 ( n N  * ). （II） S n  n 2(1 2 )  1 2  1    n 1) ( n n  2  2. n 1   2  2 n  2. 德国教育家第斯多惠说：“教学的艺术不在于传授本领，而在于激励、唤醒、鼓舞。”当学生沉浸于“我能学好”的喜悦中时，必然会产生更强烈的主动求知的心理冲动plenary session, each session of the Central Committee of national institutions and personnel problems have been arranged, you can concentrate on national development and reforms. ownership as the Foundation of a planned commodity economy; cadres ' honest and Government integrity, clean politics. the needs of the people. To deepen education reform, improve institutional mechanisms for the 13 session at a time when both the old and the new system change, governance and rectify the economic order; 14 ... Fair and efficient and authoritative Socialist judicial system, safeguard the people's interests. To form a scientific and effective coordination of power restriction and mechanisms to strengthen anti-corruption institutional innovation and institutional protection, sound improvement style normal system. Plenary session, building a socialist culture in China, enhancing national cultural soft power,must adhere to the orientation of advanced Socialist culture, adhere to the development of Socialist culture with Chinese characteristics, adhere to the people-centred work-oriented, further deepening reform of culture. Previous plenary session is often branded with a central leading collective, often by looking at the third plenum of the initiative to found the current central leadership collective governance characteristics. 12 session marked the change from rural to urban, established with public Legal authority to uphold the Constitution, deepening the reform of administrative law enforcement, ensure that the right to exercise judicial pow er independently and impartially according to law the prosecution, perfecting the running mechanism of judicial power, improve the system of judicial protection of human rights. Plenary session, Affairs the right to adhere to the system, and let the people authority to let the pow er run in the Sun, is shut up in a cage of the system pow er policy. Decision Science, implementation should be constructed strong, supervise the running of pow erful system, improve the system of punishing and preventing corruption, promoting political integrity, and strive to achieve To improve the cultural management system, establish and improve the modern market system and building modern public cultural service system, improve the level of culture opening. Plenary session, achieving development results more equitable benefit of all people, we must speed up reform of social programs and solve the issues of concern to the people the most direct and real interest, and better meet From the analysis of the process of economic reform in China, plenary session, 12 session, 14, 16 plenary session have programmatic meaning, respectively, marking the four stages of China's economic reform, and that the start-up phase of reform, reform, construction phase and perfecting the Socialist market economy framework stage of socialist market economy. Previous plenary session topics proposed to the third plenary session of "taking class struggle as the key link," shifted to socialist modernization;

rapid development of the market economy environment to explore public servants ' duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier and approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants ' duty consumption further. Implementing an "honest canteen", standardize official entertaining management; enhancing the telecommunication expense management; elimination of County traveland countryside subsidies; research "village officials" capitalization management of corporate spending, and so on. Finally, group ... 18 session to be held in Beijing from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretary pointed out that China's reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the "five in one" the General layout of socialist modernization requirements, 18 session of the decision was a "five in one" and the improvement of overall scheme of reform,will promote an integrated and One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 plenary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the party's Congress, on the theme "personnel", discussing election Central's top leaders, such as the election of the Standing Committee of the political Bureau, through the Central The "fivein one" programme is to achieve a comprehensive reform of institutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the party's construction in the area of institutional reform. Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election, mainly to discuss a new Statepersonnel issues. But by the third 17．（本题 13 分）解：这是等可能性事件的概率计算问题。（I）解法一：所有可能的申请方式有 34 种，而“没有人申请 A 片区房源”的申请方式有 24 种。记“没有人申请 A 片区房源”为事件 A，则 ( P A  ) 4 2 4 3  16 81 . 解法二：设对每位申请人的观察为一次试验，这是 4 次独立重复试验. 记“申请 A 片区房源”为事件 A，则 ( P A  ) 1 3 . 由独立重复试验中事件 A 恰发生 k次的概率计算公式知，没有人申请 A 片区房源的概率为 P 4 (0) C 0 4 1 0 ( ) ( 3 2 3 4 )  16 81 . （II）所有可能的申请方式有 34 种，而“每个片区的房源都有人申请”的申请方式有 1 C C C 3 2 4 1 2 3 ( C C或 3 2 4 ) 种. 记“每个片区的房源都有人申请”为事件 B，从而有 ( P B )  1 2 1 C C C 3 2 4 4 3  36 4 3  4 9 ( 或 ( P B )  2 3 C A 4 3 4 3  4 9 ). 18．（本题 13 分）解：（I） ( ) f x  sin 2 x  3 cos 2 x 1 2 1 2 1 2   sin 2 sin 2 x  x  3 2 3 2 (1 cos 2 ) x  cos 2 x  3 2  sin(2 x   ) 3  3 2 . 故 ( ) f x 的最小正周期为 T  2  2  .  （II）依题意 ( ) g x  ( ) f x   4  3 2  3 2  3 2  sin[2( x   sin(2 x  )    ] 4 3  ) 3. 6 

rapid development of the market economy environment to explore public servants ' duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier and approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants ' duty consumption further. Implementing an "honest canteen", standardize official entertaining management; enhancing the telecommunication expense management; elimination of County traveland countryside subsidies; research "village officials" capitalization management of corporate spending, and so on. Finally, group ... 18 session to be held in Beijing from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretary pointed out that China's reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the "five in one" the General layout of socialist modernization requirements, 18 session of the decision was a "five in one" and the improvement of overall scheme of reform,will promote an integrated and One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 plenary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the party's Congress, on the theme "personnel", discussing election Central's top leaders, such as the election of the Standing Committee of the political Bureau, through the Central The "fivein one" programme is to achieve a comprehensive reform of institutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the party's construction in the area of institutional reform. Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election, mainly to discuss a new Statepersonnel issues. But by the third 当 [0,  x  ] 时 4 ,2 x [       ], 6 6 3 , ( ) g x 为增函数，所以 ( ) g x 在 [0,  ] 4 上的最大值为 g  ( ) 4  3 3 2 . 19．（本题 12 分）解：（I）因 ( ) f x  3 2 x  2 ax  bx  1, f 故  ( ) x  2 6 x  2 . ax b  从而 f  ( ) x  6( x  a 6 2 )   b 2 a 6 , 即 y x ( ) f 关于直线 x   对称，从而由题设条件知    a 6 1 , 2 解得 a 3. a 6 a b 又由于 (1) f   0, 6 2 即    0, b 解得   12. （II）由（I）知 ( ) f x  3 2 x  2 3 x  12 x  1, f  ( ) x  2 6 x  6 x  12  6( x  1)( x  2). 令 f  ( ) x  0, 6( 即 x  1)( x  2)  0. x 解得   2, x 2 1  1. 当 (    , 2) x , 时 f  ( ) x  0, ( 故在 ( ) f x   , 2) 上为增函数；当 ( 2,1)   x , 时 f  ( ) x  0, 故在 ( ) f x ( 2,1)  上为减函数；当 (1,   x ) , 时 f  ( ) x  0, 故在 ( ) f x (1,  ) 上为增函数；从而函数 ( ) f x 2 x  在 1 处取得极大值 f ( 2)   21, 20．（本题 12 分） 在 x 2 1 处取得极小值 (1) f   6. 解法一：（I）如答（20）图 1，过 D 作 DF⊥AC 垂足为 F，故由平面 ABC⊥平面 ACD，知 DF⊥平面 ABC，即 DF 是四面体 ABCD 的面 ABC 上的高，设 G 为边 CD 的中点，则由 AC=AD，知 AG⊥CD，从而 AG  2 AC  CG 2  2 2  ( 21 ) 2  由 1 2 AC DF   1 2 CD AG DF 得   . 15 2  AC AG CD  15 . 4 由 Rt ABC AB , 中   2 AC  BC 2  3, S   ABC 1 2 AB BC   3 2 . 德国教育家第斯多惠说：“教学的艺术不在于传授本领，而在于激励、唤醒、鼓舞。”当学生沉浸于“我能学好”的喜悦中时，必然会产生更强烈的主动求知的心理冲动plenary session, each session of the Central Committee of national institutions and personnel problems have been arranged, you can concentrate on national development and reforms. ownership as the Foundation of a planned commodity economy; cadres ' honest and Government integrity, clean politics. the needs of the people. To deepen education reform, improve institutional mechanisms for the 13 session at a time when both the old and the new system change, governance and rectify the economic order; 14 ... Fair and efficient and authoritative Socialist judicial system, safeguard the people's interests. To form a scientific and effective coordination of power restriction and mechanisms to strengthen anti-corruption institutional innovation and institutional protection, sound improvement style normal system. Plenary session, building a socialist culture in China, enhancing national cultural soft power,must adhere to the orientation of advanced Socialist culture, adhere to the development of Socialist culture with Chinese characteristics, adhere to the people-centred work-oriented, further deepening reform of culture. Previous plenary session is often branded with a central leading collective, often by looking at the third plenum of the initiative to found the current central leadership collective governance characteristics. 12 session marked the change from rural to urban, established with public Legal authority to uphold the Constitution, deepening the reform of administrative law enforcement, ensure that the right to exercise judicial pow er independently and impartially according to law the prosecution, perfecting the running mechanism of judicial power, improve the system of judicial protection of human rights. Plenary session, Affairs the right to adhere to the system, and let the people authority to let the pow er run in the Sun, is shut up in a cage of the system pow er policy. Decision Science, implementation should be constructed strong, supervise the running of pow erful system, improve the system of punishing and preventing corruption, promoting political integrity, and strive to achieve To improve the cultural management system, establish and improve the modern market system and building modern public cultural service system, improve the level of culture opening. Plenary session, achieving development results more equitable benefit of all people, we must speed up reform of social programs and solve the issues of concern to the people the most direct and real interest, and better meet From the analysis of the process of economic reform in China, plenary session, 12 session, 14, 16 plenary session have programmatic meaning, respectively, marking the four stages of China's economic reform, and that the start-up phase of reform, reform, construction phase and perfecting the Socialist market economy framework stage of socialist market economy. Previous plenary session topics proposed to the third plenary session of "taking class struggle as the key link," shifted to socialist modernization;

rapid development of the market economy environment to explore public servants ' duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier and approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants ' duty consumption further. Implementing an "honest canteen", standardize official entertaining management; enhancing the telecommunication expense management; elimination of County traveland countryside subsidies; research "village officials" capitalization management of corporate spending, and so on. Finally, group ... 18 session to be held in Beijing from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretary pointed out that China's reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the "five in one" the General layout of socialist modernization requirements, 18 session of the decision was a "five in one" and the improvement of overall scheme of reform,will promote an integrated and One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 plenary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the party's Congress, on the theme "personnel", discussing election Central's top leaders, such as the election of the Standing Committee of the political Bureau, through the Central The "fivein one" programme is to achieve a comprehensive reform of institutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the party's construction in the area of institutional reform. Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election, mainly to discuss a new Statepersonnel issues. But by the third 故四面体 ABCD 的体积 V 1   3 S  ABC  DF  5 . 8 （II）如答（20）图 1，过 F 作 FE⊥AB，垂足为 E，连接 DE。由（I）知 DF⊥平面 ABC。由三垂线定理知 DE⊥AB，故∠DEF 为二面角 C—AB—D 的平面角。在 Rt AFD AF , 中   2 AD  DF 2  2 2  ( 215 ) 4  7 4 , 在 Rt ABC 中，EF//BC，从而 EF：BC=AF：AC，所以 EF  AF BC  AC  7 . 8 在 Rt△DEF 中， tan DEF  DF EF  2 15 7 . 解法二：（I）如答（20）图 2，设 O 是 AC 的中点，过 O 作 OH⊥AC，交 AB 于 H，过 O 作 OM⊥AC，交 AD 于 M，由平面 ABC⊥平面 ACD，知 OH⊥OM。因此以 O 为原点，以射线 OH， OC，OM 分别为 x 轴，y 轴，z 轴的正半轴，可建立空间坐标系 O—xyz.已知 AC=2，故点 A，C 的坐标分别为 A（0，—1，0），C（0，1，0）。设点 B 的坐标为 1 ( , B x y 1 ,0), 由  AB   BC BC ,|  | 1  ，有     2 x 1 2 x 1 解得 2 y  1 ( y  1        y 1 x 1     2 1, 1) 3 2 1 , 2 x 1 , 1,         y 1 3 , 2 ( ). 舍去    1 2 即点 B 的坐标为 B ( 3 1 2 2 , ,0). 又设点 D 的坐标为 , D y z (0, 2  CD | 1,|   AD | 2,  有 ), 由 | 2       ( ( y y 2 2 解得 2 2 1) 1)   y 2  z 2           2 2 2 2 z z 3 4 15 4 , 1, 4,        , y  2 3 4 , z   2 15 4 ( ). 舍去即点 D 的坐标为 D (0, 3 4 , 15 4 ). 从而△ACD 边 AC 上的高为 h | z 2 |  15 4 .

rapid development of the market economy environment to explore public servants ' duty consumption monetization reform has provided a good foundation. The socialization of rear service work has been launched, and rapid progress in some places and departments, duty consumption monetization of carrier and approach to management has been resolved. Third, in recent years, exploring the monetization of duty consumption has made some progress, have gained some experience and can provide reference to the comprehensive reform of the system of public servants ' duty consumption further. Implementing an "honest canteen", standardize official entertaining management; enhancing the telecommunication expense management; elimination of County traveland countryside subsidies; research "village officials" capitalization management of corporate spending, and so on. Finally, group ... 18 session to be held in Beijing from November 9, 2013 to 12th. 35 years ago blew the third plenary session of the reform and opening up in the spring breeze, changed, affect the world; today, 35 years later, in the eyes of the nation and the world expect, again to reform mark China, ushered in the 18 session. XI General Secretary pointed out that China's reform has entered a crucial period and the Sham Shui Po District, must be based on greater political courage and wisdom, lose no time in deepening reform in important fields. Dares to crack a hard nut, dares to question the Rapids, which dares to break the barrier of ideas, and dare to benefit cure barriers. Deepening reform and opening up is on schedule to achieve institutional safeguards of the moderately well-off. Under the "five in one" the General layout of socialist modernization requirements, 18 session of the decision was a "five in one" and the improvement of overall scheme of reform,will promote an integrated and One, holding time and place importance on November 9, 2013 to the 18 session of the 12th Beijing since 1978, 35, have been 7 plenary session, each time on major issues of political and economic life of the country has made important deployment. In accordance with PRC political practice, often at every session of the CPC Central Committee in a plenary session was held immediately after the party's Congress, on the theme "personnel", discussing election Central's top leaders, such as the election of the Standing Committee of the political Bureau, through the Central The "fivein one" programme is to achieve a comprehensive reform of institutional guarantees for objectives of build a well-off society, the smooth progress of the construction of a well-off society and reform the objectives of the programme. coordinated economic, political, cultural, social and ecological civilization construction of the five reforms and the party's construction in the area of institutional reform. Committee members, decisions, such as members of the Central Military Commission. The second plenary session, is held in two sessions before the general election, mainly to discuss a new Statepersonnel issues. But by the third  AB |  又 | ( 3 2 2 )  ( 1 2 2  1)  3,|  BC | 1.  故四面体 ABCD 的体积 V 1 1    3 2  AB |  BC h |  |  | 5 8 . （II）由（I）知  AB  ( 3 3 2 2 ,  AD ,0),  (0, 7 4 , 15 4 ). 设非零向量 ( , , ) l m n  n 是平面 ABD 的法向量，则由 n  AB 有  0. （1） 3 2 由 n l m 3 2  AD ，有 7 4 m  15 4 n  0. （2）取 m   ，由（1），（2），可得 1 l  3, n  7 15 15 , n 即  ( 3, 1,  7 15 15 ). 显然向量 (0,0,1) k  是平面 ABC 的法向量，从而 cos  , n k  1 故 tan  , n k  7 15 15 3 1   49 15 49 109 7 109   7 109 109 ,  2 15 7 , 即二面角 C—AB—D 的平面角的正切值为 2 15 . 7 21．（本题 12 分）解：（I）由 e  c a  2 , 2 2 a c  2 2, 解得 a  2, c  2 2, b  2 a 2  c  ，故椭圆的标准方程为 2 2 x 4 2 y 2  1. 德国教育家第斯多惠说：“教学的艺术不在于传授本领，而在于激励、唤醒、鼓舞。”当学生沉浸于“我能学好”的喜悦中时，必然会产生更强烈的主动求知的心理冲动plenary session, each session of the Central Committee of national institutions and personnel problems have been arranged, you can concentrate on national development and reforms. ownership as the Foundation of a planned commodity economy; cadres ' honest and Government integrity, clean politics. the needs of the people. To deepen education reform, improve institutional mechanisms for the 13 session at a time when both the old and the new system change, governance and rectify the economic order; 14 ... Fair and efficient and authoritative Socialist judicial system, safeguard the people's interests. To form a scientific and effective coordination of power restriction and mechanisms to strengthen anti-corruption institutional innovation and institutional protection, sound improvement style normal system. Plenary session, building a socialist culture in China, enhancing national cultural soft power,must adhere to the orientation of advanced Socialist culture, adhere to the development of Socialist culture with Chinese characteristics, adhere to the people-centred work-oriented, further deepening reform of culture. Previous plenary session is often branded with a central leading collective, often by looking at the third plenum of the initiative to found the current central leadership collective governance characteristics. 12 session marked the change from rural to urban, established with public Legal authority to uphold the Constitution, deepening the reform of administrative law enforcement, ensure that the right to exercise judicial pow er independently and impartially according to law the prosecution, perfecting the running mechanism of judicial power, improve the system of judicial protection of human rights. Plenary session, Affairs the right to adhere to the system, and let the people authority to let the pow er run in the Sun, is shut up in a cage of the system pow er policy. Decision Science, implementation should be constructed strong, supervise the running of pow erful system, improve the system of punishing and preventing corruption, promoting political integrity, and strive to achieve To improve the cultural management system, establish and improve the modern market system and building modern public cultural service system, improve the level of culture opening. Plenary session, achieving development results more equitable benefit of all people, we must speed up reform of social programs and solve the issues of concern to the people the most direct and real interest, and better meet From the analysis of the process of economic reform in China, plenary session, 12 session, 14, 16 plenary session have programmatic meaning, respectively, marking the four stages of China's economic reform, and that the start-up phase of reform, reform, construction phase and perfecting the Socialist market economy framework stage of socialist market economy. Previous plenary session topics proposed to the third plenary session of "taking class struggle as the key link," shifted to socialist modernization;

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