2003年高考数学试题(全国理)及答案.doc

thrift of excellent traditional and style lack deep of understanding, one-sided think in now of good situation Xia, economic smooth more fast development, and reform made major progress, and people living significantly improve, and social the career made new progress, no necessary always hard has, no awareness to China also has many poverty area, and also has many poverty population of exists, more living improve has, more need keep hard of style. Three is not strictly honest. Total thought units is a water sector, clean self-discipline away from himself too far, no real processing good living of improve and hard, and thrift excellent traditional of relationship, no effective do comply with Constitution and party of regulations must from I do up, no right mercy good bitter Le, and wealth of relationship, no right awareness to in comply with Constitution and party of regulations aspects everyone has accountability. Four, future direction and improvement measures 1, belief and faith, strengthen party spirit. One is to firmly establish the noble ideals of struggle for the ideals of communism, communist struggle for life, ready to sacrifice everything for the party and the people. Second is to continuously improve the quality and standard of political, conscientiously study Deng Xiaoping theory and three represents important thought and the scientific Outlook on development, implement the partys basic program for the primary stage of socialism, adhere to the correct political orientation, maintain highly consistent with the CPC Central Committee, is good at theories of socialism with Chinese characteristics to analyze and solve problems. Third, strengthening the party spirit and the world transformation, perseverance of the party Constitution, relive Party vows to establish correct world Outlook, Outlook on life and the world, practically embodies ideals and beliefs into action, combine lofty ideals and practical activities, transforming the objective world, actively participate in the great practice of building socialism with Chinese characteristics. 2, keep the purpose in concept, changing the style of work. First, keep in mind that the purpose of serving, adhere to assuming power for the people, keep in mind the people and care about people, and the joys and sorrows of the masses, .According to city discipline, and municipal organization Department requirements, today we held implement implementation independent Commission against corruption guidelines effective strengthening led cadres style construction topic democratic life, main task is close contact thought, and work actual, control check district Standing Committee team and the personal in implementation independent Commission against corruption guidelines Shang exists of problem, in-depth carried out criticism and self-critical, further clear rectification direction and measures, effective enhanced clean politics of consciousness and initiative, firm set good of ruling image. Before the meeting, the way we take surveys solicited a views, combed, related to team building2003年普通高等学校招生全国统一考试数学(理工农医类) 一、选择题（本大题共12小题，每小题5分，共60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.1已知（ ）ABCD2圆锥曲线（ ）ABCD3设函数（ ）A（1，1）B（1，+）CD4函数的最大值为（ ）ABCD25已知圆的弦长为时，则a=ABCD6已知圆锥的底面半径为R，高为3R，在它的所有内接圆柱中，全面积的最大值是（ ）ABCD7已知方程的四个根组成的一个首项为的等差数列，则（ ）A1BCD8已知双曲线中心在原点且一个焦点为M、N两点，MN中点的横坐标为则此双曲线的方程是（ ）ABCD9函数（ ）ABCD10已知长方形的四个项点A（0，0），B（2，0），C（2，1）和D（0，1），一质点从AB的中点P0沿与AB夹角为的方向射到BC上的点P1后，依次反射到CD、DA和AB上的点P2、P3和P4（入射解等于反射角），设P4坐标为（的取值范围是（ ）ABCD11（ ）A3BCD612一个四面体的所有棱长都为，四个项点在同一球面上，则此球的表面积为（ ）A3B4C3D6二、填空题：本大题共4小题，每小题4分，共16分，把答案填在题中横线上.13展开式中的系数是 .14使成立的的取值范围是 .15如图，一个地区分为5个行政区域，现给地图着色，要求相邻区域不得使用同一颜色，现有4种颜色可供选择，则不同的着色方法共有 种.（以数字作答）16下列五个正方体图形中，是正方体的一条对角线，点M、N、P分别为具所在棱的中点，能得出面MNP的图形的序号是 .（写出所有符合要求的图形序号）三、解答题：本大题共6小题，共74分. 解答应写出文字的说明，证明过程或演算步骤.17（本小题满分12分）已知复数z的辐角为60，且是和的等比中项. 求.18(本小题满分12分)如图，在直三棱柱ABCA1B1C1中，底面是等腰直角三形，ACB=90，侧棱AA1=2，D、E分别是CC1与A1B的中点，点E在平面ABD上的射影是ABD的重心G.（）求A1B与平面ABD所成角的大小（结果用反三角函数值表示）；（）求点A1到平面AED的距离.19（本小题满分12分）已知 设P：函数在R上单调递减.Q：不等式的解集为R，如果P和Q有且仅有一个正确，求的取值范围.20（本小题满分12分） 在某海滨城市附近海面有一台风，据监测，当前台风中心位于城市O（如图）的东偏南方向300km的海面P处，并以20km/h的速度向西偏北45方向移动. 台风侵袭的范围为圆形区域，当前半径为60km,并以10km/h的速度不断增大. 问几小时后该城市开始受到台风的侵袭？21（本小题满分14分）已知常数在矩形ABCD中，AB=4，BC=4，O为AB的中点，点E、F、G分别在BC、CD、DA上移动，且，P为GE与OF的交点（如图），问是否存在两个定点，使P到这两点的距离的和为定值？若存在，求出这两点的坐标及此定值；若不存在，请说明理由.22（本小题满分12分，附加题4分）（）设中所有的数从小到大排列成的数列， 即 将数列各项按照上小下大，左小右大的原则写成如下的三角形数表： 3 5 6 9 10 12 （i）写出这个三角形数表的第四行、第五行各数； （i i）求.（）（本小题为附加题，如果解答正确，加4分，但全卷总分不超过150分）设中所有的数都是从小到大排列成的数列，已知2003年普通高等学校招生全国统一考试数 学(理工农医类)答案一、选择题1D 2C 3D 4A 5C 6B 7C 8D 9D 10C 11B 12A二、填空题13 14（-1，0） 1572 16三、解答题：17 解：设，则复数由题设18（）解：连结BG，则BG是BE在ABD的射影，即EBG是A1B与平面ABD所成的角.设F为AB中点，连结EF、FC，（）解：19解：函数在R上单调递减不等式20解：如图建立坐标系以O为原点，正东方向为x轴正向.在时刻：（1）台风中心P（）的坐标为此时台风侵袭的区域是其中若在t时刻城市O受到台风的侵袭，则有即答：12小时后该城市开始受到台风的侵袭.21根据题设条件，首先求出点P坐标满足的方程，据此再判断是否存在的两定点，使得点P到两点距离的和为定值.按题意有A（2，0），B（2，0），C（2，4a），D（2，4a）设由此有E（2，4ak），F（24k，4a），G（2，4a4ak）直线OF的方程为：直线GE的方程为：从，消去参数k，得点P（x,y）坐标满足方程整理得 当时，点P的轨迹为圆弧，所以不存在符合题意的两点. 当时，点P轨迹为椭圆的一部分，点P到该椭圆焦点的距离的和为定长。当时，点P到椭圆两个焦点（的距离之和为定值。当时，点P 到椭圆两个焦点（0， 的距离之和为定值2.22（本小题满分12分，附加题4分） （）解：（i）第四行17 18 20 24 第五行 33 34 36 40 48 （i i）解：设，只须确定正整数 数列中小于的项构成的子集为 其元素个数为满足等式的最大整数为14，所以取因为100（）解：令 因 现在求M的元素个数：其元素个数为： 某元素个数为某元素个数为我乡在本轮隐患排查中共出动37组次，155人次进行安全隐患排查，对区域内山洪、堰渠、道路、输电线路铁塔等可能存在安全隐患的地方均进行多次安全排查project work, cadres, cadres selection and other aspects of a total of 19, further defined the direction of rectification, enhancing the pertinence and effectiveness of democratic life. Good for this meeting, we requested the Standing Committee of the municipal party Committee, municipal Secretary General Tang Wenjin, the City Commission for discipline inspection Standing Committee Yang Xu, Jiang Jixue, Deputy Director of the personnel office, and other leading comrades present guidance allows us to warm applause for their welcome and thanks! Below, I first District Committee member of the 20XX team annual democratic meeting implementation of the corrective measures, as well as member of the team and of my own report guidelines for the implementation of the independent Commission against corruption statement invited leaders and comrades criticism. First, annual party on the 20XX team, Member of democratic life action plan implementation year 20XX, district democratic meeting a member of the team on study and practice the scientific Outlook on development theme, find a project supporting strong enough, the industry well enough, urban construction management level needs to be improved, livelihood improvement needs to be strengthened, district team itself, such as the five aspects. Year of 20XX, we find out the problems mentioned above, based on actual Shunqing construction and development, conscientiously sum up improvements, achieving significant development results and effectiveness of their work. (A) highlight the project handle, maintain high growth of investment. Adhere to the strategy as a Foundation, carrying out projects to promote increased stamina important. One is to increase the intensity of projects towards. Actively seek national and provincial policy support, superior special transfer payments, a variety of additional income will top 700 million Yuan, a number of key infrastructure projects, livelihood projects, industrial projects into the cage. Second, increasing the project attracts. This year a total of 23 signed a major project, of which 14 billion project, China Metallurgical group, vanke group, Guangdong hengda group, Taiwan Ruentex group, on the RI group, Shenzhen Kaisa, jifeng agricultural machinery, Mercedes-Benz, Audi 4S store and other large enterprises and projects have settled in Shunqing. Third, strengthen project construction. Annual implementation focus project 39 a, fixed assets investment total will breakthrough 12 billion yuan, created district yilai history high, South door dam, and five in shop old city transformation, and Ying China industrial concentrated district construction, and city main road construction, and Northeast steam Trade Center, and modern farmers industry Park, and vocational education city, and low rental, and also room construction, and features blocks build, and farmers market transformation, and rural version Street transformation, focus engineering speed up implementation, effectiveness obviously. Expected to be achieved this year, area-wide GDP 17 billion