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1、2009年北京中考数学试卷WORD版含答案2009年北京高级中学中等学校招生考试 数学试卷 学校 姓名 准考证号 1.本试卷共6页，共五道大题，25道小题，满分120分。考试时间120分钟。 考 2.在试着和答题卡上认真填写学校名称、姓名和准考证号。 生 3.试题答案一律填涂或书写在答题卡上，在试卷上作答无效。 须 4.在答题卡上，选择题、作图题用2B铅笔作答，其他试题用黑色字迹签字笔作答。 知 5.考试结束，请将本试卷、答题卡和草稿纸一并交回。 一、选择题(本题共32分，每小题4分) 下面各题均有四个选项，其中只有一个是符合题意的。 1. 7的相反数是 117,7,A. B. C. D. 7
2、72. 改革开放以来，我国国内生产总值由1978年的3645亿元增长到2008年的300670亿元。将300670用科学记数法表示应为 6544A.0.3006710， B.3.006710， C.3.006710， D.30.06710， 3. 若右图是某几何体的三视图，则这个几何体是 A.圆柱 B.正方体 C.球 D.圆锥 主视图 左视图 俯视图 4. 若一个正多边形的一个外角是40?，则这个正多边形的边数是。 A.10 B.9 C.8 D.6 5. 某班共有41名同学，其中有2名同学习惯用左手写字，其余同学都习惯用右手写字，老师随机请1名同学解答问题，习惯用左手写字的同学被选中的概率是
3、1201A. B. C. D. 41416. 某班派9名同学参加拔河比赛，他们的体重分别是(单位:千克): 这组数据的众数和中位数分别是 67,59,61,59,63,57,70,59,65A B C D 59,6359,6159,5957,613227. 把分解因式，结果正确的是 xxyxy,，22222xxy，xxy,xxyxy，,xxxyy,，2A. B. C. D. ，8. 如图，C为?O直径AB上一动点，过点C的直线交?O于D、E两点， 且?ACD=45?，DF?AB于点F,EG?AB于点G,当点C在AB上运动yyxx时，设AF=，DE=，下列中图象中，能表示与的函数关系式demon
4、stration created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; on the other hand grasping the education and management of Party members, solidly carry out the primary school education, Party members and spring
5、training and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lectures, check problem, listen to the views, warmth, enhance the cohesion and Party member of Party organization of belonging sense. Torreya grandis;
6、 (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, financing 48 million yuan the proposed 60 kilowatts of photovoltaic power station a grid connected power generation after the village collective ann
7、ual income of 6 million yuan, at present is being docked bidding matters will be 5 million yuan to send special funds to invest invest to the villagers self-management, alg plate mesh factory every year for the village collective income of 5000 yuan; the village of three big Tang open contract, each
8、 year village collective income of 5000 yuan; 160 acres of collective Shanchang shares to the villagers to plant seedlings, is expected to 3 years after the village collective income 3 million yuan. In Qinglong mountain soil The use of per mu, the person in charge 的图象大致是 二、填空题(本题共16分，每小题4分) 325x，,9.
9、 不等式的解集是 . 10.如图，AB为?O的直径，弦CD?AB，E为上一点，若?BC,CEA=28，则?ABD= ?. 22xmk,，mk，11. 若把代数式xx,23化为的形式，其中为常数，则= mk,，. 12. 如图，正方形纸片ABCD的边长为1，M、N分别是AD、BC边上的点，将纸片的一角沿过点B的直线折叠，使A落在MN上，落点记为A，折痕交AD于点E,若M、N分别是AD、BC边的中点，则AN= ; 若M、N分别是AD、BC边的上距DCn,2最近的n等分点(,且n为整数)，则AN= (用含有n的式子表示) 三、解答题(本题共30分，每小题5分) ,11,013. 计算: ,，,200
10、92520,6,x6，,114. 解分式方程: xx,，22,CDAB,9015. 已知:如图，在?ABC中，?ACB=，于点D,点E 在 AC上，CE=BC,过E点作AC的垂线，交CD的延长线于点F .求证:AB=FC 22xxx,，12111xx,51416. 已知，求的值 ，demonstration created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; o
11、n the other hand grasping the education and management of Party members, solidly carry out the primary school education, Party members and spring training and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lect
12、ures, check problem, listen to the views, warmth, enhance the cohesion and Party member of Party organization of belonging sense. Torreya grandis; (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, fi
13、nancing 48 million yuan the proposed 60 kilowatts of photovoltaic power station a grid connected power generation after the village collective annual income of 6 million yuan, at present is being docked bidding matters will be 5 million yuan to send special funds to invest invest to the villagers se
14、lf-management, alg plate mesh factory every year for the village collective income of 5000 yuan; the village of three big Tang open contract, each year village collective income of 5000 yuan; 160 acres of collective Shanchang shares to the villagers to plant seedlings, is expected to 3 years after t
15、he village collective income 3 million yuan. In Qinglong mountain soil The use of per mu, the person in charge m17. 如图，A、B两点在函数的图象上. yx,0，x(1)求的值及直线AB的解析式; m(2)如果一个点的横、纵坐标均为整数，那么我们称这个点是格点.请直接写出图中阴影部分(不包括边界)所含格点的个数。 18. 列方程或方程组解应用题: 北京市实施交通管理新措施以来，全市公共交通客运量显著增加.据统计，2008年10月11日到2009年2月28日期间，地面公交日均客运量与
16、轨道交通日均客运量总和为1696万人次，地面公交日均客运量比轨道交通日均客运量的4倍少69万人次.在此期间，地面 公交和轨道交通日均客运量各为多少万人次, 四、解答题(本题共20分，第19题5分，第20题5分，第21题6分，第22题4分) ,19. 如图，在梯形ABCD中，AD?BC，?B=90,?C=45, AD=1,BC=4,E为AB中点，EF?DC交BC于点F,求EF的长. 20. 已知:如图，在?ABC中，AB=AC,AE是角平分线，BM平分?ABC交AE于点M,经过B,M两点的?O交BC于点G,交AB于点F,FB恰为?O的直径. (1)求证:AE与?O相切; 1(2)当BC=4,co
17、sC=时，求?O的半径. 321.在每年年初召开的市人代会上，北京市财政局都要报告上一年度市财政预算执行情况和当年预算情况。以下是根据20042008年度报告中的有关数据制作的市财政教育预算与实际投入统计图表的一部分. demonstration created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; on the other hand grasping the e
18、ducation and management of Party members, solidly carry out the primary school education, Party members and spring training and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lectures, check problem, listen to
19、the views, warmth, enhance the cohesion and Party member of Party organization of belonging sense. Torreya grandis; (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, financing 48 million yuan the pro
20、posed 60 kilowatts of photovoltaic power station a grid connected power generation after the village collective annual income of 6 million yuan, at present is being docked bidding matters will be 5 million yuan to send special funds to invest invest to the villagers self-management, alg plate mesh f
21、actory every year for the village collective income of 5000 yuan; the village of three big Tang open contract, each year village collective income of 5000 yuan; 160 acres of collective Shanchang shares to the villagers to plant seedlings, is expected to 3 years after the village collective income 3
22、million yuan. In Qinglong mountain soil The use of per mu, the person in charge 表1 20042008年北京市财政教育实际投入与预算的差值统计表(单位:亿元) 年份 2004 2005 2006 2007 2008 教育实际投入与预算的差值 6.7 5.7 14.6 7.3 请根据以上信息解答下列问题: (1)请在表1的空格内填入2004年市财政教育实际投入与预算的差值; (2)求20042008年北京市财政教育实际投入与预算差值的平均数; 7亿元.在此基础上，如果2009年北京市财政(3)已知2009年北京市财政
23、教育预算是141.教育实际投入按照(2)中求出的平均数增长，估计它的金额可能达到多少亿元, 22. 阅读下列材料: 小明遇到一个问题:5个同样大小的正方形纸片排列形式如图1所示，将它们分割后拼接成一个新的正方形.他的做法是:按图2所示的方法分割后，将三角形纸片?绕AB的中点O旋转至三角形纸片?处，依此方法继续操作，即可拼接成一个新的正方形DEFG. 请你参考小明的做法解决下列问题: (1)现有5个形状、大小相同的矩形纸片，排列形式如图3所示.请将其分割后拼接成一个平行四边形.要求:在图3中画出并 指明拼接成的平行四边形(画出一个符合条件的平行四边形即可); (2)如图4，在面积为2的平行四边形
24、ABCD中，点E、F、G、H分别是边AB、BC、CD、DA的中点，分别连结AF、BG、CH、DE得到一个新的平行四边形MNPQ请在图4中探究平行四边形MNPQ面积的大小(画图并直接写出结果). 五、解答题(本题共22分，第23题7分，第24题8分，第25题7分) 2k2410xxk，,23. 已知关于的一元二次方程有实数根，为正整x数. k(1)求的值; (2)当此方程有两个非零的整数根时，将关于x的二次函数2的图象向下平移8个单位，求平移后的图象的解yxxk,，,241析式; x(3)在(2)的条件下，将平移后的二次函数的图象在轴下方的部分x沿轴翻折，图象的其余部分保持不变，得到一个新的图象
25、.请你结合这个新的图象回答:当直线 1byxbbk,，,与此图象有两个公共点时，的取值范围. ，2demonstration created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; on the other hand grasping the education and management of Party members, solidly carry out t
26、he primary school education, Party members and spring training and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lectures, check problem, listen to the views, warmth, enhance the cohesion and Party member of P
27、arty organization of belonging sense. Torreya grandis; (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, financing 48 million yuan the proposed 60 kilowatts of photovoltaic power station a grid conne
28、cted power generation after the village collective annual income of 6 million yuan, at present is being docked bidding matters will be 5 million yuan to send special funds to invest invest to the villagers self-management, alg plate mesh factory every year for the village collective income of 5000 y
29、uan; the village of three big Tang open contract, each year village collective income of 5000 yuan; 160 acres of collective Shanchang shares to the villagers to plant seedlings, is expected to 3 years after the village collective income 3 million yuan. In Qinglong mountain soil The use of per mu, th
30、e person in charge , ABCD24. 在中，过点C作CE?CD交AD于点E,将线段EC绕点E逆时针旋转得到90线段EF(如图1) (1)在图1中画图探究: ,?当P为射线CD上任意一点(P不与C重合)时，连结EP绕点E逆时针旋转 9011得到线段EC.判断直线FC与直线CD的位置关系，并加以证明; 11?当P为线段DC的延长线上任意一点时，连结EP,将线段EP绕点E 逆时针旋转222,得到线段EC.判断直线CC与直线CD的位置关系，画出图形并直接写出你的90212结论. 4(2)若AD=6,tanB=,AE=1,在?的条件下，设CP=，S=，求与之间的yyxx1 PFC11
31、3函数关系式，并写出自变量的取值范围. xABCA,6,0B6,025. 如图，在平面直角坐标系中，三个机战的坐标分别为，xOy，1C0,43AC，延长AC到点D,使CD=,过点D作DE?AB交BC的延长线于点E. ，2(1)求D点的坐标; (2)作C点关于直线DE的对称点F,分别连结DF、EF，若过B点的直线将四边形CDFE分成周长相等的两个四ykxb,，边形，确定此直线的解析式; (3)设G为y轴上一点，点P从直线与y轴的交点出ykxb,，发，先沿y轴到达G点，再沿GA到达A点，若P点在y轴上运动的速度是它在直线GA上运动速度的2倍，试确定G点的位置，使P点按照上述要求到达A点所用的时间最
32、短。tanA不表示“tan”乘以“A”；(要求:简述确定G点位置的方法，但不要求证明) demonstration created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; on the other hand grasping the education and management of Party members, solidly carry out the pr
33、imary school education, Party members and spring training and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lectures, check problem, listen to the views, warmth, enhance the cohesion and Party member of Party
34、organization of belonging sense. Torreya grandis; (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, financing 48 million yuan the proposed 60 kilowatts of photovoltaic power station a grid connected
35、power generation after the village collective annual income of 6 million yuan, at present is being docked bidding matters will be 5 million yuan to send special funds to invest invest to the villagers self-management, alg plate mesh factory every year for the village collective income of 5000 yuan;
36、the village of three big Tang open contract, each year village collective income of 5000 yuan; 160 acres of collective Shanchang shares to the villagers to plant seedlings, is expected to 3 years after the village collective income 3 million yuan. In Qinglong mountain soil The use of per mu, the per
37、son in charge 10.三角函数的应用demonstration created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; on the other hand grasping the education and management of Party members, solidly carry out the primary school educati
38、on, Party members and spring training and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lectures, check problem, listen to the views, warmth, enhance the cohesion and Party member of Party organization of belo
39、nging sense. Torreya grandis; (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, financing 48 million yuan the proposed 60 kilowatts of photovoltaic power station a grid connected power generation aft
40、er the village collective annual income of 6 million yuan, at present is being docked bidding matters will be 5 million yuan to send special funds to invest invest to the villagers self-management, alg plate mesh factory every year for the village collective income of 5000 yuan; the village of three
41、 big Tang open contract, each year village collective income of 5000 yuan; 160 acres of collective Shanchang shares to the villagers to plant seedlings, is expected to 3 years after the village collective income 3 million yuan. In Qinglong mountain soil The use of per mu, the person in charge sin四、教
42、学重难点：demonstration created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; on the other hand grasping the education and management of Party members, solidly carry out the primary school education, Party members a
43、nd spring training and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lectures, check problem, listen to the views, warmth, enhance the cohesion and Party member of Party organization of belonging sense. Torrey
44、a grandis; (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, financing 48 million yuan the proposed 60 kilowatts of photovoltaic power station a grid connected power generation after the village coll
45、ective annual income of 6 million yuan, at present is being docked bidding matters will be 5 million yuan to send special funds to invest invest to the villagers self-management, alg plate mesh factory every year for the village collective income of 5000 yuan; the village of three big Tang open cont
46、ract, each year village collective income of 5000 yuan; 160 acres of collective Shanchang shares to the villagers to plant seedlings, is expected to 3 years after the village collective income 3 million yuan. In Qinglong mountain soil The use of per mu, the person in charge 一年级下册数学教学工作计划demonstratio
47、n created, strictly implement the two open three clear three understand village affairs and democratic management system, build sunshine village; on the other hand grasping the education and management of Party members, solidly carry out the primary school education, Party members and spring trainin
48、g and to commemorate the founding of 94 years of a series of activities, through studying the party constitution, the oath of the temperature, lectures, check problem, listen to the views, warmth, enhance the cohesion and Party member of Party organization of belonging sense. Torreya grandis; (II) to drive out of poverty for the first priority, and efforts to promote development. In view of the new village collective economic income status, financing 48 million yuan the proposed 60 kilowatts of photovoltaic power station a grid connected power