【郴州中考数学试题及答案】2009

第1页共8页二00九年郴州市初中毕业考试试卷数学注意事项：1．答题前，考生务必将自己的姓名、准考证号写在答题卡和该试题卷的封面上，并认真核对答题卡上的姓名、准考证号和科目．2．考生作答时，选择题和非选择题均需作在答题卡上，在本试题卷上作答无效．考生在答题卡上按答题卡中注意事项的要求答题．3．考试结束后，将本试题卷和答题卡一并交回．4．本试卷包括试题卷和答题卡．满分100分，考试时间120分钟．试题卷共4页．如缺页，考生需声明，否则后果自负．一、选择题（本题满分20分，共10小题，每小题2分）1．－5的绝对值是（）A．5B．5-C．15D．15-2．函数12yx=-的自变量x的取值范围是（）A．0x¹B．2x¹C．2xD．2x3．下列各式计算不正确．．．的是（）A．(3)3--=B．42=C．()3339xx=D．1122-=4．我市免费义务教育已覆盖全市城乡，2008年初中招生人数达到47600人，将数据47600用科学记数法表示为（）A．44.7610´B．54.7610´C．50.47610´D．347.610´5．点(35)p，-关于x轴对称的点的坐标为（）A．(3,5)--B．(5,3)C．(3,5)-D．(3,5)6．为了支援地震灾区学生，学校开展捐书活动，以下是某学习小组5名学生捐书的册数：3，9，3，7，8，则这组数据的中位数是（）A．3B．7C．8D．97．不等式26x≤的解集为（）A．3x≥B．3x≤C．13x≥D．13x≤8．两圆的半径分别为3cm和8cm，圆心距为7cm，则该两圆的位置关系为（）A．外离B．外切C．相交D．内含9．如图1已知扇形AOB的半径为6cm，圆心角的度数为120°，若将此扇形围成一个圆锥，则围成的圆锥的侧面积为（）A．24πcmB．26πcmC．29πcmD．212πcm第2页共8页10．如图2是一张矩形纸片ABCD，AD=10cm，若将纸片沿DE折叠，使DC落在DA上，点C的对应点为点F，若BE=6cm，则CD=（）A．4cmB．6cmC．8cmD．10cm二、填空题（本题满分16分，共8小题，每小题2分）11．7的倒数是___________．12．因式分解：2mm-=_______________．13．方程320x+=的解是______________．14．如图3，在四边形ABCD中，已知ABCD=，再添加一个条件___________（写出一个即可），则四边形ABCD是平行四边形．(图形中不再添加辅助线)15．如图4，桌面上平放着一块三角板和一把直尺，小明将三角板的直角顶点紧靠直尺的边缘，他发现无论是将三角板绕直角顶点旋转，还是将三角板沿直尺平移，1Ð与2Ð的和总是保持不变，那么1Ð与2Ð的和是_______度．16．抛物线23(1)5yx=--+的顶点坐标为__________．17．不透明的袋中装有2个红球和3个黑球，它们除颜色外没有任何其它区别，搅匀后小红从中随机摸出一球，则摸出红球的概率是__________．18．如图5，在O中，40ABACA°=?，，则BÐ=________度．三、解答题（本题满分30分，共5小题，每小题6分）19．计算：2022(π2009)2sin45+-++-?20．化简：1ababba++--21图4图1120BOA6cmFEDBAC图2DCBA图3图5ABCO40°第3页共8页21．如图6，在下面的方格图中，将△ABC先向右平移四个单位得到△A1B1C1，再将△A1B1C1绕点A1逆时针旋转90°得到DA1B2C2，请依次作出△A1B1C1和△A1B2C2。22．如图7，数学活动小组来到校园内的一盏路灯下测量路灯的高度，测角仪AB的高度为1.5米，测得仰角为30°，点B到电灯杆底端N的距离BN为10米，求路灯的高度MN是多少米？（取2=1.414，3=1.732，结果保留两位小数）23．如图8，在DABC中，已知DE∥BC，AD=4，DB=8，DE=3，（1）求ADAB的值，（2）求BC的长αNBAPM图7图6ABCACBDE图8第4页共8页四、证明题（本题满分8分）24．如图9，E是正方形ABCD对角线BD上的一点，求证：AE=CE．五、应用题（本题满分16分，共2小题，每小题8分）25．李大叔今年五月份购买了一台彩电和一台洗衣机，根据“家电下乡”的补贴标准：农户每购买一件家电，国家将按每件家电售价的13%补贴给农户．因此，李大叔从乡政府领到了390元补贴款．若彩电的售价比洗衣机的售价高1000元，求彩电和洗衣机的售价各是多少元．26．郴州市一座美丽的旅游城市，吸引了很多的外地游客，某旅行社对5月份本社接待的外地游客来郴州旅游的首选景点作了一次抽样调查．调查结果如下图表：（如图10）（1）此次共调查了多少人？（2）请将以上图表补充完整．（3）该旅行社预计6月份接待外地来郴的游客2500人，请你估计首选去东江湖的人数约有多少人．六、综合题（本题满分10分）0东江湖莽山飞天山万华岩80苏仙岭2010010景点307060409050人数图10景点频数频率东江湖8729%莽山7525%飞天山21%苏仙岭4715.7%万华岩289.3%图9DCEBA第5页共8页27．如图11，已知正比例函数和反比例函数的图像都经过点M（－2，1-），且P（1-，－2）为双曲线上的一点，Q为坐标平面上一动点，PA垂直于x轴，QB垂直于y轴，垂足分别是A、B．（1）写出正比例函数和反比例函数的关系式；（2）当点Q在直线MO上运动时，直线MO上是否存在这样的点Q，使得△OBQ与△OAP面积相等？如果存在，请求出点的坐标，如果不存在，请说明理由；（3）如图12，当点Q在第一象限中的双曲线上运动时，作以OP、OQ为邻边的平行四边形OPCQ，求平行四边形OPCQ周长的最小值．2009年郴州市基础教育课程改革实验区初中毕业学业考试试卷数学参考答案及评分标准说明：一、如果考生的解法与本答案的解法不同，可参照本答案的评分意见给分．二、评卷中，不要因解答中出现错误而中断对该题的评阅，当解答中某一步出现错影响了后继部分，但该步以后的解答未改变这道题的内容和难度，在未发生新的错误前，可视影响的程度决定后面部分的记分但不应超过后面部分应给分数的一半，如有严重概念错误，就不记分．三、各题解答中右端所注分数，表示考生正确做到这一步应得的累加分数．一、选择题（本题满分20分，共10小题，每小题2分）图11xyBhx=2xAOMQP图12xyfx=2xBCAOMPQ第6页共8页题号12345678910答案ABCADBBCDA二、填空题（本题满分16分，共8小题，每小题2分）题号1112131415161718答案17(1)mm-23x=-180180ABCDADBCADBC∥°°=????或或或等（只要答对一个即可给分）90(15)，2570三、解答题（本题满分30分，共5小题，每小题6分）19、解：原式=4212++-·······································································4分=5····························································································6分20、解：原式=1ababab-+--······································································2分=1abab-+-·················································································4分=1+1·······················································································5分=2························································································6分21、正确作出图形即可，图略．平移（4分）旋转（2分）22、解：在直角三角形MPA中，30°，10AP=米310tan30105.7733MP=窗=椿米··············································3分因为1.5AB=米所以1.55.87.27MN=+=米························································5分答：路灯的高度为7.27米·······································································6分23、解：（1）因为48ADDB==，所以4812ABADDB=+=+=·················································1分所以41123ADAB==······································································3分（2）因为DEBC∥，所以ADEABC△∽△·········································4分所以DEADBCAB=··········································································5分因为3DE=所以313BC=所以9BC=···············································································6分四、证明题（本题满分8分）24、证明：因为四边形ABCD是正方形所以ABBC=············································································2分第7页共8页ABDCBD??····································································4分又BE是公共边·······································································6分所以ABECBE△≌△····································································7分所以AECE=············································································8分五、应用题（本题满分16分，共2小题，每小题8分）25．解：设一台彩电的售价为x元，一台洗衣机的售价为y元根据题意得：100013()390xy%xyì-=ïïíï+=ïî································································4分解得20001000xyì=ïïíï=ïî············································································7分答：略·······························································································8分26．（1）300人······································