2009年湖南省湘西自治州中考数学试题(word版含答案)

请点击查看更多内容：年湘西自治州初中毕业学业考试数学试题卷姓名：准考证号：-----------------------------------------------------------------------------------------------------------------注意事项：1、本卷为试题卷，考生应在答题卡上作答，在试题卷、草稿纸上答题无效．2、答题前，考生须先将自己的姓名、准考证号分别在试题卷和答题卡上填写清楚．3、答题完成后，请将试题卷、答题卡、草稿纸放在桌上，由监考老师统一收回．4、本试卷三大题，25小题，时量120分钟，满分120分．-----------------------------------------------------------------------------------------------------------------一、填空题（本大题8小题，每小题3分，共24分．将正确答案填在答题卡相应横线上）1．数3的绝对值是．2．用代数式表示“a与b的和”，式子为．3．如果x－y＜0，那么x与y的大小关系是xy．（填＜或＞符号）4．一个圆的半径是4，则圆的面积是．（答案保留π）5．一次函数3yxb的图像过坐标原点，则b的值为．6．长方形一条边长为3cm，面积为12cm2，则该长方形另一条边长为cm．7．截止到2008年底，湘西州在校小学生中的少数民族学生数约为21.2万人，约占全州小学生总数的80%，则全州的小学生总数大致为万．（保留小数点后一位）8．对于任意不相等的两个数a，b，定义一种运算※如下：a※b=baba，如3※2=52323．那么12※4=．二、选择题（本大题8个小题，每小题3分，共24分．将每个小题所给四个选项中惟一正确选项的代号在答题卡上填涂）9．一个角是80°，它的余角是（）A．10°B．100°C．80°D．120°10．要了解一批电视机的使用寿命，从中任意抽取40台电视机进行试验，在这个问题中，40是（）A．个体B．总体C．样本容量D．总体的一个样本请点击查看更多内容：．在下列运算中，计算正确的是（）A．326aaaB．235()aaC．824aaaD．2224()abab12．在直角坐标系中，点M（sin50°，－cos70°）所在的象限是（）A．第一象限B．第二象限C．第三象限D．第四象限13．在下列命题中，是真命题的是（）A．两条对角线相等的四边形是矩形B．两条对角线互相垂直的四边形是菱形C．两条对角线互相平分的四边形是平行四边形D．两条对角线互相垂直且相等的四边形是正方形14．O⊙的半径为10cm，弦AB＝12cm，则圆心到AB的距离为（）A．2cmB．6cmC．8cmD．10cm15．一个不透明的袋中装有除颜色外均相同的3个红球和2个黄球，从中随机摸出一个，摸到黄球的概率是（）A．23B．15C．25D．3516．如图，12//ll，∠1=120°，∠2=100°，则∠3=（）A．20°B．40°C．50°D．60°三、解答题（本大题9小题，共72分，每个题目都要求在答题卡的相应位置写出计算或证明的主要步骤）17．（本题5分）先化简再计算：yxyxyx222，其中x=3，y=2．18．（本题5分）解方程：2725xyxy①②19．（本题6分）如图，在△ABC中，DE∥BC，EF∥AB，求证：△ADE∽△EFC．l1l2123ABCDEF请点击查看更多内容：．（本题6分）吉首某中学九年级学生在社会实践中，向市区的中小学教师调查他们的学历情况，并将调查结果分别用下图的扇形统计图和折线统计图（不完整）表示．（1）求这次调查的教师总数；（2）补全折线统计图．21．（本题6分）在反比例函数xky的图像的每一条曲线上，y都随x的增大而减小．（1）求k的取值范围；（2）在曲线上取一点A，分别向x轴、y轴作垂线段，垂足分别为B、C，坐标原点为O，若四边形ABOC面积为6，求k的值．22．（本题6分）如图，在离水面高度为5米的岸上有人用绳子拉船靠岸，开始时绳子与水面的夹角为30°，此人以每秒0.5米收绳．问：（1）未开始收绳子的时候，图中绳子BC的长度是多少米？（2）收绳8秒后船向岸边移动了多少米?（结果保留根号）23．（本题8分）2009年5月22日，“中国移动杯”中美篮球对抗赛在吉首进行．为组织该活动，中国移动吉首公司已经在此前花费了费用120万元．对抗赛的门票价格分别为80元、200元和400元．已知2000张80元的门票和1800张200元的门票已经全部卖出．那么，如果要不亏本，400元的门票最低要卖出多少张？人数交通工具275其它私家车公交车自行车步行030025020015010050研究生中师专科本科其它学历结构请点击查看更多内容：．（本题10分）如图，等腰直角△ABC腰长为a，现分别按图1、图2方式在△ABC内内接一个正方形ADFE和正方形PMNQ．设△ABC的面积为S，正方形ADFE的面积为S1，正方形PMNQ的面积为S2，（1）在图1中，求AD∶AB的值；在图2中，求AP∶AB的值；（2）比较S1+S2与S的大小．25．（本题20分）在直角坐标系xoy中，抛物线2yxbxc与x轴交于两点A、B，与y轴交于点C，其中A在B的左侧，B的坐标是（3，0）．将直线ykx沿y轴向上平移3个单位长度后恰好经过点B、C．（1）求k的值；（2）求直线BC和抛物线的解析式；（3）求△ABC的面积；（4）设抛物线顶点为D，点P在抛物线的对称轴上，且∠APD=∠ACB，求点P的坐标．图1图2AECFBDAQCMBNP请点击查看更多内容：年湘西自治州初中毕业学业考试数学参考答案一、（本题8小题，每题3分，共24分，填错记0分）1．3；2．a+b；3．＜；4．16π；5．0；6．4；7．26.5；8．1/2二、（本题8小题，每题3分，共24分，选错记0分）9．A10．C11．D12．D13．C14．C15．C16．B三、（本题9个题，共72分）17．（本题5分）解：原式＝yxyxyxyx2)())((····································································2分＝x＋y－2x＋y＝－x＋2y······················································································4分因为x＝3，y＝2所以原式＝－3＋4＝1···········································································5分18．（本题5分）解：①＋②得4x＝12，即x＝3·································································2分代入①有6－y＝7，即y＝－1····························································4分所以原方程的解是：13yx·········································································5分19．（本题6分）证明：∵DE∥BC，∴DE∥FC，∴∠AED＝∠C·················································3分又∵EF∥AB，∴EF∥AD，∴∠A＝∠FEC··················································5分∴△ADE∽△EFC·············································································6分20．（本题6分）解：（1）总人数＝27555%500人··················································3分（2）教师中专科学历的人数＝50010%50人········································4分作图：····························································································6分注：第(2)问虽然没明确指出专科人数为50，但只要作图准确就可得6分．501001502002503000步行自行车公交车私家车其它275交通工具人数研究生中师专科本科其它学历结构请点击查看更多内容：．（本题6分）解（1）因为y的值随x的增大而减小，所以k＞0·············································2分（2）设A（x0，y0）则由已知，应有｜x0y0｜＝6·······························································4分即｜k｜＝6而k＞０所以k＝6．·····················································································6分22．（本题6分）解（1）如图，在Rt△ABC中，BCAC＝sin30°·····················································2分∴BC＝sin305＝10米······················································3分（2）收绳8秒后，绳子BC缩短了4米，只有6米，·····································4分这时，船到河岸的距离为1125365622米．·································6分23．（本题8分）解：2000张80元的门票收入为2000×80＝160000元；········································2分1800张200元的门票收入为1800×200＝360000元；········································4分1200000－160000－360000＝680000元，·······················································5分故400元的门票至少要卖出：680000÷400＝1700张．答：400元的门票最少要卖出1700张．·······················································8分24．（本题10分）解（1）图1中，∵AD＝DF，∠B＝45°，从而DF＝DB，∴AD＝DB，∴AD∶AB＝1∶2·································································2分图2中，∵PM＝MN，∠B＝45°，从而PM＝MB，∴MN＝MB，∴MN＝MB＝NC，∴AP∶AB＝PQ∶BC＝MN∶BC＝1∶3·········································