4月鞍山市初中第一次质量检测（数学）参考答案及评分标准

参考答案一、选择题：DDCCBABC二、填空题：9、10、11、112、13、14、2或15、416、三、解答题：17、…………..….………….3……………………….……….5当时…….…………………….………………..………….6原式…….……….…………….818、证明：∵四边形是菱形∴∥∥…….……...……….3∴…….……………..…….6∴…….………………….….819、解：（1）200…….……………...............................….2（2）（人）；（人）…….……………..…….……….4画图正确…….……………….…………….…….6（3）（人）…….………………..….……….9答：约有580人。………………….….……….1020、解：（1）………………………..…….….……….2（2）…………….…….……….5此事件共有9种可能情况，且可能性相等，其中两人选择不同电影有6种可能情况，（刺，唐）（刺，你）（唐，刺）（唐，你）（你，刺）（你，唐）……………….….……….9……………….…….….……….1021、解：过作交于，设为米….……..…...................…...…….2∵∴四边形为矩形∴米∵∥∥∴….…….….……….3在中….…….….…...............................................…….5….…..............................….….……….6在中….…….….…................................................…….8米….………………..........................................9答：高度约为30米….…….….……....................................................................….1022、解：（1）∵过（2，4）∴∴…....................................................................................................................….2∵点横坐标为4时（4，2）…...............................................................................................................….3∵一次函数的图象过、两点∴…............................................................................................................….5（2）过作∥轴交于…................................................................................….6设（，0）（，）…......................................................................................................….7…...............................................................................….9（4，0）…......................................................................................................….1023、证明：（1）连接...........................................................................................................................….1∵∴∵∥∴.......................................................................................................….3∵为直径∴∴∴........................................................................................….4（2）连接，过作交于.........................................................................….5∵∴∵在中设∴.............................................................................................….7∵∴在中设∴........................................................................................….9∵四边形为圆内接四边形∴∴在中∴.....................................................................................….1024、解：（1）……….….…...............................................................…….2………...........................................................................….……….3∵∴有最大值当……….….…........................................................................................…….5（元）……….….……........................….6答：略（2）设购进烟花的价格为元/件……….….…...................................................................…….7（件）（天）……….….................................................................……….8……….….….....................................................................................…….10答：略25、证明：（1）证出..........................................................................................…….2证出........................................................................................…….3（2）证出证出为斜边中线............................................................................…….5证出∴.....................................................................…….7（3）方法1：过作交于，过作交延长线于.….8证出：证出：∴证出：∵∴∥...................................................................................…….9证出：证出：∵∥∴.................................................................................…….10证出：....................................................…….11∵∥∴∴...............................................................................…….12方法2:延长至，使得，连接.........................................................…….8证出：∴证出：后续证明同方法126、解：（1）求出：（3，0）（0，4）.........................................................…..................….2求出：解析式为....................................................................…….4（2）（0，）；（0，）..............................................................................…….8（3）方法1：过作轴交于.....................................................................…….9设证出：∴....................................................…….10证出：即...............................................................................…….11当方程有唯一实数根时，满足条件的只有一个..................................................…….12解得：（舍去）求出：（，）.........................................................…….13设平移后的抛物线为：将点坐标代入平移后解析式