23．解：(1)该商场销售家电的总收益为(元)·························· 2分

(2)依题意可设

，

有，，

解得．

所以，．··········································································· 3分

(3)

政府应将每台补贴款额定为100元，总收益有最大值．

其最大值为元．································································································ 3分

22．解：(1)设一次购物用6个袋的人数为人，则依条件有

，则记者共调查了人．··················· 2分

(2)这100位顾客平均一次购物使用购物袋的平均数为

(个)

个．

估计这三大商业集团为顾客每天提供18000个塑料购物袋．·········································· 3分

(3)74%；25；

多数人环保意识增强，(只要是涉及环保节能等方面思想向上的即可)．····················· 3分

21．解：在中，

∵，

∴．······················ 3分

在中，

∵，

∴．········································································ 3分

∴．························································································· 2分

答：发射架高为25m．

20．解：(1)当时，函数为，它的图象显然与轴

只有一个交点．·································································································· 2分

当时，依题意得方程有两等实数根．

，．

当或时函数图象与轴恰有一个交点．··················································· 2分

(2)依题意有分类讨论解得或．

当或时，抛物线顶点始终在轴上方．······················································· 4分

19．解：原式·························································· 4分

．···································································································· 2分

当时，原式．························································································ 1分

18．证明：，

，

．····················································· 2分

又，

，即．························ 2分

又，

．

．·············································································································· 3分

17．解：原式··········································································· 4分

　　　　　　 ········································································································ 3分

11．　　 12．60°　　 13．3∶5　　　 14．　　 15．　　 16．

25．(本小题满分10分)

正方形在如图所示的平面直角坐标系中，在轴正半轴上，在轴的负半轴上，交轴正半轴于交轴负半轴于，，抛物线过三点．

(1)求抛物线的解析式；(3分)

(2)是抛物线上间的一点，过点作平行于轴的直线交边于，交所在直线于，若，则判断四边形的形状；(3分)

(3)在射线上是否存在动点，在射线上是否存在动点，使得且，若存在，请给予严格证明，若不存在，请说明理由．(4分)

黄石市2009年初中毕业生学业考试

数学答案及评分标准

24．(本小题满分9分)

如图，中，点是边上一个动点，过作直线，设交的平分线于点，交的外角平分线于点．

(1)探究：线段与的数量关系并加以证明；(3分)

(2)当点在边上运动时，四边形会是菱形吗？若是，请证明，若不是，则说明理由；(3分)

(3)当点运动到何处，且满足什么条件时，四边形是正方形？(3分)