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
．
．·············································································································· 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)
(元)·························· 2分
，
有
，
，
．
，
．··········································································· 3分
定为100元，总收益有最大值．
元．································································································ 3分
，则记者共调查了
人．··················· 2分
(个)
个．
解：在
中，
，
．······················ 3分
中，
，
．········································································ 3分
．························································································· 2分
时，函数为
，它的图象显然与
．·································································································· 2分
时，依题意得方程
有两等实数根．
，
．
时函数图象与
分类讨论解得
或
．
·························································· 4分
．···································································································· 2分
时，原式
．························································································ 1分
证明：
，
，
．····················································· 2分
，
，即
．························ 2分
，
．
．·············································································································· 3分
··········································································· 4分
········································································································ 3分
12．60° 13．3∶5 14．
15．
16．
在如图所示的平面直角坐标系中，
在
在
轴的负半轴上，
交
交
，
，抛物线
过
三点．
是抛物线上
间的一点，过
于
，交
所在直线于
，若
，则判断四边形
的形状；(3分)
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)
中，点
是边
上一个动点，过
，设
交
的平分线于点
，交
与
的数量关系并加以证明；(3分)
会是菱形吗？若是，请证明，若不是，则说明理由；(3分)
是正方形？(3分)