1.下面关于分子力的说法中，错误的是(　)

A.铁丝很难被拉长，这一事实说明铁丝分子间存在相互作用的引力

B.水很难被压缩，这一事实说明水分子间存在相互作用的斥力

C.将打气管的出口端封住后向下压活塞，当空气被压缩到一定程度后很难再被压缩，这一事实说明此时空气分子间的作用力表现为斥力

D.磁铁可以吸引铁屑，这一事实说明分子间存在相互作用的引力

答案：CD

24．(本小题满分12分)

解：(1)圆心在坐标原点，圆的半径为1，

点的坐标分别为

抛物线与直线交于点，且分别与圆相切于点和点，

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

点在抛物线上，将的坐标代入

，得：　 解之，得：

抛物线的解析式为：．······································································ 4分

(2)

抛物线的对称轴为，

．···················· 6分

连结，

，，

又，

，

．····································································· 8分

(3)点在抛物线上．································································································ 9分

设过点的直线为：，

将点的坐标代入，得：，

直线为：．······················································································ 10分

过点作圆的切线与轴平行，点的纵坐标为，

将代入，得：．

点的坐标为，··························································································· 11分

当时，，

所以，点在抛物线上．···································································· 12分

说明：解答题各小题中只给出了1种解法，其它解法只要步骤合理、解答正确均应得到相应的分数．

23．(本小题满分11分)

解：(1)在四边形中，，，

四边形为直角梯形(或矩形)．

过点作，垂足为，，

又点是的中点，点是的中点，

又，

，···································································································· 3分

与是全等的等腰直角三角形，

，

是等腰直角三角形．······················································································ 5分

(2)存在点使．·················································································· 6分

以为直径，为圆心作圆．

当时，四边形为矩形，，

圆与相切于点，此时，点与点重合，存在点，使得，

此时．································································································· 7分

当时，四边形为直角梯形，

，，圆心到的距离小于圆的半径，圆与相交，上存在两点，使，··········································································································· 8分

过点作，在中，，

连结，则，

在直角三角形中，，

．

同理可得：．

综上所述，在线段上存在点，使．

当时，有一点，；当时，有两点，． 11分

22．(本小题满分10分)

(1)证明：平分

·················································································· 2分

平分

，又

为等腰三角形

····················································································· 5分

(2)解：当时，为钝角三角形，

圆心在外，

连结，

，

，

为正三角形．··············································· 8分

又知，

答：的面积为cm²．·············································································· 10分

21．(本小题满分10分)

解：(1)设两块绿地周围的硬化路面的宽都为米，根据题意，得：

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

解之，得：························································································· 5分

经检验，不符合题意，舍去．

所以，两块绿地周围的硬化路面宽都为10米．······························································ 6分

(2)设想成立．··········································································································· 7分

设圆的半径为米，到的距离为米，根据题意，得：

·············································································································· 9分

解得：．符合实际．

所以，设想成立，此时，圆的半径是10米．······························································· 10分

20．(本小题满分9分)

解：(1)过点F作，交于点．

为的中点

为的中点，．················· 2分

由，得，

··········································· 4分

·········································································· 6分

(2)

又

．············································································ 9分

19．(本小题满分9分)

解：(1)应聘者A总分为86分；应聘者B总分为82分；应聘者C总分为81分；应聘者D总分为82分．　　　 4分

(2)4位应聘者的专业知识测试的平均分数，

方差为：····················· 5分

4位应聘者的英语水平测试的平均分数，

方差为：．·············································································· 6分

4位应聘者参加社会实践与社团活动等的平均分数为，

方差为：．················· 7分

(3)对于应聘者的专业知识、英语水平的差距不大，但参加社会实践与社团活动等方面的差距较大，影响学生的最后成绩，将影响学生就业．学生不仅注重自己的文化知识的学习，更应注重社会实践与社团活动的开展，从而促进学生综合素质的提升．··························································································································· 9分

18．(本小题满分8分)

解：(1)从纸箱厂定制购买纸箱费用：

························································································································ 2分

蔬菜加工厂自己加工纸箱费用：

．···································································································· 4分

(2)

，

由，得：，

解得：．······································································································ 5分

当时，，

选择方案一，从纸箱厂定制购买纸箱所需的费用低．····················································· 6分

当时，，

选择方案二，蔬菜加工厂自己加工纸箱所需的费用低．················································· 7分

当时，，

两种方案都可以，两种方案所需的费用相同．······························································· 8分

24．如图，在平面直角坐标系中，半径为1的圆的圆心在坐标原点，且与两坐标轴分别交于四点．抛物线与轴交于点，与直线交于点，且分别与圆相切于点和点．

(1)求抛物线的解析式；

(2)抛物线的对称轴交轴于点，连结，并延长交圆于，求的长．

(3)过点作圆的切线交的延长线于点，判断点是否在抛物线上，说明理由．

1-12DBADACCBCDAB　 13．　 14．　 15．见右图　 16．　 17．

23．在四边形中，，且．取的中点，连结．

(1)试判断三角形的形状；

(2)在线段上，是否存在点，使．若存在，请求出的长；若不存在，请说明理由．