2011高一·安徽蚌埠·学业考试
1 . 如图,二次函数
的图象与反比例函数
图象相交于点
,已知点
的坐标为
,点
在第三象限内,且
的面积为3(
为坐标原点).
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721874432/STEM/61995801-d78e-4594-b7be-a7994b2a3dc0.png?resizew=233)
①求实数
的值;
②求二次函数
的解析式;
③设抛物线与
轴的另一个交点为
点为线段
上的动点(与
不重合),过
点作
交
于
,连接
设
的长为
,
的面积为
,求
与
的函数关系式;
④在③的基础上,试说明
是否存在最大值;若存在,请求出
的最大值,并求出此时
点的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333726ed57a25bc084db2b959570d76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ae286ae8a209bc659ace6354b79abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721874432/STEM/61995801-d78e-4594-b7be-a7994b2a3dc0.png?resizew=233)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
②求二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333726ed57a25bc084db2b959570d76f.png)
③设抛物线与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe964aa3574061970c9c8066df21c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a69a7547455f29e62954b7dc31bc157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c6391551862185369f6bcc6a899aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
④在③的基础上,试说明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
2 . 如图1:等边△ADE可以看作由等边△ABC绕顶点A经过旋转相似变换得到.但是我们注意到图形中的△ABD和△ACE的关系,上述变换也可以理解为图形是由△ABD绕顶点A旋转60°形成的.于是我们得到一个结论:如果两个正三角形存在着公共顶点,则该图形可以看成是由一个三角形绕着该顶点旋转60°形成的.
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721841664/STEM/567be70bbdb14ebf9dcdf54457f74cb5.png?resizew=441)
(1)利用上述结论解决问题:如图2,△ABC中,AB=3,AC=4,BC=5,△ABD,△ACE,△BFC都是等边三角形,求四边形ADFE的面积;
(2)图3中,△ABC∽△ADE,AB=AC,∠BAC=∠DAE=
,仿照上述结论,推广出符合图3的结论.(写出结论即可).
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721841664/STEM/567be70bbdb14ebf9dcdf54457f74cb5.png?resizew=441)
(1)利用上述结论解决问题:如图2,△ABC中,AB=3,AC=4,BC=5,△ABD,△ACE,△BFC都是等边三角形,求四边形ADFE的面积;
(2)图3中,△ABC∽△ADE,AB=AC,∠BAC=∠DAE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
3 . 已知
两地相距45千米,骑车人与客车分别从
两地出发,往返于
两地之间.下图中,折线表示某骑车人离开
地的距离
与时间
的函数关系.客车8点从
地出发,以45千米/时的速度匀速行驶.(乘客上、下车停车时间忽略不计)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721817088/STEM/f0351de7bc5f435b84def3d62e665159.png?resizew=365)
(1) 在阅读下图的基础上,直接回答:骑车人共休息几次?骑车人总共骑行多少千米?骑车人与客车总共相遇几次?
(2)试问:骑车人何时与客车第二次相遇?(要求写出演算过程).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721817088/STEM/f0351de7bc5f435b84def3d62e665159.png?resizew=365)
(1) 在阅读下图的基础上,直接回答:骑车人共休息几次?骑车人总共骑行多少千米?骑车人与客车总共相遇几次?
(2)试问:骑车人何时与客车第二次相遇?(要求写出演算过程).
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
4 . 设
表示不超过x的最大整数(例如:
),则方程
的解为__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fab6009ffb15a88bd843a1c2b8d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80f18bf3bfd4a15676885d39630a694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5c63372796bdb23a9f285dfb3bdc6e.png)
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
5 . 如图是一个挂在墙壁上时钟的示意图.
是其秒针的转动中心,
是秒针的另一端,
,
是过点
的铅直直线.现有一只蚂蚁
在秒针
上爬行,蚂蚁
到点
的距离与
到
的距离始终相等.则
分钟的时间内,蚂蚁
被秒针
携带的过程中移动的路程(非蚂蚁在秒针上爬行的路程)是 ______ ![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/fe456da7f8df4e8c84e8f8e2ead79cd1.png?resizew=24)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/349578f6f2004954af5fb083f6df215a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/27a2cbc597814829b2368cdd0e65c78e.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/332c351a97654b5daa09972d85becb72.png?resizew=75)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/c6fab83058d24934885c54373fce3066.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/349578f6f2004954af5fb083f6df215a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/b76a018b993a4d3eb896ce7f69bde5bd.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/16a2cca525f84f80b0fbc8395d4251cb.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/b76a018b993a4d3eb896ce7f69bde5bd.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/349578f6f2004954af5fb083f6df215a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/27a2cbc597814829b2368cdd0e65c78e.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/c6fab83058d24934885c54373fce3066.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/14918955d88e43d3a58733fd010dd5bc.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/b76a018b993a4d3eb896ce7f69bde5bd.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/16a2cca525f84f80b0fbc8395d4251cb.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/fe456da7f8df4e8c84e8f8e2ead79cd1.png?resizew=24)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721784320/STEM/644b7b49-3946-4b26-b7da-9bbb21d0cf20.png)
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
6 . 有三位学生参加两项不同的竞赛,则每位学生最多参加一项竞赛,其中一项竞赛只许有一位学生参加的概率为____________
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
7 . 如图:四边形EFGH是一个长方形台球桌面,有白、黑两球分别位于A,B两点的位置上.试问,怎样撞击白球A,才能使白球A先碰撞台边GH,再碰撞FG,经两次反弹后再击中黑球B?(将白球A移动路线画在图上,不能说明问题的不予计分)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721726976/STEM/df6b821ab12542cf9064a64a31504119.png?resizew=278)
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
8 . 已知函数
.
(1)在图的坐标系中画出
的图象;
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721702400/STEM/62f5b2cd20ce42bab46f5660d4356ed3.png?resizew=259)
(2)若
的最小值为
,当正数
,
满足
时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9527ed65d2740d81ea949515c7ebd954.png)
(1)在图的坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721702400/STEM/62f5b2cd20ce42bab46f5660d4356ed3.png?resizew=259)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8acc7885b7af2fccf3fb1056066203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219ba6c8a1b54598db1a78cab28d9d30.png)
您最近一年使用:0次
2011高一·安徽蚌埠·学业考试
9 . 如图,在直角
中,
,分别以
为圆心,以
为半径作弧,则三条弧与边
围成的图形(图中阴影部分)的面积为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93148adbc6e856da9a9d263f485d003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2011/5/20/1570213716729856/1570213721686016/STEM/535803786ac646f7b4077890385b79d2.png?resizew=228)
您最近一年使用:0次