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【330337】2020年内蒙古包头市中考数学试题

时间:2025-02-09 10:58:14 作者: 字数:27227字

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 2020年初中升学考试试卷

数学

注意事项:

1.本试卷共6页,满分为120分,考试时间为120分钟.

2.答题前,考生务必先将自己的考生号、姓名、座位号等信息填写在试卷和答题卡的指定位置,请认真核对条形码上的相关信息后,将条形码粘贴在答题卡的指定位置上.

3.答选择题时,必须使用2B铅笔将答题卡上对应题目的答案标号涂黑,修改时用橡皮擦干净,再选涂其他答案.

4.答非选择题时,必须使用0.5毫米的黑色字迹签字笔书写,作图题可先用铅笔绘出,确认后再用0.5毫米的黑色字迹签字笔描清楚.要求字体工整,笔迹清晰.严格按题号所示的答题区域作答,超出答题区域书写的答案无效;在试卷、草稿纸上答题无效.

5.保持答题卡清洁、完整,严禁折叠、损坏.严禁在答题卡上做任何标记,严禁使用涂改液、胶带纸、修正带.考试结来后,将本试卷和答题卡一并交回.

一、选择题:本大题共有12小题,每小题3分,共36分.每小题只有一个正确选项.请将答题卡上对应题目的答案标号涂黑.

1. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的计算结果是(

A. 5 B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】C

【解析】

【分析】

根据二次根式的运算法则即可求解.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

故选C

【点睛】此题主要考查二次根式的运算,解题的关键是熟知其运算法则.

2.2020年初,国家统计局发布数据,按现行国家农村贫困标准测算,截至2019年末,全国农村贫困人口减少至551万人,累计减少9348万人.将9348万用科学记数法表示为(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】B

【解析】

【分析】

科学记数法的表示形式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的形式,其中1≤|a|10n为整数.确定n的值时,要看把原数变成a时,小数点移动了多少位,n的绝对值与小数点移动的位数相同.当原数绝对值≥10时,n是正数;当原数的绝对值<1时,n是负数.

【详解】解:9348=93480000用科学记数法表示为9.348× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>
故选:B

【点睛】本题考查了科学记数法的表示方法.科学记数法的表示形式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的形式,其中1≤|a|10n为整数,解题的关键是要正确确定a的值以及n的值.

3.A在数轴上,点A所对应的数用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 表示,且点A到原点的距离等于3,则a的值为(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 1 B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 2 C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D. 1

【答案】A

【解析】

【分析】

根据绝对值 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 几何意义列绝对值方程解答即可.

【详解】解:由题意得:|2a+1|=3

2a+10时,有2a+1=3,解得a=1

2a+10时,有2a+1=-3,解得a=-2

所以a的值为1-2

故答案为A

【点睛】本题考查了绝对值的几何意义,根据绝对值的几何意义列出绝对值方程并求解是解答本题的关键.

4.下列计算结果正确的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】D

【解析】

【分析】

根据幂的乘方、积的乘方、单项式除法、分式加法以及分式乘除混合运算的知识逐项排除即可.

【详解】解:A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故A选项错误;

B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故B选项错误;

C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故C选项错误;

D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故D选项正确.

故答案为D

【点睛】本题考查了幂的乘方、积的乘方、单项式除法、分式加法以及分式乘除混合运算等知识点,掌握相关运算法则是解答本题的关键.

5.如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的外角, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的度数为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】B

【解析】

【分析】

根据平行线的性质及三角形的内角和定理即可求解.

【详解】∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∴∠B= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∴∠A=180°-∠B- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故选B

【点睛】此题主要考查三角形的内角和,解题的关键是熟知三角形的内角和等于180°

6.如图,将小立方块①从6个大小相同的小立方块所搭的几何体中移走后,所得几何体(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A. 主视图改变,左视图改变 B. 俯视图不变,左视图改变

C. 俯视图改变,左视图改变 D. 主视图不变,左视图不变

【答案】C

【解析】

【分析】

主视图是从立体图形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 正面看,俯视图是从立体图形的上面看,左视图是从立体图形的左面看,根据题意,只需要考虑小立方块移走前后三视图的变化,即可做出选择.

【详解】主视图是从立体图形的正面看,俯视图是从立体图形的上面看,左视图是从立体图形的左面看,故将小立方块移走后,主视图不变,左视图和俯视图均发生改变.

故选择C

【点睛】本题主要考查三视图,判断小立方块移走前后的变化是解决本题的关键.

7.两组数据:3ab5a4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的平均数都是3.若将这两组数据合并为一组新数据,则这组新数据的众数为(

A. 2 B. 3 C. 4 D. 5

【答案】B

【解析】

【分析】

首先根据平均数的定义列出关于ab的二元一次方程组,再解方程组求得ab的值,然后求众数即可.

【详解】∵两组数据:3ab5a4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的平均数都是3

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得a3b1

则新数据3315342

众数为3

故选B

【点睛】此题考查了众数,掌握众数的定义是解题的关键,众数是一组数据中出现次数最多的数.

8.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的中点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的延长线于点E.若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】A

【解析】

【分析】

根据题意将BD,BC算出来,再利用勾股定理列出方程组解出即可.

【详解】∵AC=2,BC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

DAB的中点,

AD=CD=BD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

由题意可得:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

两式相减得:  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

解得DE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,BE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

故选A

【点睛】本题考查直角三角形中点性质和勾股定理,关键在于找出等式列出方程组.

9.如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的直径, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是弦,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 在直径 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的两侧.若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】D

【解析】

【分析】

根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的度数,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 得到半径,运用弧长公式计算即可.

【详解】∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案选D

【点睛】本题主要考查了弧长的计算,通过已知条件计算出圆心角和半径是解题的关键.

10.下列命题正确的是(

A. 若分式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为0,则x的值为±2

B. 一个正数的算术平方根一定比这个数小.

C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 有实数根.

【答案】D

【解析】

【分析】

A选项:当x=2时,分式无意义;

B选项:1的算数平方根还是1

C选项:可以让b=2a=1,代入式子中即可做出判断;

根据根的判别式可得到结论.

【详解】A选项:当x=2时,分式无意义,故A选项错误;

B选项:1的算数平方根还是1,不符合“一个正数的算术平方根一定比这个数小”,故B选项错误;

C选项:可以假设b=2a=1,满足 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,代入式子中,通过计算发现与结论不符,故C选项错误;

D选项: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,一元二次方程有实数根,故D选项正确.

故本题选择D

【点睛】本题主要考查分式值为0时的条件、算数平方根、不等式的性质及一元二次方程根的判别式问题,掌握分式的意义、算数平方根、不等式的性质及一元二次方程根的判别式的知识是解答本题的关键.

11.如图,在平面直角坐标系中,直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> x轴、y轴分别交于点A和点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一点,过点C <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,垂足为D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,垂足为E <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若双曲线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 经过点C,则k的值为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】A

【解析】

【分析】

由直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 求出OAOB的长,设出C(x <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ),证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得出CECD的长,进而得出结论.

【详解】解:对于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

根据题意知,四边形ODCE是矩形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 轴,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

经检验, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是原方程的根,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

C在反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的图象上,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故选:A

【点睛】本题考查了反比例函数综合,用到的知识点是相似三角形的判定与性质以及待定系数法求函数的解析式等,难度适中,正确求得C的坐标是关键,注意掌握数形结合思想与方程思想的应用.

12.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,按以下步骤作图:(1)分别以点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 为圆心,以大于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长为半径作弧,两弧相交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 两点(点M <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的上方);(2)作直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点O,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点D;(3)用圆规在射线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上截取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,过点O <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,垂足为F,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点G.下列结论:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;② <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;③ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;④若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的周长为25

其中正确的结论有(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A. 1 B. 2 C. 3 D. 4

【答案】D

【解析】

【分析】

证明四边形ADBE是菱形,推出FG是△ACD的中位线,即可得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,由此判断①;根据菱形的性质得到AD=BD,再利用Rt△ACD得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可判断②;根据FG是△ACD的中位线,证得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可判断③;设OA=x,则OF=9-x,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求出OA=5得到AB=10BC=8,再根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求出BD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可判断④.

【详解】由题意知:MN垂直平分AB

OA=OBED⊥AB

OD=OE

四边形ADBE是菱形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

OF∥BCAF=CF

FG是△ACD的中位线,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故①正确;

四边形ADBE是菱形,

AD=BD

Rt△ACD中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故②正确;

FG是△ACD的中位线,

GAD的中点,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,故③正确;

AC=6

AF=3

OA=x,则OF=9-x

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得x=5

AB=10

BC=8

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得BD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的周长为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

故选:D.

【点睛】此题考查了线段垂直平分线的作图方法,菱形的判定及性质定理,勾股定理,三角形的中位线的判定及性质,三角形中线的性质,这是一道四边形的综合题.

二、填空题:本大题共有8小题,每小题3分,共24分.请把答案填在答题卡上对应的横线上.

13.在函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,自变量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的取值范围是________________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】

【分析】

在函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,分母不为0,则x-3≠0,求出x的取值范围即可.

【详解】在函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,分母不为0

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

【点睛】本题是对分式有意义的考查,熟练掌握分母不为0是解决本题的关键.

14.分式方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的解是_____

【答案】x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】

【分析】

根据分式方程的解题步骤解出即可.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

方程左右两边同乘x2, 3xx=x2

移项合并同类项, x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

经检验, x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是方程的解.

故答案为: x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】本题考查分式方程的解法,关键在于熟练掌握解法步骤注意检验.

15.计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ______

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】

【分析】

先将乘方展开,然后用平方差公式计算即可.

【详解】解: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】本题考查了二次根式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 混合运算以及平方差公式的应用,掌握二次根式混合运算的运算法则和平方差公式是解答本题的关键.

16.如图,在正方形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> E是对角线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的延长线交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点F,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ______ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】

【分析】

先证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,可得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,再根据平行线的性质得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据三角形内角和定理即可求解;

【详解】∵四边形ABCD是正方形,

AB=CBAB∥CD

又∵BD是角平分线,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】本题主要考查了利用正方形的性质求角度,准确利用三角形全等和三角形内角和定理求解是解题的关键.

17.一个不透明的盒子里放置三张完全相同的卡片,分别标有数字123.随机抽取1张,放回后再随机抽取1张,则抽得的第二张卡片上的数字大于第一张卡片上的数字的概率为_____

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】

【分析】

根据题意可得基本事件总3×3=9,然后再确定抽得的第二张卡片上的数字大于第一张卡片上的数字的事件数,最后由概率公式计算即可.

【详解】解:分别从标有数字1233张卡片中随机抽取1张,放回后再随机抽取1张,基本事件总数3×3=9,抽得的第二张卡片上的数字大于第一张卡片上的数字的情况有(12)、(13)和(233种情况

则抽得的第二张卡片上的数字大于第一张卡片上的数字的概率为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】本题考查了运用列举法求概率,运用列举法确定所有情况数和所需情况数是解答本题的关键.

18.如图,在平行四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的平分线与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的平分线交于点E,若点E恰好在边 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为______

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】16

【解析】

【分析】

根据平行线的性质和角平分线的性质,得到∠BEC=90°,然后利用勾股定理,即可求出答案.

【详解】解:如图,在平行四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> AD=BCAD∥BCAB∥CD

∴∠AEB=∠CBE,∠DEC=∠BCE,∠ABC+∠DCB=180°

BECE分别是∠ABC和∠DCB的角平分线,

∴∠ABE=∠CBE,∠DCE=∠BCE

∴∠AEB=∠ABE,∠DEC =∠DCE,∠CBE+∠BCE=90°

AB=AE=2DE=DC=2,∠BEC=90°

AD=2+2=4

BC=AD=4

Rt△BCE中,由勾股定理,得

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案为:16

【点睛】本题考查了平行四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 性质,勾股定理,平行线的性质,角平分线的性质,解题的关键是熟练掌握所学的性质,正确求出角之间的关系进行解题.

19.在平面直角坐标系中,已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上的两点,将抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的图象向上平移nn是正整数)个单位,使平移后的图象与x轴没有交点,则n的最小值为_____

【答案】4

【解析】

【分析】

通过AB两点得出对称轴,再根据对称轴公式算出b,由此可得出二次函数表达式,从而算出最小值即可推出n的最小值.

【详解】∵AB的纵坐标一样,

AB是对称的两点,

对称轴 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> , <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

b=﹣4

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

抛物线顶点(2,﹣3)

满足题意n得最小值为4,

故答案为4

【点睛】本题考查二次函数对称轴的性质及顶点式的变形,关键在于根据对称轴的性质从题意中判断出对称轴.

20.如图,在矩形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 是对角线, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,垂足为E,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,则如 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值为_____

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】

【分析】

CBD作垂线,可以构造出一个30°直角三角CDF,进而求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,设直角 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 最小边DF=a,并用a的代数式表示出其他边,即可求出答案.

【详解】解:过CCF⊥BD,垂足为F

矩形ABCD,  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

AD∥BC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> AB=CD

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∴∠DBC=∠DCF=∠BAE=30°

DF=a,CF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> CD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> BD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∴∠AEB=∠CFD=90°

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

EB=DF=a

EF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> -a-a=2a

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】本题主要考察了矩形的性质和解直角三角形知识点,三角形全等的判定与性质,掌握以上知识是解题关键.

三、解答题:本大题共有6小题,共60分.请将必要的文字说明、计算过程或推理过程写在答题卡的对应位置.

21.我国 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 技术发展迅速,全球领先.某公司最新推出一款 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 产品,为了解用户对该产品的满意度,随机调查了30个用户,得到用户对该产品的满意度评分如下(单位:分):

83 92 68 55 77 71 73 62 73 95 92 94 72 64 59

66 71 75 69 86 87 79 81 77 68 82 62 77 61 88

整理上面的数据得到尚不完整的频数直方图(如图).请根据所给信息,解答下列问题:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

1)补全频数直方图;

2)参与调查的一个用户说:“我的满意度评分在这30个用户中是中位数”,该用户的满意度评分是_____分;

3)根据用户满意度评分,将用户的满意度从低到高分为三个等级:

满意度评分

低于60

60分到89

不低于90

满意度等级

不满意

满意

非常满意



估计使用该公司这款 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 产品的1500个用户中,满意度等级为“非常满意”的人数.

【答案】1)见详解;(274;(3200

【解析】

【分析】

1)由题意,求出满意度在90~100之间的频数,补全条形图即可;

2)把数据从小到大排列,找出第1516和数,即可求出中位数;

3)求出非常满意的百分比,然后乘以1500即可得到答案;

【详解】解:(1)根据题意,满意度在70~80之间的有:77717373727175797777,共10个;

满意度在90~100之间的有:92959294,共4个;

补全条形图,如下:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

2)把数据从小到大进行重新排列,则

15个数为:73

16个数为:75

中位数为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

故答案为:74

3)根据题意,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

1500个用户中满意度等级为“非常满意”的人数大约为200人.

【点睛】本题考查了直方图,频数分布直方表,用样本估计总体,中位数等知识,解题的关键是熟练掌握所学的知识,正确对题意进行分析解答.

22.如图,一个人骑自行车由A地到C地途经B地当他由A地出发时,发现他的北偏东 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 方向有一电视塔P,他由A地向正北方向骑行了 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 到达B地,发现电视塔P在他北偏东 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 方向,然后他由B地向北偏东 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 方向骑行了 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 到达C地.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

1)求A地与电视塔P的距离;

2)求C地与电视塔P的距离.

【答案】1AP= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;(26

【解析】

【分析】

1)由题意知:∠A=45°,∠NBC=15°,∠NBP=75°,过点BBE⊥AP于点E,求出AE=BE=3

2)先利用三角函数求出BP=6,继而根据方位角求得∠CBP=60°,结合BC=6,即可证得△BCP是等边三角形,从而求得答案.

【详解】(1)由题意知:∠A=45°,∠NBC=15°,∠NBP=75°

过点BBE⊥AP于点E,如图,

Rt△ABE中,∠ABE=90°-45°=45°

AE=BE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

AE=BE=3

Rt△BEP中,∠EBP=180°-∠ABE-∠NBP=60°

PE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

AP=AE+PE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

2)∵BE=3,∠BEP=90°,∠EBP=60°

BP= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

又∵∠CBP=∠NBP-∠NBC=75°-15°=60°BC=6

∴△BCP是等边三角形,

CP=BP=6

【点睛】此题考查锐角三角函数的实际应用,方位角的运用,等边三角形的判定及性质,根据题意明确各角度及线段,正确计算即可解决问题.

23.某商店销售 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 两种商品,A种商品的销售单价比B种商品的销售单价少40元,2A种商品和3B种商品的销售总额为820元.

1)求A种商品和B种商品的销售单价分别为多少元?

2)该商店计划购进 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 两种商品共60件,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 两种商品的进价总额不超过7800元,已知A种商品和B种商品的每件进价分别为110元和140元,应如何进货才能使这两种商品全部售出后总获利最多?

【答案】1A种商品和B种商品的销售单价分别为140元和180元.(2A20件,B40件时获得利润最大.

【解析】

【分析】

1)设AB的销售单价分别是xy,根据题意列出二元一次方程组即可求解;

2)设A进货m件,根据题意可得出关于m的一元一次不等式,解不等式即可得到结果.

【详解】(1)设A种商品和B种商品的销售单价分别为x元和y元,

根据题意可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A种商品和B种商品的销售单价分别为140元和180元.

2)设购进A商品m件,则购进B商品 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 件,

根据题意可得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

令总利润为w,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,获得利润最大,此时 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

A20件,B40件时获得利润最大.

【点睛】本题主要考查了一元一次不等式与二元一次方程组的实际应用,准确计算是解题的关键.

24.如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的直径,半径 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,垂足为O,直线l <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的切线,A是切点,D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的延长线交直线l于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的延长线交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点G,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的半径为3 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

1)求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长;

2)求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值及 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的长.

【答案】1AE=2;(2CG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> cos∠CAG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【解析】

【分析】

(1)过点EEH⊥OC,交OC的延长线于点H,证明四边形AOHE是矩形得到EH=OA=3,求得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可得到AE

(2)先证明△ADE∽△OCD求得AD=1.2OD=1.8,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 求得BF=2CF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,连接BG,证明△AFC∽△GFB,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可得到CG=CF+GF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,设CO延长线交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点N,连接GN,则∠CNG=∠CAG,在Rt△CGN中,求得NG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可得到cos∠CAG=cos∠CNG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

【详解】(1)过点EEH⊥OC,交OC的延长线于点H

直线l <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的切线,A是切点,

OA⊥AE

OC⊥AB

∴∠EHO=∠OAE=∠AOH=90°

四边形AOHE是矩形,

EH=OA=3AE=OH

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

AE=OH=CH-OC=2

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

(2)∵∠OAE=∠AOC=90°

OC∥AE

∴△ADE∽△OCD

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

AD=1.2OD=1.8

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

BF=2

OF=1

AF=4CF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

连接BG

∵∠ACF=∠B,∠AFC=∠GFB

∴△AFC∽△GFB

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

CG=CF+GF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

CO延长线交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点N,连接GN,则∠CNG=∠CAG

Rt△CGN中,∠CGN=90°CN=6CG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

NG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

cos∠CAG=cos∠CNG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】此题考查矩形的判定定理及性质定理,勾股定理,圆切线的性质定理,圆周角定理,相似三角形的判定及性质,锐角三角函数解直角三角形,熟记各定理并熟练运用解题,正确连接辅助线是解此题的关键.

25.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 绕点C按顺时针方向旋转得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 交于点D

1)如图,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,过点B <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,垂足为E,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值;

2)如图,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,过点D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 于点N,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的延长线于点M,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】1)①见解析;② <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ;(23

【解析】

【分析】

1)①根据旋转性质可知∠A=∠A´,根据平行线的性质可知∠ACA´=∠A´,得到∠A=∠ACA´,推出AD=CD,再由等角的余角相等可得∠BCD=∠CBD,推出CD=BD,最后推出结论;

Rt△BCE中,BC=2,可根据相似三角形的判定和性质求出BECE的长,过点EEM⊥ACM,则可求出EM,即可求得S△BECS△ACES△ABCS△ABE,进而求得答案;

2)根据勾股定理求出AB长,根据三角形面积相等求出CD,由相似三角形的判定可知△CDB∽△ADC,推出CD2=BD·AD,求得AD的值,根据平行线分线段成比例定理可知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求出CN,由B´C∥A得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值,进而求得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的值即可.

【详解】(1)①∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 绕点C按顺时针方向旋转得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∴∠A=∠A´

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∴∠ACA´=∠A´

∴∠ACA´=∠A

AD=CD

∵∠ACD+∠BCD=90°,∠A+∠ABC=90°

∴∠BCD=∠ABC

BD=CD

AD=BD

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

②∵∠BCD=∠ABC=∠CEM,∠ACB=∠BEC=∠EMC=90°

∴△ACB∽△BEC∽△CMEBC=2AC=4

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

CE=x,在Rt△CEB中,BE=2xBC=2

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> BE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

同理可得:EM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

S△BEC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

S△ACE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

S△ABC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

S△ABE= S△ABC-S△ACE-S△BEC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

2)在Rt△ABC中,BC=2AC=4

AB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得:CD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∵∠A=∠BCD,∠ADC=∠BDC

∴△ADC∽△BDC

CD2=BD·AD

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

解得:AD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

DM∥A´B´∴∠A´=∠CDM,∠A´CB´=∠DAN

∴△CDN∽△CA´B´

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∵∠ADC=∠A´CB´=90°

CN∥AB

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】本题考查是三角形旋转综合题,涉及到旋转的性质、相似三角形的判定和性质、勾股定理、平行线分线段成比例定理、三角形的面积、等腰三角形的判定等知识,熟练掌握并灵活运用这些知识是解题的关键.

26.如图,在平面直角坐标系中,抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 经过坐标原点,与x轴正半轴交于点A,该抛物线的顶点为M,直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 经过点A,与y轴交于点B,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

1)求b的值及点M的坐标;

2)将直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 向下平移,得到过点M的直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,且与x轴负半轴交于点C,取点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

3)点E是线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一动点,点F是线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 上一动点,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 的延长线与线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 交于点G.当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,是否存在点E,使得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ?若存在,求出点E的坐标;若不存在,请说明理由.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【答案】1b=3M3-3);(2)详见解析;(3)点E的坐标为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

【解析】

【分析】

1)将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 配方后可得顶点M的坐标,利用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 求出点A的坐标后代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 即可求出b的值;

2)先求出平移后的直线CM的解析式为y=- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> x <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,过点DDH⊥直线y=- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> x <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得到直线DH的解析式为y=2x-4,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 求出交点H1-2),分别求得DH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> DM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据sin∠DMH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 得到∠DMH=45°,再利用外角与内角的关系得到结论;

3)过点GGP⊥x轴,过点EEQ⊥x轴,先求出AB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 得到∠BAO=∠AFE,设GF=4a,则AE=EF=3a,证明△AEQ∽△ABO,求得AQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> aAF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a,再证△FGP∽△AEQ,得到FP= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> aOP=PG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,由此得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> + <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a+ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a=6,求出a得到AQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,将x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,得y= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,即可得到点E的坐标.

【详解】(1)∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

顶点M的坐标为(3-3.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> y=0,得x1=0x2=6

A6,0),

将点A的坐标代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,得-3+b=0

b=3

2)∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 平移得来,

m=- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

过点M(3-3),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,解得n= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

平移后的直线CM的解析式为y=- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> x <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

过点DDH⊥直线y=- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> x <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

设直线DH的解析式为y=2x+k,将点D2,0)的坐标代入,得4+k=0

k=-4

直线DH的解析式为y=2x-4.

解方程组 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

H1-2.

D(20)H(1-2)

DH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

M(3-3)D2,0,

DM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

sin∠DMH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

∴∠DMH=45°

∵∠ACM+∠DMH=∠ADM

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

3)存在点E

过点GGP⊥x轴,过点EEQ⊥x轴,

A(60)B0,3,

AB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,∠BEF=∠BAO+∠AFE

∴∠BAO=∠AFE

AE=EF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

GF=4a,则AE=EF=3a

EQ⊥x轴,

EQ∥OB

∴△AEQ∽△ABO

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

AQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a

AF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a.

∵∠AFE=∠PFG

∴△FGP∽△AEQ

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

FP= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a

OP=PG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> + <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a+ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> a=6,

解得a= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

AQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,

OQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 中,得y= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> 时,存在点E,使得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> ,此时点E的坐标为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a> .

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1060/" title="内蒙古" class="c1" target="_blank">内蒙古</a> <a href="/tags/1061/" title="包头" class="c1" target="_blank">包头</a>

【点睛】此题考查了抛物线的性质,待定系数法求函数解析式,一次函数平移的性质,两个一次函数交点坐标与方程组的关系,相似三角形的判定及性质,等腰三角形的性质,三角形的外角的性质定理,是一道抛物线的综合题,较难.