当前位置:首页 > 七年级 > 数学试卷

【349942】年山东省潍坊市中考数学试题

时间:2025-03-05 22:03:04 作者: 字数:23619字
简介:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 山东省潍坊市中考数学真题

第Ⅰ卷 (选择题 36分)

一、选择题(本大题共12小题,共36分.在每小题给出的四个选项中,只有一项是正确的,请把正确的选项选出来,每小题选对得3分,错选、不选或选出的答案超过一个均记0分.)

1.下列图形,既是中心对称图形又是轴对称图形的是(

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】C

【解析】

【分析】

根据轴对称图形与中心对称图形的概念依次对各项进行判断即可.

【详解】A.不是轴对称图形,是中心对称图形,故此选项不符合题意;

B.是轴对称图形,不是中心对称图形,故此选项不符合题意;

C.是轴对称图形,也是中心对称图形,故此选项符合题意;

D.是轴对称图形,不是中心对称图形,故此选项不符合题意;

故选:C

【点睛】本题考查中心对称图形与轴对称图形的识别.轴对称图形的关键是寻找对称轴,图形两部分折叠后可重合,中心对称图形是要寻找对称中心,旋转180度后两部分重合.

2.下列运算正确的是(

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】B

【解析】

【分析】

根据合并同类项、幂的乘方,同底数幂乘法以及完全平方公式,逐项判断即可.

【详解】A、不是同类项,不能合并,故选项A计算错误;

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,故选项B计算正确;

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,故选项C计算错误;

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,故选项D计算错误.

故选B

【点睛】本题考查合了并同类项,同底数幂的乘法和积的乘方、以及完全平方公式,解题关键是熟记运算法则和公式.

3.今年的政府工作报告中指出:去年脱贫攻坚取得决定性成就,农村贫困人口减少1109万.数字1109万用科学记数法可表示为(

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】A

【解析】

【分析】

科学记数法 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 表示形式为a×10n,其中1≤|a|10n为整数,故先将1109万换成11090000,再按照科学记数法的表示方法表示即可得出答案.

【详解】∵1109=11090000

11090000=1.109×107

故选:A

【点睛】本题考查了科学记数法的简单应用,属于基础知识的考查,比较简单.

4.将一个大正方体的一角截去一个小正方体,得到的几何体如图所示,则该几何体的左视图是(

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】D

【解析】

【分析】

找到从左面看所得到的图形即可,注意所有的看到的棱都应表现在左视图中.

【详解】从几何体的左边看可得到一个正方形,正方形的右上角处有一个看不见的小正方形画为虚线,
故选:D

【点睛】本题考查了三视图 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 知识,左视图是从物体的左面看得到的视图;注意看到的用实线表示,看不到的用虚线表示.

5.为调动学生参与体育锻炼的积极性,某校组织了一分钟跳绳比赛活动,体育组随机抽取了10名参赛学生的成绩,将这组数据整理后制成统计表:

一分钟跳绳个数(个)

141

144

145

146

学生人数(名)

5

2

1

2


则关于这组数据的结论正确的是(

A. 平均数是144 B. 众数是141 C. 中位数是144.5 D. 方差是5.4

【答案】B

【解析】

【分析】

根据平均数,众数,中位数,方差的性质分别计算出结果,然后判判断即可.

【详解】解:根据题目给出的数据,可得:

平均数为: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,故A选项错误;

众数是:141,故B选项正确;

中位数是: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,故C选项错误;

方差是: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,故D选项错误;

故选:B

【点睛】本题考查的是平均数,众数,中位数,方差的性质和计算,熟悉相关性质是解题的关键.

6. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的值是(

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

【答案】D

【解析】

【分析】

把所求代数式 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 变形为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,然后把条件整体代入求值即可.

【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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

=4×1-3

=1

故选:D

【点睛】此题主要考查了代数式求值以及“整体代入”思想,解题的关键是把代数式 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 变形为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

7.如图,点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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的边 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上的一点,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 并延长交 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的延长线于点F,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

A. 21 B. 28 C. 34 D. 42

【答案】C

【解析】

【分析】

根据平行四边形的性质和相似三角形的判定和性质解答即可.

【详解】解:∵四边形ABCD是平行四边形,

AB∥CFAB=CD

∴△ABE∽△DFE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

AE=6AB=8

AD=AE+DE=6+3=9

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的周长为:(8+9×2=34

故选:C

【点睛】此题考查相似三角形的判定和性质,关键是根据平行四边形的性质和相似三角形的判定和性质解答.

8.关于x的一元二次方程 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 根的情况,下列说法正确的是(

A. 有两个不相等的实数根 B. 有两个相等的实数根

C. 无实数根 D. 无法确定

【答案】A

【解析】

【分析】

先计算判别式,再进行配方得到△=k-12+4,然后根据非负数的性质得到△>0,再利用判别式的意义即可得到方程总有两个不相等的实数根.

【详解】△=(k-3)2-4(1-k)

=k2-6k+9-4+4k

=k2-2k+5

=(k-1)2+4

k-12+40,即△>0

方程总有两个不相等的实数根.

故选:A

【点睛】本题考查的是根的判别式,一元二次方程ax2+bx+c=0a≠0)的根与△=b2-4ac有如下关系:①当△>0时,方程有两个不相等的实数根;②当△=0时,方程有两个相等的实数根;③当△<0时,方程无实数根.上面的结论反过来也成立.

9.如图,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的图象相交于点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 两点,则不等式 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的解集为(

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】D

【解析】

【分析】

结合图像,求出一次函数图象在反比例函数图象上方所对应的自变量的范围即可.

【详解】解:∵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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的图象相交于点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 两点,

不等式 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的解集为: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

故选:D

【点睛】本题考查了一次函数与反比例函数的交点问题,关键是注意掌握数形结合思想的应用.

10.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,以点O为圆心,2为半径的圆与 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 交于点C,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 于点D,点P是边 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上的动点.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 最小时, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> C. 1 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】B

【解析】

【分析】

延长CO <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 于点E,连接EP,交AO于点P,则PC+PD的值最小,利用平行线份线段成比例分别求出CDPO的长即可.

【详解】延长CO <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 于点E,连接ED,交AO于点P,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

CD⊥OB

∴∠DCB=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∴∠DCB=∠AOB

CD//AO

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

OC=2OB=4

BC=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

CD//AO

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,解得,PO= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

故选:B

【点睛】此题主要考查了轴对称---最短距离问题,同时考查了平行线分线段成比例,掌握轴对称性质和平行线分线段成比例定理是解题的关键.

11.若关于x的不等式组 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 有且只有3个整数解,则a的取值范围是(

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】C

【解析】

【分析】

先求出不等式组的解集(含有字母a),利用不等式组有三个整数解,逆推出a的取值范围即可.

【详解】解:解不等式 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

解不等式 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

不等式组的解集为: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

不等式组 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 有三个整数解,

三个整数解为:234

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

故选:C

【点睛】本题考查了解一元一次不等式组,一元一次不等式组的整数解的应用,解此题的关键就是根据整数解的个数求出关于a的不等式组.

12.若定义一种新运算: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 例如: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> .则函数 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的图象大致是(

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】A

【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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,可得当 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,分两种情况当 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 时和当 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 时,分别求出一次函数的关系式,然后判断即可.

【详解】解: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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,函数图像向上, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的增大而增大,

综上所述,A选项符合题意,

故选:A

【点睛】本题考查了一次函数的图象,能在新定义下,求出函数关系式是解题的关键

第Ⅱ卷(非选择题 84分)

说明:将第Ⅱ卷答案用0.5mm的黑色签字笔答在答题卡的相应位置上.

二、填空题(本大题共6小题,共18分.只要求填写最后结果,每小题填对得3分.)

13.因式分解:x2y﹣9y_____

【答案】yx+3)(x﹣3

【解析】

【分析】

先提取公因式y,再对余下的多项式利用平方差公式继续分解.

【详解】解:x2y﹣9y

yx2﹣9),

yx+3)(x﹣3).

【点睛】本题主要考查利用平方差公式分解因式,熟记公式结构是解题的关键.

14. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> _________

【答案】5

【解析】

【分析】

根据非负数的性质列式求出 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的值,然后代入代数式进行计算即可得解.

【详解】根据题意得, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

故答案为:5

【点睛】本题考查了绝对值非负性,算术平方根非负性的性质,根据几个非负数的和等于0,则每一个算式都等于0列式是解题的关键.

15.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 垂直平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,垂足为Q,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 于点P.按以下步骤作图:①以点A为圆心,以适当的长为半径作弧,分别交边 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 于点DE;②分别以点DE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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的长为半径作弧,两弧相交于点F;⑤作射线 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的夹角为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【答案】55°

【解析】

【分析】

根据直角三角形两锐角互余得∠BAC=70°,由角平分线的定义得∠2=35°,由线段垂直平分线可得△AQM是直角三角形,故可得∠1+∠2=90°,从而可得∠1=55°,最后根据对顶角相等求出 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【详解】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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∵△ABC是直角三角形,∠C=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的平分线,

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的垂直平分线,

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 是直角三角形,

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∵∠α与∠1是对顶角,

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

故答案为:55°

【点睛】此题考查了直角三角形两锐角互余,角平分线的定义,线段垂直平分线的性质,对顶角相等等知识,熟练掌握相关定义和性质是解题的关键.

16.若关于x的分式方程 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 有增根,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

先把分式方程去分母转化为整式方程,然后由分式方程有增根求出 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的值,代入到转化以后的整式方程中计算即可求出 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的值.

【详解】解:去分母得: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,整理得: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

关于 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的分式方程 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 有增根,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 代入到 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 中得: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本题主要考查了利用增根求字母的值,增根就是使最简公分母为零的未知数的值;解决此类问题的步骤:①化分式方程为整式方程;②让最简公分母等于零求出增根的值;③把增根代入到整式方程中即可求得相关字母的值.

17.如图,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 中,点GE分别在边 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 分别沿 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 折叠,使点BC恰好落在 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上的同一点,记为点F.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

根据折叠的性质结合勾股定理求得GE <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> BC=AD=8,证得Rt△EGF <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> Rt△EAG,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,再利用勾股定理得到DE的长,即可求解.

【详解】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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 中,GC=4CE =3,∠C=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

GE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

根据折叠的性质:BG=GFGF=GC=4CE=EF=3,∠AGB=∠AGF,∠EGC=∠EGF,∠GFE =∠C=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

BG=GF=GC=4

BC=AD=8

∵∠AGB+∠AGF+∠EGC+∠EGF=180 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∴∠AGE=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

Rt△EGF <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> Rt△EAG

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本考查了折叠的性质,矩形的性质,勾股定理的应用,相似三角形的判定和性质,锐角三角形函数的知识等,利用勾股定理和相似三角形的性质求线段的长度是本题的关键.

18.如图,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 是正方形,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 是由一段段90度的弧组成的.其中: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的圆心为点A,半径为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的圆心为点B,半径为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的圆心为点C,半径为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 圆心为点D,半径为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的圆心依次按点ABCD循环.若正方形 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的边长为1,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的长是_________

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 是由一段段90度的弧组成的,半径每次比前一段弧半径+1,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,再计算弧长.

【详解】解:由图可知,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 是由一段段90度的弧组成的,半径每次比前一段弧半径+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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的半径为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的弧长= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】此题主要考查了弧长的计算,弧长的计算公式: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,找到每段弧的半径变化规律是解题关键.

三、解答题(本大题共7小题,共66分.解答应与出文字说明、证明过程或演算步骤.)

19.先化简,再求值: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,其中x16的算术平方根.

【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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

先将括号里 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 进行通分运算,然后再计算括号外的除法,把除法运算转化为乘法运算,进行约分,得到最简分式,最后把x值代入运算即可.

【详解】解:原式= <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

x16的算术平方根,

x=4

x=4时,原式= <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本题考查了分式的化简求值:先把分式化简后,再把分式中未知数对应的值代入求出分式的值.在化简的过程中要注意运算顺序和分式的化简.化简的最后结果分子、分母要进行约分,注意运算的结果要化成最简分式或整式.

20.某校“综合与实践”小组采用无人机辅助的方法测量一座桥的长度.如图,桥 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 是水平并且笔直的,测量过程中,小组成员遥控无人机飞到桥 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的上方120米的点C处悬停,此时测得桥两端AB两点的俯角分别为60°45°,求桥 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的长度.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

C地点作 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ABD点,根据桥两端AB两点的俯角分别为60°45°,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,利用特殊角懂得三角函数求解即可.

【详解】解:如图示:过C地点作 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ABD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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

则有: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本题考查了特殊角的三角函数的运算,熟悉特殊角的三角函数值是解题的关键.

21.423日“世界读书日”来临之际,某校为了了解学生的课外阅读情况,从全校随机抽取了部分学生,调查了他们平均每周的课外阅读时间t(单位:小时).把调查结果分为四档,A档: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> B档: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> C档: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> D档: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> .根据调查情况,给出了部分数据信息:

A档和D档的所有数据是:777.51071077.57710.510.5

1和图2是两幅不完整的统计图.

根据以上信息解答问题:

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

1)求本次调查的学生人数,并将图2补充完整;

2)已知全校共1200名学生,请你估计全校B档的人数;

3)学校要从D档的4名学生中随机抽取2名作读书经验分享,已知这4名学生1名来自七年级,1名来自八年级,2名来自九年级,请用列表或画树状图的方法,求抽到的2名学生来自不同年级的概率.

【答案】140人,补全图形见解析;(2480人;(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

1)用A档和D档所有数据数减去D档人数即可得到A档人数,用A档人数除以所占百分比即可得到总人数;用总人数减去A档,B档和D档人数,即可得到C档人数,从而可补全条统计图;

2)先求出B档所占百分比,再乘以1200即可得到结论;

3)分别用ABCD表示四名同学,然后通过画树状图表示出所有等可能的结果数,再用概率公式求解即可.

【详解】(1)由于A档和D档共有12个数据,而D档有4个,

因此A档共有:12-4=8人,

8÷20%=40人,

补全图形如下:

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

21200× <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> (人)

答:全校B档的人数为480人,

3)用A表示七年级学生,用B 表示八年级学生,用CD分别表示九年级学生,画树状图如下,

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

所以P2名学生来自不同年级)= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本题考查条形统计图以及树状图法,注意结合题意中“写出所有可能的结果”的要求,使用列举法,注意按一定的顺序列举,做到不重不漏.

22.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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的直径,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 于点F,点C为劣弧 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的中点,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

1)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的切线;

2)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,求阴影部分的面积.

【答案】1)证明见解析;(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

1)连接BF,证明BF//CE,连接OC,证明OC⊥CE即可得到结论;

2)连接OF,求出扇形FOC的面积即可得到阴影部分的面积.

【详解】(1)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

C为劣弧 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

OC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的半径,

CE <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的切线;

2)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

C为劣弧 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

S扇形FOC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

即阴影部分的面积为: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本题主要考查了切线的判定以及扇形面积的求法,熟练掌握切线的判定定理以及扇形面积的求法是解答此题的关键.

23.因疫情防控需要,消毒用品需求量增加.某药店新进一批桶装消毒液,每桶进价50元,每天销售量y(桶)与销售单价x(元)之间满足一次函数关系,其图象如图所示.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

1)求yx之间的函数表达式;

2)每桶消毒液的销售价定为多少元时,药店每天获得的利润最大,最大利润是多少元?(利涧=销售价-进价)

【答案】1)函数的表达式为:y=-2x+220;(280元,1800元.

【解析】

【分析】

1)设yx之间的函数表达式为y=kx+b ,将点(60100)、(7080)代入一次函数表达式,即可求解;

2)由题意得w=x-50)(-2x+220=-2x-802+1800,即可求解.

【详解】(1)设y与销售单价x之间的函数关系式为:y=kx+b

将点(60100)、(7080)代入一次函数表达式得:

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

故函数的表达式为:y=-2x+220

2)设药店每天获得的利润为W元,由题意得:

w=x-50)(-2x+220=-2x-802+1800

-20,函数有最大值,

x=80时,w有最大值,此时最大值是1800

故销售单价定为80元时,该药店每天获得的利润最大,最大利润1800元.

【点睛】此题主要考查了二次函数的应用以及用待定系数法求一次函数解析式等知识,正确利用销量×每件的利润=w得出函数关系式是解题关键.

24.如图1,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,点DE分别在边 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> .现将 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 绕点A顺时针方向旋转,旋转角为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,如图2,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

1)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 时,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

2)如图3,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 时,延长 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 垂直平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

3)在旋转过程中,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的面积的最大值,并写出此时旋转角 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的度数.

【答案】1)证明见解析;(2)证明见解析;(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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的面积的最大值为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,旋转角 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

1)利用 SAS”证得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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ABD即可得到结论;

2)利用 SAS”证得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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ABD,推出∠ACE=∠ABD,计算得出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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,利用等腰三角形“三线合一”的性质即可得到结论;

3)观察图形,当点D在线段BC的垂直平分线上时, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的面积取得最大值,利用等腰直角三角形的性质结合三角形面积公式即可求解.

【详解】(1)根据题意:AB=ACAD=AE,∠CAB=∠EAD=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∵∠CAE+∠BAE =∠BAD+∠BAE =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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∴∠CAE=∠BAD

ACEABD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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ABD(SAS)

CE=BD

2)根据题意:AB=ACAD=AE,∠CAB=∠EAD=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

ACEABD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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ABD(SAS)

∴∠ACE=∠ABD

∵∠ACE+∠AEC=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,且∠AEC=∠FEB

∴∠ABD+∠FEB=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∴∠EFB=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

CF⊥BD

AB=AC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> AD=AE=1,∠CAB=∠EAD=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> CD= AC+ 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

BC= CD

CF⊥BD

CF是线段BD的垂直平分线;

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 中,边BC的长是定值,则BC边上的高取最大值时 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的面积有最大值,

当点D在线段BC的垂直平分线上时, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的面积取得最大值,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

∵∵AB=AC= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> AD=AE=1,∠CAB=∠EAD=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> DG⊥BCG

AG= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,∠GAB=45 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

DG=AG+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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,∠DAB=180 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> -45 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> =135 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的面积的最大值为: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

旋转角 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本题属于几何变换综合题,考查了等腰直角三角形的性质,全等三角形的判定和性质,线段垂直平分线的判定和性质等知识,解题的关键是正确寻找全等三角形解决问题.

25.如图,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> x轴交于点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,与y轴交于点C,顶点为D,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 与抛物线的对称轴l交于点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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

1)求抛物线的表达式;

2)点P是第一象限内抛物线上的动点,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 时,求点P的坐标;

3)点N是对称轴l右侧抛物线上的动点,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上是否存在点M,使得以点MNE为顶点的三角形与 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 相似?若存在,求点M的坐标;若不存在,请说明理由.

【答案】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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ;(3)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上存在点M,使得以点MNE为顶点的三角形与 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 相似,点M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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【解析】

【分析】

1)直接将 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,解出ab的值即可得出答案;

2)先求出点C的坐标及直线BC的解析式,再根据图及题意得出三角形PBC的面积;过点PPG <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 轴,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 轴于点G,交BC于点F,设 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> ,根据三角形PBC的面积列关于t的方程,解出t的值,即可得出点P的坐标;

3)由题意得出三角形BOC为等腰直角三角形,然后分MN=EMMN=NENE=EM三种情况讨论结合图形得出边之间的关系,即可得出答案.

【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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 过点 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 抛物线解析式 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

2)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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 直线BC解析式为: <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

过点PPG <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 轴,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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 轴于点G,交BC于点F

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 为等腰直角三角形

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 的对称轴为 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> E的横坐标为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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> E在直线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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> E的纵坐标为5

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

MN=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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> (舍去)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 此时点M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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

ME=EN <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> (舍去)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 此时点M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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>


MN=EN <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

连接CM,易知当NC关于对称轴l的对称点时, <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

此时四边形CMNE为正方形

 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> (舍去)

此时点M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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 上存在点M,使得以点MNE为顶点的三角形与 <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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a> 相似,点M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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</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/561/" title="山东" class="c1" target="_blank">山东</a> <a href="/tags/995/" title="山东省" class="c1" target="_blank">山东省</a> <a href="/tags/1068/" title="潍坊" class="c1" target="_blank">潍坊</a>

【点睛】本题是一道综合题,涉及到二次函数的综合、相似三角形的判定及性质、等腰三角形的性质、勾股定理、正方形的性质等知识点,综合性比较强,解答类似题的关键是添加合适的辅助线.



www.ishijuan.cn 爱试卷为中小学老师学生提供免费的试卷下载关注”试卷家“微信公众号免费下载试卷