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【330362】2020年四川省内江市中考数学试题

时间:2025-02-09 11:10:10 作者: 字数:30502字

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 内江市2020年初中学业水平考试暨高中阶段学校招生考试试卷

数学试题

A卷(共100分)

注意事项:

1、答题前,考生务必将将自己的姓名、学号、班级等填写好.

2、答A卷时,每小题选出答案后,用钢笔或水笔把答案直接填写在对应题目的后面括号.

第Ⅰ卷(选择题 36分)

一、选择题(本大题共12小题,每小题3分,共36分.在每小题给出的四个选项中,只有一项是符合题目要求的.)

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的倒数是(

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】A

【解析】

【分析】

根据乘积是1的两个数叫做互为倒数,求解.

【详解】解:∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的倒数是2

故选:A

【点睛】本题考查倒数的概念,掌握概念正确计算是解题关键.

2.下列四个数中,最小的数是(   )

A. 0 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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> C. 5 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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】D

【解析】

【分析】

先根据有理数的大小比较法则比较大小,即可得出选项.

【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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

最小的数是 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>
故选:D

【点睛】本题考查了有理数的大小比较,其方法如下:(1)负数<0<正数;(2)两个负数,绝对值大的反而小.

3.下列图形是我国国产品牌汽车的标识,在这些汽车标识中,是中心对称图形的是(

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】B

【解析】

由中心对称图形的定义:“把一个图形绕一个点旋转180°后,能够与自身完全重合,这样的图形叫做中心对称图形”分析可知,上述图形中,ACD都不是中心对称图形,只有B是中心对称图形.

故选B.


4.如图,已知直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】B

【解析】

【分析】

利用平行线的性质即可解决问题.

【详解】如图,∵a∥b

∴∠1=∠350°

∴∠2180°−50°130°

故选: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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题考查平行线的性质,解题的关键是熟练掌握基本知识,属于中考常考题型.

5.小明参加学校举行的“保护环境”主题演讲比赛,五位评委给出的评分分别为:9085809095,则这组数据的中位数和众数分别是(  )

A. 8090 B. 9090 C. 9085 D. 9095

【答案】B

【解析】

【分析】

根据中位数、众数的定义即可求解.

【详解】把分数从小到大排列为:80,85,90,90,95

故中位数为90,众数为90

故选B

【点睛】此题主要考查中位数、众数,解题的关键是熟知中位数、众数的定义.

6.将直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 向上平移两个单位,平移后的直线所对应的函数关系式为(   )

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】C

【解析】

【分析】

向上平移时,k的值不变,只有b发生变化.

【详解】解:原直线的k=-2b=-1;向上平移两个单位得到了新直线,
那么新直线的k=-2b=-1+2=1
新直线的解析式为y=-2x+1
故选:C

【点睛】本题主要考查了一次函数图象的变换,求直线平移后的解析式时要注意平移时kb的值发生变化.

7.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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 中,DE分别是ABAC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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

A. 30 B. 25 C. 225 D. 20

【答案】D

【解析】

【分析】

首先判断出△ADE∽△ABC,然后根据相似三角形的面积比等于相似比的平方即可求出△ABC的面积.

【详解】解:根据题意,点D和点E分别是ABAC的中点,则DE∥BCDE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> BC,故可以判断出△ADE∽△ABC,根据相似三角形的面积比等于相似比的平方,可知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =14,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =34,题中已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,故可得 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =20

故本题选择D

【点睛】本题主要考查相似三角形的判定与性质,解答本题的关键是得出DE是中位线,从而判断△ADE∽△ABC,然后掌握相似三角形的面积比等于相似比的平方即可求解本题.

8.如图,点ABCD在⊙O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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,点B <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的中点,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的度数是(

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】A

【解析】

【分析】

根据圆心角、弧、弦的关系定理得到∠AOB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> AOC,再根据圆周角定理解答.

【详解】连接OB

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的中点,

∴∠AOB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> AOC60°

由圆周角定理得,∠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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> AOB30°

故选: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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题考查的是圆心角、弧、弦的关系定理、圆周角定理,掌握在同圆或等圆中,同弧或等弧所对的圆周角相等,都等于这条弧所对的圆心角的一半是解题的关键.

9.如图,点A是反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 图象上的一点,过点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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 轴,垂足为点CDAC的中点,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的面积为1,则k的值为(   )

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> C. 3 D. 4

【答案】D

【解析】

【分析】

先设出点A的坐标,进而表示出点D的坐标,利用△ADO的面积建立方程求出 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,即可得出结论.

【详解】点A的坐标为(m2n),
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>
∵D
AC的中点,
∴D
mn),
∵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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 轴,△ADO的面积为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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>
故选:D

【点睛】本题考查反比例函数系数k的几何意义、反比例函数图象上点的坐标特征,解答本题的关键是明确题意,找出所求问题需要的条件,利用反比例函数的性质解答.

10.我国古代数学著作《增删算法统宗》记载“绳索量竿”问题:“一条竿子一条索,索比竿子长一托.折回索子却量竿,却比竿子短一托.”其大意为:现有一根竿和一条绳索,用绳索去量竿,绳索比竿长5尺;如果将绳索对半折后再去量竿,就比竿短5尺.设绳索长x尺.则符合题意 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 方程是(  )

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】A

【解析】

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 分析】

设索为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 尺,杆子为( <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> )尺,则根据“将绳索对半折后再去量竿,就比竿短5尺”,即可得出关于 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 一元一次方程.

【详解】设索为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 尺,杆子为( <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> )尺,

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

故选:A

【点睛】本题考查了一元一次方程的应用,找准等量关系是解题的关键.

11.如图,矩形ABCD中,BD为对角线,将矩形ABCD沿BEBF所在直线折叠,使点A落在BD上的点M处,点C落在BD上的点N处,连结EF.已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,则EF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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

A. 3 B. 5 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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】C

【解析】

【分析】

由矩形的性质和已知求出BD=5,根据折叠的性质得△ABE≌△MBE,设AE的长度为x,在Rt△EMD中,由勾股定理求出DE的长度,同理在Rt△DNF中求出DF的长度,在Rt△DEF中利用勾股定理即可求出EF的长度.

【详解】解:∵四边形ABCD是矩形,AB=3BC=4

BD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =5

AE的长度为x

由折叠可得:△ABE≌△MBE

EM=AE=xDE=4-xBM=AB=3DM=5-3=2

Rt△EMD中,EM2+DM2=DE2

x2+22=4-x2

解得:x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ED=4- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

CF的长度为y

由折叠可得:△CBF≌△NBF

NF=CF=yDF=3-yBN=BC=4DN=5-4=1

Rt△DNF中,DN2+NF2=DF2

y2+12=3-y2

解得:x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> DF=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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

Rt△DEF中,EF= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

故答案为:C

【点睛】本题考查矩形的性质、折叠的性质、全等三角形的判定与性质和勾股定理,运用勾股定理求出DEDF的长度是解题的关键.

12.在平面直角坐标系中,横坐标和纵坐标都是整数的点叫做整点,已知直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> )与两坐标轴围成的三角形区域(不含边界)中有且只有四个整点,则t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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】D

【解析】

【分析】

画出函数图象,利用图象可得t的取值范围.

【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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

y=0时,x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ;当x=0时,y=2t+2

直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x轴的交点坐标为( <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 0),与y轴的交点坐标为(02t+2),

t>0

2t+2>2

t= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,2t+2=3,此时 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =-6,由图象知:直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> )与两坐标轴围成的三角形区域(不含边界)中有且只有四个整点,如图1

t=2时,2t+2=6,此时 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =-3,由图象知:直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> )与两坐标轴围成的三角形区域(不含边界)中有且只有四个整点,如图2

t=1时,2t+2=4 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =-4,由图象知:直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> )与两坐标轴围成的三角形区域(不含边界)中有且只有三个整点,如图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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

故选: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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】此题考查一次函数的图象的性质,一次函数图象与坐标轴交点坐标,根据t的值正确画出图象理解题意是解题的关键.

第Ⅱ卷(非选择题 64分)

注意事项:

1、第Ⅱ卷共4页,用钢笔或圆珠笔将答案直接答在试卷上.

2、答题前将密封线内的项目填写清楚.

二、填空题(本大题共4小题,每小题5分,共20分)

13.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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 中,自变量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的取值范围是_____

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【详解】根据函数可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

14.2020623943分,我国在西昌卫星发射中心用长征三号乙运载火箭,成功发射北斗系统第五十五颗导航卫星,标志着北斗三号卫星导航定位系统正式建成.根据最新数据,目前兼容北斗的终端产品至少有7亿台,其中7亿用科学记数法表示为______________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

科学记数法的表示形式为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,其中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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ∣﹤10n为整数,确定a值和n值即可解答.

【详解】7亿=700000000= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】此题考查科学记数法的表示,正确确定a的值和n的值是解答的关键.

15.已知关于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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 有一实数根为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,则该方程的另一个实数根为_____________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

根据一元二次方程的解的定义把x=-1代入原方程得到关于m的一元二次方程,解得m的值,然后根据一元二次方程的定义确定m的值.

【详解】解:把x=-1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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> m2-5m+4=0,解得m1=1,m2=4
∵(m-1)
2≠0
∴m
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 1

m=4.

方程为9x2+12x+3=0.

设另一个根为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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题考查了一元二次方程的解:能使一元二次方程左右两边相等的未知数的值是一元二次方程的解.又因为只含有一个未知数的方程的解也叫做这个方程的根,所以一元二次方程的解也称为一元二次方程的根.也考查了一元二次方程的定义.

16.如图,在矩形ABCD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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,若点MN分别是线段DBAB上的两个动点,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的最小值为___________________

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

如图,过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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,使 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 最短,再利用矩形的性质与锐角三角函数求解 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 即可得到答案.

【详解】解:如图,过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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,使 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 最短,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 为矩形, <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的最小值为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题考查的是矩形的性质,锐角三角函数的应用,同时考查利用轴对称与垂线段最短求线段和的最小值问题,掌握以上知识是解题的关键.

三、解答题(本大题共5小题,共44分,解答应写出必要的文字说明或推演步骤)

17.计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】-3

【解析】

【分析】

根据负整数指数幂、绝对值、特殊角的三角函数值、二次根式和零次幂的运算法则分别对每项进行化简,再进行加减计算即可.

【详解】解: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题考查实数的混合运算、熟练掌握负整数指数幂、绝对值、特殊角的三角函数值、二次根式和零次幂的运算法则是解题的关键.

18.如图,点CEFB在同一直线上,点ADBC异侧,ABCDAEDF,∠A=∠D

1)求证:AB=CD

2)若ABCF,∠B40°,求∠D的度数.

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】1ABCD270°

【解析】

【分析】

1)根据平行线的性质求出∠B=∠C,根据AAS推出ABE≌△CDF,根据全等三角形的性质得出即可;

2)根据全等得出AB=CDBE=CF,∠B=∠C,求出CF=CD,推出∠D=∠CFE,即可求出答案.

【详解】(1)证明:∵AB∥CD

∴∠B=∠C

ABECDF中,

B=∠CAE=DF ,∠A=∠D

∴△AEB≌△DFC

ABCD.

2)∵ABCD

ABCF

CDCF

∵∠B=∠C=40°

∴∠D(180°40°)÷270°

【点睛】本题考查了全等三角形的性质和判定,平行线的性质,三角形内角和定理的应用,能根据全等三角形的判定求出ABE≌△CDF是解此题的关键.

19.我市某中学举行“法制进校园”知识竞赛,赛后将学生的成绩分为ABCD四个等级,并将结果绘制成如图所示的条形统计图和扇形统计图.请你根据统计图解答下列问题.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

1)成绩为“B等级”的学生人数有 名;

2)在扇形统计图中,表示“D等级”的扇形的圆心角度数为 ,图中m的值为

3)学校决定从本次比赛获得“A等级”的学生中选出2名去参加市中学生知识竞赛.已知“A等级”中有1名女生,请用列表或画树状图的方法求出女生被选中的概率.

【答案】15272°403 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

1)先根据“A等级”的人数及占比求出学生总人数,再减去各组人数即可求出成绩为“B等级”的学生人数;

2)根据“D等级”的占比即可求出其圆心角度数,根据“C等级”的人数即可求出m的值;

3)根据题意画树状图,再根据概率公式即可求解.

【详解】(1)学生总人数为3÷15%=20(人)

成绩为“B等级”的学生人数有20-3-8-4=5(人)

故答案为:5

2)“D等级” <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 扇形的圆心角度数为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

m= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

故答案为:72°40

3)根据题意画树状图如下:

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

P(女生被选中)= <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】此题主要考查统计调查的应用,解题的关键是根据题意求出学生总人数及概率的求解方法.

20.为了维护我国海洋权力,海监部门对我国领海实行了常态化巡航管理.如图,正在执行巡航任务的海监船以每小时60海里的速度向正东方向航行,在A处测得灯塔P在北偏东 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 方向上,海监船继续向东航行1小时到达B处,此时测得灯塔P在北偏东 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 方向上.

1)求B处到灯塔P的距离;

2)已知灯塔P的周围50海里内有暗礁,若海监船继续向正东方向航行是否安全?

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】1B处到灯塔P的距离为60海里;(2)海监船继续向正东方向航行是安全的

【解析】

【分析】

1)作PD⊥ABD.求出∠PAB、∠PBA、∠P的度数,证得△ABP为等腰三角形,即可解决问题;
2)在Rt△PBD中,解直角三角形求出PD的值即可判定.

【详解】(1)过点PPD⊥AB于点D

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

由题意得,AB=60(海里),∠PAB=30°,∠PBD=60°
∴∠APB=∠PBD-∠PAB=60°-30°=30°=∠PAB

PB=AB=60(海里),

答:B处到灯塔P的距离为60海里;
2)由(1)可知∠APB=∠PAB=30°
∴PB=AB=60
(海里)

Rt△PBD中,
PD=BPsin60°
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 60 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> (海里),

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

海监船继续向正东方向航行是安全的.

【点睛】本题考查了解直角三角形的应用-方向角问题,正确根据题意画出图形、准确标注方向角、熟练掌握锐角三角函数的概念是解题的关键.

21.如图,AB是⊙O的直径,C是⊙O上一点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 于点D,过点C作⊙O 的切线,交OD的延长线于点E,连结BE

1)求证:BE是⊙O的切线;

2)设OE交⊙O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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,求线段EF的长;

3)在(2)的条件下,求阴影部分的面积.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】1)见解析;(2EF=4;(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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

1)连接OC,如图,根据垂径定理由OD⊥BC得到CD=BD,则OEBC的垂直平分线,所以EB=EC,根据等腰三角形的性质得∠EBC=∠ECB,加上∠OBC=∠OCB,则∠OBE=∠OCE;再根据切线的性质得∠OCE=90°,所以∠OBE=90°,然后根据切线的判定定理得BE与⊙O相切;
2)设⊙O的半径为R,则OD=R-DF=R-2OB=R,在Rt△OBD,利用勾股定理解得R=4,再利用含30º角的直角三角形边角关系可求得OE,利用EF=OE-OF即可解答;

3)利用(2)中可求得∠BOC=120º,然后利用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 代入数值即可求解.

【详解】(1)证明:连接OC,如图,
∵OD⊥BC

∴CD=BD

∴OE
BC的垂直平分线,
∴EB=EC

∴∠EBC=∠ECB

∵OB=OC

∴∠OBC=∠OCB

∴∠OBC+∠EBC=∠OCB+∠ECB
,即∠OBE=∠OCE
∵CE
为⊙O的切线,
∴OC⊥CE

∴∠OCE=90°

∴∠OBE=90°

∴OB⊥BE

∴BE
与⊙O相切.

2)设⊙O的半径为R,则OD=R-DF=R-2OB=R

Rt△OBD中,BD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

OD2+BD2=OB2
 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,解得R=4
∴OD=2
OB=4
∴∠OBD=30°

∴∠BOD=60°

Rt△OBE中,∠BEO=30ºOE=2OB=8

EF=OE-OF=8-4=4

EF=4

3)由∠OCD=∠OBD=30ºOD⊥BC知:∠COD=∠BOD=60º

∴∠BOC=120º,又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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> OE=8

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题考查了切线的判定与性质、垂径定理、扇形面积的计算、含30º角的直角三角形边角关系、勾股定理等知识,熟练掌握每个知识点是解答的关键.

B卷(共60分)

四、填空题(本大题共4小题,每小题6分,共24分.)

22.分解因式: <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

先根据十字相乘法,再利用平方差公式即可因式分解.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】此题主要考查因式分解,解题的关键是熟知因式分解的方法.

23.若数a使关于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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的解为非负数,且使关于y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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,则符合条件的所有整数a的积为_____________

【答案】40

【解析】

【分析】

根据分式方程的解为正数即可得出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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 5a≠3,根据不等式组的解集为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,即可得出a>0,找出0<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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 5a≠3中所有的整数,将其相乘即可得出结论.

【详解】解: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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的解为x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x≠1

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的解为非负数,

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 1.

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 5a≠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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

解不等式①,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> .

解不等式,得y<a.

关于y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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

a>0.

0<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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 5a≠3.

a为整数,则a的值为1245.

符合条件的所有整数a的积为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> .

故答案为:40.

【点睛】本题考查了分式方程的解以及解一元一次不等式,根据分式方程的解为正数结合不等式组的解集为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,找出a的取值范围是解题的关键.

24.如图,在平面直角坐标系中,点A-20),直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x轴交于点B,以AB为边作等边 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 轴,交直线l于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 为边作等边 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 轴,交直线l于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 为边作等边 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,以此类推……,则点 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的纵坐标是______________

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

如图,过A1A1C⊥ABC,过A2A2C1⊥A1B1C1,过A3A3C2⊥A2B2C2,先根据直线方程与x轴交于点B-10),且与x轴夹角为30º,则有AB=1,然后根据平行线的性质、等边三角形的性质、含30º的直角三角形的性质,分别求的A1A2A3、的纵坐标,进而得到An的纵坐标,据此可得A2020的纵坐标,即可解答.

【详解】如图,过A1A1C⊥ABC,过A2A2C1⊥A1B1C1,过A3A3C2⊥A2B2C2,先根据直线方程与x轴交于点B-10),与y轴交于点D0 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ),

OB=1,OD= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,

∴∠DBO=30º

由题意可得:∠A1B1B=∠A2B2B1=30º,∠B1A1B=∠B2A2B1=60º

∴∠A1BB1=∠A2B1B2=90º

AB=1A1B1=2A1B=21A2B2=2A2B1=22A3B3=2A3B2=23,…AnBn=2n
∴A
1C= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ×1

A1纵坐标为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ×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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

A2C1= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> A1B1= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

A2的纵坐标为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ×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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

A3C2= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> A2B2= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,

A3的纵坐标为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ×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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

由此规律可得:AnCn-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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,

An的纵坐标为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

A2020= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】

本题是一道点的坐标变化规律探究,涉及一次函数的图象、等边三角形的性质、含30º角的直角三角形的性质,数字型规律等知识,解答的关键是认真审题,观察图象,结合基本图形的有关性质,找到坐标变化规律.

25.已知抛物线 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> (如图)和直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> .我们规定:当x取任意一个值时,x对应的函数值分别为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,取 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 中较大者为M;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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,记 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,M的最大值为4;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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,使 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x的取值范围是 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ;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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,使 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x的值是 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ;④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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,Mx的增大而增大.上述结论正确的是____(填写所有正确结论的序号)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】②③④

【解析】

【分析】

根据题目中的较大者M的定义逐个分析即可.

【详解】解:对于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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,显然只要 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,则M的值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,故①错误;

对于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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,在同一直角坐标系内画出 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的图像,如下图所示,其中红色部分即表示M,联立 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的函数表达式,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,求得交点横坐标为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,观察图形可知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x的取值范围是 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,故②正确;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

对于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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,在同一直角坐标系内画出 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的图像,如下图所示,其中红色部分即表示M

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

联立 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的函数表达式,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,求得其交点的横坐标为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

M=3时分类讨论: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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> (),故③正确;

对于④: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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 时,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,此时 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 图像一直在 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 图像上方,如下图所示,故此时M= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,故Mx的增大而增大,故④正确.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

故答案为:②③④.

【点睛】本题考查了二次函数与一次函数的图像性质及交点坐标,本题的关键是要能理解M的含义,学会用数形结合的方法分析问题.

五、解答题(本大题共3小题,每小题12分,共36分)

26.我们知道,任意一个正整数x都可以进行这样的分解: <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> mn是正整数,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ),在x的所有这种分解中,如果mn两因数之差的绝对值最小,我们就称 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x的最佳分解.并规定: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

例如:18可以分解成 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,因为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,所以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 18的最佳分解,所以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

1)填空: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

2)一个两位正整数t <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ab为正整数),交换其个位上的数字与十位上的数字得到的新数减去原数所得的差为54,求出所有的两位正整数;并求 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的最大值;

3)填空:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 1;(2t392817 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的最大值 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

161×62×3,由已知可求 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 9=1×9=3×3,由已知可求 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =1

2)由题意可得:交换后的数减去交换前的数的差为:10ba−10a−b9b−a)=54,得到b−a6,可求t的值,故可得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的最大值;

3)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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的定义即可依次求解.

【详解】(161×62×3

6−13−2

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

9=1×9=3×3

9−13−3

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =1

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 1

2)由题意可得:交换后的数减去交换前的数的差为:

10ba−10a−b9b−a)=54

b−a6

1≤a≤b≤9

b9a3b8a2b7a1

t392817

391×393×13

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

281×282×144×7

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

171×17

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的最大值 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

3)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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =20×21

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =28×30

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =56×30

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

④∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> =56×60

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题考查因式分解的应用;理解题意,从题目中获取信息,列出正确的代数式,再由数的特点求解是解题的关键.

27.如图,正方形ABCD中,P是对角线AC上的一个动点(不与AC重合),连结BP,将BP绕点B顺时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> BQ,连结QPBC于点EQP延长线与边AD交于点F

1)连结CQ,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的值;

3)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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【答案】(1)见解析;(2)  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> (3)见解析

【解析】

【分析】

(1)由旋转知△PBQ为等腰直角三角形,得到PB=QB,∠PBQ=90°,进而证明△APB≌△CQB即可;

(2)AP=x,则AC=4xPC=3x,由(1)CQ=AP=x,又△ABC为等腰直角三角形,所以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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> PQ= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,再证明△BQE∽△BCQ,由此求出BE,进而求出CE:BC的值;

(3)CE上截取CG,并使CG=FA,证明△PFA≌△QGC,进而得到PF=QG,然后再证明∠QGE=∠QEG即可得到QG=EQ,进而求解.

【详解】解:∵四边形ABCD为正方形,

AB=BC,∠ABC=90°

BP绕点B顺时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> BQ

BP=BQ,∠PBQ=90°

∴∠ABC-∠PBC=∠PBQ-∠PBC,

∴∠ABP=∠CBQ

在△APB和△CQB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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

∴△APB≌△CQB(SAS)

AP=CQ

(2) AP=x,则AC=4xPC=3x,由(1)CQ=AP=x

ABC为等腰直角三角形,∴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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> Rt△PCQ中,由勾股定理有: <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

且△PBQ为等腰直角三角形,

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

又∠BCQ=∠BAP=45°,∠BQE=45°

∴∠BCQ=∠BQE=45°,且∠CBQ=∠CBQ

∴△BQE∽△BCQ

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,代入数据: <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

BE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,∴CE=BC-BE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

(3) CE上截取CG,并使CG=FA,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

∵∠FAP=∠GCQ=45°

且由(1)AP=CQ,且截取CG=FA

故有△PFA≌△QGC(SAS)

PF=QG,∠PFA=∠CGQ

又∵∠DFP=180°-∠PFA,∠QGE=180°-∠CGQ

∴∠DFP=∠QGE

DA <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> BC

∴∠DFP=∠CEQ

∴∠QGE=∠CEQ

∴△QGE为等腰三角形,

GQ=QE

PF=QE

【点睛】本题考查了正方形的性质、旋转的性质、三角形全等的判定和性质、相似三角形判定和性质的综合,具有一定的综合性,本题第(3)问关键是能想到在CE上截取CG,并使CG=FA这条辅助线.

28.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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 经过A-10)、B40)、C02)三点,点Dxy)为抛物线上第一象限内的一个动点.

1)求抛物线所对应的函数表达式;

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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 的面积为3时,求点D的坐标;

3)过点D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ,垂足为点E,是否存在点D,使得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 中的某个角等于 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 2倍?若存在,求点D的横坐标;若不存在,请说明理由.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ;(2)(32)或(13);(3)存在,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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【解析】

【分析】

1)根据点ABC的坐标,利用待定系数法即可求出抛物线的解析式;

2)根据三角形面积公式可求与BC平行的经过点Dy轴上点M的坐标,再根据待定系数法可求DM的解析式,再联立抛物线可求点D的坐标;

3)分∠DCE2∠ABC及∠CDE2∠ABC两种情况考虑:①当∠DCE2∠ABC时,取点F0,−2),连接BF,则CD∥BF,由点BF的坐标,利用待定系数法可求出直线BFCD的解析式,联立直线CD及抛物线的解析式组成方程组,通过解方程组可求出点D的坐标;②当∠CDE2∠ABC时,过点CCN⊥BF于点N,交OBH.作点N关于BC的对称点P,连接NPBC于点Q,由△OCH∽△OBF求出H点坐标,利用待定系数法求出直线CN的解析式,联立直线BF及直线CN成方程组,通过解方程组可求出点N的坐标,利用对称的性质可求出点P的坐标,由点CP的坐标,利用待定系数法可求出直线CP的解析式,将直线CP的解析式代入抛物线解析式中可得出关于x的一元二次方程,解之取其非零值可得出点D的横坐标.依此即可得解.

【详解】解答:解:(1)将A(−10)、B40)、C02)代入yax2bxc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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

故抛物线的解析式为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

2)如图2,过点DDM∥BC,交y轴于点M,设点M的坐标为(0m),使得△BCM的面积为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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

CM=3×2÷41.5

m21.5 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

M0 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

B40),C02),

直线BC的解析式为y=−  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x2

DM的解析式为y=−  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

联立抛物线解析式 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

D的坐标为(32)或(13).

3)分两种情况考虑:

当∠DCE2∠ABC时,取点F0,−2),连接BF,如图3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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

OCOFOB⊥CF

∴∠ABC=∠ABF

∴∠CBF2∠ABC

∵∠DCB2∠ABC

∴∠DCB=∠CBF

CD∥BF

B40),F0,−2),

直线BF的解析式为y <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x−2

直线CD的解析式为y <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x2

联立直线CD及抛物线的解析式成方程组得: <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

D的坐标为(23);

当∠CDE2∠ABC时,过点CCN⊥BF于点N,交OBH.作点N关于BC的对称点P,连接NPBC于点Q,如图4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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

∵∠OCH90°−∠OHC,∠OBF90°−∠BHN

OHC=∠BHN

∴∠OCH=∠OBF

在△OCH与△OBF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

∴△OCH∽△OBF

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

OH1H10).

设直线CN的解析式为ykxnk≠0),

C02),H10),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

直线CN的解析式为y=−2x2

连接直线BF及直线CN成方程组得:

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

N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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ).

B40),C02),

直线BC的解析式为y=−  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x2

NP⊥BC,且点N <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ),

直线NP的解析式为y2x− <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

联立直线BC及直线NP成方程组得:

 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

Q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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ).

N <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ),点NP关于BC对称,

P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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ).

C02),P <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> ),

直线CP的解析式为y <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x2

y <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> x2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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> 整理,得:11x2−29x0

解得:x10(舍去),x2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

D的横坐标为 <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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

综上所述:存在点D,使得△CDE的某个角恰好等于∠ABC2倍,点D的横坐标为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/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1005/" title="内江" class="c1" target="_blank">内江</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a>

【点睛】本题是二次函数综合题,考查了待定系数法求二次函数解析式、二次函数图象上点的坐标特征、勾股定理、等腰三角形的性质、平行线的判定与性质、相似三角形的判定与性质、待定系数法求一次函数解析式以及一次函数图象上点的坐标特征,解题的关键是:(1)根据点的坐标,利用待定系数法求出抛物线的解析式;(2)根据三角形面积公式和待定系数法求出点D的坐标;(3)分∠DCE2∠ABC及∠CDE2∠ABC两种情况求出点D的横坐标.