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【330365】2020年四川省宜宾市中考数学试题

时间:2025-02-09 11:10:25 作者: 字数:17892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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 宜宾市2020年初中学业水平即高中阶段学校招生考试

数学

一、选择题

1.6的相反数为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>    <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

A. -6 B. 6 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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】A

【解析】

【分析】

根据相反数的定义进行求解.

【详解】6的相反数为:﹣6.故选A.

【点睛】本题主要考查相反数的定义,熟练掌握相反数的定义是解答的关键,绝对值相等,符号相反的两个数互为相反数.

2.我国自主研发的北斗系统技术世界领先,2020623日在西昌卫星发射中心成功发射最后一颗北斗三号组网卫星,该卫星发射升空的速度是7100/秒,将7100用科学记数法表示为(

A. 7100 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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】D

【解析】

【分析】

科学记数法的表示形式为a×10n的形式,其中1≤|a|10n为整数.确定n的值时,要看把原数变成a时,小数点移动了多少位,n的绝对值与小数点移动的位数相同.当原数绝对值≥10时,n是正数;当原数的绝对值<1时,n是负数.

【详解】7100 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

故选:D

【点睛】此题主要考查科学记数法的表示方法.科学记数法的表示形式为a×10n的形式,其中1≤|a|10n为整数,表示时关键要正确确定a的值以及n的值.

3.如图所示,圆柱的主视图是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】B

【解析】

【分析】

根据主视图是从正面看得到的图形,可得答案.

【详解】解:从正面看圆柱的主视图是矩形,
故选:B

【点睛】本题考查了简单组合体的三视图,从正面看得到的图形是主视图.

4.计算正确的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】C

【解析】

【分析】

对每个选项进行计算判断即可.

【详解】解:A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 不是同类项,不能合并,选项错误;

B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,选项错误;

C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,选项正确;

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,选项错误.

故选:C

【点睛】本题考查了合并同类项、积的乘方、同底数幂的乘法、完全平方公式,熟练掌握整式的运算法则是解题的关键.

5.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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的解集在数轴上表示正确的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】A

【解析】

【分析】

先求出各不等式的解集,然后得到不等式组的解集即可得到答案.

【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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

由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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

由②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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

不等式组的解集为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

故选:A

【点睛】本题考查了解不等式组,以及在数轴上表示不等式的解集,熟练掌握解不等式是解题的关键.

6.7名学生 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 鞋号(单位:厘米)由小到大是:202122222323,则这组数据的众数和中位数分别是(

A. 2021 B. 2122 C. 2222 D. 2223

【答案】C

【解析】

【分析】

根据中位数和众数的定义进行求解即可.

【详解】解:数据按从小到大的顺序排列为20212222222323,所以中位数是22
数据22出现了3次,出现次数最多,所以众数是22
故选:C

【点睛】本题考查了众数与中位数的定义,中位数是将一组数据从小到大(或从大到小)重新排列后,最中间的那个数(最中间两个数的平均数);众数是出现次数最多的数据.

7.如图,MN分别是 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的边ABAC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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> =

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】D

【解析】

【分析】

MN分别是 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的边ABAC的中点,可知MN为△ABC的中位线,即可得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,从而可求出∠B的值.

【详解】解:∵MN分别是 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的边ABAC的中点,

MN∥BC

∴∠ANM=∠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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

故选:D

【点睛】本题考查了三角形的中位线,注意三角形的中位线平行于第三边是解题的关键.

8.学校为了丰富学生的知识,需要购买一批图书,其中科普类图书平均每本的价格比文学类图书平均每本的价格多8元,已知学校用15000元购买科普类图书的本数与用12000元购买文学书的本数相等,设文学类图书平均每本x元,则列方程正确的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】B

【解析】

【分析】

设文学类图书平均每本x元,根据购买的书本数相等即可列出方程.

【详解】设文学类图书平均每本x元,依题意可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

故选B

【点睛】此题主要考查分式方程的应用,解题的关键是根据题意找到等量关系列方程.

9.如图,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的直径,点C是圆上一点,连结ACBC,过点C <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> D,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的周长为(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】A

【解析】

【分析】

先根据勾股定理求出BC,再根据圆周角的性质得到AC⊥BC,得到cosB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,代入即可求出AB,故可求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的周长.

【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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的直径,

AC⊥BC

cosB= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

解得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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的周长为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

故选A

【点睛】此题主要考查圆内线段的求解,解题的关键是熟知圆周角定理、三角函数的运用.

10.某单位为响应政府号召,需要购买分类垃圾桶6个,市场上有A型和B型两种分类垃圾桶,A型分类垃圾桶500/个,B型分类垃圾桶550/个,总费用不超过3100元,则不同的购买方式有(

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

【答案】B

【解析】

【分析】

设购买A 型分类垃圾桶x个,则购买B型垃圾桶(6-x),然后根据题意列出不等式组,确定不等式组整数解的个数即可.

【详解】解:设购买A 型分类垃圾桶x个,则购买B型垃圾桶(6-x)个

由题意得: <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,解得4≤x≤6

x可取456,即有三种不同的购买方式.

故答案为B

【点睛】本题考查了一元一次方程组的应用,弄清题意、列出不等式组并确定不等式组的整数解是解答本题的关键.

11.如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 都是等边三角形,且BCD在一条直线上,连结 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,点MN分别是线段BEAD上的两点,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的形状是(

 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

A. 等腰三角形 B. 直角三角形

C. 等边三角形 D. 不等边三角形

【答案】C

【解析】

【分析】

先证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,根据已知条件可得 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,即可得到结果;

【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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 都是等边三角形,

 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 中,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 是等边三角形.

故答案选C

【点睛】本题主要考查了等边三角形的性质与判定,正确分析题目条件是解题的关键.

12.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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的图象与x轴交于点(20),顶点坐标为(-1n),其中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,以下结论正确的是(

 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 处的函数值相等;

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的图象与的函数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 图象总有两个不同的交点;

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 内既有最大值又有最小值.

A. ①③ B. ①②③ C. ①④ D. ②③④

【答案】C

【解析】

【分析】

根据题意作出函数图像,根据系数与图像的关系即可求解.

【详解】如图,根据题意作图,

a0b0c0

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,①正确;

对称轴为x=-1

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 处的函数值相等,故②错误;

图中函数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的图象与的函数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 图象无交点,故③错误;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 时,x=-1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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 有最大值

x=3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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 有最小值,故④正确;

故选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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】此题主要考查二次函数的图像与性质,解题的关键是根据题意画出函数大致图像进行求解.

二、填空题

13.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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> .

【解析】

【分析】

首先提取公因式a,再利用平方差公式进行二次分解即可.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

14.如图,ABC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 上的三点,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 是等边三角形,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ________________

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

由△OBC是等边三角形、则∠COB =60°,然后由圆周角定理可得∠A=30°,然后运用余弦定义求解即可.

【详解】解:∵△OBC是等边三角形

∴∠COB=60°

∴∠A= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> =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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】本题考查了等边三角形的性质和圆周角定理,掌握同弦所对的圆周角为圆心角的一半是解答本题的关键.

15.一元二次方程 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的两根为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

根据根与系数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 关系表示出 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 即可;

【详解】∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】本题主要考查了一元二次方程根与系数的关系,准确利用知识点化简是解题的关键.

16.如图,四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> AB上一动点,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的最小值是________________

 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

C点关于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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 对称点C’,连接C’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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的最小值即为C’D的长,作C’E⊥DA的延长线于点E,根据勾股定理即可求解.

【详解】如图,作C点关于AB的对称点C’,连接C’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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的最小值即为C’D的长,

C’E⊥DA的延长线于点E

四边形ABC’E是矩形

DE=AD+AE=AD+BC’=5,

C’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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】此题主要考查对称性的应用,解题的关键是熟知对称的性质及勾股定理的应用.

17.定义:分数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> mn为正整数且互为质数)的连分数(其中为整数,且等式右边的每一个分数的分子都为1),记作 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> :例如 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的连分数是 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,记作 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

根据连分数的定义即可求解.

【详解】依题意可设a <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】此题主要考查新定义运算,解题的关键是根据题意进行求解.

18.在直角三角形ABC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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> AB的中点,BE平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> AC于点E连接CDBE于点O,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,则OE的长是________

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

E点作EG⊥ABG点,根据三角形面积公式求出CE=EG=3,延长CD交过BBF⊥BCF,可得△ACD≌△BFD,得到BF=8,再根据△CEO∽△FBO,找到比例关系得到EO= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> BE,再求出BE即可求解.

【详解】过E点作EG⊥ABG点,

BE平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

CE=EG,

CE=EG=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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

S△ABC= S△ABE+S△BCE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

解得x=3

CE=3,

延长CD交过BBF⊥BCF

DAB中点

AD=BD

AC∥BF

∴∠A=∠DBF,由∠ADC=∠DBF

∴△ACD≌△BFD

BF=AC=8,

AC∥BF

∴△CEO∽△FBO

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

EO= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> × <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】此题主要考查相似三角形的判定与性质,解题的关键是熟知全等三角形的判定、角平分线的性质及相似三角形的判定与性质.

三、解答题

19.1)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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

2)化简: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】11;(22

【解析】

【分析】

1)运用负指数幂、零指数幂、绝对值性质进行求解即可;

2)先算括号里面的,然后进行分式乘除运算即可;

【详解】(1)原式=4-1-3+1

=1

2)原式=  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

=2

【点睛】本题主要考查了实数的计算和分式的化简,计算准确是解题的关键.

20.如图,在三角形ABC中,点DBC上的中点,连接AD并延长到点E,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,连接CE

1)求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的面积为5,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】1)详见解析;(210

【解析】

【分析】

1)根据中点定义、对顶角相等以及已知条件运用SAS即可证明;

2)先根据三角形中点的性质和全等三角形的性质得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,再结合 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 以及 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 解答即可.

【详解】证明:(1)∵DBC的中点,

BD=CD

在△ABD和△CED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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

(2)∵在△ABC中,D BC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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

答:三角形ACE的面积为10

【点睛】本题考查了全等三角形的判定与性质、三角形中位线的性质等知识,其中掌握全等三角形的判定与性质是解答本题的关键.

21.在疫情期间,为落实停课不停学,某校对本校学生某一学科在家学习的情况进行抽样调查,了解到学生的学习方式有:电视直播、任教老师在线辅导、教育机构远程教学、自主学习,参入调查的学生只能选择一种学习方式,将调查结果绘制成不完整的扇形统计图和条形统计图,解答下列问题.

1)本次受调查的学生有________人;

2)补全条形统计图;

3)根据调查结果,若本校有1800名学生,估计有多少名学生与任课教师 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 线辅导?

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】160;(2)详见解析;(3900

【解析】

【分析】

1)根据A得占比和人数已知可得结果;

2)算出C的人数,然后补全条形统计图;

3)用总人数乘以在线辅导的学生占比即可;

【详解】(1)由题可知受调查人数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

故答案为60

2)补全图形如图:C的人数= <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

3)学生数为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

答:在线辅导的有900人.

【点睛】本题主要考查了数据分析的知识点应用,准确分析题中数据是解题的关键.

22.如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 两楼地面距离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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 米,楼AB30米,从楼AB的顶部点A测得楼CD顶部点D的仰角为45度.

1)求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的大小;

2)求楼CD的高度(结果保留根号).

 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】175°;(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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

1)如图: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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 于点E,在Rt△ABC中运用三角函数可得 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 、进一步可得∠EAC=30°,再结合 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 即可解答;

2)先根据题意求得DE=AE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,然后在Rt△ACE中解直角三角形求得CE,最后利用CD=CE+DE进行计算即可.

【详解】(1)如图: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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 于点E

Rt△ABC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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

AE//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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

(2)∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> RtAED中,AE=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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,∠DAE=45°

DE=AE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

Rt△ACE中,∠CAE=30°

CE=tan30°·AE=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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】本题主要考查了运用三角函数值求角的大小和解直角三角形,灵活应用三角函数知识是解答本题的关键.

23.如图,一次函数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的图像与反比例函数 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的图像交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 两点,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 于点P

1)求一次函数和反比例函数的表达式;

2)求四边形ABOC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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

1)将点B(-1-3)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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,可得反比例函数解析式 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,即可求出A点的坐标,将AB代入解析式即可求解;

2)过点BBE垂直于y轴于点E,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 关系式可求解;

【详解】解:(1)将点B(-1-3)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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

所以反比例函数的表达式为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

将点A(-3n)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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 有,n=-1

AB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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

所以一次函数表达式为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

2)过点BBE垂直于y轴于点E

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

答:四边形的面积为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】本题主要考查了反比例函数与一次函数综合,准确利用函数性质进行求解是解题的关键.

24.如图,已知AB是圆O的直径,点C是圆上异于AB的一点,连接BC并延长至点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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,连接AD <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 于点E,连接BE

1)求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 是等腰三角形;

2)连接OC并延长,与B以为切点的切线交于点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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的长.

 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【答案】1)详见解析;(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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【解析】

【分析】

1)根据直径所对圆周角是直角及三线合一性质求解即可;

2)根据等腰三角形的性质和切线的性质证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,即可求出DE

【详解】(1)证明:因为AB是圆O的直径,

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

所以点CBD的中点,

所以AB=AD

所以三角形ABD是等腰三角形.

2)因为三角形ABD是等腰三角形,

 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

因为BF是切线,

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

因为AB是直径,

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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

【点睛】本题主要考查了圆的综合应用,准确运用相似三角形的性质是解题的关键.

25.如图,已知二次函数图像的顶点在原点,且点(21)在二次函数的图像上,过点F(01)x轴的平行线交二次函数的图像于MN两点

1)求二次函数的表达式;

2P为平面内一点,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 时等边三角形时,求点P的坐标;

3)在二次函数的图象上是否存在一点E,使得以点E为圆心的圆过点F和和点N,且与直线 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 相切,若存在,求出点E的坐标,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的半径;若不存在,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ;(3)在二次函数图像上存在点E,使得以点E为圆心,半径为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的圆,过点FN且与直线 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 相切.

【解析】

【分析】

1)由二次函数的顶点是原点,则设二次函数的解析式为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,然后将(21)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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 求得a即可;

2)将y=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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,可确定MN的坐标,进而确定MN的长度;再根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 是等边三角形确定PM的长,然后解三角形确定PF的长,最后结合F点坐标即可解答;

3)先假设这样的点存在,设点QFN的中点,即 Q(11)

【详解】解:(1)∵二次函数的顶点是原点

设二次函数的解析式为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

将(21)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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

所以二次函数的解析式为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

2)如图:将y=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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> ,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 是等边三角形

Py轴上且PM=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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

3)假设在二次函数的图像上存在点E满足条件

设点QFN的中点,即 Q(11)

EFN的垂直平分线上

EFN的垂直平分线x=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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的图像的交点,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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

E到直线y=-1的距离为 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a>

在二次函数图像上存在点E,使得以点E为圆心,半径为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1004/" title="四川" class="c1" target="_blank">四川</a> <a href="/tags/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 的圆,过点FN且与直线 <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/1074/" title="四川省" class="c1" target="_blank">四川省</a> <a href="/tags/1081/" title="宜宾" class="c1" target="_blank">宜宾</a> 相切.

【点睛】本题属于二次函数综合题,考查了二次函数的解析式、等边三角形、解三角形、垂直平分线等知识,掌握并综合应用所学知识是解答本题的关键.