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【334305】2020年全国统一高考数学试卷文科新课标Ⅲ

时间:2025-01-21 17:57:42 作者: 字数:19145字
简介:

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学校:___________姓名:___________班级:___________考号:___________

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Shape3 Shape4

绝密★启用前

2020年全国统一高考数学试卷(文科)(新课标Ⅲ)

试卷副标题

考试范围:xxx;考试时间:100分钟;命题人:xxx

学校:___________姓名:___________班级:___________考号:___________

题号

总分

得分





注意事项:

1.答题前填写好自己的姓名、班级、考号等信息$2.请将答案正确填写在答题卡上


I卷(选择题)

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评卷人

得分




一、单选题

1Logistic模型是常用数学模型之一,可应用于流行病学领城.有学者根据公布数据建立了某地区新冠肺炎累计确诊病例数I(t)(t的单位:天)Logistic模型: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,其中K为最大确诊病例数.当I( <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> )=0.95K时,标志着已初步遏制疫情,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 约为( )(ln19≈3

A60 B63 C66 D69

【答案】C

【解析】

【分析】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 代入函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 结合 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 即可得解.

【详解】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故选:C.

【点睛】

本题考查对数的运算,考查指数与对数的互化,考查计算能力,属于中等题.

2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为坐标原点,直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 与抛物线C <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 交于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 两点,若 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的焦点坐标为(

A <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> B <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> C <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> D <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【答案】B

【解析】

【分析】

根据题中所给的条件 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,结合抛物线的对称性,可知 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,从而可以确定出点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的坐标,代入方程求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的值,进而求得其焦点坐标,得到结果.

【详解】

因为直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 与抛物线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 交于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 两点,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据抛物线的对称性可以确定 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

代入抛物线方程 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以其焦点坐标为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

故选:B.

【点睛】

该题考查的是有关圆锥曲线的问题,涉及到的知识点有直线与抛物线的交点,抛物线的对称性,点在抛物线上的条件,抛物线的焦点坐标,属于简单题目.

3下图为某几何体的三视图,则该几何体的表面积是(

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

A6+4 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> B4+4 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> C6+2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> D4+2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【答案】C

【解析】

【分析】

根据三视图特征,在正方体中截取出符合题意的立体图形,求出每个面的面积,即可求得其表面积.

【详解】

根据三视图特征,在正方体中截取出符合题意的立体图形

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据立体图形可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据勾股定理可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 是边长为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的等边三角形

根据三角形面积公式可得:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 该几何体的表面积是: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故选:C.

【点睛】

本题主要考查了根据三视图求立体图形的表面积问题,解题关键是掌握根据三视图画出立体图形,考查了分析能力和空间想象能力,属于基础题.

4已知集合 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则AB中元素的个数为(

A2 B3 C4 D5

【答案】B

【解析】

【分析】

采用列举法列举出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 中元素的即可.

【详解】

由题意, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 中元素的个数为3.

故选:B

【点晴】

本题主要考查集合的交集运算,考查学生对交集定义的理解,是一道容易题.

5 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则z=

A1–i B1+i Ci Di

【答案】D

【解析】

【分析】

先利用除法运算求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,再利用共轭复数的概念得到 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 即可.

【详解】

因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故选:D

【点晴】

本题主要考查复数的除法运算,涉及到共轭复数的概念,是一道基础题.

6设一组样本数据x1x2xn的方差为0.01,则数据10x110x210xn的方差为(

A0.01 B0.1 C1 D10

【答案】C

【解析】

【分析】

根据新数据与原数据关系确定方差关系,即得结果.

【详解】

因为数据 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的方差是数据 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的方差的 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 倍,

所以所求数据方差为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

故选:C

【点睛】

本题考查方差,考查基本分析求解能力,属基础题.

7已知 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

A <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> B <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> C <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> D <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【答案】B

【解析】

【分析】

将所给的三角函数式展开变形,然后再逆用两角和的正弦公式即可求得三角函数式的值.

【详解】

由题意可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

则: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

从而有: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故选:B.

【点睛】

本题主要考查两角和与差的正余弦公式及其应用,属于中等题.

8在平面内,AB是两个定点,C是动点,若 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则点C的轨迹为(

A B椭圆 C抛物线 D直线

【答案】A

【解析】

【分析】

首先建立平面直角坐标系,然后结合数量积的定义求解其轨迹方程即可.

【详解】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,以AB中点为坐标原点建立如图所示的平面直角坐标系,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

则: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

从而: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

结合题意可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

整理可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

即点C的轨迹是以AB中点为圆心, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为半径的圆.

故选:A.

【点睛】

本题主要考查平面向量及其数量积的坐标运算,轨迹方程的求解等知识,意在考查学生的转化能力和计算求解能力.

9(0,﹣1)到直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 距离的最大值为(

A1 B <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> C <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> D2

【答案】B

【解析】

【分析】

首先根据直线方程判断出直线过定点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,当直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 垂直时,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 到直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 距离最大,即可求得结果.

【详解】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 可知直线过定点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

当直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 垂直时,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 到直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 距离最大,

即为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故选:B.

【点睛】

该题考查的是有关解析几何初步的问题,涉及到的知识点有直线过定点问题,利用几何性质是解题的关键,属于基础题.

10 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则(

A <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> B <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> C <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> D <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【答案】A

【解析】

【分析】

分别将 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 改写为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,再利用单调性比较即可.

【详解】

因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故选:A.

【点晴】

本题考查对数式大小的比较,考查学生转化与化归的思想,是一道中档题.

11在△ABC中,cosC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> AC=4BC=3,则tanB=

A <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> B2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> C4 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> D8 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【答案】C

【解析】

【分析】

先根据余弦定理求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,再根据余弦定理求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,最后根据同角三角函数关系求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【详解】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

故选:C

【点睛】

本题考查余弦定理以及同角三角函数关系,考查基本分析求解能力,属基础题.

12已知函数f(x)=sinx+ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则(

Af(x)的最小值为2 Bf(x)的图像关于y轴对称

Cf(x)的图像关于直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 对称 Df(x)的图像关于直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 对称

【答案】D

【解析】

【分析】

根据基本不等式使用条件可判断A;根据奇偶性可判断B;根据对称性判断C,D.

【详解】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 可以为负,所以A错;

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 关于原点对称;

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> B错;

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 关于直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 对称,故C错,D

故选:D

【点睛】

本题考查函数定义域与最值、奇偶性、对称性,考查基本分析判断能力,属中档题.


II卷(非选择题)

请点击修改第II卷的文字说明


评卷人

得分




二、填空题

13xy满足约束条件 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则z=3x+2y的最大值为_________

【答案】7

【解析】

【分析】

作出可行域,利用截距的几何意义解决.

【详解】

不等式组所表示的可行域如图

因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,易知截距 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 越大,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 越大,

平移直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 经过A点时截距最大,此时z最大,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故答案为:7.

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【点晴】

本题主要考查简单线性规划的应用,涉及到求线性目标函数的最大值,考查学生数形结合的思想,是一道容易题.

14已知圆锥的底面半径为1,母线长为3,则该圆锥内半径最大的球的体积为_________

【答案】 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【解析】

【分析】

将原问题转化为求解圆锥内切球的问题,然后结合截面确定其半径即可确定体积的值.

【详解】

易知半径最大球为圆锥的内切球,球与圆锥内切时的轴截面如图所示,

其中 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,且点MBC边上的中点,

设内切圆的圆心为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

由于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

设内切圆半径为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

解得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,其体积: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【点睛】

与球有关的组合体问题,一种是内切,一种是外接.解题时要认真分析图形,明确切点和接点的位置,确定有关元素间的数量关系,并作出合适的截面图,如球内切于正方体,切点为正方体各个面的中心,正方体的棱长等于球的直径;球外接于正方体,正方体的顶点均在球面上,正方体的体对角线长等于球的直径.

15设双曲线C <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> (a>0b>0)的一条渐近线为y= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> x,则C的离心率为_________

【答案】 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【解析】

【分析】

根据已知可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,结合双曲线中 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的关系,即可求解.

【详解】

由双曲线方程 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 可得其焦点在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 轴上,

因为其一条渐近线为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【点睛】

本题考查的是有关双曲线性质,利用渐近线方程与离心率关系是解题的关键,要注意判断焦点所在位置,属于基础题.

16设函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .若 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则a=_________

【答案】1

【解析】

【分析】

由题意首先求得导函数的解析式,然后得到关于实数a的方程,解方程即可确定实数a的值

【详解】

由函数的解析式可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

则: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,据此可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

整理可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,解得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

故答案为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【点睛】

本题主要考查导数的运算法则,导数的计算,方程的数学思想等知识,属于中等题.


评卷人

得分




三、解答题

17某学生兴趣小组随机调查了某市100天中每天的空气质量等级和当天到某公园锻炼的人次,整理数据得到下表(单位:天):

锻炼人次

空气质量等级

[0200]

(200400]

(400600]

1(优)

2

16

25

2(良)

5

10

12

3(轻度污染)

6

7

8

4(中度污染)

7

2

0


1)分别估计该市一天的空气质量等级为1234的概率;

2)求一天中到该公园锻炼的平均人次的估计值(同一组中的数据用该组区间的中点值为代表);

3)若某天的空气质量等级为12,则称这天空气质量好;若某天的空气质量等级为34,则称这天空气质量不好.根据所给数据,完成下面的2×2列联表,并根据列联表,判断是否有95%的把握认为一天中到该公园锻炼的人次与该市当天的空气质量有关?


人次400

人次>400

空气质量好



空气质量不好




附: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

P(K2k)

0.050

0.010

0.001

k

3.841

6.635

10.828



【答案】1)该市一天的空气质量等级分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的概率分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ;(2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ;(3)有,理由见解析.

【解析】

【分析】

1)根据频数分布表可计算出该市一天的空气质量等级分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的概率;

2)利用每组的中点值乘以频数,相加后除以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 可得结果;

3)根据表格中的数据完善 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 列联表,计算出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的观测值,再结合临界值表可得结论.

【详解】

1)由频数分布表可知,该市一天的空气质量等级为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的概率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,等级为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的概率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,等级为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的概率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,等级为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的概率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

2)由频数分布表可知,一天中到该公园锻炼的人次的平均数为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

3 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 列联表如下:


人次 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

人次 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

空气质量不好

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

空气质量好

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>


 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

因此,有 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的把握认为一天中到该公园锻炼的人次与该市当天的空气质量有关.

【点睛】

本题考查利用频数分布表计算频率和平均数,同时也考查了独立性检验的应用,考查数据处理能力,属于基础题.

18已知椭圆 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的离心率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的左、右顶点.

1)求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的方程;

2)若点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 在直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的面积.

【答案】1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ;(2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【解析】

【分析】

1)因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,根据离心率公式,结合已知,即可求得答案;

2)点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 在直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,过点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 轴垂线,交点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 轴交点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,可求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点坐标,求出直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的直线方程,根据点到直线距离公式和两点距离公式,即可求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的面积.

【详解】

1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据离心率 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ()

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的方程为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

2)不妨设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> x轴上方

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 在直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

过点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 轴垂线,交点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 轴交点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据题意画出图形,如图

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据三角形全等条件“ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ”,

可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点纵坐标为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,将其代入 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

解得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 时,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

画出图象,如图

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

可求得直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的直线方程为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据点到直线距离公式可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 到直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的距离为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据两点间距离公式可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 面积为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 时,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

画出图象,如图

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

可求得直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的直线方程为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据点到直线距离公式可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 到直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的距离为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据两点间距离公式可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 面积为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

综上所述, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 面积为: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【点睛】

本题主要考查了求椭圆标准方程和求三角形面积问题,解题关键是掌握椭圆的离心率定义和数形结合求三角形面积,考查了分析能力和计算能力,属于中档题.

19abc <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> Ra+b+c=0abc=1

1)证明:ab+bc+ca<0

2)用max{abc}表示abc中的最大值,证明:max{abc}≥ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【答案】1)证明见解析(2)证明见解析.

【解析】

【分析】

1)由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 结合不等式的性质,即可得出证明;

2)不妨设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,由题意得出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,结合基本不等式,即可得出证明.

【详解】

1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 均不为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

2)不妨设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 可知, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

当且仅当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 时,取等号,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【点睛】

本题主要考查了不等式的基本性质以及基本不等式的应用,属于中档题.

20设等比数列{an}满足 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

1)求{an}的通项公式;

2)记 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为数列{log3an}的前n项和.若 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,求m

【答案】1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ;(2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【解析】

【分析】

1)设等比数列 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的公比为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,根据题意,列出方程组,求得首项和公比,进而求得通项公式;

2)由(1)求出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的通项公式,利用等差数列求和公式求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,根据已知列出关于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的等量关系式,求得结果.

【详解】

1)设等比数列 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的公比为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据题意,有 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

2)令 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

根据 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

整理得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【点睛】

本题考查等比数列通项公式基本量的计算,以及等差数列求和公式的应用,考查计算求解能力,属于基础题目.

21如图,在长方体 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 中,点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 分别在棱 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .证明:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

1)当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 时, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

2)点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 在平面 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 内.

【答案】1)证明见解析;(2)证明见解析.

【解析】

【分析】

1)根据正方形性质得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,根据长方体性质得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,进而可证 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 平面 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,即得结果;

2)只需证明 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 即可,在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上取点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 使得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,再通过平行四边形性质进行证明即可.

【详解】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

1)因为长方体 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 平面 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,

因为长方体 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以四边形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为正方形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 平面 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,因此 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 平面 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,

因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 平面 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

2)在 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上取点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 使得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,

因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以四边形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为平行四边形, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

因为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 四点共面,所以四边形 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为平行四边形,  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 四点共面,

因此 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 在平面 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【点睛】

本题考查线面垂直判定定理、线线平行判定,考查基本分析论证能力,属中档题.

22已知函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

1)讨论 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的单调性;

2)若 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 有三个零点,求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的取值范围.

【答案】1)详见解析;(2) <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【解析】

【分析】

1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,对 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 两种情况讨论即可;

2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 有三个零点,由(1)知 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,解不等式组得到 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的范围,再利用零点存在性定理加以说明即可.

【详解】

1)由题, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 时, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 恒成立,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上单调递增;

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 时,令 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,令 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上单调递减,在

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上单调递增.

2)由(1)知, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 有三个零点,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 时, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上有唯一一个零点,

同理 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上有唯一一个零点,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上有唯一一个零点,所以 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 有三个零点,

综上可知 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的取值范围为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【点晴】

本题主要考查利用导数研究函数的单调性以及已知零点个数求参数的范围问题,考查学生逻辑推理能力、数学运算能力,是一道中档题.

23在直角坐标系xOy中,曲线C的参数方程为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> (t为参数且t≠1)C与坐标轴交于AB两点.

1)求| <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> |

2)以坐标原点为极点,x轴正半轴为极轴建立极坐标系,求直线AB的极坐标方程.

【答案】1 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 2 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

【解析】

【分析】

1)由参数方程得出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的坐标,最后由两点间距离公式,即可得出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的值;

2)由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的坐标得出直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的直角坐标方程,再化为极坐标方程即可.

【详解】

1)令 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> (舍),则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,解得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> (舍),则 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

2)由(1)可知 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a>

则直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的方程为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,即 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 可得,直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的极坐标方程为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> .

【点睛】

本题主要考查了利用参数方程求点的坐标以及直角坐标方程化极坐标方程,属于中档题.


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