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【334303】2020年全国统一高考数学试卷文科新课标Ⅰ

时间:2025-01-21 17:57:26 作者: 字数:19596字
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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Ⅰ)

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

1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>

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】D

【解析】

【分析】

首先解一元二次不等式求得集合A,之后利用交集中元素的特征求得 <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> ,得到结果.

【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> 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>

又因为 <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.

【点睛】

本题考查的是有关集合的问题,涉及到的知识点有利用一元二次不等式的解法求集合,集合的交运算,属于基础题目.

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> ,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>

A0 B1

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】C

【解析】

【分析】

先根据 <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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 化简,再根据向量的模的计算公式即可求出.

【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:C

【点睛】

本题主要考查向量的模的计算公式的应用,属于容易题.

3埃及胡夫金字塔是古代世界建筑奇迹之一,它的形状可视为一个正四棱锥,以该四棱锥的高为边长的正方形面积等于该四棱锥一个侧面三角形的面积,则其侧面三角形底边上的高与底面正方形的边长的比值为(

 <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 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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】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> ,利用 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 得到关于 <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> 的方程,解方程即可得到答案.

【详解】

如图,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> ,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>

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> ,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> ,化简得 <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> (负值舍去).

故选: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>

【点晴】

本题主要考查正四棱锥的概念及其有关计算,考查学生的数学计算能力,是一道容易题.

4O为正方形ABCD的中心,在OABCD中任取3点,则取到的3点共线的概率为(

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】A

【解析】

【分析】

列出从5个点选3个点的所有情况,再列出3点共线的情况,用古典概型的概率计算公式运算即可.

【详解】

如图,从 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 5个点中任取3个有

 <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>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 种不同取法,

3点共线只有 <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> 2种情况,

由古典概型的概率计算公式知,

取到3点共线的概率为 <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> .

故选: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>

【点晴】

本题主要考查古典概型的概率计算问题,采用列举法,考查学生数学运算能力,是一道容易题.

5某校一个课外学习小组为研究某作物种子的发芽率y和温度x(单位:°C)的关系,在20个不同的温度条件下进行种子发芽实验,由实验数据 <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> 得到下面的散点图:

 <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>

由此散点图,在10°C40°C之间,下面四个回归方程类型中最适宜作为发芽率y和温度x的回归方程类型的是(

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】D

【解析】

【分析】

根据散点图的分布可选择合适的函数模型.

【详解】

由散点图分布可知,散点图分布在一个对数函数的图象附近,

因此,最适合作为发芽率 <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> 和温度 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的回归方程类型的是 <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:D.

【点睛】

本题考查函数模型的选择,主要观察散点图的分布,属于基础题.

6已知圆 <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> ,过点(12)的直线被该圆所截得的弦的长度的最小值为(

A1 B2

C3 D4

【答案】B

【解析】

【分析】

当直线和圆心与点 <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> 的连线垂直时,所求的弦长最短,即可得出结论.

【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> 化为 <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> 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> ,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>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 的直线和直线 <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> 垂直时,圆心到过点 <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> 的直线的距离最大,所求的弦长最短,此时 <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>

根据弦长公式得最小值为 <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】

本题考查圆的简单几何性质,以及几何法求弦长,属于基础题.

7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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的图像大致如下图,则f(x)的最小正周期为(

 <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 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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】C

【解析】

【分析】

由图可得:函数图象过点 <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> ,即可得到 <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> ,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> 是函数 <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> 图象与 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 轴负半轴的第一个交点即可得到 <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> ,再利用三角函数周期公式即可得解.

【详解】

由图可得:函数图象过点 <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>

将它代入函数 <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> 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> 是函数 <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> 图象与 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 轴负半轴的第一个交点,

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> ,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> 的最小正周期为 <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】

本题主要考查了三角函数的性质及转化能力,还考查了三角函数周期公式,属于中档题.

8 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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】

根据已知等式,利用指数对数运算性质即可得解

【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> 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> ,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>

故选:B.

【点睛】

本题考查的是有关指对式的运算的问题,涉及到的知识点有对数的运算法则,指数的运算法则,属于基础题目.

9执行下面的程序框图,则输出的n=

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

A17 B19 C21 D23

【答案】C

【解析】

【分析】

根据程序框图的算法功能可知,要计算满足 <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> 的最小正奇数 <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> ,根据等差数列求和公式即可求出.

【详解】

依据程序框图的算法功能可知,输出的 <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> 是满足 <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> 的最小正奇数,

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> ,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>

所以输出的 <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>

故选:C.

【点睛】

本题主要考查程序框图的算法功能的理解,以及等差数列前 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 项和公式的应用,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> 是等比数列,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> ,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>

A12 B24 C30 D32

【答案】D

【解析】

【分析】

根据已知条件求得 <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,再由 <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> 可求得结果.

【详解】

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> ,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>

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> .

故选:D.

【点睛】

本题主要考查等比数列基本量的计算,属于基础题.

11 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 是双曲线 <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> 的两个焦点, <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> 为坐标原点,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> ,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> 的面积为(

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> B3 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】


 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 是以P为直角直角三角形得到 <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> ,再利用双曲线的定义得到 <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> ,联立即可得到 <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> ,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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 中计算即可.

【详解】


由已知,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> ,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> 为直径的圆上,

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 是以P为直角顶点的直角三角形,

 <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>

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

故选:B

【点晴】


本题考查双曲线中焦点三角形面积的计算问题,涉及到双曲线的定义,考查学生的数学运算能力,是一道中档题.

12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> 为球 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的球面上的三个点,⊙ <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> 的外接圆,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> 的面积为 <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> ,则球 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的表面积为(

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】A

【解析】

【分析】

由已知可得等边 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的外接圆半径,进而求出其边长,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,根据球的截面性质,求出球的半径,即可得出结论.

【详解】

设圆 <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> 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> ,球的半径为 <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> ,依题意,

 <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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 为等边三角形,

由正弦定理可得 <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> ,根据球的截面性质 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 的表面积 <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> .

故选: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>
【点睛】

本题考查球的表面积,应用球的截面性质是解题的关键,考查计算求解能力,属于基础题.


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> z=x+7y的最大值为______________.

【答案】1

【解析】

【分析】

首先画出可行域,然后结合目标函数的几何意义即可求得其最大值.

【详解】

绘制不等式组表示的平面区域如图所示,

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

目标函数 <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> 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>

其中z取得最大值时,其几何意义表示直线系在y轴上的截距最大,

据此结合目标函数的几何意义可知目标函数在点A处取得最大值,

联立直线方程: <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> ,可得点A的坐标为: <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>

据此可知目标函数的最大值为: <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> .

故答案为:1

【点睛】

求线性目标函数zaxby(ab≠0)的最值,当b0时,直线过可行域且在y轴上截距最大时,z值最大,在y轴截距最小时,z值最小;当b0时,直线过可行域且在y轴上截距最大时,z值最小,在y轴上截距最小时,z值最大.

14设向量 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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 href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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】5

【解析】

【分析】

根据向量垂直,结合题中所给的向量的坐标,利用向量垂直的坐标表示,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>

又因为 <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>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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:5.

【点睛】

本题考查有关向量运算问题,涉及到的知识点有向量垂直的坐标表示,属于基础题目.

15曲线 <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> 的一条切线的斜率为2,则该切线的方程为______________.

【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】

设切线的切点坐标为 <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> ,对函数求导,利用 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> ,代入曲线方程求出 <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> ,得到切线的点斜式方程,化简即可.

【详解】

设切线的切点坐标为 <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>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,所以切点坐标为 <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>

所求的切线方程为 <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> ,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> .

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】

本题考查导数的几何意义,属于基础题.

16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> 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> ,前16项和为540,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> ______________.

【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】

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为奇偶数分类讨论,分别得出奇数项、偶数项的递推关系,由奇数项递推公式将奇数项用 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 表示,由偶数项递推公式得出偶数项的和,建立 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 方程,求解即可得出结论.

【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> 为奇数时, <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> ;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> 为偶数时, <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> .

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

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

本题考查数列的递推公式的应用,以及数列的并项求和,考查分类讨论思想和数学计算能力,属于较难题.


评卷人

得分




三、解答题

17某厂接受了一项加工业务,加工出来的产品(单位:件)按标准分为ABCD四个等级.加工业务约定:对于A级品、B级品、C级品,厂家每件分别收取加工费90元,50元,20元;对于D级品,厂家每件要赔偿原料损失费50.该厂有甲、乙两个分厂可承接加工业务.甲分厂加工成本费为25/件,乙分厂加工成本费为20/.厂家为决定由哪个分厂承接加工业务,在两个分厂各试加工了100件这种产品,并统计了这些产品的等级,整理如下:

甲分厂产品等级的频数分布表

等级

A

B

C

D

频数

40

20

20

20


乙分厂产品等级的频数分布表

等级

A

B

C

D

频数

28

17

34

21


1)分别估计甲、乙两分厂加工出来的一件产品为A级品的概率;

2)分别求甲、乙两分厂加工出来的100件产品的平均利润,以平均利润为依据,厂家应选哪个分厂承接加工业务?

【答案】1)甲分厂加工出来的 <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> 级品的概率为 <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> ,乙分厂加工出来的 <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> 级品的概率为 <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)选甲分厂,理由见解析.

【解析】

【分析】

1)根据两个频数分布表即可求出;

2)根据题意分别求出甲乙两厂加工 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 件产品的总利润,即可求出平均利润,由此作出选择.

【详解】

1)由表可知,甲厂加工出来的一件产品为 <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> 级品的概率为 <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> ,乙厂加工出来的一件产品为 <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> 级品的概率为 <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)甲分厂加工 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 件产品的总利润为 <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> 元,

所以甲分厂加工 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 件产品的平均利润为 <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> 元每件;

乙分厂加工 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 件产品的总利润为

 <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> 元,

所以乙分厂加工 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 件产品的平均利润为 <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> 元每件.

故厂家选择甲分厂承接加工任务.

【点睛】

本题主要考查古典概型的概率公式的应用,以及平均数的求法,并根据平均值作出决策,属于基础题.

18 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的内角ABC的对边分别为abc.已知B=150°.

1)若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> cb=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> ,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;

2)若sinA+ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> sinC= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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C.

【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)已知角 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 边,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> 关系,由余弦定理建立 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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,求解得出 <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> ,利用面积公式,即可得出结论;

2)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> 代入已知等式,由两角差的正弦和辅助角公式,化简得出有关 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 角的三角函数值,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> 的范围,即可求解.

【详解】

1)由余弦定理可得 <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> 的面积 <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>

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>

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

【点睛】

本题考查余弦定理、三角恒等变换解三角形,熟记公式是解题的关键,考查计算求解能力,属于基础题.

19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> 为圆锥的顶点, <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> 是圆锥底面的圆心, <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> 是底面的内接正三角形, <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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 上一点,∠APC=90°

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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)证明:平面PAB平面PAC

2)设DO= <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,圆锥的侧面积为 <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> ,求三棱锥PABC的体积.

【答案】1)证明见解析;(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)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> ,进而有 <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> ,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 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> ,从而证得 <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> 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> ,即可证得结论;

2)将已知条件转化为母线 <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> 和底面半径 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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,进而求出底面半径,由正弦定理,求出正三角形 <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> 边长,在等腰直角三角形 <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> 中求出 <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> ,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> 中,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> ,即可求出结论.

【详解】

1)连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 为圆锥顶点, <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> 为底面圆心, <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> 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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 是圆内接正三角形, <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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> ,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> 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> 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> 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> 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>

2)设圆锥的母线为 <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> ,底面半径为 <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> ,圆锥的侧面积为 <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> ,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>

在等腰直角三角形 <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> 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>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 三棱锥 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的体积为 <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>

【点睛】

本题考查空间线、面位置关系,证明平面与平面垂直,求锥体的体积,注意空间垂直间的相互转化,考查逻辑推理、直观想象、数学计算能力,属于中档题.

20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)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,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> 有两个零点,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 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的减区间为 <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> ,增区间为 <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 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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)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> 代入函数解析式,对函数求导,分别令导数大于零和小于零,求得函数的单调增区间和减区间;

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> 有两个零点,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> 有两个解,将其转化为 <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> 有两个解,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> ,求导研究函数图象的走向,从而求得结果.

【详解】

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> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> ,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> ,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> 的减区间为 <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> ,增区间为 <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)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> 有两个零点,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> 有两个解,

从方程可知, <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> 不成立,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> 有两个解,

 <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> ,则有 <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> ,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> ,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> ,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>

所以函数 <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> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 上单调递增,

且当 <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>

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

所以当 <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> 有两个解时,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>

所以满足条件的 <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> 的取值范围是: <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> .

【点睛】

本题考查的是有关应用导数研究函数的问题,涉及到的知识点有应用导数研究函数的单调性,根据零点个数求参数的取值范围,在解题的过程中,也可以利用数形结合,将问题转化为曲线 <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> 和直线 <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> 有两个交点,利用过点 <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> 的曲线 <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> 的切线斜率,结合图形求得结果.

21已知AB分别为椭圆E <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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>1)的左、右顶点,GE的上顶点, <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> P为直线x=6上的动点,PAE的另一交点为CPBE的另一交点为D

1)求E的方程;

2)证明:直线CD过定点.

【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)证明详见解析.

【解析】

【分析】

1)由已知可得: <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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> ,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> ,结合已知即可求得: <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> ,问题得解.

2)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> ,联立直线 <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> 的方程与椭圆方程即可求得点 <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> ,同理可得点 <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> ,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,可表示出直线 <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> 的方程,整理直线 <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> ,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,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> ,直线过点 <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> ,命题得证.

【详解】

1)依据题意作出如下图象:

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

由椭圆方程 <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: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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>

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

2)证明: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>

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>

联立直线 <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> 的方程与椭圆方程可得: <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> ,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> 代入直线 <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> 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>

所以点 <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> .

同理可得: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> 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> 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>

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>

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>

所以直线 <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> 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>

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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,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> ,直线过点 <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>

故直线CD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>

【点睛】

本题主要考查了椭圆的简单性质及方程思想,还考查了计算能力及转化思想、推理论证能力,属于难题.

22在直角坐标系 <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> 中,曲线 <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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 为参数 <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> .以坐标原点为极点, <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> 轴正半轴为极轴建立极坐标系,曲线 <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>

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> 是什么曲线?

2)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,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>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的公共点的直角坐标.

【答案】1)曲线 <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> 表示以坐标原点为圆心,半径为1的圆;(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)利用 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 消去参数 <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> ,求出曲线 <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> 的普通方程,即可得出结论;

2)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> ,曲线 <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> 的参数方程化为 <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> 为参数),两式相加消去参数 <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> ,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> 普通方程,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> ,将曲线 <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> 化为直角坐标方程,联立 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 方程,即可求解.

【详解】

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,曲线 <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> 为参数),

两式平方相加得 <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>

所以曲线 <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> 表示以坐标原点为圆心,半径为1的圆;

2)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,曲线 <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> 为参数),

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> ,曲线 <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> 的参数方程化为 <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> 为参数),

两式相加得曲线 <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> 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> ,平方得 <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>

曲线 <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>

曲线 <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> 直角坐标方程为 <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>

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

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> ,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> (舍去),

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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> 公共点的直角坐标为 <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> .

【点睛】

本题考查参数方程与普通方程互化,极坐标方程与直角坐标方程互化,合理消元是解题的关系,要注意曲线坐标的范围,考查计算求解能力,属于中档题.

23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)画出 <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> 的图像;

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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)求不等式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的解集.

【答案】1)详解解析;(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)根据分段讨论法,即可写出函数 <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> 的解析式,作出图象;

2)作出函数 <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> 的图象,根据图象即可解出.

【详解】

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> ,作出图象,如图所示: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" 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)将函数 <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> 的图象向左平移 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 个单位,可得函数 <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> 的图象,如图所示:

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

所以不等式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/881/" title="统一" class="c1" target="_blank">统一</a> <a href="/tags/1120/" title="文科" class="c1" target="_blank">文科</a> 的解集为 <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】

本题主要考查画分段函数的图象,以及利用图象解不等式,意在考查学生的数形结合能力,属于基础题.


试卷第21页,总3