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【334310】2021年北京市高考数学试卷

时间:2025-01-21 17:58:26 作者: 字数:16542字
简介:

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Shape2

绝密·启用前

2021年北京市高考数学试卷

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



评卷人

得分




一、选择题

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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

2.在复平面内,复数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

3.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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 是定义在上 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的函数,那么“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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上单调递增”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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上的最大值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ”的( )
A
.充分而不必要条件
B
.必要而不充分条件
C
.充分必要条件
D
.既不充分也不必要条件

4.某四面体的三视图如图所示,该四面体的表面积为( )
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

5.若双曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 离心率为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,过点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,则该双曲线的方程为( )
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

6.《中国共产党党旗党徽制作和使用的若干规定》指出,中国共产党党旗为旗面缀有金黄色党徽图案的红旗,通用规格有五种.这五种规格党旗的长 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> (单位:cm)成等差数列,对应的宽为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> (单位: cm),且长与宽之比都相等,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
A
64
B
96
C
128
D
160

7.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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
A
.奇函数,且最大值为2
B
.偶函数,且最大值为2
C
.奇函数,且最大值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
D
.偶函数,且最大值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

8.某一时间段内,从天空降落到地面上的雨水,未经蒸发、渗漏、流失而在水平面上积聚的深度,称为这个时段的降雨量(单位: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ).24h降雨量的等级划分如下:
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
在综合实践活动中,某小组自制了一个底面直径为200 mm,高为300 mm的圆锥形雨量器.若一次降雨过程中,该雨量器收集的24h的雨水高度是150 mm(如图所示),则这24h降雨量的等级是
A
.小雨
B
.中雨
C
.大雨
D
.暴雨

9.已知直线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 为常数)与圆 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 交于点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 变化时,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的最小值为2,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

10.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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 是各项均为整数的递增数列,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的最大值为( )
A
9
B
10
C
11
D
12

评卷人

得分




二、填空题

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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的展开式中,常数项为__________

12.若点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 轴对称点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,写出 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的一个取值为___

13.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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,给出下列四个结论:
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 恰 有2个零点;
存在负数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,使得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 恰有个1零点;
存在负数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,使得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 恰有个3零点;
存在正数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,使得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 恰有个3零点.
其中所有正确结论的序号是_______

评卷人

得分




三、双空题

14.已知抛物线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的焦点为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 在抛物线上, <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 垂直 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 轴与于点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,则点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的横坐标为_______  <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的面积为_______

15.已知向量 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 在正方形网格中的位置如图所示.若网格纸上小正方形的边长为1,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

评卷人

得分




四、解答题

16. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
1)求 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
2)再从条件①、条件②、条件③这三个条件中选择一个作为已知,使 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 存在且唯一确定,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 边上中线的长.
条件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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
条件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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的周长为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
条件③: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

17.如图:在正方体 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 中点, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 与平面 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 交于点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
1)求证: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的中点;
2)点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 是棱 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上一点,且二面角 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的余弦值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值.

18.在核酸检测中, “k1” 混采核酸检测是指:先将k个人的本混合在一起1检测,如果k个人都没有感染新冠病毒,则检测结阴性,得到每人的检测结果都阴性,检测结:如果k个人中有人感染新冠病毒,则检测结阳性,此每人再1检测,得到每人的检测结果,检测结.
现对100行核酸检测,假其中只有2人感染新冠病毒,并假每次检测结果准确.
I)将100人随机分成10,每10人,且都采用101”混采核酸检测.
(i)
如果感染新冠病毒的2人在同一,求检测次数;
(ii)
已知感染新冠病毒的2人分在同一的概率 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .X检测次数,求X
分布列与数学期望E(X).
(II
)将100人随机分成20,每5人,且都采用51”混采核酸检测.Y检测次数,判断数学期望E(Y)(I)E(X)的大小.(结论不要求)

19.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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
1)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,求曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 在点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 处的切线方程;
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 处取得极值,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的单调区间,以及其最大值与最小值.

20.已知椭圆 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 一个顶 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,以椭圆 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的四个顶点为顶点的四边形面积为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
1)求椭圆E的方程;
2P(0-3)的直线l斜率k的直线椭圆E交于不同的两点BC,直线ABAC与直线y=-3交于点MN,当|PM|+|PN|≤15,求k的取

21.p为实.若无数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 足如下三个性 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
1)如果数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的前4项为2-2-2-1,那么 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 是否可能 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 数列?明理由;
2)若数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 数列,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
3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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .是否存在 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,使得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 恒成立?如果存在,求出所有的p;如果不存在,明理由.

参考答案

1.B

【解析】
结合题意利用并集的定义计算即可.
由题意可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
故选:B.

2.D

【解析】
由题意利用复数的运算法则整理计算即可求得最终结果.
由题意可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
故选:D.

3.A

【解析】
利用两者之间的推出关系可判断两者之间的条件关系.
若函数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上单调递增,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上的最大值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上的最大值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
比如 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 为减函数,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 为增函数,
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上的最大值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 推不出 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上单调递增,
故“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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上单调递增”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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 上的最大值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ”的充分不必要条件,
故选:A.

4.A

【解析】
根据三视图可得如图所示的几何体(三棱锥),根据三视图中的数据可计算该几何体的表面积.
根据三视图可得如图所示的几何体-正三棱锥 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
其侧面为等腰直角三角形,底面等边三角形,
由三视图可得该正三棱锥的侧棱长为1
故其表面积为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

5.B

【解析】
分析可得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,再将点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 代入双曲线的方程,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值,即可得出双曲线的标准方程.
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,则双曲线的方程为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
将点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的坐标代入双曲线的方程可得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
因此,双曲线的方程为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
故选:B

6.C

【解析】
设等差数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 公差为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,结合党旗长与宽之比都相等和 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,列出方程,即可求解.
由题意,五种规格党旗的长 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> (单位:cm)成等差数列,设公差为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
又由长与宽之比都相等,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
故选:C.

7.D

【解析】
由函数奇偶性的定义结合三角函数的性质可判断奇偶性;利用二倍角公式结合二次函数的性质可判断最大值.
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,所以该函数为偶函数,
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 取最大值 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
故选:D.

8.B

【解析】
计算出圆锥体积,除以圆面的面积即可得降雨量,即可得解.
由题意,一个半径为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的圆面内的降雨充满一个底面半径为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,高为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的圆锥,
所以积水厚度 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,属于中雨.
故选:B.


9.C

【解析】
先求得圆心到直线距离,即可表示出弦长,根据弦长最小值得出 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
由题可得圆心为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,半径为2
则圆心到直线的距离 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
则弦长为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
则当 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 时,弦长 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 取得最小值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
故选:C.

10.C

【解析】
使数列首项、递增幅度均最小,结合等差数列的通项及求和公式求得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 可能的最大值,然后构造数列满足条件,即得到 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的最大值.
若要使n尽可能的大, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 增幅度要尽可能小,
不妨数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 是首项为3,公差1的等差数列,其前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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
取数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 项为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
所以n的最大值为11
C

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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

【解析】
利用二项式定理求出通项公式并整理化简,然后令 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的指数为零,求解并计算得到答案.
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的展开式的通项 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
故常数项为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .

12. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 即可)

【解析】
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 在单位圆上,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 轴对称,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 求解.
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 轴对称,
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 轴对称,
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 时,可取 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的一个值为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 即可).

13.①②④

【解析】
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 可得出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,考查直线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 与曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的左、右支分别相切的情形,利用方程思想以及数形结合可判断各选项的正误.
对于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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 时,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,①正确;
对于②,考查直线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 与曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 相切于点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
对函数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 求导得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,由题意可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
所以,存在 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,使得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 只有一个零点,②正确;
对于③,当直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 过点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 与曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 有两个交点,
若函数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 有三个零点,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 与曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 有两个交点,
直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 与曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 有一个交点,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,此不等式无解,
因此,不存在 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,使得函数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 有三个零点,③错误;
对于④,考查直线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 与曲线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 相切于点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
对函数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 求导得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,由题意可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 时,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 有三个零点,④正确.
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
故答案为:①②④.

14.     5      <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

【解析】
根据焦半径公式可求 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的横坐标,求出纵坐标后可求 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
因为抛物线的方程为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
故答案为:5 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .

15.     0     3

【解析】
根据坐标求出 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,再根据数量积的坐标运算直接计算即可.
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 交点为坐标原点,建立直角坐标系如图所示:
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
故答案为:03.

16.1 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ;(2)答案不唯一,具体见解析.

【解析】
1)由正弦定理化边为角即可求解;
2)若选择①:由正弦定理求解可得不存在;
若选择②:由正弦定理结合周长可求得外接圆半径,即可得出各边,再由余弦定理可求;
若选择③:由面积公式可求各边长,再由余弦定理可求.
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,则由正弦定理可得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
2)若选择①:由正弦定理结合(1)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 矛盾,故这样的 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 不存在;
若选择②:由(1)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的外接圆半径为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
则由正弦定理可得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
则周长 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 边上的中线的长度为:
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
若选择③:由(1)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
则由余弦定理可得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 边上的中线的长度为:
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .

17.1)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

【解析】
(1)
首先将平面 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 进行扩展,然后结合所得的平面与直线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的交点即可证得题中的结论;
(2)
建立空间直角坐标系,利用空间直角坐标系求得相应平面的法向量,然后解方程即可求得实数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值.
(1)
如图所示,取 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的中点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,连结 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
由于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 为正方体, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 为中点,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
从而 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 四点共面,即平面CDE即平面 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
据此可得: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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 交平面 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 于点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
当直线与平面相交只有唯一的交点,故点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 重合,
即点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 中点.
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
(2)
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 原点, <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 方向分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 正方向,建立空直角坐 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
不妨正方体的棱长为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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
从而: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的法向量 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的法向量 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
从而: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 舍去).

18.1)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 次;②分布列见解析;期望为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

【解析】
1)①由题设条件还原情境,即可得解;
求出X的取情况,求出各情况下的概率,而可得分布列,再由期望的公式即可得解;
2)求出两名感染者在一的概率,而求出 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,即可得解.
1组进检测,需要10次;再对结阳性的每个人检测,需要10次;
所以总检测次数20次;
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 可以取2030
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的分布列:


 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
2)由意, <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 可以取2530
两名感染者在同一的概率 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,不在同一的概率 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .


19.1 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ;(2)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的增区间为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,单调递减区间为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .

【解析】
1)求出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值,利用点斜式可得出所求切线的方程;
2)由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 可求得实数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值,然后利用导数分析函数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的单调性与极值,由此可得出结果.
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
此时,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 在点 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 处的切线方程为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
2)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
由题意可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,列表如下:

 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

极大值

极小值


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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的增区间为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,单调递减区间为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .

20.1 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

【解析】
1)根据椭圆所过的点及四个顶点围成的四边形的面积可求 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,从而可求椭圆的标准方程.
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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,求出直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的方程后可得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的横坐标,从而可得 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的方程和椭圆的方程,结合韦达定理化简 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,从而可求 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的范围,注意判别式的要求.
1)因为椭圆过 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
因为四个顶点围成的四边形的面积为 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
故椭圆的标准方程为: <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
因为直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的斜率存在,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
故直线 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,同理 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,故 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
综上, <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .

21.1)不可以是 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 数列;理由见解析;(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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ;(3)存在; <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>

【解析】
(1)
由题意考查 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值即可说明数列不是 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 数列;
(2)
由题意首先确定数列的前4项,然后讨论计算即可确定 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值;
(3)
构造数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,易知数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的,结合(2)中的结论求解不等式即可确定满足题意的实数 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 的值.
(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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
所以数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,不可能是 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 数列.
(2)
性质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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
由性质③ <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,由性质②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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,矛盾;
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,矛盾.
因此只能是 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
不满足 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 前四项为:0001
下面用数学归纳法证明 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 时,经验证命题成立,假设当 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 时命题成立,
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,利用性质③:
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,此时可得: <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
否则,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,取 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
而由性质②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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 矛盾.
同理可得:
 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
即当 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 时命题成立,证毕.
综上可得: <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> .
(3)
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,由性质③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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
由于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a>
因此数列 <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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> 数列.
由(2)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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</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/56/" title="北京" class="c1" target="_blank">北京</a> <a href="/tags/217/" title="北京市" class="c1" target="_blank">北京市</a> ,满足题意.


Shape4 3页,总1