当前位置:首页 > 高考 > 数学试卷

【334314】2021年全国高考乙卷数学文试卷

时间:2025-01-21 17:59:06 作者: 字数:14099字
简介:

…………○…………外…………○…………装…………○…………订…………○…………线…………○…………

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

…………○…………内…………○…………装…………○…………订…………○…………线…………○…………

Shape2

绝密·启用前

2021年全国高考乙卷数学(文)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.已知全集 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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> ,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
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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>
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>
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>

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

3.已知命题 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ﹔命题 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,则下列命题中为真命题的是( )
A
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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>
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>
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>

4.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> 的最小正周期和最大值分别是( )
A
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 2
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 2

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> 满足约束条件 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的最小值为( )
A
18
B
10
C
6
D
4

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

7.在区间 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 随机取1个数,则取到的数小于 <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> 的概率为( )
A
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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>
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>
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>

8.下列函数中最小值为4的是( )
A
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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>
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>
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>

9.设函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,则下列函数中为奇函数的是( )
A
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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>
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>
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>

10.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> 中,P <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的中点,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 所成的角
A
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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>
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>
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>

11.B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> 的上点,点PC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> 的最大值为
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>
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>
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>
D
2

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> ,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> 为函数 <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> 的极大值点,则( )
A
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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>
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>
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>

评卷人

得分




二、填空题

13.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> ,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> ,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> _________

14.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> 的右焦点到直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的距离为________

15. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的内角ABC对边别为abc,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ________

16.以图①为正视图,在图②③④⑤中选两个分别作为侧视图和俯视图,组成某个三棱锥的三视图,则所选侧视图和俯视图的编号依次为_________(写出符合要求的一组答案即可).
 <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>

评卷人

得分




三、解答题

17.某厂研制了一种生产高精产品的设备,为检验新设备生产产品的某项指标有无提高,用一台旧设备和一台新设备各生产了10件产品,得到各件产品该项指标数据如下:

旧设备

9.8

10.3

10.0

10.2

9.9

9.8

10.0

10.1

10.2

9.7

新设备

10.1

10.4

10.1

10.0

10.1

10.3

10.6

10.5

10.4

10.5


旧设备和新设备生产产品的该项指标的样本平均数分别记为 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,样本方差分别记为 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
2)判断新设备生产产品的该项指标的均值较旧设备是否有显著提高(如果 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,则认为新设备生产产品的该项指标的均值较旧设备有显著提高,否则不认为有显著提高).

18.如图,四棱锥 <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> 的底面是矩形, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 底面 <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> M <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的中点,且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
1明: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> 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>
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> ,求四棱 <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> 的体

19. <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 是首项为1的等比数列,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> 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> .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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 成等差数列.
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的通项公式;
2)记 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 分别为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的前n和.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>

20.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> 的焦点F到准线的距离2
1)求C的方程;
2)已知O原点,点PC上,点Q <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,求直线 <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> 斜率的最大.

21.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>
1)讨论 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的单调性;
2)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> 过坐标原点的切线与曲线 <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> 的公共点的坐标.

22.在直角坐标系 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 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> 的圆心为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,半径为1
1)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> 的一个参数方程;
2)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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的两条切线.以坐标原点为极点,x正半轴为建立极坐系,求两条切线的极坐方程.

23.已知函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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> 时,求不等式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的解集;
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> ,求a的取

参考答案

1.A

【解析】
首先进行并集运算,然后进行补集运算即可.
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> ,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> .
故选:A.

2.C

【解析】
由题意结合复数的运算法则即可求得z的值.
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> .
故选:C.

3.A

【解析】
由正弦函数的有界性确定命题 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的真假性,由指数函数的知识确定命题 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的真假性,由此确定正确选项.
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> ,所以命题 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 为真命题;
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 上为增函数, <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> ,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> ,所以命题 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 为真命题;
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> 为真命题, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 为假命题.
故选:A

4.C

【解析】
利用辅助角公式化简 <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> ,结合三角函数周期性和值域求得函数的最小正周期和最大值.
由题, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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> 的最小正周期为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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> .
故选:C

5.C

【解析】
由题意作出可行域,变换目标函数为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,数形结合即可得解.
由题意,作出可行域,如图阴影部分所示,
 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 可得点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,
转换目标函数 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
上下平移直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,数形结合可得当直线过点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> , <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 取最小值,
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> .
故选:C.

6.D

【解析】
由题意结合诱导公式可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,再由二倍角公式即可得解.
由题意, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .
故选:D.

7.B

【解析】
根据几何概型的概率公式即可求出.
 <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> “区间 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 随机取1个数”,对应集合为:  <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> ,区间长度为 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 取到的数小于 <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> ”, 对应集合为: <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> ,区间长度为 <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>
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>
故选:B

8.C

【解析】
根据二次函数的性质可判断 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 选项不符合题意,再根据基本不等式“一正二定三相等”,即可得出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 不符合题意, <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> 符合题意.
对于A <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,当且仅当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 时取等号,所以其最小值为 <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不符合题意;
对于B,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,当且仅当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 时取等号,等号取不到,所以其最小值不为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> B不符合题意;
对于C,因为函数定义域为 <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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,当且仅当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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> 时取等号,所以其最小值为 <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> C符合题意;
对于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> ,函数定义域为 <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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,如当 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> D不符合题意.
故选:C

9.B

【解析】
分别求出选项的函数解析式,再利用奇函数的定义即可.
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>
对于A <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 不是奇函数;
对于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> 是奇函数;
对于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> ,定义域不关于原点对称,不是奇函数;
对于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> ,定义域不关于原点对称,不是奇函数.
故选:B

10.D

【解析】
平移直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,将直线 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 所成的角转化为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 所成的角,解三角形即可.
 <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>
如图,连接 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 或其补角为直线 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 所成的角,
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> 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> ,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> ,又 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
设正方体棱长为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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> .
故选:D

11.A

【解析】
设点 <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> ,由依题意可知, <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,再根据两点间的距离公式得到 <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> ,然后消元,即可利用二次函数的性质求出最大值.
设点 <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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 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> 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>
故选:A

12.D

【解析】
先考虑函数的零点情况,注意零点左右附近函数值是否编号,结合极大值点的性质,对 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 进行分类讨论,画出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 图象,即可得到 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 所满足的关系,由此确定正确选项.
 <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> ,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> 为单调函数,无极值点,不符合题意,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 两个不同零点,且在 <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> 左右附近是不变号,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> 左右附近是变号的.依题意, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 为函数 <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> 的极大值点, <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 左右附近都是小于零的.
 <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> 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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,画出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的图象如下图所示:
 <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>
由图可知 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 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> ,画出 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的图象如下图所示:
 <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>
由图可知 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> .
综上所述, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 成立.
故选:D

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

【解析】
利用向量平行的充分必要条件得到关于 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的方程,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> 的值.
由题意结合向量平行的充分必要条件可得: <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>
解方程可得: <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> .
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> .

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

【解析】
先求出右焦点坐标,再利用点到直线的距离公式求解.
由已知, <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> ,所以双曲线的右焦点为 <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>
所以右焦点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 到直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的距离为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .
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>

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

【解析】
由三角形面积公式可得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,再结合余弦定理即可得解.
由题意, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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>
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> ,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> (负值舍去).
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> .

16.③④(答案不唯一)

【解析】
由题意结合所给的图形确定一组三视图的组合即可.
选择侧视图为③,俯视图为④,
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
如图所示,长方体 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 分别为棱 <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> 的中点,
则正视图①,侧视图③,俯视图④对应的几何体为三棱锥 <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> .
故答案为:③④.

17.1 <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> ;(2)新设备生产产品的该项指标的均值较旧设备有显著提高.

【解析】
1)根据平均数和方差的计算方法,计算出平均数和方差.
2)根据题目所给判断依据,结合(1)的结论进行判断.
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .
2)依题意, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,所以新设备生产产品的该项指标的均值较旧设备有显著提高.


18.1)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>

【解析】
1)由 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 底面 <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> 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> ,又 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,由线面垂直的判定定理可得 <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> 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> ,再根据面面垂直的判定定理即可证出平面 <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> 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>
2)由(1)可知, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,由平面知识可知, <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> ,由相似比可求出 <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> ,再根据四棱锥 <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> 的体积公式即可求出.
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> 底面 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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>
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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>
所以平面 <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> 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>
2)由(1)可知, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 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> ,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>
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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> ,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> ,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>
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> 底面 <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>
故四棱锥 <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> 的体积为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>

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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ;(2)证明见解析.

【解析】
利用等差数列的性质及 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> ,解方程即可;
利用公式法、错位相减法分别求出 <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> ,再作差比较即可.
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> 是首项为1的等比数列且 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 成等差数列,
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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> ,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>
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> .
2)证明: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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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>
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> .
(
点晴)
本题主要考查数列的求和,涉及到等差数列的性质,错位相减法求数列的和,考查学生的数学运算能力,是一道中档题,其中证明不等式时采用作差法,或者作商法要根据式子得结构类型灵活选择,关键是要看如何消项化简的更为简洁.

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> ;(2)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> .

【解析】
1)由抛物线焦点与准线的距离即可得解;
2)设 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,由平面向量的知识可得 <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> ,进而可得 <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> ,再由斜率公式及基本不等式即可得解.
1)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> 的焦点 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,准线方程为 <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>
由题意,该抛物线焦点到准线的距离为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
所以该抛物线的方程为 <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>
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> ,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>
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 在抛物线上可得 <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> ,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>
所以直线 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的斜率 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 时,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>
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> ,当且仅当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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> 时,等号成立;
 <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> 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>
综上,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> 的斜率的最大值为 <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> .

21.(1)答案见解析;(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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .

【解析】
(1)
首先求得导函数的解析式,然后分类讨论导函数的符号即可确定原函数的单调性;
(2)
首先求得导数过坐标原点的切线方程,然后将原问题转化为方程求解的问题,据此即可求得公共点坐标.
(1)
由函数的解析式可得: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
导函数的判别式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> R上单调递增,
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 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> 的解为: <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 单调递增;
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 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> 单调递减;
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 单调递增;
综上可得: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> 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> R上单调递增,
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
单调递增,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> 上单调递减.
(2)
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
则切线方程为: <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>
切线过坐标原点,则: <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,
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> ,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>
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> ,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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 联立得 <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>
化简得 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,由于切点的横坐标1必然是该方程的一个根, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的一个因式,∴该方程可以分解因式 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
综上,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> 过坐标原点的切线与曲线 <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> 的公共点的坐标为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .

22.1 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 为参数);(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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .

【解析】
1)直接利用圆心及半径可得的圆的参数方程;
2)先求得过(41)的圆的切线方程,再利用极坐标与直角坐标互化公式化简即可.
1)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> 的普通方程为 <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>
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> 的参数方程为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,( <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 为参数)
2)由题意,切线的斜率一定存在,设切线方程为 <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> ,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>
由圆心到直线的距离等于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>
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> ,所以切线方程为 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 代入化简得
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
(
点晴)
本题主要考查直角坐标方程与极坐标方程的互化,涉及到直线与圆的位置关系,考查学生的数学运算能力,是一道基础题.

23.1 <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> .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> .

【解析】
1)利用绝对值的几何意义求得不等式的解集.
2)利用绝对值不等式化简 <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> ,由此求得 <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> 的取值范围.
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> 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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 表示数轴上的点到 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的距离之和,
 <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> 表示数轴上的点到 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 的距离之和不小于 <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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 时所对应的数轴上的点到 <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> 所对应的点距离之和等于6
数轴上到 <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> 所对应的点距离之和等于大于等于6得到所对应的坐标的范围是 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>  <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> 的解集为 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a>
2)依题意 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,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> 恒成立,
 <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>
当且仅当 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> 时取等号, <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> ,
 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</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> .
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> 的取值范围是 <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> .


Shape4 3页,总1