2021钦州高二下学期期末考试数学（文）试题扫描版含答案

钦州市2021年春季学期教学质量监测参考答案

高二 数 学（文科）

一、选择题答案：（每小题5分，共60分）

二、填空题答案：（每小题5分，共20分）

13. ;          14． ;        15． ;     16．

三、解答题：本大题共6题，共70分．解答应写出文字说明、证明过程或演算步骤．

17．解：（1），，.

，即直线的极坐标方程.  ······································3分

由

化得.

即圆的极坐标方程为.    ·······································5分

（2）将代入，   ·················································7分

得，

则.

的值为    ················································10分

18解：①当时，，所以，所以； ········································2分

②当时，，所以，所以；········································4分

③当时，，所以，所以.

综上，当时，不等式的解集为.   ···································6分

（2）因为，

所以.      ················································8分

又因为有实数解，

所以，          ·············································10分

解得：，

故实数的取值范围为.    ·········································12分

19解：（1）根据题意,1000名患者中

潜伏期超过6天的共有250+130+15+5=400人，   ·······················2分

所以1000名患者中取1人，此患者为潜伏期超过6天的

概率.    ···················································4分

（2）由（1）可知，200人应该抽取潜伏期超过6天的有人，

补充完整的列联表如下：

则，   ·····················································10分

，

所以没有的把握认为潜伏期与患者年龄有关. ························12分

20.解：解：(1)因为：，

消去参数得.

曲线的普通方程为.  ··········································4分

（2）将代入的普通方程为，    ·········································6分

得，整理得.

    ····························································8分

又

.

弦长的值为.    ·················································12分

21.解：（1）要证，

    因为，

只要证

即要证，······················································3分

即要证，

即要证，

即要证.

因为上式成立，

所以.   ······················································6分

（2）因为

所以     ·····················································8分

，

当且仅当时，等号成立，

所以所求的最小值为.   ·········································12分

22.解：（1）由频率分布直方图知，

由解得，  ·····················································2分

设总共调查了个人，则满意的为，

解得人．

不满意的频率为，

所以共有人，

即不满意的人数为120人.    ·········································4分

（2）评分等级为“不满意”的120名市民中按年龄分层抽取人，

则男生人数为人，分别记为，

女生人数为人，分别记为，

从6人中选取人担任整改督导员的所有的抽取方法有

共15种，

有女生的情况为9种，

 所以至少有一位女生督导员的概率．    ·······························8分

（3）所选样本满意程度的平均得分为：

，

估计市民满意程度的平均得分为，

所以市民满意指数为，

故该项目能通过验收．     ·········································12分