湖南省常德市2022-2023高三上学期期末检测答案

3.0 envi 2024-12-10 4 4 326.95KB 8 页 3知币
侵权投诉
2022-2023 学年度上学期常德市高三检测考试
数 学（参考答案）
一、选择题：本题共 8小题，每小题 5分，共 40 分．
题号 1 2 3 4 5 6 7 8
答案 B A D D A A C B
二、选择题：本题共 4小题，每小题 5分，共 20 分．全部选对的得 5分，部分选对的得 2分，有选错
的得 0分.
题号 9 10 11 12
答案 BD BC BCD ABC
三、填空题：本题共 4小题，每小题 5分，共 20 分．
13. 14. 15. 16.
三、解答题：本大题共 70 分，解答应写出文字说明、证明过程或演算步骤．
17. (本小题满分 10 分)
解：(1) , ·····································································2 分
，
是以 为首项， 为公比的等比数列················································5 分
(2)由(1)可得： ，
即： ······················································································.8 分
令 ，当 n时， ， 单调递增；
又 ， ，
满足不等式的最大整数 ·········································································10 分
18．（本小题满分 12 分）
解：(1)在 中，由余弦定理得 ·····························1 分
在 中，由余弦定理得 ································2 分
由 有， ，解得 ·············································3 分
，又 ， ···································4 分
梯形 的面积
·································6 分
法二：(1)取BC 的中点 E，连 AE，则 BE=CE=2·················································1 分
AD=EC，AD//EC， 四边形 AECD 为平行四边形···········································2 分
AE=DC=2·······························································································3 分
在 中，
又，········································································4 分
梯形 的面积 ·······················6 分
(2)设 ， ，则 ， ，
在中，由正弦定理得 ，即 ①
在中，由正弦定理得 ，即 ②····························8 分
由①②得： ············································································9 分
化简得，
又
所以 ························································································11 分
又
所以 ， ， 为直角三角形·····················································12 分
法二：取 BC 的中点 E，连 AE，则 BE=CE=2
AD=EC，AD//EC， 四边形 AECD 为平行四边形·················································8 分
·································································································10 分
，为直角三角形··········································································12 分
19．（本小题满分 12 分）
(1)证明：取 DE 的中点 M，连 MG、MH····································································1 分
·············································································2 分
，又 平面 CGF
····························································································3 分
，又 平面 CGF
·····························································································4 分
·····················································································5 分
(2)如图，以 C为原点，CB 为x轴，CF 为y轴，CD 为z轴建立空间直角坐标系，
则A(2,0,2)，C(0,0,0)，F(0,2,0)，G(―1,1,2)，H(1,0,0)，E(0,2,2)···································6 分
则,设面 CGF 的法向量
令 得 ,
即·······································8 分
··········9 分
设所求线面角为 ，
则········································11 分
所以当 时， 取得最大值为 ······························································12 分
20．（本小题满分 12 分）
解：(1)仅乘坐一站的乘客有 10+10+10+30=60 人该乘客仅乘坐一站的概率 ······2 分
(2)从常德上车的乘客到长沙下车的概率 ·····················································3 分
故这 3人到长沙下车的人数 ， ······································5 分
X 0 1 2 3
P
························································································································7 分
·······························································································8 分
(3)记事件 A：该乘客在过益阳南站后到长沙站下车，记事件 B1:该乘客在常德站上车，记事件 B2:该乘客
湖南省常德市2022-2023高三上学期期末检测答案.docx

共8页,预览3页

还剩页未读， 继续阅读

相关推荐

更多
立即下载
作者：envi 分类：分省 价格：3知币 属性：8 页 大小：326.95KB 格式：DOCX 时间：2024-12-10

开通VIP享超值会员特权

  • 多端同步记录
  • 高速下载文档
  • 免费文档工具
  • 分享文档赚钱
  • 每日登录抽奖
  • 优质衍生服务

作者详情

相关内容

更多

推荐作者

热门标签

大联考 高考地理 英语真题 听力 语法填空 石家庄 数学竞赛 读后续写 英语阅读 深圳中学
/ 8
评分 收藏
分享
立即下载
客服
关注