山东省青岛地区2021-2022学年高二下学期期中考试数学试题答案

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侵权投诉
2021—2022 学年度第二学期期中学业水平检测
高二数学答案及评分标准
一、单项选择题：本大题共 8小题．每小题 5分，共 40 分．
A D C A B A C D
二、多项选择题：本大题共 4小题．每小题 5分，共 20 分．
9．AC； 10．BC； 11．BD； 12．ACD.
三、填空题：本大题共 4小题，每小题 5分，共 20 分．
13．； 14．； 15．； 16．；.
四、解答题：本大题共 6小题，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：选择条件①：
（1）设切点为 ·····································································································1 分
因为 ，所以 ·················································································3 分
所以切线的斜率为 ······················································································4 分
解得 ····························································································································· 5 分
所以切点为 ················································································································6 分
（2）由（1）知切点为 ，
因为点 在直线 上························································································8 分
所以 ，即 ······································································································10 分
选择条件②：
（1）设切点设切点为 ······················································································1 分
因为 ，所以 ···············································································3 分
所以切线的斜率为 ······················································································4 分
解得 ······························································································································ 5 分
所以切点为 ················································································································6 分
（2）由（1）知切点为
因为点 在直线 上························································································8 分
所以 ，即 ···································································································10 分
18. （本小题满分 12 分）
解：（1）根据图可得，女生中得分不超过 分的人数 ，
女生得分超过 分的人数 ，
男生中得分不超过 分的人数 ，男生得分超过 分的人数 ，
则列联表为：
性别
了解航空航天知识程度
合计
得分不超过 分的人数 得分超过 分的人数
女生
男生
合计
······················································································3 分
（2）因为
····················6 分
所以，依据 的独立性检验，认为该学校高中生了解航空航天知识程度与性别有关联，
此推断犯错误的概率不大于 ．···················································································7 分
（3）由（1）可得，得分超过 分的学生中男生：女生 ，
从得分超过 分的同学中采用分层抽样的方法抽取 人，
则男生占 人，女生占 人···································································································8 分
则 取值可能为 ， ，
， ， ，
所以随机变量 的分布列为
········································································································11 分
所以 ．···········································································12 分
19．（本小题满分 12 分）
解：（1）设 “取出的 球中有红球”， “第 次取出的是红球” ················1 分
（ⅰ）由题意知，随机试验为从 号箱中不放回的进行 次取球
则················································································································ 2 分
又···························································································3 分
所以由古典概型的概率公式得，
故故所求的概率为 ···········································································································4 分
（ⅱ）因为 ···············································································5 分
所以由条件概率公式得，
故所求的概率为 ···············································································································6 分
山东省青岛地区2021-2022学年高二下学期期中考试数学试题答案.docx

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作者：envi 分类：分省 价格：3知币 属性：8 页 大小：317.95KB 格式：DOCX 时间：2024-12-08

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