解题方法
1 . 甲、乙、丙、丁四人相互做传球训练,第1次由甲将球传出,每次传球时,传球者都等可能地将球传给另外三个人中的任何一个人.则4次传球的不同方法总数为_________ (用数字作答);4次传球后球在甲手中的概率为_________ .
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2 . 假设视网膜为一个平面,光在空气中不折射,眼球的成像原理为小孔成像. 思考如下成像原理: 如图,地面内有圆
,其圆心在线段
上,且与线段
交于不与
重合的点
,
地面,且
,
点为人眼所在处,视网膜平面与直线
垂直. 过
点作平面
平行于视网膜平面. 科学家已经证明,这种情况下圆
上任意一点到
点的直线与平面
交点的轨迹(令为曲线
)为椭圆或圆,且由于小孔成像,曲线
与圆
在视网膜平面上的影像是相似的,则当视网膜平面上的圆
的影像为圆时,圆
的半径
为____________ . 当圆
的半径
满足
时,视网膜平面上的圆
的影像的离心率的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dc6893e52bbca0d011ac46845334d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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2024-05-09更新
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99次组卷
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2卷引用:四川省成都市实验外国语学校2023-2024学年高二上学期期末能力测评数学试题
3 . 已知全校共3000名学生,其中有1800名男生,1200名女生,为调查学生的身高情况,按分层随机抽样的方法抽取20名学生的身高作为样本,样本中男生身高的平均数为170,方差为30,女生身高的平均数为160,方差为45,则利用样本估计总体的平均数为________ ,估计总体的方差为________ .
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4 . 已知在平面直角坐标系xOy中,
,动点P满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420d464c96149bd9cb5c7b1b3548133c.png)
则P点的轨迹Γ为圆_______ ,过点A的直线交圆Γ于两点C,D,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7b02a080e9c7d2b9d2c621bcde2d67.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2ba05abdc8179e5ff980fb2d15ce2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420d464c96149bd9cb5c7b1b3548133c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a3363fbd9527e8aef45af8b302d01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7b02a080e9c7d2b9d2c621bcde2d67.png)
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5 . 已知双曲线
的方程为
,其左右焦点分别为
,已知点
坐标为
,双曲线
上的点
满足
,设
内切圆半径为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
_____________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8506adc46d5d5e3aca20a0cf68c97699.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d111bc4c539ccc83d1741b334f2a8b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e529901df4c719765b069f0745c6e84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4085b194990fc17f8073878b8eca1a29.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8506adc46d5d5e3aca20a0cf68c97699.png)
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206次组卷
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4卷引用:湖南省怀化市2022-2023学年高二上学期期末数学试题
湖南省怀化市2022-2023学年高二上学期期末数学试题重庆市九龙坡区2023-2024学年高二上学期教育质量全面监测数学试题安徽省淮北市实验高级中学2023-2024学年高二上学期期末考试数学试题(已下线)2.3.1 双曲线的标准方程(十二大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
6 . 甲同学进行投篮练习,每次投中的概率都是
,连续投3次.每次投篮互不影响.则该同学恰好只有第3次投中的概率为________ :该同学至少两次投中的概率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
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7 . 如图,椭圆
与双曲线
有公共焦点
,椭圆的离心率为
,双曲线的离心率为
,点
为两曲线的一个公共点,且
为
的内心,
三点共线,且
轴上点
满足
,则
的最小值为__________ ;
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29eb5ce3f09c49dfa489a3b0bd5beafb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65abb60103949a9cbe1e4890df8bd3ab.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8597c617617900e3265b9eacb0fed1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c07b101a1a118c7558a9e59b13c95c.png)
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8 . 在
中,已知
边上的高等于
,当角
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33e8045277a342dbbaff481815bd532.png)
_____ ;当角
时,
的最大值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc78256f4c7a57810c48a113c6f1fe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4376af85e07b29051a812ff3fcda61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33e8045277a342dbbaff481815bd532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67acf6f4fc0f4005864e9ca5b41859bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a24a8f5e8fb89381f8add6549170345.png)
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827次组卷
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4卷引用:广东省东莞市2023-2024学年高一上学期教学质量检查数学试卷
9 . 已知点A为抛物线
上一点(点A在第一象限),点F为抛物线的焦点,准线为l,线段AF的中垂线交准线l于点D,交x轴于点E(D、E在AF的两侧),四边形
为菱形,若点P、Q分别在边DA、EA上,
,
,若
则
的最小值为______ ,
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08c14e87a2bcf7090eab2fea73667d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1074ae4cfaa6c7ab2eabe04bf97513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7112901e241c4db02f538795d1b79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8b5ad14031c353573710741dc68549.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ef5824baf830ec04377a49df11513c.png)
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10 . 学习于才干信仰,犹如运动于健康体魄,持之已久、行之愈远愈受益.为实现中华民族伟大复兴,全国各行各业掀起了“学习强国”的高潮.某老师很喜欢“学习强国”中“挑战答题”模块,他记录了自己连续七天每天一次最多答对的题数如下表:
参考数据:
,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41b6d98a983e9a4cf831d669e149935.png)
相关系数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084e78dabc30e451c12dcca2520f3270.png)
由表中数据可知该老师每天一次最多答对题数y与天数x之间是______ 相关(填“正”或“负”),其相关系数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eee5ebaaba44aeff46980da804b7539.png)
______ (结果保留两位小数)
天数x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
一次最多答对题数y | 12 | 15 | 16 | 18 | 21 | 24 | 27 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967a00752ac887b78032b1ce73eca591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7c87659b8dd53524a86fa348960b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd718d005b26af98758e4492e40a4465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d33a4ead18c6f2d688eb759a8c6b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba078df5ee0cc1831134de7f2a9d226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41b6d98a983e9a4cf831d669e149935.png)
相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084e78dabc30e451c12dcca2520f3270.png)
由表中数据可知该老师每天一次最多答对题数y与天数x之间是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eee5ebaaba44aeff46980da804b7539.png)
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2024-01-22更新
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848次组卷
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7卷引用:天津市八校联考2023-2024学年高三上学期期末质量调查数学试卷
天津市八校联考2023-2024学年高三上学期期末质量调查数学试卷(已下线)第八章 成对数据的统计分析(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第三册)(已下线)模块八 概率与统计(测试)(已下线)第01讲 8.1 成对数据的统计相关性(知识清单+5类热点题型精讲+强化分层精练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第三册)(已下线)8.1.1变量的相关关系+8.1.2样本相关系数 第一课 解透课本内容(已下线)8.1 成对数据的统计相关性——课后作业(提升版)(已下线)8.1 成对数据的统计相关性(4大题型)精讲-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第三册)