名校
解题方法
1 . 已知点
,
,
中恰有两个点在抛物线
上.
(1)求
的标准方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若点
,
在
上,且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590337b3868db8523eeb7f448efcf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f0ee968f9a247871a54e505fbd111b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9158f21b372fd0390fab040ad65c586.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb2356a3833defed220ee1fa481aad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-03-29更新
|
877次组卷
|
2卷引用:山东省青岛市2023-2024学年高二上学期期末学业水平检测数学试题
2 . 在通信技术中由
和
组成的序列有着重要作用,序列中数的个数称为这个
序列的长度
如
是一个长度为
的
序列
长为
的
序列中任何两个
不相邻的序列个数设为
,长度为
的
序列为:
,
,都满足数列
,
长度为
且满足数列
的
序列为:
,
,
,
.
(1)求
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634e70033857b751723d34d1ca86f375.png)
(2)求数列
中
,
,
的递推关系![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(3)记
是数列
的前
项和,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aec18fcd4df134d5037dd56f3d82841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f43677db00ba65a7f96fc49627d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2581813c187d2e230d97567d649d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e222c99263ff290929466f52bdb07404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a3257d015e9b178850734cfc3a5b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f43677db00ba65a7f96fc49627d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d786bde127368fd1b2ed7a7d233db866.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbeed5324c432101be517dd6f5c735b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634e70033857b751723d34d1ca86f375.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41ae64e37ebcddccabd64e12b0afc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7085d141e33ba0188e58fa2177d89ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1c13936c1d87bc8fc19a215f8a138f.png)
您最近一年使用:0次
3 . 如图(1)所示
中,
,
.
分别为
中点.将
沿
向平面
上方翻折至图(2)所示的位置,使得
.连接
得到四棱锥
.记
的中点为
,连接
.
平面
;
(2)点
在线段
上且
,连接
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d390782b8ea7016628ee68403dcbfbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1d18e7acbf1db4243914a885261ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d240ea67c239b0d9213448c11cba18c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36aae82d53f2a35d2f95f467bd5b76cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9742fb0549cb89e808d50e81bcef49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bb1063e139610045f3bca5ca0b2766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c25c4259d935d6e6fabe5c3fc1f43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef77cfa13de39e9ef424e386f84056e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6592783d1f83c37b051221a7a3a17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f947fd286e0c37fdcc8d1b6ce4295c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-02-17更新
|
751次组卷
|
5卷引用:山东省济南市2023-2024学年高二上学期1月期末质量检测数学试题
山东省济南市2023-2024学年高二上学期1月期末质量检测数学试题山东省临沂市第十九中学2023-2024学年高二下学期第一次质量调研考试数学试题2024届高三新改革数学模拟预测训练四(九省联考题型)(已下线)模块4 二模重组卷 第2套 复盘卷(已下线)湖北省武汉市(武汉六中)部分重点中学2024届高三第二次联考数学试题变式题17-22
名校
解题方法
4 . 如图,正方形
的边长为
,点W,E,F,M分别在边
,
,
,
上,
,
,
与
交于点
,
,记
.
的面积为
的函数
,周长为
的函数
,
(i)证明:
;
(ii)求
的最大值;
(2)求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/399e7902cf319a4ecc40aebda074eda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e6a56e600facb7fbc764ca30df94cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1767d0189b880f3e88dfd7734315fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd46fa96457001cfff7fc5dd49898f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc761c3cacbd33884eb2fcd32db72643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b723326b1d59ee18d42001987aaee091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a33c392fc16e95f3e0941a2f5947bc9.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a099343653ac9e68e3ef0c50d38f4191.png)
您最近一年使用:0次
2024-02-06更新
|
390次组卷
|
7卷引用:山东省青岛市2023-2024学年高一上学期(期末)选科测试数学试卷
山东省青岛市2023-2024学年高一上学期(期末)选科测试数学试卷(已下线)专题7 圆的包含问题(已下线)1.8 三角函数的简单应用-同步精品课堂(北师大版2019必修第二册)(已下线)第八章:向量的数量积与三角恒等变换(单元测试)-同步精品课堂(人教B版2019必修第三册)广东省佛山市顺德区容山中学2023-2024学年高一下学期3月月考数学试题四川省南充高级中学2023-2024学年高一下学期第一次月考(3月)数学试题内蒙古赤峰二中2023-2024学年高一下学期第一次月考数学试题
解题方法
5 . (1)设
,
用反证法证明:若
,则
或
.
(2)设
,比较
与
的值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae3aa00a59d5e1db4efb0aa7ece4623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec336faee8689281a6f6b465e7fcff9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc997a4317a3b64369178b27abc44b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f814b4dc5876d8bf3aa145593bf4cc66.png)
您最近一年使用:0次
2023-11-09更新
|
72次组卷
|
2卷引用:山东省泰安市泰山外国语学校2024届高三上学期期末数学试题
名校
解题方法
6 . 临沂一中校本部19、20班数学小组在探究函数的性质时,发现通过函数的单调性、奇偶性和周期性,还无法准确地描述出函数的图象,例如函数
和
,虽然它们都是增函数,但是图像上却有很大的差异. 通过观察图像和阅读数学文献,该小组了解到了函数的凹凸性的概念. 已知定义:设连续函数f(x)的定义域为
,如果对于
内任意两数
,都有
,则称
为
上的凹函数;若
,则
为凸函数. 对于函数的凹凸性,通过查阅资料,小组成员又了解到了琴生不等式(Jensen不等式):若f(x)是区间
上的凹函数,则对任意的
,有不等式
恒成立(当且仅当
时等号成立). 小组成员通过询问数学竞赛的同学对他们研究的建议,得到了如下评注:在运用琴生不等式求多元最值问题,关键是构造函数.小组成员选择了反比例型函数
和对数函数
,研究函数的凹凸性.
(1)设
,求W=
的最小值.
(2)设
为大于或等于1的实数,证明
(提示:可设
)
(3)若a>1,且当
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7cd59277a15b4d9063be84a40d5541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a4ab6155e1fd2c8f9508efa3adcda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f87a3affc8cd30c21af57157d156c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6933733e82337e6d4a95fc2946ff26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2697ef67790838c84cc238a0334c5d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83aa9d22736190332e01260e5a7803de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b7a76267b71e6fc828cf2a2e81173d.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dd60e2cd1a1aae21a9c07820214290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0823f59998a025e80b46881993e89d1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01262e3dd65728a29f3bbfa584dccede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7425d1d31f6188375d44137c2b219b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cda4049695561dab3e0803c3a287fe.png)
(3)若a>1,且当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89c2336e46cbbe2b978d7d8fcd340be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc069f6b9d1623e1c06879cef933e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-02-20更新
|
347次组卷
|
2卷引用:山东省临沂第一中学2023-2024学年高一上学期期末模拟数学试题
7 . 如图,已知圆
,圆心是点T,点G是圆T上的动点,点H的坐标为
,线段CH的垂直平分线交线段TC于点R,记动点R的轨迹为曲线E.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
,
,试探究
是否为定值?若是,求出该定值;若不是,请说明理由;
(3)过点
作两条直线MP,MQ,分别交曲线E于P,Q两点,使得
.且
,点D为垂足,证明:存在定点F,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ebdc37c4828abb80c0f3bffb9e54e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5510fbff7fdcc083ef172d4b401c2229.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9545ecde4068ea16914263cddb3e8f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cff2d267cabb5318d29e319fe65c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b385adf402cd17bddace02fdb32030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ebcef3ed51c751de97752bbf40e87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b14463c252e686a3cd0a8c4e33c02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0165236f973be829fd3dbabe9507243.png)
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名校
8 . 射影几何学中,中心投影是指光从一点向四周散射而形成的投影,如图,
为透视中心,平面内四个点
经过中心投影之后的投影点分别为
.对于四个有序点
,定义比值
叫做这四个有序点的交比,记作
.
;
(2)已知
,点
为线段
的中点,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d33747c77ff8ec31b1d8787a2a99748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fc6388f7dd9e393808bfcfb41b499e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d4c674a3fe91bd4bffd3dcd9ea58f1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29998510e4ecded4acfc9e981da9110f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ead0dc6f5e5881fd26b1a07f37024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32f2d4d1d2c16c54b2caef17840bfcb.png)
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2023-07-11更新
|
1012次组卷
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10卷引用:山东省济南市2022-2023学年高一下学期期末数学试题
山东省济南市2022-2023学年高一下学期期末数学试题(已下线)上海市高一下学期期末真题必刷04-期末考点大串讲(沪教版2020必修二)(已下线)重组2 高一期末真题重组卷(山东卷)B提升卷(已下线)模块四 专题5 暑期结束综合检测5(能力卷)黑龙江省鹤岗市工农区鹤岗市第一中学2023-2024学年高三上学期开学数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大题型)(练习)(已下线)第11章 解三角形 单元综合检测(难点)--《重难点题型·高分突破》(苏教版2019必修第二册)吉林省长春市东北师范大学附属中学2023-2024学年高一下学期5月期中考试数学试题(已下线)专题01 平面向量及其应用(2)-期末真题分类汇编(新高考专用)【人教A版(2019)】专题09解三角形(第三部分)-高一下学期名校期末好题汇编
名校
9 . 独立事件是一个非常基础但又十分重要的概念,对于理解和应用概率论和统计学至关重要.它的概念最早可以追湖到17世纪的布莱兹·帕斯卡和皮埃尔·德·费马,当时被定义为彼此不相关的事件.19世纪初期,皮埃尔·西蒙·拉普拉斯在他的《概率的分析理论》中给出了相互独立事件的概率乘法公式.对任意两个事件
与
,如果
成立,则称事件
与事件
相互独立,简称为独立.
(1)若事件
与事件
相互独立,证明:
与
相互独立;
(2)甲、乙两人参加数学节的答题活动,每轮活动由甲、乙各答一题,已知甲每轮答对的概率为
,乙每轮答对的概率为
.在每轮活动中,甲和乙答对与否互不影响,各轮结果也互不影响,求甲乙两人在两轮活动中答对3道题的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292d72646168e258f3c4a280116e3e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)若事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21778974e8491fe2a158e70b459217be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)甲、乙两人参加数学节的答题活动,每轮活动由甲、乙各答一题,已知甲每轮答对的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
您最近一年使用:0次
2023-07-11更新
|
687次组卷
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3卷引用:山东省济南市2022-2023学年高一下学期期末数学试题
解题方法
10 . 如图1,在边长为4的菱形
中,
,
,
分别为
,
的中点,将
沿
折起到
的位置,得到如图2所示的三棱锥
.
;
(2)
为线段
上一个动点(
不与端点重合),设二面角
的大小为
,三棱锥
与三棱锥
的体积之和为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284e282bb1d9fbf8634b3506ee5358ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a33d27a9c655d01f606e9bce02b0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedb55703d202771dd11987cf4f30bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432129b84db4beea3395281639c6684e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f4e64c96f4c48b158c7f918243fbd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7b329612a9159b0b2dce46120b409e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
2023-07-11更新
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2卷引用:山东省泰安市2022-2023学年高一下学期期末数学试题