1 . 如图,在平面直角坐标系中,
和
是
轴上关于原点对称的两个点,过点
倾斜角为
的直线
与抛物线
交于
两点,且
.
为
的焦点,求证:
;
(2)过点
作
轴的垂线,垂足为
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08136e6bc876f29a13d1204d9d621db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea0b6471289760543596f5f45aa43ae.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14cc1572ca21da2e3271484f127a5094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-06-03更新
|
509次组卷
|
3卷引用:浙江省绍兴市第一中学2024届高三下学期5月模拟数学试题
2 . 盒子中装有大小形状相同的4个小球,其中2个白色2个红色. 每次取一球,若取出的是白球,则不放回;若取出的是红球,则取完放回.
(1)取两次,求恰好一红一白的概率;
(2)取两次,记取到白球的个数为随机变量
,求随机变量
的分布列及均值;
(3)在第2次取出的球是红球的条件下,求第1次取出的球是白球的概率.
(1)取两次,求恰好一红一白的概率;
(2)取两次,记取到白球的个数为随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)在第2次取出的球是红球的条件下,求第1次取出的球是白球的概率.
您最近一年使用:0次
名校
解题方法
3 . 书接上回.麻将学习小组中的炎俊同学在探究完问题后返回家中观看了《天才麻将少女》,发现超能力麻将和现实麻将存在着诸多不同.为了研究超能力麻将,他使用了一些”雀力值”和”能力值”来确定每位角色的超能力麻将水平,发现每位角色在一局麻将中的得分与个人值和该桌平均值之差存在着较大的关系.(注:平均值指的是该桌内四个人各自的“雀力值”和“能力值”之和的平均值,个人值类似.)为深入研究这两者的关系,他列出了以下表格:
(1)①计算
的相关系数
,并判断
之间是否基本上满足线性关系,注意:保留至第一位非9的数.
②求出
与
的经验回归方程.
③以下为《天才麻将少女》中几位角色的”雀力值”和”能力值”:
试估计此四位角色坐在一桌打麻将每一位的得分(近似至百位)
(2)在分析了更多的数据后,炎俊发现麻将中存在着很多运气的成分.为衡量运气对于麻将对局的影响,炎俊建立了以下模型,其中他指出:实际上的得分并不是一个固定值,而是具有一定分布的,存在着一个标准差.运气实际上体现在这一分布当中取值的细微差别.接下去他便需要得出得分的标准差.他发现这一标准差来源自两个方面:一方面是在(1)②问当中方程斜率
存在的标准差
;另一方面则是在不影响平均值的情况下,实际表现“个人值”X符合正态分布规律
.(
为评估得出的个人值.)已知松实玄实际表现个人值满足
,求(1)③中其得分的标准差.(四舍五入到百位)
(3)现在新提出了一种赛制:参赛者从平均值为10开始进行第一轮挑战,之后每一轮对手的”雀力值”和”能力值”均会提升至原来的
.我们设进行了i轮之后,在前i轮内该参赛者的总得分为
;若园城寺怜参加了此比赛,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b244e1fc240f8af39cc432c0bdc688.png)
参考数据和公式:①
;
.
②相关系数
;
经验回归方程
,
,
;
,其中
为回归数据组数.
③对于随机变量
,
,
,
.
④
时,
,
;
⑤对间接计算得出的值
有标准差
满足
.
⑥
;
;
个人值与平均值之差 | 0 | 3 | 6 | 9 | |||
得分 | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
②求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
③以下为《天才麻将少女》中几位角色的”雀力值”和”能力值”:
角色 | 宫永照 | 园城寺怜 | 花田煌 | 松实玄 |
雀力值 | 24 | 9 | 10 | 4 |
能力值 | 24 | 16 | 3 | 6 |
(2)在分析了更多的数据后,炎俊发现麻将中存在着很多运气的成分.为衡量运气对于麻将对局的影响,炎俊建立了以下模型,其中他指出:实际上的得分并不是一个固定值,而是具有一定分布的,存在着一个标准差.运气实际上体现在这一分布当中取值的细微差别.接下去他便需要得出得分的标准差.他发现这一标准差来源自两个方面:一方面是在(1)②问当中方程斜率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9a5a756248e63ccb381391a536c7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290917c2c835b61384480b335cc1d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ad52b5d7044b8628cac082b7c12fe8.png)
(3)现在新提出了一种赛制:参赛者从平均值为10开始进行第一轮挑战,之后每一轮对手的”雀力值”和”能力值”均会提升至原来的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e304a36d2cdfe1735fb6996bb115b07d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b244e1fc240f8af39cc432c0bdc688.png)
参考数据和公式:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da086bd372ecb12ca1f10aa90b3f8719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974ea4eb8cea88db4ef02e90ec0bd2a0.png)
②相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368976f08508d324aa73ec6a9ceca54f.png)
经验回归方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929ef3bed0a4bdd22f39e036506dc481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9218b61bbc7b5304adf61be07f0a98ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d35f886f6b590a2db330269ea9d939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67dd3a4864e96f1dda457d4ea0a6e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
③对于随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290917c2c835b61384480b335cc1d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8f8641d4e8bbabc1e726417ac3c8cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1c9871a68a9f90d1a27d3559aa974a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9546031173beb4c429883aae0e16e03b.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116a2ed855825981b8a1192011965989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f5b5832b3a66d6527d09d2cd2a1d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9883e09b1ac40ccaebcaec21e2871c56.png)
⑤对间接计算得出的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c6eb9fb2fb74de6696c3c1b90d56e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331ddc2602421701eef926d55293d9fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b511bbadf9b7a211430994992cde584.png)
⑥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcd4238a75699911d8cc12b6feb0da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e744614f8d01a805b4c71a8623740393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03405dd7ea215f7dd9d4f60dc41e441b.png)
您最近一年使用:0次
名校
4 . 定义2*2数表
,
,
,其中
称为
中的元素.
和
属于复数集合. 我们定义
,其中
,
(共
个),
,
,
:
(1)证明:
(i)
.
(ii)
.
(2)若存在A,B,C,使得
,且
,
,
:
(ⅰ)请列出所有满足条件的有序数对
.
(ⅱ)对
,
,
,试验证其是否满足上述条件.
(3)(ⅰ) 在上一题的(ⅱ)中,
以及
合称为Pauli数表. 任意
均可以表示为:
,
为复数,试用
表示
.
(ⅱ) 设
,请证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b32cd779049dfa4b55b955e8885dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67236be30275de9ab515dc663ad9cc92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75a92b76b4b5ae3c4571525b102491d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cd9eab3d56d2fe1c6611ccf5be1695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fa3364d3a162682f50528680cf4403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af76198c7bcd4ba4661c8ecb1fbf7930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855e9b47dd2df4781211d458bbb2dd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0d82117f3aeb73a48ad24e9b563e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f9b77ac8d2930cf5bed9fd31aa3791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04d42748ae6abf54a9ba61fb833a8fd.png)
(1)证明:
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82643b4b9e28d0227c419de4e66df227.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3e9de425ba79559cd0a2feb7d2109a.png)
(2)若存在A,B,C,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163d61d1df6137585249c17bdf1aff0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce53a57261f19484bf9cda89208d87b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc07d8e94e79abf1a6f717096df42c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c904bea2eaec0153be54e2ca1abb75.png)
(ⅰ)请列出所有满足条件的有序数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52aaa08d0d339d57f466de67d31f54c7.png)
(ⅱ)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021cb7c01071fa8fb9ae6bc4312d2e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425989826f834d15fe877946eb5e674f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3ad3326af484fb2493e45b1d8a98b7.png)
(3)(ⅰ) 在上一题的(ⅱ)中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5d6bebc33fde49c8b270b1887de4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05e6ffe5ec0915b52dcaabe337a3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3356935218122dea72e8a911cc4dd203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc11dc86b57dab7d0a07bace5ac7a13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc80e3e48f5109325489205c77f742c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc11dc86b57dab7d0a07bace5ac7a13a.png)
(ⅱ) 设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225b723bf52d579f519c13c41074cbbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe37acacda21f0768703d5217cf14de.png)
您最近一年使用:0次
名校
5 . 如图所示,四棱台
,底面
为一个菱形,且
. 底面与顶面的对角线交点分别为
,
.
,
,
与底面夹角余弦值为
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
平面
;
(2)现将顶面绕
旋转
角,旋转方向为自上而下看的逆时针方向. 此时使得底面与
的夹角正弦值为
,此时求
的值(
);
(3)求旋转后
与
的夹角余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07c321ebb740613ff53c1d6e496ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a61472439de1ba85cfe33840b775f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d76ce5fcc2291de26b44b4b082df5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb34d99a48c5d1d8f21af99c1b70ea49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)现将顶面绕
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2236f820e9625bcc1e81f101e9ab7713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4967af4c76d238fea5695537dfc9e91e.png)
(3)求旋转后
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
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6 . 已知抛物线
:
的焦点
,直线
过
且交C于两点
,已知当
时,
中点纵坐标的值为
.
(1)求
的标准方程.
(2)令
,P为C上的一点,直线
,
分别交C于另两点A,B.证明:
.
(3)过
分别作
的切线
,
与
相交于
,同时与
相交于
,求四边形
面积取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901eaab225137c0db994996875667279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6a55260653d60c2157a15ce3aebc8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3198d4ac606acfd7c6d7f60d619336ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c2293f93791a597bf0162411f3395f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77451286f0f5e470162aaa7f00b55933.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81687c0af83f550bcb802e2d82c76a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8801df26d9cb76bc289b64a3a26902e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
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2024-04-23更新
|
572次组卷
|
2卷引用:浙江省绍兴市第一中学2024届高三下学期4月创新班联合测评二数学试卷
7 . 已知
,集合
其中
.
(1)求
中最小的元素;
(2)设
,
,且
,求
的值;
(3)记
,
,若集合
中的元素个数为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b0d89736a10c53998013df4a354396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8165d6243c2ce6dac87a9bcc2be577ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b76979d0a46e9b56e2f7f3e44c48423.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8e702da77e0bd37abdd29d9b12992e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6b5d77069ced356d738aea8e3efb63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e56e0fa5fb1fc2a2dbd0a152812a1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d103dda0bac3393c7544c4d0c8a37e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1ebce51879137ab48c506e9cdb0187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045c531b9582478b5f0ea99c7ccf686c.png)
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2024-04-18更新
|
1767次组卷
|
4卷引用:浙江省绍兴市2024届高三下学期4月适应性考试数学试卷
浙江省绍兴市2024届高三下学期4月适应性考试数学试卷(已下线)数学(九省新高考新结构卷03)(已下线)压轴题05数列压轴题15题型汇总-3上海市育才中学2023-2024学年高三下学期5月质量调研考试数学试题
名校
解题方法
8 . 2024年3月12日是我国第46个植树节,为建设美丽新重庆,重庆市礼嘉中学高二年级7名志愿者参加了植树节活动,3名男生和4名女生站成一排.(最后答案用数字作答)
(1)甲不在中间也不在两端的站法有多少种?
(2)男、女相间的站法有多少种?
(3)甲、乙、丙三人从左到右顺序一定的站法有多少种?
(1)甲不在中间也不在两端的站法有多少种?
(2)男、女相间的站法有多少种?
(3)甲、乙、丙三人从左到右顺序一定的站法有多少种?
您最近一年使用:0次
2024-04-01更新
|
664次组卷
|
3卷引用:浙江省绍兴市上虞区华维外国语学校2023-2024学年高二上学期期中考试数学试卷
9 . 如图1,在梯形
中,
,
是线段
上的一点,
,
,将
沿
翻折到
的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
为直二面角,
,
分别是
,
的中点,若直线
与平面
所成角为
,
,求平面
与平面
所成锐二面角的余弦值的取值范围;
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
为线段
的中点,
,
分别在线段
,
上(不包含端点),且
为
,
的公垂线,如图3所示,记四面体
的内切球半径为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb15c7f8fd604976818ff6de254b6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9d5946fba71d0623ab27f24c6b57fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e184efd65dfaa5d62242c482d2158d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da424b529ab73775b90cd4089d18419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57d8c0d92f5b6bede99e8d9d227e40.png)
您最近一年使用:0次
10 . 抛物线C:
,椭圆M:
,
.
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
作椭圆M的两条切线分别交抛物线C于点P,Q,当
时,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e61e0a1bc2ab34fe0cd1de9f59b0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181820d1a015068701cfdbdf48b24c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8adb3358f321cc2c429b9c20674b271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b38040230a7f5674f13c690e780ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次