名校
解题方法
1 . 如图,在圆台
中,
为轴截面,
为下底面圆周上一点,
为下底面圆
内一点,
垂直下底面圆
于点
.
平面
;
(2)若
为等边三角形,求平面
和平面
的交线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64beb125bd45dde1a2b17cdd74001ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d0f9440606475f093d453bfa4d08e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1e2381971c4dbd3d53dea8ce33e086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd1c4e883518a7ac5a7517615e47e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eddaf3f33bd9a99162c061c9dd99aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61dc0fec2de4694075281e882d3c5ac.png)
您最近一年使用:0次
2024-05-01更新
|
888次组卷
|
3卷引用:陕西省安康市高新中学、安康中学高新分校2023-2024学年高三阶段性测试(八)理科数学试题
解题方法
2 . 如图是一个半圆柱,
分别是上、下底面圆的直径,
为
的中点,且
是半圆
上任一点(不与
重合).
平面
,并在图中画出平面
与平面
的交线(不用证明);
(2)若点
满足
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217ef4133057ffd2a3b1a2da7c59045a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadd8b2668c34be82fc42346382380a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49af9bef16bb8575c46d9a3658e1b016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1077520a4816bbb5a37fc45359e34c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823f4e614dd9290178c2b9c9fd2460a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1077520a4816bbb5a37fc45359e34c5c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08971c21f32470f773ef57614ae0131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823f4e614dd9290178c2b9c9fd2460a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
您最近一年使用:0次
名校
解题方法
3 . 已知双曲线
的左、右顶点分别是
,直线
与
交于
两点(不与
重合),设直线
的斜率分别为
,且
.
(1)判断直线
是否过
轴上的定点.若过,求出该定点;若不过,请说明理由.
(2)若
分别在第一和第四象限内,证明:直线
与
的交点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b30352c43707c4e54b94ce5b61f2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29dd91ef1fd4c744e89c83b0a6a58152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595ba5dc88bf92a4d6a32b81ca103f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41441b3d2da6447c7545bd8c11821141.png)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe61d39d080872caa8973a70a3b4955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439c8a01a6626d7a3f53af31ef0bcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-04-18更新
|
634次组卷
|
3卷引用:陕西省安康市高新中学、安康中学高新分校2023-2024学年高三阶段性测试(八)理科数学试题
4 . 某课题实验小组共有来自
三个不同班级的45名学生,这45名学生中,
,B,C三个班级的人数比为4:3:2.
(1)某次实验活动需从这45人中用分层抽样的方法随机抽取9人组成一个核心小组,再从这9人中随机抽取3人负责核心工作,记随机抽取的3人中来自B班级的人数为
,求
的分布列和数学期望;
(2)由于不同的实验需要的人数不同,所以为便于进行实验的配合,实验过程中有2人一组,也有多人一组(多于2人),其中2人一组的为基础实验,其他的为研发实验,实验结束后进行实验结果交流.记发言的小组来自研发实验的概率为
,若共有5组进行发言,用
表示恰有3组来自研发实验的概率,证明:
的最大值不会超过
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)某次实验活动需从这45人中用分层抽样的方法随机抽取9人组成一个核心小组,再从这9人中随机抽取3人负责核心工作,记随机抽取的3人中来自B班级的人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
(2)由于不同的实验需要的人数不同,所以为便于进行实验的配合,实验过程中有2人一组,也有多人一组(多于2人),其中2人一组的为基础实验,其他的为研发实验,实验结束后进行实验结果交流.记发言的小组来自研发实验的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752d689c989b1de6af501079bc79c7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752d689c989b1de6af501079bc79c7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
您最近一年使用:0次
5 . 2022年北京冬奥会仪式火种台(如图①)以“承天载物”为设计理念,创意灵感来自中国传统青铜礼器——尊(如图②),造型风格与火炬、火种灯和谐一致.仪式火种台采用了尊的曲线造型,基座沉稳,象征“地载万物”.顶部舒展开阔,寓意着迎接纯洁的奥林匹克火种.祥云纹路由下而上渐化为雪花,象征了“双奥之城”的精神传承.红色丝带飘逸飞舞、环绕向上,与火炬设计和谐统一.红银交映的色彩,象征了传统与现代、科技与激情的融合.现建立如图③所示的平面直角坐标系,设图中仪式火种台外观抽象而来的曲线对应的函数表达式为
.
(1)求函数
的图象在点
处的切线方程;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ad93dc19938b18b0a9a7dcfe3a7bf1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/20/74fa53e3-3998-4d0f-8f9e-266b5d590b43.png?resizew=388)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714621c52d929e662febee72b9d68351.png)
您最近一年使用:0次
2023-10-30更新
|
124次组卷
|
2卷引用:陕西省榆林市定边县第四中学2024届高三上学期第四次月考数学(文)试题
名校
解题方法
6 . 已知椭圆
的离心率为
,椭圆
的动弦
过椭圆
的右焦点
,当
垂直
轴时,椭圆
在
处的两条切线的交点为
.
(1)求点
的坐标;
(2)若直线
的斜率为
,过点
作
轴的垂线
,点
为
上一点,且点
的纵坐标为
,直线
与椭圆
交于
两点,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069ffc1e3936d254303d588e1a70a3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a60e77043cfa243c212f9e340c5f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f43b5d69bd0a55499a8d70bf88077f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360496a4f5cc8a5faca5e089ae4f9531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769e7e506800af0ce9e6ecdc15fe4459.png)
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名校
解题方法
7 . “拐点”又称“反曲点”,是曲线上弯曲方向发生改变的点.设
为函数
的导数,若
为
的极值点,则
为曲线
的拐点.
已知函数
有两个极值点
,且
为曲线C:
的拐点.
(1)求a的取值范围;
(2)证明:C在Q处的切线与其仅有一个公共点;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85be63b7da7f1174c96176de8d1ecc9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85be63b7da7f1174c96176de8d1ecc9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ce95d0450bc59111b516c56586cb78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d05faec455cea37e004e18cfb7e290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c12d99bdf82674ac9a1edceff81d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求a的取值范围;
(2)证明:C在Q处的切线与其仅有一个公共点;
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e804ae37438267dd3a4b9c26d3d7c33.png)
您最近一年使用:0次
名校
解题方法
8 . 如图1,山形图是两个全等的直角梯形
和
的组合图,将直角梯形
沿底边
翻折,得到图2所示的几何体.已知
,
,点
在线段
上,且
在几何体
中,解决下面问题.
平面
;
(2)若平面
平面
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10de2459bc376f9a3de90f74cc18ca7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde387abe3ecba7cde65df9c58131b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a39a7453e6994a580038828513c68c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3b8602719b3d371bc9ec6c441bb9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7513c5dc6e1d35f76020f8f60c95669.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c897a54f2e36bc4b52fba74b41c89d2d.png)
您最近一年使用:0次
2023-11-24更新
|
606次组卷
|
8卷引用:陕西省榆林市府谷县第一中学2024届高三上学期第五次月考数学(理)试题
陕西省榆林市府谷县第一中学2024届高三上学期第五次月考数学(理)试题江西省部分地区2023-2024学年高三上学期11月质量检测数学试题河北省部分高中2024届高三上学期11月联考数学试题山西省运城市盐湖区第五高级中学2024届高三上学期一轮复习成果检测数学试题(已下线)热点6-1 线线、线面、面面的平行与垂直(6题型+满分技巧+限时检测)(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)(已下线)13.2.4 平面与平面的位置关系(2)-【帮课堂】(苏教版2019必修第二册)(已下线)11.4.2平面与平面垂直-同步精品课堂(人教B版2019必修第四册)
名校
解题方法
9 . 如图,几何体
为三棱台.
平面
.
(2)已知平面
平面
,求三棱台
的体积.
参考公式:台体的体积
,其中
分别为台体的上底面面积、下底面面积,
为台体的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
(2)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7d82423b6f211a7ac51a850b55e73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546468c4f030e2474ab4485c59a7947b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
参考公式:台体的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0df98384885fe5d6b67eb6d03f42dc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
您最近一年使用:0次
2023-10-19更新
|
183次组卷
|
2卷引用:陕西省西安市第一中学2024届高三第四次质量监测文科数学试题
名校
解题方法
10 . 已知
,
分别是圆柱上、下底面圆的直径,圆柱的高与
的长相等,均为2.且异面直线
与
所成的角为
,
分别为上、下底面的圆心,连接
,过
作圆柱的母线
,且
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/a64ce805-fd99-4675-ad2a-0f8d68f87bdb.png?resizew=135)
(1)证明:
平面
;
(2)求圆柱挖去三棱锥
后的几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cef469b1ee29d124cfd6f62423724cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5913ac8f576f9389802005ae712205d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70eafcad4e630099a332f14925d10065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/a64ce805-fd99-4675-ad2a-0f8d68f87bdb.png?resizew=135)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218661d1f4436696d1f506944c8be593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求圆柱挖去三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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