1 . 如图,在四棱锥
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/4b937e57-9ebd-4b89-ae02-824272e1ecc9.png?resizew=175)
(1)求证:平面
平面
;
(2)若
,点
是
中点,且四棱锥
的体积为
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2d5ab801f2a84b78139b0ea2c5032b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b2f446cccf2652c090e99a75beb3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/4b937e57-9ebd-4b89-ae02-824272e1ecc9.png?resizew=175)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac93e58e9bba899df62a4cda5f1a5ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2023-11-28更新
|
221次组卷
|
2卷引用:宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(四)
名校
解题方法
2 . 已知椭圆
的半焦距为
,且过点
.
(1)求椭圆的方程;
(2)设直线
交椭圆
于
两点,且线段
的中点
在直线
上,求证:线段
的中垂线恒过定点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
(1)求椭圆的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becdcb8a871e8965853acf0687034c28.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2023-11-25更新
|
654次组卷
|
4卷引用:宁夏回族自治区石嘴山市平罗中学2024届高三下学期第三次模拟考试数学(文)试题
宁夏回族自治区石嘴山市平罗中学2024届高三下学期第三次模拟考试数学(文)试题贵州省贵阳市五校2023届高三联合考试(四)数学(理)试题贵州省贵阳市五校2023届高三联合考试(四)数学(文)试题(已下线)重难点7-2 圆锥曲线综合应用(7题型+满分技巧+限时检测)
名校
解题方法
3 . 设
的前
项和为
,且
.
(1)求
的通项公式;
(2)已知
,且
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102c5ada24b668a4fccbf39ed0a3eeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e9d3644920a6654c41de61b7f3636d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1d14cae0b93387644996a97ccfd47b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8762d7601949a0c847efd57552a862.png)
您最近一年使用:0次
2024-01-22更新
|
887次组卷
|
3卷引用:宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(二)
名校
解题方法
4 . 如图,在平行六面体
中,以顶点A为端点的三条棱长都是1,且它们彼此的夹角都是
,M为
与
的交点.若
.
(1)求
;
(2)求证:直线
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfb9769a14ebf5cbc5fa0c06ce96435.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/ecedd36e-65e0-44d0-8a80-025431568976.png?resizew=178)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1980afc16db40189b8dcc545602c63d.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
您最近一年使用:0次
2023-11-15更新
|
206次组卷
|
3卷引用:宁夏回族自治区2023-2024学年高二上学期期末测试数学训练卷(一)(范围:选择性必修第一册)
名校
解题方法
5 . 如图,在三棱柱
中,所有棱长均为1,
.
平面
.
(2)求三棱柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01805084c9e7371b1f869711a2d89b99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
2024-04-23更新
|
1283次组卷
|
3卷引用:宁夏回族自治区银川一中2024届高三第三次模拟考试文科数学试题
宁夏回族自治区银川一中2024届高三第三次模拟考试文科数学试题陕西省西安市部分学校2024届高三下学期高考模拟检测文科数学试卷(已下线)专题04 第八章 立体几何初步(2)-期末考点大串讲(人教A版2019必修第二册)
名校
解题方法
6 . 已知函数
.
(1)当
时,证明:
.
(2)若
在
上恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20a21999ea818acdfb48d3641f70d3b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cbbf4d5b8ecbfccc5de39781396d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
您最近一年使用:0次
2024-04-18更新
|
838次组卷
|
3卷引用:宁夏吴忠市吴忠中学2023-2024学年高二下学期期中考试数学试卷
名校
7 . 已知函数
,其中
.
(1)当
时,求不等式
的解集;
(2)若对任意的
恒成立时m的最小值为t,且正实数a,b满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2379c1c2d0e095625f77f7883003df7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975af98526d943ccd1ab7b9f0e022374.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624070d66d05a0f5244648e5d1cffe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0fd3296a0ecf275a161134518dba8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b0e403c5f00d0357d3fa30d6c2717c.png)
您最近一年使用:0次
2024-04-16更新
|
342次组卷
|
3卷引用:宁夏银川市、石嘴山市2024届普通高中学科教学质量检测理科数学试题
名校
解题方法
8 . 已知四棱柱
如图所示,底面
为平行四边形,其中点
在平面
内的投影为点
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ba8b53e76a625f3c70b89c46fcc6d.png)
.
平面
;
(2)已知点
在线段
上(不含端点位置),且平面
与平面
的夹角的余弦值为
,求
的值.
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ba8b53e76a625f3c70b89c46fcc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e95842967bd771494cc758fa29a1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31094f1b430f65336dfc222c91d9f35.png)
您最近一年使用:0次
2024-04-05更新
|
3903次组卷
|
7卷引用:宁夏银川市第二中学2023-2024学年高三下学期适应性考试数学(理科)试题
2024·全国·模拟预测
名校
9 . 如图,P为圆锥的顶点,O为圆锥底面的圆心,AB为底面直径,四边形POBC是梯形,且
,
,
,D为圆O上一点.
(1)若点M在线段AD上,且
,求证:
∥平面CDB;
(2)当直线PD与平面PAB所成的角为30°时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061248f4e3932ad43c1abd52ada56a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b93b8e3f2196f571782a283f2e10ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3530ee12bd68b53970b83f28985b31.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/b1f43728-6dfd-4cfb-9393-8828e4fb8ffa.png?resizew=168)
(1)若点M在线段AD上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963f0cda34e54f15725cee9448a4537e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
(2)当直线PD与平面PAB所成的角为30°时,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6a0cee8226e82cc57916e10d533369.png)
您最近一年使用:0次
名校
10 . 如图,在四棱锥
中,
平面
,
,
,
,
,
为
的中点.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d6ee72557cb3c3830212d74bca615a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db1d8f228c87b65a3609f825fc441d5.png)
您最近一年使用:0次
2024-04-10更新
|
721次组卷
|
2卷引用:宁夏吴忠市吴忠中学2023-2024学年高二下学期期中考试数学试卷