名校
解题方法
1 . 如图,
平面
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7f68c056-f362-451b-ac15-7f03d54bd305.png?resizew=228)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)若二面角
的余弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80637f43cf748a2ce0aaf4cd0037749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883200c4d4e82a5411064a644aabfe33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bb994c172c6e9a318f6bef13d149c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fa988a1b4a8e1ef706f8ff773b038d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc82184408c19cc5f3474be38def4dc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/7f68c056-f362-451b-ac15-7f03d54bd305.png?resizew=228)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d888c0b616792a2c41ff180de99fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4e1bdc9d0df390a30d7c27d6d3a0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1dd362f843e640ce551ad1787c9873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
2022-10-20更新
|
573次组卷
|
6卷引用:新疆乌鲁木齐市第八中学2023届高三上学期第一次月考数学(理)试题
新疆乌鲁木齐市第八中学2023届高三上学期第一次月考数学(理)试题天津市南开中学2023-2024学年高三上学期第五次统练数学试题山东省青岛市部分中学2022-2023学年高二上学期12月教学质量检测数学试题广东省人大附中深圳学校2022-2023学年高二上学期期末数学试题山东省青岛市青岛第二中学2022-2023学年高二上学期12月月考数学试题(已下线)第一章 空间向量与立体几何(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)
名校
2 . 如图,在四棱锥
中,底面ABCD是直角梯形,侧棱
底面ABCD,AB垂直于AD和BC,SA=AB=BC=2,AD=1,M是棱SB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/11/eecc847d-3654-4850-a209-c2e2d52535b2.png?resizew=236)
(1)求证:
平面SCD;
(2)求平面SCD与平面SAB所成锐二面角的余弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/11/eecc847d-3654-4850-a209-c2e2d52535b2.png?resizew=236)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
(2)求平面SCD与平面SAB所成锐二面角的余弦值;
您最近一年使用:0次
2022-10-08更新
|
553次组卷
|
2卷引用:新疆阿克苏市生产建设兵团第一师高级中学2023届高三上学期第二次月考数学(理)试题
名校
解题方法
3 . 如图,在四棱锥
中,
平面
,
,底面ABCD是边长为4的菱形,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/795f868f-ed75-4857-8a92-b366d4066bc5.png?resizew=143)
(1)求证:
;
(2)求平面PAC与平面PCD夹角的余弦值.
![](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/c19f0fcacac715a1200770516d1e4a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/795f868f-ed75-4857-8a92-b366d4066bc5.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)求平面PAC与平面PCD夹角的余弦值.
您最近一年使用:0次
2023-01-13更新
|
201次组卷
|
2卷引用:新疆昌吉州行知学校2023届高三下学期第一次月考数学(理)试题
名校
4 . 在四棱锥
中,底面ABCD是等腰梯形,
,
,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/3fddd46f-f511-43df-ad16-9b16f395655d.png?resizew=155)
(1)求证:
为直角三角形;
(2)若
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a8b1c432c1266ec43fb9a78f7a77fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b77a5c3865855fbb3d24f9522ced8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3c74b930d4e691b519965e436f2c37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/3fddd46f-f511-43df-ad16-9b16f395655d.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da7bcea5a45eeae211f5851f12a7517.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e4e97a4bd7675f12f73266254dd435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc407e2b3e9da16eba881fd7a83845a.png)
您最近一年使用:0次
2023-01-06更新
|
443次组卷
|
2卷引用:新疆部分学校2023届高三上学期第一次联考数学(理)试题
名校
解题方法
5 . 在平面直角坐标系
中,已知点
在抛物线
上,圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
,
为圆
上的动点,求线段
长度的最小值;
(2)若点
的纵坐标为4,过
的直线
与圆
相切,分别交抛物线
于
(异于点
),求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-12-11更新
|
525次组卷
|
2卷引用:新疆维吾尔自治区乌鲁木齐市第四十中学2023届高三下学期4月月考理科数学试题
名校
解题方法
6 . 已知抛物线
上的点
到其焦点的距离为
.
(1)求
和
的值;
(2)若直线
交抛物线
于
、
两点,线段
的垂直平分线交抛物线
于
、
两点,求证:
、
、
、
四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365c238724dea5c24c3e326678c9ed54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ce81c2674a74d4704f9ce387ef954f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2022-09-01更新
|
1705次组卷
|
11卷引用:新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三上学期9月月考数学(文)试题
新疆维吾尔自治区乌鲁木齐市第十二中学2024届高三上学期9月月考数学(文)试题四川省泸州市2021届高三三模数学(文)试题(已下线)第46讲 解析几何中的四点共圆问题-2022年新高考数学二轮专题突破精练(已下线)专题7 解决曲线的几何性质的运算(提升版)四川省南充市阆中中学校2022-2023学年高三上学期10月月考数学(文)试题(已下线)考向36 直线与圆锥曲线最全归纳(十六大经典题型)-3(已下线)专题38 圆锥曲线中的圆问题-2(已下线)第五篇 向量与几何 专题10 圆锥曲线中的四点共圆问题 微点2 圆锥曲线中的四点共圆问题(二)(已下线)重难点突破15 圆锥曲线中的圆问题(四大题型)2023版 湘教版(2019) 选修第一册 过关斩将 第3章 综合拔高练(已下线)专题03 圆锥曲线题型全归纳(九大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)
名校
7 . 如图,在多面体
中,四边形
是矩形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e3a8f4ea4c49537514dd22064100f9.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4146b39-5172-455e-95ca-7865cb927a8b.png?resizew=188)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e3a8f4ea4c49537514dd22064100f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307492a5106b38351e52cd4fff8b1ec8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4146b39-5172-455e-95ca-7865cb927a8b.png?resizew=188)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e49a850dd76dc1162ff2eda8791b772.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
您最近一年使用:0次
2023-01-16更新
|
282次组卷
|
2卷引用:新疆乌鲁木齐市第六十一中学2024届高三上学期12月月考数学试题
名校
8 . 如图,在四棱锥
中,已知四边形
是梯形,
,
是正三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/683b6788-5b7e-4317-b643-bf3b4dbf07ac.png?resizew=179)
(1)求证:
;
(2)当四棱锥
体积最大时,二面角
的大小为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f2693cdb3751a8fd3a5d6f597dcfbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e68c3b4e4aff8c6b7f8b6189e3985f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/683b6788-5b7e-4317-b643-bf3b4dbf07ac.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3723525244e12b59101e1c0b5fb912ca.png)
(2)当四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8860d255b9c6cec4c062d73720aa8a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2930e3d72846688f8389ab8cf178e062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b8b77522dfc890b99f0a86a690de94.png)
您最近一年使用:0次
2022-10-23更新
|
248次组卷
|
3卷引用:新疆生产建设兵团第三师图木舒克市第二中学2023届高三上学期月考数学(理)试题
名校
解题方法
9 . 如图,正三棱柱
中,
分别是棱
,
上的点,
平面
,且M是AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/5cf17122-cce0-48ff-80cc-bcb365818b82.png?resizew=160)
(1)证明:平面
平面
;
(2)若
,求平面BEF与平面BCE夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b96dce1ec94eb90c243b2eddb78476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa14afe6f0aad22e8e869c39a60be657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/5cf17122-cce0-48ff-80cc-bcb365818b82.png?resizew=160)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a2ab6940dca62be1f3b2b5f8531990.png)
您最近一年使用:0次
2022-11-14更新
|
699次组卷
|
3卷引用:新疆石河子市第一中学2024届高三上学期11月月考数学试题
10 . 如图,在四边形ABCD中,AC⊥BD,AC∩BD=O,OD=OB=1,OC=2.E,F分别是AB,AD上的点,EF∥BD,AC∩EF=H,AH=2,HO=1.将△AEF沿EF折起到△
EF的位置,得到五棱锥
-BCDFE,如图3.
![](https://img.xkw.com/dksih/QBM/2022/5/16/2980477599154176/2994995396550656/STEM/f7ee8c7a-54f3-42a6-bb53-dcf57fbb254b.png?resizew=572)
(1)求证:EF⊥平面
HC;
(2)若平面
EF⊥平面BCDFE,求二面角D-
C-H的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/16/2980477599154176/2994995396550656/STEM/f7ee8c7a-54f3-42a6-bb53-dcf57fbb254b.png?resizew=572)
(1)求证:EF⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
您最近一年使用:0次
2022-06-05更新
|
181次组卷
|
2卷引用:新疆昌吉州行知学校2023届高三下学期第一次月考数学(理)试题