解题方法
1 . 证明:
(1)已知a>b>0,c<d<0,e<0,求证:
;
(2)已知x>0,y>0,x+y=1,求证:
.
(1)已知a>b>0,c<d<0,e<0,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d2a05075997525049a368aba1c2b46.png)
(2)已知x>0,y>0,x+y=1,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0050f60381c11bd08745623096f0a66e.png)
您最近一年使用:0次
2011·北京西城·二模
2 . 如图,已知菱形
的边长为
,
,
.将菱形
沿对角线
折起,使
,得到三棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/e16d49b7-88bf-4480-af0e-45ffb09e6a85.png?resizew=342)
(Ⅰ)若点
是棱
的中点,求证:
平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)设点
是线段
上一个动点,试确定
点的位置,使得
,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57abb19d63cad8f06c62f2ed75d70dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41ffdaecfb3c73d403179e5745c71a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/e16d49b7-88bf-4480-af0e-45ffb09e6a85.png?resizew=342)
(Ⅰ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280247d7df395bb9ea78c51e67b458d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b661fc2f6213ff6dab5e0b10bee383c5.png)
(Ⅲ)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d9ebeeefbd4bd27023709d01b5dc95.png)
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解题方法
3 . 如图,已知AB⊥平面ACD,DE⊥平面ACD,
为等边三角形,
,F为CD的靠近C的四等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/12/19723d5e-3a0a-4cab-90c7-5c98716114fa.png?resizew=220)
(1)求证:AF∥平面BCE;
(2)请问:平面BCE与平面CDE是否互相垂直?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e80ffdaa7e672d194d86b5e4a7ddf931.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/12/19723d5e-3a0a-4cab-90c7-5c98716114fa.png?resizew=220)
(1)求证:AF∥平面BCE;
(2)请问:平面BCE与平面CDE是否互相垂直?请证明你的结论.
您最近一年使用:0次
名校
解题方法
4 . 已知函数
,
满足
.
(1)设
,求证:函数
在区间
上为减函数,在区间
上为增函数;
(2)设
.
①当
时,求
的最小值;
②若对任意实数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d0fa6692dabe155895e6deca98da84.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4a90cfdbfa05577b6ec0b22739e7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95167d339851668666c00819537737c4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56251c77cc3fd1db89c33003519a116.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5db0c90f213d6bf3ef7949cc00aa27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a37e21a940c03985a1458167b5e6c24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-11-27更新
|
403次组卷
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5卷引用:湖北省黄冈市浠水县第一中学2023-2024学年高一上学期期中数学试题
湖北省黄冈市浠水县第一中学2023-2024学年高一上学期期中数学试题山东省潍坊市2023-2024学年高一上学期11月期中质量监测数学试题山东省淄博市美达菲双语高级中学2023-2024学年高一上学期期中数学试题江西省抚州市资溪县第一中学2023-2024学年高一上学期期中调研数学试题(已下线)专题04 函数的性质与应用1-期末复习重难培优与单元检测(人教A版2019)
名校
解题方法
5 . 在四棱锥
中
底面
,底面
是菱形,
,
,点
在
上.
平面
;
(2)若
为
中点,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba172e1d3af3079d5d8fcb3791d6484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df49b91d399a0b28d5ad86b84b1f42d.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/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
2023-11-22更新
|
385次组卷
|
4卷引用:湖北省黄冈市部分高中2023-2024学年高二上学期阶段性教学质量监测数学试题
湖北省黄冈市部分高中2023-2024学年高二上学期阶段性教学质量监测数学试题陕西省咸阳市永寿县中学2023-2024学年高二上学期第三次月考数学试题安徽省马鞍山市第二中学2023-2024学年高二下学期阶段性检测数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点3 平面法向量求法及其应用综合训练【培优版】
名校
解题方法
6 . 求证:函数
在区间
上是减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d6d5dfc6719d1280c6545491a29d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33778e53d3ecd04cf471378a133db478.png)
您最近一年使用:0次
2023-05-12更新
|
1418次组卷
|
6卷引用:湖北省黄冈中学2022-2023学年高一下学期(鄂东南省级示范高中教育教学改革联盟学校)期中联考模拟数学试题
湖北省黄冈中学2022-2023学年高一下学期(鄂东南省级示范高中教育教学改革联盟学校)期中联考模拟数学试题(已下线)第三章 函数的概念与性质 讲核心 02(已下线)第10讲 函数的单调性与最大(小)值-【暑假自学课】(人教A版2019必修第一册)(已下线)3.2.1 函数的单调性(精讲)-《一隅三反》(已下线)3.2 函数的基本性质(AB分层训练)-【冲刺满分】(已下线)第03讲 3.2.1单调性与最大(小)值(精讲精练)(1)-【帮课堂】
名校
7 . 已知圆
,直线
.
(1)求证:直线l与圆C恒有两个交点;
(2)若直线l与圆C交于点A,B,求
面积的最大值,并求此时直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f356f73c8c44081d7facda01d0aee0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e79f9bde1bbe9195ece6a443297120d.png)
(1)求证:直线l与圆C恒有两个交点;
(2)若直线l与圆C交于点A,B,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41663d9e5e18891475aeaa98794f33d.png)
您最近一年使用:0次
2023-09-19更新
|
2327次组卷
|
9卷引用:湖北省黄冈市2022-2023学年高二上学期期中数学试题
湖北省黄冈市2022-2023学年高二上学期期中数学试题吉林省长春市朝阳区长春外国语学校2023-2024学年高二上学期期中数学试题陕西省西安市鄠邑区2023-2024学年高二上学期期中数学试题广东省云浮市罗定市罗定中学城东学校2023-2024学年高二上学期11月期中数学试题广东省河源市龙川县第一中学2023-2024学年高二上学期11月期中考试数学试题湖北省A9高中联盟2023-2024学年高二上学期期中联考数学试题(已下线)考点巩固卷19 直线与圆(十二大考点)(已下线)第二章 直线和圆的方程(单元测试)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第一册)(已下线)通关练10 直线的方程大题10考点精练(57题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
解题方法
8 . 已知抛物线
和圆
交于
两点,且
,其中O为坐标原点.
(1)求
的方程.
(2)过
的焦点
且不与坐标轴平行的直线
与
交于
两点,
的中点为
,
的准线为
,且
,垂足为
.证明:直线
的斜率之积
为定值,并求该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ebe959b8ff2bbabce1f0f09a36e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7919338a4271bfa738a67e7630441ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db36b4497b911bc047253b832ae01c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e775e1c7a1a275384e9ed500a3cadf4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/b1241216f3c1cb5e73043dd1037f556d.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436a0215888457c11878ec53937d6c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ec409450dfbbbb57adee4ca3472b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2024-01-20更新
|
289次组卷
|
5卷引用:湖北省黄冈市蕲春县2020-2021学年高二下学期期中数学试题
名校
解题方法
9 . 如图①,在直角梯形
中,
,
,
.将
沿
折起,使平面
平面
,连
,得如图②的几何体.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/bc15d5d7-ca8a-41f7-85b8-c1689d85c4b2.png?resizew=331)
(1)求证:平面
平面
;
(2)若
,二面角
的平面角的正切值为
,在棱
上是否存在点
使二面角
的平面角的余弦值为
,若存在,请求出
的值,若不存在,说明理由.
![](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/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.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/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/bc15d5d7-ca8a-41f7-85b8-c1689d85c4b2.png?resizew=331)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d3f5f4c4419913c1232b7aae03ade.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2898853a3396f0878af9eac934416d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.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/30e536ceabd66ab4850e9207bf8e6e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfba1cb9288115959f1b843a328aaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1612a0a4df3353fba4da6678c6a0cf4b.png)
您最近一年使用:0次
2023-11-22更新
|
1185次组卷
|
6卷引用:湖北省黄冈市部分高中2023-2024学年高二上学期阶段性教学质量监测数学试题
湖北省黄冈市部分高中2023-2024学年高二上学期阶段性教学质量监测数学试题重庆市第八中学校2023-2024学年度高二上学期检测六数学试题广东省广州市第八十九中学2023-2024学年高二上学期第十五周测数学试题(已下线)模块一 专题2 利用空间向量解决立体几何问题 (讲)2 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)专题01 空间向量及其应用常考题型归纳(1)(已下线)专题01 空间向量与立体几何(2)
解题方法
10 . 如图,在三棱柱
中,四边形
是边长为3的正方形,平面
平面
,
,
,
(1)求证:
;
(2)求平面
与平面
夹角的余弦值;
(3)在线段
上确定点D,使得
,并求三棱锥
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/7ec73457-b1f0-4746-b950-f4bf7f1176f1.png?resizew=142)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0a886f1192d450ced9fd875e78425e.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f664c0db517bec6886ff0b6100fd474.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84a436704964dc76f16c2c23665ab3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41ffdaecfb3c73d403179e5745c71a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e2e124548b9d5cb8283febd612ab3a.png)
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