1 . 如图所示,点
为斜三棱柱
的侧棱
上一点,
交
于点
,
交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/10/22/1573089691934720/1573089698439168/STEM/7972e989-11cc-4b62-94c9-7f0e0d290d3f.png?resizew=194)
(1)求证:
;
(2)在任意
中有余弦定理:
.拓展到空间,类比三角形的余弦定理,写出斜三棱柱的三个侧面面积与其中两个侧面所成的二面角之间的关系式,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60b83e5a713c9d0409bf544c514f602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88d952630ddac66a1f077dcc9439990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2016/10/22/1573089691934720/1573089698439168/STEM/7972e989-11cc-4b62-94c9-7f0e0d290d3f.png?resizew=194)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0937dc905b06383bd34d5f9ae8384a.png)
(2)在任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e46534c1cb9de14c258eef9244272b5.png)
您最近一年使用:0次
2016-12-04更新
|
627次组卷
|
6卷引用:2004 年普通高等学校招生考试数学试题(上海卷)
2004 年普通高等学校招生考试数学试题(上海卷)2016-2017学年江西南昌市高三新课标一轮复习一数学试卷沪教版(上海) 高三年级 新高考辅导与训练 第九章 空间图形与简单几何体 三、多面体上海市闵行第三中学2022-2023学年高二上学期10月月考数学试题沪教版(2020) 必修第三册 高效课堂 第十章 每周一练(2)(已下线)第五章 破解立体几何开放探究问题 专题一 立体几何存在性问题 微点1 立体几何存在性问题的解法【培优版】
真题
解题方法
2 . 如图,已知两个正四棱锥
与
的高都是2,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/35af81b4-67ef-422a-9c7b-798a8c4f1daf.png?resizew=206)
(1)证明:
平面
;
(2)求异面直线
与
所成的角;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/35af81b4-67ef-422a-9c7b-798a8c4f1daf.png?resizew=206)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40cae1138ce408cf7ebbe14f152d6e9.png)
您最近一年使用:0次
真题
解题方法
3 . 如图1,E,F分别是矩形ABCD的边AB,CD的中点,G是EF上的一点,将
分别沿AB,CD翻折成
,并连接
,使得平面
平面ABCD,
,且
,连接
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/33851505-64b4-4f3c-acf8-c02b72f7e1e1.png?resizew=421)
(1)证明:平面
平面
;
(2)当
时,求直线
和平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21f7392b348717bad30167d87f959d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64bf472d11d49b130b5fe3aabd3feeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af9a10717d214e599ee121de74bf451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80aecacfa887e53407eb02a32f510ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1101659bacb66165c5293e6baaf64571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88c0117b251e91cd16feaa1144cd78e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77914a4462c30293bef6f989ade88ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/33851505-64b4-4f3c-acf8-c02b72f7e1e1.png?resizew=421)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80aecacfa887e53407eb02a32f510ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4836fb713073d6843503549591d894c7.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f25a517b3948d74a4b8fdbf66f8c879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77914a4462c30293bef6f989ade88ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4836fb713073d6843503549591d894c7.png)
您最近一年使用:0次
真题
解题方法
4 . 如图,某地为了开发旅游资源,欲修建一条连接风景点P和居民区O的公路,点P所在的山坡面与山脚所在水平面
所成的二面角为
,且
,点P到平面
的距离
.沿山脚原有一段笔直的公路AB可供利用,从点O到山脚修路的造价为a万元
,原有公路改建费用为
万元
,当山坡上公路长度为
时,其造价为
万元,已知
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/e6de8ea8-1f69-4f8f-a111-bf2bb2c3adc3.png?resizew=345)
(1)在AB上求一点D,使沿折线PDAO修建公路的总造价最小;
(2)对于(1)中得到的点D,在DA上求一点E,使沿折线PDEO修建公路的总造价最小;
(3)在AB上是否存在两个不同的点
,使沿折线
修建公路的总造价小于(2)中得到的最小总造价,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f5d1218c4f7d9263da333a4edf06af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0503736d21c5e5432d933990cf511c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e689190fd5a655655c264d4b134ba00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98024ce2e23a5e81b2bcdd7c96ccef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576833b76e9cad3b523f87132308df99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98024ce2e23a5e81b2bcdd7c96ccef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6db945cfc09c3a78843068acc18fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48dc9c56c4d2ed0d3529460ef2cf8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ac747fa7e033b09ab20370fd27d5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e4c39ba72d14560e283ad7f75353a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5881bc21725be10ac0151c445393b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d645ac2b7ccb0f0d290c05dc5d328d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/e6de8ea8-1f69-4f8f-a111-bf2bb2c3adc3.png?resizew=345)
(1)在AB上求一点D,使沿折线PDAO修建公路的总造价最小;
(2)对于(1)中得到的点D,在DA上求一点E,使沿折线PDEO修建公路的总造价最小;
(3)在AB上是否存在两个不同的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c18dea2399109b0d0e1c23e31f227bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6003623c3413d3e2a3c1e41049fa31b2.png)
您最近一年使用:0次
真题
5 . 已知函数
(a为正常数),且函数
与
的图象在y轴上的截距相等.
(1)求a的值;
(2)求函数
的单调递增区间;
(3)若n为正整数,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a86da8d6deadb069d0696506891b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求a的值;
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfcc567b95a320abcb25509923cd001.png)
(3)若n为正整数,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e8e5b71f94363cb784224577b68740.png)
您最近一年使用:0次
真题
6 . 已知实数p满足不等式
,试判断方程
有无实根,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e12778dd7cb67bcb0804b9bb4e69e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cef1caa5d9f9f05693017d4077fcd0c.png)
您最近一年使用:0次
7 . 若A、B是抛物线
上的不同两点,弦
(不平行于y轴)的垂直平分线与x轴相交于点P,则称弦
是点P的一条“相关弦”.已知当
时,点
存在无穷多条“相关弦”.给定
.
(1)证明:点
的所有“相关弦”的中点的横坐标相同;
(2)试问:点
的“相关弦”的弦长中是否存在最大值?若存在,求其最大值(用
表示);若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.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/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924886b76c218169b2f4d00bb7e9563c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b042740af8a73f8add3ec9c586b4e540.png)
(1)证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c9b882323edba16b3625458239b6f3.png)
(2)试问:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c9b882323edba16b3625458239b6f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
真题
解题方法
8 . 已知函数
,数列
满足:
,
.证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52142482df6bbd431d300f011e3ccb12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4738119275a2f952503cd073b9bfec47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bce6187f3f11e0ceead8a645f5f9d32.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89948adf1e13b6abee5aa37fb5eaefb4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16496a925991d2be8befa69c6c32c1e5.png)
您最近一年使用:0次
真题
9 . 如图,已知两个正四棱锥
与
的高分别为1和2,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/cbd9fa58-be46-4261-a7f5-915183231f1b.png?resizew=232)
(1)证明:
平面
;
(2)求异面直线
与
所成的角;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/cbd9fa58-be46-4261-a7f5-915183231f1b.png?resizew=232)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40cae1138ce408cf7ebbe14f152d6e9.png)
您最近一年使用:0次
真题
10 . 如图1,已知
是上.下底边长分别为2和6,高为
的等腰梯形,将它沿对称轴
折成直二面角,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/3d9c392e-b93d-4be9-9f17-297f8d70b851.png?resizew=414)
(1)证明:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/3d9c392e-b93d-4be9-9f17-297f8d70b851.png?resizew=414)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400d97da3779f117510058b0526df75a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8faef5f821d00d9c69e65e0988fe1f.png)
您最近一年使用:0次
2022-11-09更新
|
480次组卷
|
2卷引用:2005年普通高等学校招生考试数学(文)试题(湖南卷)