名校
1 . 如图,在四棱锥
中,平面
平面PAD,
,
,
,
,
,E是PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75999df6-7b26-4bc9-b456-9eece69fa814.png?resizew=168)
(1)求证:
;
(2)若点M在线段PC上,异面直线BM和CE所成角的余弦值为
,求面MAB与面PCD夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7ae4091a3a2767fde8e9f5a604c1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646d135e77c1ea69390d9e937f88b85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/75999df6-7b26-4bc9-b456-9eece69fa814.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371853a703a8dafa6f8e942f46cb8706.png)
(2)若点M在线段PC上,异面直线BM和CE所成角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
您最近一年使用:0次
2022-12-27更新
|
2194次组卷
|
7卷引用:山东省莱西市第一中学2022-2023学年高二学业水平检测(二) 数学试题
名校
解题方法
2 . 如图,在四棱锥P-ABCD中,底面ABCD为正方形,PA⊥平面ABCD,PA=AD=1,E,F分别是PB,AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/c1ebc8d8-22c0-499d-81b2-1468f911a3d2.png?resizew=170)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/c1ebc8d8-22c0-499d-81b2-1468f911a3d2.png?resizew=170)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90deda6e128fade762bdb3b74bedf511.png)
您最近一年使用:0次
2021-12-15更新
|
1554次组卷
|
12卷引用:山东省2021年冬季普通高中学业水平合格性考试仿真模拟数学试题
山东省2021年冬季普通高中学业水平合格性考试仿真模拟数学试题甘肃省天水市第一中学2021-2022学年高二下学期学业水平模拟考试(二)数学试题吉林省长春外国语学校2020-2021学年高三上学期期初考试数学试题广西玉林市育才中学2020-2021学年高二3月月考数学(文)试题四川省眉山市仁寿第一中学南校区2021-2022学年高二上学期入学考试数学试题四川省遂宁市射洪中学2021-2022学年高二上学期第一次月考数学理试题(已下线)专题13.3 空间图形的表面积和体积(基础练)-2020-2021学年高一数学十分钟同步课堂专练(苏教版2019必修第二册)新疆乌鲁木齐市第八中学2021-2022学年高二上学期第二次月考数学(问卷)试题贵州省六盘水红桥学校2021-2022学年高二上学期期中考试数学试题(已下线)第8.5讲 空间直线、平面的平行河北省石家庄市元氏县第四中学2022-2023学年高二上学期开学考试数学试题四川省遂宁市射洪中学校2022-2023学年高二上学期第一次学月考试数学(理科)试题
名校
解题方法
3 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d978e4e41c7b382a640d8c548e8ccb5.png)
(1)判断并用定义证明
的单调性;
(2)求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5289aad39fb9f7b30d1cf1d501ced8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d978e4e41c7b382a640d8c548e8ccb5.png)
(1)判断并用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2021-10-30更新
|
1049次组卷
|
3卷引用:山东省2021年冬季普通高中学业水平合格性考试仿真模拟数学试题
解题方法
4 . 如图,斜三棱柱
中,
是边长为2的正三角形,
为
的中点,
平面
,点
在
上,
,
为
与
的交点,且
与平面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/5bd35e24-40cb-453b-8580-5cbfded9946d.png?resizew=226)
(1)求证:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1cac8174f8a30b7be0dc8419ed8ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec275f823ae17afdba53301fcbd2aa43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/5bd35e24-40cb-453b-8580-5cbfded9946d.png?resizew=226)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e1ac4a3e715fea3e38a59d86eb272ca.png)
您最近一年使用:0次
2020-05-12更新
|
550次组卷
|
4卷引用:山东省2019-2020学年普通高中学业水平等级考试4月(模拟)数学试题
山东省2019-2020学年普通高中学业水平等级考试4月(模拟)数学试题2020届山东省临沂市高三一模数学试题(已下线)专题九 立体几何与空间向量-2020山东模拟题分类汇编江苏省无锡市江阴市成化高级中学2020-2021学年高三上学期12月第二次月考数学试题
解题方法
5 . 如图,在三棱锥
中,
,
分别是棱
,
的中点.求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1777619bfe1167d487f3a8507fba7fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/aebfedb2-143a-424e-b710-a7ffaed46b77.png?resizew=157)
您最近一年使用:0次
6 . 过函数
的图象
上一点
作倾斜角互补的两条直线,分别与
交与异于
的
,
两点.
(1)求证:直线
的斜率为定值;
(2)如果
,
两点的横坐标均不大于0,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108c18cb76d7d34b05c991a644c8b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)如果
![](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/62c7b00bbc388a57080f7dab4aca8286.png)
您最近一年使用:0次
7 . 如图,在三棱锥
中,
.求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c537bb823a0e838f40477e6727f8e78e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
![](https://img.xkw.com/dksih/QBM/2020/3/10/2416734348419072/2417433693102080/STEM/e30d0b1a4eb64e568f4a7338ff4f657e.png?resizew=157)
您最近一年使用:0次
2020-03-11更新
|
239次组卷
|
2卷引用:山东省2017年冬季普通高中学业水平考试数学试题
名校
8 . 设数列
的前
项和为
,且满足
.
(1)证明:数列
是等比数列,并求它的通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a082c8e0cf5b00de13ba761ab200800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a09766e919de55a5b11ca3c1b04afb6.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a082c8e0cf5b00de13ba761ab200800.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add02169a8f58417880df4e302a7c498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2019-12-29更新
|
514次组卷
|
3卷引用:2018级山东师大附中第五次学分认定考试数学试题
名校
解题方法
9 . 已知
是定义在
上的奇函数.
(1)求
的值;
(2)判断
在
上的单调性,并用定义证明;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6f9b8202451375dddc577c0964d38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f7d061ccc00e8f410fc840fe7cc57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-10-22更新
|
4712次组卷
|
6卷引用:山东省2021年冬季普通高中学业水平合格性模拟考试数学试题
解题方法
10 . 已知定义在
上的二次函数
,且
在
上的最小值是8.
(1)求实数
的值;
(2)设函数
,若方程
在
上的两个不等实根为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c009c79f5a2e63c0c06f6d61d70352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9d86203ddeaab06bdd2f634f1538dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2401f1358466ad761052b98564ae5873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6ffa6fe2387ee19234c2ad0fcb92ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2d40035607cb9eb4ba2def79d08f0d.png)
您最近一年使用:0次
2020-03-11更新
|
726次组卷
|
2卷引用:山东省2017年冬季普通高中学业水平考试数学试题