名校
1 . 如图所示,在四棱锥
中,底面
是边长为2的正方形,侧棱
的长为3,且
,N是
的中点,设
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/15/425cd91e-fb99-4381-b6a8-562e90898cef.png?resizew=173)
(1)用
、
、
表示向量
,并求
的长;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030fcafba4a3fee230a1475c93a062f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21841338587f28e2b8adbc39897a145b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3bfd659390349bb6dd15bb4ae57260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252b637d25263b74a01ec59e691c3a45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/15/425cd91e-fb99-4381-b6a8-562e90898cef.png?resizew=173)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350f162ee9aa08f4c9779481a5ef1025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
您最近一年使用:0次
2 . 如图,在四棱锥
中,
底面
,底面
是直角梯形,
,
,
,
是
的中点.
(1)求证:
平面
;
(2)若二面角
的余弦值为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd3c2e2199cd4565c05b949bc21fc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/13/505ca1b6-0de8-49a2-896d-9b29a5425143.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5102c216393e133fa25dba98cd78535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
您最近一年使用:0次
解题方法
3 . 已知函数
是定义在
上的奇函数,且
.
(1)求a,b的值,并用定义证明:函数
在区间
上的单调性;
(2)若
,求实数a的取值范围;
(3)写出函数
的值域(不必写出解答过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4456fb2e3fd38c13353aa0d894ec43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3213a7a72b5e376ee25efd535398fb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd60e05922c00cf442c5099a3d73959.png)
(1)求a,b的值,并用定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3213a7a72b5e376ee25efd535398fb7d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e9dba36c87a25407342e262f9f9c30.png)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
您最近一年使用:0次
名校
4 . 如图,在棱长为2的正方体
中,
为棱
的中点,
为棱
的中点.
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/28/661a8f37-cd3d-41f7-9718-a887246ed99a.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f71c40e463a7cec4314f2c7ebb431a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd7d2bc169d4467ad7d70861ed6351.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd7d2bc169d4467ad7d70861ed6351.png)
您最近一年使用:0次
2023-09-26更新
|
1310次组卷
|
24卷引用:福建省厦门市新店中学2023-2024学年高二上学期期中考试数学试题
福建省厦门市新店中学2023-2024学年高二上学期期中考试数学试题湖北省十堰市城区普高协作体2021-2022学年高二上学期期中数学试题黑龙江省哈尔滨市第七十三中学校2022-2023学年高二上学期第一次月考数学试题黑龙江省齐齐哈尔市三立高级中学2022-2023学年高二上学期期中考试数学试题河南省郑州市第一〇六高级中学2022-2023学年高二上学期9月月考数学试题湖北省十堰市天河英才高中2022-2023学年高二上学期期中数学试题吉林省吉林市吉化第一高级中学校2022-2023学年高三上学期12月月考数学试题海南省海口市上海世外附属海口学校2022-2023学年高二上学期期中数学试题安徽省芜湖市无为襄安中学2022-2023学年高二上学期12月月考数学试题河南省TOP二十名校2023届高三猜题大联考(二)数学(理科)试题江西省湖口中学2022-2023学年高二下学期5月期中考试数学试题第一章 空间向量与立体几何 (练基础)(已下线)模块三 专题4 空间向量的应用1直线与平面的夹角、二面角 B能力卷辽宁省大连市第八中学2021-2022学年高二上学期12月月考数学试题(已下线)模块三 专题5 直线与平面的夹角、二面角 B能力卷 (人教B)河南省濮阳市第一高级中学2023-2024学年高二上学期9月月考数学试题山东省临沂市临沭县临沭第一中学2023-2024学年高二上学期10月月考数学试题海南省琼海市海桂中学2023-2024学年高二上学期第一次学情监测数学试题内蒙古自治区赤峰市赤峰二中2023-2024学年高二上学期第一次月考数学试题新疆维吾尔自治区喀什地区巴楚县2023-2024学年高二上学期10月期中考试数学试题山西省晋中市博雅培文实验学校2023-2024学年高二上学期期中数学试题黑龙江省哈尔滨市宾县第二中学2023-2024学年高二上学期第三次月考数学试题 天津市武清区南蔡村中学2023-2024学年高二上学期第二次月考数学试题山西省晋城市第一中学校(南岭爱物校区)2023-2024学年高二上学期12月月考数学试卷
名校
5 . 已知函数
,
.
(1)判断该函数的奇偶性,并说明理由;
(2)判断函数
在
上的单调性,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983c9b1ea7e8cc0e4098d17bb0694ddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6855784817151468771f29c0fc38fc9.png)
(1)判断该函数的奇偶性,并说明理由;
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
您最近一年使用:0次
2023-10-21更新
|
1064次组卷
|
5卷引用:福建省厦门海沧实验中学2023-2024学年高一上学期11月阶段性测试数学试题
名校
6 . 如图,在三棱柱
中,底面
侧面
.
平面
;
(2)若
,求三棱锥
的体积;
(3)在(2)的条件下,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b3e80d3a58ac3cf00b42f41747c311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab8cba157598642cb6b42734861a184.png)
(3)在(2)的条件下,求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
您最近一年使用:0次
2024-02-29更新
|
320次组卷
|
2卷引用:福建省厦门市湖滨中学2023-2024学年高二下学期期中考试数学试题
名校
解题方法
7 . 如图,在平面直角坐标系中,锐角
的终边分别与单位圆交于
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/623b6ccf-4b5a-43ce-9911-89c8ca3b010c.png?resizew=168)
(1)如果
,
点的横坐标为
,求
的值;
(2)设
的终边与单位圆交于
均与
轴垂直,垂足分别为
,求证:以线段
的长为三条边长能构成三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/623b6ccf-4b5a-43ce-9911-89c8ca3b010c.png?resizew=168)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aeb448d0392a08f89781e63b49cd3da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954795d1842974a705f9468f3b952ab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bc6ce7e631bcd313e0f30a13e47f5a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ca6eb58473c449af9f3671c793733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fc107c4b33d6dd648b396156494ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4800e4284cd62d449987a7c714810521.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥
中,底面
是正方形,且
,平面
平面
,
,点
为线段
的中点,点
是线段
上的一个动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/a7d9681e-6540-4ca4-b36c-4be66de79629.png?resizew=162)
(1)求证:平面
平面
;
(2)设二面角
的平面角为
,试判断在线段
上是否存在这样的点
,使得
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b388f9915195687e417e2ffc4a55a311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88197da08544c0dd0f8fb1359797ac9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/a7d9681e-6540-4ca4-b36c-4be66de79629.png?resizew=162)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6dd051db98c531f9ef18cdfd793f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c539709f3b8449ef9cd00a86e194c099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876a3c70fc77700b22f3f9c4f2b2ffde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6f832355c03fad4f13c994289d6b6.png)
您最近一年使用:0次
2023-11-22更新
|
283次组卷
|
3卷引用:福建省厦门市第二中学2023-2024学年高二上学期第二次月考数学试题
9 . 已知函数
.
(1)判断
在区间
上的单调性,并用定义证明;
(2)当
时,
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49e790b1d37f231c10c6c93facc372c.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898506a838975df680ab85d84e1a6874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418c2b25a108bd0328c6b25a7f6092e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
10 . 在平面直角坐标系
中,点
,点A为动点,以线段
为直径的圆与
轴相切,记A的轨迹为
,直线
交
于另一点B.
(1)求
的方程;
(2)
的外接圆交
于点
(不与O,A,B重合),依次连接O,A,C,B构成凸四边形
,记其面积为
.
(i)证明:
的重心在定直线上;
(ii)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(i)证明:
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2024-02-18更新
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3卷引用:2024届福建省厦门市一模考试数学试题