名校
1 . 如图,在四棱锥
中, 已知
底面
, 底面
是正方形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/a6b85879-3c8c-42d8-b823-a40468058c00.png?resizew=160)
(1)求证: 直线
平面
;
(2)求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b0de5237c88a9bfffc207bab17191a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/a6b85879-3c8c-42d8-b823-a40468058c00.png?resizew=160)
(1)求证: 直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c306e49fd17d29f0174793cb5e1decbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d39f37441ee55dbc8f1a6ca199a66b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3142b1af4ce67d3e55417b4c0de257.png)
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2023-01-10更新
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4卷引用:重庆市云阳凤鸣中学校2022-2023学年高二上学期期末数学试题
重庆市云阳凤鸣中学校2022-2023学年高二上学期期末数学试题河南省周口市项城市第三高级中学2022-2023学年高二下学期开学考试数学试题(已下线)江苏省盐城市、南京市2022届高三上学期1月第一次模拟考试数学试题变式题17-22四川省雅安市名山区第三中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
2 . 如图
,
分别是矩形
上的点,
,
,把四边形
沿
折叠,使其与平面
垂直,如图
所示,连接
,
得到几何体
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d6fc6d97-472e-47df-b156-95842dfa848b.png?resizew=385)
(1)当点
在棱
上移动时,证明:
;
(2)在棱
上是否存在点
,使二面角
的平面角为
?若存在,求出
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775df7ba0dc94c15e9e706194a463f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbad56884c1cb3160d481fc560da5228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e8d4e60eb30cf8df1ff219b5b445e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22ebcc4aa98d46366df48f751a5f368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b3b4c5ce7aca81becc07ed4903736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90d36d93be9e89f1053d42735686e2d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d6fc6d97-472e-47df-b156-95842dfa848b.png?resizew=385)
(1)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa81c1f81266b4ef3d471bc6bfc38d.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35988677892d6ffdf4773f7a861f26a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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2022-11-26更新
|
1027次组卷
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7卷引用:重庆市云阳凤鸣中学校2022-2023学年高二上学期期末数学试题
重庆市云阳凤鸣中学校2022-2023学年高二上学期期末数学试题重庆市新高考2023-2024学年高二上学期期末模拟数学试题江苏省徐州市2022-2023学年高三上学期期中复习数学试题重庆市万州第二高级中学2023届高三上学期2月月考数学试题重庆市万州第二高级中学2023届高三下学期2月月考数学试题(已下线)6.3.3 空间角的计算(练习)-2022-2023学年高二数学同步精品课堂(苏教版2019选择性必修第二册)(已下线)第6章 空间向量与立体几何 单元综合检测(练习)-2022-2023学年高二数学同步精品课堂(苏教版2019选择性必修第二册)
3 . 已知
为等差数列,前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
,
是首项为3且公比
大于0的等比数列,
,
,
.
(1)求
和
的通项公式;
(2)求数列
的前
项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/89ba85f74cda4ddd621278e558bc036f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1873618dd629f7bc007e659e1e6c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c2bdaea39bdf737331cc7950371971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7efa7f144945e6e0b3bb96c5c80a8a0d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ba85f74cda4ddd621278e558bc036f.png)
您最近一年使用:0次
2022-12-11更新
|
723次组卷
|
6卷引用:重庆市云阳凤鸣中学校2022-2023学年高二上学期期末数学试题
4 . 已知数列
的前
项和
满足
.
(1)求
及数列
的通项公式;
(2)求数列
的前
项和
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/26d37ddb9a1b42d7160189d255a1a7e2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a44cfbb86a4eb76261c00ddc6bff181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f86bd9ed4b6f3b1b49e5d54db38b.png)
您最近一年使用:0次
2022-04-12更新
|
727次组卷
|
3卷引用:重庆市云阳江口中学校2022届高三上学期期末数学试题
名校
解题方法
5 . 已知双曲线
:
的一条渐近线方程为
,焦点到渐近线的距离为1.
(1)求双曲线
的标准方程.
(2)已知斜率为
的直线
与双曲线
交于
轴上方的A,
两点,
为坐标原点,直线
,
的斜率之积为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5212f9b39ca710f0349e1b3652bc6a.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e165ecb6f59aff040ac62edd49cc5551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2022-12-09更新
|
605次组卷
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3卷引用:重庆市云阳凤鸣中学校2022-2023学年高二上学期期末数学试题
名校
解题方法
6 . 双曲线
与椭圆
的焦点相同,且渐近线方程为
,双曲线
的上下顶点分别为A,B.过椭圆
上顶点R的直线l与双曲线
交于点P,Q(P,Q不与A,B重合),记直线
的斜率为
,直线
的斜率为
.
(1)求双曲线
的方程;
(2)证明
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b103566a4645e48ee0671b4eacb1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a7ae9d8dba2d5fad2a260cb42457a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6bb019e2d7c6d17d15ec4d9043f5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
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2022-04-12更新
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653次组卷
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5卷引用:重庆市云阳江口中学校2022届高三上学期期末数学试题
重庆市云阳江口中学校2022届高三上学期期末数学试题江西省宜春市2022届高三4月模拟考试数学(理)试题(已下线)回归教材重难点04 圆锥曲线-【查漏补缺】2022年高考数学(理)三轮冲刺过关(已下线)必刷卷03(理)-2022年高考数学考前信息必刷卷(全国甲卷)江西省上饶市广丰区重点高中2022-2023学年高二上学期第一次月考数学试题
名校
解题方法
7 . 某学校为调查了解学生体能状况,决定对高三学生进行一次体育达标测试,具体测试项目有100米跑、立定跳远、掷实心球.测试规定如下:
①三个测试项目中有两项测试成绩合格即可认定为体育达标;
②测试时要求考生先从三个项目中随机抽取两个进行测试,若抽取的两个项目测试都合格或都不合格时,不再参加第三个项目的测试;若抽取的两个项目只有一项合格,则必须参加第三项测试.
已知甲同学跑、跳、掷三个项目测试合格的概率分别是
、
、
,各项测试时间间隔恰当,每次测试互不影响.
(1)求甲同学恰好先抽取跳、掷两个项目进行测试的概率;
(2)求甲同学经过两个项目测试就能达标的概率;
(3)若甲按规定完成测试,参加测试项目个数为X,求X的分布列和期望.
①三个测试项目中有两项测试成绩合格即可认定为体育达标;
②测试时要求考生先从三个项目中随机抽取两个进行测试,若抽取的两个项目测试都合格或都不合格时,不再参加第三个项目的测试;若抽取的两个项目只有一项合格,则必须参加第三项测试.
已知甲同学跑、跳、掷三个项目测试合格的概率分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
(1)求甲同学恰好先抽取跳、掷两个项目进行测试的概率;
(2)求甲同学经过两个项目测试就能达标的概率;
(3)若甲按规定完成测试,参加测试项目个数为X,求X的分布列和期望.
您最近一年使用:0次
2022-04-08更新
|
517次组卷
|
2卷引用:重庆市云阳江口中学校2022届高三上学期期末数学试题
名校
解题方法
8 . 已知圆
,直线
.
(1)求圆
的圆心坐标和半径;
(2)若直线
与圆
相切,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4927e8d705a7d54894e0abceda1d5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a8eae05beab5bfc6d7e74c4d573bd4.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2022-12-29更新
|
322次组卷
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3卷引用:重庆市云阳凤鸣中学校2022-2023学年高二上学期期末数学试题