名校
1 . 如图,在三棱柱
中,
平面
,已知
,
,
,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/84a21c80-1bfc-4df9-a527-6aa0cd4a8d66.png?resizew=164)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)在棱
上是否存在一点
,使得
与平面
所成角的正弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2771c7ab952986d5afcce9fa827042b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7932b50fa677dfcd8e3b5061a90c133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/84a21c80-1bfc-4df9-a527-6aa0cd4a8d66.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ad7c180d6d084ecb25f23cb6fe9b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914d46f7e72b55d2ff3d9bc38e02b31d.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914d46f7e72b55d2ff3d9bc38e02b31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0f4f8e3032f67e672b63791cc4d9df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7e6f1b753b73381b71eb5f8cc7da42.png)
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3卷引用:天津市咸水沽第一中学2024届高三上学期第二次月考数学试题
2 . 已知数列
的前
项和
是公比大于0的等比数列,且满足
.
(1)求
和
的通项公式;
(2)若数列
的前
项和为
,求证:
;
(3)对任意的正整数
,设数列
满足
,求数列
的前
项和
.
![](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/60bf54c01e156b315b1c9d3364ea2830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfe547380a8854f9544ed74cf358950.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ce93a537dd5f816d822ed7cd7cfc4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91760076292a3a227fa34834e880f1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
(3)对任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef8539a7a09303a95b4e79fb9949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3bafbbd939a48d5fcb8aa7a79f3e77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef8539a7a09303a95b4e79fb9949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
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4卷引用:天津市双港中学2022-2023学年高二上学期期末数学试题
天津市双港中学2022-2023学年高二上学期期末数学试题山东省滨州市2023-2024学年高三上学期期中数学试题山东省滨州市惠民县2024届高三上学期期中数学试题(已下线)第06讲:数列求和 (必刷5大考题+5大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
3 . 如图,
平面
,
.
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07013206f53d36de080c451a7a2a1266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411d1139c919736044af6379743b3d5c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/1de5508f-7c17-43b0-b503-4cd6edebedc8.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
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2023-09-26更新
|
560次组卷
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4卷引用:天津市双港中学2022-2023学年高二上学期期末数学试题
天津市双港中学2022-2023学年高二上学期期末数学试题(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版福建省福州市平潭县新世纪学校2023-2024学年高二上学期12月适应性练习数学试题(已下线)第02讲:空间向量与立体几何交汇(必刷6大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019选择性必修第一册)
名校
解题方法
4 . 在平面直角坐标系
中,已知椭圆
的长轴为4,过坐标原点的直线交
于
两点,若
分别为椭圆
的左、右顶点,且直线
与直线
的斜率之积为
.
(1)求椭圆的标准方程;
(2)若点
在第一象限,
轴,垂足为
,连
并延长交
于点
,
(i)证明:
为直角三角形;
(ii)若
的面积为
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求椭圆的标准方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae95e96ce568efee50145f8d017353df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a0a6891259bf27be2280c6b6ba7430.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a0a6891259bf27be2280c6b6ba7430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b282c337227aa697d420b8c3c8d4309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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2023-05-28更新
|
992次组卷
|
2卷引用:天津市咸水沽第一中学2023届高三押题卷(五)数学试题
名校
解题方法
5 . 已知函数
,其中
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
,
(i)证明:
;
(ii)判断函数
在
上的单调性,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc292b41b68cb16d0c048f566d2965e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4211f33625593f00e8bbea25362ef.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf46dc84732526c826d84a71c407ea89.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3176cd595cf999e7c8d4370cfffea8dd.png)
(ii)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34340ef0d177a645a631405eaa3592e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4396f093f90acdc9e5b2a2f7c48c7034.png)
您最近一年使用:0次
名校
6 . 如图,在三棱柱
中,平面
平面
,
是
的中点,且
.
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc7e6b6fe46c62e34f63893cf44e50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873a9ac1ef91b7f8edfed1df655cf1ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/1/92c8cff9-65fd-41c4-86b1-85f5502674ad.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfaad4c4467e27421876d8f2a4371d2.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfaad4c4467e27421876d8f2a4371d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
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2023-05-28更新
|
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4卷引用:天津市咸水沽第一中学2023届高三押题卷(五)数学试题
天津市咸水沽第一中学2023届高三押题卷(五)数学试题(已下线)专题1-3 空间向量综合:斜棱柱、不规则几何体建系计算(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)(已下线)模块二 专题2 利用空间向量解决不方便建立坐标系的方法 期末终极研习室(高二人教A版)(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 立体几何非常规建系问题 微点1 立体几何非常规建系问题(一)【培优版】
7 . 已知
是单调递增的等差数列,其前
项和为
.
是公比为
的等比数列.
.
(1)求
和
的通项公式;
(2)设
,求数列
的前
项和
.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cc6db65304d2424d93a1add0540da0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4aa026716a11f9f7c0a2339fba4ea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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
名校
解题方法
8 . 在
中,
.
(1)求
的值;
(2)求
的值;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2488ff2852166d09e1331e0c206569.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32f2d4d1d2c16c54b2caef17840bfcb.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c20c10cb27e8970fa04b52d35640f1.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在四棱锥
中,
底面ABCD,
,
,
,
,点E为棱PC的中点.
(1)证明:
;
(2)求直线BE与平面PBD所成角的正弦值;
(3)若F为棱PC上一点,满足
,求平面FAB与平面PAB所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba814113887c21637c1954f244812f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/a9ce548f-c184-427c-83eb-bd3dbfe2945e.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c38bbe49284a2ceab26001ced8cfd56.png)
(2)求直线BE与平面PBD所成角的正弦值;
(3)若F为棱PC上一点,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2a245381e615882ee5feb7793a1df6.png)
您最近一年使用:0次
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|
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|
2卷引用:天津市咸水沽第一中学2023届高考押题卷(一)数学试题
10 . 已知
是公比为q的等比数列.对于给定的
,设
是首项为
,公差为
的等差数列
,记
的第i项为
.若
,且
.
(1)求
的通项公式;
(2)求
;
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecea6aa3b0b367dbd8d0e38c65829c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac24dd2ff15d115696e8a9f8dad264f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c66a0c50c32fba396a322f0ddbeda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac24dd2ff15d115696e8a9f8dad264f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f686d89f95d2dc846e53eab5ca99ddde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33c0acaa66514a4f1493b158ebd09e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2608df648efc5364a2dc2c67cfe14cd9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27dd9877202542cc6975d5a4d78724a.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88b0922dc08ae6398dfc0296037c759.png)
您最近一年使用:0次
2023-05-20更新
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1157次组卷
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3卷引用:天津市咸水沽第一中学2023届高考押题卷(一)数学试题