名校
解题方法
1 . 已知数列
为等差数列,
是数列
的前
项和,且
,
,数列
满足
.
(1)求数列
、
的通项公式;
(2)令
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fcd86b9ed6819116a261629f96fae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cf0e722239dd3c7f44795f74aa6bf4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1796d3b3d59e53a318ced796ebda0538.png)
您最近一年使用:0次
2023-01-18更新
|
762次组卷
|
5卷引用:吉林省通化梅河口市第五中学2021-2022学年高二下学期开学考试数学试题
名校
解题方法
2 . 已知数列
中,
,其前n项和为
,
.
(1)求数列
的通项公式;
(2)设
,若数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f1c9bdfb252a71b1fc88d7f8082240.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5214360ac0152818f5b95b805f6e615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50048f2ab3c89aa1dd2ddb75df35b47f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c215db1d8f69757118ad405b78035628.png)
您最近一年使用:0次
2022-10-29更新
|
672次组卷
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4卷引用:吉林省通化市辉南县第六中学2022-2023学年高二上学期期中数学试题
吉林省通化市辉南县第六中学2022-2023学年高二上学期期中数学试题湖南省郴州市2022-2023学年高三上学期第一次教学质量监测数学试题江苏省南京市第一中学2022-2023学年高三上学期9月质量检测数学试题(已下线)4.3.1 等比数列的概念(第2课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)
名校
3 . 如图,三棱锥
中,
,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/049bcfd0-fa83-46d4-8cd5-f34db022679e.png?resizew=203)
(1)求证:
平面
;
(2)若点
在线段
上,直线
与直线
所成的角为
,求平面
与平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1777619bfe1167d487f3a8507fba7fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee98db8495cf1f203abe99795102e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069fb06e0428a1cb2b4ce4c17eeab7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c075a9952e8a47ae7a39fba0e5ec4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b1b01db19ea917c24cff42156a2412.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/049bcfd0-fa83-46d4-8cd5-f34db022679e.png?resizew=203)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e6956d407141c5d3a08f840ffa8b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b69099d2b74ffbb1f365e1468bd8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
2022-10-19更新
|
635次组卷
|
6卷引用:吉林省通化市辉南县第六中学2022-2023学年高二上学期期中数学试题
4 . 已知函数
.
(1)求
的单调区间;
(2)若
有两个不同的零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457c6fbb4596e9dd6c7739aca53a7a6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a415767156945ea8ada9ed3756019fc.png)
您最近一年使用:0次
2022-08-26更新
|
964次组卷
|
7卷引用:吉林省梅河口市第五中学2022-2023学年高三上学期开学考试数学试题
名校
5 . 如图,四边形
为菱形,
,
,平面
平面
,
,
,
,点
在线段
上(不包含端点).
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967162640728064/2973808589365248/STEM/500e26f6-644d-43fc-a61d-22c91ed5d3dc.png?resizew=229)
(1)求证:
;
(2)是否存在点
,使得二面角
的余弦值为
?若存在,则求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f36d315245b63a811d5c6f348c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda6866897c9d51d68798bb0466c5946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48248d557704ad9de4d0b52a8edd7a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967162640728064/2973808589365248/STEM/500e26f6-644d-43fc-a61d-22c91ed5d3dc.png?resizew=229)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1cb818977a967130ef41cd3f9f4fc6.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479b251fdb01bae6d16abb7f2d694a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34892d160c72edfc3d1e3f12adca89f.png)
您最近一年使用:0次
2022-05-06更新
|
1060次组卷
|
5卷引用:吉林省梅河口市第五中学2022-2023学年高三上学期开学考试数学试题
22-23高二上·江苏南通·开学考试
名校
解题方法
6 . 已知直线
与圆
.
(1)求证:直线l过定点,并求出此定点坐标;
(2)设O为坐标原点,若直线l与圆C交于M,N两点,且直线OM,ON的斜率分别为
,
,则
是否为定值?若是,求出该定值:若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ebf7674b0925e89edac36d86e84550e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77276d70a9e00ec4adb72b430985d888.png)
(1)求证:直线l过定点,并求出此定点坐标;
(2)设O为坐标原点,若直线l与圆C交于M,N两点,且直线OM,ON的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2022-09-05更新
|
1794次组卷
|
9卷引用:吉林省通化市辉南县第六中学2022-2023学年高二上学期期中数学试题
吉林省通化市辉南县第六中学2022-2023学年高二上学期期中数学试题(已下线)江苏省南通市如皋市2022-2023学年高二上学期期初调研数学试题江苏省宿迁市泗阳县实验高级中学2022-2023学年高二上学期第一次调研测试数学试题江苏省连云港市赣榆智贤中学2022-2023学年高二上学期第一次学情检测数学试题江苏省连云港高级中学2022-2023学年高二上学期第一次阶段测试数学试题江西省宜春市第十中学2022-2023学年高二上学期第一次月考数学试题(已下线)专题2.17 直线与圆的方程大题专项训练(30道)-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)江苏省盐城市滨海县东元高级中学、射阳高级中学等三校2022-2023学年高二上学期期中数学试题江苏省盐城市伍佑中学2022-2023学年高二上学期12月月考数学试题
名校
解题方法
7 . 在三棱锥
中,D,E,F分别为棱AB,CP,AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/f2544763-3ec2-4152-88e0-5c23e8876a7d.png?resizew=149)
(1)求证
∥平面DEF;
(2)若面
底面ABC,
,
为等边三角形,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/f2544763-3ec2-4152-88e0-5c23e8876a7d.png?resizew=149)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(2)若面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147de24f071e316b68fd2e78e3c84545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8243b46e0b4bd441e5fcffb29a8a49.png)
您最近一年使用:0次
2022-06-30更新
|
381次组卷
|
4卷引用:吉林省通化市部分重点中学校2021-2022学年高一下学期期末数学试题
吉林省通化市部分重点中学校2021-2022学年高一下学期期末数学试题(已下线)广西柳州铁一中学2021-2022学年高一5月月考数学试题山东省烟台市2019-2020学年高一下学期期末考试数学试题山东省烟台市2019—2020学年度高一第二学期期末学业水平诊断数学试题
8 . 已知函数
的定义域是
,若对于任意的
,
,当
时,都有
,则称函数
在
上为不减函数.现有定义在
上的函数
满足下述条件:
①对于
,总有
,且
,
;
②对于
,
,若
,则
.
试证明下列结论:
(1)对于
,
,若
,则
;
(2)
在
上为不减函数;
(3)对
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61c8d37c767ba727cc7f5f7e00a7d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e264b11a47db447a7a0a19f2c3b8900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
②对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d4d545db5f08ab066c08f621bdf83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7563ceaa2d4ae02f31d47b53708edc75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff755b55a86b26a7f3e7def591b5b315.png)
试证明下列结论:
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59387e75e13dce643d327893df0edfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa468658500142da664ca688d4d4d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096dd04098cafabf4211054353feec8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(3)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e511095b9802e0e54c3bcac8be160e58.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,正方形
和矩形
所在的平面互相垂直,
,
,
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/10abf3ff-e569-4b11-8802-8bdf95b1896b.png?resizew=196)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求平面
与平面
夹角的余弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/10abf3ff-e569-4b11-8802-8bdf95b1896b.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
您最近一年使用:0次
2022-01-22更新
|
401次组卷
|
2卷引用:吉林省通化市梅河口市第五中学2021-2022学年高二上学期期末数学试题
2021高二·江苏·专题练习
10 . 已知圆C:
关于直线
对称,且圆心在x轴上.
(1)求圆C的标准方程;
(2)若动点M在直线
上,过点M引圆C的两条切线MA,MB,切点分别为A,B.
①记四边形MACB的面积为S,求S的最小值;
②求证:直线AB恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/775d16d0308e646ce2285740b4b4e7b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512f4c29ff276b7f35052ad4cc255ab5.png)
(1)求圆C的标准方程;
(2)若动点M在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ff06692c025b869a7bcdcff15dca9e.png)
①记四边形MACB的面积为S,求S的最小值;
②求证:直线AB恒过定点.
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