2024·全国·模拟预测
1 . 已知
则方程
可能有( )个解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ce124fd5d9db9e0722ed1670efe4da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a5c5b2fcb512ee0bc8a9997bde1e47.png)
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2 . 已知实数
,满足
,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819060769d52da4b87df58dfd7490fdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3c5261469d69d9d079221a349be85.png)
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2024-05-12更新
|
1135次组卷
|
3卷引用:模块五 专题6 全真拔高模拟6(苏教版高二期中研习)
名校
解题方法
3 . 在锐角三角形
中,已知
,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b473ccb69f1341bd3c084da64d6e55b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f4e9bb8b453665bfe9b8fa24711cb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046387911745f43ff3b6804ea58eb26a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6105ce0cf660bbd473c3c7008dcd8cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc903c19f7b3b0aa58cdb0cdb7b062a0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . “0,1数列”在通信技术中有着重要应用,它是指各项的值都等于0或1的数列.设
是一个有限“0,1数列”,
表示把
中每个0都变为
,每个1都变为
,所得到的新的“0,1数列”.例如
,则
.设
是一个有限“0,1数列”,定义
.若有限“0,1数列”
,则数列
的所有项之和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e3d87be9f706832ef25537d78a201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823b15e6dc9fce202c3c57e7d18df0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f32df58be46198b2e7a112ed255d8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e502eff0c1fe80b2a546ea4af17a9755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde81bb00224b2a80ba56c6ce27b94a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36091df0a9c71ef14161ba59dbaa4230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374de27c75bc2269806d5b44d1518c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645ae0b78ad4ca300e3889ca3f9bcce.png)
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2024高三·全国·专题练习
6 . 已知函数
的定义域为
,且满足
(
为函数
的导函数),
,若存在
,使得
,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0180636f755be941a12f200d968f1b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfd98d2f6f0797bd5aee729b9cd680e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed2e7e1741062b0a3a20010b4ebcf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13b7c666b9a0745158fa5e9d8dc8fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 数列
满足
,
(
).
(1)计算
,
,猜想数列
的通项公式并证明;
(2)求数列
的前
项和;
(3)设
(
),数列
前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be815a472dbc3112591a3c311750b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109c4b28048ec9e72ba8ecd6311d9f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f87f83fa06ebdc980a6b307d7f54ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/86ea385391aa939b21c3ce2a1437fac4.png)
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解题方法
8 . 若实数列
满足
,有
,称数列
为“
数列”.
(1)判断
是否为“
数列”,并说明理由;
(2)若数列
为“
数列”,证明:对于任意正整数
,且
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97bb4c969108ebef4ebadd5acc5ca4.png)
(3)已知数列
为“
数列”,且
.令
,其中
表示
中的较大者.证明:
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fee3639b8e3ff9717f3ffd9633927f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8414472e2121e1796eb40408d820053a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f1bc95528c774ce919f7c5a0ef0d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d7e68d0c8bd9a32d826c721ab74d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e517c32ed93de4d9cb6e0926337000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce97bb4c969108ebef4ebadd5acc5ca4.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93846b72089bd425864969f2edabdb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8957564d30af14db69fdc36be2eaee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065f8a641aab5c39f73be89a6f2e7a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4dc7e8bd20e9d38b4d248a8c253ccd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8131eb05d480f0da6c61ebda3ce48.png)
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解题方法
9 . 在
中,角
、
、
的对边分别为
、
、
,若
,又
的面积
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0037c350daed54ed9a4d8f67c87c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2df1d745380af6b8305bfd345b2f455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759ee5f5ca252f6acce1aacea9d17fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92501bab17937ad492dfb8f1fb988a0a.png)
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2024-05-04更新
|
479次组卷
|
10卷引用:高一 模块3 专题1 第2套 小题进阶提升练
(已下线)高一 模块3 专题1 第2套 小题进阶提升练重庆市巴蜀中学校2023-2024学年高一下学期3月月考数学试题重庆市长寿中学校2023-2024学年高一下学期学段考试一(4月)试题(已下线)高一 模块3 专题1 第2套 小题进阶提升练1黑龙江省大庆市实验中学实验二部2023-2024学年高一下学期期中考试数学试卷山东省青岛市第五十八中学2023-2024学年高一下学期期中考试数学试题福建省南平市高级中学2023-2024学年高一下学期期中考试数学试题福建省南平高级中学2023-2024学年高一下学期期中数学试卷(已下线)专题04 解三角形小题常考题型归类-期末考点大串讲(人教B版2019必修第四册)重庆市清华中学校2023-2024学年高一下学期4月阶段测试数学试题
10 . 已知等比数列
的前
项和为
,
,且
成等差数列.
(1)求
;
(2)设
,
是数列
的前
项和,求
;
(3)设
,
是
的前
项的积,求证:
(
为正整数).
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae1fb6143a59cb6c6e4a2c838d98680.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26222fab28d45935efbeb96dccc9f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35926bf4b8e2c163c20942173cffcce.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6582a3657759ff3f6ae698edba3afd52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.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/be6dfd8c41024b1f33e2ace6af0c50d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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