名校
1 . 在
中,
,
,
与
交于点
,
,
,用
和
表示
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb4713985fd15713e52c5001059345c.png)
______ ;过点
的直线
交
,
于点
,
,设
,
(
,
),则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e7376fefe18d435f4adbb6226d7aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f09a9d6f118c19854f944a8a258b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb4713985fd15713e52c5001059345c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70fa908112806dc176b8abdc3b3aaa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a93a467f11c29aa3ec6124398b1c5a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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名校
2 . 在
中,M是边BC的中点,N是线段BM的中点.设
,
,试用
,
表示
为______ ,若
,
的面积为
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f386f5b56b07b96f2600da1be15414a1.png)
![](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/8962b0c33df0302e741501c1491bf643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32220fd969663f42cd619f8cc8b355c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6f0e94393fc6bbd9b4b83ede534ac.png)
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解题方法
3 . 设实数
满足
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af2d38cf365e4389c0d3f18ecfa890e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b97818db86c5b893eee3bc4365f1184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ad49024afac575989a816db7592bd0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
4 . 已知正实数m,n,满足
,则
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb86fe293191e92233b879cdaad341b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26da2191b66fee9b260a21b37e53d183.png)
您最近一年使用:0次
2023-06-14更新
|
1461次组卷
|
4卷引用:天津市滨海新区塘沽第一中学2023届高三三模数学试题
5 . 在
中,
,
,记
,用
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6b56918d5b5d82ee166dee0889874d.png)
_________ ;若
,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c801026e1446b8b7f1ea8f59dd8da1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91751034826c4e3435c8a7e5c16c4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ba495e8f9fe02229a4248fdbfb4710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eea45a8f50799dbe8ac66d5b920cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6b56918d5b5d82ee166dee0889874d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c21a8c8f5987d350cbab0d56d9bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59809f2fa9ce4c833cdf5fe102feb8d8.png)
您最近一年使用:0次
2023-06-08更新
|
13866次组卷
|
24卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷1
天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷12023年天津高考数学真题专题04平面向量与不等式(成品)(已下线)2023年天津高考数学真题变式题11-15上海市育才中学2024届高三上学期10月调研数学试题(已下线)第02讲 平面向量的数量积及其应用(练习)(已下线)【一题多变】 巧用换元 均值显灵(已下线)模块6 平面几何篇 第1讲:向量合成定理与三角形四心【练】(已下线)模块6 平面几何篇 第3讲:平面向量的范围问题【练】(已下线)模块5 周期变化篇 第5讲:三角形中的最值范围问题【练】(已下线)模块6 平面几何篇 第2讲:向量的数量积与极化恒等式【练】(已下线)模块5 周期变化篇 专题4:解三角形以及实际应用【练】(已下线)第2讲:不等式的解法与性质、基本不等式【练】(已下线)考点4 平面向量的范围问题 --2024届高考数学考点总动员【讲】(已下线)1.3 不等式(高考真题素材之十年高考)专题05平面向量与复数专题04平面向量(已下线)模块五 专题3 期末全真拔高模拟3(已下线)模块一 专题1 向量数量积的范围问题(已下线)模块一 专题1 向量数量积的范围问题(高一人教B)湖北省武汉市部分重点中学2023-2024学年高二上学期9月阶段性检测数学试题天津市津衡高级中学2023-2024学年高一下学期第一次(3月)质量检测数学试题(已下线)第20题 平面向量最值范围,解法灵活数形为本(优质好题一题多解)四川省成都市成飞中学2023-2024学年高一下学期5月月考数学试题
解题方法
6 . 已知
,
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bdc8d2686a05f12a2ba8a7e3b01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1dcfaae797d253d74badcad68bd9980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e2397c5f3a1f04b2efab36a68ff6298.png)
A.4 | B.6 | C.8 | D.10 |
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名校
7 . 在
中,点
满足
,若线段
上的一点
满足
(
,
),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68bb85ea6aa8aa2efa116edcdeb15cd.png)
__________ ,
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f40e60892ec7dbc55d0251584a5c81e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36965c4fa2678fe61578db7f38ac37c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68bb85ea6aa8aa2efa116edcdeb15cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05743d5fc1671f25464dea7073a31e29.png)
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2023-05-20更新
|
258次组卷
|
2卷引用:天津市滨海新区田家炳中学2023-2024学年高三上学期期中考试数学试题
8 . 已知数列
满足
,
,令
,设数列
前
项和为
.
(1)求证:数列
为等差数列;并求数列
的通项公式;
(2)若存在
,使不等式
成立,求实数
的取值范围.
![](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/e89bddd9c021a9caccc72cd0189e1ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.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)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb3185977be193745f403547d1e9800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c00e421d661234aea679759d5fc64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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名校
9 . 平面四边形
中,
,
,
,
,
,点
在直线
上,点
在直线
上,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13a6d893fc9e66d39ec5e15f13224b4.png)
,
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f461f7dcbb83261ee131c959e2a199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13a6d893fc9e66d39ec5e15f13224b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f334b95af405ecc4d4d7385a895732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221a7aadd90eff6787dcd3734c1cd22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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名校
10 . 在
中,
为
的中点,
,过点
任作一条直线,分别交线段
、
于
、
两点,设
,
,若用
、
表示
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea710df180d840bacf40404075be89e.png)
__________ ;若
,
,则
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae15e429b1f97e484c2669954d2d66f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad2785c82f621c4b807bb9a2493c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a6facc3f8956c8fea30f60455804f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0735144f6e24b6b32028ff14c17c1cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea710df180d840bacf40404075be89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eacdc33a7a86911a9de1e896fd333a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345adbdcf430d08466e215db7d0edb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0946479c941fbedaec12db71df4db991.png)
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2023-03-24更新
|
1221次组卷
|
3卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷3