名校
1 . 如图,在棱长为2的正方体
中,E,F,G分别是
,
,
的中点,点P在线段
上,
平面
,则以下错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f05389f5270a557638d69fc0b0f9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f475878dd1b32b0486cbf7b5ffbedd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
A.![]() ![]() ![]() | B.点P为线段![]() |
C.三棱锥![]() ![]() | D.平面![]() ![]() |
您最近一年使用:0次
解题方法
2 .
的内角
的对边分别为
已知
.
(1)若
的周长等于3,求
;
(2)若
为锐角三角形,且
;
①求
;
②求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c5353aa379b38ff11ce0e79200bd14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbedf6a68d2dd2ef0ca9faa7903d39a.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
3 . 点O是平面
上一定点,A,B,C是平面
上
的三个顶点,
,
分别是边AC,AB的对角.有以下四个命题:
①动点P满足
,则
的外心一定在满足条件的P点集合中;
②动点P满足
,则
的内心一定在满足条件的P点集合中;
③动点P满足
,则
的重心一定在满足条件的P点集合中;
④动点P满足
,则
的垂心一定在满足条件的P点集合中.其中正确命题的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
①动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194928662ef5170ec329fa0839e96810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f06ef8a11b1b7e4977bd57fbf89aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
③动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34459872490d5f5a616999415532470a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
④动点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b31a28180fdba611bcaedadbddd67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
名校
解题方法
4 . 在等腰梯形
中,
,
,
,点F在线段AB上且
.
(1)用
和
表示
;
(2)若点
为线段
上的动点,且
,求
的最大值;
(3)若点
为直线
上的动点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d318ccd750364557b52b8e2fd9e47eb0.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a754ad0537577221e7be168127d7cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc3c7d64ba3f82cb0853d6f674a1f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf814115dc9fea36cc1b6cd2b293390.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4262b00ecc79ba6235a0118138da4f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665dff688b01dadc549e0d354b836aa1.png)
您最近一年使用:0次
名校
解题方法
5 . 已知向量
;定义函数
,称向量
为
的特征向量,
为
的特征函数.
(1)设
,求
的特征向量;
(2)设向量
的特征函数为
,求当
且
时,
的值;
(3)设向量
的特征函数为
,记
,若
在区间
上至少有40个零点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9987768637e8aa2fe051499381acc3d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c6e203b4b2ddb496ba5e241140051d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7426e927be203401a7ea80f7e35e3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d806f27eecf5aee1e75bf35acbcd4c.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09853b4ab5476d41940f81de7985c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c5022fcadbebddb7be00d5a8d79c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a23ec821b5896710d79bfe703cec01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f5a04aef63712bb14cd11854ab79b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8c56d09485b718a85ed23f637e2d77.png)
(3)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b059c2d0041f3f0ae98e3995b723c289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354a3bc958749d6abbcfe8f29bc79773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
您最近一年使用:0次
2024-04-07更新
|
213次组卷
|
2卷引用:天津外国语大学附属河北外国语中学2023-2024学年高一下学期第一次月考数学试题
名校
解题方法
6 . 在
中,
,
,
为线段
上的动点不包括端点,且
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121d14d2024ab5479798521780f4b708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386eb659fda09b15da83566e79f20e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddfca740eeaeb1abe0ec1cf0b8043bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbcec5ae4d2e103fa77f2fd8b50bd873.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-29更新
|
1527次组卷
|
8卷引用:天津市第七中学2023-2024学年高一下学期3月月考数学试卷
天津市第七中学2023-2024学年高一下学期3月月考数学试卷广西壮族自治区贵百河联考2023-2024学年高一下学期4月月考数学试题福建省泉州市泉港区第一中学2023-2024学年高一下学期第一次月考(3月)数学试题(已下线)高一 模块3 专题1 第4套 小题进阶提升练(已下线)高一 模块3 专题1 第4套 小题进阶提升练(苏教版)江苏省盐城市东台市安丰中学等六校2024届高三下学期4月联考数学试题(已下线)【讲】专题7 解三角形与其它知识的交汇问题(已下线)【讲】 专题三 平面向量与其他知识的交汇问题(压轴大全)
名校
7 . 如图,将正四棱柱
斜立在平面
上,顶点
在平面
内,
平面
,点
在平面
内,且
.若将该正四棱柱绕
旋转,
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db768f2ad30b15e6d533056ee6332ea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e7842ec06f4f0c29b7ca67810e68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
2024-03-07更新
|
490次组卷
|
6卷引用:天津市耀华中学2023-2024学年高一下学期学科训练(二)数学试卷
名校
解题方法
8 . 在
中,M是边BC的中点,N是线段BM的中点.设
,
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
__________ ;若
,
的面积为
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a779e711b3900db89bd868360dcfaa.png)
__________ 时,
取得最小值.
![](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/fc51bdc8c2c18379db1affbb06f8923f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06393c604df2200ce9fd4bc9e67c2ab.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/c6a779e711b3900db89bd868360dcfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6f0e94393fc6bbd9b4b83ede534ac.png)
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2024-03-01更新
|
1447次组卷
|
6卷引用:天津市实验中学滨海学校2023-2024学年高一下学期随堂质量监测(月考)数学试题
天津市实验中学滨海学校2023-2024学年高一下学期随堂质量监测(月考)数学试题天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷(已下线)信息必刷卷04(天津专用)(已下线)2024年天津高考数学真题平行卷(提升)(已下线)第2套 新高考新结构全真模拟2(艺体生)(已下线)压轴题03不等式压轴题13题型汇总 -1
解题方法
9 . 已知函数
,若函数
有9个不同的零点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9b2815ca39ac04fec50b4f8287728b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a634207fbe456d614de64e66aab60dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 设函数
,若函数
恰有三个不同的零点,分别为
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a214e6e3def115dcaa9844866865e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9c82c1ec9a0ff6eec86178962285f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcee20976de0e0e8c1ccd7a951674691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd43286b58600b12e973f4c7b2b7e3f8.png)
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