名校
解题方法
1 . 在
中,
为边
上两点,且满足
,
,
,
,
;
(2)求证:
为定值;
(3)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cc2450dc300ce26b513c2abae28cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb08f6a798dc293f3d8de281190f65e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f341b98caabf99bc683ce8407068735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c5c9cc1ed4bce98b7fae77e70b227f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449771e8910f45e2757cec3211a256c7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea79586df2029edb34c7cb2f67dc3722.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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|
802次组卷
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5卷引用:福建省福州第一中学2023-2024学年高一下学期4月第三学段模块考试数学试题
福建省福州第一中学2023-2024学年高一下学期4月第三学段模块考试数学试题河北省沧州市泊头市第一中学2023-2024学年高一下学期5月月考数学试题(已下线)专题02 高一下期末真题精选(1)-期末考点大串讲(人教A版2019必修第二册)江苏省南京外国语学校2023-2024学年高一下学期5月阶段性测试数学试题山东省枣庄市第三中学2023-2024学年高一下学期6月月考数学试题
名校
解题方法
2 . 对于数集
,其中
,
,定义向量集
,若对任意
,存在
使得
,则称
具有性质
.
(1)判断
是否具有性质
;
(2)若
,且
具有性质
,求
的值;
(3)若
具有性质
,求证:
且当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc74f637a475398749159a361026793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3fe482c5e20abfc9f89c876f653ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ef0ee89b74da72ed80e51b06788cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec1c65f144bd63ed516e001e57852de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f923fcc615e579b8dda937faa9fa40c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01243e3fb9bd7a7711a593f5395b06cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee021c7c1a5df78501eaca655726212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f63c40ece6a988e75c73eb8ab1c626b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551ee6e86b2c6e79236dfe3e2e2c24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346549f9adda7eb363f16d355ae68b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
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2024-04-29更新
|
357次组卷
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7卷引用:北京市第一六六中学2021-2022学年高一下学期期中考试数学试题
3 .
个有次序的实数
所组成的有序数组
称为一个n维向量,其中
称为该向量的第
个分量.特别地,对一个n维向量
,若
,
,称
为n维信号向量.设
,则
和
的内积定义为
,且
.
(1)写出所有3维信号向量;
(2)直接写出4个两两垂直的4维信号向量;
(3)证明:不存在14个两两垂直的14维信号向量;
(4)已知
个两两垂直的2024维信号向量
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de4e0337716e1d89eb1a6cfd7b8335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e51ca089ee13a138e985e20f1b7b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43d0d6f87afa8b4fd5f6cf81f2bdcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da796531c7b6c590a22b811df1fcef53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293e6a784d135c77e3bded6f48f6eec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6be373930634c9aa53fec30bec8896.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/ea2978e42bc0f5abe31fe2536969afa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c7c807358869b70becd16ca80e1714.png)
(1)写出所有3维信号向量;
(2)直接写出4个两两垂直的4维信号向量;
(3)证明:不存在14个两两垂直的14维信号向量;
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9cae65660b220cc622b87ed9eea092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
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名校
4 . 函数
的最小正周期为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd76433be5ab044ab54d5561e5795bc.png)
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5 . 已知k是正整数,且
,则满足方程
的k有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbef345705fbe5c6b8276e726db9c0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4a1b10c239c9ac0934679337b375fb.png)
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解题方法
6 . 三角形的布洛卡点是法国数学家、数学教育学家克洛尔于1816年首次发现,但他的发现并未被当时的人们所注意.1875年,布洛卡点被一个数学爱好者布洛卡重新发现,并用他的名字命名.当
内一点
满足条件
时,则称点
为
的布洛卡点,角
为布洛卡角.如图,在
中,角
所对边长分别为
,点
为
的布洛卡点,其布洛卡角为
.
.求证:
①
(
为
的面积);
②
为等边三角形.
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec15e5cb6d4dc2cf6ba0bedd87514448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7b9d9bf0d5fc25c99170ab27fa4045.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa010342528037783c29e6fc705d5bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6492fa033f83d0775b049476612b86ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e02df6f963e47a894cce8b4ad469ec.png)
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2024-04-24更新
|
641次组卷
|
3卷引用:江苏省常州市教育学会2023-2024学年高一下学期4月学业水平监测数学试题
名校
7 . 函数
的图象关于坐标原点成中心对称图形的充要条件是函数
为奇函数,有同学发现可以将其推广为:函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数.已知函数
.
(1)若函数
的对称中心为
,求函数
的解析式.
(2)由代数基本定理可以得到:任何一元
次复系数多项式
在复数集中可以分解为n个一次因式的乘积.进而,一元n次多项式方程有n个复数根(重根按重数计).如设实系数一元二次方程
,在复数集内的根为
,
,则方程
可变形为
,展开得:
则有
,即
,类比上述推理方法可得实系数一元三次方程根与系数的关系.
①若
,方程
在复数集内的根为
,当
时,求
的最大值;
②若
,函数
的零点分别为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684eae051519f6aba934423a7182fa0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018e805194ffdc598b05f066b3ea6ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3279d65343e1b0bcdf8aed2d8522df0d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257dd4ddacb8667a761be897568f3674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)由代数基本定理可以得到:任何一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd7cf9e14c5762b28e2b626ee5a7c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad4bce39424043f2693a5f49f48d85e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7096476deb4b0b86a15c66856b93ba79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c9080eed5461a719145aa1e768c6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad2afb260459e1708cd3b619f1f5a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15e691d7c439329b7c74ae0bc678ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8824ecc19d6daa94cb22ea94716296d6.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb291880ef86317d079c0e0b349403e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0150d1fd43abcd4894550d40c5ac9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bc4081a1bbf3e7b0a1c856975a0b9e.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87f1b2ac4c09de232650533da16a300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b00232b29c9fe2cc1b3f8bcb4dcaad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c1d26e119ff006209f50b5326fc3bb.png)
您最近一年使用:0次
名校
8 . 已知集合
,对于
,
,定义A与B的差为
,A与B之间的距离为
.
(1)直接写出
中元素的个数,并证明:任意
,有
;
(2)证明:任意
,有
是偶数;
(3)证明:
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb64b23cfbc03c6ac0372a87bf81e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0135cb7ffda469b422df0aa1817d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c76f1774902da4c8da18791b5a35c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f960a435af66d6f53c96cf5d0d7ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e77ba8c90d21237670483bbcd8ac63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a0663324985d2901305e58b066e763.png)
(2)证明:任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81345ca73b711411e665820b5672913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639d6bbfe09dcd8af9c993a086b25105.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5318f129bfbfca89f51c03144251ce79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac18fa333be06b2ba3711b0c7171913.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在棱长为1的正方体
中,
为平面
内一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若![]() ![]() ![]() ![]() |
B.平面![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.对于给定的点![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-18更新
|
1680次组卷
|
3卷引用:广东省东莞市东华高级中学、东华松山湖高级中学2023-2024学年高一下学期期中教学质量检查(二)数学试题
名校
解题方法
10 .
的内角A,B,C的对边分别为a,b,c,已知
,点D在AC上,且
,
.
(1)求角B;
(2)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937594aeca6ecbbb2800fb6e150e7525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f157aab917082b835f4213ed81a3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
(1)求角B;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-04-17更新
|
738次组卷
|
3卷引用:新疆乌鲁木齐市第十九中学2023-2024学年高一下学期第一次月考数学试卷
新疆乌鲁木齐市第十九中学2023-2024学年高一下学期第一次月考数学试卷(已下线)专题05 解三角形大题常考题型归类-期期末考点大串讲(人教B版2019必修第四册)湖南省永州市部分学校2023-2024学年高一下学期6月质量检测卷数学试题