1 . 已知函数
满足:对
,有
,若存在唯一的
值,使得
在区间
上单调递减,则实数m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e221ad8f28f138eac3d428051da7ace7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a6f10336eaca61cb1a302a76f5757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402fca14f868a8d8c23294ec2c21cf85.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 在
中,
,
,
为
内的一点,设
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8817091d0f4b7d7ac6df560cb63c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.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/36965c4fa2678fe61578db7f38ac37c3.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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3 . 给出定义:对于向量
,若函数
,则称向量
为函数
的伴随向量,同时称函数
为向量
的伴随函数.
(1)设向量
的伴随函数为
,若
,且
,求
的值;
(2)已知
,
,函数
的伴随向量为
,请问函数
的图象上是否存在一点
,使得
,若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c85e3f270228f575ce19d616ccc6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce34827ae0930934dc5a6f1d52acd5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
(1)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136d9091bebc9137052a129f6b2ce0a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b29cbe1cd5532afd6ae70d27be77bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca7583f1a94fb9e8101fbdb0570260d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad963e4119950b4762f513012b273a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df46b800478f98f9f7b4f4c51a90a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3439b741456cee344e7f9cbf2cc293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4cde2cd329c08d92abda7098137d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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4 . 几何表示酷似奔驰的标志得来,是平面向量中一个非常优美的结论.奔驰定理与三角形四心(重心、内心、外心、垂心)有着神秘的关联.它的具体内容是:已知
是
内一点,
,
,
的面积分别为
,
,
,且
.以下命题正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d011d6ad89d0b033f96c2efbb314d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e8ecb371ce77dca5554e8e03b41386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4b0c4b339f44bbac0e275eb0718234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319b6a5373bc8eb13772b8e6d047779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea3c7cd2f23b4521e64a7e64844ec48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e8a7f6c535fc3cd270af428d55f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf4b6e78e857749e0da486c5c4f0583.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
5 . 已知圆O的半径为1,直线
与圆O相切于点A,直线
与圆O交于B,C两点,D为
的中点.若
,则
的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70fa2c1e50403dd1cdd969d6308692eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992907998c85cf872f6e66df0b0c1030.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 如图,正方形ABCD的边长为1,P,Q分别为边BC,CD上的点,且
;
(2)求
面积的最小值;
(3)某同学在探求过程中发现PQ的长也有最小值,结合(2)他猜想“
中PQ边上的高为定值”,他的猜想对吗?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e50966267b44a653055ab15c490536.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
(3)某同学在探求过程中发现PQ的长也有最小值,结合(2)他猜想“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
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2024-03-29更新
|
534次组卷
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2卷引用:吉林省长春市第二实验中学2023-2024学年高一下学期4月月考数学试题
7 . 已知函数
在区间
上有且仅有一个零点,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa56e3fe8f51eccaa2f101b9bea083e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68d62482d548bcd517188178fd36bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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8 . 已知
,
均为锐角,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61b9cbe39e5cd38e0c046e26e5f1c31.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
9 . 已知向量
,
为单位向量,且
,向量
与
共线,则
的最小值为__________ .
![](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/d6607738f937c4226021bb3dc4e96159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31b07a2081bfaaf77c0062193ab173e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32024fbbcd5313513029e62ee90c04ff.png)
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2024-01-29更新
|
3165次组卷
|
4卷引用:吉林省长春市五校2023-2024学年高三上学期联合模拟考试数学试题
吉林省长春市五校2023-2024学年高三上学期联合模拟考试数学试题重庆市渝北中学校2023-2024学年高三下学期2月月考数学试题(已下线)第三套 新高考新结构全真模拟3(艺体生)(已下线)第15题 向量小题归类(高三二轮每日一题)
10 . 海水受日月的引力,在一定的时候发生涨落的现象叫潮.一般地,早潮叫潮,晚潮叫汐.在通常情况下,船在涨潮时驶进航道,靠近码头;卸货后,在落潮时返回海洋.已知某港口水深
(单位:
)与时间
(单位:
)从
时的关系可近似地用函数
来表示,函数
的图象如图所示,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a5277d8f-4c21-45c5-a889-05290b673f9c.png?resizew=207)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e185b692db47bcd945aa6e49ec48e249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933311c0c090e1138e4dd388b7adf8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136a11abcbdd648dc8e89fec1cac3253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe601394cbbce633fab7131738e5a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e185b692db47bcd945aa6e49ec48e249.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a5277d8f-4c21-45c5-a889-05290b673f9c.png?resizew=207)
A.![]() |
B.函数![]() ![]() |
C.当![]() ![]() |
D.已知函数![]() ![]() ![]() ![]() ![]() ![]() |
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