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1 . 已知点
,点
是
内(包含边界)一动点,请你结合所学向量的知识,求出
的最大值为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d15519119f08636c1e7425418d30b39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcda62388ba3f9747413103bd48e1630.png)
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2 . 定义向量
的“伴随函数”为.
函数.
的“伴随向量”为 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a854b25cf3b9e8e29344c273fbcf0da.png)
(1)在
中,已知
点M 为边AB上的点,且
求出向量
的“伴随函数”
, 并直接写出
的最大值
;
(2)已知向量
函数
求函数
的“伴随向量”
的坐标;
(3)已知
向量
的“伴随函数”分别为
、
, 设
且
的“伴随函数”为
,其最大值为m. 求证: 向量
的充要条件为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b7fac7580249609cae6e1661f46603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a7ac204567c63bb09f9f77eccb4f33f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a854b25cf3b9e8e29344c273fbcf0da.png)
(1)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f700c81072d62ea8dab79827fe079ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118155f8e69b4357c10c268e1626e1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.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/ac047e91852b91af639feec23a9598b2.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c97a2082d6f10ee9f1f9fdfcb40357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dce7cf69b669aed4b8cfc79abf4e302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d48e306c486d1a8d5c94babc242e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5b3d769fd3c7f81cdf25971039e9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1494c135e3724ebeb35aa2c0e1bf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce3b04d127bd23abc88cdd77d091a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99586040e486554f9a561c6a1567c10.png)
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3 . 在通用技术课上,老师给同学们提供了一个如图所示的木质正四棱锥模型
,点E在棱PB上,满足
, 点F在棱PC上,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5903fee1829219bc74dac66cc9c539d.png)
要求同学们按照以下方案进行切割:
平面
,并说明理由;
(2)过点A,E,F的平面α交PD于点H,沿平面α平将四棱锥模型切割成两部分,在实施过程中为了方便切割,需先在模型中确定H 点的位置;
①请求出
的值;
②若正四棱锥模型
的棱长均为6,求直线
与平面α所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae488b3296fac8508330bc4e3bda5c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5903fee1829219bc74dac66cc9c539d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90131175c3fb6a3837a22d7d5bbc268d.png)
(2)过点A,E,F的平面α交PD于点H,沿平面α平将四棱锥模型切割成两部分,在实施过程中为了方便切割,需先在模型中确定H 点的位置;
①请求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019c01a933a1844d9a7909e7bcf1b103.png)
②若正四棱锥模型
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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4 . 如图,矩形
中,
,
,
为边
的中点,沿
将
折起,点
折至
处(
平面
),若
为线段
的中点,平面
与平面
所成二面角
,直线
与平面
所成角为
,则在
折起的过程中,下列说法正确的是()
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8588e18e27bfebf7c81c7e3c7efb1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483f030abf61c6a0882d656d63cf4512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483f030abf61c6a0882d656d63cf4512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
A.存在某个位置,使得![]() |
B.![]() ![]() |
C.![]() |
D.三棱锥![]() ![]() ![]() |
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5 . 已知函数
,定义
表示不超过
的最大整数(如
).
(1)若
在
上单调递增,求实数
的取值范围;
(2)已知当
时,
有唯一极大值
,此时令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
. 对
,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53219f63721ef5731f5b1e07ffc6303d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54a0e82778f606d95a486835ac9f56.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521976f4b831d5e16926de504af83567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f429e3b5f3e5fa07ac120ce42aacdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4761151a69551a7fed269fa9fe992a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3b2f14e4591a5c15ef0ee73aade7bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 已知点
是圆
上一动点,点
,线段
的垂直平分线交线段
于点
.当点
运动时,设点
的轨迹为E.
(1)求点
的轨迹方程;
(2)已知过点
的直线
分别交E于
和
,且两直线的斜率之积为1,设
的中点分别为
,探究
轴上是否存在定点
,使得
,若存在,求出定点;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f9dc1bbc5193d7c1e6a2bc1f459990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996dadd8544543637bd2d32a1f79579e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0235e0e72a28b90c4abe7b84f3dfa9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b1a8ebfbce5db9fe9d0e2c8b9598c7.png)
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7 . “
数”在量子代数研究中发挥了重要作用.设
是非零实数,对任意
,定义“
数”
利用“
数”可定义“
阶乘”
且
和“
组合数”,即对任意
,
,根据上述定义,以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f76e5c4f5d0373dc716b113881ee5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f76e5c4f5d0373dc716b113881ee5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0dee336ed12a9b1b273d7fada509737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f76e5c4f5d0373dc716b113881ee5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f76e5c4f5d0373dc716b113881ee5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c995f040779bdf8fd8086b8e0cdc2dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68166431e6d8d78213cf1c19b8c9e7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f76e5c4f5d0373dc716b113881ee5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c7ba785351ac3d88c79e05bcbf484e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f396c36366fa0f636ae68bcdeac787d.png)
A.![]() |
B.对任意![]() |
C.对于任意![]() ![]() |
D.即对任意![]() ![]() |
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8 . 已知点
在圆
上,点
是直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
上一点,过点
作圆
的两条切线,切点分别为
、
,又设直线
分别交
轴于
,
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b31422fa6d9a8461a4c0ac344cd6ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ca1a0c83eb6a2058ae381c5775830a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
A.![]() ![]() | B.直线![]() |
C.满足![]() | D.![]() ![]() |
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9 . 已知函数
.
(1)当
时,求函数
的极值;
(2)讨论函数
的单调性;
(3)当
时,记
的最小值为
,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca155e2035d82dbc165b419426a337f9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2ac429737efebf150a1bd088ba846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4f6be791e028adc74128d9404b7255.png)
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2024-04-15更新
|
621次组卷
|
2卷引用:广东省中山市华侨中学2023-2024学年高二下学期第一次段考数学试题
10 . 为丰富同学的课余生活,学校开设了形式多样的选修课程.某班级学生进行选课,为达学分要求,每位同学需要在6个课程中任选3个.因特殊原因,有5位同学委托班长帮忙选课.已知各课程缺额人数如下表(缺额人数总和恰好为15),且甲同学要求选择C课程,乙同学要求选择E课程,其余同学无要求.
则在满足甲、乙要求的情况下,这5位同学选课的可能情况共有________ 种(用数字作答).
课程 | A | B | C | D | E | F |
缺额人数 | 0 | 3 | 4 | 2 | 1 | 5 |
您最近一年使用:0次
2024-04-15更新
|
180次组卷
|
2卷引用:广东省中山市华侨中学2023-2024学年高二下学期第一次段考数学试题