名校
1 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)讨论
的单调性;
(2)当
时,以
为切点,作直线
交
的图像于异于
的点
,再以
为切点,作直线
交
的图像于异于
的点
,…,依此类推,以
为切点,作直线
交
的图像于异于
的点
,其中
.求
的通项公式.
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10baf6f91bdd98c34b2a6d2daa8a5941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cdcb07faea873c3806619ee80ed50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4c4437b7525abf772d03c9214af20e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5abd8e8b1d06e38b1bdfb694537d1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d519c9c36247cadf8836b7a47cd637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f88b8f344f9d62ea2343eaa3316786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e20deff6168833a0482f854017e87c.png)
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解题方法
2 . “费马点”是由十七世纪法国数学家费马提出并征解的一个问题,该问题是:“在一个三角形内求作一点,使其与此三角形的三个顶点的距离之和最小”.如图1,三个内角都小于
的
内部有一点
,连接
,求
的最小值.我们称三角形内到三角形三个顶点距离之和最小的点为费马点.要解决这个问题,首先应想办法将这三条端点重合于一点的线段分离,然后再将它们连接成一条折线,并让折线的两个端点为定点,这样依据“两点之间,线段最短”,就可求出这三条线段和的最小值.某数学研究小组先后尝试了翻折、旋转、平移的方法,发现通过旋转可以解决这个问题,具体的做法如图2,将
绕点
顺时针旋转
,得到
,连接
,则
的长即为所求,此时与三个顶点连线恰好三等分费马点
的周角.同时小组成员研究教材发现:已知对任意平面向量
,把
绕其起点沿逆时针方向旋转
角得到向量
.
,把点
绕点
沿顺时针方向旋转
后得到点
,求点
的坐标;
(2)在
中,
,借助研究成果,直接写出
的最小值;
(3)已知点
,求
的费马点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b861d6d1f1d0b9f52b041cb40eb62.png)
![](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/19bb1063e139610045f3bca5ca0b2766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ed53a398b1d6b7b4abbb43a9abcf1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f850c705372b8a85489505da53239fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5643311f49a8c6f64b2a2788f79458e4.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/5f478a74bccc9b8d7745b08c5484f238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89756ef947f1add6a68efa8998430dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de03fc9682ff77d327a5681010ab3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11bf8ee11289d13cf5dd0ea9505e699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ed53a398b1d6b7b4abbb43a9abcf1f.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a65f35281b21fdfaf7c437fbd321eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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今日更新
|
219次组卷
|
2卷引用:四川省广元市川师大万达中学2023-2024学年高一下学期6月月考数学试题
名校
3 . 已知函数
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda318adf65c6b6fd45f651365f52346.png)
(1)求
的最大值
(2)写出
与
的大小关系,并给出证明
(3)试问
能否作为
三边长?若能,给出证明,并探究
的外接圆的半径是否为定值?若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda318adf65c6b6fd45f651365f52346.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b692262286e03cc0536598789fab8699.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fd5c1ef0fc722337a4984834829c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7bb46b41cd3f1f9b5621c20bf7fe07.png)
(3)试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b799aaa36edd0d10fc38925ce2e55045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
昨日更新
|
178次组卷
|
3卷引用:江苏省江都中学、江苏省高邮中学、江苏省仪征中学2023-2024学年高一下学期5月联合测试数学试卷
江苏省江都中学、江苏省高邮中学、江苏省仪征中学2023-2024学年高一下学期5月联合测试数学试卷福建省泉州市安溪第八中学2023-2024学年高一下学期6月份质量检测数学试题(已下线)作业02 三角恒等变换-【暑假分层作业】(苏教版2019必修第二册)
4 . 已知函数
,
.
(1)当
时,求函数
的在点
处的切线;
(2)若函数
在区间
上单调递减,求
的取值范围;
(3)若函数
的图象上存在两点
,
,且
,使得
,则称
为“拉格朗日中值函数”,并称线段
的中点为函数的一个“拉格朗日平均值点”.试判断函数
是否为“拉格朗日中值函数”,若是,判断函数
的“拉格朗日平均值点”的个数;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595e513cd2f3cf78c51ec868fd8b32a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a89be1009f96de083175f681f6ae1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f8dca2e85a1231ca1a20d5e35739cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
解题方法
5 . 对给定的实数a,b,q,其中
,
.如果函数
,
:满足(1)对任意的
,
且
;(2)对任意的
,
.则称
为在区间
上的一个“q-压缩函数”.区间
上所有“q-压缩函数”构成的集合记作
.
(1)判断下列函数,是否属于集合
?(直接写出结论)
①
②
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80e8d2d66b432fd2b8a2830ba21e5dd.png)
(2)设
,若
求实数a的取值范围.
(3)设
.若对任意的
,
,均有
,求M的最小值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae99e050d0f1cfc0447304f06424d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e207cf62e3a7e282eac4c4a3455bbf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48318c1b3f9dffc48e3ce0626b277e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664c92988d61280ed12488f270151940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a8b4f05d2ba1a5514ebf390dbbd325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a293e0b4f751f4102c795b567a633194.png)
(1)判断下列函数,是否属于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c564b7a711c6ac5945a0d41b2564c8.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a740cdaca0afce73f68c890f86acc6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef72cf8297d91045117d50b4e9d3476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80e8d2d66b432fd2b8a2830ba21e5dd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0e64d809acabedccf8a8516ff8b6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c109bacd687055d3a6a79978dfa7c0e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e39b23fb1290ed449f1700c42c3efc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcd04b625189228b6d697edf095f7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c97169936ca9785dfca39ca368c65c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0aa28b363cb79e6f8988b9b2bad7dc.png)
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名校
6 . 射影几何学中,中心投影是指光从一点向四周散射而形成的投影,如图,光从
点出发,平面内四个点
经过中心投影之后的投影点分别为
.对于四个有序点
,若
,
,定义比值
叫做这四个有序点的交比,记作
.
时,称
为调和点列,若
,求
的值;
(2)①证明:
;
②已知
,点
为线段
的中点,
,
,求
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fc2a215a63f1846cdc94cc0260d4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcda6a2a013e61f30eac744d57ab86fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9440bcb5362e00e5a6b4af27940b3007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a881d00bcb6fcdc1029c55898c464d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c84057882768f20a01365c81b6760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e839a2f596ac7266b6ff41a35c4a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274f162e5e5a9d358342ddbe2b6c1519.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73966616bd0b56416b4089a6dc884347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5ed371ae0038e0d5d2717418869b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70bcf4326b5da2c4cf1caf567b55d1a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb0c703f6effcbcf1770569971b3cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34da8e5ecc3d124fd1455c8a18bd45a.png)
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名校
解题方法
7 . 在平面直角坐标系中,点
在运动过程中,总满足关系式
.
(1)求点
的轨迹
的方程;
(2)过点
作两条斜率分别为
的直线
和
,分别与
交于
和
,线段
和
的中点分别为
,若
,证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62b58e1ce45cfd3fe723345eaf411f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17aa130296d594a23b0a7a864fc33320.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3b260036958c271fee22820b05fdb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f5fac15de56be6dfb7ba2429b54cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d762c4e0c2e788c94066aeea1530f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227c1d105f7abf228e7a4f3097ae93f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2026c8a047f60c7b84f4078466dcce6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077aaf808a6243d4af30a3eb9320fb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
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2024-06-21更新
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114次组卷
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4卷引用:河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
名校
解题方法
8 . 记
.
(1)若
,求
和
;
(2)若
,求证:对于任意
,都有
,且存在
,使得
.
(3)已知定义在
上
有最小值,求证“
是偶函数”的充要条件是“对于任意正实数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80225e12934cd8d4ffc73d5fad815d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1b9f62690647a1597f4000ad5a64b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c8381377b90826897eb4bf16cb3bae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28034dcafe542a98d95d4504ad7d8a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4def7108b0a2338f07a0143b00b48271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3761d7ab4d00c91177fdbde67af36089.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625e9d3c298a595678933b59583632c2.png)
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名校
9 . 为应对新一代小型无人机武器,某研发部门开发了甲、乙两种不同的防御武器,现对两种武器的防御效果进行测试.每次测试都是由一种武器向目标无人机发动三次攻击,每次攻击击中目标与否相互独立,每次测试都会使用性能一样的全新无人机.对于甲种武器,每次攻击击中目标无人机的概率均为
,且击中一次目标无人机坠毁的概率为
,击中两次目标无人机必坠毁;对于乙种武器,每次攻击击中目标无人机的概率均为
,且击中一次目标无人机坠毁的概率为
,击中两次目标无人机坠毁的概率为
,击中三次目标无人机必坠毁.
(1)若
,分别使用甲、乙两种武器进行一次测试.
①求甲种武器使目标无人机坠毁的概率;
②记甲、乙两种武器使目标无人机坠毁的数量为
,求
的分布列与数学期望.
(2)若
,且
,试判断在一次测试中选用甲种武器还是乙种武器使得目标无人机坠毁的概率更大?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5db9fa0bc36e2308bd3eecd5e78351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9f0aaaa2695dff4b08d7a52e4c905e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29be23f689eb01e57963495377501257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66577f4cb97c0d2a213ab1a9a02d1324.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f98df968dec4cb1b7e44cb47a5c216.png)
①求甲种武器使目标无人机坠毁的概率;
②记甲、乙两种武器使目标无人机坠毁的数量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f2beb272e7c3342233f5cb681ac24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b70d4a3fc3e01b5a6358cf4e57578e6.png)
您最近一年使用:0次
2024-06-19更新
|
792次组卷
|
3卷引用:山东省菏泽第一中学人民路校区2024届高三下学期5月月考数学试题
名校
解题方法
10 . 2024年初,冰城哈尔滨充分利用得天独厚的冰雪资源,成为2024年第一个“火出圈”的网红城市,冰城通过创新营销展示了丰富的文化活动,成功提升了吸引力和知名度,为其他旅游城市提供了宝贵经验,从2024年1月1日至5日,哈尔滨太平国际机场接待外地游客数量如下:
(1)计算
的相关系数
(计算结果精确到0.01),并判断是否可以认为日期与游客人数的相关性很强;
(2)请根据上表提供的数据,用最小二乘法求出
关于
的线性回归方程;
(3)为了吸引游客,在冰雪大世界售票处针对各个旅游团进行了现场抽奖的活动,具体抽奖规则为:从该旅游团中随机同时抽取两名游客,两名游客性别不同则为中奖.已知某个旅游团中有5个男游客和
个女游客,设重复进行三次抽奖中恰有一次中奖的概率为
,当
取多少时,
最大?
参考公式:
,
,
,
参考数据:
.
![]() | 1 | 2 | 3 | 4 | 5 |
![]() | 45 | 50 | 60 | 65 | 80 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d708cb763716467219215cdc0782c0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)请根据上表提供的数据,用最小二乘法求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)为了吸引游客,在冰雪大世界售票处针对各个旅游团进行了现场抽奖的活动,具体抽奖规则为:从该旅游团中随机同时抽取两名游客,两名游客性别不同则为中奖.已知某个旅游团中有5个男游客和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ea3a20cdf5915c2b51d0c401b9e834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609343476099195950454b8809930066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebff20f21ae41fd8d1f1e3145895842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62e7e496bab282e2475829358054202.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb3f35e3db7c1f3a3dd3eb20151b5f.png)
您最近一年使用:0次
2024-06-19更新
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1668次组卷
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3卷引用:甘肃省天水市第一中学2023-2024学年高二下学期第二学段检测考试(6月)数学试题
甘肃省天水市第一中学2023-2024学年高二下学期第二学段检测考试(6月)数学试题黑龙江省哈尔滨市第六中学校2024届(2021级)高三下学期四模数学试题 (已下线)高二数学下学期期末模拟--高二期末考点大串讲(苏教版2019选择性必修第二册)