名校
解题方法
1 . 某考试分为笔试和面试两个部分,每个部分的成绩分为A,B,C三个等级,其中A等级得3分、B等级得2分、C等级得1分.甲在笔试中获得A等级、B等级、C等级的概率分别为
,
,
,在面试中获得A等级、B等级、C等级的概率分别为
,
,
,甲笔试的结果和面试的结果相互独立.
(1)求甲在笔试和面试中恰有一次获得A等级的概率;
(2)求甲笔试和面试的得分之和X的分布列与期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
(1)求甲在笔试和面试中恰有一次获得A等级的概率;
(2)求甲笔试和面试的得分之和X的分布列与期望.
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6卷引用:重庆市第四十九中学校、江津第二中学校等九校2023-2024学年高二下学期5月联考数学试题
名校
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
时,求
的零点;
(2)若
恰有两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5卷引用:重庆市第四十九中学校、江津第二中学校等九校2023-2024学年高二下学期5月联考数学试题
名校
解题方法
3 . 在圆锥PO中,AC为底面直径,
为底面圆O的内接边长为
的正三角形,点E为PC中点,且母线PC与底面圆O夹角为
.
(1)求证:平面
平面
.
(2)求二面角
的平面角的正弦值.
(3)在PO上是否存在点M,使得DM与平面
所成角为
,若存在,请求出所在位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e384e0ffc3d599303b77ee2a12221e.png)
(3)在PO上是否存在点M,使得DM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
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名校
4 . 代数基本定理:任何一个
次复系数多项式方程
至少有一个复根.由此可得如下推论:
推论一:任何一元
次复系数多项式
在复数集中可以分解为
个一次因式的乘积;
推论二:一元
次多项式方程有
个复数根,最多有
个不同的根.即一元一次方程最多有1个实根,一元二次方程最多有2个实根等.
推论三:若一个
次方程有不少于
个不同的根,则必有各项的系数均为0.
已知
.请利用代数基本定理及其推论解决以下问题:
(1)求
的复根;
(2)若
,使得关于
的方程
至少有四个不同的实根,求
的值;
(3)若
的图像上有四个不同的点
,以此为顶点构成菱形
,设
,
,求代数式
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b7bff9b2431134f7683a9cc4e68acd.png)
推论一:任何一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
推论二:一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
推论三:若一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14c686bfce270ec65d068555d1866ff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadabea3f5008d97a32382752e62bdd8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec4e65c4c043edef8084b292675395c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcecb855c13987b207aec2db73c9ec5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc04eee630e386f7be4ac709ff4e16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df74fc4cedb204eb6dcce64b706e99c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0c942fae0e9dd2d219ad8269511898.png)
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解题方法
5 . 在棱长为2的正方体
中,E,F,M,N分别为
,
,
,
中点.
(1)求证:
平面
;
(2)求直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e619f087b6b7ab764362b8b64b220cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc65c549059934e69355d8ecc245da57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f257d6a77d394ddca1f825559aadd5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3225b8916372c7e0e4d7b71b26571e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/17/8ea83e69-f4b4-44da-a585-6110ad87a320.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073a88b42836fb88433679932b48ad03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bdc4f7de61cf83503ccb8a81b36c47.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b686178c52fdf7ac270e75c0795417.png)
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解题方法
6 . 在△ABC中,
.
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575212f03d6cd6a84ddcf1c4c955324e.png)
(2)若M为BC上一点,
求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485688133c06eae9cb558df2f30f8c2a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575212f03d6cd6a84ddcf1c4c955324e.png)
(2)若M为BC上一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1649b4453e7a76485b8287e0f9bc5072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e8ecb371ce77dca5554e8e03b41386.png)
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解题方法
7 . 在
中,内角
所对的边分别为
,已知
,
.
(1)求
.
(2)若
为锐角三角形,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759e6d90078d6d79e68c55e39e118d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2129fc59f4fbcc28ac8ea3df9c550eac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
8 . 在
中,已知
,
,
分别为角
,
,
的对边.若向量
,向量
,且
.
(1)求
的值;
(2)若
,
,
成等比数列,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b6f33527b8b1f88f5a95d3ac7d7f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad48e851308f7753c3672143a8d84d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e260f0b2fb0cfe402df585d5cf1f629.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e563e032dfdef69b0f357060c27bd4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0190aba7ad7fb483aa3f07ab324016cb.png)
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2024-06-10更新
|
1030次组卷
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3卷引用:重庆市乌江新高考协作体2023-2024学年高二下学期第二阶段性学业质量联合调研抽测(5月)数学试题
重庆市乌江新高考协作体2023-2024学年高二下学期第二阶段性学业质量联合调研抽测(5月)数学试题广东省惠州市2024届高三下学期模拟考试(一模)数学试题(已下线)广东省阳江市2024届高三下学期5月模拟数学试题
名校
解题方法
9 . 任意一个复数z的代数形式都可写成复数三角形式,即
,其中i为虚数单位,
,
.棣莫弗定理由法国数学家棣莫弗(1667~1754)创立.设两个复数用三角函数形式表示为:
,
,则:
.如果令
,则能导出复数乘方公式:
.请用以上知识解决以下问题.
(1)试将
写成三角形式;
(2)试应用复数乘方公式推导三倍角公式:
;
;
(3)计算:
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a0f4e84ca890b19f1a2d39b9c4d6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826ff108f47b7dc4dd2e63e14c204a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34f45fe480fe6100c86a13db7ac652f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d74cc1db74efb3bf74930e0ca3621a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b20d6f11c0a25c45c86eced22ec6405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1681d16c04032fcc92d7931524106b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed43030ca376eb5e3331d75f103fc762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785e47874ebcab903e4ac95fbd8f30aa.png)
(1)试将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb232df15bbcb2addccf8d5e7adc4d1f.png)
(2)试应用复数乘方公式推导三倍角公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47bdf9c678020d1d50082f7bb208557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1266e4d6e189cbd788785b44eb4491d6.png)
(3)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b5976d1eab3219c6be0f3e85b4f406.png)
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2024-06-07更新
|
696次组卷
|
4卷引用:重庆市育才中学校2023-2024学年高一下学期阶段测试数学试题
重庆市育才中学校2023-2024学年高一下学期阶段测试数学试题江西省南昌市江西科技师范大学附属中学2023-2024学年高一下学期第二次月考数学试卷江西省南昌市江西科技学院附中2023-2024学年高一下学期5月份月考数学试卷(已下线)10.3 复数的三角形式及其运算-【帮课堂】(人教B版2019必修第四册)
名校
解题方法
10 . 定义:函数
满足对于任意不同的
,都有
,则称
为
上的“
类函数”.
(1)若
,判断
是否为
上的“2类函数”;
(2)若
为
上的“3类函数”,求实数a的取值范围;
(3)若
为
上的“2类函数”,且
,证明:
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d6fe21d6ed78bfc1d2b9cc41a766c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2a699f43d6836c18eaced5758a37a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ece875296333d786d8a671b2749255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93ed0f3a123e0e3b1c08db887fa1697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47e734b17201fe992be7775714e9558.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2db4bd08a64c7ceefac83e2fce50b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea6e1bfbda5c4f6421ed18e802aba04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ab2e5e3dd3a1c768a88eb182b44d9.png)
您最近一年使用:0次
2024-06-04更新
|
378次组卷
|
2卷引用:重庆市求精中学校2023-2024学年高二下学期第二阶段考试数学试题