名校
解题方法
1 . 已知函数
,则方程
在区间
上的所有实根之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d114a9b8c3264711e25db9515aec56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9c64ba837387d640de4b8e2191b1b5.png)
A.2 | B.4 | C.6 | D.8 |
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解题方法
2 . 在长方体
中,已知
,
,
,点
为底面
内一点,若
和底面
所成角与二面角
的大小相等,点
在底面
的投影为点
,则三棱锥
体积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b59ab6bf6111dda4a3d428454768b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad3a1ea6790177130e16c2124984087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adebae2f9d7543915eb5a36427f9b6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e07010ccdf2d83b7d3a6944034d3c95.png)
A.![]() | B.2 | C.![]() | D.![]() |
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解题方法
3 . 在平面直角坐标系
中,已知动点
到定点
的距离和它到定直线
的距离之比为
,记
的轨迹为曲线
.
(1)求
的方程;
(2)已知点
,不过
的直线
与
交于
,
两点,直线
,
,
的斜率依次成等比数列,求
到
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ce47fde921058026708a4321a0e213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e9efa96b6ec20a6ce18c7f458e4379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4 . 设动直线
与函数
,
的图象分别交于点
,已知
,则
的最小值与最大值之积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1fc40e64ec427b41693c21c20890bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c982eeb9b2a3d426a7aa70a0d3a91c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f0c11fcf4c537bdf8982b91359f098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
5 . 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)
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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
6 . 已知函数
,
.
(1)讨论
的单调性;
(2)若
有两个零点,求实数
的取值范围;
(3)若
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eaa6d55cdb24cff59f22f8a09b27160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026d50aeb347823e800aa11442b80331.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780876acd6f251de9b8510f4def91b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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632次组卷
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3卷引用:山东省菏泽第一中学八一路校区2024届高三5月月考数学试题
7 . 已知椭圆
的左、右焦点分别为
,
,过点
的动直线l交E于A,B两点,且点A在x轴上方,直线
与E交于另一点C,直线
与E于另一点D.
(1)求
的面积最大值;
(2)证明:直线CD过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff1455a4045eb93f482c0751840aea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
(2)证明:直线CD过定点.
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3卷引用:云南省昆明市第一中学2024届高三第十次考前适应性训练数学试卷
名校
解题方法
8 . 某人在
次射击中击中目标的次数为
,
,其中
,
,击中奇数次为事件
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870528aa6be6f56bae0eb6b10a765c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.若![]() ![]() ![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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132次组卷
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20卷引用:湖北省武昌实验中学2023-2024学年高三上学期10月月考数学试题
湖北省武昌实验中学2023-2024学年高三上学期10月月考数学试题山东省泰安肥城市2023届高考适应性训练数学试题(三)山东省新高考质量检测联盟2024届高三第一次质量检测数学试题(A)(已下线)第四篇 概率与统计 专题7 常见分布 微点3 常见分布综合训练(已下线)单元提升卷11 统计与概率(已下线)考点13 二项分布与超级几何分布 2024届高考数学考点总动员【练】(已下线)随机变量及其分布(已下线)黄金卷02(已下线)专题10.1 概率与统计的综合运用【十一大题型】(举一反三)(新高考专用)-1辽宁省大连市第八中学2023-2024学年高二下学期4月月考数学试题(已下线)模块一 专题2 概率(北师大2019版)(已下线)模块一 专题4 随机变量及其分布 (人教A)(已下线)模块一 专题3 概率 (苏教版)(已下线)第11讲 二项分布与超几何分布-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)(已下线)专题04 超几何分布+二项分布+正态分布压轴题(4)(已下线)7.4.1 二项分布(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第三册)(已下线)专题7.10 随机变量及其分布全章综合测试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)(已下线)第七章:随机变量及其分布章末重点题型复习-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第三册)黑龙江省牡丹江市第一高级中学2023-2024学年高二下学期5月期中考试数学试题(已下线)高二下期末考前押题卷02--高二期末考点大串讲(人教B版2019选择性必修)
名校
解题方法
9 . 已知抛物线
的焦点为
,其准线
与
轴的交点为
,过点
的直线与C交于
,
两点,点
为点
在
上的射影,线段
与
轴的交点为
,线段
的延长线交
于点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/159a2d4945049c5a8f525f18763eba91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() |
B.![]() |
C.直线![]() ![]() |
D.![]() ![]() ![]() |
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