解题方法
1 . 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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解题方法
2 . 现有甲、乙两个盒子中都有大小、形状、质地相同的2个红球和1个黑球.从两个盒子中各任取一个球交换,记为一次操作.重复进行
次操作后,记甲盒子中黑球个数为
,甲盒中恰有1个黑球的概率为
,恰有2个黑球的概率为
.
(1)求随机变量
的分布列;
(2)求数列
的通项公式;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6368fec0c2c25db7c29b014d60270e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e067aeb203bc5ce00c9dc47aa34cee5e.png)
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解题方法
3 . 已知函数
在
上单调递增,在
上单调递减,设
为曲线
的对称中心.
(1)求
;
(2)记
的角
对应的边分别为
,若
,求
边上的高
长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfa22404f8f7208b7601367dcc75d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f56f79c0b80b7340be885e4dad6901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a960e24187acf3a6e5075fb31ca1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9938230f82e91cf09f8157b532baaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275a078c4e7732e05ae34c754f03417b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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名校
4 . 设集合
为
的非空子集,随机变量X,Y分别表示取到子集
中的最大元素和最小元素的数值.
(1)若
的概率为
,求
;
(2)若
,求
且
的概率;
(3)求随机变量
的均值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6a4cff8424ced7841221e2d54d95d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c4b25a0b76fba785d5769c08714b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab109ec88d6f3d24b2f01ca77e7038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe08722cf9300fe188dbbb71989c06c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e32a2f594955e456f0fddad1e090bb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b3576b4d98a5b4ddc380ddaa0fa281.png)
(3)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9f6ea6346066054b5c722763d6b026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f8506fbcb1fae930e1503065b9327a.png)
您最近一年使用:0次
2024-06-16更新
|
96次组卷
|
2卷引用:江苏省苏州大学2024届高三下学期高考考前数学指导卷
名校
5 . 已知向量
,
.
(1)若
且
,求x的值;
(2)记
,
R.
①求
的单调增区间;
②若任意
,均满足
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca410f7a4ee908d2594a1aae9d38ea04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c530004c5bf440311037956c42a5429.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03481e6a73207be03fdbc1f8e9965b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e7b2150ed88d3ffdec3d142617eacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44c45ef0334070fc149b452dee26ae5.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②若任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e241cc7a7d15fbd4d0c1e388b952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc581fcbeb240944abaf3d994937e55.png)
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2024-05-06更新
|
448次组卷
|
4卷引用:江苏省苏州市相城区陆慕高级中学2023-2024学年高一下学期5月月考数学试题
江苏省苏州市相城区陆慕高级中学2023-2024学年高一下学期5月月考数学试题江苏省南京市金陵中学2023-2024学年高二下学期4月期中测试数学试题(已下线)专题02 三角恒等变换题型归纳-《期末真题分类汇编》(江苏专用)(已下线)专题07 一轮复习三角函数(2)--高二期末考点大串讲(人教A版2019)
解题方法
6 . 某工厂有三个车间生产同一种通讯器材,第1个车间生产该通讯器材的优等品率为
,第2和第3个车间生产该通讯器材的优等品率均为
,生产出来的产品混放在同一个仓库里.已知第1,2,3车间生产的通讯器材数量分别占总数的
,
,
.
(1)现从仓库中任取一个该通讯器材,试问它是优等品的概率是多少?
(2)如果取到的通讯器材是优等品,计算它是第
个车间生产的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c23313b7b754da3bec8a586e02a68ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad2925d2ce0e1e8ef352f9501f2590d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ab5c1b86983380e75e0d12ddc92705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51efd0ca4b6c3d42afdc6b8feb330a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b267e290d2db301797edd8afef98afc7.png)
(1)现从仓库中任取一个该通讯器材,试问它是优等品的概率是多少?
(2)如果取到的通讯器材是优等品,计算它是第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30269c1b04c96bce8e590971b7856165.png)
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名校
解题方法
7 . 已知
.
(1)求
的值;
(2)求
的值;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd9f8795ad6ff657333afcef71bfd04.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d59728ea7f7ac72ffe5e508bcd17d0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1412de831b49cb76a553ecd0761bdc26.png)
您最近一年使用:0次
2024-04-24更新
|
591次组卷
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3卷引用:江苏省苏州南航苏附2023-2024学年高二下学期5月月考数学试题
8 . (1)解关于
的不等式
;
(2)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e197de68e7d35c22dfc573c6be677cd6.png)
(2)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e88d57ca69f58353ab986ff5be88af3.png)
您最近一年使用:0次
2024-04-22更新
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844次组卷
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3卷引用:江苏省苏州青云实验中学2023-2024学年高二下学期3月月考数学试题
江苏省苏州青云实验中学2023-2024学年高二下学期3月月考数学试题浙江省金华市曙光学校2023-2024学年高二下学期4月月考数学试题(已下线)6.2.1排列-6.2.2排列数——课时作业(巩固版)
名校
解题方法
9 . 为鼓励消费,某商场开展积分奖励活动,消费满100元的顾客可拋掷骰子两次,若两次点数之和等于7,则获得5个积分:若点数之和不等于7,则获得2个积分.
(1)记两次点数之和等于7为事件A,第一次点数是奇数为事件B,证明:事件A,B是独立事件;
(2)现有3位顾客参与了这个活动,求他们获得的积分之和X的分布列和期望.
(1)记两次点数之和等于7为事件A,第一次点数是奇数为事件B,证明:事件A,B是独立事件;
(2)现有3位顾客参与了这个活动,求他们获得的积分之和X的分布列和期望.
您最近一年使用:0次
2024-04-19更新
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986次组卷
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3卷引用:江苏省苏州市南京航空航天大学苏州附属中学2024届高三下学期五月阳光测试数学试题
名校
10 . 甲、乙两人进行知识问答比赛,共有
道抢答题,甲、乙抢题的成功率相同.假设每题甲乙答题正确的概率分别为
和
,各题答题相互独立.规则为:初始双方均为0分,答对一题得1分,答错一题得﹣1分,未抢到题得0分,最后累计总分多的人获胜.
(1)若
,
,求甲获胜的概率;
(2)若
,设甲第
题的得分为随机变量
,一次比赛中得到
的一组观测值
,如下表.现利用统计方法来估计
的值:
①设随机变量
,若以观测值
的均值
作为
的数学期望,请以此求出
的估计值
;
②设随机变量
取到观测值
的概率为
,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
;在一次抽样中获得这一组特殊观测值的概率应该最大,随着
的变化,用使得
达到最大时
的取值
作为参数
的一个估计值.求
.
表1:甲得分的一组观测值.
附:若随机变量
,
的期望
,
都存在,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fafbc94594b8c877de8883dea10e374c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69656b7a5085c9033cfb16a838c0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
①设随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88738de257f3fdf71154ebc8d4c1d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69656b7a5085c9033cfb16a838c0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9383b6387e1a94d4929663769ab5ab7.png)
②设随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69656b7a5085c9033cfb16a838c0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927068f621940e6731e02a0db41060bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58b2b4120cd1e093a9b3052779d5a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58b2b4120cd1e093a9b3052779d5a73.png)
题目 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
得分 | 1 | 0 | 0 | ﹣1 | 1 | 1 | ﹣1 | 0 | 0 | 0 |
题目 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
得分 | ﹣1 | 0 | 1 | 1 | ﹣1 | 0 | 0 | 0 | 1 | 0 |
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71701db4b413f2364dbcbd612fbc8a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67962bdeee331b3e908dd05e3a8899c.png)
您最近一年使用:0次
2024-04-19更新
|
2761次组卷
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8卷引用:江苏省苏州实验中学2023-2024学年高二下学期5月月考数学试题
江苏省苏州实验中学2023-2024学年高二下学期5月月考数学试题浙江省天域全国名校协作体2023-2024学年高三二模数学试题山东省青岛第二中学2024届高三下学期二模考试数学试题(已下线)数学(江苏专用02)河北省重点高中2024届高三下学期5月模拟考试数学试题(一)(已下线)模块4 二模重组卷 第6套 全真模拟卷广东省广州市执信中学2024届高三下学期教学情况检测(三)数学试题(已下线)专题03 第七章 随机变量及其分布列--高二期末考点大串讲(人教A版2019)