名校
解题方法
1 . 台州是全国三大电动车生产基地之一,拥有完整的产业链和突出的设计优势.某电动车公司为了抢占更多的市场份额,计划加大广告投入、该公司近5年的年广告费
(单位:百万元)和年销售量
(单位:百万辆)关系如图所示:令
,数据经过初步处理得:
现有①
和②
两种方案作为年销售量y关于年广告费x的回归分析模型,其中a,b,m,n均为常数.
(1)请从相关系数的角度,分析哪一个模型拟合程度更好?
(2)根据(1)的分析选取拟合程度更好的回归分析模型及表中数据,求出y关于x的回归方程,并预测年广告费为6(百万元)时,产品的年销售量是多少?
(3)该公司生产的电动车毛利润为每辆200元(不含广告费、研发经费).该公司在加大广告投入的同时也加大研发经费的投入,年研发经费为年广告费的199倍.电动车的年净利润受年广告费和年研发经费影响外还受随机变量
影响,设随机变量
服从正态分布
,且满足
.在(2)的条件下,求该公司年净利润的最大值大于1000(百万元)的概率.(年净利润=毛利润×年销售量-年广告费-年研发经费-随机变量).
附:①相关系数
,
回归直线
中公式分别为
,
;
②参考数据:
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d0c9a653c10633c52141a289d21f40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/18/f060882c-7f5e-4eaf-8449-116449dbb1ab.png?resizew=221)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
44 | 4.8 | 10 | 40.3 | 1.612 | 19.5 | 8.06 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b447ac3d1a965572c31b6e4c18d4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02539241ac975790e5e4c9ccc8b1a79.png)
(1)请从相关系数的角度,分析哪一个模型拟合程度更好?
(2)根据(1)的分析选取拟合程度更好的回归分析模型及表中数据,求出y关于x的回归方程,并预测年广告费为6(百万元)时,产品的年销售量是多少?
(3)该公司生产的电动车毛利润为每辆200元(不含广告费、研发经费).该公司在加大广告投入的同时也加大研发经费的投入,年研发经费为年广告费的199倍.电动车的年净利润受年广告费和年研发经费影响外还受随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a71645a2321d01bc0f0d36beda3e876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ffa2c34737bc1ecfe4a6aa43ece657.png)
附:①相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98f0dbd3089bfafb006a6f021f81990.png)
回归直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10cb9fd6d5c388cd9d28556d9e9dd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da681f395dbaeeb19432f63b6f1a39ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebff20f21ae41fd8d1f1e3145895842.png)
②参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d8bb7e3173862c8fcc12decd05e4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602b31e9240529d6d3b7cc2fc4ccdbd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e36492ded42e594c63855802dee601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a531afc6e63700f1ca2b45d229efb9ea.png)
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|
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7卷引用:山西省太原市第五中学2023-2024学年高二下学期5月月考数学试题
山西省太原市第五中学2023-2024学年高二下学期5月月考数学试题浙江省台州市2024届高三下学期第二次教学质量评估数学试题(已下线)第八章 成对数据的统计分析总结 第一练 考点强化训练(已下线)模块二 专题1统计案例中决策分析问题(北师大高二)(已下线)8.5 二项分布、超几何分布与正态分布(高考真题素材之十年高考)(已下线)专题04 第八章 成对数据的统计分析--高二期末考点大串讲(人教A版2019)湖北省襄阳市第五中学2024届高三下学期第四次适应性测试数学试题
2 . 由椭圆的两个焦点和短轴的一个顶点组成的三角形称为该椭圆的“特征三角形”.如果椭圆
的“特征三角形”为
,椭圆
的“特征三角形”为
,若
,则称椭圆
与
“相似”,并将
与
的相似比称为椭圆
与
的相似比.已知椭圆
:
与椭圆
:
相似.
(1)求椭圆
的离心率;
(2)若椭圆
与椭圆
的相似比为
,设
为
上异于其左、右顶点
,
的一点.
①当
时,过
分别作椭圆
的两条切线
,
,切点分别为
,
,设直线
,
的斜率为
,
,证明:
为定值;
②当
时,若直线
与
交于
,
两点,直线
与
交于
,
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5518f853e3a929edf3dd3cee8ec0760d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8321b4034b3ab70b6cbfa25bca18df2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaf9a32b79eb97becf706682da7115d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5518f853e3a929edf3dd3cee8ec0760d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8321b4034b3ab70b6cbfa25bca18df2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5532211b42702f7b281834d500c666d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249767ae3bf665f1c8db866dbb366940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2451835b9ad821bc17a317bc0189a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2451835b9ad821bc17a317bc0189a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e260f5fe6e3637a415344ff137c7a6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f685277f6c178fb1fcd5e8387886721.png)
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2024-03-29更新
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3卷引用:山西省长治市2023-2024学年高二下学期3月质量检测数学试题
名校
解题方法
3 .
元向量(
)也叫
维向量,是平面向量的推广,设
为正整数,数集
中的
个元素构成的有序组
称为
上的
元向量,其中
为该向量的第
个分量.
元向量通常用希腊字母
等表示,如
上全体
元向量构成的集合记为
.对于
,记
,定义如下运算:加法法则
,模公式
,内积
,设
的夹角为
,则
.
(1)设
,解决下面问题:
①求
;
②设
与
的夹角为
,求
;
(2)对于一个
元向量
,若
,称
为
维信号向量.规定
,已知
个两两垂直的120维信号向量
满足它们的前
个分量都相同,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d617b088816e03a283123e29e4dbdca.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee470d0232b6b37f2fb2ab15aae0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948eea3409b959c7248d68a1a081819d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b1e734f151a88ccb702148615db27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5ab6e54fc0c6b846c8d860860c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db1cd89b86c99ce96a9336eb3b09c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be594c4e8c6693571d71fa7c1951796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a7cf91ca4cddeef99e8873ecc6fc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05932f1afdfa963def3c811591eb62bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d69dab2a6743011b461f62448890316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c21920a0a39b1604e130601f061b056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eab8e66f785800a153d34421b2e5540.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a22804cdf4a90edff02dbb01b7481b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23c7e4c34891b3435c39f4989470ccf.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac852f327effde190b9ebf3dd08e037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f7e488464e41e1a1e1eed427154aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(2)对于一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e363087dcbe11e11a9ec545570735c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94fcc44ac04f54d5fcc1a6154b8b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac852f327effde190b9ebf3dd08e037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2772cf7495c2c4c70086e7d936752d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3c80a2adf39204ce112bda7115bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8af44e1a8c05007f2137fa2d1907db.png)
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2024-03-26更新
|
540次组卷
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5卷引用:山西省大同市第二中学校2023-2024学年高一下学期3月月考数学试题
名校
4 . 已知集合
,其中
都是
的子集且互不相同,记
的元素个数,
的元素个数
.
(1)若
,直接写出所有满足条件的集合
;
(2)若
,且对任意
,都有
,求
的最大值;
(3)若
且对任意
,都有
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13757649d1059dabada7fbafde58e6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96fa7b00ef7b8cf8e5a42aeb29f5154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf783a679243d115e602912050e47ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/775adbe6736b3ec038d45a4f209ac290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f71a52871eb36b27836d6b9d72029ac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/144e563700d35bb31aa51bab681f3118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebd42fc2af57877e06f485b50ae4d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19eee6183061532e744ef9086ffcb8b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a245761c2403d38b654894e0c78cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebd42fc2af57877e06f485b50ae4d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27d4e5e05097560b51f888f8b234bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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|
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4卷引用:山西省天一名校2023-2024学年高三下学期联考仿真模拟(二模)数学试题
5 . 已知
,且
,函数
.
(1)记
为数列
的前
项和.证明:当
时,
;
(2)若
,证明:
;
(3)若
有3个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff69be9f14b645d71fe4547677db36de.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48241aafc046ccde27f7d63ae3018161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c98250092857464fbe6cc0707b89ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5a00e9328fe28c7f1f81377e05b044.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950581caec90a28b5fa8f1e81bf21d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7a75bcd70f6b1a6d02dbb92e964e1b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 某次比赛中,甲乙二人进入决赛并争夺冠军.比赛规则为:①每局比赛后,胜者获得3分,负者获得1分,比赛没有平局;②连续2局获胜或积分率先达到11分者可获得冠军,比赛结束.已知在单局比赛中,甲乙获胜的概率均为
.
(1)求甲乙决出冠军时比赛局数
的分布列与数学期望
;
(2)求在甲获得冠军的条件下其积分达到11分的概率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求甲乙决出冠军时比赛局数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(2)求在甲获得冠军的条件下其积分达到11分的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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名校
解题方法
7 . 在
中,已知
,
,设
分别是
的重心、垂心、外心,且存在
使
.
(1)求点
的轨迹
的方程;
(2)求
的外心
的纵坐标
的取值范围;
(3)设直线
与
的另一个交点为
,记
与
的面积分别为
,是否存在实数
使
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f05b013e4b7166cbc87c5a83d6a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0b4afd16b79370532de44989d6c43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629fa2d45c98294868b7e6f822fe06aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddec257c9be12df3a3e4caa3d4bca66c.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4a16b9e9d730d7b152f59f69dea2c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662f3139dd0eaf3cf83c4c81ba9ee11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a4305caeb7703718b82440d3bb2be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594c39b1ac50a490bc7970c97607603c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-03-19更新
|
1146次组卷
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5卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第二次调研考试数学试题
山西省晋城市第一中学校2023-2024学年高二下学期第二次调研考试数学试题上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试卷(已下线)上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试题变式题17-21河南省信阳高级中学2024届高三5月测试(一)二模数学试题(已下线)专题13 学科素养与综合问题(解答题18)
8 . 英国数学家泰勒发现的泰勒公式有如下特殊形式:当
在
处的
阶导数都存在时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661a2ffa74a30c0b1c0a0ea0fdc8bb3c.png)
.注:
表示
的2阶导数,即为
的导数,
表示
的
阶导数,该公式也称麦克劳林公式.
(1)根据该公式估算
的值,精确到小数点后两位;
(2)由该公式可得:
.当
时,试比较
与
的大小,并给出证明;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1d8cb672db61735be7cbcd3d50bf9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661a2ffa74a30c0b1c0a0ea0fdc8bb3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35993bd1db970330494665d925c0be7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)根据该公式估算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67aace59c071f37a444495678497ef0.png)
(2)由该公式可得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba15a427babacf319deb9c4dd8d58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea093173f74807332e08bde42f25e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd9f874878e11c3fa25143023e8f95a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5cf9c12181dd8683944b2b30bf8e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa80dea5928f0be2b39075a434742686.png)
您最近一年使用:0次
2024-03-14更新
|
3385次组卷
|
13卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第二次调研考试数学试题
山西省晋城市第一中学校2023-2024学年高二下学期第二次调研考试数学试题湖北省八市2024届高三下学期3月联考数学试卷江苏省连云港市东海高级中学2023-2024学年高二下学期强化班第一次月考数学试题(已下线)第10题 导数压轴大题归类(2)(高三二轮每日一题)河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷安徽省蚌埠市第二中学2023-2024学年高二下学期3月月巩固检测数学试题江苏省苏州市张家港市沙洲中学2023-2024学年高二下学期3月阶段性测试数学试题广东省东莞市外国语学校2023-2024学年高二下学期第一次阶段性考试(4月)数学试题河南省许昌市禹州市高级中学2024届高三下学期4月月考数学试题吉林省长春市第二中学2023-2024学年高二下学期第一学程考试(4月)数学试题(已下线)压轴题05数列压轴题15题型汇总-1甘肃省兰州市第五十八中学2024届高三第二次高考仿真考试数学试题广东省深圳市2024届高三下学期三模数学试题
9 . 光明高级中学高三年级理科考生800人都参加了本学期的期中调研测试,学校把本次测试数学成绩达到120分以上(包含120分)的同学的数学成绩等第定为优秀,物理成绩达到90分以上(包含90分)的同学的物理成绩等第定为优秀.现从理科考生中随机抽取10名同学调研本次测试的数学和物理成绩,如下表:
(1)试列出
列联表,并依据
的独立性检验分析能否认为本次测试理科考生的数学成绩的等第优秀与物理成绩的等第是否优秀有关?
(2)①数学组的章老师打算从这10个同学中,按照这次测试数学的等第是否优秀,利用分层随机抽样的方法抽取5人,再从这5人中抽取3个人,并仔细考查这3个人的答题情况.设最后抽出的3个人中数学等第优秀的人数为
,求
的分布列及数学期望
;
②如果本次测试理科考生的物理成绩
,用样本估计总体,以10名同学物理成绩的平均数为
,方差为
,若从参加考试的800名理科考生中随机抽取4人,求这4人中至少有1人的物理成绩的等第优秀的概率.
参考数据:取
.
若
,则
,
.
.
数学(分) | 119 | 145 | 99 | 95 | 135 | 120 | 122 | 85 | 130 | 120 |
物理(分) | 84 | 90 | 82 | 84 | 83 | 81 | 83 | 81 | 90 | 82 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f81f285940b14b97f368469121efab.png)
(2)①数学组的章老师打算从这10个同学中,按照这次测试数学的等第是否优秀,利用分层随机抽样的方法抽取5人,再从这5人中抽取3个人,并仔细考查这3个人的答题情况.设最后抽出的3个人中数学等第优秀的人数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
②如果本次测试理科考生的物理成绩
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c1ed67167078ea4f5f1ee53ee14164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d3e642d52e01899f66df411100838.png)
参考数据:取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f492e0be29ed7a710609025f29f550.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c1ed67167078ea4f5f1ee53ee14164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa3e415bdd85e6b47bb1c74de26d8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ca90ea0b9c050c6525ca9a15eb149f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedb26578090f09dd6b9f18d9a47a235.png)
0.10 | 0.05 | 0.025 | 0.010 | 0.005 | |
2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
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10 . 一袋中有
个均匀硬币,其中有
个普通硬币,普通硬币的一面为面值,另一面为花朵图案,如下图,其余
个硬币的两面均为面值.每次试验从袋中随机摸出两个硬币各掷一次,用事件
表示“两个硬币均是面值朝上”,用事件
表示“两个硬币均是花朵图案朝上”,又把两个硬币放回袋中,如此重复
次试验.
(1)若
,
①求
次试验中摸出普通硬币个数
的分布列;
②求
次试验中事件
发生的次数
的期望;
(2)设
次试验中事件
恰好发生
次的概率为
,当
取何值时,
最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d649f22c090b2980a4fcccdd75a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3143ddb1813fa9a0ad3786132686908.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/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/4/913ef47b-f3f1-4432-9f29-6c468fbd5ca2.png?resizew=245)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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