解题方法
1 . 曲率在数学上是表明曲线在某一点的弯曲程度的数值.对于半径为
的圆,定义其曲率
.对于一般曲线,我们可通过曲线上某点处的密切圆半径来描述该点的曲率,其中对于曲线
在点
处的密切圆半径计算公式为
.已知函数
,椭圆
:
,则曲线
在点
处的曲率为____________ ;
上任一点处曲率的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e4bc563e77980d3b3d3fdb31149dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead22014c0d0bdbcb918fd592d1b81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f4eff3125c5e63a994ba1ad5be58e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f682f9060f6fe3cfe6c1881325f95619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a02752ec05e9283525a0bf5c792e50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cc55a797baf71de6d9c6baa4fc8597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7451b947d1adea22bc04070efdd2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f749e2471684db63546a9ce817a6415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46d60036bbef9075ab9cd3b0b0b3507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
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解题方法
2 . 某企业于近期推出了一款盲盒,且该款盲盒分为隐藏款和普通款两种,其中隐藏款的成本为50元/件,普通款为10元/件,且企业对这款盲盒的零售定价为
元/件.现有一批有限个盲盒即将上市,其中含有20%的隐藏款.某产品经理现对这批盲盒进行检验,每次只检验一个盲盒,且每次检验相互独立,检验后将盲盒重新包装并放回.若检验到隐藏款,则检验结束;若检验到普通款,则继续检验,且最多检验20次.记X为检验结束时所进行的检验次数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
A.![]() |
B.![]() |
C.若小明从这批盲盒中一次性购买了5件,则他抽到隐藏款的概率为0.5094 |
D.若这款盲盒最终全部售出,为确保企业能获利,则![]() |
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2022-10-24更新
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927次组卷
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4卷引用:江苏省2023届高三上学期起航调研测试(Ⅱ)数学试题
3 . 在矩形
中,
,
,
为平面
外一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当平面![]() ![]() ![]() ![]() |
D.当平面![]() ![]() ![]() ![]() |
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2022-11-22更新
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425次组卷
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2卷引用:江苏省"清宵一数"2022-2023学年高三上学期11月第二次学情调研数学试题
4 . 已知
为坐标原点,双曲线
.
上一点
处的切线与
的渐近线交于点
,
,且
的面积为
.
(1)求
;
(2)若过点
的另一条直线与
的渐近线交于点
,
,且
,直线
与圆
相切,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53977ab088f164e44a841b2628b7523c.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/c5db41a1f31d6baee7c69990811edb9f.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/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/288399a4bd34af6663e020b93a53c9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a0dadd00cdcdb69c01997801c9326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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5 . 已知一系列圆
,
,
,
依次外切,且均与过原点的两条直线相切,记圆
的半径为
,且
.若圆
:
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc79ca8bfa3b4a321e72c1b906967d.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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135cb036833400f3fa1edc92d5ce410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bb73c7713c79e5aa50ace92dfa8dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be51ca81c4e72ec876fa31cf705373b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc79ca8bfa3b4a321e72c1b906967d.png)
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名校
6 . “碳达峰”,是指二氧化碳的排放不再增长,达到峰值之后开始下降;而“碳中和”,是指企业、团体或个人通过植树造林、节能减排等形式,抵消自身产生的二氧化碳排放量,实现二氧化碳“零排放”.某地区二氧化碳的排放量达到峰值a(亿吨)后开始下降,其二氧化碳的排放量S(亿吨)与时间t(年)满足函数关系式
,若经过5年,二氧化碳的排放量为
(亿吨).已知该地区通过植树造林、节能减排等形式,能抵消自产生的二氧化碳排放量为
(亿吨),则该地区要能实现“碳中和”,至少需要经过多少年?(参考数据:
)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a7c2b6e0e13ae5453addc734c6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f6da49c72a0768c3fafe823391b3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7081727a19eba3003a689f78872086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5114e1dbd4fc973e99293e1fdb3def.png)
A.28 | B.29 | C.30 | D.31 |
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2022-11-16更新
|
3175次组卷
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14卷引用:江苏省南京市第五高级中学2023届高三二模热身测试数学试题
江苏省南京市第五高级中学2023届高三二模热身测试数学试题江苏省南京市第一中学2023届高三下学期2月期初考试数学试题山东省日照实验高级中学2023届高三模数学试题四川省绵阳市三台中学2024届高三一模数学(理)试题(一)江苏省南通市通州区2022-2023学年高三上学期期中数学试题江苏省南通市海安高级中学2022-2023学年高三上学期期中质量监测数学试题四川省绵阳博美实验高级中学2022-2023学年高一上学期12月月考数学试题江苏省常州市横林高级中学 2022-2023学年高三上学期期中调研数学试题(四)(已下线)专题4 指数函数与对数函数河北省衡水中学2023届高三下学期一调数学试题(已下线)押新高考第5题 数学新文化(已下线)“8+4+4”小题强化训练(25)(已下线)模块一 情境1 以函数为背景(已下线)专题06 对数函数1-期末复习重难培优与单元检测(人教A版2019)
名校
解题方法
7 . 在平面直角坐标系xOy中,抛物线
.
,
为C上两点,且
,
分别在第一、四象限.直线
与x正半轴交于
,与y负半轴交于
.
(1)若
,求
横坐标的取值范围;
(2)记
的重心为G,直线
,
的斜率分别为
,
,且
.若
,证明:λ为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65939cf088d8c68a40575c7b8b7599bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0507fb626aa715e783551b4b3c3bea64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948be0f24a49534e473158761de1ee39.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/6c3071b3b063a35df2196580f20315ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a0c1e3ae17d6bdf98b9ca7c2798f30.png)
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2022-10-05更新
|
630次组卷
|
3卷引用:江苏省2023届高三上学期起航调研测试(Ⅱ)数学试题
名校
解题方法
8 . 已知平面α和平面β是空间中距离为2的两平行平面,球面M与平面α、平面β的交线分别为圆A、圆B.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/11/dc1ac7b2-c5a6-4c23-8828-5816e8be9124.png?resizew=255)
(1)若平面γ与平面α、平面β的交线分别为
,
,证明:
;
(2)若球面M的半径为2,求以圆A为上底面,圆B为下底面的几何体AB的体积的最大值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/11/dc1ac7b2-c5a6-4c23-8828-5816e8be9124.png?resizew=255)
(1)若平面γ与平面α、平面β的交线分别为
![](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/02e03566282ef39ad17821036f228174.png)
(2)若球面M的半径为2,求以圆A为上底面,圆B为下底面的几何体AB的体积的最大值.
您最近一年使用:0次
2022-10-05更新
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2卷引用:江苏省2023届高三上学期起航调研测试(Ⅱ)数学试题
9 . 设
,
.若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479cc5b6a99bacc9307bc008f79b83ee.png)
,则称序列
是长度为n的0—1序列.若
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479cc5b6a99bacc9307bc008f79b83ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85719767bc8b764fcde16731c1ea45c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed37b5147eea8c290d314466f5b8200b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bd14ac501ab1c7a67d279dd04dd83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253d4be096bc92f6cd177d3980d4b8f9.png)
A.长度为n的0—1序列共有![]() | B.若数列![]() ![]() |
C.若数列![]() ![]() | D.数列![]() |
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2022-10-05更新
|
1423次组卷
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5卷引用:江苏省2023届高三上学期起航调研测试(Ⅱ)数学试题
名校
解题方法
10 . 若
,从X的取值中随机抽取
个数据,记这k个数据的平均值为Y,则随机变量
以下问题的求解中可以利用这一结论.
根据以往的考试数据,某学校高三年级数学模考成绩
,设从X的取值中随机抽取25个数据的平均值为随机变量Y.现在从X的取值中随机抽取25个数据从小到大排列为
,
,
,其余5个数分别为97,97,98,98,98.
(1)求
的中位数及平均值;
(2)求
.
附:随机变量
服从正态分布
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290917c2c835b61384480b335cc1d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee8937927d074628df8022fce45fd9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd38f684099124b3d8df5f4989d3da.png)
根据以往的考试数据,某学校高三年级数学模考成绩
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7404fd9eb378fcb5ef7d7e324cf277c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee68755cc146525ccfd4a01e93e486f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4703b77c210e0576f8b53e185ac5c97e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4677fdc29389b36edc10a90630b204.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee68755cc146525ccfd4a01e93e486f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fce18e3bd9b79c21c5348330cebffb.png)
附:随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcc248a7770a16fa10fc4602d71e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a437cf61e1a1cd147cc1a10a5cff035f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d20690162aafbefe5176084a39573f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a262564752e3be57524e156fc781894.png)
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2022-07-09更新
|
1360次组卷
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4卷引用:江苏省南京市第一中学2023届高三上学期第一次模拟考试数学试题
江苏省南京市第一中学2023届高三上学期第一次模拟考试数学试题湖南省三湘名校教育联盟、五市十校教研教改共同体2021-2022学年高二下学期期末数学试题(已下线)第09讲 高考中的概率与统计 (精讲)-2(已下线)考向43二项分布、正太分布及其应用(重点)-2