解题方法
1 . 已知定义在
上不为常数的函数
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1273c46b7fcc753edffec8da083f60b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 在棱长为2的正方体
中,
为
的中点,以
为原点,OB,OD,OO1所在直线分别为
轴、
轴、
轴,建立如何所示空间直角坐标系.若该正方体内一动点
,满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a20b689283cc8b311eddae4c8c4242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ea83a384f056dadaacfa349cc84130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfcaf2a345411411cf94422703e9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e588cb555e36f28c5db66d213ef064d4.png)
A.点![]() ![]() | B.![]() ![]() |
C.![]() | D.三棱锥![]() ![]() |
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解题方法
3 . 若一个多面体的各面都与一个球的球面相切,则称这个球是这个多面体的内切球.在四棱锥
中,侧面
是边长为1的等边三角形,底面
为矩形,且平面
平面
.若四棱锥
存在一个内切球,设球的体积为
,该四棱锥的体积为
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
4 . “熵”常用来判断系统中信息含量的多少,也用来判断概率分布中随机变量的不确定性大小,一般熵越大表示随机变量的不确定性越明显.定义:随机变量
对应取值
的概率为
,其单位为bit的熵为
,且
.(当
,规定
.)
(1)若抛掷一枚硬币1次,正面向上的概率为
,正面向上的次数为
,分别比较
与
时对应
的大小,并根据你的理解说明结论的实际含义;
(2)若拋掷一枚质地均匀 的硬币
次,设
表示正面向上的总次数,
表示第
次反面向上的次数(0或1).
表示正面向上
次且第
次反面向上
次的概率,如
时,
.对于两个离散的随机变量
,其单位为bit的联合熵记为
,且
.
(ⅰ)当
时,求
的值;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b23512db3961f941a63a3d8254afb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449a066c87681f1f006aef2faeeba4c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c94a17b49550283be4ec1a348c8534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c84b931f584765cd30253af0e0d71b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1dc00bf0db4bf56d99cf9583938bcba.png)
(1)若抛掷一枚硬币1次,正面向上的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109ac38599926de9fd89470f561f6664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4479d54b1eced7c425e2deaefb18c233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6c6ec3ea184362694ba9c2dd2cbfd0.png)
(2)若拋掷一枚
![](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/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5470e9ee422d970529663964b84c45a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65362f7197f0e2cc05d879b3341584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0010cb466163db1349fc1040f6b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf395de82112cb78f446c6e7a245556a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8f9de90ca38f627eba375b15eb3e8f.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbabe5b63ff142225e3ae59e7b88b3c.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1109931e8c85ff6b8bb894e6d5d4017.png)
您最近一年使用:0次
2024-05-13更新
|
1239次组卷
|
2卷引用:江苏省南通、扬州、泰州七市2024届高三第三次调研测试数学试题
5 . 若
是一个集合,
是一个以
的某些子集为元素的集合,且满足:①
属于
,空集
属于
;②
中任意多个元素的并集属于
;③
中任意多个元素的交集属于
,则称
是集合
上的一个拓扑.已知函数
,其中[x]表示不大于
的最大整数,当
时,函数
值域为集合
,则集合
上的含有4个元素的拓扑
的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89d1c17a43495542eaade6426cf4c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668efc94065bc0b990673bf77c40eeeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2024-04-29更新
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182次组卷
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2卷引用:江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题
名校
解题方法
6 . 已知椭圆C:
的右焦点为
,右顶点为A,直线l:
与x轴交于点M,且
,
(1)求C的方程;
(2)B为l上的动点,过B作C的两条切线,分别交y轴于点P,Q,
①证明:直线BP,BF,BQ的斜率成等差数列;
②⊙N经过B,P,Q三点,是否存在点B,使得,
?若存在,求
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eecbc96a8c7c9fa3c8c175931731b2.png)
(1)求C的方程;
(2)B为l上的动点,过B作C的两条切线,分别交y轴于点P,Q,
①证明:直线BP,BF,BQ的斜率成等差数列;
②⊙N经过B,P,Q三点,是否存在点B,使得,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d484860d9392ecacc942edecd37b6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c2f99ac2b6bc91b983628b68a5cd0d.png)
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2024-03-22更新
|
2355次组卷
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6卷引用:江苏省南京市、盐城市2024届高三第一次模拟考试数学试题
名校
解题方法
7 . 在平面直角坐标系xOy中,已知椭圆Γ:
的离心率为
,直线l与Γ相切,与圆O:
相交于A,B两点.当l垂直于x轴时,
.
(1)求Γ的方程;
(2)对于给定的点集M,N,若M中的每个点在N中都存在距离最小的点,且所有最小距离的最大值存在,则记此最大值为
.
(ⅰ)若M,N分别为线段AB与圆O上任意一点,P为圆O上一点,当
的面积最大时,求
;
(ⅱ)若
,
均存在,记两者中的较大者为
.已知
,
,
均存在,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42aaceb687ffc763bdc5af3463c051a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631586067d81160678c2ddea983e62de.png)
(1)求Γ的方程;
(2)对于给定的点集M,N,若M中的每个点在N中都存在距离最小的点,且所有最小距离的最大值存在,则记此最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
(ⅰ)若M,N分别为线段AB与圆O上任意一点,P为圆O上一点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8207405e0cca2ccbd7643671bee4e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a34aca6d603ad0587bd4e3f1a0b01d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad8c255f18185a9b643c70edf9b00b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89815ff222757cbfc9b0ae2bf096a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed107042c263ccf28435954b8a02082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e99cb8baa4733c0d58735590ddaf51.png)
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2024-03-21更新
|
2783次组卷
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10卷引用:江苏省南通市2024届高三第二次调研测试数学试题
江苏省南通市2024届高三第二次调研测试数学试题江苏省扬州市2024届高三第二次调研测试数学试题江苏省泰州市2024届高三第二次调研测试数学试题(已下线)模块4 二模重组卷 第2套 全真模拟卷(已下线)高三数学考前押题卷3(已下线)江苏省南通市2024届高三第二次调研测试数学试题变式题 16-19(已下线)江苏省泰州市2024届高三第二次调研测试数学试题变式题16-19天津市南开中学2023-2024学年高三下学期第五次月考数学试题(已下线)专题8 考前押题大猜想36-40(已下线)压轴题02圆锥曲线压轴题17题型汇总-3
名校
解题方法
8 . 设集合
,其中
.若对任意的向量
,存在向量
,使得
,则称A是“T集”.
(1)设
,判断M,N是否为“T集”.若不是,请说明理由;
(2)已知A是“T集”.
(i)若A中的元素由小到大排列成等差数列,求A;
(ii)若
(c为常数),求有穷数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642ae5a0ccf07cc09fb140685e5fa2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247dbdb60e5215115103ba8e33a10611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bdf7f57b61c21324e21d25941135270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4483cc4e4c07bda4b90f4550b40b0ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2bf51f13526eb5b6f6732236bbe772.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab2da56e4587a8f90af2fe37f958f1f.png)
(2)已知A是“T集”.
(i)若A中的元素由小到大排列成等差数列,求A;
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c9df01c8fb5139e8a90d4d68cb8df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d02a8555da4dbbc7820a50a95b071ee.png)
您最近一年使用:0次
2024-03-20更新
|
985次组卷
|
3卷引用:江苏省扬州市高邮市临泽中学2024届高三下学期一模模拟数学试题
9 . 对于每项均是正整数的数列P:
,定义变换
,
将数列P变换成数列
:
.对于每项均是非负整数的数列
,定义
,定义变换
,
将数列Q各项从大到小排列,然后去掉所有为零的项,得到数列
.
(1)若数列
为2,4,3,7,求
的值;
(2)对于每项均是正整数的有穷数列
,令
,
.
(i)探究
与
的关系;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50dbc39a6a06eb8bd7b295f8cc95a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4d9c1555c406f37a85ff5ddd2275af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3926a18ee86236e7cf53467ac04f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3c54bcc0bd04c304d6513732584b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29422ba63f79b2087f0dcce4879d8c78.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00061b36983bb547aa63f9a9f6222105.png)
(2)对于每项均是正整数的有穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131cac59d4d568a27dbb220810dbb014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef96396caccbf2f959e9d233f060317.png)
(i)探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00061b36983bb547aa63f9a9f6222105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c496ba1d329d5fd94f4fdb1da8c7cde.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5de2726fe544faf83d4ab88e9116135.png)
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2024-03-12更新
|
1089次组卷
|
3卷引用:江苏省徐州市2024届高三下学期新高考适应性测试数学试卷
解题方法
10 . 已知函数
,其中
,
为自然对数的底数.
(1)函数
,求
的最小值
;
(2)若
为函数
的两个零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a1a108a57a9d4fbc34d85fedefc822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c93f6e9a237967967e92d53d55b68f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb34715867f6e7c145ccf1410d9afef.png)
您最近一年使用:0次