名校
1 . 设a,b为非负整数,m为正整数,若a和b被m除得的余数相同,则称a和b对模m同余,记为
.
(1)求证:
;
(2)若p是素数,n为不能被p整除的正整数,则
,这个定理称之为费马小定理.应用费马小定理解决下列问题:
①证明:对于任意整数x都有
;
②求方程
的正整数解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73aeb67aa5fa6797d0a68cfbf1a3d5.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfac455432b5ddc11bbbb62b165f1ef.png)
(2)若p是素数,n为不能被p整除的正整数,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b82d58ea4cb94ff8dc3aeb1c345a0e.png)
①证明:对于任意整数x都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366bfef60e3b2c6fd95003cddbd66605.png)
②求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc16a57919b711a9d34eed86b437f35.png)
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2024-02-27更新
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5卷引用:河北省2024届高三下学期大数据应用调研联合测评(V)数学试题
河北省2024届高三下学期大数据应用调研联合测评(V)数学试题河北省秦皇岛市昌黎县开学联考2024届高三下学期开学考试数学试题河北省沧州市泊头市大数据联考2024届高三下学期2月月考数学试题(已下线)压轴题高等数学背景下新定义题(九省联考第19题模式)讲(已下线)新题型02 新高考新结构竞赛题型十五大考点汇总-2
2 . 对于数列
,记
,称数列
为数列
的一阶差分数列;记
,称数列
为数列
的二阶差分数列,…,一般地,对于
,记
,规定:
,称
为数列
的
阶差分数列.对于数列
,如果
(
为常数),则称数列
为
阶等差数列.
(1)数列
是否为
阶等差数列,如果是,求
值,如果不是,请说明为什么?
(2)请用
表示
,并归纳出表示
的正确结论(不要求证明);
(3)请你用(2)归纳的正确结论,证明:如果数列
为
阶等差数列,则其前
项和为
;
(4)某同学用大小一样的球堆积了一个“正三棱锥”,巧合用了2024个球.第1层有1个球,第2层有3个,第3层有6个球,…,每层都摆放成“正三角形”,从第2层起,每层“正三角形”的“边”都比上一层的“边”多1个球,问:这位同学共堆积了多少层?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa321950b10e074ed9636a2f45a1a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1b87726fc455bda6b57a6bbf945370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ea6a77537d0cc290f38e2f6879d9e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91bedc5708c3a0fd109a53174902fce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812e3f80ce9ee8d0bdba2d1b846e1fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c04a9e337665339e34c3874a2c5710e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da0ba7c15a05f519d47b5eaf09c0a8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff0dd5f1a1c9399cea2cc938964470d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc2d03374de76c9ba32b90436cd98b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a075be43e898d86fa07e9328978c8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198cd4d7bf7a133fbc36aee884edf5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)请用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17243bec73e79bab1216123cc094eecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c932d437f90d874026f052d65a8402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)请你用(2)归纳的正确结论,证明:如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec08af85b4b2f52c85f449611a688d6d.png)
(4)某同学用大小一样的球堆积了一个“正三棱锥”,巧合用了2024个球.第1层有1个球,第2层有3个,第3层有6个球,…,每层都摆放成“正三角形”,从第2层起,每层“正三角形”的“边”都比上一层的“边”多1个球,问:这位同学共堆积了多少层?
您最近一年使用:0次
名校
解题方法
3 . 基本不等式可以推广到一般的情形:对于
个正数
,它们的算术平均不小于它们的几何平均,即
,当且仅当
时,等号成立.若无穷正项数列
同时满足下列两个性质:①
;②
为单调数列,则称数列
具有性质
.
(1)若
,求数列
的最小项;
(2)若
,记
,判断数列
是否具有性质
,并说明理由;
(3)若
,求证:数列
具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efff8ec14cb242e793afab4468bf2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2617515e5ce81b3f5d9f4e806b21b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6879960be91ea52297d587e9a014f54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce59ae5baacab766b0915722377a746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bc99b9545c8c838e99b7be9c6d1046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20e03ee7d9307a0a4d242fffda381d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247739746b8ddf1403541047e8b5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-02-21更新
|
3161次组卷
|
7卷引用:安徽省部分省示范高中2024届高三开学联考数学试卷
安徽省部分省示范高中2024届高三开学联考数学试卷湖南省2024年高三数学新改革提高训练三(九省联考题型)湖北省荆州市沙市中学2024届高三下学期3月月考数学试题(已下线)黄金卷04(2024新题型)广东省广州市西关外国语学校2023-2024学年高二下学期期中数学试题(已下线)压轴题03不等式压轴题13题型汇总-2辽宁省朝阳市建平县实验中学2024届高三第五次模拟考试数学试题
名校
解题方法
4 . 如图,在圆锥
中,若轴截面
是正三角形,C为底面圆周上一点,F为线段
上一点,D(不与S重合)为母线上一点,过D作
垂直底面于E,连接
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/4a784b01-e920-40f1-82dd-3d86a0610067.png?resizew=153)
(1)求证:平面
平面
;
(2)若
为正三角形,且F为
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23354ef3b5664149f9c77564d668885f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cbba955e542f4f53713c208c45cf9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/4a784b01-e920-40f1-82dd-3d86a0610067.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1010b502298fdffba6d90265a199ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd1c4e883518a7ac5a7517615e47e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2024-03-07更新
|
792次组卷
|
2卷引用:山东省部分名校2023-2024学年高三下学期2月大联考数学试题
22-23高三下·北京海淀·开学考试
名校
解题方法
5 . 若无穷数列
的各项均为整数.且对于
,
,都存在
,使得
,则称数列
满足性质P.
(1)判断下列数列是否满足性质P,并说明理由.
①
,
,2,3,…;
②
,
,2,3,….
(2)若数列
满足性质P,且
,求证:集合
为无限集;
(3)若周期数列
满足性质P,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9672f1800f9544e878955f289aa3fc6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f2c7c9305b404f7363a376af101aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa38a89b95fa1ea7bfc91630f6c7437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0fbad04faddb5408ce4e7e6e3ed816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)判断下列数列是否满足性质P,并说明理由.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ce6401cf48b9546342b1b96ac2cc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f224a5a66c91792eceb8f8c725183f67.png)
(3)若周期数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2024-02-10更新
|
1547次组卷
|
14卷引用:北京市第四中学2023-2024学年高三下学期开学考试数学试题
(已下线)北京市第四中学2023-2024学年高三下学期开学考试数学试题湖南省张家界市民族中学2023-2024学年高二下学期入学考试数学试题(已下线)北京市海淀区清华大学附属中学2023届高三下学期开学调研测试数学试题北京市海淀区首都师范大学附属中学2023-2024学年高三上学期阶段练习(1月)数学试题湖南省2024届高三数学新改革提高训练一(九省联考题型)2024届高三新改革数学模拟预测训练一(九省联考题型)(已下线)压轴题05数列压轴题15题型汇总-1北京市顺义区第一中学2024届高三下学期高考考前适应性检测数学试卷广东省广州市执信中学2024届高三下学期教学情况检测(二)数学试题北京市第五中学2023届高三下学期3月检测数学试题北京市海淀区教师进修学校附属实验学校2023届高三零模数学试题北京市海淀区中国人民大学附属中学2022-2023学年高二下学期期中数学复习试题(2)(已下线)2023年北京高考数学真题变式题16-21北京市清华大学附属中学2023届高三下学期4月月考数学试题
名校
解题方法
6 . 复数是由意大利米兰学者卡当在十六世纪首次引入,经过达朗贝尔、棣莫弗、欧拉、高斯等人的工作,此概念逐渐为数学家所接受.形如
的数称为复数,其中
称为实部,
称为虚部,i称为虚数单位,
.当
时,
为实数;当
且时,
为纯虚数.其中
,叫做复数
的模.设
,
,
,
,
,
,
如图,点
,复数
可用点
表示,这个建立了直角坐标系来表示复数的平面叫做复平面,
轴叫做实轴,
轴叫做虚轴.显然,实轴上的点都表示实数;除了原点外,虚轴上的点都表示纯虚数.按照这种表示方法,每一个复数,有复平面内唯一的一个点和它对应,反过来,复平面内的每一个点,有唯一的一个复数和它对应.一般地,任何一个复数
都可以表示成
的形式,即
,其中
为复数
的模,
叫做复数
的辐角,我们规定
范围内的辐角
的值为辐角的主值,记作
.
叫做复数
的三角形式.
,
,求
、
的三角形式;
(2)设复数
,
,其中
,求
;
(3)在
中,已知
、
、
为三个内角
的对应边.借助平面直角坐标系及阅读材料中所给复数相关内容,证明:
①
;
②
,
,
.
注意:使用复数以外的方法证明不给分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c0c72c17b74f9a5a175ec2b9d77e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c789a7cd7ac2b8b96dc879c6c8161ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fe68ea0bf368925909606949da47f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0bf9b2a7378e73e9fd06c693bfda07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f9e12546277731776041c73dbe58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e80e5baee553150c67a91f1017a7be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6958203312cbda12fd2683a819dd9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e472aea001d179c284e3687a9aacf384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e472aea001d179c284e3687a9aacf384.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/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec45476379fb51aa1ef0a93f849f48be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e283f3168c0b5e8f68dda92c43651e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eec3e684af41f9ed4db5b931b9ccfb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f56cfb41ee7cb758fee138ab09e0d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec45476379fb51aa1ef0a93f849f48be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b40b6895776e0807c2baecbc8f33a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3665b2dac544bfb2a0c175f95a480e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b3a15906b84b98a3ac563e7e2ec9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe615164ed2995bdeea0f5b0ba94231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
(2)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd87d6e1987cf95d102de1045d3722a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398d8980d3ec9fbf536a1efa6312a19a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0492634f27279b6470798af0185be67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c723970ac738976e0130e1438b67058.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1501d4035822b34fcc2378f1e316f159.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63471f592531e46277365ed319e2acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923694c299d953e02cb79dfcef9f56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ce2f54d69a5987c1de19da53342811.png)
注意:使用复数以外的方法证明不给分.
您最近一年使用:0次
2024-03-12更新
|
587次组卷
|
4卷引用:黑龙江省哈尔滨师范大学附属中学2023-2024学年高一下学期开学考试数学试卷
黑龙江省哈尔滨师范大学附属中学2023-2024学年高一下学期开学考试数学试卷重庆市缙云教育联盟2023-2024学年高一下学期3月月度质量检测数学试题(已下线)模块五 专题六 全真拔高模拟2(已下线)第七章:复数(新题型)-同步精品课堂(人教A版2019必修第二册)
名校
7 . 设正整数
,若由实数组成的集合
满足如下性质,则称
为
集合:对
中任意四个不同的元素
,均有
.
(1)判断集合
和
是否为
集合,说明理由;
(2)若集合
为
集合,求
中大于1的元素的可能个数;
(3)若集合
为
集合,求证:
中元素不能全为正实数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ead6fe08a80379f496eab2129655bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be0f5b704e46d64481197273b2e2557.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ccef0bee54b52b069616251fbea584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9cba4a6e473e359492361f51d8556a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def70b21b73d0d0156f8ffb526413d97.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37fb28a9d01dfd12b13bce4ac4c3c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def70b21b73d0d0156f8ffb526413d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ead6fe08a80379f496eab2129655bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2024-01-19更新
|
211次组卷
|
2卷引用:湖南省长沙市明德中学2023-2024学年高一下学期开学考试数学试卷
名校
解题方法
8 . 三阶行列式是解决复杂代数运算的算法,其运算法则如下:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c685c6a79c8293c8b5083c3a8dc4c.png)
若
,则称
为空间向量
与
的叉乘,其中
,
,
为单位正交基底. 以
为坐标原点、分别以
,
,
的方向为
轴、
轴、
轴的正方向建立空间直角坐标系,已知
,
是空间直角坐标系中异于
的不同两点
(1)①若
,
,求
;
②证明
.
(2)记
的面积为
,证明:
.
(3)证明:
的几何意义表示以
为底面、
为高的三棱锥体积的
倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c685c6a79c8293c8b5083c3a8dc4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e91aaddb8691f8afa477a96bf630631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aba64ae92194bc4f0f6e49725471542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8643f24c3af715421ec0ccd3224ed453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d541143135cb9b8166bc631a85ac6a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a471332d4f3731d90f62fdf819f39824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73db31aecdde14e0002f082d9091df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2980a18e4d0a2a795b7983a1a1866db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1821c677712026f8de34fe924b1f52a.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41ef077626c88964805a45849471a1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb22d1c614d99e2639864e43f4b6277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00db2bada2cfc90c5213aca8af17df4c.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb8623a42db5ceb745a16d72739f513.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0505ce82dd5726c22fcaac54d01d630b.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8191a760981f2d67648905665c8b167a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad58b362528b814739ceb7fe5febfc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
您最近一年使用:0次
2024-03-07更新
|
891次组卷
|
8卷引用:江苏省扬州市仪征中学2024届高三下学期期初调研测试数学试题
江苏省扬州市仪征中学2024届高三下学期期初调研测试数学试题河南省部分重点高中2024届高三普通高等学校招生全国统一考试(期末联考)数学试卷 河南省部分重点高中(青桐鸣)2023-2024学年高三上学期期末大联考数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)江苏省江都中学2023-2024学年高二下学期3月联考数学试卷江苏省盱眙中学2023-2024学年高二下学期第一次学情调研数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点2 平面法向量求法及其应用(二)【培优版】(已下线)专题08 期末必刷解答题专题训练的7种常考题型归类-期末真题分类汇编(北师大版2019必修第二册)
9 . 已知函数
.
(1)讨论函数
的单调性;
(2)设函数
.
(ⅰ)求
的值;
(ⅱ)证明:存在实数
,使得曲线
关于直线
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd428ff2a8bdc70849d01cf619aa23.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0a821d6c0dd7c6f34f1a060fd51ad0.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e071bea69bf2c954277c4e904dfee34.png)
(ⅱ)证明:存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
您最近一年使用:0次
名校
解题方法
10 . 某学校食堂每天中午为师生提供了冰糖雪梨汤和苹果百合汤,其均有止咳润肺的功效.某同学每天中午都会在两种汤中选择一种,已知他第一天选择冰糖雪梨汤的概率为
,若前一天选择冰糖雪梨汤,则后一天继续选择冰糖雪梨汤的概率为
,而前一天选择苹果百合汤,后一天继续选择苹果百合汤的概率为
,如此往复.
(1)求该同学第二天中午选择冰糖雪梨汤的概率.
(2)记该同学第
天中午选择冰糖雪梨汤的概率为
,证明:
为等比数列.
(3)求从第1天到第10天中,该同学中午选择冰糖雪梨汤的概率大于苹果百合汤概率的天数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求该同学第二天中午选择冰糖雪梨汤的概率.
(2)记该同学第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfe0ccc18feef217770312ac21ade7e.png)
(3)求从第1天到第10天中,该同学中午选择冰糖雪梨汤的概率大于苹果百合汤概率的天数.
您最近一年使用:0次
2024-02-27更新
|
1353次组卷
|
5卷引用:湖南省三湘创新发展联合体2023-2024学年高三下学期2月开学统试数学试题
湖南省三湘创新发展联合体2023-2024学年高三下学期2月开学统试数学试题贵州省黔东南苗族侗族自治州2023-2024学年高三上学期九校联考(开学考)数学试题广西壮族自治区桂林市2023-2024学年高二下学期入学联合检测卷数学试题湖南省邵阳市新邵县第二中学2024届高三下学期开学考试数学试题(已下线)专题3.5马尔科夫链模型(强化训练)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)