名校
解题方法
1 . 已知
,其中
.
(1)当
,
时,
①任意写出
的一条对称轴;
②求证:
;
(2)若对任意
,
,求
所能取到的最小值和最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba354888ba7e2065e85656c20f31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191d9381c4f252fbb5553ba72462d0aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5805d32dc3582d0a706c015875c15eb9.png)
①任意写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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2 . 已知
为实数集的一个非空子集,称
是一个加法群,如果
连同其上的加法运算满足如下四条性质:
①
,
;
②
,
;
③
,
,使得
;
④
,
,使得
.
例如
是一个无限元加法群,
是一个单元素加法群.
(1)令
,
,分别判断
,
是否为加法群,并说明理由;
(2)已知非空集合
,并且
,有
,求证:
是一个加法群;
(3)已知非空集合
,并且
,有
,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd242f355d5128425429a83e4b6632c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8362f15e544684164f38ff9ad7c38ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea5a550b5452df9abdbca776c2ff500.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509a09a7391de2cc86e5e44ccccc981b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8236622218d4d4012d8637538ac9032.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef35ae51107e991163ea418c8dec53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc118659264aca9e263cb8edc41e9c44.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f0119b6de9149150071fe7ed848aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a065a5ddaa18900ee15a8b436f0fcb95.png)
例如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178e8cc61b87b4dc63105ab4fca8680c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7cb4e4e98b375294dc1dccbeebbd6c2.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809b2e00ab8e43a0f886c7f83846d3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b113752e4f989a338747b95a40cf386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18f9bbb6b9feb166f7ecfb49013262d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ee969e5c3d880e0209235bb9cfc49f.png)
(2)已知非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a02a810b3332821bc444f215183c9e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7d3e3d84e1fdee95574817741d731e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08152bab36dca188978d125e4b7a935a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489ea5a5f5b5de37e238cbfbb4a01143.png)
(3)已知非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28cc3165eef94c22c442b2f30c87cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4034552829008c1daaee2701d2afe8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e0f9ba8419972cff845bfd91f64297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ddc4872d58eaa6bcc432b7b94939f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5eb4f6f84d264f3403eece1e7c37b7.png)
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3 . 已知实数x,y满足方程
.
(1)求
的值;
(2)设
与
是方程组
两组不同的解,其中
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1beb6812158ca2a3082bd13ca07578f0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1afbc87ccffbc98b9ab58df8c69bee.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99307ab4373fbe72422ae5aa980db61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41039d45e37899d233232de3d802b105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccee8eb181dc117834582bc433eca559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab3cf6695638d5bcd26580174d7cbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
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解题方法
4 . 已知二项式
,且
满足
.
(1)求
值,并求二项式系数最大的项;
(2)求二项展开式中含
项的系数;
(3)请直接写出展开式中所有项的系数的和.(此题涉及的系数一律用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee670f683d771efae44b74f22754d36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55542eb4ace8f54bee50dd3d5d8a15a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求二项展开式中含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3336c8ed5361c10c37300e41e03f9f2f.png)
(3)请直接写出展开式中所有项的系数的和.(此题涉及的系数一律用数字作答)
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解题方法
5 . 将
三个人随机安排到甲、乙、丙、丁这四个部门工作,已知甲部门一定有人,则不同的安排方法种数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
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解题方法
6 . 某校运动会负责播出稿件的志愿者有2人,负责给运动员引领的志愿者有5人,现要从这7人中选出3人组成慰问团,要求每项志愿服务都要有人参与,则不同的选法共有( )
A.16种 | B.20种 | C.25种 | D.28种 |
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7 . 已知
,
是
的子集,定义集合
,若
,则称集合A是
的恰当子集.用
表示有限集合X的元素个数.
(1)若
,
,求
并判断集合A是否为
的恰当子集;
(2)已知
是
的恰当子集,求a,b的值并说明理由;
(3)若存在A是
的恰当子集,并且
,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd261358114fe2d2106376b86577dd6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de04e7bd1c120d55e09bc0ee11be3fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57880ac18aed3eef69c1a762d09bd281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10938a26383470fe22142017fcaf2fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37765d2927d24d4b582423c843aebcd4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fb97962a729a7a5ec1e311c8f3be9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398ba56f5a708d2d85a02320e1a389d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27182444d3da4003680f07ec299087c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3dec17407438d4fe273345a03ad77a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194592cb77de8a597d5d64e1c85c3249.png)
(3)若存在A是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2734b136f9961df15bb51c31e29e28.png)
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2023-11-25更新
|
213次组卷
|
2卷引用:北京市顺义牛栏山第一中学2023-2024学年高一上学期期中考试数学试题
名校
解题方法
8 . 已知二次函数
的图象经过点
,在从条件①、条件②中选择一个作为已知,求:
(1)
的解析式;
(2)证明:
在区间
上单调递增;
(3)若函数
(其中
)的图象与直线
有两个不同交点,求m的取值范围.(写出详细解答过程)
①点
,点
在函数
的图象上;
②不等式
的解集为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97ab84192e12bb292bc9fbd0b29fbee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48befa5d90fafd8bfdb6c90fd241ebfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ca651bfc89628a3b05c6e87ce5d6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
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解题方法
9 . 给出下列命题:
①经过点
的直线都可以用方程
表示;
②若直线
的方向向量
,平面
的法向量
,则
;
③直线
必过定点
;
④如果向量
与任何向量不能构成空间向量的一个基底,那么
一定共线.
其中真命题的个数是( )
①经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75db25985d446632b3a2675347b08815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914e6f4d048ccd9d8538d5f14ce04ef2.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc44c2c100d504f3bd2b71db08dc412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4cd9a0008660e60d0cc8b2b8e67d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac3b69009a27d28fa04fd88c9bb102.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51156bf5f18f9bbe5c80680252e43414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
④如果向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
其中真命题的个数是( )
A.3 | B.2 | C.1 | D.0 |
您最近一年使用:0次
2023-10-17更新
|
558次组卷
|
3卷引用:北京市顺义区第二中学2023-2024学年高二上学期期中考试数学试题
北京市顺义区第二中学2023-2024学年高二上学期期中考试数学试题北京市顺义牛栏山第一中学2023-2024学年高二上学期10月月考数学试题(已下线)专题07 直线过定点综合问题(期末选择题7)-2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)
名校
10 . 已知某生物技术公司研制出一种新药,并进行了临床试验,该临床试验的成功概率是失败概率的2倍.若记一次试验中成功的次数为X,则随机变量X的数学期望为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-07-10更新
|
476次组卷
|
5卷引用:北京市顺义区第一中学2023-2024学年高二下学期期中考试数学试卷
北京市顺义区第一中学2023-2024学年高二下学期期中考试数学试卷北京市丰台区2022~2023学年高二下学期期末数学试题(已下线)第7.3.1讲 离散型随机变量的均值-2023-2024学年新高二数学同步精讲精练宝典(人教A版2019选修第三册)【北京专用】专题07概率与统计(第二部分)-高二上学期名校期末好题汇编(已下线)专题06 离散型随机变量分布列及成对数据统计分析6种常考题型归类-1