名校
解题方法
1 . 二次函数
满足
,且
.
(1)求
的解析式;
(2)若
时,
的图象恒在
图象的上方,试确定实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42b6975b22e99c0148e6952d174ebba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17ee5f43412795671704ab0e8d0b2f5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f2ee5e48cce77eb4a2cb9f11ccfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a0ac4bfe4ded00b4400f913e0c9862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
7日内更新
|
518次组卷
|
2卷引用:河北省邯郸市永年区第二中学2023-2024学年高二下学期6月月考数学试卷
解题方法
2 . 已知集合
,
.
(1)若
,求
;
(2)若“
”是“
”的必要条件,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97a364fe3348933be396a0261a9e217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973e8173f5b67e01f9cebd9d868d3c52.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe344fe369fb629b89eb956c85498ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
3 . 对于任意给定的四个实数
,
,
,
,我们定义方阵
,方阵
对应的行列式记为
,且
,方阵
与任意方阵
的乘法运算定义如下:
,其中方阵
,且
.设
,
,
.
(1)证明:
.
(2)若方阵
,
满足
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e76d1d8e50dda4d50229a8a20c57e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc29ee719feeedfbc8c529cf11348abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e11a5b70e1e2e685d1783a4707872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ec97af19b15cd584710a3faf30c716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f44b167b4e75af29a18637f71f3ebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b39fcc210ec89dbc7d684a70a34542c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d17ebf9f595cdb9dab841dec703b512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a4ed514630bd37fab9765b3fb5f2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709d09c76c222f156df31a1bba5f2ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e4a35eca00ea2f4580d62515d54d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95035eeae686e910be45f08093e406c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e7d309cb178b71c6e56f5b7f610413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109b4ece615b08a89a7f69d436f448b0.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb109c49695bce8c5b5cf4fad95772.png)
(2)若方阵
![](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/2221c60bc15c59fa1b3ac74a23b57cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa9bfe3bf3e3b7265da3c49d31f1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35536fb98d8b24cead230c8df95fd9d3.png)
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7日内更新
|
128次组卷
|
3卷引用:2024届河北省保定市九县一中三模联考数学试题
名校
解题方法
4 . 柯西是一位伟大的法国数学家,许多数学定理和结论都以他的名字命名,柯西不等式就是其中之一,它在数学的众多分支中有精彩应用,柯西不等式的一般形式为:设
,则
当且仅当
或存在一个数
,使得
时,等号成立.
(1)请你写出柯西不等式的二元形式;
(2)设P是棱长为
的正四面体
内的任意一点,点
到四个面的距离分别为
、
、
、
,求
的最小值;
(3)已知无穷正数数列
满足:①存在
,使得
;②对任意正整数
,均有
.求证:对任意
,
,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a8a1b208f491296432e9e6bf0e91c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0653d6a0e8778ad47b06d5f6b88cffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419c991c4022ef12d4801e119018b587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31a068fb311eff550b3088a212fb2f0.png)
(1)请你写出柯西不等式的二元形式;
(2)设P是棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d0252c1b2f7d2a84b5c985d19d547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d31659f106fba3c9750661eb0e3c3eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dde93376f5d29f8f7d501122759b0ab.png)
(3)已知无穷正数数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c24ecf9e59082e563372b12981d03fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee33826e02eda7aa6221649355a5709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9db6b0bf3d360830fff618193c595b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a33ac34aa03dc7f0a5faad6dc664ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
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2024-06-04更新
|
347次组卷
|
2卷引用:河北省邯郸市2024届高三下学期高考保温数学试题
解题方法
5 . 如图,某市城建部门计划在一块半径为
,圆心角为
的扇形空地AOB内设计一个五边形花境,具体方案设计如下:在圆弧AB上取点P(P与A,B不重合),点M,N分别在半径OA,OB上,且
,
,连接PA,PB,MN,在由
,
,
组成的五边形MNBPA内种植三种花境植物,设
.
的取值范围;
(2)已知
内花境植物种植费用为400元/
,
,
内花境植物种植费用为500元/
,试预测此五边形花境最低造价为多少万元?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc8bd8fef0c480e9ad908b7fcde315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a69f6a208dd6671c46271b78430d79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7025b43a8991cf07b35323ee6e042695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd34b25a45696964c166bbc33585028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35a9ec7088381262f8ca327bd377660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ff139f605ee0df463ad9f64089e542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c974c20de0e31685d64e26522969e2f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd34b25a45696964c166bbc33585028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35a9ec7088381262f8ca327bd377660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
您最近一年使用:0次
名校
解题方法
6 . 已知角
的终边落在直线
上,求
,
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cd2a180ae300bbf2388a709e4c28e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
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2024-04-27更新
|
272次组卷
|
7卷引用:河北省张家口市张北成龙高级中学2023-2024学年高一下学期3月阶段测试数学试题
河北省张家口市张北成龙高级中学2023-2024学年高一下学期3月阶段测试数学试题河北省张家口市尚义县第一中学等校2023-2024学年高一下学期3月阶段测试数学试题(已下线)7.2.1 三角函数的定义-【帮课堂】(人教B版2019必修第三册)(已下线)复习题一北师大版(2019)必修第二册课本习题第一章复习题(已下线)第五章:三角函数章末重点题型复习(1)-同步精品课堂(人教A版2019必修第一册)(已下线)第五章:三角函数章末重点题型复习(1)-【题型分类归纳】(人教A版2019必修第一册)
2024高三·全国·专题练习
名校
解题方法
7 . 设函数
(1)若不等式
对一切实数x恒成立,求a的取值范围;
(2)解关于
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87269d6002a4f78fe4ee9aa53b4cd01c.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e674bf3f00e008ef510c783fcfa18219.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f1040777491b882fa89809cdf337cd.png)
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2024-04-26更新
|
1322次组卷
|
3卷引用:河北省保定市定州中学2023-2024学年高二下学期五月半月考数学试题
名校
8 . 已知定义在
上的函数
满足:
.
(1)判断
的奇偶性并证明;
(2)若
,求
;
(3)若
,判断并证明
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca24be2290ac9cf976edce22eb8d060.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4886e28e9ecd40f7edd25f25bde28453.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146e32ccd4375d7898e8381ef7bee7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a360203717effe5e60f78c5b2b7a95d.png)
您最近一年使用:0次
名校
9 . 对于函数
,若在定义域内存在实数x满足
,则称函数
为“局部奇函数”.
(1)若函数
在区间
上为“局部奇函数”,求实数m的取值范围;
(2)若函数
在定义域R上为“局部奇函数”,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d88a41a8c39757a1bbcc8ae9052c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50554244cd4658513a4378609f97322b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c213e338d529fed5aa83722b5e94d85.png)
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名校
解题方法
10 . 对于函数
.
(1)若
,求
在
上的值域;
(2)若
与
图象恰有一个交点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1a2d0e68f5ec27ffc95e0b995099ed.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b587e5f500e7fb3f4482cc8250255a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4790cdd2c83f810e3527356f686e7946.png)
您最近一年使用:0次