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1 . 2023年“国际进口博览会”即将在上海举行,现要在场馆入口布置一个大型立体花卉景观,景观的框架由中空钢管搭建的而成,外型是由若干个小正方体叠加而成的大正方体,己知搭建此立体花卉景观的脚手架钢管安装呈现东-西、南-北、上-下的网络状,每三根钢管相交处需要焊接,这些焊接点(小正方体的顶点)称为格点,相邻焊接点之间的距离都为1米(即每个小正方体的棱长都为1米),若以互相垂直的三条钢管为轴建立空间直角坐标系,现要在一个格点处接入水源,并在下述6个格点:
,
,
,
,
,
处安装喷淋,使6处喷淋与水源接入口所排水管的总长度最小,则此时水管总长度的最小值为______ 米(水管必须在连通的钢管内部穿行,不计各接头处的水管损耗).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e12d9792e52b9aa1becb41b2cb466c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9133716445647a631e061f0db999a30.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc34aa52ba67336faab0e1b7011aed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc88b7ba754ce79db2568cb024d2204.png)
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解题方法
2 . 已知问题:“
恒成立,求实数
的取值范围”.两位同学对此问题展开讨论:小明说可以分类讨论,将不等式左边的两个绝对值打开;小新说可以利用三角不等式解决问题.请你选择一个适合自己的方法求解此题,并写出实数
的取值范围___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4bd663b032332fcb460f03a191d720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-01-12更新
|
468次组卷
|
6卷引用:上海市浦东新区2021-2022学年高一上学期期末数学试题
上海市浦东新区2021-2022学年高一上学期期末数学试题(已下线)2.3 三角不等式(第3课时)(1)(已下线)专题02等式与不等式(8个考点)(2)(已下线)第07讲 基本不等式及其应用(2大考点4种解题方法)(2)上海市徐汇区2023-2024学年高一上学期学习能力诊断卷(期末)数学试卷上海市育才中学2023-2024学年高一上学期期末质量检测数学试卷
3 . (1)写出不等式
等号成立的一个充要条件是______ ,一个充分非必要条件是______ ,一个必要非充分条件是______ ;
(2)写出不等式
等号成立的一个充要条件是______ ;
(3)写出不等式
等号成立的一个充要条件是______ ;
(4)写出不等式
等号成立的一个充要条件是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17dfe017b47a6c698367a734178ad318.png)
(2)写出不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15638f1e66350b1341d7a123f438079d.png)
(3)写出不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c7dc7fede94988efae9af48562ab65.png)
(4)写出不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae8a569e980980633d59b7b6de9dc18.png)
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4 . 我们知道平面直角坐标系内直线的一般式方程为
,对此进行类比,可知空间直角坐标系内平面的一般方程为
;运用上述知识,已知实数
,
,
满足
,则
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01fa45cefa203889bab7f3b68c60b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a83e5d490ea07656d457fb3d81d4e82.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/794361beee8b56d9bf49d8d6a0990811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97502047959344e89522d31c05deff35.png)
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5 . 当且仅当
(其中
)时,函数
的图像在函数
图像的下方,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1698eb2b7eb35ba842bd4e9089d8f863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed71b5f6cf02b7e4c52c1181669a3879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bfd6f4f114107a8531b97079725497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc9500da43d762652277fcc768e4bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0f46282728fa51ff142a5ad59b06dc.png)
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6 . 用实数
(
或1)表示命题
的真假,其中
表示命题
为假,
表示命题
为真.设命题
:
,
(
).
(1)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ ;(2)当
时,实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0076be2c8160ef6a60be1a0ca51617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a27a05295f527284bc5a1598ac6db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 已知函数
,则当
时,函数
有最小值,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2ff94d4949458e796737ef8dde6ee6.png)
____________ .此时![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04ed688267b217a90d5d88c6f88c39.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6321b05c883f202c0962d26c498fdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2ff94d4949458e796737ef8dde6ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04ed688267b217a90d5d88c6f88c39.png)
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8 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7de9ae5e7f20f9b0c6088205defc60.png)
_______
(填入等号或者不等式)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7de9ae5e7f20f9b0c6088205defc60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480cb64dc2434fbcbe338e7b87b92991.png)
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9 . 已知
,
,
,则
的最大值是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5faa5fdcd94e4dc99906d78a198f2049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75eaf97713f43e771a3f9603c19ee24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258dbe016982a678fa64b423907b4386.png)
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解题方法
10 . 不等式
中
的取值范围是
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f511d6169cf710fde7988bc598da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5374dfeacbb54f1d1e9f14bc29fe406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
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