解题方法
1 . (1)证明:
,
,
;
(2)已知
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cccdff49c3efe6e7a7dbbf69db9319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8276612c55546d158057d21f7fa6ff.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85bbd9601e85689067611bf9e5f017c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a024140be537e2e72d01e0d81a09fa23.png)
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解题方法
2 . 已知
为任意给定的正实数,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2b05214c8b22507f0c36b110593d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff668b944a65587a1bbcae01936fabc8.png)
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3 . 若实数
满足
,则称
比
远离
.
(1)若
比
远离1,求实数
的取值范围;
(2)若
,试问:
与
哪一个更远离
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d32d4403d0e81eacfbe429dc51f07f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b782dd2de9c9caa840838cd63d817de.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/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384644d7bf34625fd3af5083436f5e25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ebc856291255f2d4a6c20b982a2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
4 . 解答下列各题.
(1)已知
,试比较
与
的大小;
(2)设
均为正数,且
,证明:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca24341509c05e672999202f2df0ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444b88d2de0c2e06f5efae2578e3ef8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef758c8f9983a4dacaaa1eed75ad455.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09fc94ae8293ad1de55d2990502588e.png)
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名校
5 . (1)求方程组
的解集;
(2)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43094b425ee07c42d07bd461696a6b6e.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d576f866d604c49f83f9435815698.png)
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2卷引用:辽宁省沈阳市第二十中学2023-2024学年高一上学期10月月考数学试题
6 . 已知
,且
都是正数.
(1)若
,求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a6f362a7f8f972d6b329a882e940d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba9c88a847d8483a887b088159c7c0f1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f917a19a15bceb9a3769e59e25dd9c.png)
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名校
解题方法
7 . 上海世博会某国要建一座八边形的展馆区,它的主体造型的平面图是由两个相同的矩形ABCD和EFGH构成的面积为200m2的十字型地域,计划在正方形MNPQ上建一座“观景花坛”,造价为4200元/ m2,在四个相同的矩形上(图中阴影部分)铺花岗岩地坪,造价为210元/ m2,再在四个空角(如
等)上铺草坪,造价为80元/ m2.设AD长为x m,DQ长为y m.
(1)写出
与
满足的等量关系式;
(2)设总造价为
元,求当
为何值时,
最小?并求出这个最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e70ac2a2eb20a7184cb1b80db8ee1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/fb2049fa-ee5a-4ead-8aee-a207426b3e2e.png?resizew=138)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)设总造价为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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解题方法
8 . 已知关于
的不等式
的解集为
.
(1)求
的值;
(2)试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b4ae85c34559da6650b58b37527f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfa87d2b879cb327b3f542bc155f145.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9916909cb5c61acac70888de7671cfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
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5卷引用:河北省保定市部分高中2023-2024学年高一上学期选科调考第一次联考(10月)数学试题
河北省保定市部分高中2023-2024学年高一上学期选科调考第一次联考(10月)数学试题河北省沧州市大数据联考2023-2024学年高一上学期10月月考数学试题辽宁省部分高中2023-2024学年高一上学期10月月考数学试题贵州省黔东南苗族侗族自治州从江县第一民族中学2023-2024学年高一上学期10月月考数学试题(已下线)第二章 一元二次函数、方程和不等式【单元提升卷】-【满分全攻略】(人教A版2019必修第一册)
名校
解题方法
9 . 求下列不等式组的解集:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af06041259a63a098940db36d92166a.png)
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解题方法
10 . 已知
均为正实数.
(1)求证:
,
(2)若一个直角
的两条直角边分别为
,斜边
,求直角
周长
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb2e31608320e989afeeed9a7a8482d.png)
(2)若一个直角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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