1 . 已知集合
,
.
(1)若
,求实数
的取值范围;
(2)若
是
的充分不必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2b424a118d1c3823eb6e348105e82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbabfeb3c21f67567e2bd94dccb8617.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 求下列关于
的不等式的解集:
(1)
;
(2)
(其中
常数,
);
(3)
(其中
常数,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0432f4e2161f2d82b8afbcccb799f8db.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ace91dbe03f5345e737b36ec262d344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085f0aa35d8f86b5e4fd152bc6b123e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
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3 . 求下列不等式解集.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3f2596bd86548d7d46a470f6b20dbb.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3f2596bd86548d7d46a470f6b20dbb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd25048201c7b72588d3720dccd1e3b7.png)
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2023-10-17更新
|
731次组卷
|
2卷引用:北京市第六十六中学2023-2024学年高一上学期第一次质量检测数学试题
名校
解题方法
4 . 已知x,y都是正数,且
.
(1)分别求x,y的取值范围;
(2)求
的最小值及此时x,y的取值;
(3)不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04645353d91a5beb6d02c06bb62683a9.png)
(1)分别求x,y的取值范围;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fc838e1477179b36ca7481ee2cc1e8.png)
(3)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcebe10ae382d181636f14889c24f15.png)
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解题方法
5 . 已知b克糖水中含有a克糖,再添加m克糖也全部溶解了,此时糖水变甜。请将这一事实表示为一个关于不等式的命题,并证明之.
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解题方法
6 . 已知
,且
.
(1)求证:
;
(2)求
的最小值以及此时的
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b40b1544e62be8b9e9f4dc9f2c0c74.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b07a360d3c53a6ed3bfd8833766cdf6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b327194e0645ad53a7beb2e4ce1a68fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef260c152a7a0e1d61b05c98cad2917.png)
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解题方法
7 . (1)比较
与
的大小;
(2)若命题“
时,一次函数
的图象在
轴上方”为真命题时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4484b4566dad04eb0068ef1f08f94cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80427a12dc89e29aa067288684c4da67.png)
(2)若命题“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a933eddb3696edb5dc547b7d047bb923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d31d3dffb55d744c8078ab73e1567c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 分别用符号语言、文字语言叙述并证明基本不等式.
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9 . 解下列不等式:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d141f34f18f4802d04ef2e4e5e803aba.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac590b3f1fceb93f0b397f75e442e44.png)
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解题方法
10 . (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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