名校
解题方法
1 . 求下列不等式组的解集:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af06041259a63a098940db36d92166a.png)
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2 . 已知
,且
,
,则
的取值范围为_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d0927085e4dfbf6fa021a48045aa67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b2d527e76722fc897e2b8b29df89c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af843f03248254832458e9a803d8bc1.png)
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解题方法
3 . 比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cc0b4997cae4d8aec791a1d3923314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272f801e4afe574af5706f49868941d7.png)
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解题方法
4 . 对于函数
与
,记集合
;
(1)设
,
,求
;
(2)设
,
,
.如果
,求实数
的取值范围;
(3)设
,
,若存在两个负实数
,
(
),使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5797e9e58e4a1d9d66a15cad9fb067.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897a078c9641d987c2187db279e241c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c2f0f6057426020708ecd49e5b197e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00606a7fafb0a948a31739bfe79fcae.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c363eaede7ba4628518660f695f1a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bdf334aa48d59950a2bd3c7bd3d6ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a95308c3cd363d2e706e78eb8629928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f141c88a96d3eaf70d6570f8bc0086b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dca80f189a0953676e46ec1291dd17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bef6529fc7170b5dee77c2c205e7ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd1d36c3c069c7e50674e3bdfa2d1fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 定义:关于
的不等式
的解集叫
的
邻域.若
的
领域为区间
,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddd254a4d1483bcbae47ab75d9cf84f.png)
![](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/3e96056d539eea51d56e5f92d5475d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d6c3d38e6d514f65dd6dee0e6c55b3.png)
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6 . 对在直角坐标系的第一象限内的任意两点作如下定义:若
,那么称点
是点
的“上位点”,同时点
是点
的“下位点”.
(1)试写出点
的一个“上位点”坐标和一个“下位点”坐标;
(2)已知点
是点
的“上位点”,判断点
是否是点
的“下位点”,证明你的结论;
(3)设正整数
满足以下条件:对集合
内的任意元素
,总存在正整数
,使得点
既是点
的“下位点”,又是点
的“上位点”,求满足要求的一个正整数
的值,并说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2356786e0b902deee0fac769f27dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b807b9b8da58da1b6778865efccb01b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b807b9b8da58da1b6778865efccb01b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(1)试写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b807b9b8da58da1b6778865efccb01b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc2e5975afec220e764b66e49694beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(3)设正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dacb3bc44cffd3717db1f0d9fd8f7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2079202f6a373961631b33c2e0b81e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceb955cff0a243b938fe2d2d1e8a5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a287703170ebf98ba2b52e4f0beb43f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3766ab172f0d65eab0ab0ae1fd84d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
7 . 已知
对所有实数x恒成立,则等号成立时x的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1df950f8e842746f4419faa55b8e781.png)
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2023-10-09更新
|
192次组卷
|
2卷引用:上海市宜川中学2023-2024学年高一上学期10月月考数学试题
名校
8 . 已知
,
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4d422ecdb25865c8bfb3a362a83095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915ad1a611b5edd3e8f743a9e2e234aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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名校
解题方法
9 . 已知
,则下列命题为真命题的序号是______ .
①若
,则
; ②若
且
,则
;③若
,则
;④若
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eb9b6fe8959ae9e71e857b6d6fed49.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf826871e9ae79302042977350b0a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4993894ad04ca915f2cfa7b6c6bd8705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2128a00f52af4427721f0ebba591daa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec8201ff29a2091d40eee10db6bbc1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497d269c30eec393e3f0e877ddbe2983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0664a93f7447b43e286e13602de15a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677724afd5918ede1ca5cff893c5dfd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411100df59e7a9dc8d4ad77d497b6fa9.png)
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10 . 证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69bf4686e4b23ff0a14ebeef826baf8.png)
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