1 . 已知函数
(
为常数),函数
.
(1)若函数
有两个零点,求实数
的取值的范围;
(2)当
,设函数
,若
在
上有零点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adcd74b99f824e4b2a5e10256deb181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f490a2f04be198d2e9f61a36a601e61d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d22b4beb798f9b1b12b9036e725f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b4e7aafb01b2104404fc9f0e5205c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
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名校
2 . 已知不等式
的解集为
,若
中只有唯一整数,则称A为“和谐解集”,若关于
的不等式
在区间
上存在“和谐解集”,则实数
的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8870876779e79db7033f2617b8535eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:河北省衡水中学2023届高三上学期三调数学试题
名校
解题方法
3 . 已知集合
,命题p:
,
.
(1)若命题p为真命题,求实数a的取值范围;
(2)若命题p为真命题时,a的取值构成集合B,且
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab128145ccd470c4dad09d6a5c55ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83025679ed826bd9c8a08992f15bd3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
(1)若命题p为真命题,求实数a的取值范围;
(2)若命题p为真命题时,a的取值构成集合B,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
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7卷引用:河北省辛集市第三中学2023-2024学年高三上学期第一次月考数学试题
4 . 设
为正实数,若各项均为正数的数列
满足:
,都有
.则称数列
为
数列.
(1)判断以下两个数列是否为
数列:
数列
:3,5,8,13,21;
数列
:
,
,5,10.
(2)若数列
满足
且
,是否存在正实数
,使得数列
是
数列?若存在,求
的取值范围;若不存在,说明理由.
(3)若各项均为整数的数列
是
数列,且
的前
项和
为150,求
的最小值及取得最小值时
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428dccc2ca7913400fd6644fb78de601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
(1)判断以下两个数列是否为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5faff5d08e2976e15f0cec988ced37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d765033fa3e470b4b4bae90a28514587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585e3a2fda3f7f3b5b484c9113a3c59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee7ed704a954d0414be6c3148bd566d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若各项均为整数的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8f894492a8126f5f133dec4cd68833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1071ac8657ef1c4e1ea7e0530196298d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc94ddf603ec2e0af31695f6654b2d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b47bfab3010d4aa7e17cd1b54e26c157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
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5 . 已知关于
的函数
为
上的偶函数,且在区间
上的最大值为10.设
.
(1)求函数
的解析式.
(2)若不等式
在
上恒成立,求实数
的取值范围.
(3)是否存在实数
,使得关于
的方程
有四个不相等的实数根?如果存在,求出实数
的范围,如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39a21c80ae3e990027ecea33bfb6424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85564659d145e38c0887d186db1c8573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba94b35258a2fbde34d7e26be524fb6e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e567c3e841ba226b51543b0dc43e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4d001c51cf7b47102f641ded56b01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6544efd3f7cea29d879628d508f0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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8卷引用:河北省行唐县启明中学2023届高三下学期5月月考数学试题
名校
解题方法
6 . 已知函数
.
(1)若不等式
的解集为
,求实数a的值;
(2)
时,
恒成立,求实数x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585c861f339d170f806e3e31f1fe95fa.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfdecc7f8089cb23c20d0a93ee1b601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42226c99901dbfc0b75ec3a2deb611a2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b98ffee92a7948602e86e7ffa5dd1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6beda797b9b42f555d84a3211ed12df9.png)
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7 . 已知函数
,其中
且
.
(1)若
,
,求不等式
的解集;
(2)若
,
,求b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78357a4692ab7d75157333f49a62439b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d03b9867f112114f33627d8c28600a8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b713856f459dcb717f4e5be71b022e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5be1c986ef462966026705615ddb66.png)
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4卷引用:河北省邢台市质检联盟2023-2024学年高一上学期第四次月考(12月)数学试题
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8 . (1)当
,若关于
的不等式
的解集不空,求实数a的取值范围;
(2)求关于
的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88b6d0df0ee20bf56477f867015a08c.png)
(2)求关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097ca32934ef96f84e79ef007f2d8708.png)
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3卷引用:河北省唐县第一中学2022-2023学年高一上学期10月月考数学试题
河北省唐县第一中学2022-2023学年高一上学期10月月考数学试题(已下线)第3章 不等式综合能力测试-【帮课堂】(苏教版2019必修第一册)天津市武清区杨村第一中学2023-2024学年高一上学期第一次月考数学试题
9 . 定义一种新的运算“
”:
,都有
.
(1)对于任意实数a,b,c,试判断
与
的大小关系;
(2)若关于x的不等式
的解集中的整数恰有3个,求实数a的取值范围;
(3)已知函数
,
,若对任意的
,总存在
,使得
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2671f593186fa00f17ad26eba7b8f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8c23336002eb5d7c478479fcda799f.png)
(1)对于任意实数a,b,c,试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fda9c56c7993236c0ebdfe08d110ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98e8a20e1e3d328265269df6b2927ad.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80fef6a2dd7e822d83ae45ea79a5357.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fc1f7733bebb86885b6e6fd0534e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8b60555f0d82c386c5b935c23ff952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12965bbc260bdbb0df0a110e59fb8d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bf66ef253242900ca1702121238b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52dc0bb1b1d25a0e86babc0edc627e44.png)
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3卷引用:河北省石家庄市第二中学2023-2024学年高一下学期学情调研(一)数学试题
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解题方法
10 . 已知
的解集是
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5f28031b036e4a37be931d5ff28368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148d97803c3b16893ced41ad5cd9aba4.png)
A.若c满足题目要求,则有![]() |
B.![]() |
C.函数![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() ![]() |
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