1 . 已知
,
是关于x的方程
的两个不相等的实数根,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a626dee272a3286879377414f9aef03c.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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2 . 设
为实数,函数
和
.
(1)若函数
在区间
上存在零点,求
的取值范围;
(2)设
,若存在
,使得
,则称
和
“零点贴近”.当
时,函数
与
“零点贴近”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b024f9c7f405363117c248ff84a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ddc4306abe3a4338a5ec79b3a94d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0722499bd84b19aaa03e01d609f6b8c5.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11fb7a7299354642cfd8e8bb3eed5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b37d8888a776ebf75fae979f35cafb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac944968625853364eb2c655fcb78ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](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/36a1b09c653185842513e24ebba60bb3.png)
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名校
解题方法
3 . 已知二次函数
的图象经过点
,在从条件①、条件②中选择一个作为已知,求:
(1)
的解析式;
(2)证明:
在区间
上单调递增;
(3)若函数
(其中
)的图象与直线
有两个不同交点,求m的取值范围.(写出详细解答过程)
①点
,点
在函数
的图象上;
②不等式
的解集为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97ab84192e12bb292bc9fbd0b29fbee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48befa5d90fafd8bfdb6c90fd241ebfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ca651bfc89628a3b05c6e87ce5d6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
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4 . “反解”是求解函数值域的常用方法,如求函数
(
)值域时,可将x表示为
,再由
得到
,从而解得
.
(1)求函数
的值域;
(2)若函数
在区间
上有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b57694c0bde777137f70911b117c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542c88d831af30623ae5402ef1deeafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c197a8bd6c5ff898dba2df83656e35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2630bcf15969e2a17c1044d34652f7.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c4c415cc09a882826133d8427277e8.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5965ab6b5f60b6b97c1273d3c347e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69abe959988e4c8c0739f5857ccfb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed5eb26f7e7ec1691e977fddaff9ef8.png)
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5 . 已知幂函数
在
上单调递增.
(1)求
的函数解析式;
(2)设
,若
的零点至少有一个在原点右侧,求实数
的取值范围;
(3)若
,
,
,若
,求满足条件的
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c14aa8187552ea9709319e80d23d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5104b3421459142f5125c1cdb52ecc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b82de1f098bcf34fbd1aaf4326f5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f75446914cf9b3425cb0ddcd08fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097a9ab1898d84021c65b050101b0dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4578f38c7b8d01161469fcadfeff7c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
6 . 已知
,一次函数
的图象是线段
,二次函数
的图象是开口向下的抛物线.
(1)①若抛物线与线段
相切,求实数m的值;
②若抛物线与线段
只有一个交点,求实数m的取值范围;
(2)求证:抛物线与线段
恰有两个不同交点的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feeab04dc65757f3f7a480df503cf4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b74eb226474d2253bf4cab617b1162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7eb0a8085326caeeda415aa2c98723.png)
(1)①若抛物线与线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②若抛物线与线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求证:抛物线与线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa30fb9013cce23517a5e99cd67fcc70.png)
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名校
7 . 单位向量
,
,
的两两夹角为
,若实数
,
,
满足
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccfda9afde4441cfd1d4df5fe9622d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.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/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145ec8e9ef187afb4bf6d27a8ab8be22.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2023-07-27更新
|
740次组卷
|
3卷引用:浙江省台州市名校联盟2022-2023学年高二上学期11月五科联赛数学试题
8 . 已知函数
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f12658f65ede8d329a1ba55174b3b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e228067dbbd535c24d7555d0bbfa19.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若方程![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
9 . 如图,已知一酒杯的内壁是由抛物线旋转形成的抛物面,当放入一个半径为1的玻璃球时,玻璃球可碰到酒杯底部的A点,当放入一个半径为2的玻璃球时,玻璃球不能碰到酒杯底部的A点,则p的取值范围为
您最近一年使用:0次
2023-02-25更新
|
672次组卷
|
7卷引用:福建省福州市八县(市)2022-2023学年高二上学期期末联考数学试题
福建省福州市八县(市)2022-2023学年高二上学期期末联考数学试题福建省福州市八县(市、区)一中2022-2023学年高二上学期期末联考数学试题(已下线)第三章 圆锥曲线的方程 章末重难点归纳总结-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)第三章 圆锥曲线的方程(易错必刷30题9种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)期末真题必刷压轴60题(23个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)期末真题必刷易错60题(34个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)专题3.3 抛物线(6个考点十大题型)(2)
10 . 设函数
,其中
.
(1)若
,求
在
上的最大值;
(2)已知
满足对一切实数x均有
,求函数
的值域;
(3)若
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97306b2fb2023559e74fd632d4325ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0729eb6f1f14582b37b5cdcdda2c5c5a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c01ef6036d39379287b6444b3446ada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d19e8dd827a3c1a4dea84f385b02813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd95ae33c06d271d7e1fe1557a707e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9085a9b1ceed4ab947c21669e85c5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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