1 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90943f55ade0f0df3038e08cb9c2d371.png)
A.对任意实数![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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名校
2 . 如果存在实数对
使函数
,那么我们就称函数
为实数对
的“
型正余弦生成函数”,实数对
为函数
的“
型正余弦生成数对”.
(1)已知函数
的“4型正余弦生成数对”为
,求方程
在区间
上所有实根之和;
(2)若实数对
的“2型正余弦生成函数”
在
处取最大值,其中
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b660b878e6c0f3590c50bf52f896acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595044a7750ab4f84519041979c3d780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595044a7750ab4f84519041979c3d780.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425bdb703e21f599b68315be995b551b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c40363783d0e33e6a40e68957391ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e57682d2fe6f71ce86a38502e2f119.png)
(2)若实数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d552855e04ac50648a15e9b4aec868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fc13c376b1423dc2cefb3018bdc26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee0a78ef89b08120fcf8b7cb0d013b1.png)
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2024高三下·全国·专题练习
解题方法
3 . 已知点
,
都是函数
图象上的点,且点
,
到
轴的距离均为1,把
的图象向左平移
个单位长度后,点
,
分别平移到点
,
,且点
,
关于坐标原点对称,则
的值不可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7639f3b8e00c5204d871fa2bbd82cc8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58d6f9653fea3f462c15e0182470da8.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.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/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.3 | B.5 | C.9 | D.12 |
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4 . 已知函数
,现有如下说法:
①若
,函数
在
上有最小值,无最大值,且
,则
;
②若直线
为函数
图象的一条对称轴,
为函数
图象的一个对称中心,且
在
上单调递减,则
的最大值为
;
③若
在
上至少有2个解,至多有3个解,则
;
则正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973bd09ae9775d390177e5bc07d091c1.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d47dbed3333b180fce58a6d9e440f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3697c286ea301d21ff0dc4305d935883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83d5782f737d37aca7f120d007e0018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a72b38ff26cd0c812d6bcbbeb80ae3b.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc07c41b0edfc14cc49914c02ec6d6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394a003540c7ddb2086f5dd305cdd159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d4befb403831c40b77b3644020d835.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad56942439368d413f74e0ab7d9fb23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c5feb0608338d11ab9153185e3df98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e14bbcd89836543ba9ffa79a9c41932.png)
则正确的个数为( )
A.0 | B.1 | C.2 | D.3 |
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5 . 设函数
,若将函数
的图象向右平移
个单位长度后得到曲线
,则曲线
关于
轴对称.
(1)求
的值;
(2)若直线
与曲线
在区间
上从左往右仅相交于
三点,且
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585a3c8c2c9ea53b96f76cd1cb9d6416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdaf49f9611922348aa2784465da614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e28cc90f3ab5b1f9cc083cc21b0ff3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
6 . 若函数
在
上恰有2个零点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23bf3aa51497b4d02fe2eba8c03484f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e9a5ba12522f68daaa341f38b1c6d3.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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名校
7 . 下列说法不正确的有( )
A.已知角![]() ![]() ![]() ![]() |
B.周长为8,面积为3的扇形所对的圆心角为![]() |
C.函数![]() ![]() ![]() |
D.函数![]() ![]() |
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解题方法
8 . 已知函数
.甲:函数
图象一个最高点和相邻的最低点距离为
;乙:函数
为偶函数;丙:当
时,函数
取得极值;丁:函数
图象的一个对称中心为
.甲、乙、丙、丁四人对函数
的论述中有且只有两人正确,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cccd6b3ae9bcaafe3c9a0db80d6f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7447cf1fad6b31006d050c16c82f1b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c3319647314c3b6d82958a909acd2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c52273a1af76b9ae9de76b168edc8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知
,若方程
在
上恰有3个不同实根
,则当
取最小值
时,下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a287499fe51d9948d1ab8769eb2cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b0e5f52141a59e09c369b917a1130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcee20976de0e0e8c1ccd7a951674691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00caa3b28e26231108f7c81bca82bc2b.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
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2023-10-06更新
|
469次组卷
|
2卷引用:江西省部分学校2023-2024学年高二上学期开学考试数学试题
解题方法
10 . 判断正误(正确的写正确,错误的写错误)
(1)
时,函数
取得最大值为
.( )
(2)函数
关于
对称,则
.( )
(3)
,则
为锐角.( )
(4)函数
的值域是
.( )
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60eeccd121aa2d2bfe10b29a058e4866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c793183ec51b2304e5f3eb0e422a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0bedc0b60d6b4ec18ff582bbbb1e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60eeccd121aa2d2bfe10b29a058e4866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d6401d284eac57ec45e9833713e382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(4)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720a213c84fe098182f268548c73845f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
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