1 . 已知
,函数
.
(1)函数
的图象经过点
,且关于
的不等式
的解集为
,求
的解析式;
(2)若
有两个零点
,
,且
的最小值为
,当
时,判断函数
在
上的单调性,并说明理由;
(3)设
,记
为集合
中元素的最大者与最小者之差,若对
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad9a11b81b7a8643005608eacc7f9d9.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd5452c267983506a7cb3373e19fd5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0268e85df43d66b031e0eccb11284452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f88a76f947e7022ef0c5efd6db060c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3c6cdb19ac03dc3c28cd63b09dc907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4802dfb4352b1162b6cda12fa469f91e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc20d351d51723c9b0a07a20ac14114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0225bca34eaf19544939b29153aac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0e3589ab6dda85eb6dc9cab30878f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136da7c9e087330c312e31d1c2083d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8119e4e1c474bc2adbe014628043609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 如图,在四棱锥
中,底面
是正方形,
平面
,
,
,
分别是
,
的中点.
平面
;
(2)求证:
平面
;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
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解题方法
3 . 已知向量
,
,
.
(1)若
,求
的值;
(2)若
,求向量
与
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993e9681181da32d59da5aa14daa853a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc2d0fb8a6b049073027ccfe1dce109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/865aba38107ea2bd90913b0e781cb342.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7d8b42c85013ba07ba18e5e46d8716.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3962d41791025f3acecf477ef8a1c676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a06c8eae3652486cf9e416ce3a8ffc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
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解题方法
4 . 已知
,
是第二象限角.
(1)求
和
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bc052a11cf1a01445992672dde2836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5b6bda1df4487146778acc9ab02264.png)
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解题方法
5 .
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9da282ff262b6698bf5f0ba9ef974e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024高三·全国·专题练习
6 . 已知圆锥的母线长为2
,其侧面展开图是一个半圆,则该圆锥的底面面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
A.π | B.2π | C.3π | D.4π |
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2024高三·全国·专题练习
7 . 命题“
,
”的否定是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16076741a179412e97d81d3fd1d83cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37660096fb35820bc02bb27d58195fc.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
8 . 兴化千岛菜花风景区素有“全国最美油菜花海”之称,以千岛样式形成的垛田景观享誉全国,与享誉世界的普罗旺斯薰衣草园、荷兰郁金香花海、京都樱花并称,跻身全球四大花海之列.若将每个小岛近似看成正方形,在
正方形方格中A,B,C三位游客所在位置如图所示,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea92928d6f4e79241b698c1283c8f91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-24更新
|
173次组卷
|
2卷引用:2024年天津市河北区普通高中学业水平合格性考试模拟检测数学试题
9 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4b5914a8de9ee917dae41ea68c586e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fed3bd5bc925cf990e057f43395bff.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-19更新
|
510次组卷
|
5卷引用:2024年天津市河北区普通高中学业水平合格性考试模拟检测数学试题
10 . 已知
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163ed3d861493fe2d7a5549f203c866e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
A.![]() | B.3 | C.![]() | D.5 |
您最近一年使用:0次
2024-04-18更新
|
847次组卷
|
2卷引用:2024年天津市河北区普通高中学业水平合格性考试模拟检测数学试题