2025高三·全国·专题练习
1 . 已知函数
.
(1)若关于x的不等式
的解集为R,求实数a的取值范围;
(2)解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bd5717f62b4fe9c5995a45ccd7a8d5.png)
(1)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
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2025高三·全国·专题练习
2 . 解关于实数
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61901f0c23f1994acb34bd8c0c793e8e.png)
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3 . 已知甲、乙两个圆台上、下底面的半径均为
和
,母线长分别为
和
,则两个圆台的体积之比![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509322d1ac9bebd7cb434c17a7ee53ec.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9c70db11cd811fc2ff0fff93988b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b252300558bc5528b39b0bd8bc9b8074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509322d1ac9bebd7cb434c17a7ee53ec.png)
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2025高三·全国·专题练习
4 .
的定义域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e7d79b7b91deb70aef8a35d671c088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2025高三·全国·专题练习
5 . 解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7c158bffa566dd65f29f3667d7592a.png)
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2025高三·全国·专题练习
6 . 等差数列
的前
项和为
,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc1ec50ff0c75ebb3d136144ddc8d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259b2e755105c0ee479eabf7265a76a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
A.![]() | B.![]() | C.1 | D.2 |
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2025高三·全国·专题练习
7 . 若实数
满足约束条件
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2a3bb3bd1bf87f61f17b7c22c6e282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c933f75333c29fe87468c5ab038edb79.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 在
中内角
所对边分别为
,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe7a93172d308a58200e3c722fe1072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280e3d69e0c10d6a9ba6d4227b3f3d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe6e6b495c56a3618936dc96b91bf43.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2025高三·全国·专题练习
解题方法
9 . 已知双曲线
的上、下焦点分别为
,点
在该双曲线上,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad29d7c31087e13e266793832af17bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c7f66cac2517f8a68d82a12ca65f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8680fdb33fa1b9d30819518462191af.png)
A.4 | B.3 | C.2 | D.![]() |
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名校
解题方法
10 . 已知等差数列
的前
项和为
.
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156ff12ebc86677c4215a8f0563ef4ed.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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