1 . 已知正数
满足
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254aebe3ef7eabdf41e46c1cd857c705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df852e5c8d439fbf69f83fa9e080a638.png)
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解题方法
2 . 在实际应用中,通常用吸光度
和透光率
来衡量物体的透光性能,它们之间的换算公式为
,下表为不同玻璃材料的透光率,设材料1、材料2、材料3的吸光度分别为
、
、
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86ab72ebbf972a8ee1f10faacabb90d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
玻璃材料 | 材料1 | 材料2 | 材料3 |
0.7 | 0.8 | 0.9 |
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 当实数
时,函数
有且只有一个可导极值点,则实数
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d62e8db36dd051407d4308239c113b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知直线
满足:原点到它的距离为
,点
到它的距离为
,请写出满足条件的直线
的一个方程:______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c3a2f5b0702ea9fbb9dc8904579737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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5 . 设函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce60d1325780279e5c8d600c01b6b1e.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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解题方法
6 . 设等差数列
的公差不为0,其前
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/e4610798219c3ced9f3402c63125b9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679d32bb89a6b15bd9e2b626223ffa7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d238a52feae87b0778ba324dc144d50.png)
A.0 | B.![]() | C.2020 | D.4040 |
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解题方法
7 . 已知向量
,
,设
,
的夹角为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda3f2bbb62d0e0abc140c174944aa89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66de249b7c29faff4f8ff786ba21d500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d05fafe20525f3f7029e6c15bcf7d13.png)
A.![]() | B.-![]() | C.![]() | D.![]() |
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解题方法
8 . 定义在
上的函数
满足
为奇函数,函数
满足
,若
与
恰有2023个交点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93822852f7b503265d10ab7fb9e656c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237098a8678a32add77d40ce9f46bb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684686b23c9fc63c120ab59dafff9336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2953b408847ff0ae7d99e0874d09d773.png)
A.![]() | B.![]() |
C.2为![]() | D.![]() |
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解题方法
9 . 在
中,角
所对的边分别是
,且
.
(1)证明:
成等比数列.
(2)求(1)中数列的公比的取值范围.
![](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/88f2599ca8b6b683e57a82699c8b1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ef74b24d959783dc7eed4550728938.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4a8c2c7845cfb1b094d13e66e0ed87.png)
(2)求(1)中数列的公比的取值范围.
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解题方法
10 . 如图,已知正方体
的棱长为2,
,
,
分别为
,
,
的中点,以下说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/cdbdc961-2337-4d86-9834-9f7b056d1a84.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/cdbdc961-2337-4d86-9834-9f7b056d1a84.png?resizew=170)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.过点![]() ![]() ![]() ![]() |
D.平面![]() ![]() ![]() |
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