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1 . 设
是两条不同的直线,
是两个不同的平面,则下列四个命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b4218f00da487d3f63b9360144708f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474929dd8e89d9ce37448ae72b48d04f.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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2 . 设点A,B在曲线
上两点,且
中点
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2702a5539ca829b8b7a08407f0996e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b93b11d2942b8c99c3a19a2a00d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.1 | B.2 | C.![]() | D.![]() |
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3 . 五一小长假前夕,甲、乙、丙三人从
四个旅游景点中任选一个前去游玩,其中甲到过
景点,所以甲不选
景点,则不同的选法有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2740d2f1f18082f6299bd23e0be289c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.64 | B.48 | C.36 | D.24 |
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4 . 设集合
,
,则
的子集个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38d70f23e78a00dcbf9074bf564ff9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d1451201f16941711b00d398f24d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
A.2 | B.4 | C.8 | D.16 |
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5 . 已知复数z满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f72f48181514c3cfa0053b27d79c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35845a775881218a4d0a4944dee85ed9.png)
A.![]() | B.1 | C.![]() | D.2 |
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解题方法
6 . 如图,三棱柱
中,
是边长为2的等边三角形,
.
;
(2)若三棱柱
的体积为3,且直线
与平面ABC所成角为60°,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cbafbd47a57b0a24799ca61af682f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2f04faf03ca18388df766d654af211.png)
(2)若三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
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7 . 已知函数
,其中
是自然对数的底数.
(1)当
时,求曲线
在点
处的切线的斜截式方程;
(2)当
时,求出函数
的所有零点;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e13355778854f8c54090201ba91bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c94550573090575b08e641d69980610.png)
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8 . 已知函数
,若曲线
与直线
恰有2个公共点,则a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14992f6e55eac3212fe6ca43e27966af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1447dbe580ac5c825776995118e75acf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知函数
.
(1)当
时,求
的最大值;
(2)讨论函数
在区间
上零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d7abebebf906a845461e157c5c9a0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf613d5ed2a4b75ee70638f28fd9f44f.png)
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解题方法
10 . 已知
是定义域为
的偶函数,
,
,若
是偶函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096f5d916ff9ca84f0cf4c7bff8745e.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3e8e493fcf1f4e1c384721d32d43cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4343f10c051cab3f0522ccbaae21a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6d578f9c98ce402d4cf6e4a23281c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096f5d916ff9ca84f0cf4c7bff8745e.png)
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