2023高二上·上海·专题练习
解题方法
1 . 已知,如图P是平面
外一点,PA是平面
的斜线,交
于点A,过点P作平面
的垂线PO,垂足是O,直线OA是PA在平面α上的投影.求证:对平面
上任一直线a,a⊥OA是a⊥PA的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/2024/1/14/3410882133221376/3411248924524544/STEM/436e3dd819c745ba9a2ab8f9a094476e.png?resizew=161)
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解题方法
2 . 已知四面体
.分别对于下列三个条件:
①
;②
;③
,
是
的充要条件的共有几个( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcf0148aeba9b23f1dc95d753790b60.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8f950a001b6108071e8d630c058b82.png)
是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
A.0 | B.1 | C.2 | D.3 |
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3 . 设函数
的表达式为
.
(1)求证:“
”是“函数
为偶函数”的充要条件;
(2)若
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45494d4b53dc74f60ba02fff732ac736.png)
(1)求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5437056082d003772d881174d47c5d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 已知a,b,
,则“
”的一个充要条件是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f306d2b261f4c39a9fc0858d96e647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知集合
;
;
;
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e1ed58e1c3eac439553a125b922bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9d19578e25e279abab693dcea35f857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7171a1480948fc6032d5617486967f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d4797ebddc00a1bc30aaf143ed50e0.png)
A.p是![]() | B.p是![]() |
C.p是![]() | D.以上都不对 |
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6 . 已知关于
的不等式
的解集为A,关于
的不等式
的解集为
,其中
、
都是非零常数,
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c119ebd9187763c23a70d7ca1e478a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e255df48f6dd0164663647371088cc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7f14bf7f60fe19b509223284455f05.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既非充分也非必要条件 |
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7 . 有限集合
中元素的个数记做
,设
,
都为有限集合,给出下列命题:
①
的充要条件是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc3207397a0c7d72ac87bfd66c6eb4c.png)
②
的必要不充分条件是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829420dda89e325419729da7a73b719c.png)
③
的充分不必要条件是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3965d233c40d376a62e6fc10247c3177.png)
④
的充要条件是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dafc0b3c56e5f50489b754d14ae307.png)
其中,真命题有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e00e3684bdebff71a511eef7a8d114d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc3207397a0c7d72ac87bfd66c6eb4c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829420dda89e325419729da7a73b719c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a502d6cf8ca4760f10817bf785886181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3965d233c40d376a62e6fc10247c3177.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dafc0b3c56e5f50489b754d14ae307.png)
其中,真命题有( )
A.①②③ | B.①② | C.②③ | D.①④ |
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23-24高二上·上海·课后作业
解题方法
8 . 已知:如图,
是平面
的一条斜线,
是
在
内的射影,直线
在平面
上.求证:
当且仅当
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d7df4b723be4b6685475a19c899a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0270feaf08534fe711c915f4bfc8900.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/06d4c562-972c-4244-bf2e-475265dd4d62.png?resizew=134)
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9 . 如图直线l以及三个不同的点A,
,O,其中
,设
,
,直线l的一个方向向量的单位向量是
,下列关于向量运算的方程甲:
,乙:
,其中是否可以作为A,
关于直线l对称的充要条件的方程(组),下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3693a1ef6bf8e10418b3bd5823e34d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14390e9b6b44472bdc7a131133ab39b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeba5431cae247a8111f1bbd3cc37af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c984376f5475184e0d3e4f7e1bb65f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e224e9d95ffda83c35b81a05637c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2aa08953d98591cba8f7d5edce376ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
A.甲乙都可以 | B.甲可以,乙不可以 |
C.甲不可以,乙可以 | D.甲乙都不可以 |
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2023-06-02更新
|
860次组卷
|
5卷引用:上海市嘉定区第一中学2023届高三三模数学试题
名校
10 . 在
中,“
是锐角三角形”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166f792a201a8ff4a7c73aa5ec3aa026.png)
A.充分不必要条件 | B.必要不充分条件 | C.充要条件 | D.既不充分也不必要条件 |
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2023-02-27更新
|
849次组卷
|
2卷引用:上海市交通大学附属中学2022-2023学年高一下学期3月卓越考试数学试题