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解题方法
1 . 对于
,定义
,
,其中
为
中最大的数,例如:
,
,
. 给定正整数
,根据以上内容,对于
,请回答下列问题:
(1)
(用
和
表示);
(2)满足
的有序数对
有多少个?
(3)满足
的有序数对
有多少个?
(4)满足
的有序数对
有多少个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d7720b93b6a0ebf04ea3b8545901da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf7efd1e98a1bac7832ef6367c88c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3a946cb466ad8db7174a8d318ce578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb5694de40f2b01518fc88f0d556c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8436f067b7e4048dd0335f3fdb7e27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca92c9a09bd82e0ebe8e065e09bfbc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563d6edf4e17adf966f50a2e919f0212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fbd87eb7ee8470dcce89f059473895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be431af86fc0b0ba9b05d04c5586d82f.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149c9303df43cbe149c0f02b0737688e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df09d267ae01dcf773ffbc14ead57740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
(3)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8586c1fac679cb347a28b2baeb988d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
(4)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c259473293191a421065b88c80622359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
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2 . 已知集合
,记集合
的元素个数为
.当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
__________ (用数字表示);当
(
且
)时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
__________ .(用含有
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2590bb37cb7630923a429d4a1d847efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8b3217efbef2d705f5beedb40c1fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddbd996153d8fa0640bae56e0328c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98de99e0441b45f322a34566393e022f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056d6e45df3b36b7ace1c1e0d3f16d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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3 . 已知整数
,集合
,
,
,满足
,对任意的
,都有
且
.记
.
(1)若
,写出两组满足条件的集合
,
并写出相应的
;
(2)证明:
;
(3)求
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652fd852e080c91df90888d0449d63d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7bb58dca886fc65d874e2b30040c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f906607b8f6606742f496f73fff2ffd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd31439e275791f4fcd3d22b5ae30ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab4a9bfa50054c808dd8190305d0abd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607a272bff596f86f25dd99f5a69fbbe.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
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4 . 函数
,
,如图所示,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d789e4a7ca6fe5e2501763c6a410fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7774026e395632d1326deecc8f084cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346363143f4c60f935e2c2376391e664.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知A,B为同一次试验中的两个随机事件,且
,
,命题甲:若
,则事件A与B相互独立;命题乙:“A与B相互独立”是“
”的充分不必要条件;则命题( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2a3318f82fec39c53c0e4fea00f75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9561f0ed50a5e48d8642cc51264a4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b377d29e6bf63b76a7b17d9bda86296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9e51c7480e18fee2195e617c9a5b4.png)
A.甲乙都是真命题 | B.甲是真命题,乙是假命题 |
C.甲是假命题,乙是真命题 | D.甲乙都是假命题 |
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2024-05-08更新
|
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6 . 若集合
含有
个元素,则称
为
元集,
的子集中含有
个元素的子集叫做
的
元子集.已知集合
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8efd2f8884ae8c029728ffee11bf3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc03ec3d78487844b44cd273efc9188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb08c3c3a2c1752a0b4b1248da28d203.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() ![]() |
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7 . 已知集合
(
,
),若存在数阵
满足:
①
;
②
.
则称集合
为“好集合”,并称数阵
为
的一个“好数阵”.
(1)已知数阵
是
的一个“好数阵”,试写出
,
,
,
的值;
(2)若集合
为“好集合”,证明:集合
的“好数阵”必有偶数个;
(3)判断
是否为“好集合”.若是,求出满足条件
的所有“好数阵”;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7c07bd06408ada63e19cd38444a8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5790497e607490f8d6c184f11ad260.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f799bc4317846951767f4aa196bfc105.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54946204c502727ffaee3c0172d195a3.png)
则称集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
(1)已知数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93838d1ac2b07386b69165fe00d9e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa71450b470cb7d6464339873d74b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595044a7750ab4f84519041979c3d780.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1acb90636d27c85b45c0204035594f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c95469d8d40311c876b3724f032d7e.png)
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|
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8 . 以下四个命题正确的有( )
A.直线![]() ![]() ![]() |
B.直线l过定点![]() ![]() ![]() ![]() |
C.点![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() |
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|
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解题方法
9 . 已知函数
的导函数为
,
,且
在R上为严格增函数,关于下列两个命题的判断,说法正确的是( )
①“
”是“
”的充要条件;
②“对任意
都有
”是“
在R上为严格增函数”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
①“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc1a317e2e6f1caf1e67bf4073cf789.png)
②“对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e702d87b7d70bf870bc04ef6df889d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
A.①真命题;②假命题 | B.①假命题;②真命题 |
C.①真命题;②真命题 | D.①假命题;②假命题 |
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2023-12-12更新
|
765次组卷
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7卷引用:广东省广州市第二中学2023-2024学年高二下学期期中考试数学试题
广东省广州市第二中学2023-2024学年高二下学期期中考试数学试题(已下线)上海市高二下学期期末真题必刷03(常考题)--高二期末考点大串讲(沪教版2020选修)上海市闵行区2024届高三上学期学业质量调研(一模)数学试卷江西省上饶市广丰一中2024届高三上学期12月月考数学试题湖南省衡阳市第八中学2024届高三上学期第五次月考数学试题(已下线)专题09 导数(三大类型题)15区新题速递(已下线)专题01 集合(15区真题速递)
10 . 下列命题正确的是( )
A.集合![]() |
B.若直线![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.长、宽、高分别为1、2、3的长方体的外接球的表面积是![]() |
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