名校
1 . 已知集合
,其中
且
,非空集合
,记
为集合B中所有元素之和,并规定当
中只有一个元素
时,
.
(1)若
,写出所有可能的集合B;
(2)若
,且
是12的倍数,求集合B的个数;
(3)若
,证明:存在非空集合
,使得
是
的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcbde10b7bc82536072ca38f32b2f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe11d564517c04437b9884da859002b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9bc3a22bc9cb056df1e6d5218877c8c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6e90ea92c80c31653e4ac972bf56c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d725be6acff620b47bb7a8a7a0c6e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af5e68b8592c14157df8db05904c8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
您最近一年使用:0次
2024-01-20更新
|
323次组卷
|
2卷引用:北京市北师大附中平谷第一分校2023-2024学年高一下学期2月开学测试数学试题
名校
2 . 已知函数
.请从条件①、条件②这两个条件中选择一个作为已知,解答下面的问题.
条件①:
;
条件②:
.
注:如果选择条件①和条件②分别解答,按第一个解答记分.
(1)求实数k的值;
(2)设函数
,判断函数
在区间
上的单调性,并给出证明;
(3)设函数
,指出函数
在区间
上的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f7d13f97baaeb36f1785d09d389f0c.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a38b1e7496745c92fabb36b1c5d6f16.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b3d8321b8a85830c2af2ead9f36867.png)
注:如果选择条件①和条件②分别解答,按第一个解答记分.
(1)求实数k的值;
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d825ec419a668aa8efb06d43d3c2a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f4afb555297200a8cbc59a428ed8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
您最近一年使用:0次
2024-01-17更新
|
370次组卷
|
5卷引用:北京市第二十中学2023-2024学年高一下学期开学模拟考试数学试题
名校
3 . 设函数
与
的两个交点为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
,点
.求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646e11d5bff57e56ce82c2339f2d71ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba743f102d7b9497a9a2fc20d97d1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6910a983f59fa03e7c171cecee740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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4 . 已知点
,O为坐标原点,点B在第一象限且在反比例函数的图象上,若
为等边三角形,则此反比例函数的解析式是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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5 . 若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692f0df58ba49655844e0bf4f0d240db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.12 | B.10 | C.8 | D.6 |
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6 . 若
为正整数,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a296772b32c3a9d0844de389327a06.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 有一电脑程序:每按一次按键,屏幕的
区就会自动加上
,同时
区就会自动减去
,且均显示化简后的结果.已知
两区初始显示的分别是
和
,如图,第一次按键后,
两区分别显示:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/54c243d1-3018-4f7c-8878-46d595048b2b.png?resizew=261)
(1)从初始状态按2次后,分别求
两区显示的结果;
(2)从初始状态按4次后,计算
两区代数式的和,请判断这个和能为负数吗?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cc0b4997cae4d8aec791a1d3923314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06fc7811f9525e8b8c833746d6af5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec54f53122364c46e1e43d1a84f210fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/54c243d1-3018-4f7c-8878-46d595048b2b.png?resizew=261)
(1)从初始状态按2次后,分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(2)从初始状态按4次后,计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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8 . 如图是8个台阶的示意图,每个台阶的高和宽分别是1和2,每个台阶凸出的角的顶点记作
(
为
的整数).函数
的图象为曲线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/caf6e77f-62c0-4b9a-b59e-967504c9a71b.png?resizew=197)
(1)若
过点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
__________ .
(2)若
过点
,则它必定还过另一点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
__________ .
(3)若曲线
使得
这些点分布在它的两侧,每侧各4个点,则
的整数值有__________ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e74be91bfe4bc209da7539dbf9b72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee9ff72d210845d3dfd48842e448d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cb90e72041e9139d4964f529ae1728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/caf6e77f-62c0-4b9a-b59e-967504c9a71b.png?resizew=197)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2114a0fe21dc0e5bf831c146ef02b113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e74be91bfe4bc209da7539dbf9b72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
(3)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513bdca9473fc5263b449f58945ac5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
9 . 如图是用三块正方形纸片以顶点相连的方式设计的“毕达哥拉斯”图案.现有五种正方形纸片,面积分别是1,2,3,4,5,选取其中三块(可重复选取)按图的方式组成图案,使所围成的三角形是面积最大的直角三角形,则选取的三块纸片的面积分别是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/a515a05f-77ef-44d5-b213-b6064c2ca662.png?resizew=130)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/a515a05f-77ef-44d5-b213-b6064c2ca662.png?resizew=130)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
10 . 在“□1□2□3□4□5□6□7□8□9”的小方格中填上“+”“-”号,如果可以使其代数和为n,就称数n是“可被表出的数”,否则,就称数n是“不可被表出的数”(如1是可被表出的数,这是因为
是1的一种可能被表出的方法).
(1)求证:7是可被表出的数,而8是不可被表出的数;
(2)求25可被表出的不同的方法种数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49df552f9b40ffb9aae0a804ce232982.png)
(1)求证:7是可被表出的数,而8是不可被表出的数;
(2)求25可被表出的不同的方法种数.
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