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
|
324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
2 . 在直角坐标系中,
为坐标原点,曲线
的方程是
,
为
上的任意一点.给出下面四个命题:
①曲线
上的点关于
轴,
轴对称; ②曲线
上两点间的最大距离为
;
③
的取值范围为
; ④曲线
围成的图形的面积小于
.
则以上命题中正确的序号有______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c299e12f0743fa135d5d101435d1a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.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/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1279ef84071f5ad7c4c1681357edd84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
则以上命题中正确的序号有
您最近一年使用:0次
名校
3 . 设棱长为2的正方体
,
是
中点,点
、
分别是棱
、
上的动点,给出以下四个结论:
①存在
;
②存在
平面
;
③存在无数个等腰三角形
;
④三棱锥
的体积的取值范围是
.
则所有结论正确的序号是______ .
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d2909b0333b9b28c081c68cde04f96.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590d2b3c62a9c24be67a0bc8a8f6c057.png)
③存在无数个等腰三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868a98a5d6337c3dd9bca228e3545665.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c68898e115b33957e49efdae523cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e612714cb045799fb2abc4a98ec10e.png)
则所有结论正确的序号是
您最近一年使用:0次
2022-03-10更新
|
1525次组卷
|
5卷引用:北京平谷区2022届高三零模数学试题
北京平谷区2022届高三零模数学试题北京市第一六一中学2022届高三考前热身训练数学试题(已下线)数学-2022年高考押题预测卷01(北京卷)北京市清华附中2023届高三下学期3月调研数学试题(已下线)专题01 空间向量与立体几何(6)
4 . 已知等差数列
,若存在有穷等比数列
,其中
,公比为
,满足
,其中
,则称数列
为数列
的长度为
的“等比伴随数列”.
(1)数列
的通项公式为
,写出数列
的一个长度为
的“等比伴随数列”;
(2)等差数列
的公差为
,若
存在长度为
的“等比伴随数列”
,其中
,求
的最大值;
(3)数列
的通项公式为
,数列
为数列
的长度为
的“等比伴随数列”,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268349d135096d5b4651512594f5cadc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fea9ae5ae646d99ad7ed8a9855396b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9be70445cd8e813baea0f526a2637c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb9807bed05b28ea4609862544d435d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d619035a661b75bb5f35f03017d30f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(2)等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bb72b3ebbca741b3eda49cd617c058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2022-01-16更新
|
630次组卷
|
4卷引用:北京市平谷区北京实验学校2023届高三上学期9月练习数学试题
北京市平谷区北京实验学校2023届高三上学期9月练习数学试题北京市昌平区2022届高三上学期期末质量抽测数学试题(已下线)高二数学下学期期末精选50题(压轴版)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)北京市昌平区第一中学2023届高三上学期11月学情调研数学试题