2023高三·全国·专题练习
名校
1 . 数学美的表现形式不同于自然美或艺术美那样直观,它蕴藏于特有的抽象概念、公式符号、推理论证、思维方法等之中,揭示了规律性,是一种科学的真实美.在平面直角坐标系中,曲线
就是一条形状优美的曲线,
则下列结论正确的是_______________ .(填写序号)
①曲线
围成的图形的周长是
;
②曲线
上的任意两点间的距离不超过4;
③曲线
围成的图形的面积是
;
④若
是曲线
上任意一点,则
的最小值是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9556dfc485a8b60178f3b97bf622fa68.png)
则下列结论正确的是
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4a83cecb1e5ed89001d698f014542c.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d696caba21653bfc3570bb1cc6d713.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21872d8f6a518e0a2993ccf7a795ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4795c3c15b735594587558923759ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171809b0bbbd2e54dabd50110b368165.png)
您最近一年使用:0次
解题方法
2 . 如图,在棱长为1的正方体
中,Q是棱
上的动点,则下列说法正确的是___________ .(把所有正确结论的序号填写在横线上)
①存在点Q,使得
;
②存在点Q,使得
;
③对于任意点Q,Q到
的距离的取值范围为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f911cf6124dc2521e02b114bb6c9e1.png)
④对于任意点Q,
都是钝角三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/e29603fa-06df-4a14-bd5c-03cb397ecc28.png?resizew=163)
①存在点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a88b17886b8bd5899dd3e5b9065408.png)
②存在点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8862258e8fba3e5698b517e09727aafb.png)
③对于任意点Q,Q到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f911cf6124dc2521e02b114bb6c9e1.png)
④对于任意点Q,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87725bb524fd611eb530ac1f92875f9.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,已知在长方体
中,
,
,
,点E为
上的一个动点,平面
与棱
交于点F,给出下列命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/186040db-9a02-4c63-af08-5c5419f0bcfc.png?resizew=147)
①四棱锥
的体积为20;
②存在唯一的点E,使截面四边形
的周长取得最小值
;
③当点E不与C,
重合时,在棱AD上均存在点G,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
平面
;
④存在唯一的点E,使得
平面
,且
.
其中正确的是___________ (填写所有正确的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/186040db-9a02-4c63-af08-5c5419f0bcfc.png?resizew=147)
①四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b492d99c54c1d881aa0532d918c19389.png)
②存在唯一的点E,使截面四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6069dc466eec75bbeb3d5c9b51cb3a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f734ed6ddf5b05e496519b15a4edc30.png)
③当点E不与C,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
④存在唯一的点E,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be76345fa868237ae80c1a79809ee54f.png)
其中正确的是
您最近一年使用:0次
2021-12-21更新
|
834次组卷
|
8卷引用:广东省佛山市顺德区罗定邦中学2020-2021学年高二上学期期中数学试题
广东省佛山市顺德区罗定邦中学2020-2021学年高二上学期期中数学试题新疆维吾尔自治区乌鲁木齐市2019-2020学年高三第一次诊断性测试数学理试题2020届湖南省长沙市长郡中学高三下学期3月“停课不停学”阶段性检测数学(文)试题安徽省淮北市第一中学2020届高三下学期第七次月考数学(理)试题江西省吉安市第一中学2022-2023学年高二上学期期末考试数学试题新疆伊犁新源县2021-2022学年高二上学期期末考试数学(理)试题(已下线)1.4.1 用空间向量研究直线、平面的位置关系(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点4 面积、体积的范围与最值问题(二)【基础版】
名校
4 . 如图,多面体
中,面
为正方形,
平面
,
,且
,
,
为棱
的中点,
为棱
上的动点,有下列结论:
为棱
的中点时,
平面
;
②存在点
,使得
;
③三棱锥
的体积为定值;
④三棱锥
的外接球表面积为
.
其中正确的结论序号为______ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6615992e260ded5b9f9c26eb719386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95893879ed5feeef3cb2cf68a1a88632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e8a0ee201f2b9860cdf63ef168eab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3f8b5c2dba20d42a8c551cd75a38fe.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93240c1473e10c736cc33b65053de761.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26712d1a7a5864cd18498f16f7bd96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ae3e6e1924f2f92529860e905c9d32.png)
其中正确的结论序号为
您最近一年使用:0次
2022-04-09更新
|
1915次组卷
|
8卷引用:广东省江门市新会陈经纶中学2022-2023学年高二上学期期中数学试题
广东省江门市新会陈经纶中学2022-2023学年高二上学期期中数学试题新疆维吾尔自治区乌鲁木齐市第101中学第2021-2022 学年高一下学期期中考试数学试题(问卷)东北三省三校2022届高三第二次联合模拟考试数学(文科)试题(已下线)查补易混易错点06 立体几何-【查漏补缺】2022年高考数学(文)三轮冲刺过关山西省山西大学附属中学校2022届高三三模(总第七次模块)文科数学试题第一章 空间向量与立体几何章末检测(基础篇)贵州省凯里实验高级中学2022-2023学年高一下学期6月月考数学试题(已下线)专题01 空间向量与立体几何(4)
解题方法
5 . 如图,在正方体
中,
,
,
,
分别是
,
,
,
各棱的中点.
(1)画出过点
,
,
,
的平面截正方体所得的截面并指出截面的形状(不必说明画法和理由)
(2)求(1)中的截面与平面
所成的二面角的正弦值.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/1a236a4a-0e29-4beb-9d65-454d77290784.png?resizew=157)
(1)画出过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)求(1)中的截面与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次