1 . 定义函数
,其中
表示不超过
的最大整数,例如,
,
,
,当
时,
的值域为
,记集合
中元素的个数为
,数列
的前
项和为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36304502dd9ae85a33ed38d59c655ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985227b7b4703f3ed8717d0abc4febfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525c5748729c08162cf70b7c746b6bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9feb047004eb507de484a7f8c5b6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db394e5d73a3a77cd93704a41d370c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf19c8d1c1721dbf61b48b62fe6840d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78d551e6cc415f570dc7fc49b825cb1.png)
A.![]() | B.2 | C.![]() | D.![]() |
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解题方法
2 . 在平面直角坐标系中,两点
、
的“曼哈顿距离”定义为
,记为
,如点
、
的“曼哈顿距离”为9,记为
.
(1)点
,
是满足
的动点
的集合,求点集
所占区域的面积;
(2)动点
在直线
上,动点
在函数
图像上,求
的最小值;
(3)动点
在函数
的图像上,点
,
的最大值记为
,请选择下列二问中的一问,做出解答:
①求证:不存在实数
、
,使
;
②求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bd36d19352628cb54c214436ee3322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27bd43bc4af1e3b28d0de0cc561b879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c59185f3d9547cd9065d10dcbb4127d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e66b64267481405cc49dad9d8916c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9404ad60dd25cb0df6c37032d50b72ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dafabc98a78486af4fbf346e7cfad11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd35a290bbcf999ec26930c747084b.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9404ad60dd25cb0df6c37032d50b72ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7bce4bf9358998e26ff0715c909a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea05a2396e436b4df62d6328dbeaddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e66b64267481405cc49dad9d8916c7.png)
(3)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c064084f6326c8b994c2bcb80ad258da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4a30a3210d0a8130d5a1183289c23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e66b64267481405cc49dad9d8916c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
①求证:不存在实数
![](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/8d41cfe4280d2384c9dd4287c8f07954.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
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3 . 英国数学家布鲁克泰勒通过研究发现了如下正、余弦公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ab08491d327ffd0cfabccb639e6030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c868fcf317426476af632cac3c028629.png)
其中
,
,
,例如:
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c510ee5e16312f9d01fb3e24cd28d8.png)
在
中,已知
,
弧度,
米,则BC的长约为_________ 米(精确到0.01米)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ab08491d327ffd0cfabccb639e6030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c868fcf317426476af632cac3c028629.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ef8db418ece9675eecd645717806ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306da3f46a4e2a78bb84727e26b5ea9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c510ee5e16312f9d01fb3e24cd28d8.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddda8bee262f17d51ee3d70cf63d6b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1cf0ae3ce752f851cceca482cbec31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71807a35b3170fce28ee6edf4c00d083.png)
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4 . 如图1,在边长为2的正方形
中,
,
,
分别为
,
,
的中点,沿
、
及
把这个正方形折成一个四面体,使得
、
、
三点重合于
,得到四面体
(如图2).下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/7ce26cb7-5ea8-445f-a356-5c8f0b0150d2.png?resizew=318)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922dae27e2bef111979574e15de3a4cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/7ce26cb7-5ea8-445f-a356-5c8f0b0150d2.png?resizew=318)
A.四面体![]() ![]() |
B.顶点![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.过点![]() ![]() ![]() |
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5卷引用:第一章 空间向量与立体几何单元检测(能力挑战卷)-【一堂好课】2021-2022学年高二数学上学期同步精品课堂(人教A版2019选择性必修第一册)
(已下线)第一章 空间向量与立体几何单元检测(能力挑战卷)-【一堂好课】2021-2022学年高二数学上学期同步精品课堂(人教A版2019选择性必修第一册)广东省广州市广州大学附属中学2021-2022学年高二上学期9月入学考试数学试题湖北省武汉市蔡甸区汉阳一中2021-2022学年高二上学期9月月考数学试题湖南省长沙市长郡中学2020-2021学年高一下学期期末数学试题湖南省邵阳市第二中学2021-2022学年高二下学期入学考试数学试题
名校
5 .
是棱长为2的正方体,
分别为
的中点,过
的平面截正方体的截面面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6241f9ef86cd0a902cbadaf336767dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe78780328385710b9cc5d676cddbe02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6241f9ef86cd0a902cbadaf336767dbc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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4卷引用:广西南宁市宾阳县宾阳中学2021-2022学年高二上学期月考数学试题
6 . 复数
满足
,其中
为虚数单位,
是
的共轭复数,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d66d7548ef30e619cfe9761a7d8b0b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
A.![]() | B.1 | C.![]() | D.![]() |
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7 . 2020年底,中国科学家成功构建了76个光子的量子计算机“九章”,推动全球量子计算的前沿研究达到一个新高度.该量子计算机取名“九章”,是为了纪念中国古代著名的数学专著《九章算术》.在《九章算术》中,底面是直角三角形的直三棱柱被称为“堑堵”.如图,棱柱
为一“堑堵”,
是
的中点,
,设平面
过点
且与
平行,现有下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/64171989-d6a6-49f9-8368-547c404701e6.png?resizew=141)
①当平面
截棱柱的截面图形为等腰梯形时,该图形的面积等于
;
②当平面
截棱柱的截面图形为直角梯形时,该图形的面积等于
;
③异面直线
与
所成角的余弦值为
;
④三棱锥
的体积是该“堑堵”体积的
.
所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ba708880f5eb782acbf2c961c2494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/64171989-d6a6-49f9-8368-547c404701e6.png?resizew=141)
①当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
②当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
③异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2176b70550fd08006109e9b87727b957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
所有正确结论的序号是
您最近一年使用:0次
2021-05-31更新
|
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7卷引用:四川省遂宁市射洪中学2021-2022学年高二上学期第一次月考数学理试题
四川省遂宁市射洪中学2021-2022学年高二上学期第一次月考数学理试题全国100所名校2021年最新高考冲刺卷(样卷一)理科数学试题湖南省(全国卷)2021届高三高考数学模拟试题(样卷一)全国100所名校新高考2021届高三最新高考冲刺卷数学试题(样卷一)(已下线)考点16 空间几何体-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)模块四 专题3 暑期结束综合检测3(基础卷)(人教B)(已下线)第六章 突破立体几何创新问题 专题一 跨学科交汇问题 微点3 跨学科交汇问题综合训练【培优版】
名校
8 . 设正四棱柱
的底面边长为1,高为2,平面
经过顶点
,且与棱
所在直线所成的角都相等,则满足条件的平面
共有( )个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af55b84645a6a98e36ad57c96938af8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.1 | B.2 | C.3 | D.4 |
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|
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4卷引用:上海市实验学校2020-2021学年高二下学期期末数学试题
上海市实验学校2020-2021学年高二下学期期末数学试题上海市长宁区2021届高三二模数学试题(已下线)课时41 空间直线与平面的位置关系-2022年高考数学一轮复习小题多维练(上海专用)(已下线)第19讲 立体几何初步-3
20-21高二下·浙江·期末
名校
解题方法
9 . 已知
是函数
的导函数,
,其中
是自对数的底数,对任意
,恒有
,则不等式
的解集为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b333dc802c26603a14f19a0b1b7732d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd143a57a268a5a8ef486e2a4d5c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ad268bd8d24f3afe2a69d71c4dfa39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684d9984bc7681b48ac1b65da1f7c09b.png)
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2021-05-18更新
|
1193次组卷
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5卷引用:【新东方】高中数学20210513-002【2021】【高二下】
(已下线)【新东方】高中数学20210513-002【2021】【高二下】天津市蓟州一中、芦台一中、英华国际学校三校2020-2021学年高二下学期期末联考数学试题(已下线)综合测试卷-新教材2020-2021学年高二数学尖子生培优AB卷(人教B版2019选择性必修第三册)浙江省台州市9+1高中联盟2020-2021学年高二下学期期中联考数学试题辽宁省抚顺市第一中学2021-2022学年高二下学期4月月考数学试题
10 . 设复数z满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315b1b70eb062a5c0bcdad17b32f054b.png)
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8卷引用:专题03 数系的扩充与复数-2020-2021学年高二数学下学期期末专项复习(苏教版选修2-2、2-3)
(已下线)专题03 数系的扩充与复数-2020-2021学年高二数学下学期期末专项复习(苏教版选修2-2、2-3)(已下线)第三章 数系的扩充和复数的引入【专项训练】-2020-2021学年高二数学(文)下学期期末专项复习(人教A版选修1-2)江苏省园三2020-2021学年高一下学期期中数学试题(已下线)专题04 复数-2020-2021学年高一数学下学期期末专项复习(北师大版2019必修第二册)(已下线)期末复习【真题训练】-2020-2021学年新教材高一数学下册单元复习一遍过(沪教版2020必修第二册)江苏省苏州西交大附中、昆山中学、昆山一中2020-2021学年高一下学期期中数学试题河北省深州市长江中学2020-2021学年高一下学期期末数学试题单元测试B卷——第七章 复数