名校
解题方法
1 . 已知函数
在
上不是单调函数,且其图象完全位于直线
与
之间(不含边界),则
的一个取值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199fc1eb0897f0d666542dd3edb0f07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5428b040be21dcd503d350478c0a4773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc8e0a4e596e6b0a2f81e1f03fa0430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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6卷引用:北京市师大附属中学2023届高三适应性练习数学试题
北京市师大附属中学2023届高三适应性练习数学试题北京市海淀区北京大学附属中学2023届高三三模数学试题(已下线)专题04 导数及其应用-1(已下线)专题06 三角函数的图像与性质(已下线)专题12 导数及其应用广东省广州市广雅中学2024届高三下学期教学情况检测(三)数学试题
2 . 分形几何学是一门以不规则几何形态为研究对象的几何学,它研究的几何对象具有自相似的层次结构,适当的放大或缩小几何尺寸,整个结构不变,具有很多美妙的性质.其中科赫(Koch)曲线是几何中最简单的分形.科赫曲线的产生方式如下:如图,将一条线段三等分后,以中间一段为边作正三角形并去掉原线段生成1级科赫曲线“”,将1级科赫曲线上每一线段重复上述步骤得到2级科赫曲线,同理可得3级科赫曲线,……在分形几何中,若一个图形由
个与它的上一级图形相似,且相似比为
的部分组成,则称
为该图形分形维数.那么科赫曲线的分形维数是( )
A.![]() | B.![]() | C.1 | D.![]() |
您最近一年使用:0次
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6卷引用:北京市师大附属中学2023届高三适应性练习数学试题
3 . 给定奇数
,设
是
的数阵.
表示数阵第
行第
列的数,
且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de075cbe45f637a11f53685a018e340a.png)
.定义变换
为“将数阵中第
行和第
列的数都乘以
”,其中
.设
.将
经过
变换得到
,
经过
变换得到
,
,
经过
变换得到
.记数阵
中
的个数为
.
(1)当
时,设
,
,写出
,并求
;
(2)当
时,对给定的数阵
,证明:
是
的倍数;
(3)证明:对给定的数阵
,总存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604a3f7f0c00236993c4659ff12fd63c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de075cbe45f637a11f53685a018e340a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4f7f26c112216d9a548b5ad082ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca81e328c01121c81869e7d304f01054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0393f387f255f7ade0e5c7bf1a8a9a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e524eaa9507cc5c8c81a0831d853ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8e7d8908eb361e60af9da39fc1b1ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d2c0b8dcec87c9655bbb1a37d9884e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c9bcf77059762fc46fc437ca8b060c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84221a34d3afe2b194c604aa642aa922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b003c008551d85cda4fe287d0742216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd55ae46a41a37f90a3d745b9e8f879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d6bc8e1dc170db94a6caf502b9b187.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c0d07535b2eca42f44b8109c6ccd11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbf9bc3b31e16bd645b864a346187f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d13fffd82b0a6b66580a17a6e0d2802.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae537905eee4d73c55298fa4280794b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84406a04370c0c0834550b1f22b49d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(3)证明:对给定的数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666a2f30e071ff37c5545baa18276fe7.png)
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4 . 体重指数(
,简称
)是国际上衡量人体胖瘦程度的一项常用指标.已知
,其中
表示体重(单位:
),
表示身高(单位:
).对成人,若
,则身体处于肥胖状态.某企业为了解员工的身体状况,从全体员工中随机抽取
人,测量他们的体重(单位:
)和身高(单位:
),得到如下散点图(图中曲线表示
时体重和身高的关系),假设用频率估计概率.
![](https://img.xkw.com/dksih/QBM/2023/5/8/3233425156571136/3233909931794432/STEM/cbbdb51e502f47a68e4a84dc9eb9c181.png?resizew=399)
(1)该企业员工总数为
人,试估计该企业员工身体处于肥胖状态的人数;
(2)从该企业身体处于肥胖状态的员工中随机抽取
人,设其中体重在
以上的人数为
,估计
的分布列和数学期望
;
(3)从样本中身高大于或等于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
的员工中随机抽取
人,若其身体处于肥胖状态的概率小于
,写出
的所有可能取值.(结论不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d30ac3884e8807aec07aa3d2c14a851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c851d5b6da1f56e74a5aea5cc8fdeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35127d16626724faa9cf50ad5228242e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f7c4a8558eff6427d22b6c0c855721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f28316233c1d0f88cd4bece085b6e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f7c4a8558eff6427d22b6c0c855721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e42a46db8c517259003cdcec6b83967.png)
![](https://img.xkw.com/dksih/QBM/2023/5/8/3233425156571136/3233909931794432/STEM/cbbdb51e502f47a68e4a84dc9eb9c181.png?resizew=399)
(1)该企业员工总数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69c0fc5595aadf8e59662c20c515b58.png)
(2)从该企业身体处于肥胖状态的员工中随机抽取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51a293b9810a569e5240db168296044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
(3)从样本中身高大于或等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62baf91e02d4df0a5409eb11f4542a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f733b1ceeead9ff892539d46a23f3626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 在坐标平面内,横、纵坐标均为整数的点称为整点.点
从原点出发,在坐标平面内跳跃行进,每次跳跃的长度都是
且落在整点处.则点
到达点
所跳跃次数的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eee9827d1b6efa514f66de2fcaf2f09.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:北京市西城区2023届高三二模数学试题
6 . 某放射性物质的质量每年比前一年衰减
,其初始质量为
,
年后的质量为
,则下列各数中与
最接近的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb25dc4b4432d36c3c983d72cbceb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e93d8fb77f5bd2c0fc690752dfd771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7093538ecfb10a639b23863e7331a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bd792db1d3034534ebb5c581694dab.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:北京市西城区2023届高三二模数学试题
7 . 已知数轴上两点
的坐标为
,现
两点在数轴上同时相向运动.点
的运动规律为第一秒运动
个单位长度,以后每秒比前一秒多运动
个单位长度;点
的运动规律为每秒运动
个单位长度.则点
相遇时在数轴上的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db36b4497b911bc047253b832ae01c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63184599ff2a30141048f6ebe482791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db36b4497b911bc047253b832ae01c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db36b4497b911bc047253b832ae01c4.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 某班主任在其工作手册中,对该班每个学生用十二项能力特征加以描述.每名学生的第
项能力特征用
表示,
,若学生
的十二项能力特征分别记为
,
,则
两名学生的不同能力特征项数为_______ (用
表示).如果两个同学不同能力特征项数不少于
,那么就说这两个同学的综合能力差异较大.若该班有
名学生两两综合能力差异较大,则这
名学生两两不同能力特征项数总和的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871ab8c56e6645fdae5661f8608ae7bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4f40376a71f97fa5eebedd59892b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b831bc2f81587579fe3ce35efb146a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b532e3ca16b2a4ba7acb104ded8f646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d1a67fb0ce500b872db999ceddf551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
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名校
9 . 在
的展开式中,
的系数为________ .设复数z满足
,则它的共轭复数________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979fb4524978e69eac5d1fda30ddcef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf5b0e287ca97be4a45bbf82bdd35fe.png)
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名校
10 . 阅读下段文字:“已知
为无理数,若
为有理数,则存在无理数
,使得
为有理数;若
为无理数,则取无理数
,
,此时
为有理数.”依据这段文字可以证明的结论是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc50ddc2d997f68c67ce935d47d934e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00514018beea46f18f6547ad68201aac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cde6da5e4a71a3df6cd950ff1a90920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc50ddc2d997f68c67ce935d47d934e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f453e024936d78d0ac04783d5f5c09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2c7796c6c4006bd3152ee2e27cbf47.png)
A.![]() | B.![]() |
C.存在无理数a,b,使得![]() | D.对任意无理数a,b,都有![]() |
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2023-04-13更新
|
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10卷引用:北京市第三十五中学2024届高三上学期开学考数学试题
北京市第三十五中学2024届高三上学期开学考数学试题湖北省武汉市2023届高三下学期四月调研数学试题(已下线)模块六 专题3 易错题目重组卷(湖北卷)安徽省滁州市定远中学2023届高三下学期毕业生调研考试(二)数学试卷安徽省安庆市桐城中学2023届高三下学期第二次模拟数学试卷福建省厦门市双十中学2022-2023学年高二下学期期中数学试题(已下线)第01讲 4.1指数-【帮课堂】(已下线)4.1.1 n次方根与分数指数幂+4.1.2无理数指数幂及其运算性质【第三练】(已下线)专题04 指数函数与对数函数2-2024年高一数学寒假作业单元合订本广东省肇庆市肇庆中学2023届高三下学期4月月考数学试题