1 . 观察下列等式:
①
;
②
;
③
;
④
;
⑤![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7f6f2938b45f7ccd9b0c5feb504a84.png)
则
的值为__________ .
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e12df1322bb7b3347de3e9feddb55ab.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f6bc6e974d027dd135b76e3e42c62.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f83372082315e87f0fd7e8bcca5607.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f5dbe1b6c0fc39b71fce84fd354383.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7f6f2938b45f7ccd9b0c5feb504a84.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07a3d01163a4407a9af3895cef65b21.png)
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2 . 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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3 . 在黑板上从左到右写2,0,2,3四个数,对两个相邻的数,每次用右边的数减左边的数的差填在这两数中间,从3开始到最左边的2为止,称为填一次.比如填第一次:2,-2,0,2,2,1,3,其中划线部分是填的右边的数减左边的数的差.则这样填2023次之后,黑板上所有数的和是( )
A.2023 | B.2025 | C.2028 | D.2030 |
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4 . 2023年2月22日,中国厦门市一名8岁男孩用时4.305秒单手完成4层汉诺塔游戏,成为新的世界纪录保持者.汉诺塔游戏源于1883年法国数学家卢卡斯提出的汉诺塔问题,有
,
,
三根柱子,在
柱上放着由下向上逐渐变小的
个盘子,现要求把
柱上的盘子全部移到
柱上,且需遵循以下的移动规则:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/1/d4751208-a68e-4736-a4fb-05fb20c3b7d7.png?resizew=191)
①每次只能移动一个盘子;
②任何时候都不允许大盘子放在小盘子的上面;
③移动过程中盘子可以放在
,
,
中任意一个柱子上.
若用
表示
个盘子时最小的移动次数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98396740a39a6a2e1fbaf5f0b1978ea9.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cb4ec5b02c810fd3bb29f99d90d919.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/1/d4751208-a68e-4736-a4fb-05fb20c3b7d7.png?resizew=191)
①每次只能移动一个盘子;
②任何时候都不允许大盘子放在小盘子的上面;
③移动过程中盘子可以放在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
若用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2bf3a57d272f43de9f9108841183ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98396740a39a6a2e1fbaf5f0b1978ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cb4ec5b02c810fd3bb29f99d90d919.png)
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5 . 在中学数学中,从特殊到一般,从具体到抽象是常见的一种思维形式.如从指数函数中可抽象出
的性质;从对数函数中可抽象出
的性质.那么从函数______ (写出一个具体函数即可)可抽象出
的性质.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7708640b13e4a01faeaf9e33b50d4a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4e9b0e8693d64d9a59287e4802c535a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656f0b5d3194a8cfef50f8823547ff1e.png)
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6 . 两千多年前,古希腊毕达哥拉斯学派的数学家曾经在沙滩上研究数学问题.他们在沙滩上画点或用小石子表示数,按照点或小石子能排列的形状对数进行分类.下图中实心点的个数5,9,14,20,
,被称为梯形数.根据图形的构成,记第2018个梯形数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c612fb2fed7c255a981cff9013063f4f.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08be9681cf2689ffe4049c6dbb7b171f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c612fb2fed7c255a981cff9013063f4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/29/6e7cad3c-7f93-44c6-9ef6-20f0620120c8.png?resizew=413)
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7 . 杨辉三角由我国南宋数学家杨辉在其所著的《详解九章算术》中提出,是二项式系数在三角形中的一种几何排列,图形如图.记从上往下每一行各数之和为数列
,比如
,
,
,则数列
的前n项之和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df1038200f2d97a52c716aab6c3bcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/29/f77aadab-360b-4e45-8d60-e0504d14d79c.png?resizew=248)
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8 . 下面几种推理过程是演绎推理的是( )
A.由等边三角形、等腰三角形的内角和是180°,推测所有三角形的内角和都是180° |
B.由三角形的两边之和大于第三边,推测四面体任意三个面的面积之和大于第四个面的面积 |
C.平行四边形的对角线互相平分,菱形是平行四边形,所以菱形的对角线互相平分 |
D.在数列![]() ![]() ![]() ![]() |
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名校
解题方法
9 . 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.作为当今世界十分风靡和活跃的新理论、新学科,它的出现使人们重新审视这个世界:世界是非线性的,分形无处不在.分形几何学不仅让人们感悟到科学与艺术的融合,数学与艺术审美的统一,而且还具有深刻的科学方法论意义,由此可见分形的重要性.美国物理学大师JohnWheeler曾说过:今后谁不熟悉分形,谁就不能被称为科学上的文化人.koch雪花曲线是一种典型的分形曲线,它的制作步骤如下:
第一步:任意画一个正三角形,记为
,并把
的每一条边三等分;
第二步:以三等分后的每一条边中间一段为边向外作正三角形,并把这“中间一段”擦掉,记所得图形为
;
第三步:把
的每一条边三等分,重复第二步的制作,记所得图形为
;
同样的制作步骤重复下去,可以得到
,直到无穷,所画出的曲线叫做koch雪花曲线.
若下图中
的边长为1,则图形
的周长为( )
第一步:任意画一个正三角形,记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
第二步:以三等分后的每一条边中间一段为边向外作正三角形,并把这“中间一段”擦掉,记所得图形为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
第三步:把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
同样的制作步骤重复下去,可以得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b09c945e76becac63f4ab34a0cde756.png)
若下图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/8/333e86bd-45f9-4f16-81ae-a8c2fb5a3d69.png?resizew=436)
A.6 | B.![]() | C.![]() | D.![]() |
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2023-04-23更新
|
666次组卷
|
5卷引用:四川省蓉城联盟2023届高三三模数学试题(理)
四川省蓉城联盟2023届高三三模数学试题(理)四川省蓉城联盟2023届高三三模数学试题(文)(已下线)第五篇 向量与几何 专题20 分形几何 微点2 分形几何综合训练四川省成都市新津区蓉城联考2023届高三下学期4月月考理科数学试题四川省成都市蓉城联盟2023届高三下学期第三次联考文科数学试题
10 . 观察下列等式:
,根据上述规律写出第九个等式为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49560428edc1b4af21746a745d6ed9e1.png)
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2023-04-23更新
|
211次组卷
|
2卷引用:江西省鹰潭市2023届高三一模数学(文)试题