1 . 是否存在常数a、b,使等式
对一切正整数n都成立?猜测并用数学归纳法证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac55ec78cf89ada567432d5412b182f.png)
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2 . 设
…,一般地,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6bd97607745e4e94ce2833513efa76.png)
其中n∈N*,则使方程
有2018个根的n的值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933391d3a92f664b4fcbe82026784a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6bd97607745e4e94ce2833513efa76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0294d0afc26b899bc5c5b4eb9a621436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c37bf74694373dc60f1ddd89211ee82.png)
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3 . 两位数
和两位数
,它们各个数位上的数字都不为0,将数
和数
的个位数字与十位数字交叉相乘再求和所得的结果记为
.例如:
.又如:
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dd8061aa6b0803d371f9d418b6f0dd.png)
____________ ;若一个两位数
,两位数
(
,
,且
,
都取整数),交换
的十位数字和个位数字得到新两位数
,当
与
的个位数字的5倍的和能被11整除时,称这样的两个数
和
为“快乐数对”,则所有“快乐数对”
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b40e34f3f8e31cd6882fbceed3f72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f365c6a314b26500b860f145810e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ec4f99213b50854169318c1002993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dd8061aa6b0803d371f9d418b6f0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8676003f043a1220213c8fa169a7e71c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25fa0a6b9c3be012cb5b6908b155eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f9560f8f90d4addcf5fb6fdcc7956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9807e2182a8ef6ded07aef5ca0d6d6.png)
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7093538ecfb10a639b23863e7331a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7093538ecfb10a639b23863e7331a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b40e34f3f8e31cd6882fbceed3f72f.png)
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2023-09-14更新
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2卷引用:重庆市七校2023-2024学年高一上学期开学联考数学试题
4 . 绝对值
的集合意义是数轴上的点
与点1之间的距离,那么对于实数
,
的几何意义即为点
与点
、点b的距离之和.
(1)直接写出
与
的最小值,并写出取到最小值时
满足的条件;
(2)设
是给定的
个实数,记
,
;
试猜想:若
,
,
,则当
___________时
取到最小值;若
,
,
,则当
___________时,
取到最小值;(直接写出结果即可)
(3)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fd577bf5527f3b871e67292b36a0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6486c37eab1a00d884e4db6e7ade88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332257fa189ce0cc2c256005ef753d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35517c0a8ac06bbbe5f2f708c75b49a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bbf6d02c754d5596a262901fd51e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7844b064de3c3384a7fa4e7f24b0b27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02418d59ae2795ffe006508efd5d7a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d839d02d5c3486b09c590cd7fc3b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1782eeb4a85a5d31019b2bbf9ba15775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff2aa68223dfc02f39d7d10fa005387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397df3279607612ea3cbef101ee0bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44c45ef0334070fc149b452dee26ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c990bb0645f28fde7b3b4775ca2e57fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff2aa68223dfc02f39d7d10fa005387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397df3279607612ea3cbef101ee0bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44c45ef0334070fc149b452dee26ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885002f9877ae27ac8185d6290f7ded5.png)
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5 . 将正整数排成下表:
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
……………
则在表中数字2017出现在
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
……………
则在表中数字2017出现在
A.第44行第80列 | B.第45行第80列 | C.第44行第81列 | D.第45行第81列 |
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2017-12-26更新
|
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5卷引用:安徽省滁州市定远县育才学校2019-2020学年高一下学期5月月考数学(理)试题
6 . 已知数列1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,…,其中第一项是
,接下来的两项是
,
,再接下来的三项是
,
,
,依此类推,则该数列的前94项和是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ad4668cc927e277289b2af718f0d91.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:【全国校级联考】石家庄四县七校2017-2018学年第二学期期末教学质量检测高一数学
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7 . 当
时,可以得到不等式
,
,
,由此可以推广为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e989c65b1aaa8812e0e8bb6983c2bd0.png)
________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb005769d5478c56fc5a01d824167d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63af71b9e6f71cd26e6e97541154cd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9caafdc3771dd6d3c7828a70bebee2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e52cac635d52c514fc8cec1271e66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e989c65b1aaa8812e0e8bb6983c2bd0.png)
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2卷引用:【市级联考】上海市七宝中学2018-2019学年高一上学期数学期中考试
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8 . 给出以下数对序列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0c810c8a393da8ada5a855738865b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5911a41d6c75e304eb2ecb2b060ad74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee6073adf4c57b4d5907f9e79cbdacf.png)
……
记第
行的第
个数对为
,如
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df31e80f7f07ee8073d315bac82103b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0c810c8a393da8ada5a855738865b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5911a41d6c75e304eb2ecb2b060ad74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee6073adf4c57b4d5907f9e79cbdacf.png)
……
记第
![](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/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f602bdec88645c52034d0308f24ab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df31e80f7f07ee8073d315bac82103b3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2017-10-29更新
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569次组卷
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9卷引用:安徽省滁州市定远县西片三校2017-2018学年高一4月月考数学试题
安徽省滁州市定远县西片三校2017-2018学年高一4月月考数学试题湖南省永州市祁阳县第一中学2018届高三10月月考数学(文)试题吉林省东丰县第三中学2017-2018学年高二下学期期中考试数学(文)试题【校级联考】河南省豫南九校2018-2019学年高二下学期第二次联考数学(文)试题步步高高二数学暑假作业:【文】作业19 推理与证明、算法初步、复数步步高高二数学暑假作业:【理】作业20 推理与证明、算法初步、复数福建省莆田第八中学2018-2019学年高二下学期期中数学(文)试题天津市静海县第一中学2017-2018学年高二6月学生学业能力调研数学(理)试题辽宁省营口市部分重点高中2017-2018学年高二下学期期中考试数学(文)试题
9 . 在代数运算中有下列乘法公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02afa7c7ab445f4332b1aa67d00874cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f5f4ad27d1ca1028de903270ac3b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c6199ef03b3c389c4dcf15f48b1bf2.png)
.
(1)观察上述结果,你能做出怎样的猜想?
(2)证明你的猜想,并判断
是否是99的倍数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02afa7c7ab445f4332b1aa67d00874cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f5f4ad27d1ca1028de903270ac3b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c6199ef03b3c389c4dcf15f48b1bf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf7616d4e0060ca37d9526f4f17111e.png)
(1)观察上述结果,你能做出怎样的猜想?
(2)证明你的猜想,并判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac869d216f9d7281770cedd34a420d95.png)
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2卷引用:河北省保定市易县第三中学2023-2024学年高一上学期收心考试数学试题
10 . 中国古代十进位制的算筹记数法,在世界数学史上是一个伟大的创造.算筹记数的方法是:个位、百位、万位……的数按纵式的数码摆出;十位、千位、十万位……的数按横式的数码摆出. 1~9这9个数字的纵式与横式表示数码如下图所示:
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402335031967744/2402494237130752/STEM/78d61032adf84d919c36b752a32f9554.png?resizew=315)
如138可用算筹表示为
,则
的运算结果可用算筹表示为______ .
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402335031967744/2402494237130752/STEM/78d61032adf84d919c36b752a32f9554.png?resizew=315)
如138可用算筹表示为
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402335031967744/2402494237130752/STEM/d3c3338089734f16ac0d282190248a9d.png?resizew=25)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3c6c3995634f983bdc86c0e470e6da.png)
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2020-02-19更新
|
189次组卷
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2卷引用:山东省泰安市肥城市2018-2019学年高一上学期期中数学试题