1 . 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
|
45次组卷
|
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
名校
2 .
、
、
、
、
五个队进行单循环赛(单循环赛制是指所有参赛队在竞赛中均能相遇一次),胜一场得3分,负一场得0分,平局各得1分.若
队2胜2负,
队得8分,
队得9分,
队胜了
队,则
队得分为___________ .
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2023-04-07更新
|
1491次组卷
|
3卷引用:重庆市南开中学校2023-2024学年高一上学期开学考试数学试题
名校
3 . 天干地支纪年法是上古文明的产物,又称节气历或中国阳历.有十天干与十二地支,如下表:
算法如下:先用年份的尾数查出天干,再用年份除以12的余数查出地支.如2008年,尾数8为戊,2008除以12余数为4,4为子,那么2008年就是戊子年.2021年是伟大、光荣、正确的中国共产党成立100周年,则2021年是_____ 年.(用天干地支纪年法表示)
天干 | 甲 | 乙 | 丙 | 丁 | 戊 | 己 | 庚 | 辛 | 壬 | 癸 | ||
4 | 5 | 6 | 7 | 8 | 9 | 0 | 1 | 2 | 3 | |||
地支 | 子 | 丑 | 寅 | 卯 | 辰 | 巳 | 午 | 未 | 申 | 酉 | 戌 | 亥 |
4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 1 | 2 | 3 |
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名校
4 . 数列
,
,
,
,…,则
是该数列的第__________ 项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68c1d20a422a363e356a160f096503c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ba5418a60abb24191ef4cabddc4fd8.png)
您最近一年使用:0次
5 . 数列
,则
是该数列的第__________ 项.
![](https://img.xkw.com/dksih/QBM/2016/6/7/1572707443105792/1572707449126912/STEM/e38724c01ee94099adff45147c43880c.png?resizew=189)
![](https://img.xkw.com/dksih/QBM/2016/6/7/1572707443105792/1572707449126912/STEM/662af1d86b1842bfa040d166702434c8.png?resizew=15)
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6 . 古希腊毕达哥拉斯学派的数学家研究过各种多边形数.如三角形数1,3,6,10,…,第
个三角形数为
.记第
个
边形数为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818ed1b032c481e08f713c7b0dbd65d6.png)
,以下列出了部分
边形数中第
个数的表达式:
三角形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db6b941b3ec97fa4e43dd503dc0f60e.png)
正方形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24af989345fe45f4f3bc8394f64d58b5.png)
五边形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c352d9cd4eff69ba46e752313e4091d.png)
六边形数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5abe0f1b4b08a0b29e2048e66d95d2.png)
……
可以推测
的表达式,由此计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e154bf3322578b064341ece695d9ec3e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635f7984672c31bef79c9aab577204cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818ed1b032c481e08f713c7b0dbd65d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c0902ac3138d1276afdcababfa04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
三角形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db6b941b3ec97fa4e43dd503dc0f60e.png)
正方形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24af989345fe45f4f3bc8394f64d58b5.png)
五边形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c352d9cd4eff69ba46e752313e4091d.png)
六边形数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5abe0f1b4b08a0b29e2048e66d95d2.png)
……
可以推测
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818ed1b032c481e08f713c7b0dbd65d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e154bf3322578b064341ece695d9ec3e.png)
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