1 .
,
,则不超过2024的正整数中可以作为
函数值的个数为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95749241ac8431d2e731e69769c1cdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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2 . 从1,2,⋯,2024中任取两数
(可以相同),则
个位为
的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff03c70269c31117bef45eb47e618e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
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3 . 使
恰有2个整数解的正整数n的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db6187cc7a8e5c863f95fa721065f8b.png)
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解题方法
4 .
中,
,
,
分别在
,
上各取一点
,
,使
平分
的面积,求
长度的最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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5 . 设
,
,则
=______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6123443832507911255a4378124b8d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d0a8dfc3620c557571e954abea5627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25da493a41219082d08558a7dd41bcde.png)
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解题方法
6 .
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3f7da4088c7a6d0ecb32bb1dff53d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648be19842417354d580603906ca4eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a514a53cbbc30ee0217cdbd8b7e35fe9.png)
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7 . 首项是整数的等差数列,公差
,前n项和
,求所有n值的和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf94d263ea1e5ddad405ccbc1eb2a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccb2d4dc9c91e09d96c8228da6bfbd3.png)
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8 . 用6种不同颜色染正方体的6个面,不同面颜色不同,正方体旋转后颜色相同认为是同种染色,则染色的种数有多少?
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9 . 已知函数
,使得任取实数x,y,z都有
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445ca04eff5078b77fcb78234faf9207.png)
__________ .(其中
表示不大于x的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a17e36b57a381a274173902e8a020d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5673732a290720249ab8011de7ca1c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445ca04eff5078b77fcb78234faf9207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e90b41a295a4b424cf37f5640430dc.png)
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10 . 若方程
仅有一个实根,则满足条件的k的最大值等于___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2f4782619ae9824b5af276ba0ff9db.png)
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