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试卷难度归档#6 - 郑州二质检(简评)

  • 2026-04-28 14:09:00
试卷难度归档#6 - 郑州二质检(简评)
郑州学生也有自己的压力训练。
其实2025年郑州二质检未尝不是压力训练，但是之前郑州的卷子一般是比较中规中矩的，只能说对于河南学生没那么好的数学水平可能有点压力，但是这次不一样，这次的压力上升到了“国家级”水平，终于是能跟其他模拟卷放一块说说了。
1~4 +2(除2) 起手不凡，这4道题放在任何模拟卷里都是一个不好的预感，1i^2026这种东西已经好久没怎么见了，3的估计做起来很抽象，4更抽象，实际上BC,AC是共线的，有些不知所谓。
5 +1 实际上是一个三角函数题+解二次方程，这种题高一很常见
6 +2 这道题出现在这里又是何意味？我不知道有什么好的解法，不管用什么二级结论似乎都没法让此题的计算量和难度小于7
7 +0.5 能看懂ln(x+1/3-x)在说什么这道题就没有任何难度了，考点很机械，做法很直接。
8 0 作为一个第八题，这道题其实算不上难，需要列出三个式子，注意到x_1满足的关系和x_2,x_3有所区别，利用对数的性质，将lnx_1x_2x_3=3lnx_2化出来之后就简单了，之后求解公比即可
9 0 
10 0 画完图像也就做完了
11 ?(+1)暂时还没有理解这个四点共圆是怎么处理的，还在考试进程中目前不太想对答案。看C,D就知道这个题目必然是偏难的一类
12 0 注意是极值点
13 0 开闭区间别搞错，正负公差别搞错，第7项是a_1+6d别搞错
14 +1.2 变异内切球问题，是2025全国二卷14的变体。对于这种问题，需要首先一步拆解出一个可以入手的问题部分，比如两个球的圆心所在的圆锥最大截面，两个截面拼在一起构成一个立体的三角形，转角120度（因为三个球彼此相切），然后利用球的截面圆结合角平分线，再加上球彼此相切得到一些可用的长度关系全部套上一通乱解得答案
15 15.8 反常规。实际上考一个小小的外角平分线定理及其推导（也可以用正弦定理做）并不能算是什么反引导，只能说是反常规。对于训练了“正常”题目比较多的学生，这种题是很有挑战性的......但是高考中似乎正常题目也不多了，2025年比例相比2024年还回升了一些。
16 16.9 正统反引导，难度全在第一问。给一个底面面积求解还要结合一个抽象的面面垂直关系，除了建系别的做法都会有点奇妙，但C也是一个奇妙的动点，使得整个题目略显诡异，这种诡异感在高考也会出现，只不过只是偶尔。
17 17.85 难度大膨胀时代，连这种题目都放到17来考察了，郑州二质检逼着考生将多条切线问题掌握为一个常用技巧，即便这种题其实熟悉了以后也不难（难度迅速下滑到17.5附近），但是也不能就这么在（1）考吧......也太过分了。（2）看似有广州一模18遗风，其实除了a,b,逻辑量词相似以外没什么共同点，这是一个较为复杂的隐零点问题，但是相比之下思维还是比较直接。
18 ?[3](~18.3)(2)(3)各自不沾边，有种拼题的美感。
（3）的P点任取都有定值，不知道这个结论怎么证合适，似乎也可以直接硬解，不过既然有垂直，还在某个圆上，应该直径也能在PQ,QB两条线上找到。
是能看出来是一小段圆弧的。
19 ?[3](~18.6)一个经典题目，最正常的一集，(1)(2)(i)(ii)简单如喝水，（3）给点时间要证不难。和盐城二模的形式很像，似乎也有联系。在考场上我只能看出来E(X)=n-一个收敛到e^(-1)+e^(-2)+...+e^(-n)的数列，而且这个数列的后部分的绝对值应该是单调递增的（可惜错位相减好像不是很好用），而要证的式子中后部分是单调递减的，这就能证出来了（不过真的是这样吗？我也不好确定）
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  1. CONNECT:[ UseTime:0.000591s ] mysql:host=127.0.0.1;port=3306;dbname=i460;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000777s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.010222s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000327s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000696s ]
  6. SELECT * FROM `set` [ RunTime:0.002607s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000712s ]
  8. SELECT * FROM `article` WHERE `id` = 521162 LIMIT 1 [ RunTime:0.003101s ]
  9. UPDATE `article` SET `lasttime` = 1777465643 WHERE `id` = 521162 [ RunTime:0.021699s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.000353s ]
  11. SELECT * FROM `article` WHERE `id` < 521162 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000495s ]
  12. SELECT * FROM `article` WHERE `id` > 521162 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000366s ]
  13. SELECT * FROM `article` WHERE `id` < 521162 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000565s ]
  14. SELECT * FROM `article` WHERE `id` < 521162 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.001133s ]
  15. SELECT * FROM `article` WHERE `id` < 521162 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.001419s ]
0.116469s