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试卷难度归档#3 - 郑外高三调研七

  • 2026-04-01 08:04:04
试卷难度归档#3 - 郑外高三调研七
郑州外国语学校调研*，你真是个魔丸啊！
*注：此卷实际由郑州外国语新枫杨学校老师命制。
全卷综合难度 TEHD [+1.1]
我们郑外的调研难度十分具有稳定性，上次是[-0.4]，这次是[+1.1]，下次可能就超越2022新高考I卷了**（笑）
**注：难度不代表试卷恶心程度。
1~2 +1.4 全卷最正常的两个题，不过第二题（复数）也算不上正常。
3 +2.3 第三题就上等比数列递推，你真的是人类吗？还给一个这么长的背景，Bro想要干什么？让人想到2022新高考I的劲爆棱台体积计算（估算）题。
4 +1.2 非常好的将二项式定理和复数结合的题目，但是却因为能够直接看出每一项的虚实和正负性直接不用算出来n就能skip了。但是如果真的要硬解才能解出来，那这题目计算量确实是有点过于逆天了。
5 +1 一道平凡的周期函数题目。非常平凡。
6 +1.5 需要首先看到圆的半径，x^2+(y-m)^2=2，所以半径是2^(1/2)。然后将切点设出来，斜率(k)和与圆心连线的斜率(-1/k)拉出来之后列方程，当然大家肯定不是这么做的，大家的做法应该是直接蒙出来。
7 ? 我也成大家了，这题看上去像同构，实际上还真没啥思路，我是试出来的，如果后续有严谨过程我会补充。
8 0 将题目稍作转化后会发现这是类似求切线斜率的一个过程，但是在这个坐标系下处理起来比较混乱，不如转化成y=x^2/4的情况处理，设出来切线方程然后将(0,-1)代进去，很快就能解出来需要的值(2^(1/2))。
9 0 全卷最像人的一道题。我说不如加一个求D(X)保持出题人逆天风格有没有懂的？
10 +1.6？？？？你到底出了一坨什么东西啊我去
需要利用(sinA)^2+(sinB)^2=(sinA)^2+(cosA)^2+(cosC)^2，然后变成(sin(A+C))^2=(cosA)^2+(cosC)^2=(sinAcosC+sinCcosA)^2=(sin^2(A)cos^2(C)+sin^2(C)cos^2(A)+2sinAcosCsinCcosA)，进而
(cosC)^2(1-(sinA)^2)+(cosA)^2(1-(sinC)^2)=(cosCcosA)^2+(cosAcosC)^2=2(cosAcosC)^2=2sinAcosCsinCcosA，所以
sinAsinC=cosAcosC.但是这对吗？注意到，如果cosA=0，则原式无意义。我们需要将另外一种变形sinBsinC=cosBcosC进行考虑，发现只有后者是有意义的，A=\pi/2。之后就简单了。这题目的考虑量确实有点难绷。
11 -0.5无言以对的套路题。刚才不是还很能出吗怎么真到难题又不难了？
12 +1.5 公式题目。
13 +1 这里需要注意到，只有当b<0的时候才会有一个可以被我们的操作影响的极小值点，否则操作的是极大值点。我们也可以先求导，再干脆让极大值点极小值点都>0，这样还稍微好考虑一些。这也是一道坑题。
14 ？考场上没做出来，等等解析之后补上。利用二级结论a是好求的，然后之后不管怎么做计算量都很大，足以让人望而却步。
15 15.3 哇哦，是独立性检验。
16 17.1 对于2025全国一卷16的Super plus加强版。
17 16.9 立体几何小综合，其实(3)考的挺没意思的，要描述还不好描述。
18 17.7 计算量全在(2)(i)爆炸，不知道(2)(ii)意义何在的一道题目。
19 19.0我去，劲爆！熟悉的题目，熟悉的配方，不太熟悉的做法。将隐零点，不等式，和一系列莫名其妙的技巧全部熔铸到一起变成的一个超级无解大综合，明天等我将学校卷子取回后必定对这道题详细解析（没时间就等到周末吧），经过考虑决定将19.0的门槛给予这道题目。（可能高估了其难度，日后会再加考虑仔细评估）由于题目没有任何引导，函数也毫无可以投机取巧的点，使得这道题高度综合复杂。
（模拟的该函数和导数的图像，不知道对不对）
其实如果真是画出来这样的话用必要性探路好像是比较合适的，毕竟如果能直接看出来就先猜后证即可。
如果用这种方法能证出来难度就准备调到18.5+，这个18.5是给观察难度的。另外这个+则代表这并不是一个常规的方法。这个观察是相当困难的，没有任何其他的东西可以帮助我们观察到m=1，只有一种直觉。但这个直觉需要大量的计算来验证，其实和瞎猫碰上死耗子没什么区别。
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  1. CONNECT:[ UseTime:0.000498s ] mysql:host=127.0.0.1;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000681s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000323s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000301s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000492s ]
  6. SELECT * FROM `set` [ RunTime:0.000197s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000584s ]
  8. SELECT * FROM `article` WHERE `id` = 469176 LIMIT 1 [ RunTime:0.000427s ]
  9. UPDATE `article` SET `lasttime` = 1775067638 WHERE `id` = 469176 [ RunTime:0.014372s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.006872s ]
  11. SELECT * FROM `article` WHERE `id` < 469176 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.003014s ]
  12. SELECT * FROM `article` WHERE `id` > 469176 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000814s ]
  13. SELECT * FROM `article` WHERE `id` < 469176 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.003925s ]
  14. SELECT * FROM `article` WHERE `id` < 469176 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.006475s ]
  15. SELECT * FROM `article` WHERE `id` < 469176 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.001421s ]
0.113029s