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全国中考真题选——暑月玖题

  • 2026-08-01 19:14:47
全国中考真题选——暑月玖题

全国中考真题选

暑月玖题

PART Ⅰ

前言

诸君暑期修习，马老将不定期发布全国中考真题。凡所选之题，皆不出吾等已学之法，或昔日已通之巧。此番所求，重在独立思考，独立完解；尤盼百花齐放，方法纷呈，各骋其思。事毕，请以清晰如扫描之影像发我。限期二日。

PART Ⅱ

暑月玖题

诸君，本题为今年黑龙江省绥化市中考第27题，亦是全卷倒数第二题。

此题难度不显，核心在于面积相关问题(求最值)，以及初一一条重要根基之识：角平分+平行线，等腰三必呈现。

请先观马老视频解析，静品其中妙趣。

P

ART Ⅲ

马老解析

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PART Ⅳ

周易晓解析

观周易晓同学之解析，几近完美，无可指摘。唯一微憾，反在吾身：末一问马老竟未改题，留为直接写出。其图中思考痕迹宛然可辨，足见洞明，惜乎推演过程未曾尽录。若能将末一问之步骤从容落笔，则锦上添花，更臻圆满。

PART Ⅴ

王艺涵解析

观王艺涵同学之解析，思路缜密，颇见功力。唯一微憾，反在吾身：末一问马老未作删改，留为直接写出。然细察其图，标记分明，思考之迹宛然可辨，推演之工实已落于草稿之间。往后日常练习，纵遇直接写出之题，亦望将过程从容落笔，以固其本。

PART Ⅵ

王子予解析

观王子予同学之解析，思路确然无误。第二问以配方法求面积最值，驾轻就熟；第三问思路通达，其要在于角平分配平行线，等腰三角自然呈现。然自身态度，仍须端肃，以臻更善。

PART Ⅶ

李昭糈解析

观李昭糈同学之解析，前二问思路无碍。第三问以角平分配平行线，等腰三角自然呈现为径，大方向确然无误。然解方程之际，似有一解见遗，未加深究。试问：另一解真可舍乎？第二处F点，安知其不存在？考虑问题，务求周全，莫使遗漏。

PART Ⅷ

杨梓豪解析

↑向左滑动查看完整解析↑

观杨梓豪同学之解析，前二问思路无碍。第三问取角平分配平行线，等腰三角自然呈现，亦属得法。然其后续推演，借勾股定理分而治之，两度落笔。若径取两点距离公式，实则勾股演变，一炮双响，一举并擒，岂不更为爽利？君以为何如？

PART Ⅸ

孔奕宸解析

观孔奕宸同学之解析，第二问表达面积之后，横坐标何以得2，其间推演，尚需仔细掂量。或配方，或取对称轴公式，皆为正途，然马老未见其详，无从印证。第三问思路无误，以角平分配平行线，等腰三角自然呈现，大方向确然可嘉。惟请细察倒数第三行之“+”处，是否笔下微误？一字之差，恐涉全盘，切须审慎。

PART X

总结

以上诸生之外，尚有其他同学发来解析，马老皆已逐一指点，此处不再赘述。路漫漫其修远兮，初三这一程，须得吃透马老之思路，通晓相似模型之运用，熟稔解确定三角形之法。吾深信，但持勤勉之心，解题之功，自当日渐精进，水到渠成。

作者：马孜旻老师

编排：晴

2026.08.01

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  1. CONNECT:[ UseTime:0.000401s ] mysql:host=127.0.0.1;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000543s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000229s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000378s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000525s ]
  6. SELECT * FROM `set` [ RunTime:0.000231s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000612s ]
  8. SELECT * FROM `article` WHERE `id` = 509164 LIMIT 1 [ RunTime:0.000687s ]
  9. UPDATE `article` SET `lasttime` = 1785617131 WHERE `id` = 509164 [ RunTime:0.006023s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000278s ]
  11. SELECT * FROM `article` WHERE `id` < 509164 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000447s ]
  12. SELECT * FROM `article` WHERE `id` > 509164 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000420s ]
  13. SELECT * FROM `article` WHERE `id` < 509164 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000580s ]
  14. SELECT * FROM `article` WHERE `id` < 509164 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.001466s ]
  15. SELECT * FROM `article` WHERE `id` < 509164 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000978s ]
0.087582s