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全国中考真题选——暑月次题

  • 2026-07-12 04:54:10
全国中考真题选——暑月次题

全国中考真题选

暑月次题

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

暑月次题

P

ART Ⅲ

马老解析

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PART Ⅳ

胡心悦解析

观胡心悦同学之解析，第（1）问三题处理颇见得当，分寸合宜。第（2）问稍显繁琐，然不失为一种解题策略，亦可备一格。届时再观分析视频，当有所悟。

PART Ⅴ

金子昕解析

观金子昕同学之解析，第（1）问三题处理颇见得当。其中第二问求比值一题，与马老思路相异，别辟转折之径，颇可称道。末一问构造，虽与胡心悦同学同出一辙，然解决策略各有千秋。惟马老思之，何不借力于第（1）问之垂直，类比构造，岂非更见精彩，更为捷乎？诸君不妨共思之。

PART Ⅵ

周易晓解析

观周易晓同学之解析，第（1）问三题处理皆善。其中第二问之构造，尤令马老耳目一新，颇见巧思。第（2）问能类比前问辅助线之法，承续有方。然此问行文稍显繁复，未能尽简。届时不妨一观马老视频讲解，当可化繁为简，更上层楼。

PART Ⅶ

王博远解析

观王博远同学之解析，第（1）问三题皆无大碍。其中第二问思路与马老契合，殊为可取。第（2）问之解，其实亦有可观，然其自谓稍显繁复，此感不虚。既有此觉，何不求其至简？届时且看马老视频，一览便知。

PART Ⅷ

李昭糈解析

观李昭糈同学之解析，第（1）问①之相似判定，垂直与内错角，二者足矣，此处似可更简。②问运用得当，虽与马老解法有异，然殊为可取；③问亦见条理。末一问结论无误，惟推演稍繁。思路既通，不妨再求其简。届时一观马老视频，自可化繁为简。

PART Ⅸ

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

2026.07.11

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  1. CONNECT:[ UseTime:0.000450s ] mysql:host=127.0.0.1;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000531s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000278s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000283s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000475s ]
  6. SELECT * FROM `set` [ RunTime:0.000206s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000521s ]
  8. SELECT * FROM `article` WHERE `id` = 507762 LIMIT 1 [ RunTime:0.016606s ]
  9. UPDATE `article` SET `lasttime` = 1783892144 WHERE `id` = 507762 [ RunTime:0.000658s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000290s ]
  11. SELECT * FROM `article` WHERE `id` < 507762 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000401s ]
  12. SELECT * FROM `article` WHERE `id` > 507762 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000443s ]
  13. SELECT * FROM `article` WHERE `id` < 507762 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.005126s ]
  14. SELECT * FROM `article` WHERE `id` < 507762 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.008259s ]
  15. SELECT * FROM `article` WHERE `id` < 507762 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.002927s ]
0.105865s