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全国中考真题选——暑月拾题

  • 2026-08-05 08:59:00
全国中考真题选——暑月拾题

全国中考真题选

暑月拾题

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

暑月拾题

诸君，本题为今年江苏省苏州市中考第27题，亦是全卷压轴之题。

此题以新定义为衣，以二次函数性质为核。第二问侧在最值之求，第三问重在面积之思，其最佳策略，当属铅垂线法。凡此种种，皆为吾等所必修、所必精之思路与方法。

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

夏子轩解析

↑向左滑动查看完整解析↑

观夏子轩同学之解析，题意理解透彻，了然于胸。

第（1）问基础扎实，轻取无碍。第（2）问善用课上所授顶点纵坐标之表述，列出等量关系，明辨n与m呈二次函数关系，故n之取值范围全然无误。第（3）问铅垂线法运用得宜，且辅以作图，思路清晰。实则头脑明澈者，一图足矣，而绝对值之表述精准得当，答案全然正确。

PART Ⅴ

周易晓解析

观周易晓同学之解析，整体大抵到位，思路明晰。然于第二问n之取值范围，似思之过深，反受其限。二次函数对称性之妙，于此体悟未彻。试问：m=-4之时，n岂不可为0乎？一隅之障，破之即明。

PART Ⅵ

王艺涵解析

观王艺涵同学之解析，朴实无华而思路精准，颇见沉稳。然马老有一言相询：第二问何不径取顶点纵坐标之公式，一步到位，直取结果？君以为何如？

PART Ⅶ

胡心悦解析

观胡心悦同学之解析，策略完全无误。每一问皆丝丝入扣，环环相扣，滴水不漏，可谓出色。然学无止境，汝当下之要，在于刷题之锤炼与秋季专题之吸纳巩固。根基已立，更待精进，以期从熟练走向通透。

PART Ⅷ

金子昕解析

观金子昕同学之解析，大方向无碍。然有数处，略作提点。

其一，第二问中，顶点纵坐标之公式，课上已然讲授，若能熟稔于心，径取直用，便可直接呈现n与m之二次函数关系，省却迂回。

其二，汝断言n≠0，此则有失。试问：若m=-4，n不正是0么？思之过深，反为所困。究其根源，在于二次函数对称性之体悟未彻，以致错判。

对称之妙，贵在通透。一障既破，自见清明。

PART Ⅸ

邹思辰解析

↑向左滑动查看完整解析↑

观邹思辰同学之解析，三问答案皆无偏差，然解法之道，尚有精进之必要。

第一问，新定义本可迅捷破之，却略显迂回。两点既在横轴之上，何不径取交点式，一步到位？答案虽确，策略未臻简净。

第二问，套用顶点纵坐标公式，本无可厚非。然于描述n与m关系之时，展开复又配方，步骤淆乱，反失其序。实则表达之后，n与m呈二次函数顶点式之关系，一目了然，n之取值范围自可直取。此中症结，在于代数计算之根基尚未稳固，须着力夯实。

第三问，以铅垂线法处理面积相关问题，思路无碍，关键在于熟练与否。

综观全篇，答案俱对，然解法是否纯熟，是否精炼，恰是该同学当下所必须直面之课题。望尽早警醒，着力解决，以求更上层楼。

PART Ⅹ

陈信烨解析

观陈信烨同学之解析，答案俱确，然数处可再精进。

其一，第一问两点同在横轴之上，何不径取交点式，岂不更为迅捷？

其二，第二问套用顶点纵坐标公式，思路无碍。

其三，第三问以铅垂线法处理面积，方向可取。然MN之长如何表达，未见具体推演，终觉有缺。

综而言之，解法之道，贵在纯熟与严谨并行。望于以上数点，着力打磨。

PART ⅩI

李昭糈解析

观李昭糈同学之解析，整体大抵到位。然数处可再求精进。

其一，第一问两点同在横轴之上，何不径取交点式，岂不更为轻捷？用一般式反添迂回。

其二，第二问何必舍近求远，取配方法？马老课上所授顶点纵坐标之公式，直取即可，岂不更快？

其三，第三问铅垂线法运用得当，思路全然成立，此节当继续保持。

总之，解法之道，贵在择其善者而从之。以最简之笔，成最明之析，方为至境。

PART ⅩII

杨梓豪解析

观杨梓豪同学之解析，整体思路无碍，答案俱确。

唯末一问稍可商榷：此处既用顶点纵坐标公式，第二问用之得宜，然于第三问中，此公式于后续推演并无实质助益，恐为赘步。三问以铅垂线法驭面积问题，方为得当之选，亦是最佳之径。

PART XIII

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

2026.08.04

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  1. CONNECT:[ UseTime:0.000685s ] 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:0.000238s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000283s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000477s ]
  6. SELECT * FROM `set` [ RunTime:0.000203s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000508s ]
  8. SELECT * FROM `article` WHERE `id` = 509531 LIMIT 1 [ RunTime:0.001064s ]
  9. UPDATE `article` SET `lasttime` = 1785978625 WHERE `id` = 509531 [ RunTime:0.010487s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000230s ]
  11. SELECT * FROM `article` WHERE `id` < 509531 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000433s ]
  12. SELECT * FROM `article` WHERE `id` > 509531 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000361s ]
  13. SELECT * FROM `article` WHERE `id` < 509531 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.001583s ]
  14. SELECT * FROM `article` WHERE `id` < 509531 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.010047s ]
  15. SELECT * FROM `article` WHERE `id` < 509531 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.001499s ]
0.172938s