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【人教版】八年级数学下册培优讲义-----重难点模型

  • 2026-11-01 22:20:56
【人教版】八年级数学下册培优讲义-----重难点模型
【人教版】八年级数学下册培优讲义-----

《八年级数学下册培优讲义》由一线教师编辑，按照重难点知识模型讲解+典型例题+针对练习的模式编辑，包含了本册所有重难点考点，讲出题型本质，学完达到举一反三的能力，从而培养数学思维，拒绝偏难怪。

如需要看下方详情。

不算答案共150页左右，答案100多页为电子版，共250多页，讲解重难点、模型。例题+适量针对练习，微信laoyangsx32
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往期文章

【北师大版】七年级数学下册培优讲义-----重难点模型，电子版/书籍版

七年级数学下学期培优----- 一线编辑，重难点模型例题练习

八年级数学上学期培优-----一线三等角模型

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【2027考研】王晶婷《词汇讲义》电子版pdf

基本 文件 流程 错误 SQL 调试
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  1. CONNECT:[ UseTime:0.000745s ] mysql:host=172.18.0.4;port=3306;dbname=a_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000967s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000474s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000333s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000592s ]
  6. SELECT * FROM `set` [ RunTime:0.000380s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000704s ]
  8. SELECT * FROM `article` WHERE `id` = 459086 LIMIT 1 [ RunTime:0.000383s ]
  9. UPDATE `article` SET `lasttime` = 1794172112 WHERE `id` = 459086 [ RunTime:0.001489s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000329s ]
  11. SELECT * FROM `article` WHERE `id` < 459086 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000418s ]
  12. SELECT * FROM `article` WHERE `id` > 459086 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000383s ]
  13. SELECT * FROM `article` WHERE `id` < 459086 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000534s ]
  14. SELECT * FROM `article` WHERE `id` < 459086 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000690s ]
  15. SELECT * FROM `article` WHERE `id` < 459086 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000620s ]
0.093051s