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【华东师大版】八年级数学下册培优讲义-----重难点模型

  • 2026-04-06 15:01:55
【华东师大版】八年级数学下册培优讲义-----重难点模型

【华东师大版】八年级数学下册培优讲义-----重难点模型

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。

华东师大版中的分式、一次函数、反比例函数非常重要，比如等腰三角形存在性问题、直角三角形存在性问题、45°角问题等等。一定要研究明白噢，到了初三就能轻松很多。

如需要看下方详情。

不算答案共130页左右，详细答案50多页，共180多页讲解重难点、模型。例题+适量针对练习，微信laoyangsx32

 扫码可查看纸质书籍

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【人教版】八年级数学下册培优讲义-----重难点模型

【人教版】九年级数学上学期培优----- 重难点专题书籍介绍

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【华东师大版】七年级数学上册培优讲义-----重难点模

【华师大版】八年级数学上学期培优----- 重难点专题书籍介绍

【华东师大版】九年级数学下学期培优----- 重难点专题书籍介绍

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  1. CONNECT:[ UseTime:0.000553s ] mysql:host=127.0.0.1;port=3306;dbname=a_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000855s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000311s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000334s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000490s ]
  6. SELECT * FROM `set` [ RunTime:0.000206s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000593s ]
  8. SELECT * FROM `article` WHERE `id` = 467743 LIMIT 1 [ RunTime:0.004799s ]
  9. UPDATE `article` SET `lasttime` = 1775475472 WHERE `id` = 467743 [ RunTime:0.005367s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000241s ]
  11. SELECT * FROM `article` WHERE `id` < 467743 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000494s ]
  12. SELECT * FROM `article` WHERE `id` > 467743 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000382s ]
  13. SELECT * FROM `article` WHERE `id` < 467743 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000656s ]
  14. SELECT * FROM `article` WHERE `id` < 467743 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.010402s ]
  15. SELECT * FROM `article` WHERE `id` < 467743 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.013475s ]
0.109992s