当前位置：首页>讲义>【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

【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

  • 2026-04-13 02:06:48
【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
【北师大版】七年级数学下册培优讲义-----

七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。

北师大版中的三角形全等模型非常重要，比如手拉手模型，截长补短模型等等。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。

                                   扫码到小红书购买电子版

不算练习答案共200页左右，讲解重难点、模型。例题+适量针对练习

答案150多页为电子版，微信laoyangsx32

 扫码可查看纸质书籍

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【北师大版】九年级数学上册培优讲义-----重难点模型

【北师大版】九年级数学下册培优讲义-----重难点模型

【人教版】七年级数学上学期培优----- 重难点专题书籍介绍

【人教版】七年级数学下学期培优----- 一线编辑，重难点模型例题练习

【人教版】八年级数学上学期培优----- 重难点专题模型讲义书

【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

【人教版】九年级数学下学期培优----- 重难点专题书籍介绍

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【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

【湘教版】七年级数学上册培优讲义----重难点模型例题练习

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  1. CONNECT:[ UseTime:0.000613s ] mysql:host=127.0.0.1;port=3306;dbname=a_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000980s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000311s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000297s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000653s ]
  6. SELECT * FROM `set` [ RunTime:0.000222s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000763s ]
  8. SELECT * FROM `article` WHERE `id` = 460481 LIMIT 1 [ RunTime:0.000440s ]
  9. UPDATE `article` SET `lasttime` = 1777154173 WHERE `id` = 460481 [ RunTime:0.013362s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000313s ]
  11. SELECT * FROM `article` WHERE `id` < 460481 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000513s ]
  12. SELECT * FROM `article` WHERE `id` > 460481 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000449s ]
  13. SELECT * FROM `article` WHERE `id` < 460481 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000940s ]
  14. SELECT * FROM `article` WHERE `id` < 460481 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.001007s ]
  15. SELECT * FROM `article` WHERE `id` < 460481 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.002300s ]
0.124853s