跳到内容
当前位置:首页>考研真题>欧几里得2027备考资料:讲义与分类题怎样搭配

欧几里得2027备考资料:讲义与分类题怎样搭配

  • 2026-11-10 21:24:12
欧几里得2027备考资料:讲义与分类题怎样搭配
欧几里得2027备考资料
讲义与分类题搭配指南
准备欧几里得数学竞赛,资料选择比盲目刷题更重要。本文讲清历年真题、翰林讲义和分类题册如何配合使用,帮助不同基础的学生找到适合自己的备考路径。
针对2027赛季报名与备考规划,核心原则是:讲义搭框架、分类题练专项、真题验水平,三者按阶段切换而非同时铺开。
翰林欧几里得往届战绩展示,不代表本赛季结果或获奖保证
欧几里得的关键问题,下文逐一讲清
具体安排与咨询方式见文末海报
01 / 欧几里得有哪些核心备考资料?
翰林提供的欧几里得备考资料主要包括四大类:历年真题及解析、分类题册、公式书以及翰林专属讲义。每类资料承担不同功能,不能互相替代。
历年真题是了解命题趋势的基础。欧几里得共10道大题100分,难度跨度大,前几题接近课内水平,后几题需要综合多模块知识。通过研究历年题目分布,可以判断哪些模块出题频率高、哪些题型逐年变难。
分类题册按代数、几何、数论、组合与概率等模块整理,适合专项突破薄弱环节。比如数论题连续出错时,集中做分类题册中的数论部分比随机刷整套试卷效率更高。
公式书汇总竞赛常用定理与推导过程,便于快速查阅。翰林讲义则系统梳理知识框架与解题思路,包含典型例题的完整推导过程,帮助理解"为什么这样做"而非只记结论。
欧几里得历年真题目录示例,包含多年份试卷资源
扫码添加顾问老师,获取1对1咨询服务!
02 / 讲义与分类题如何搭配使用?
基础阶段应以翰林讲义为主,建立完整知识体系。具体做法是:先通读一个模块的概念与定理,理解定义、性质与应用场景,再合上讲义尝试复述核心结论,确认真正掌握后才进入下一步。
学完一个模块后,立即配合分类题册进行对应练习。建议按难度从低到高排列,先做基础题确认概念理解无误,再挑战中高难度题训练综合应用能力。每道错题标注卡在哪一步,是概念不清还是计算失误。
强化阶段采用"讲义查漏+真题实战"模式。做历年真题时严格限时,模拟考场压力。做完后逐题对照解析,发现知识盲区立刻回到讲义补学对应章节,形成"做题—发现缺口—回补—再练"的闭环。
冲刺阶段重点研究错题,回归讲义中的经典例题,巩固高频考点与标准解题步骤。此时不再大量刷新题,而是把已做过的题目按错误类型归类,反复练习同类问题直到稳定正确。
欧几里得报名与备考安排,详见海报
扫码添加顾问老师,获取1对1咨询服务!
03 / 不同基础学生如何选择资料组合?
零基础学生应优先使用翰林讲义打牢基础,配合分类题册中的简单题目逐步建立信心。此阶段暂缓直接刷真题,因为欧几里得后几题综合性强,基础不牢时做真题容易产生挫败感且效率低。
有一定数学基础的学生可采用"讲义+分类题+真题"三线并行策略。每周安排固定时间做一套真题限时模拟,其余时间按模块推进讲义学习和分类题练习,保持知识输入与输出节奏平衡。
目标冲击前25%证书的高水平学生,应以真题为核心训练材料。用讲义补充高阶知识点与复杂解题技巧,重点研究最后几道大题的多模块交叉思路,练习在有限时间内写出完整推导过程。
无论何种基础,都建议配备公式书作为速查工具。竞赛中遗忘某个定理是常见情况,平时练习时养成"先回忆再查阅"的习惯,比直接翻书更能强化记忆。
翰林欧几里得讲义示例,含历史版本与2024版资料
扫码添加顾问老师,获取1对1咨询服务!
04 / 备考资料使用时机与注意事项
2027年3月8日前完成翰林协助报名,确保获得参赛资格,之后进入密集备考期。报名与备考可以同步推进,不必等报名完成再开始学习。
考试时间为4月7日(中国等非美洲地区),美洲地区为4月6日。建议提前一个月开始限时模拟,适应150分钟完成10道大题的答题节奏,合理分配每道题的时间预算。
欧几里得要求写出完整过程,仅给答案不得分。平时练习就要养成规范书写习惯,每一步推导都要有依据,避免"心算跳过关键步骤"的坏习惯。
资料不在多而在精,选定一套讲义和题库后坚持用完,频繁更换反而降低学习效率。翰林课程支持40小时大纲体系,具体开班安排可咨询顾问老师了解最新班表。
常见问题
Q:欧几里得需要哪些数学知识储备?
涵盖代数、几何、数论、组合与概率、三角函数、指数对数六大模块,需具备高中及以上数学基础。
Q:低年级学生可以参加吗?
通常面向11-12年级,低年级学生可按基础规划尝试,但不保证提前学习就能获奖。
Q:2027年有真题资料包吗?
2027尚未开考,不存在当年真题。可用的是历年真题及解析,下图展示的目录包含2024版等历史资料,具体可获取的年份可咨询顾问确认。
Q:前25%证书需要多少分?
分数线每年浮动,不承诺固定分数。前25%为官方奖项等级,具体达标情况以当次评分为准。
了解欧几里得报名与备考安排,可咨询顾问老师
扫描文中顾问二维码,了解适合自己的安排
继续了解备考安排
#欧几里得 #竞赛备考 #翰林教育 #国际竞赛
基本 文件 流程 错误 SQL 调试
  1. 请求信息 : 2026-11-11 03:32:14 HTTP/1.1 GET : http://www.sjds.net/a/543729.html
  2. 运行时间 : 0.091135s [ 吞吐率:10.97req/s ] 内存消耗:4,329.86kb 文件加载:140
  3. 缓存信息 : 0 reads,0 writes
  4. 会话信息 : SESSION_ID=67dc570660b390c883f6f7d4fe7f0af5
  1. /www/wwwroot/www.sjds.net/public/index.php ( 0.79 KB )
  2. /www/wwwroot/www.sjds.net/vendor/autoload.php ( 0.17 KB )
  3. /www/wwwroot/www.sjds.net/vendor/composer/autoload_real.php ( 2.49 KB )
  4. /www/wwwroot/www.sjds.net/vendor/composer/platform_check.php ( 0.90 KB )
  5. /www/wwwroot/www.sjds.net/vendor/composer/ClassLoader.php ( 14.03 KB )
  6. /www/wwwroot/www.sjds.net/vendor/composer/autoload_static.php ( 4.90 KB )
  7. /www/wwwroot/www.sjds.net/vendor/topthink/think-helper/src/helper.php ( 8.34 KB )
  8. /www/wwwroot/www.sjds.net/vendor/topthink/think-validate/src/helper.php ( 2.19 KB )
  9. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/helper.php ( 1.47 KB )
  10. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
  11. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
  12. /www/wwwroot/www.sjds.net/vendor/topthink/think-container/src/Facade.php ( 2.71 KB )
  13. /www/wwwroot/www.sjds.net/vendor/symfony/deprecation-contracts/function.php ( 0.99 KB )
  14. /www/wwwroot/www.sjds.net/vendor/symfony/polyfill-mbstring/bootstrap.php ( 8.26 KB )
  15. /www/wwwroot/www.sjds.net/vendor/symfony/polyfill-mbstring/bootstrap80.php ( 9.78 KB )
  16. /www/wwwroot/www.sjds.net/vendor/symfony/var-dumper/Resources/functions/dump.php ( 1.49 KB )
  17. /www/wwwroot/www.sjds.net/vendor/topthink/think-dumper/src/helper.php ( 0.18 KB )
  18. /www/wwwroot/www.sjds.net/vendor/symfony/var-dumper/VarDumper.php ( 4.30 KB )
  19. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/App.php ( 15.30 KB )
  20. /www/wwwroot/www.sjds.net/vendor/topthink/think-container/src/Container.php ( 15.76 KB )
  21. /www/wwwroot/www.sjds.net/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
  22. /www/wwwroot/www.sjds.net/app/provider.php ( 0.19 KB )
  23. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Http.php ( 6.04 KB )
  24. /www/wwwroot/www.sjds.net/vendor/topthink/think-helper/src/helper/Str.php ( 7.29 KB )
  25. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Env.php ( 4.68 KB )
  26. /www/wwwroot/www.sjds.net/app/common.php ( 0.03 KB )
  27. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/helper.php ( 18.78 KB )
  28. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Config.php ( 5.54 KB )
  29. /www/wwwroot/www.sjds.net/config/app.php ( 0.95 KB )
  30. /www/wwwroot/www.sjds.net/config/cache.php ( 0.78 KB )
  31. /www/wwwroot/www.sjds.net/config/console.php ( 0.23 KB )
  32. /www/wwwroot/www.sjds.net/config/cookie.php ( 0.56 KB )
  33. /www/wwwroot/www.sjds.net/config/database.php ( 2.48 KB )
  34. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
  35. /www/wwwroot/www.sjds.net/config/filesystem.php ( 0.61 KB )
  36. /www/wwwroot/www.sjds.net/config/lang.php ( 0.91 KB )
  37. /www/wwwroot/www.sjds.net/config/log.php ( 1.35 KB )
  38. /www/wwwroot/www.sjds.net/config/middleware.php ( 0.19 KB )
  39. /www/wwwroot/www.sjds.net/config/route.php ( 1.89 KB )
  40. /www/wwwroot/www.sjds.net/config/session.php ( 0.57 KB )
  41. /www/wwwroot/www.sjds.net/config/trace.php ( 0.34 KB )
  42. /www/wwwroot/www.sjds.net/config/view.php ( 0.82 KB )
  43. /www/wwwroot/www.sjds.net/app/event.php ( 0.25 KB )
  44. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Event.php ( 7.67 KB )
  45. /www/wwwroot/www.sjds.net/app/service.php ( 0.13 KB )
  46. /www/wwwroot/www.sjds.net/app/AppService.php ( 0.26 KB )
  47. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Service.php ( 1.64 KB )
  48. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Lang.php ( 7.35 KB )
  49. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/lang/zh-cn.php ( 13.70 KB )
  50. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/initializer/Error.php ( 3.31 KB )
  51. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
  52. /www/wwwroot/www.sjds.net/vendor/services.php ( 0.14 KB )
  53. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
  54. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
  55. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/service/ModelService.php ( 2.04 KB )
  56. /www/wwwroot/www.sjds.net/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
  57. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Middleware.php ( 6.72 KB )
  58. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
  59. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/Paginator.php ( 11.86 KB )
  60. /www/wwwroot/www.sjds.net/vendor/topthink/think-validate/src/Validate.php ( 63.20 KB )
  61. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/Model.php ( 23.55 KB )
  62. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 21.05 KB )
  63. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/model/concern/AutoWriteData.php ( 4.21 KB )
  64. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 6.44 KB )
  65. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/model/concern/DbConnect.php ( 5.16 KB )
  66. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.33 KB )
  67. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 28.29 KB )
  68. /www/wwwroot/www.sjds.net/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
  69. /www/wwwroot/www.sjds.net/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
  70. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/model/contract/Modelable.php ( 0.09 KB )
  71. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Db.php ( 2.88 KB )
  72. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/DbManager.php ( 8.52 KB )
  73. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Log.php ( 6.28 KB )
  74. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Manager.php ( 3.92 KB )
  75. /www/wwwroot/www.sjds.net/vendor/psr/log/src/LoggerTrait.php ( 2.69 KB )
  76. /www/wwwroot/www.sjds.net/vendor/psr/log/src/LoggerInterface.php ( 2.71 KB )
  77. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Cache.php ( 4.92 KB )
  78. /www/wwwroot/www.sjds.net/vendor/psr/simple-cache/src/CacheInterface.php ( 4.71 KB )
  79. /www/wwwroot/www.sjds.net/vendor/topthink/think-helper/src/helper/Arr.php ( 16.63 KB )
  80. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/cache/driver/File.php ( 7.84 KB )
  81. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/cache/Driver.php ( 9.03 KB )
  82. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 1.99 KB )
  83. /www/wwwroot/www.sjds.net/app/Request.php ( 0.09 KB )
  84. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Request.php ( 55.78 KB )
  85. /www/wwwroot/www.sjds.net/app/middleware.php ( 0.25 KB )
  86. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
  87. /www/wwwroot/www.sjds.net/vendor/topthink/think-trace/src/TraceDebug.php ( 3.40 KB )
  88. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/middleware/SessionInit.php ( 1.94 KB )
  89. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Session.php ( 1.80 KB )
  90. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/session/driver/File.php ( 6.27 KB )
  91. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/contract/SessionHandlerInterface.php ( 0.87 KB )
  92. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/session/Store.php ( 7.12 KB )
  93. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Route.php ( 23.73 KB )
  94. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/route/RuleName.php ( 5.75 KB )
  95. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/route/Domain.php ( 2.53 KB )
  96. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/route/RuleGroup.php ( 22.43 KB )
  97. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/route/Rule.php ( 26.95 KB )
  98. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/route/RuleItem.php ( 9.78 KB )
  99. /www/wwwroot/www.sjds.net/route/app.php ( 1.72 KB )
  100. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/facade/Route.php ( 4.70 KB )
  101. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 4.74 KB )
  102. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/route/Dispatch.php ( 10.44 KB )
  103. /www/wwwroot/www.sjds.net/app/controller/Index.php ( 4.81 KB )
  104. /www/wwwroot/www.sjds.net/app/BaseController.php ( 2.05 KB )
  105. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/facade/Db.php ( 0.93 KB )
  106. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 5.44 KB )
  107. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/PDOConnection.php ( 52.47 KB )
  108. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/Connection.php ( 8.39 KB )
  109. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.57 KB )
  110. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 16.58 KB )
  111. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/Builder.php ( 24.06 KB )
  112. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/BaseBuilder.php ( 27.50 KB )
  113. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/Query.php ( 15.71 KB )
  114. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/BaseQuery.php ( 45.13 KB )
  115. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.43 KB )
  116. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
  117. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 20.07 KB )
  118. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.66 KB )
  119. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 7.01 KB )
  120. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 19.37 KB )
  121. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 7.11 KB )
  122. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.63 KB )
  123. /www/wwwroot/www.sjds.net/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.77 KB )
  124. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/log/driver/File.php ( 5.96 KB )
  125. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
  126. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/log/Channel.php ( 3.89 KB )
  127. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/event/LogRecord.php ( 1.02 KB )
  128. /www/wwwroot/www.sjds.net/vendor/topthink/think-helper/src/Collection.php ( 16.47 KB )
  129. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/facade/View.php ( 1.70 KB )
  130. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/View.php ( 4.39 KB )
  131. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Response.php ( 8.81 KB )
  132. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/response/View.php ( 3.29 KB )
  133. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/Cookie.php ( 6.06 KB )
  134. /www/wwwroot/www.sjds.net/vendor/topthink/think-view/src/Think.php ( 8.38 KB )
  135. /www/wwwroot/www.sjds.net/vendor/topthink/framework/src/think/contract/TemplateHandlerInterface.php ( 1.60 KB )
  136. /www/wwwroot/www.sjds.net/vendor/topthink/think-template/src/Template.php ( 46.61 KB )
  137. /www/wwwroot/www.sjds.net/vendor/topthink/think-template/src/template/driver/File.php ( 2.41 KB )
  138. /www/wwwroot/www.sjds.net/vendor/topthink/think-template/src/template/contract/DriverInterface.php ( 0.86 KB )
  139. /www/wwwroot/www.sjds.net/runtime/temp/022a5b1eae5a9e3c31e54f699d8ae600.php ( 8.36 KB )
  140. /www/wwwroot/www.sjds.net/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.000464s ] mysql:host=172.18.0.4;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000652s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000410s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000341s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000625s ]
  6. SELECT * FROM `set` [ RunTime:0.000296s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000716s ]
  8. SELECT * FROM `article` WHERE `id` = 543729 LIMIT 1 [ RunTime:0.000398s ]
  9. UPDATE `article` SET `lasttime` = 1794339134 WHERE `id` = 543729 [ RunTime:0.001137s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000312s ]
  11. SELECT * FROM `article` WHERE `id` < 543729 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000444s ]
  12. SELECT * FROM `article` WHERE `id` > 543729 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000391s ]
  13. SELECT * FROM `article` WHERE `id` < 543729 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000758s ]
  14. SELECT * FROM `article` WHERE `id` < 543729 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000686s ]
  15. SELECT * FROM `article` WHERE `id` < 543729 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000817s ]
0.103054s