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2025秋天津一中高二期末数学试卷分析

  • 2026-07-13 16:46:41
2025秋天津一中高二期末数学试卷分析
【转发即送】转发本文至朋友圈/聊天界面。即可领取《天津数列模块基本功题库》与《天津卷数学真题2003-2025》(含答案)电子版一份。领取方式：添加微信sigxgx或文末扫码添加好友
这套卷子的数列还是很能体现近两年高三复习趋势的。
第13题：
常规写法可以是待定系数，我的处理方法是“知识迁移”自抽象函数小题。
题中S符合上面f(xy)=f(x)f(y)的结构，就能立刻反映出S是幂函数(1倍x的a次幂)，再结合S是等差的和，轻松得到Sn=n².
第14题：
作差得到an是等差，然后要不写S_2/S_3=S_4/S_6，要不就写原式找定值。后者的计算结构值得说一下，和我椭圆计算模块中讲过的“函数过定点问题”类似
15题偷懒没写，插项的题各位需要非常非常熟练了。
第16题：椭圆题是真简单，第三问也可以写齐次化但没必要。我写的过程相对比较随意，考场上还是要多写清楚一些的。
第17题：
第一问互嵌式结构，不过有没有听过这个词都没影响。跟着引导去作和作差就行。相当于讲义中提到的“提醒作用→写定义式/向目标变形”
第二问放缩，也是讲义里书后题。奇项用糖水不等式放掉，偶项直接扔常数。保留前两项即可
第三问高斯取整+奇偶分项。理清红框那个求和本质就行
第18题：
题干容易有歧义，“从第二层起，每一层的...记作{a_n}”。那第二层的是a₁还是a₂？
而且题干上它还把“从第二层起”加粗了。我偏向于第二层的数据对应a₁。所以如果猜测错出题人意思的话，答案也就肯定不对了，后面重点看思路：
整道题的难度其实不大，把这个放最后一题我感觉是有点偏简单的。
第三问我去年4月份在知识星球发过一道题：
题意和这道题完全一样。对于从b_{n-1}变化到bn，考虑增量是如何构成的：把增量保持(1+4),(4+3),...,(5+2)这样的结构，如果左右再额外+1，+2，那么增量就能被理解成2倍b_{n-1}
于是得到b_n=3b_{n-1}-3。后面待定系数就好
知识星球内包含更多题目分析文章
·寒假班课计划
扫码领取天津卷高考数学历年真题(含答案）
·系统课介绍
课程信息：
目前天津高考复习系统课已录制完数列(1600)、椭圆(1000)、计算(200)三个模块。
每个模块均分为正课（与讲义内容同步）+加餐（持续更新优质习题精讲）两部分。基本按正课1小时100元的价格定价。 
以下图片扫码后点击“听课列表”可以看到课程目录和试听部分
购买课程均会邮寄相应讲义（讲义介绍见下文）
课程特色：
所有课程与讲义设计仅针对天津地区高考。讲义与例题均为我近10年教学经验，逐年修改优化而来。课程质量高、直抓天津卷特点。各模块方法体系完善，紧跟今年天津卷改革方向，且持续免费更新每次模拟考/校统练优质习题讲解。市五所学生报名率60%+，课程内容广受好评。
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  1. CONNECT:[ UseTime:0.000413s ] mysql:host=127.0.0.1;port=3306;dbname=www_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000812s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000279s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000284s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000530s ]
  6. SELECT * FROM `set` [ RunTime:0.000208s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000554s ]
  8. SELECT * FROM `article` WHERE `id` = 506839 LIMIT 1 [ RunTime:0.000711s ]
  9. UPDATE `article` SET `lasttime` = 1784083485 WHERE `id` = 506839 [ RunTime:0.000638s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000234s ]
  11. SELECT * FROM `article` WHERE `id` < 506839 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000422s ]
  12. SELECT * FROM `article` WHERE `id` > 506839 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.002981s ]
  13. SELECT * FROM `article` WHERE `id` < 506839 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.010854s ]
  14. SELECT * FROM `article` WHERE `id` < 506839 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.021139s ]
  15. SELECT * FROM `article` WHERE `id` < 506839 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.021220s ]
0.128980s