diff --git a/工具/关键字筛选题号.ipynb b/工具/关键字筛选题号.ipynb index e0ba7204..024d31c3 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 17, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 17, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" } @@ -21,7 +21,7 @@ "\n", "\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n", "keywords_dict_table = [\n", - " {\"usages3\":[\"2023\"],\"usages\":[r\"高三02班[^\\n]*?0.[6]\"],\"content_not\":[\"函数\",\"周期\",\"最\"],\"usages_not\":[r\"0\\.[0-39]\"],\"tags\":[\"三\",\"五\",\"六\"]}\n", + " {\"tags\":\"导数\"}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", @@ -85,7 +85,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -99,12 +99,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb index 42542199..b1c29d58 100644 --- a/工具/批量添加题库字段数据.ipynb +++ b/工具/批量添加题库字段数据.ipynb @@ -2,29 +2,241 @@ "cells": [ { "cell_type": "code", - "execution_count": 8, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 030276 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.969\t1.000\t1.000\t1.000\n", - "题号: 009736 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.781\n", - "题号: 010539 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.500\n", - "题号: 000218 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t1.000\n", - "题号: 000219 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.938\n", - "题号: 000223 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.406\t1.000\t0.969\n", - "题号: 000332 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.812\n", - "题号: 000401 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.406\n", - "题号: 002662 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.875\n", - "题号: 002664 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.625\n", - "题号: 003660 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t1.000\n", - "题号: 010544 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.750\n", - "题号: 000227 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t1.000\n", - "题号: 000512 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.875\n", - "题号: 009745 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.344\n", - "题号: 010550 , 字段: usages 中已添加数据: 20221030\t2023届高三08班\t0.812\n" + "题号: 030290 , 字段: objs 中已添加数据: K0227001X\n", + "题号: 030305 , 字段: objs 中已添加数据: K0227001X\n", + "题号: 030388 , 字段: objs 中已添加数据: K0227001X\n", + "题号: 030390 , 字段: objs 中已添加数据: K0227001X\n", + "题号: 030291 , 字段: objs 中已添加数据: K0227002X\n", + "题号: 030290 , 字段: objs 中已添加数据: K0227002X\n", + "题号: 030298 , 字段: objs 中已添加数据: K0227002X\n", + "题号: 030303 , 字段: objs 中已添加数据: K0227002X\n", + "题号: 030305 , 字段: objs 中已添加数据: K0227002X\n", + "题号: 030309 , 字段: objs 中已添加数据: K0227003X\n", + "题号: 030310 , 字段: objs 中已添加数据: K0227003X\n", + "题号: 030326 , 字段: objs 中已添加数据: K0227003X\n", + "题号: 030339 , 字段: objs 中已添加数据: K0227003X\n", + "题号: 030388 , 字段: objs 中已添加数据: K0227003X\n", + "题号: 030380 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030390 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030295 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030302 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030304 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030306 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030312 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030315 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030322 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030338 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030342 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030373 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030374 , 字段: objs 中已添加数据: K0227004X\n", + "题号: 030294 , 字段: objs 中已添加数据: K0227005X\n", + "题号: 030297 , 字段: objs 中已添加数据: K0227005X\n", + "题号: 030292 , 字段: objs 中已添加数据: K0228001X\n", + "题号: 030307 , 字段: objs 中已添加数据: K0228001X\n", + "题号: 030341 , 字段: objs 中已添加数据: K0228001X\n", + "题号: 030292 , 字段: objs 中已添加数据: K0228002X\n", + "题号: 030340 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030381 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030391 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030392 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030401 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030404 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030370 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030405 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030412 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030294 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030299 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030300 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030318 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030319 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030324 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030329 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030333 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030334 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030336 , 字段: objs 中已添加数据: K0228003X\n", + "题号: 030293 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030299 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030301 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030308 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030310 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030311 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030313 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030370 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 030389 , 字段: objs 中已添加数据: K0228004X\n", + "题号: 010827 , 字段: objs 中已添加数据: K0228005X\n", + "题号: 009912 , 字段: objs 中已有该数据: K0228005X\n", + "题号: 030317 , 字段: objs 中已添加数据: K0229001X\n", + "题号: 030318 , 字段: objs 中已添加数据: K0229001X\n", + "题号: 030319 , 字段: objs 中已添加数据: K0229001X\n", + "题号: 030328 , 字段: objs 中已添加数据: K0229001X\n", + "题号: 030324 , 字段: objs 中已添加数据: K0229002X\n", + "题号: 030394 , 字段: objs 中已添加数据: K0229002X\n", + "题号: 030327 , 字段: objs 中已添加数据: K0229003X\n", + "题号: 030337 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030338 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030339 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030340 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030342 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030381 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030396 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030398 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030399 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030327 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030328 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030329 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030330 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030331 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030332 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030333 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030334 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030335 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030336 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030314 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030316 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030317 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030318 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030319 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030320 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030321 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030321 , 字段: objs 中已有该数据: K0229004X\n", + "题号: 030323 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030325 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 030326 , 字段: objs 中已添加数据: K0229004X\n", + "题号: 009912 , 字段: objs 中已添加数据: K0229005X\n", + "题号: 010827 , 字段: objs 中已有该数据: K0229005X\n", + "题号: 030320 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030323 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030324 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030332 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030335 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030336 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030337 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030339 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030342 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030381 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030394 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030396 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030398 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030399 , 字段: objs 中已添加数据: K0230001X\n", + "题号: 030321 , 字段: objs 中已添加数据: K0230002X\n", + "题号: 030321 , 字段: objs 中已有该数据: K0230002X\n", + "题号: 030322 , 字段: objs 中已添加数据: K0230002X\n", + "题号: 030323 , 字段: objs 中已添加数据: K0230002X\n", + "题号: 030333 , 字段: objs 中已添加数据: K0230002X\n", + "题号: 030334 , 字段: objs 中已添加数据: K0230002X\n", + "题号: 030393 , 字段: objs 中已添加数据: K0230002X\n", + "题号: 030314 , 字段: objs 中已添加数据: K0230003X\n", + "题号: 030316 , 字段: objs 中已添加数据: K0230003X\n", + "题号: 030323 , 字段: objs 中已添加数据: K0230003X\n", + "题号: 030342 , 字段: objs 中已添加数据: K0230003X\n", + "题号: 030327 , 字段: objs 中已添加数据: K0230004X\n", + "题号: 030330 , 字段: objs 中已添加数据: K0230004X\n", + "题号: 030331 , 字段: objs 中已添加数据: K0230004X\n", + "题号: 030325 , 字段: objs 中已添加数据: K0231002X\n", + "题号: 030326 , 字段: objs 中已添加数据: K0231002X\n", + "题号: 030330 , 字段: objs 中已添加数据: K0231002X\n", + "题号: 030331 , 字段: objs 中已添加数据: K0231002X\n", + "题号: 030402 , 字段: objs 中已添加数据: K0231002X\n", + "题号: 030403 , 字段: objs 中已添加数据: K0231002X\n", + "题号: 030331 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030330 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030327 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030325 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030323 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030371 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030395 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030400 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030406 , 字段: objs 中已添加数据: K0231003X\n", + "题号: 030315 , 字段: objs 中已添加数据: K0231004X\n", + "题号: 030316 , 字段: objs 中已添加数据: K0231004X\n", + "题号: 030320 , 字段: objs 中已添加数据: K0231004X\n", + "题号: 030323 , 字段: objs 中已添加数据: K0231004X\n", + "题号: 030327 , 字段: objs 中已添加数据: K0231004X\n", + "题号: 030328 , 字段: objs 中已添加数据: K0231004X\n", + "题号: 030329 , 字段: objs 中已添加数据: K0231004X\n", + "题号: 030330 , 字段: objs 中已添加数据: K0231004X\n", 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, 字段: objs 中已添加数据: K0232002X\n", + "题号: 030361 , 字段: objs 中已添加数据: K0232002X\n", + "题号: 030375 , 字段: objs 中已添加数据: K0232002X\n", + "题号: 030380 , 字段: objs 中已添加数据: K0232002X\n", + "题号: 030385 , 字段: objs 中已添加数据: K0232002X\n", + "题号: 030387 , 字段: objs 中已添加数据: K0232002X\n", + "题号: 030415 , 字段: objs 中已添加数据: K0232003X\n", + "题号: 030372 , 字段: objs 中已添加数据: K0232004X\n", + "题号: 030379 , 字段: objs 中已添加数据: K0232004X\n", + "题号: 009922 , 字段: objs 中已有该数据: K0233001X\n", + "题号: 010821 , 字段: objs 中已有该数据: K0233001X\n", + "题号: 030377 , 字段: objs 中已添加数据: K0233001X\n", + "题号: 010827 , 字段: objs 中已添加数据: K0233002X\n", + "题号: 010821 , 字段: objs 中已添加数据: K0233002X\n", + "题号: 030377 , 字段: objs 中已添加数据: K0233002X\n", + "题号: 030411 , 字段: objs 中已添加数据: K0233003X\n", + "题号: 030412 , 字段: objs 中已添加数据: K0233003X\n", + "题号: 030414 , 字段: objs 中已添加数据: K0233003X\n", + "题号: 030417 , 字段: objs 中已添加数据: K0233003X\n", + "题号: 030425 , 字段: objs 中已添加数据: K0233003X\n", + "题号: 030350 , 字段: objs 中已添加数据: K0233003X\n", + "题号: 030351 , 字段: objs 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K0234005X\n", + "题号: 030357 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030359 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030364 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030365 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030366 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030367 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030368 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030380 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030382 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030383 , 字段: objs 中已添加数据: K0235001X\n", + "题号: 030384 , 字段: objs 中已添加数据: K0235001X\n" ] } ], @@ -122,7 +334,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -136,12 +348,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb index 7b572ebb..a864ab92 100644 --- a/工具/批量题号选题pdf生成.ipynb +++ b/工具/批量题号选题pdf生成.ipynb @@ -2,116 +2,60 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0901001B_教师用_20221020.tex\n", + "开始编译教师版本pdf文件: 临时文件/批量生成题目/29_K0232001X_教师用_20221031.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0901001B_学生用_20221020.tex\n", + "开始编译学生版本pdf文件: 临时文件/批量生成题目/29_K0232001X_学生用_20221031.tex\n", "0\n", - "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0901002B_教师用_20221020.tex\n", + "开始编译教师版本pdf文件: 临时文件/批量生成题目/29_K0232002X_教师用_20221031.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0901002B_学生用_20221020.tex\n", + "开始编译学生版本pdf文件: 临时文件/批量生成题目/29_K0232002X_学生用_20221031.tex\n", "0\n", - "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0901003B_教师用_20221020.tex\n", + 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"\"K0903001B\":\"030219,030221,030230,030231\",\n", - "\"K0903002B\":\"030220\",\n", - "\"K0903005B\":\"030170,030200,030201,030202,030204,030233,030265\",\n", - "\"K0903006B\":\"000234,000240,030196\",\n", - "\"K0904003B\":\"000235,030242\",\n", - "\"K0904004B\":\"000239\",\n", - "\"K0904005B\":\"030207,030210,030213,030238,030239\",\n", - "\"K0905001B\":\"000236\",\n", - "\"K0905002B\":\"030208\",\n", - "\"K0905003B\":\"030212\",\n", - "\"K0905004B\":\"000233\",\n", - "\"K0906004B\":\"030211,030214,030222,030234,030244,030259,030263,030264\",\n", - "\"K0906005B\":\"030246,030247,030252,030253,030254,030255,030268\",\n", - "\"K0906007B\":\"000238\",\n", - "\"K0906008B\":\"030241\",\n", - "\"K0906009B\":\"000237,030209,030248,030249,030258,030260,030269,030274\",\n", - "\"K0906010B\":\"030225,030227,030235,030250,030261\",\n", - "\"K0907001B\":\"030215\",\n", - "\"K0907003B\":\"000242,030243,030251,030270,030271,030272\",\n", - "\"K0907004B\":\"030206,030236,030237,030240,030245,030256,030257,030267\"\n", + "\"K0232001X\":\"030344,030374,030407\",\n", + "\"K0232002X\":\"004013,009918,009919,010819,010820,010823,010824,030343,030345,030347,030348,030349,030356,030360,030361,030375,030385,030387,030408,030409,030410,030416,030422\",\n", + "\"K0232003X\":\"030415\",\n", + "\"K0232004X\":\"030372,030379\",\n", + "\"K0233001X\":\"004007\",\n", + "\"K0233002X\":\"010825,010827,030377\",\n", + "\"K0233003X\":\"004005,004009,009920,009921,010803,010822,010828,030350,030351,030362,030411,030412,030417,030425\",\n", + "\"K0234001X\":\"009922,010821\",\n", + "\"K0234003X\":\"004006,004014,005114,005115,005116,005121,005135,009923,009924,010826,030051,030352,030354,030363,030378,030413,030418,030419,030420,030424,030426\",\n", + "\"K0234004X\":\"030346,030376\",\n", + "\"K0234005X\":\"030353,030355,030358,030369,030386,030414,030421,030423\",\n", + "\"K0235001X\":\"004010,004011,004012,009925,009926,010829,010830,030357,030359,030364,030365,030366,030367,030368,030380,030382,030383,030384\"\n", "}\n", "\n", "\"\"\"---设置题目列表结束---\"\"\"\n", "\n", "\"\"\"---设置文件保存路径---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "directory = \"临时文件/批量生成题目/\"\n", + "directory = \"临时文件/批量生成题目/29_\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 47ba8837..b4ab2cd5 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,50 +1,915 @@ -usages +objs -030276 -20221030 2023届高三08班 0.969 1.000 1.000 1.000 +30290 +K0227001X -009736 -20221030 2023届高三08班 0.781 -010539 -20221030 2023届高三08班 0.500 +30305 +K0227001X -000218 -20221030 2023届高三08班 1.000 -000219 -20221030 2023届高三08班 0.938 +30388 +K0227001X -000223 -20221030 2023届高三08班 0.406 1.000 0.969 -000332 -20221030 2023届高三08班 0.812 +30390 +K0227001X -000401 -20221030 2023届高三08班 0.406 -002662 -20221030 2023届高三08班 0.875 +30291 +K0227002X -002664 -20221030 2023届高三08班 0.625 -003660 -20221030 2023届高三08班 1.000 +30290 +K0227002X -010544 -20221030 2023届高三08班 0.750 -000227 -20221030 2023届高三08班 1.000 +30298 +K0227002X -000512 -20221030 2023届高三08班 0.875 -009745 -20221030 2023届高三08班 0.344 +30303 +K0227002X + + +30305 +K0227002X + + +30309 +K0227003X + + +30310 +K0227003X + + +30326 +K0227003X + + +30339 +K0227003X + + +30388 +K0227003X + + +30380 +K0227004X + + +30390 +K0227004X + + +30295 +K0227004X + + +30302 +K0227004X + + +30304 +K0227004X + + +30306 +K0227004X + + +30312 +K0227004X + + +30315 +K0227004X + + +30322 +K0227004X + + +30338 +K0227004X + + +30342 +K0227004X + + +30373 +K0227004X + + +30374 +K0227004X + + +30294 +K0227005X + + +30297 +K0227005X + + +30292 +K0228001X + + +30307 +K0228001X + + +30341 +K0228001X + + +30292 +K0228002X + + +30340 +K0228003X + + +30381 +K0228003X + + +30391 +K0228003X + + +30392 +K0228003X + + +30401 +K0228003X + + +30404 +K0228003X + + +30370 +K0228003X + + +30405 +K0228003X + + +30412 +K0228003X + + 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+ + +30380 +K0235001X + + +30382 +K0235001X + + +30383 +K0235001X + + +30384 +K0235001X + -010550 -20221030 2023届高三08班 0.812 diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index f0b6d5de..6a85e844 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1 +1 @@ -000179,000749,001895,001999,002004,002013,003113,003135,003138,003356,003505,003522,003528,003538,003985,004539,004672,005086,006147,006288,008101,008107,009673,010222,010453,010523,030058,030061,030062,030101,030106,030107,030154 \ No newline at end of file +030290,030291,030292,030293,030294,030295,030296,030297,030298,030299,030300,030301,030302,030303,030304,030305,030306,030307,030308,030309,030310,030311,030312,030313,030314,030315,030316,030317,030318,030319,030320,030321,030322,030323,030324,030325,030326,030327,030328,030329,030330,030331,030332,030333,030334,030335,030336,030337,030338,030339,030340,030341,030342,030343,030344,030345,030346,030347,030348,030349,030350,030351,030352,030353,030354,030355,030356,030357,030358,030359,030360,030361,030362,030363,030364,030365,030366,030367,030368,030369,030370,030371,030372,030373,030374,030375,030376,030377,030378,030379,030380,030381,030382,030383,030384,030385,030386,030387,030388,030389,030390,030391,030392,030393,030394,030395,030396,030397,030398,030399,030400,030401,030402,030403,030404,030405,030406,030407,030408,030409,030410,030411,030412,030413,030414,030415,030416,030417,030418,030419,030420,030421,030422,030423,030424,030425,030426 \ No newline at end of file diff --git a/工具/根据目标列表批量生成对应题目的字典.ipynb b/工具/根据目标列表批量生成对应题目的字典.ipynb index 6e1c0acc..3776dfba 100644 --- a/工具/根据目标列表批量生成对应题目的字典.ipynb +++ b/工具/根据目标列表批量生成对应题目的字典.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 8, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -14,94 +14,53 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# 输入目标列表\n", - "t = \"\"\"K0901001B\n", - "K0901002B\n", - "K0901003B\n", - "K0901004B\n", - "K0902001B\n", - "K0902002B\n", - "K0902003B\n", - "K0902004B\n", - "K0903001B\n", - "K0903002B\n", - "K0903003B\n", - "K0903004B\n", - "K0903005B\n", - "K0903006B\n", - "K0904001B\n", - "K0904002B\n", - "K0904003B\n", - "K0904004B\n", - "K0904005B\n", - "K0904006B\n", - "K0904007B\n", - "K0905001B\n", - "K0905002B\n", - "K0905003B\n", - "K0905004B\n", - "K0905005B\n", - "K0906001B\n", - "K0906002B\n", - "K0906003B\n", - "K0906004B\n", - "K0906005B\n", - "K0906006B\n", - "K0906007B\n", - "K0906008B\n", - "K0906009B\n", - "K0906010B\n", - "K0907001B\n", - "K0907002B\n", - "K0907003B\n", - "K0907004B\"\"\"" + "t = \"\"\"K0232001X \n", + "K0232002X \n", + "K0232003X \n", + "K0232004X \n", + "K0233001X \n", + "K0233002X \n", + "K0233003X \n", + "K0234001X \n", + "K0234002X \n", + "K0234003X \n", + "K0234004X \n", + "K0234005X \n", + "K0235001X\"\"\"" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "\"K0901001B\":\"030197,030198,030262\",\n", - "\"K0901002B\":\"000232,030195\",\n", - "\"K0901003B\":\"000241\",\n", - "\"K0902002B\":\"030226\",\n", - "\"K0902003B\":\"030199,030217,030223,030224,030229\",\n", - "\"K0902004B\":\"030203,030218,030228,030266\",\n", - "\"K0903001B\":\"030219,030221,030230,030231\",\n", - "\"K0903002B\":\"030220\",\n", - "\"K0903005B\":\"030170,030200,030201,030202,030204,030233,030265\",\n", - "\"K0903006B\":\"000234,000240,030196\",\n", - "\"K0904003B\":\"000235,030242\",\n", - "\"K0904004B\":\"000239\",\n", - "\"K0904005B\":\"030207,030210,030213,030238,030239\",\n", - "\"K0905001B\":\"000236\",\n", - "\"K0905002B\":\"030208\",\n", - "\"K0905003B\":\"030212\",\n", - "\"K0905004B\":\"000233\",\n", - "\"K0906004B\":\"030211,030214,030222,030234,030244,030259,030263,030264\",\n", - "\"K0906005B\":\"030246,030247,030252,030253,030254,030255,030268\",\n", - "\"K0906007B\":\"000238\",\n", - "\"K0906008B\":\"030241\",\n", - "\"K0906009B\":\"000237,030209,030248,030249,030258,030260,030269,030274\",\n", - "\"K0906010B\":\"030225,030227,030235,030250,030261\",\n", - "\"K0907001B\":\"030215\",\n", - "\"K0907003B\":\"000242,030243,030251,030270,030271,030272\",\n", - "\"K0907004B\":\"030206,030236,030237,030240,030245,030256,030257,030267\",\n" + "\"K0232001X\":\"030344,030374,030407\",\n", + "\"K0232002X\":\"004013,009918,009919,010819,010820,010823,010824,030343,030345,030347,030348,030349,030356,030360,030361,030375,030385,030387,030408,030409,030410,030416,030422\",\n", + "\"K0232003X\":\"030415\",\n", + "\"K0232004X\":\"030372,030379\",\n", + "\"K0233001X\":\"004007\",\n", + "\"K0233002X\":\"010825,010827,030377\",\n", + "\"K0233003X\":\"004005,004009,009920,009921,010803,010822,010828,030350,030351,030362,030411,030412,030417,030425\",\n", + "\"K0234001X\":\"009922,010821\",\n", + "\"K0234003X\":\"004006,004014,005114,005115,005116,005121,005135,009923,009924,010826,030051,030352,030354,030363,030378,030413,030418,030419,030420,030424,030426\",\n", + "\"K0234004X\":\"030346,030376\",\n", + "\"K0234005X\":\"030353,030355,030358,030369,030386,030414,030421,030423\",\n", + "\"K0235001X\":\"004010,004011,004012,009925,009926,010829,010830,030357,030359,030364,030365,030366,030367,030368,030380,030382,030383,030384\",\n" ] } ], "source": [ "dict1 = {}\n", - "for o in [l for l in t.split(\"\\n\") if len(l.strip())>0]:\n", + "for o in [l.strip() for l in t.split(\"\\n\") if len(l.strip())>0]:\n", " dict1[o] = []\n", "for id in pro_dict:\n", " for o in dict1:\n", @@ -132,7 +91,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -146,12 +105,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb index 10b0574c..dd716a1f 100644 --- a/工具/添加关联题目.ipynb +++ b/工具/添加关联题目.ipynb @@ -50,7 +50,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -64,12 +64,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index 5c90a1de..1b989178 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -13,11 +13,9 @@ "题块 1 处理完毕.\n", "正在处理题块 2 .\n", "题块 2 处理完毕.\n", - "正在处理题块 3 .\n", - "题块 3 处理完毕.\n", - "开始编译教师版本pdf文件: 临时文件/测验05_教师_20221027.tex\n", + "开始编译教师版本pdf文件: 临时文件/29_导数的应用_教师_20221031.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/测验05_学生_20221027.tex\n", + "开始编译学生版本pdf文件: 临时文件/29_导数的应用_学生_20221031.tex\n", "0\n" ] } @@ -30,19 +28,19 @@ "\"\"\"---设置模式结束---\"\"\"\n", "\n", "\"\"\"---设置模板文件名---\"\"\"\n", - "# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n", - "template_file = \"模板文件/测验周末卷模板.tex\"\n", + "template_file = \"模板文件/第一轮复习讲义模板.tex\"\n", + "# template_file = \"模板文件/测验周末卷模板.tex\"\n", "# template_file = \"模板文件/日常选题讲义模板.tex\"\n", "\"\"\"---设置模板文件名结束---\"\"\"\n", "\n", "\"\"\"---设置其他预处理替换命令---\"\"\"\n", "#2023届第一轮讲义更换标题\n", - "# exec_list = [(\"标题数字待处理\",\"26\"),(\"标题文字待处理\",\"大数定律及独立性\")] \n", + "exec_list = [(\"标题数字待处理\",\"29\"),(\"标题文字待处理\",\"导数的应用\")] \n", "# enumi_mode = 0\n", "\n", "#2023届测验卷与周末卷\n", - "exec_list = [(\"标题替换\",\"测验05\")]\n", - "enumi_mode = 1\n", + "# exec_list = [(\"标题替换\",\"测验05\")]\n", + "# enumi_mode = 1\n", "\n", "# 日常选题讲义\n", "# exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n", @@ -51,15 +49,14 @@ "\"\"\"---其他预处理替换命令结束---\"\"\"\n", "\n", "\"\"\"---设置目标文件名---\"\"\"\n", - "destination_file = \"临时文件/测验05\"\n", + "destination_file = \"临时文件/29_导数的应用\"\n", "\"\"\"---设置目标文件名结束---\"\"\"\n", "\n", "\n", "\"\"\"---设置题号数据---\"\"\"\n", "problems = [\n", - "\"3632,3636,4144,3986,4081,4124,3658,4313,4278,4257,4153,4154\",\n", - "\"4365,4420,4460,4461\",\n", - "\"4485,30282,4763,4465,4466\"\n", + "\"30374,9919,30343,30356,30408,30410,30372,30377,4009,9922,10828,30411,30352,30418,30353,30355,9926,30382\",\n", + "\"30406,30331,30407,10824,30347,30385,30415,30379,10803,5116,30419,30369,30421,30359\"\n", "]\n", "\"\"\"---设置题号数据结束---\"\"\"\n", "\n", @@ -210,7 +207,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -224,12 +221,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/课时目标及课时划分信息汇总.ipynb b/工具/课时目标及课时划分信息汇总.ipynb index 5ccefbac..995d8f2d 100644 --- a/工具/课时目标及课时划分信息汇总.ipynb +++ b/工具/课时目标及课时划分信息汇总.ipynb @@ -172,7 +172,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -186,12 +186,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb index 48ed670f..b426fa18 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/待填tag_教师用_20221030.tex\n", + "开始编译教师版本pdf文件: 临时文件/29预选_教师用_20221031.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/待填tag_学生用_20221030.tex\n", + "开始编译学生版本pdf文件: 临时文件/29预选_学生用_20221031.tex\n", "0\n" ] } @@ -26,14 +26,16 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n", "problems = r\"\"\"\n", - "011988,011989,011990,011991,011992,011993,011994,011995,011996,011997,011998,011999,012000,012001,012002,012003,012004,012005,012006,012007,012008,012009,012010,012011,012012,012013,012014,012015,012016,012017,012018,012019,012020,012021,012022,012023,012024,012025,012026,012027,012028,012029,030077,030078,030079,030080,030081,030082,030083,030084,030085,030086,030087,030088,030089,030090,030091,030092,030093,030094,030095,030096,030097,030098,030100,030103,030113,030114,030115,030116,030117,030118,030119,030120,030121,030122,030123,030124,030125,030126,030127,030128,030129,030130,030131,030132,030133,030134,030135,030136,030137,030138,030139,030140,030141,030142,030283,030284,030285,030286,030287,030288,030289,030290,030291,030292,030293,030294,030295,030296,030297,030298,030299,030300,030301,030302,030303,030304,030305,030306,030307,030308,030309,030310,030311,030312,030313,030314,030315,030316,030317,030318,030319,030320,030321,030322,030323,030324,030325,030326,030327,030328,030329,030330,030331,030332,030333,030334,030335,030336,030337,030338,030339,030340,030341,030342,030343,030344,030345,030346,030347,030348,030349,030350,030351,030352,030353,030354,030355,030356,030357,030358,030359,030360,030361,030362,030363,030364,030365,030366,030367,030368,030369,030370,030371,030372,030373,030374,030375,030376,030377,030378,030379,030380,030381,030382,030383,030384,030385,030386,030387,030388,030389,030390,030391,030392,030393,030394,030395,030396,030397,030398,030399,030400,030401,030402,030403,030404,030405,030406,030407,030408,030409,030410,030411,030412,030413,030414,030415,030416,030417,030418,030419,030420,030421,030422,030423,030424,030425,030426\n", + "30374,30407,9919,10824,30343,30347,30356,30385,30408,30410,30415,30372,30379,30377,4009,10803,10828,30411,9922,5116,30352,30418,30419,30353,30355,30369,30421,9926,30359,30382\n", + "\n", + "\n", "\n", "\"\"\"\n", "\"\"\"---设置题目列表结束---\"\"\"\n", "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/待填tag\"\n", + "filename = \"临时文件/29预选\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", @@ -174,7 +176,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -188,12 +190,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/题库0.3/LessonObj.json b/题库0.3/LessonObj.json index 850076f0..50edab38 100644 --- a/题库0.3/LessonObj.json +++ b/题库0.3/LessonObj.json @@ -847,7 +847,7 @@ "K0229003X": { "id": "K0229003X", "unit_obj": "D02005X", - "content": "会通过定义求$f(x)=x^\\frac 12$的导数, 掌握其中的分子有理化的方法." + "content": "会通过定义求$f(x)=x^{\\frac 12}$的导数, 掌握其中的分子有理化的方法." }, "K0229004X": { "id": "K0229004X", @@ -952,7 +952,7 @@ "K0234002X": { "id": "K0234002X", "unit_obj": "D02006X", - "content": "结合图像直观, 知道比区间上的连续函数一定存在最大值和最小值." + "content": "结合图像直观, 知道闭区间上的连续函数一定存在最大值和最小值." }, "K0234003X": { "id": "K0234003X", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 4afd4f2b..17a3f07d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -124920,7 +124920,7 @@ }, "004915": { "id": "004915", - "content": "已知函数$y=(k^2+4k-5)x^2+4(1-k)x+3$的图象都在$x$轴的上方, 求实数$k$的取值范围.", + "content": "已知函数$y=(k^2+4k-5)x^2+4(1-k)x+3$的图像都在$x$轴的上方, 求实数$k$的取值范围.", "objs": [ "K0115001B" ], @@ -170011,7 +170011,7 @@ }, "006869": { "id": "006869", - "content": "已知二次函数$f(x)=n(n+1)x^2-(2n+1)x+1$, 当$n$取所有自然数时, 求它的图象在$x$轴上截得的所有线段长度的总和.", + "content": "已知二次函数$f(x)=n(n+1)x^2-(2n+1)x+1$, 当$n$取所有自然数时, 求它的图像在$x$轴上截得的所有线段长度的总和.", "objs": [ "KNONE" ], @@ -238115,7 +238115,8 @@ "content": "证明函数$y=\\ln x$与$y=\\mathrm{e}^x$没有驻点.", "objs": [ "K0229004X", - "K0228005X" + "K0228005X", + "K0229005X" ], "tags": [ "第二单元" @@ -258121,8 +258122,7 @@ "id": "010797", "content": "根据导数的几何意义, 求函数$y=\\sqrt{4-x^2}$在下列各点处的导数:\\\\\n(1) $x=-1$;\\\\\n(2) $x=0$;\\\\\n(3) $x=1$.", "objs": [ - "K0229003X", - "K0229002X" + "K0228002X" ], "tags": [ "第二单元" @@ -258191,7 +258191,7 @@ "id": "010800", "content": "求下列函数$y=f(x)$的导数:\\\\\n(1) $f(x)=\\pi$;\\\\\n(2) $f(x)=\\sqrt[3]{x^5}$;\\\\\n(3) $f(x)=\\dfrac1{x^3}$.", "objs": [ - "K0229002X" + "K0229004X" ], "tags": [ "第二单元" @@ -258692,7 +258692,8 @@ "content": "某函数图像如图所示, 它在$[a, b]$上哪一点处取得最大值? 它是极大值点吗? 在哪一点处取得最小值? 它是极小值点吗? \n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.6,yscale = 0.4]\n\\draw [->] (-5,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (-4,-2.5) coordinate (A) .. controls (-3.8,-2) and (-3.3,-1) .. (-3,-1) coordinate (B) .. controls (-2.7,-1) and (-2.3,-2) .. (-2,-2) coordinate (C) .. controls (-1.8,-2) and (-1.3,1) .. (-1,1) coordinate (D) .. controls (-0.1,1) and (0.1,-2.8) .. (1,-2.8) coordinate (E) .. controls (1.5,-2.8) and (3.2,1) .. (4,1) coordinate (F) .. controls (4.3,1) and (4.6,0.5) .. (5,0.5) coordinate (G) .. controls (5.2,0.5) and (5.5,1.3) .. (6,1.8) coordinate (H);\n\\draw [dashed] (A) -- (-4,0) node [above] {$a$} (B) -- (-3,0) node [above] {$x_1$} (C) -- (-2,0) node [above] {$x_2$} (D) -- (-1,0) node [below] {$x_3$} (E) -- (1,0) node [above] {$x_4$} (F) -- (4,0) node [below] {$x_5$} (G) -- (5,0) node [below] {$x_6$} (H) -- (6,0) node [below] {$b$};\n\\end{tikzpicture}\n\\end{center}", "objs": [ "K0233001X", - "K0234001X" + "K0234001X", + "K0233002X" ], "tags": [ "第二单元" @@ -258831,7 +258832,9 @@ "id": "010827", "content": "判断下列函数在$(-\\infty, +\\infty)$上是否存在驻点, 是否存在极值点, 并说明理由:\\\\\n(1) $y=x^n$, $n$为正奇数;\\\\\n(2) $y=x^n$, $n$为正偶数.", "objs": [ - "K0229005X" + "K0229005X", + "K0228005X", + "K0233002X" ], "tags": [ "第二单元" @@ -266119,7 +266122,7 @@ }, "011139": { "id": "011139", - "content": "已知函数$f(x)=a^{x+1}-2$($a>0$且$a\\ne 1$), 设$f^{-1}(x)$是$f(x)$的反函数. 若$y=f^{-1}(x)$的图象不经过第二象限, 则$a$的取值范围为\\blank{50}.", + "content": "已知函数$f(x)=a^{x+1}-2$($a>0$且$a\\ne 1$), 设$f^{-1}(x)$是$f(x)$的反函数. 若$y=f^{-1}(x)$的图像不经过第二象限, 则$a$的取值范围为\\blank{50}.", "objs": [], "tags": [ "" @@ -297007,7 +297010,7 @@ }, "030211": { "id": "030211", - "content": "如图所示的茎叶图记录了甲、乙两组各$5$名工人某日的产量数据(单位: 件). 若这两组数据的中位数相等, 且平均值也相等, 则$x$和$y$的值分别为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{r|c|l}\n甲组 & & 乙组 \\\\ \n$6$ & $5$ & $9$ \\\\ \n$2\\ 5$ & $6$ & $1\\ 7\\ y$ \\\\ \n$x\\ 4$ & $7$ & $8$ \n\\end{tabular}\n\\end{center}", + "content": "如图所示的茎叶图记录了甲、乙两组各$5$名工人某日的产量数据(单位: 件). 若这两组数据的中位数相等, 且平均值也相等, 则$x$和$y$的值分别为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{r|c|l}\n甲组 & & 乙组 \\\\ \n$6$ & $5$ & $9$ \\\\ \n$2\\ 5$ & $6$ & $1\\ y\\ 7$ \\\\ \n$x\\ 4$ & $7$ & $8$ \n\\end{tabular}\n\\end{center}", "objs": [ "K0905001B", "K0906004B" @@ -298201,7 +298204,7 @@ }, "030262": { "id": "030262", - "content": "为了了解某地参加计算机水平测试的$5000$名学生的成绩, 从中抽取了$200$名学生进行调查分析, 在这个问题中, 被抽取的$200$名学生是\\bracket{20}.\n\\fourch{总体}{个体}{样本}{样本量}", + "content": "为了了解某地参加计算机水平测试的$5000$名学生的成绩, 从中抽取了$200$名学生进行调查分析, 在这个问题中, 被抽取的$200$名学生的成绩是\\bracket{20}.\n\\fourch{总体}{个体}{样本}{样本量}", "objs": [ "K0901001B" ], @@ -298215,7 +298218,8 @@ "usages": [], "origin": "人教A版2019年必修二教材统计例题与习题", "edit": [ - "20221019\t王伟叶" + "20221019\t王伟叶", + "20221031\t吴惠群" ], "same": [], "related": [], @@ -298570,7 +298574,7 @@ }, "030277": { "id": "030277", - "content": "甲乙两人根据比赛结果分一项奖金, 赛制为五局三胜, 在甲与乙比分是$2:1$时, 比赛因某些不可抗力不得不中止, 此时如何分奖金公平?", + "content": "甲乙两人根据比赛结果分一项奖金, 赛制为五局三胜(每一局中两人获胜的概率都为$\\dfrac 12$, 且各局的结果独立), 在甲与乙比分是$2:1$时, 比赛因某些不可抗力不得不中止, 此时如何分奖金公平?", "objs": [ "K0808002B", "K0808004B", @@ -298874,7 +298878,10 @@ "030290": { "id": "030290", "content": "火箭发射$t\\text{s}$后, 其高度(单位: $\\text{m}$)为$h(t)=0.9t^2$. 求:\\\\\n(1) 在$1\\le t\\le 2$这段时间里, 火箭爬高的平均速度;\\\\ \n(2) 发射后第$10\\text{s}$时, 火箭爬高的瞬时速度.", - "objs": [], + "objs": [ + "K0227001X", + "K0227002X" + ], "tags": [ "第二单元", "导数" @@ -298896,7 +298903,9 @@ "030291": { "id": "030291", "content": "一个小球从$5\\text{m}$的高处自由下落, 其位移$y$(单位: $\\text{m}$)与时间: (单位: $\\text{s}$)之间的关系为$y(t)=-4.9t^2$. 求$t=1\\text{s}$\n时小球的瞬时速度.", - "objs": [], + "objs": [ + "K0227002X" + ], "tags": [ "第二单元", "导数" @@ -298918,7 +298927,10 @@ "030292": { "id": "030292", "content": "你认为应该怎样定义抛物线$f(x)=x^2$在点$(x_0,x_0^2)$处的切线? 试求抛物线\n$f(x)=x^2$在点$(-1,1)$处切线的斜率.", - "objs": [], + "objs": [ + "K0228001X", + "K0228002X" + ], "tags": [ "第二单元", "导数" @@ -298940,7 +298952,9 @@ "030293": { "id": "030293", "content": "求抛物线$f(x)=x^2+1$在点$(0, 1)$处的切线方程.", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -298962,7 +298976,10 @@ "030294": { "id": "030294", "content": "设$f(x)=\\dfrac 1x$, 求 $f'(1)$.", - "objs": [], + "objs": [ + "K0227005X", + "K0228003X" + ], "tags": [ "第二单元", "导数" @@ -298984,7 +299001,9 @@ "030295": { "id": "030295", "content": "将原油精炼为汽油、柴油、塑胶等各种不同产品, 需要对原油进行冷却和加热, 已知在第$x\\text{h}$时, 原油的温度(单位: $\\text{C}^\\circ$)为$y=f(x)=x^2-7x+15$($0\\le x\\le 8$). 计算第$2\\text{h}$与第$6\\text{h}$时, 原油温度的瞬时变化率, 并说明它们的意义.", - "objs": [], + "objs": [ + "K0227004X" + ], "tags": [ "第二单元", "导数" @@ -299028,7 +299047,9 @@ "030297": { "id": "030297", "content": "设$f(x)=x$, 求$f'(1)$.", - "objs": [], + "objs": [ + "K0227005X" + ], "tags": [ "第二单元", "导数" @@ -299050,7 +299071,9 @@ "030298": { "id": "030298", "content": "一质点$A$沿直线运动, 位移$y$(单位: $\\text{m}$)与时间$t$(单位: $\\text{s}$)之间的关系为$y(t)=2t^2+1$, 求质点$A$在$t=2.7\\text{s}$时的瞬时速度.", - "objs": [], + "objs": [ + "K0227002X" + ], "tags": [ "第二单元", "导数" @@ -299072,7 +299095,10 @@ "030299": { "id": "030299", "content": "设函数$f(x)=x^2-1$, 求:\\\\ \n(1) 当自变量$x$由$1$变到$1.1$时, 函数的平均变化率;\\\\\n(2) 函数在$x=1$处的导数.", - "objs": [], + "objs": [ + "K0228003X", + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -299094,7 +299120,9 @@ "030300": { "id": "030300", "content": "函数$f(x)$的图像如图所示, 下列数值排序正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (0,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0.5) .. controls (1,2.5) and (2,2.8) .. (3.5,3);\n\\foreach \\i in {1,2,3}{\\draw (\\i,0.2) -- (\\i,0) node [below] {$\\i$};};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$f'(1)>f'(2)>f'(3)>0$}{$f'(1)f'(2)>0>f'(3)$}", - "objs": [], + "objs": [ + "K0228003X" + ], "tags": [ "第二单元", "导数" @@ -299116,7 +299144,9 @@ "030301": { "id": "030301", "content": "求曲线$y=-2x^2+1$在点$(1, -1)$处的切线方程.", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -299137,8 +299167,10 @@ }, "030302": { "id": "030302", - "content": "吹气球时, 气球的半径$r$(单位: $\\text{dm}$)与体积$V$(单位:$\\text{L}$)之间的函数关系是$r(V)=\\sqrt[3]{\\dfrac{3V}{4\\pi}}$. 利用信息技术工具, 画出$0\\le V\\le 5$时函数的图象, 并根据其图象估计$V=0.6,1.2\\text{L}$时, 气球的瞬时膨胀率.", - "objs": [], + "content": "吹气球时, 气球的半径$r$(单位: $\\text{dm}$)与体积$V$(单位:$\\text{L}$)之间的函数关系是$r(V)=\\sqrt[3]{\\dfrac{3V}{4\\pi}}$. 利用信息技术工具, 画出$0\\le V\\le 5$时函数的图像, 并根据其图像估计$V=0.6,1.2\\text{L}$时, 气球的瞬时膨胀率.", + "objs": [ + "K0227004X" + ], "tags": [ "第二单元", "导数" @@ -299160,7 +299192,9 @@ "030303": { "id": "030303", "content": "一个物体从$10\\text{m}$高处做自由落体运动, $t\\text{s}$时该物体距离地面的高度(单位: $\\text{m}$)为$h(t)=-4.9t^2+10$. 求该物体在$t=1$时的瞬时速度, 并解释此时物体的运动状况.", - "objs": [], + "objs": [ + "K0227002X" + ], "tags": [ "第二单元", "导数" @@ -299182,7 +299216,9 @@ "030304": { "id": "030304", "content": "圆的面积$S$(单位: $\\text{cm}^2$)与半径$R$(单位: $\\text{m}$)的关系为$S=\\pi R^2$. 求$R=5\\text{cm}$时面积关于半径的瞬时变化率.", - "objs": [], + "objs": [ + "K0227004X" + ], "tags": [ "第二单元", "导数" @@ -299204,7 +299240,10 @@ "030305": { "id": "030305", "content": "某质点沿直线运动, 位移$y$(单位: $\\text{m}$)与时间$t$: (单位: $\\text{s}$)之间的关系为$y(t)=5t^2+6$. 求:\\\\\n(1) $2\\le t\\le 3$这段时间内的平均速度;\\\\\n(2) $t=2\\text{s}$时的瞬时速度.", - "objs": [], + "objs": [ + "K0227001X", + "K0227002X" + ], "tags": [ "第二单元", "导数" @@ -299226,7 +299265,9 @@ "030306": { "id": "030306", "content": "已知车轮旋转的角度$\\theta$(单位: $\\text{rad}$)与时间(单位: $\\text{s}$)之间的关系为$\\theta(t)=\\dfrac{25\\pi}{8}t^2$. 求车轮转动开始后第$3.2\\text{s}$时的瞬时角速度.", - "objs": [], + "objs": [ + "K0227004X" + ], "tags": [ "第二单元", "导数" @@ -299247,8 +299288,10 @@ }, "030307": { "id": "030307", - "content": "小明骑车上学, 开始时匀速行驶, 途中因交通堵塞停留了一段时间, 后为了赶时间加快速度行驶, 与以上事件吻合得最好的图象是\\bracket{20}.\n\\fourch{\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) -- (1,0.5) .. controls (1.8,0.6) .. (2,1.3);\n\\end{tikzpicture}\n}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,1.1) -- (0.6,0.8) -- (0.9,0.8) -- (2.5,0);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,1.1) -- (0.6,0.8) -- (0.8,0.8) .. controls (1.7,0.8) .. (2.1,0);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,1.1) -- (1,0.8) -- (2,0);\n\\end{tikzpicture}}", - "objs": [], + "content": "小明骑车上学, 开始时匀速行驶, 途中因交通堵塞停留了一段时间, 后为了赶时间加快速度行驶, 与以上事件吻合得最好的图像是\\bracket{20}.\n\\fourch{\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) -- (1,0.5) .. controls (1.8,0.6) .. (2,1.3);\n\\end{tikzpicture}\n}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,1.1) -- (0.6,0.8) -- (0.9,0.8) -- (2.5,0);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,1.1) -- (0.6,0.8) -- (0.8,0.8) .. controls (1.7,0.8) .. (2.1,0);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$t$};\n\\draw [->] (0,0) -- (0,2) node [right] {距学校的距离};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,1.1) -- (1,0.8) -- (2,0);\n\\end{tikzpicture}}", + "objs": [ + "K0228001X" + ], "tags": [ "第二单元", "导数" @@ -299270,7 +299313,9 @@ "030308": { "id": "030308", "content": "求曲线$y=\\dfrac 12 x^2-2$在点$(1, -\\dfrac 32)$处的切线的倾斜角.", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -299292,7 +299337,9 @@ "030309": { "id": "030309", "content": "一个质量为$3\\text{kg}$的物体做直线运动, 设位移$y$(单位: $\\text{m}$)与时间: (单位: $\\text{s}$)之间的关系为$y(t)=1+t^2$, 并且物体的动能$E_k=\\dfrac 12 mv^2$. 求物体开始运动后第$5\\text{s}$时的动能.", - "objs": [], + "objs": [ + "K0227003X" + ], "tags": [ "第二单元", "导数" @@ -299313,8 +299360,11 @@ }, "030310": { "id": "030310", - "content": "根据下面的文字叙述, 画出相应的路程关于时间的函数图象的大致形状.\\\\ \n(1) 汽车在笔直的公路上匀速行驶;\\\\\n(2) 汽车在笔直的公路上不断加速行驶;\\\\\n(3) 汽车在笔直的公路上不断减速行驶.", - "objs": [], + "content": "根据下面的文字叙述, 画出相应的路程关于时间的函数图像的大致形状.\\\\ \n(1) 汽车在笔直的公路上匀速行驶;\\\\\n(2) 汽车在笔直的公路上不断加速行驶;\\\\\n(3) 汽车在笔直的公路上不断减速行驶.", + "objs": [ + "K0227003X", + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -299336,7 +299386,9 @@ "030311": { "id": "030311", "content": "已知函数$f(x)$的图像, 试画出其导函数$f'(x)$图像的大致形状.\\\\\n(1) \n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (-0.5,1.5) -- (1.5,-0.5);\n\\draw (1,0.1) -- (1,0) node [below] {$1$};\n\\draw (0.1,1) -- (0,1) node [left] {$1$};\n\\end{tikzpicture}\n(2) \n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0.1,0.5) .. controls (1.3,0.6) .. (1.8,1.3);\n\\draw (1,0.1) -- (1,0) node [below] {$1$};\n\\draw (0.1,1) -- (0,1) node [left] {$1$};\n\\end{tikzpicture}\n(3)\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1.4:1.4] plot (\\x,{pow(\\x,2)});\n\\draw (1,0.1) -- (1,0) node [below] {$1$};\n\\draw (0.1,1) -- (0,1) node [left] {$1$};\n\\end{tikzpicture}", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -299358,7 +299410,9 @@ "030312": { "id": "030312", "content": "在高台跳水运动中, $t\\text{s}$时运动员的重心相对于水面的高度(单位: $\\text{m}$)是$h(t)=-4.9t^2+4.8t+11$. 高度$h$关于时间$t$的导数是速度$v$, 速度$v$关于时间$t$的导数$v'$的物理意义是什么? 试求$v$, $v'$关于时间$t$的函数解析式.", - "objs": [], + "objs": [ + "K0227004X" + ], "tags": [ "第二单元", "导数" @@ -299380,7 +299434,9 @@ "030313": { "id": "030313", "content": "根据下列条件, 分别画出函数$y=f(x)$的图像在这点附近的大致形状:\\\\\n(1) $f(1)=-5$, $f'(1)=-1$;\\\\\n(2) $f(5)=10$, $f'(5)=15$;\\\\\n(3) $f(10)=20$, $f'(10)=0$.", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -299402,7 +299458,10 @@ "030314": { "id": "030314", "content": "求下列函数的导数:\\\\\n(1) $y=x^{\\frac 23}$;\\\\\n(2) $y=\\log_2 x$.", - "objs": [], + "objs": [ + "K0229004X", + "K0230003X" + ], "tags": [ "第二单元", "导数" @@ -299424,7 +299483,10 @@ "030315": { "id": "030315", "content": "假设某地在$20$年间的年均通货膨胀率为$5\\%$, 物价$p$(单位: 元)与时间$t$(单位: 年)之间的关系为$p(t)=p_0(1+5\\%)^t$, 其中$p_0$为$t=0$时的物价. 假定某种商品的$p_0=1$, 那么在第$10$个年头, 这种商品的价格上涨的速度大约是多少(精确到$0.01$元/年)?", - "objs": [], + "objs": [ + "K0227004X", + "K0231004X" + ], "tags": [ "第二单元", "导数" @@ -299446,7 +299508,11 @@ "030316": { "id": "030316", "content": "求下列函数的导数:\\\\\n(1) $y=\\dfrac 1{x^4}$;\\\\\n(2) $y=\\sqrt[3]{x^4}$;\\\\\n(3) $y=3^x$;\\\\\n(4) $y=(\\dfrac 12)^x$;\\\\\n(5) $y=\\log_4 x$;\\\\\n(6) $y=\\log_{\\frac 12} x$.", - "objs": [], + "objs": [ + "K0229004X", + "K0230003X", + "K0231004X" + ], "tags": [ "第二单元", "导数" @@ -299468,7 +299534,10 @@ "030317": { "id": "030317", "content": "求下列函数在给定点的导数:\\\\\n(1) $y=x^5$在$x=3$处的导数;\\\\\n(2) $y=\\ln x$在$x=\\dfrac 23$处的导数;\\\\\n(3) $y=\\sin x$在$x=2\\pi$处的导数;\\\\\n(4) $y=\\mathrm{e}^x$在$x=0$处的导数.", - "objs": [], + "objs": [ + "K0229001X", + "K0229004X" + ], "tags": [ "第二单元", "导数" @@ -299490,7 +299559,11 @@ "030318": { "id": "030318", "content": "求余弦曲线$y=\\cos x$在点$(\\dfrac \\pi 2,0)$处的切线方程.", - "objs": [], + "objs": [ + "K0228003X", + "K0229001X", + "K0229004X" + ], "tags": [ "第二单元", "导数" @@ -299512,7 +299585,11 @@ "030319": { "id": "030319", "content": "求曲线$y=x^{\\frac 12}$在点$(4,2)$处的切线方程.", - "objs": [], + "objs": [ + "K0228003X", + "K0229001X", + "K0229004X" + ], "tags": [ "第二单元", "导数" @@ -299534,7 +299611,11 @@ "030320": { "id": "030320", "content": "求下列函数的导数:\\\\\n(1) $y=x^3-x+3$;\\\\\n(2) $y=2^x+\\cos x$.", - "objs": [], + "objs": [ + "K0229004X", + "K0230001X", + "K0231004X" + ], "tags": [ "第二单元", "导数" @@ -299556,7 +299637,10 @@ "030321": { "id": "030321", "content": "求下列函数的导数:\\\\\n(1) $y=x^3\\mathrm{e}^x$;\\\\\n(2) $y=\\dfrac{2\\sin x}{x^2}$.", - "objs": [], + "objs": [ + "K0229004X", + "K0230002X" + ], "tags": [ "第二单元", "导数" @@ -299578,7 +299662,10 @@ "030322": { "id": "030322", "content": "日常生活中的饮用水通常是经过净化的. 随着水的纯净度的提高, 所需净化费用不断增加. 已知将$1\\text{t}$水净化到纯净度为$x\\%$时所需费用(单位: 元)为\n$c(x)=\\dfrac{5284}{100-x}$($800$的解集.", - "objs": [], + "objs": [ + "K0229004X", + "K0230001X" + ], "tags": [ "第二单元", "导数" @@ -299930,7 +300083,11 @@ "030338": { "id": "030338", "content": "氡气是一种由地表自然散发的无味的放射性气体, 如果最初有$500\\text{g}$氡气, 那么$t$天后, 氡气的剩余量为$A(t)=500\\times 0.834^t\\text{g}$.\\\\\n(1) 氡气的散发速度是多少?\\\\\n(2) $A'(7)$的值是什么(精确到$0.1$)? 它表示什么意义?", - "objs": [], + "objs": [ + "K0227004X", + "K0229004X", + "K0231004X" + ], "tags": [ "第二单元", "导数" @@ -299952,7 +300109,11 @@ "030339": { "id": "030339", "content": "设某高山滑雪运动员在一次滑雪训练中滑行的路程$l$(单位: $\\text{m}$)与时间: (单位: $\\text{s}$)之间的关系为$l(t)=2t^2+\\dfrac 32t$.\n(1) 求$l$关于$t$的导数, 并解释它的实际意义;\\\\\n(2) 当$t=3\\text{s}$时, 求运动员的滑雪速度;\\\\ \n(3) 当运动员的滑雪路程为$38\\text{m}$时, 求此时的滑雪速度.", - "objs": [], + "objs": [ + "K0227003X", + "K0229004X", + "K0230001X" + ], "tags": [ "第二单元", "导数" @@ -299974,7 +300135,11 @@ "030340": { "id": "030340", "content": "设曲线$y=\\mathrm{e}^{2ax}$在点$(0, 1)$处的切线与直线$2x-y+1=0$垂直, 求$a$的值.", - "objs": [], + "objs": [ + "K0228003X", + "K0229004X", + "K0231004X" + ], "tags": [ "第二单元", "导数" @@ -299996,7 +300161,9 @@ "030341": { "id": "030341", "content": "请按步骤, 完成下面的任务.\\\\\n(1) 利用信息技术工具, 分别画出$h=1,0.5,0.1,0.05$时, 函数$y=\\dfrac{\\sin(x+h)-\\sin x}h$的图像;\\\\\n(2) 画出函数$y=\\cos x$的图像, 并与上面的四个图像比较, 当$h$越来越小时, 你观察到了什么?\\\\\n(3) 猜测$y=\\sin x$的导数, 它与基本初等函数的导数公式表中$\\sin x$的导数公式一样吗?", - "objs": [], + "objs": [ + "K0228001X" + ], "tags": [ "第二单元", "导数" @@ -300018,7 +300185,12 @@ "030342": { "id": "030342", "content": "某海湾拥有世界上最大的海潮, 其高低水位之差可达到$15\\text{m}$. 假设在该海湾某一固定点, 大海水深$d$(单位: $\\text{m}$)与午夜后的时间: (单位: $\\text{h}$)之间的关系为$d(t)=10+4\\cos t$. 求下列时刻潮水的速度(精确到$0.01\\text{m}/\\text{h}$):\\\\\n(1) 上午$6:00$;\\\\ \n(2) 上午$9:00$;\\\\\n(3) 中午$12:00$;\\\\ \n(4) 下午$6:00$.", - "objs": [], + "objs": [ + "K0227004X", + "K0229004X", + "K0230001X", + "K0230003X" + ], "tags": [ "第二单元", "导数" @@ -300040,7 +300212,9 @@ "030343": { "id": "030343", "content": "利用导数判断下列函数的单调性:\\\\\n(1) $f(x)=x^3+3x$;\\\\\n(2) $f(x)=\\sin x-x$, $x\\in (0,\\pi)$;\\\\\n(3) $f(x)=\\dfrac{x-1}x$.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300062,7 +300236,9 @@ "030344": { "id": "030344", "content": "已知导函数$f'(x)$的下列信息: 当$10$; 当$x<1$, 或$x>4$时, $f'(x)<0$; 当$x=1$, 或$x=4$时, $f'(x)=0$. 试画出函数$f(x)$图像的大致形状.", - "objs": [], + "objs": [ + "K0232001X" + ], "tags": [ "第二单元", "导数" @@ -300084,7 +300260,9 @@ "030345": { "id": "030345", "content": "判断下列函数的单调性:\\\\\n(1) $f(x)=x^2-2x+4$;\\\\\n(2) $f(x)=\\mathrm{e}^x-x$.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300106,7 +300284,9 @@ "030346": { "id": "030346", "content": "利用导数讨论二次函数$f(x)=ax^2+bx+c$的单调区间.", - "objs": [], + "objs": [ + "K0234004X" + ], "tags": [ "第二单元", "导数" @@ -300128,7 +300308,9 @@ "030347": { "id": "030347", "content": "求函数$f(x)=\\dfrac 13x^3-\\dfrac 12x^2-2x+1$的单调区间.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300150,7 +300332,9 @@ "030348": { "id": "030348", "content": "判断下列函数的单调性, 并求出单调区间:\\\\\n(1) $f(x)=3x-x^3$;\\\\\n(2) $f(x)=x^3-x^2-x$.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300172,7 +300356,9 @@ "030349": { "id": "030349", "content": "证明函数$f(x)=2x^3-6x^2+7$在区间$(0,2)$上单调递减.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300194,7 +300380,9 @@ "030350": { "id": "030350", "content": "求函数$f(x)=\\dfrac 13 x^3-4x+4$的极值.", - "objs": [], + "objs": [ + "K0233003X" + ], "tags": [ "第二单元", "导数" @@ -300216,7 +300404,9 @@ "030351": { "id": "030351", "content": "求下列函数的极值:\\\\\n(1) $f(x)=6x^2-x-2$;\\\\\n(2) $f(x)=x^3-27x$;\\\\\n(3) $f(x)=6+12x-x^3$;\\\\\n(4) $f(x)=3x-x^3$.", - "objs": [], + "objs": [ + "K0233003X" + ], "tags": [ "第二单元", "导数" @@ -300237,8 +300427,10 @@ }, "030352": { "id": "030352", - "content": "求函数$f(x)=\\dfrac 13 x^3-4x+4$的最大值与最小值.", - "objs": [], + "content": "求函数$f(x)=\\dfrac 13 x^3-4x+4$在区间$[0,3]$上的最大值与最小值.", + "objs": [ + "K0234003X" + ], "tags": [ "第二单元", "导数" @@ -300260,7 +300452,9 @@ "030353": { "id": "030353", "content": "证明: 当$x>0$时, $1-\\dfrac 1x\\le \\ln x$.", - "objs": [], + "objs": [ + "K0234005X" + ], "tags": [ "第二单元", "导数" @@ -300282,7 +300476,9 @@ "030354": { "id": "030354", "content": "求下列函数在给定区间上的最大值与最小值:\\\\\n(1) $f(x)=6x^2-x-2$, $x\\in [0,2]$;\\\\\n(2) $f(x)=x^3-27x$, $x\\in [-4,4]$;\\\\\n(3) $f(x)=6+12x-x^3$, $x\\in [-\\dfrac 13,3]$;\\\\\n(4) $f(x)=3x-x^3$, $x\\in [2,3]$.", - "objs": [], + "objs": [ + "K0234003X" + ], "tags": [ "第二单元", "导数" @@ -300304,7 +300500,9 @@ "030355": { "id": "030355", "content": "证明不等式: $x-1\\ge \\ln x$, $x\\in (0,+\\infty)$.", - "objs": [], + "objs": [ + "K0234005X" + ], "tags": [ "第二单元", "导数" @@ -300326,7 +300524,9 @@ "030356": { "id": "030356", "content": "给定函数$f(x)=(x+1)\\mathrm{e}^x$.\\\\\n(1) 判断函数$f(x)$的单调性, 并求出$f(x)$的极值;\\\\\n(2) 画出函数$f(x)$的大致图像;\\\\\n(3) 求出方程$f(x)=a$($a\\in \\mathbf{R}$)的解的个数.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300348,7 +300548,9 @@ "030357": { "id": "030357", "content": "某制造商制造并出售球形瓶装的某种饮料, 瓶子的制造成本是$0.8\\pi r^2$\n分, 其中$r$(单位: $\\text{cm}$)是瓶子的半径, 已知每出售$1\\text{mL}$的饮料, 制造商可获利$0.2$分, 且制造商能制作的瓶子的最大半径为$6\\text{cm}$.\\\\\n(1) 瓶子半径多大时, 能使每瓶饮料的利润最大?\\\\\n(2) 瓶子半径多大时, 每瓶饮料的利润最小?", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300370,7 +300572,9 @@ "030358": { "id": "030358", "content": "利用函数的单调性, 证明下列不等式, 并通过函数图像直观验证: $\\sin x=latex]\n\\draw (0,0) arc (0:180:1) --++ (0,-2) --++ (2,0) --++ (0,2);\n\\draw [dashed] (0,0) -- (-2,0);\n\\end{tikzpicture}\n\\end{center}", - "objs": [], + "content": "如图, 用铁丝围成一个上面是半圆, 下面是矩形的图形, 其面积为$a$, 为使所用材料最省, 圆的直径应为多少? \n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) arc (0:180:1) --++ (0,-2) --++ (2,0) --++ (0,2);\n\\draw [dashed] (0,0) -- (-2,0);\n\\end{tikzpicture}\n\\end{center}", + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300414,7 +300620,9 @@ "030360": { "id": "030360", "content": "判断下列函数的单调性, 并求出单调区间:\\\\\n(1) $f(x)=-2x+1$;\\\\\n(2) $f(x)=x+\\cos x$, $x\\in (0,\\dfrac\\pi 2)$;\\\\\n(3) $f(x)=2x-4$;\\\\\n(4) $f(x)=2x^3+4x$.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300436,7 +300644,9 @@ "030361": { "id": "030361", "content": "判断下列函数的单调性, 并求出单调区间:\\\\\n(1) $f(x)=x^2+2x-4$;\\\\\n(2) $f(x)=2x^2-3x+3$;\\\\\n(3) $f(x)=3x+x^3$;\\\\\n(4) $f(x)=x^3+x^2-x$.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300458,7 +300668,9 @@ "030362": { "id": "030362", "content": "求下列函数的极值:\\\\\n(1) $f(x)=6x^2+x+2$;\\\\\n(2) $f(x)=x^3-12x$;\\\\\n(3) $f(x)=6-12x+x^3$;\\\\\n(4) $f(x)=48x-x^3$.", - "objs": [], + "objs": [ + "K0233003X" + ], "tags": [ "第二单元", "导数" @@ -300480,7 +300692,9 @@ "030363": { "id": "030363", "content": "求下列函数在给定区间上的最大值与最小值:\\\\\n(1) $f(x)=6x^2+x+2$, $x\\in [-1,1]$;\\\\\n(2) $f(x)=x^3-12x$, $x\\in [-3,3]$;\\\\\n(3) $f(x)=6-12x+x^3$, $x\\in [-\\dfrac 13,1]$;\\\\\n(4) $f(x)=48x-x^3$, $x\\in [-3,5]$.", - "objs": [], + "objs": [ + "K0234003X" + ], "tags": [ "第二单元", "导数" @@ -300502,7 +300716,9 @@ "030364": { "id": "030364", "content": "将一条长为$l$的铁丝截成两段, 分别弯成两个正方形, 要使两个正方形的面积和最小, 两段铁丝的长度分别是多少?", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300524,7 +300740,9 @@ "030365": { "id": "030365", "content": "将一个边长为$a$的正方形铁片的四角截去四个边长均为$x$的小正方形, 做成一个无盖方盒.\\\\\n(1) 试把方盒的容积$V$表示为$x$的函数;\\\\ \n(2) $x$多大时, 方盒的容积$V$最大?", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300546,7 +300764,9 @@ "030366": { "id": "030366", "content": "用测量工具测量某物体的长度, 由于工具的精度以及测量技术的原因, 测得$n$个数据$a_1,a_2,a_3,\\cdots,a_n$.\n证明: 用$n$个数据的平均值$x=\\dfrac 1n\\displaystyle\\sum_{i=1}^na_i$表示这个物体的长度, 能使$f(x)=\\dfrac 1n\\displaystyle\\sum_{i=1}^n(x-a_i)^2$最小.", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300568,7 +300788,9 @@ "030367": { "id": "030367", "content": "已知某商品的生产成本$C$与产量$q$之间的关系为$C=100+4q$, 单价$p$与产量$q$之间的关系为$p=25-\\dfrac 18q$. 产量$q$为何值时, 利润最大?", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300590,7 +300812,9 @@ "030368": { "id": "030368", "content": "已知某商品进价为$a$元/件, 根据以往经验, 当售价是$b$($b\\ge \\dfrac 43 a$)元/件时, 可卖出$c$件. 市场调查表明, 当售价下降$10\\%$时, 销量可增加$40\\%$, 现决定一次性降价, 销售价为多少时, 可获得最大利润?", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300611,8 +300835,10 @@ }, "030369": { "id": "030369", - "content": "利用函数的单调性, 证明下列不等式, 并通过函数图象直观验证:\\\\\n(1) $\\mathrm{e}^x>1+x$, $x\\ne 0$;\\\\\n(2) $\\ln x0$.", - "objs": [], + "content": "利用函数的单调性, 证明下列不等式, 并通过函数图像直观验证:\\\\\n(1) $\\mathrm{e}^x>1+x$, $x\\ne 0$;\\\\\n(2) $\\ln x0$.", + "objs": [ + "K0234005X" + ], "tags": [ "第二单元", "导数" @@ -300634,7 +300860,10 @@ "030370": { "id": "030370", "content": "已知点$P$和点$Q$是曲线$y=x^2-2x-3$上的两点, 且点$P$的横坐标是$1$, 点$Q$的横坐标是$4$. 求:\\\\ \n(1) 割线$PQ$的斜率;\\\\ \n(2) 点$P$处的切线方程.", - "objs": [], + "objs": [ + "K0228003X", + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -300656,7 +300885,9 @@ "030371": { "id": "030371", "content": "求下列函数的导数:\\\\\n(1) $y=2x\\tan x$;\\\\\n(2) $y=2^x\\ln x$;\\\\\n(3) $y=(x-2)^3(3x+1)^2$;\\\\\n(4) $y=\\dfrac{x^2}{(2x+1)^3}$;\\\\\n(5) $y=\\mathrm{e}^{-2x+1}\\cos(-x^2+x)$;\\\\\n(6) $y=\\dfrac{\\sin 2x}{\\sqrt{x}}$.", - "objs": [], + "objs": [ + "K0231003X" + ], "tags": [ "第二单元", "导数" @@ -300677,8 +300908,10 @@ }, "030372": { "id": "030372", - "content": "已知函数$y=f(x)$的图像是下列四个图像之一, 且其导函数$y=f'(x)$的图像如图所示, 则该函数的图象是\\bracket{20}.\\\\\n\\begin{minipage}[t]{.25\\linewidth}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1] plot (\\x,{1-\\x*\\x});\n\\draw (-1,0) node [below] {$-1$} (1,0) node [below] {$1$};\n\\draw (0,1.5) node [right] {$y=f'(x)$};\n\\end{tikzpicture}\n\\end{minipage}\n\\begin{minipage}[t]{.75\\linewidth}\n\\fourch{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -1:1] plot (\\x,{\\x-pow(\\x,3)/3});\n\\end{tikzpicture}\n}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -1:1] plot ({(\\x-pow(\\x,3)/3)*3/2},{\\x*2/3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (-1,{-2/3}) .. controls (0.5,-0.4) .. (1,{2/3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (-1,{-2/3}) .. controls (-0.5,0.4) .. (1,{2/3});\n\\end{tikzpicture}}\n\\end{minipage}", - "objs": [], + "content": "已知函数$y=f(x)$的图像是下列四个图像之一, 且其导函数$y=f'(x)$的图像如图所示, 则该函数的图像是\\bracket{20}.\\\\\n\\begin{minipage}[t]{.25\\linewidth}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1] plot (\\x,{1-\\x*\\x});\n\\draw (-1,0) node [below] {$-1$} (1,0) node [below] {$1$};\n\\draw (0,1.5) node [right] {$y=f'(x)$};\n\\end{tikzpicture}\n\\end{minipage}\n\\begin{minipage}[t]{.75\\linewidth}\n\\fourch{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -1:1] plot (\\x,{\\x-pow(\\x,3)/3});\n\\end{tikzpicture}\n}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain = -1:1] plot ({(\\x-pow(\\x,3)/3)*3/2},{\\x*2/3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (-1,{-2/3}) .. controls (0.5,-0.4) .. (1,{2/3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (-1,{-2/3}) .. controls (-0.5,0.4) .. (1,{2/3});\n\\end{tikzpicture}}\n\\end{minipage}", + "objs": [ + "K0232004X" + ], "tags": [ "第二单元", "导数" @@ -300700,7 +300933,9 @@ "030373": { "id": "030373", "content": "一个距地心距离为$r$, 质量为$m$的人造卫星, 与地球之间的万有引力$F$由公式$F=\\dfrac{GMm}{r^2}$给出, 其中$M$为地球质量, $G$为引力常量, 求$F$对于$r$的瞬时变化率.", - "objs": [], + "objs": [ + "K0227004X" + ], "tags": [ "第二单元", "导数" @@ -300722,7 +300957,10 @@ "030374": { "id": "030374", "content": "一杯$80\\text{C}^\\circ$的热红茶置于$20\\text{C}^\\circ$的房间里, 它的温度会逐渐下降, 温度$T$(单位: $\\text{C}^\\circ$)与时间(单位: $\\text{min}$)之间的关系由函数$T=f(t)$给出.\\\\\n(1) 判断$f'(t)$的正负, 并说明理由;\\\\\n(2) $f'(3)=-4$的实际意义是什么? 如果$f(3)=65$, 你能画出函数$f(t)$在$t=3$时图像的大致形状吗?", - "objs": [], + "objs": [ + "K0227004X", + "K0232001X" + ], "tags": [ "第二单元", "导数" @@ -300744,7 +300982,9 @@ "030375": { "id": "030375", "content": "求函数$f(x)=\\sqrt[3]{x^2}$的单调区间.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300766,7 +301006,9 @@ "030376": { "id": "030376", "content": "已知函数$f(x)=x^2+px+q$, 试确定$p,q$的值, 使得当$x=1$时, $f(x)$有最小值$4$.", - "objs": [], + "objs": [ + "K0234004X" + ], "tags": [ "第二单元", "导数" @@ -300788,7 +301030,10 @@ "030377": { "id": "030377", "content": "已知函数$f(x)=x(x-c)^2$在$x=2$处有极大值, 求$c$的值.", - "objs": [], + "objs": [ + "K0233001X", + "K0233002X" + ], "tags": [ "第二单元", "导数" @@ -300810,7 +301055,9 @@ "030378": { "id": "030378", "content": "过点$P(1,1)$作直线$AB$, 分别与$x$轴的正半轴、$y$轴的正半轴交于点$A, B$. 当直线$AB$在什么位置时, $\\triangle AOB$的面积最小? 最小面积是多少?", - "objs": [], + "objs": [ + "K0234003X" + ], "tags": [ "第二单元", "导数" @@ -300832,7 +301079,9 @@ "030379": { "id": "030379", "content": "如图, 直线$l$和圆$P$, 当$l$从$l_0$开始在平面上按逆时针方向绕点$O$匀速转动(转动角度不超过$90^\\circ$时, 它扫过的圆内阴影部分的面积$S$是时间$t$的函数, 这个函数的图像大数是\\bracket{20}.\\\\\n\\begin{minipage}[t]{.25\\linewidth}\n\\begin{tikzpicture}[>=latex]\n\\begin{scope}\n\\draw [clip] (0,0) circle (1); \n\\draw (0.71,0.71) node [above right] {$P$};\n\\filldraw [pattern = north east lines] (1.2,0) -- (-1,-1) -- (1,-1);\n\\end{scope}\n\\draw (0,0) circle (1);\n\\draw (-1,-1) node [left] {$O$}-- (1,-1) node [right] {$l_0$};\n\\draw (-1,-1) -- (1.2,0) node [right] {$l$};\n\\end{tikzpicture}\n\\end{minipage}\n\\begin{minipage}[t]{.75\\linewidth}\n\\fourch{\\begin{tikzpicture}[>=latex, scale = {2/pi}]\n\\draw [->] (0,0) -- ({2*pi/3},0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,pi) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) -- (pi/2,pi);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = {2/pi}]\n\\draw [->] (0,0) -- ({2*pi/3},0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,pi) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) ..controls (pi/4,0.2) .. (pi/2,pi);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = {2/pi}]\n\\draw [->] (0,0) -- ({2*pi/3},0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,pi) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) ..controls (0.2,0.8) .. (pi/4,pi/2) ..controls ({pi/2-0.2},{pi-0.8}) .. (pi/2,pi);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = {2/pi}]\n\\draw [->] (0,0) -- ({2*pi/3},0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,pi) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:pi/2,samples = 100] plot (\\x,{acos(cos(\\x/pi*180)-sin(\\x/pi*180))/180*pi-0.5*sin(2*acos(cos(\\x/pi*180)-sin(\\x/pi*180))});\n\\end{tikzpicture}}\n\\end{minipage}", - "objs": [], + "objs": [ + "K0232004X" + ], "tags": [ "第二单元", "导数" @@ -300854,7 +301103,11 @@ "030380": { "id": "030380", "content": "当室内的有毒细菌开始增加时, 就要使用杀菌剂, 刚开始使用的时候, 细菌数量还会继续增加, 随着时间的增加, 它增加的幅度逐渐变小, 到一定时间, 细菌数量开始减少, 已知使用杀菌剂$t\\text{h}$后的细菌数量为$b(t)=10^5+10^4t-10^3t^2$.\\\\\n(1) 求细菌数量在$t=5$与$t=10$时的瞬时变化率;\\\\\n(2) 细菌数量在哪段时间增加, 在哪段时间减少? 为什么?", - "objs": [], + "objs": [ + "K0227004X", + "K0232002X", + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300876,7 +301129,11 @@ "030381": { "id": "030381", "content": "已知曲线$y=x+\\ln x$在点$(1,1)$处的切线与曲线$y=ax^2+(2a+3)x+1$只有一个公共点, 求$a$的值.", - "objs": [], + "objs": [ + "K0228003X", + "K0229004X", + "K0230001X" + ], "tags": [ "第二单元", "导数" @@ -300898,7 +301155,9 @@ "030382": { "id": "030382", "content": "用总长$14.8\\text{m}$的钢条制作一个长方体容器的框架, 如果所制容器底面一边的长比另一边的长多$0.5\\text{m}$, 那么高为多少时容器的容积最大? 最大容积是多少?", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300920,7 +301179,9 @@ "030383": { "id": "030383", "content": "用半径为$R$的圆形铁皮剪出一个圆心角为$\\alpha$的扇形, 制成一个圆锥形容器, 扇形的圆心角$\\alpha$为多大时, 容器的容积最大?", - "objs": [], + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300941,8 +301202,10 @@ }, "030384": { "id": "030384", - "content": "已知$A$, $B$两地的距离是$130\\text{km}$, 根据交通法规, 两地之间的公路车速应限制在$50$至$100\\text{km}$, 假设油价是$7元$/$\\text{L}$, 以$x\\text{km}/\\text{h}$的速度行驶时, 汽车的耗油率为$(3+\\dfrac{x^2}{360})\\text{L}/\\text{h}$, 司机每小时的工资是$35$元, 那么最经济的车速是多少? 如果不考虑其他费用, 这次行车的总费用是多少?", - "objs": [], + "content": "已知$A$, $B$两地的距离是$130\\text{km}$, 根据交通法规, 两地之间的公路车速应限制在$50$至$100\\text{km}$, 假设油价是$7$元/$\\text{L}$, 以$x\\text{km}/\\text{h}$的速度行驶时, 汽车的耗油率为$(3+\\dfrac{x^2}{360})\\text{L}/\\text{h}$, 司机每小时的工资是$35$元, 那么最经济的车速是多少? 如果不考虑其他费用, 这次行车的总费用是多少?", + "objs": [ + "K0235001X" + ], "tags": [ "第二单元", "导数" @@ -300964,7 +301227,9 @@ "030385": { "id": "030385", "content": "作函数$y=\\dfrac{\\mathrm{e}^x(2x-1)}{x-1}$的大致图像.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -300986,7 +301251,9 @@ "030386": { "id": "030386", "content": "已知函数$f(x)=\\mathrm{e}^x-\\ln (x+m)$. 当$x\\le 2$时, 求证$f(x)>0$.", - "objs": [], + "objs": [ + "K0234005X" + ], "tags": [ "第二单元", "导数" @@ -301008,7 +301275,9 @@ "030387": { "id": "030387", "content": "已知函数$f(x)=a\\cdot \\mathrm{e}^{2x}+(a-2)\\mathrm{e}^x-x$.\\\\\n(1) 讨论$f(x)$的单调性;\\\\\n(2) 若$f(x)$有两个零点, 求$a$的取值范围.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -301030,7 +301299,10 @@ "030388": { "id": "030388", "content": "(1) 已知$f'(x_0)=2$, 则$\\displaystyle \\lim_{h\\to 0}\\dfrac{f(x_0-4h)-f(x_0)}{h}=$\\blank{50}.\\\\\n(2) 已知某物体的运动方程为$s=24t-3t^2$($s$的单位: $\\text{m}$, $t$的单位: $\\text{s}$), 则物体在$t=$\\blank{50}$\\text{s}$时的瞬时速度为$12\\text{m}/\\text{s}$.", - "objs": [], + "objs": [ + "K0227001X", + "K0227003X" + ], "tags": [ "第二单元", "导数" @@ -301052,7 +301324,9 @@ "030389": { "id": "030389", "content": "已知曲线$y=2x^2-7$在点$P$处的切线方程为$8x-y-15=0$, 则切点$P$的坐标为\\blank{50}.", - "objs": [], + "objs": [ + "K0228004X" + ], "tags": [ "第二单元", "导数" @@ -301074,7 +301348,10 @@ "030390": { "id": "030390", "content": "已知二次函数$f(x)=ax^2+bx+c$, 求:\\\\\n(1) 函数从$x_1=1$到$x_2=3$的平均变化率;\\\\\n(2) 函数在$x=2$处的瞬时变化率;\\\\ \n(3) 当$x$为何值时, 函数在$x$处的瞬时变化率等于从$x_1=1$到$x_2=3$的平均变化率?", - "objs": [], + "objs": [ + "K0227001X", + "K0227004X" + ], "tags": [ "第二单元", "导数" @@ -301096,7 +301373,9 @@ "030391": { "id": "030391", "content": "已知函数$f(x)=x^6-x$, 直线$l$是曲线$y=f(x)$的一条切线.\\\\\n(1) 若$l$与直线$16x-13y=0$垂直, 求$l$与曲线$y=f(x)$的切点坐标;\\\\\n(2) 若$l$经过点$(0,-5)$, 求$l$的方程.", - "objs": [], + "objs": [ + "K0228003X" + ], "tags": [ "第二单元", "导数" @@ -301118,7 +301397,9 @@ "030392": { "id": "030392", "content": "已知函数$f(x)=\\dfrac 13x^3-\\dfrac 12 ax^2+(a-1)x+2$($a\\in \\mathbf{R}$), $y=f(x)$满足$f(x)+f(-x)=4$, 已知点$M$是曲线$y=f(x)$上任意一点, 曲线在$M$处的切线为$l$.\\\\\n(1) 求切线$l$的倾斜角$\\alpha$的取值范围;\\\\ \n(2) 若过点$P(1,m)$($m\\ne \\dfrac 43$)可作曲线$y=f(x)$的三条切线, 求实数$m$的取值范围.", - "objs": [], + "objs": [ + "K0228003X" + ], "tags": [ "第二单元", "导数" @@ -301140,7 +301421,9 @@ "030393": { "id": "030393", "content": "等比数列$\\{a_n\\}$中, $a_2a_7=8$, 函数$f(x)=x(x+a_1)(x+a_2)\\cdots (x+a_8)$, 则$f'(0)=$\\bracket{20}.\n\\fourch{$2^6$}{$2^9$}{$2^{12}$}{$2^{15}$}", - "objs": [], + "objs": [ + "K0230002X" + ], "tags": [ "第二单元", "导数" @@ -301162,7 +301445,10 @@ "030394": { "id": "030394", "content": "已知函数$y=f(x)$的导数为$y=f'(x)$, 而且$f(x)=x^2+3xf'(2)+\\ln x$, 求$f'(2)$.", - "objs": [], + "objs": [ + "K0229002X", + "K0230001X" + ], "tags": [ "第二单元", "导数" @@ -301184,7 +301470,9 @@ "030395": { "id": "030395", "content": "求下列函数的导数:\\\\\n(1) $f(x)=\\dfrac{(x-2)^2}{x+1}$;\\\\\n(2) $f(x)=(x^2+9)(x-\\dfrac 3x)$;\\\\\n(3) $f(x)=\\dfrac{\\ln x}{x}$;\\\\\n(4) $f(x)=x^2\\cos x$;\\\\\n(5) $f(x)=\\ln (2x+1)$;\\\\\n(6) $f(x)=\\cos(\\dfrac \\pi 3-2x)$.", - "objs": [], + "objs": [ + "K0231003X" + ], "tags": [ "第二单元", "导数" @@ -301206,7 +301494,10 @@ "030396": { "id": "030396", "content": "设函数$f(x)=\\sin x-\\cos x$, $x\\in \\mathbf{R}$.\\\\\n(1) 求$y=f^2(x)$的最大值和图像的对称中心;\\\\\n(2) $y=f'(x)$为$y=f(x)$的导数, 若$f'(x_0)=2f(x_0)$, 求$\\sin 2x_0+\\cos^2 x_0+\\tan(\\dfrac\\pi 4+x_0)$的值.", - "objs": [], + "objs": [ + "K0229004X", + "K0230001X" + ], "tags": [ "第二单元", "导数" @@ -301250,7 +301541,10 @@ "030398": { "id": "030398", "content": "已知函数$f_0(x)=\\sin x+\\cos x$, $f_1(x)=f_0'(x)$, $f_2(x)=f_1'(x)$, $\\cdots$, $f_{n+1}(x)=f_n'(x)$, $n$为正整数, 则$f_{2022}(x)=$\\blank{50}.", - "objs": [], + "objs": [ + "K0229004X", + "K0230001X" + ], "tags": [ "第二单元", "导数" @@ -301271,8 +301565,11 @@ }, "030399": { "id": "030399", - "content": "拉格朗日中值定理是微分学中的基本定理之一, 定理内容: 如果函数$y=f(x)$\n在闭区间$[a,b]$上的图像连续不间断, 在开区间$(a,b)$内的导数为$y=f'(x)$, 那么在区间$(a,b)$内至少存在一点$c$, 使得$f(b)-f(a)=f'(c)(b-a)$成立, 其中$c$称为$y=f(x)$在$[[a, b]$的``拉格朗日中值点''. 根据这个定理, 可得函数$f(x)=x^3-3x$在$[-2,2]$上的``拉格朗日中值点''的个数为\\blank{50}.", - "objs": [], + "content": "拉格朗日中值定理是微分学中的基本定理之一, 定理内容: 如果函数$y=f(x)$\n在闭区间$[a,b]$上的图像连续不间断, 在开区间$(a,b)$内的导数为$y=f'(x)$, 那么在区间$(a,b)$内至少存在一点$c$, 使得$f(b)-f(a)=f'(c)(b-a)$成立, 其中$c$称为$y=f(x)$在$[a, b]$的``拉格朗日中值点''. 根据这个定理, 可得函数$f(x)=x^3-3x$在$[-2,2]$上的``拉格朗日中值点''的个数为\\blank{50}.", + "objs": [ + "K0229004X", + "K0230001X" + ], "tags": [ "第二单元", "导数" @@ -301294,7 +301591,9 @@ "030400": { "id": "030400", "content": "给出定义: 若函数$y=f(x)$在$D$上可导, 即$y=f'(x)$存在, 且导数$y=f'(x)$在$D$上也可导, 则称$y=f(x)$在$D$上存在二阶导数, 记$f''(x)=(f'(x))'$, 若$f''(x)<0$在$D$上恒成立, 则称$y=f(x)$在$D$上为严格凸函数, 以下四个函数在$(0,\\dfrac \\pi 2)$上是严格凸函数的是\\bracket{20}.\n\\fourch{$f(x)=\\sin x+\\cos x$}{$f(x)=-\\ln x-2x$}{$f(x)=x^3+2x-1$}{$f(x)=x\\mathrm{e}^x$}", - "objs": [], + "objs": [ + "K0231003X" + ], "tags": [ "第二单元", "导数" @@ -301316,7 +301615,9 @@ "030401": { "id": "030401", "content": "已知曲线$f(x)=(ax+b)\\mathrm{e}^x$在点$(0,2)$处的切线方程为$x+y-2=0$, 则$a=$\\blank{50}.", - "objs": [], + "objs": [ + "K0228003X" + ], "tags": [ "第二单元", "导数" @@ -301338,7 +301639,9 @@ "030402": { "id": "030402", "content": "写出一个同时满足性质\\textcircled{1}, \\textcircled{2}的函数$f(x)=$\\blank{50}. ($y=f(x)$不是常值函数)\\\\\n\\textcircled{1} $y=f'(x)$为偶函数; \\textcircled{2} $f(x+\\pi)=f'(x)$.", - "objs": [], + "objs": [ + "K0231002X" + ], "tags": [ "第二单元", "导数" @@ -301360,7 +301663,9 @@ "030403": { "id": "030403", "content": "求下列函数的导数.\\\\\n(1) $f(x)=x^2\\sin x+2\\cos x$;\\\\\n(2) $f(x)=\\dfrac{\\mathrm{e}^x+1}{\\mathrm{e}^x-1}$;\\\\\n(3) $f(x)=\\cos(3x+4)$;\\\\\n(4) $f(x)=(2x-1)^5$.", - "objs": [], + "objs": [ + "K0231002X" + ], "tags": [ "第二单元", "导数" @@ -301382,7 +301687,9 @@ "030404": { "id": "030404", "content": "已知曲线$y=x^3+x-2$在点$P_0$处的切线$l_1$平行于直线$4x-y-1=0$, \n且点$P_0$在第三象限.\\\\\n(1) 求$P_0$的坐标;\\\\ \n(2) 若直线$l\\perp l_1$, 且$l$也过切点$P_0$, 求直线$l$的方程.", - "objs": [], + "objs": [ + "K0228003X" + ], "tags": [ "第二单元", "导数" @@ -301404,7 +301711,9 @@ "030405": { "id": "030405", "content": "直线$y=kx+2$交抛物线$C:x^2=4y$于$A,B$两点, 分别过点$A,B$作抛物线$C$的切线$l_1,l_2$, 若$l_1,l_2$分别交$x$轴于点$M,N$, 求四边形$ABNM$面积的最小值.", - "objs": [], + "objs": [ + "K0228003X" + ], "tags": [ "第二单元", "导数" @@ -301426,7 +301735,9 @@ "030406": { "id": "030406", "content": "当$x\\ne 1$时, 在恒等式$1+x+x^2+\\cdots+x^n=\\dfrac{1-x^{n+1}}{1-x}$的两边对$x$求导, 得$1+2x+3x^2+\\cdots+nx^{n-1}=\\dfrac{1+(nx-n-1)x^n}{(1-x)^2}$. 利用上述方法, 试由等式$(1+x)^n=\\mathrm{C}_n^0+\\mathrm{C}_n^1x+\\cdots+\\mathrm{C}_n^nx^n$($x\\in \\mathbf{R}$, 正整数$n\\ge 2$),\\\\\n(1) 证明: $n((1+x)^{n-1}-1)=\\sum_{k=2}^{n}k\\mathrm{C}_n^kx^{k-1}$;(提示: $\\sum_{i=1}^n a_i=a_1+a_2+\\cdots+a_n$)\\\\\n(2) 求$\\mathrm{C}_{10}^1+2\\mathrm{C}_{10}^2+3\\mathrm{C}_{10}^3+\\cdots+10\\mathrm{C}_{10}^{10}$;\\\\\n(3) 求$1^2\\mathrm{C}_{100}^1+3^2\\mathrm{C}_{100}^3+5^2\\mathrm{C}_{100}^5+\\cdots+99^2\\mathrm{C}_{100}^{99}$.", - "objs": [], + "objs": [ + "K0231003X" + ], "tags": [ "第二单元", "导数" @@ -301447,8 +301758,10 @@ }, "030407": { "id": "030407", - "content": "设$a$为实数, 函数$f(x)=x^3+ax^2+(a-3)x$, 且$y=f'(x)$是偶函数, 则$y=f(x)$得单调递增区间为\\blank{50}.", - "objs": [], + "content": "设$a$为实数, 函数$f(x)=x^3+ax^2+(a-3)x$, 且$y=f'(x)$是偶函数, 则$y=f(x)$的单调递增区间为\\blank{50}.", + "objs": [ + "K0232001X" + ], "tags": [ "第二单元", "导数" @@ -301470,7 +301783,9 @@ "030408": { "id": "030408", "content": "若函数$f(x)=2x^2-\\ln x$在定义域内的一个子区间$(k-1,k+1)$上不是单调函数, 则实数$k$的取值范围是\\blank{50}.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -301492,7 +301807,9 @@ "030409": { "id": "030409", "content": "已知函数$f(x)=x^3-3ax^2+9x+5$($a<0$), 若曲线$y=f(x)$的的切线斜率最小时与直线$3x+y-2=0$平行.\\\\\n(1) 求$a$的值;\\\\\n(2) 求函数$y=f(x)$的单调区间.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -301514,7 +301831,9 @@ "030410": { "id": "030410", "content": "已知函数$f(x)=ax^3+bx^2+cx+d$($a+b<0$)在$\\mathbf{R}$上是增函数, 求\n$\\dfrac c{a+b}$的最大值.", - "objs": [], + "objs": [ + "K0232002X" + ], "tags": [ "第二单元", "导数" @@ -301536,7 +301855,10 @@ "030411": { "id": "030411", "content": "已知函数$f(x)=ax^3-9x+1$, $a>0$.\\\\\n(1) 若$a=3$, 求函数$y=f(x)$的极值;\\\\\n(2) 若函数$y=f(x)$恰有三个零点, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0232002X", + "K0233003X" + ], "tags": [ "第二单元", "导数" @@ -301558,7 +301880,10 @@ "030412": { "id": "030412", "content": "已知函数$f(x)=x^3+ax^2-2$在$x=2$时取得极值.\\\\\n(1) 求$y=f(x)$在$(-1,f(-1))$处的切线方程;\\\\\n(2) 求$y=f(x)$在区间$[-1,2]$上的最大值与最小值.", - "objs": [], + "objs": [ + "K0228003X", + "K0233003X" + ], "tags": [ "第二单元", "导数" @@ -301580,7 +301905,9 @@ "030413": { "id": "030413", "content": "已知函数$f(x)=ax-\\ln x$($a$为常数).\\\\\n(1) 当$a=1$时, 求函数$y=f(x)$的最值;\\\\\n(2) 求函数$y=f(x)$在$[1,+\\infty)$上的最值.", - "objs": [], + "objs": [ + "K0234003X" + ], "tags": [ "第二单元", "导数" @@ -301602,7 +301929,10 @@ "030414": { "id": "030414", "content": "(1) 设函数$f(x)=\\ln x-x+1$, 求$y=f(x)$的极大值;\\\\\n(2) 求证: 当$x>1$时, $x-10$且$a\\ne 1$时, $y=f(x)$存在一个极小值点$x_0$, 若$x_0>3$, 求实数$a$的取值范围.", - "objs": [], + "objs": [ + "K0232002X", + "K0233003X" + ], "tags": [ "第二单元", "导数" @@ -301866,7 +302221,9 @@ "030426": { "id": "030426", "content": "已知函数$f(x)=\\ln x-kx+1$.\n(1) 若$f(x)\\le 0$恒成立, 求实数$k$的取值范围;\\\\\n(2) 证明: $(1+\\dfrac 13)(1+\\dfrac 1{3^2})(1+\\dfrac 1{3^3})\\cdots(1+\\dfrac 1{3^n})<\\sqrt{\\mathrm{e}}$($n\\in \\mathbf{N}$, $n>0$).", - "objs": [], + "objs": [ + "K0234003X" + ], "tags": [ "第二单元", "第四单元",