diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb index 4575f53d..2cb4e484 100644 --- a/工具/寻找tex文件中未赋答案的题目.ipynb +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -2,72 +2,90 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "周末卷02.tex\n", - "010944\n", + "14_正弦函数及正弦型函数.tex\n", + "003148\n", "\n", "\n", - "030017\n", + "003155\n", "\n", "\n", - "010946\n", + "003158\n", "\n", "\n", - "010947\n", + "003149\n", "\n", "\n", - "010948\n", + "003156\n", "\n", "\n", - "010949\n", + "003163\n", "\n", "\n", - "010950\n", + "003162\n", "\n", "\n", - "010951\n", + "000119\n", "\n", "\n", - "010952\n", + "003175\n", "\n", "\n", - "010953\n", + "008287\n", "\n", "\n", - "010954\n", + "003169\n", "\n", "\n", - "010955\n", + "001554\n", "\n", "\n", - "010956\n", + "003176\n", "\n", "\n", - "010958\n", + "003178\n", "\n", "\n", - "010959\n", + "003181\n", "\n", "\n", - "010960\n", + "003167\n", "\n", "\n", - "010961\n", + "003171\n", "\n", "\n", - "010962\n", + "003166\n", "\n", "\n", - "010963\n", + "003168\n", "\n", "\n", - "010964\n", + "008337\n", + "\n", + "\n", + "003153\n", + "\n", + "\n", + "003160\n", + "\n", + "\n", + "003183\n", + "\n", + "\n", + "003164\n", + "\n", + "\n", + "003182\n", + "\n", + "\n", + "000131\n", "\n", "\n" ] @@ -77,9 +95,9 @@ "import os,json,re\n", "\n", "#这里需要修改, 设定路径与选择文件\n", - "fileind = 1\n", + "fileind = 13\n", "# path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", - "path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\上学期周末卷\"\n", + "path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", "\n", "with open(\"../题库0.3/Problems.json\",\"r\",encoding = \"utf8\") as f:\n", " jsondata = f.read()\n", @@ -106,7 +124,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -120,12 +138,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, 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 451c75f4..62e71ab7 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 @@ -2,274 +2,47 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 001992 , 字段: objs 中已添加数据: K0511003B\n", - "题号: 002025 , 字段: objs 中已添加数据: K0511004B\n", - "题号: 002025 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 002025 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000387 , 字段: objs 中已添加数据: K0511004B\n", - "题号: 000387 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003514 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003514 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 003514 , 字段: objs 中已添加数据: K0512002B\n", - "题号: 003516 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003516 , 字段: objs 中已添加数据: K0511008B\n", - "题号: 003516 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 003516 , 字段: objs 中已添加数据: K0514003B\n", - "题号: 003517 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003517 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 003517 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 003517 , 字段: objs 中已添加数据: K0513002B\n", - "题号: 003523 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003523 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 003523 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 003553 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003504 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003504 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 003504 , 字段: objs 中已添加数据: K0511007B\n", - "题号: 003505 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003505 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 003510 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003510 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 003510 , 字段: objs 中已添加数据: K0511007B\n", - "题号: 003510 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 003511 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003511 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 003511 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 003511 , 字段: objs 中已添加数据: K0513002B\n", - "题号: 003511 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 003513 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003513 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 002022 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 002022 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 002022 , 字段: objs 中已添加数据: K0513002B\n", - "题号: 002022 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 002024 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 002024 , 字段: objs 中已添加数据: K0514003B\n", - "题号: 002024 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 002029 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 002032 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 002032 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 002032 , 字段: objs 中已添加数据: K0513002B\n", - "题号: 003502 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 003502 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 001999 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 001999 , 字段: objs 中已添加数据: K0511008B\n", - "题号: 002001 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 002001 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 002004 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 002004 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 002008 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 002008 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 002008 , 字段: objs 中已添加数据: K0512002B\n", - "题号: 002008 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 002008 , 字段: objs 中已添加数据: K0513002B\n", - "题号: 000788 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000788 , 字段: objs 中已添加数据: K0513001B\n", - "题号: 000788 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 000817 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000872 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000872 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000872 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 000872 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000933 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000933 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000933 , 字段: objs 中已添加数据: K0512002B\n", - "题号: 000953 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000953 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000509 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000509 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 000618 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000618 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000649 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000649 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000649 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 000718 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000718 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000328 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000328 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000366 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000366 , 字段: objs 中已添加数据: K0512002B\n", - "题号: 000427 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000427 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 000447 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000447 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 000169 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000169 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000169 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000170 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000170 , 字段: objs 中已有该数据: K0512005B\n", - "题号: 000170 , 字段: objs 中已有该数据: K0514001B\n", - "题号: 000174 , 字段: objs 中已有该数据: K0511005B\n", - "题号: 000174 , 字段: objs 中已有该数据: K0512005B\n", - "题号: 000174 , 字段: objs 中已添加数据: K0512006B\n", - "题号: 000162 , 字段: objs 中已添加数据: K0511005B\n", - "题号: 000162 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000162 , 字段: objs 中已有该数据: K0513004B\n", - "题号: 000166 , 字段: objs 中已有该数据: K0511005B\n", - "题号: 000166 , 字段: objs 中已有该数据: K0511006B\n", - "题号: 003503 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 003503 , 字段: objs 中已添加数据: K0512002B\n", - "题号: 002003 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 002003 , 字段: objs 中已添加数据: K0511008B\n", - "题号: 002005 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 002007 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 002007 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000881 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000881 , 字段: objs 中已添加数据: K0511007B\n", - "题号: 000460 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000460 , 字段: objs 中已添加数据: K0512002B\n", - "题号: 000469 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000477 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000477 , 字段: objs 中已添加数据: K0512002B\n", - "题号: 000566 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000566 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 000609 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000609 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 000628 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000628 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000637 , 字段: objs 中已添加数据: K0511006B\n", - "题号: 000637 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 003550 , 字段: objs 中已添加数据: K0511007B\n", - "题号: 003550 , 字段: objs 中已添加数据: K0511009B\n", - "题号: 000858 , 字段: objs 中已添加数据: K0511007B\n", - "题号: 000858 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 003539 , 字段: objs 中已添加数据: K0511008B\n", - "题号: 003540 , 字段: objs 中已添加数据: K0511008B\n", - "题号: 002026 , 字段: objs 中已添加数据: K0511008B\n", - "题号: 002026 , 字段: objs 中已添加数据: 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- "题号: 000163 , 字段: objs 中已有该数据: K0513003B\n", - "题号: 003506 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 003506 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 003508 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 003508 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 003508 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 003509 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 002023 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 002023 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 002000 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 001993 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 001994 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000164 , 字段: objs 中已添加数据: K0512003B\n", - "题号: 000164 , 字段: objs 中已有该数据: K0513003B\n", - "题号: 003519 , 字段: objs 中已添加数据: K0512005B\n", - "题号: 003519 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 000165 , 字段: objs 中已有该数据: K0512005B\n", - "题号: 002010 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 002010 , 字段: objs 中已添加数据: K0513004B\n", - "题号: 002013 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000892 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000892 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000490 , 字段: objs 中已有该数据: K0514001B\n", - "题号: 000167 , 字段: objs 中已添加数据: K0514001B\n", - "题号: 000167 , 字段: objs 中已有该数据: K0514004B\n", - "题号: 000557 , 字段: objs 中已添加数据: K0514003B\n", - "题号: 000557 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 003515 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 003507 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 002027 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000777 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000838 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000847 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000677 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000687 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000339 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000348 , 字段: objs 中已添加数据: K0514004B\n", - "题号: 000348 , 字段: objs 中已添加数据: K0514002B\n", - "题号: 000171 , 字段: objs 中已有该数据: K0514004B\n", - "题号: 000173 , 字段: objs 中已有该数据: K0514004B\n", - "题号: 003535 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 003535 , 字段: objs 中已添加数据: K0513005B\n", - "题号: 003531 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 003520 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 003528 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 003528 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 002012 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 002014 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 002014 , 字段: objs 中已添加数据: K0513005B\n", - "题号: 000902 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 000902 , 字段: objs 中已添加数据: K0514002B\n", - "题号: 000422 , 字段: objs 中已添加数据: K0513003B\n", - "题号: 003522 , 字段: objs 中已添加数据: K0513004B\n", - "题号: 002020 , 字段: objs 中已添加数据: K0513005B\n", - "题号: 002018 , 字段: objs 中已添加数据: K0514006B\n", - "题号: 002018 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 003532 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 003533 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 003534 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 003524 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 003527 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 003530 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 002015 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 002016 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 002017 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 002021 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 000831 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 000598 , 字段: objs 中已添加数据: K0514007B\n", - "题号: 003542 , 字段: objs 中已添加数据: K0515002B\n", - "题号: 003542 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 003542 , 字段: objs 中已添加数据: K0515004B\n", - "题号: 003542 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 003542 , 字段: objs 中已添加数据: K0515006B\n", - "题号: 002055 , 字段: objs 中已添加数据: K0515002B\n", - "题号: 002057 , 字段: objs 中已添加数据: K0515002B\n", - "题号: 003541 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 003541 , 字段: objs 中已添加数据: K0515004B\n", - "题号: 003544 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 003544 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 003544 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 003544 , 字段: objs 中已有该数据: K0515007B\n", - "题号: 003551 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 003551 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 003551 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 003545 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 003545 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 003545 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 002076 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 002076 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 002078 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 002085 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 002086 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 002086 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 000763 , 字段: objs 中已添加数据: K0515003B\n", - "题号: 000763 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 000168 , 字段: objs 中已有该数据: K0515003B\n", - "题号: 002079 , 字段: objs 中已添加数据: K0515004B\n", - "题号: 003549 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 003549 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 000900 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 000900 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 001998 , 字段: objs 中已添加数据: K0515005B\n", - "题号: 001998 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 002080 , 字段: objs 中已添加数据: K0515007B\n", - "题号: 002081 , 字段: objs 中已添加数据: K0515007B\n" + "题号: 003148 , 字段: ans 中已修改数据: $\\{x|\\dfrac\\pi 2+2k\\pi\\le x\\le \\dfrac{3\\pi}2+2k\\pi, \\ k\\in \\mathbf{Z}\\}$\n", + "题号: 003155 , 字段: ans 中已修改数据: (1) $\\{x|2k\\pi=latex,scale = 0.5]\n", + "\\draw [->] (-1,0) -- (15,0) node [below] {$x$};\n", + "\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n", + "\\draw (0,0) node [below left] {$O$};\n", + "\\draw [domain = 0:720] plot ({\\x/180*pi},{2*sin(\\x/2)});\n", + "\\draw [dashed] (pi,0) node [below] {$\\pi$} -- (pi,2) -- (0,2) node [left] {$2$};\n", + "\\draw [dashed] ({3*pi},0) node [above] {$3\\pi$} -- ({3*pi},-2) -- (0,-2) node [left] {$-2$};\n", + "\\draw ({4*pi},0) node [above] {$4\\pi$} ({2*pi},0) node [below left] {$2\\pi$};\n", + "\\end{tikzpicture}\n", + "题号: 003169 , 字段: ans 中已修改数据: $y=\\sin(2x+\\dfrac\\pi 3)$\n", + "题号: 001554 , 字段: ans 中已修改数据: \\textcircled{1} 横坐标不变, 纵坐标变为原来的$\\dfrac 12$倍, \\textcircled{2} 向上平移$\\dfrac 54$个单位, \\textcircled{3} 向左平移$\\dfrac \\pi 6$个单位, \\textcircled{4} 纵坐标不变, 横坐标变为原来的$\\dfrac 12$倍.\n", + "题号: 003176 , 字段: ans 中已修改数据: $f(x)=-4\\sin(\\dfrac \\pi 8 x+\\dfrac \\pi 4)$\n", + "题号: 003178 , 字段: ans 中已修改数据: B\n", + "题号: 003181 , 字段: ans 中已修改数据: $-\\dfrac{\\sqrt{3}}3$\n", + "题号: 003167 , 字段: ans 中已有该数据: \n", + "题号: 003171 , 字段: ans 中已有该数据: \n", + "题号: 003166 , 字段: ans 中已有该数据: \n", + "题号: 003168 , 字段: ans 中已有该数据: \n", + "题号: 008337 , 字段: ans 中已有该数据: \n", + "题号: 003153 , 字段: ans 中已有该数据: \n", + "题号: 003160 , 字段: ans 中已有该数据: \n", + "题号: 003183 , 字段: ans 中已有该数据: \n", + "题号: 003164 , 字段: ans 中已有该数据: \n", + "题号: 003182 , 字段: ans 中已有该数据: \n", + "题号: 000131 , 字段: ans 中已有该数据: \n" ] } ], 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 72432260..22fa49b4 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": 2, + "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/赋能01_教师用_20220923.tex\n", + "开始编译教师版本pdf文件: 临时文件/题库_教师用_20220923.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/赋能01_学生用_20220923.tex\n", + "开始编译学生版本pdf文件: 临时文件/题库_学生用_20220923.tex\n", "0\n" ] } @@ -26,14 +26,13 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库\n", "problems = r\"\"\"\n", - "326,327,328,329,30021,331,332,30022,30026,335\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/赋能01\"\n", + "filename = \"临时文件/题库\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", @@ -158,12 +157,14 @@ "execution_count": null, "metadata": {}, "outputs": [], - "source": [] + "source": [ + "\n" + ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -177,12 +178,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index a592098e..cf0ba549 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -2773,7 +2773,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 等腰三角形($a=b$)或直角三角形($C=90^\\circ$); (2) 等腰三角形($a=b$)或直角三角形($C=90^\\circ$).", "solution": "", "duration": -1, "usages": [], @@ -2843,7 +2843,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) \\textcircled{1} $B$不存在, \\textcircled{2} $B=90^\\circ$, \\textcircled{3} $B=\\arcsin\\dfrac 9{13}$或$\\pi-\\arcsin \\dfrac 9{13}$, \\textcircled{4} $B=30^\\circ$, \\textcircled{5} $B=\\arcsin\\dfrac 9{44}$; (2) 当$0\\arctan 1$}{$\\tan 1<\\arctan 1$}{不能确定}", + "content": "$\\tan 1$与$\\arctan 1$之间的大小关系是\\bracket{20}\n\\fourch{$\\tan 1=\\arctan 1$}{$\\tan 1>\\arctan 1$}{$\\tan 1<\\arctan 1$}{不能确定}", "objs": [], "tags": [ "第三单元" @@ -40072,7 +40072,7 @@ }, "001576": { "id": "001576", - "content": "$\\arccos x$大于$\\arccos (-x)$的充分必要条件是\\blank{50}.\n\\fourch{$x \\in [0,1]$}{$x\\in [-1,0)$}{$x=0$}{$x\\in [-1,1]$}", + "content": "$\\arccos x$大于$\\arccos (-x)$的充分必要条件是\\bracket{20}.\n\\fourch{$x \\in [0,1]$}{$x\\in [-1,0)$}{$x=0$}{$x\\in [-1,1]$}", "objs": [], "tags": [ "第三单元" @@ -40339,7 +40339,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{x|x=\\arctan\\dfrac 43+k\\pi, \\ k\\in \\mathbf{Z}\\}$", "solution": "", "duration": -1, "usages": [ @@ -41755,7 +41755,7 @@ }, "001643": { "id": "001643", - "content": "在正方体$ABCD-A'B'C'D'$中, 已知$P,Q$分别是棱$AA'$, $CC'$的中点, 则过点$B,P,Q$的截面是\\blank{30}.\\\\ \n\\twoch{邻边不等的平行四边形}{菱形但不是正方形}{邻边不等的矩形}{正方形}", + "content": "在正方体$ABCD-A'B'C'D'$中, 已知$P,Q$分别是棱$AA'$, $CC'$的中点, 则过点$B,P,Q$的截面是\\bracket{20}.\\\\ \n\\twoch{邻边不等的平行四边形}{菱形但不是正方形}{邻边不等的矩形}{正方形}", "objs": [], "tags": [ "第六单元" @@ -41779,7 +41779,7 @@ }, "001644": { "id": "001644", - "content": "在正方体$ABCD-A'B'C'D'$中, 已知$E,F$分别是棱$BB'$, $B'C'$的中点, 则过$A,E,F$的截面是\\blank{30}.\\\\ \n\\twoch{五边形}{平行四边形}{梯形}{六边形}", + "content": "在正方体$ABCD-A'B'C'D'$中, 已知$E,F$分别是棱$BB'$, $B'C'$的中点, 则过$A,E,F$的截面是\\bracket{20}.\\\\ \n\\twoch{五边形}{平行四边形}{梯形}{六边形}", "objs": [], "tags": [ "第六单元" @@ -41875,7 +41875,7 @@ }, "001648": { "id": "001648", - "content": "有下列四个命题: (1) 分别在两个平行平面内的两条直线平行; (2) 若两个平面平行, 则其中一个平面内的直线必平行于另一个平面; (3) 如果一个平面内的两条直线平行于另一个平面, 则这两个平面平行; (4) 如果一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.\\\\ \n其中正确命题的个数是\\blank{30}.\\\\ \n\\fourch{1}{2}{3}{4}", + "content": "有下列四个命题: (1) 分别在两个平行平面内的两条直线平行; (2) 若两个平面平行, 则其中一个平面内的直线必平行于另一个平面; (3) 如果一个平面内的两条直线平行于另一个平面, 则这两个平面平行; (4) 如果一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.\\\\ \n其中正确命题的个数是\\bracket{20}.\\\\ \n\\fourch{1}{2}{3}{4}", "objs": [], "tags": [ "第六单元" @@ -41923,7 +41923,7 @@ }, "001650": { "id": "001650", - "content": "有下列四个命题: (1) 若直线$a\\parallel$直线$b$, 则$a$和$b$与平面$\\alpha$所成的角相等; (2) 若直线$a$和$b$与平面$\\alpha$所成的角相等, 则$a\\parallel b$; (3) 若$\\alpha\\parallel \\beta$, 则直线$a$与平面$\\alpha$, 平面$\\beta$所成的角相等; (4) 若平面$\\alpha$, 平面$\\beta$都与直线$a$平行, 则$\\alpha\\parallel \\beta$.\\\\ \n其中正确的命题是\\blank{30}.\\\\ \n\\fourch{(1)(3)}{(1)(3)(4)}{(1)(2)(3)}{(1)(2)(3)(4)}", + "content": "有下列四个命题: (1) 若直线$a\\parallel$直线$b$, 则$a$和$b$与平面$\\alpha$所成的角相等; (2) 若直线$a$和$b$与平面$\\alpha$所成的角相等, 则$a\\parallel b$; (3) 若$\\alpha\\parallel \\beta$, 则直线$a$与平面$\\alpha$, 平面$\\beta$所成的角相等; (4) 若平面$\\alpha$, 平面$\\beta$都与直线$a$平行, 则$\\alpha\\parallel \\beta$.\\\\ \n其中正确的命题是\\bracket{20}.\\\\ \n\\fourch{(1)(3)}{(1)(3)(4)}{(1)(2)(3)}{(1)(2)(3)(4)}", "objs": [], "tags": [ "第六单元" @@ -41947,7 +41947,7 @@ }, "001651": { "id": "001651", - "content": "若平面$\\alpha\\parallel$平面$\\beta$, 直线$l\\subsetneqq \\alpha$, 且$\\alpha,\\beta$间的距离为$d$, 有下列四个命题: (1) $\\beta$内有且只有一条直线与$l$的距离等于$d$; (2) $\\beta$内所有直线与$l$的距离都等于$d$; (3) $\\beta$内有无数条直线与$l$的距离等于$d$; (4) $\\beta$内所有直线与$\\alpha$的距离都等于$d$.\\\\ \n其中正确的命题是\\blank{30}.\\\\ \n\\fourch{(1)}{(2)}{(1)(4)}{(3)(4)}", + "content": "若平面$\\alpha\\parallel$平面$\\beta$, 直线$l\\subsetneqq \\alpha$, 且$\\alpha,\\beta$间的距离为$d$, 有下列四个命题: (1) $\\beta$内有且只有一条直线与$l$的距离等于$d$; (2) $\\beta$内所有直线与$l$的距离都等于$d$; (3) $\\beta$内有无数条直线与$l$的距离等于$d$; (4) $\\beta$内所有直线与$\\alpha$的距离都等于$d$.\\\\ \n其中正确的命题是\\bracket{20}.\\\\ \n\\fourch{(1)}{(2)}{(1)(4)}{(3)(4)}", "objs": [], "tags": [ "第六单元" @@ -42067,7 +42067,7 @@ }, "001656": { "id": "001656", - "content": "已知二面角$\\alpha-l-\\beta=\\theta$, $\\theta\\in \\left(\\dfrac{\\pi}{2},\\pi\\right)$, 线段$AB$在$\\alpha$内, 线段$CD$在$\\beta$内, 且$AB\\perp l$, $CD\\perp l$, 若直线$AB$与直线$CD$所成的角为$\\varphi$, 则\\blank{30}.\n\\fourch{$\\varphi=\\theta$}{$\\varphi=\\theta-\\dfrac{\\pi}{2}$}{$\\varphi=\\theta+\\dfrac{\\pi}{2}$}{$\\varphi=\\pi-\\theta$}", + "content": "已知二面角$\\alpha-l-\\beta=\\theta$, $\\theta\\in \\left(\\dfrac{\\pi}{2},\\pi\\right)$, 线段$AB$在$\\alpha$内, 线段$CD$在$\\beta$内, 且$AB\\perp l$, $CD\\perp l$, 若直线$AB$与直线$CD$所成的角为$\\varphi$, 则\\bracket{20}.\n\\fourch{$\\varphi=\\theta$}{$\\varphi=\\theta-\\dfrac{\\pi}{2}$}{$\\varphi=\\theta+\\dfrac{\\pi}{2}$}{$\\varphi=\\pi-\\theta$}", "objs": [], "tags": [ "第六单元" @@ -42091,7 +42091,7 @@ }, "001657": { "id": "001657", - "content": "自二面角内一点分别向它的两个半平面引垂(射)线(要求均与半平面相交), 则这两条射线所夹的角和二面角的平面角之间的关系是\\blank{30}.\n\\fourch{相等}{互补}{互余}{和等于$2\\pi$}", + "content": "自二面角内一点分别向它的两个半平面引垂(射)线(要求均与半平面相交), 则这两条射线所夹的角和二面角的平面角之间的关系是\\bracket{20}.\n\\fourch{相等}{互补}{互余}{和等于$2\\pi$}", "objs": [], "tags": [ "第六单元" @@ -42477,7 +42477,7 @@ }, "001673": { "id": "001673", - "content": "已知平面$\\alpha$与平面$\\beta$互相垂直, $\\alpha\\cap \\beta=l$, 点$P\\in l$, 给出以下四个结论:\\\\ \n(1) 过$P$和$l$垂直的直线在$\\alpha$内;\\\\ \n(2) 过$P$和$\\beta$垂直的直线在$\\alpha$内;\\\\ \n(3) 过$P$和$l$垂直的直线也和$\\beta$垂直;\\\\ \n(4) 过$P$和$\\beta$垂直的平面也和$l$垂直.\\\\ \n其中真命题的个数是\\blank{30}\\\\ \n\\fourch{$1$}{$2$}{$3$}{$4$}", + "content": "已知平面$\\alpha$与平面$\\beta$互相垂直, $\\alpha\\cap \\beta=l$, 点$P\\in l$, 给出以下四个结论:\\\\ \n(1) 过$P$和$l$垂直的直线在$\\alpha$内;\\\\ \n(2) 过$P$和$\\beta$垂直的直线在$\\alpha$内;\\\\ \n(3) 过$P$和$l$垂直的直线也和$\\beta$垂直;\\\\ \n(4) 过$P$和$\\beta$垂直的平面也和$l$垂直.\\\\ \n其中真命题的个数是\\bracket{20}\\\\ \n\\fourch{$1$}{$2$}{$3$}{$4$}", "objs": [], "tags": [ "第六单元" @@ -42525,7 +42525,7 @@ }, "001675": { "id": "001675", - "content": "已知矩形$ADEF$所在平面垂直于矩形$BCEF$所在平面, 记$\\angle DBE=\\alpha$, $\\angle DCE=\\beta$, $\\angle BDC=\\theta$(如图), 则下列各式中成立的是\\blank{30}\n\\twoch{$\\sin\\alpha=\\sin\\beta\\cos\\theta$}{$\\sin\\beta=\\sin\\alpha\\cos\\theta$}{$\\cos\\alpha=\\cos\\beta\\cos\\theta$}{$\\cos\\beta=\\cos\\alpha\\cos\\theta$}", + "content": "已知矩形$ADEF$所在平面垂直于矩形$BCEF$所在平面, 记$\\angle DBE=\\alpha$, $\\angle DCE=\\beta$, $\\angle BDC=\\theta$(如图), 则下列各式中成立的是\\bracket{20}\n\\twoch{$\\sin\\alpha=\\sin\\beta\\cos\\theta$}{$\\sin\\beta=\\sin\\alpha\\cos\\theta$}{$\\cos\\alpha=\\cos\\beta\\cos\\theta$}{$\\cos\\beta=\\cos\\alpha\\cos\\theta$}", "objs": [], "tags": [ "第六单元" @@ -42549,7 +42549,7 @@ }, "001676": { "id": "001676", - "content": "$a,b$为两条互不垂直的异面直线, 过$a,b$分别作平面$\\alpha,\\beta$, 给出以下四个结论: (1) $b\\parallel \\alpha$, (2) $b\\perp \\alpha$, (3) $\\alpha\\parallel\\beta$, (4) $\\alpha\\perp \\beta$. 其中绝对不可能出现的结论个数是\\blank{30}\n\\fourch{$1$}{$2$}{$3$}{$4$}", + "content": "$a,b$为两条互不垂直的异面直线, 过$a,b$分别作平面$\\alpha,\\beta$, 给出以下四个结论: (1) $b\\parallel \\alpha$, (2) $b\\perp \\alpha$, (3) $\\alpha\\parallel\\beta$, (4) $\\alpha\\perp \\beta$. 其中绝对不可能出现的结论个数是\\bracket{20}\n\\fourch{$1$}{$2$}{$3$}{$4$}", "objs": [], "tags": [ "第六单元" @@ -44077,7 +44077,7 @@ }, "001739": { "id": "001739", - "content": "已知数列$\\{a_n\\}$中, $a_n=\\dfrac{1}{4}n^2-\\dfrac{17}{12}n+\\dfrac{13}6, \\ (n \\in \\mathbf{N}^*)$, 下列各数中, 是这数列的某一项的是\\blank{30}.\n\\fourch{$\\dfrac{1}{10}$}{$\\dfrac{1}{5}$}{$\\dfrac{1}{2}$}{$0$}", + "content": "已知数列$\\{a_n\\}$中, $a_n=\\dfrac{1}{4}n^2-\\dfrac{17}{12}n+\\dfrac{13}6, \\ (n \\in \\mathbf{N}^*)$, 下列各数中, 是这数列的某一项的是\\bracket{20}.\n\\fourch{$\\dfrac{1}{10}$}{$\\dfrac{1}{5}$}{$\\dfrac{1}{2}$}{$0$}", "objs": [], "tags": [ "第四单元" @@ -44173,7 +44173,7 @@ }, "001743": { "id": "001743", - "content": "若数列$\\{a_n\\}$的前$4$项的值两两不同, 且对任意正整数$n$均成立$a_{n+4}=a_n$. 则下列该数列的子列中, 可取遍数列$\\{a_n\\}$的前$4$项值的有\\blank{100}.\n\\varfourch{$\\{a_{2n}\\}$}{$\\{a_{3n+2}\\}$}{$\\{a_{5n+3}\\}$}{$\\{a_{6n+3}\\}$}", + "content": "若数列$\\{a_n\\}$的前$4$项的值两两不同, 且对任意正整数$n$均成立$a_{n+4}=a_n$. 则下列该数列的子列中, 可取遍数列$\\{a_n\\}$的前$4$项值的有\\bracket{20}.\n\\varfourch{$\\{a_{2n}\\}$}{$\\{a_{3n+2}\\}$}{$\\{a_{5n+3}\\}$}{$\\{a_{6n+3}\\}$}", "objs": [], "tags": [ "第四单元" @@ -44437,7 +44437,7 @@ }, "001754": { "id": "001754", - "content": "下列条件中, 能确定数列$\\{a_n\\}$是等差数列的条件为\\blank{50}.\n\\vartwoch{$2a_n=a_{n+1}+a_{n-1}(n\\geq2)$}{$\\{a_{2n-1}\\}$与$\\{a_{2n}\\}$都是等差数列}{$a_n=pn+q$, $p,q$是常数}{$\\{2a_{n}+1\\}$是等差数列}", + "content": "下列条件中, 能确定数列$\\{a_n\\}$是等差数列的条件为\\bracket{20}.\n\\vartwoch{$2a_n=a_{n+1}+a_{n-1}(n\\geq2)$}{$\\{a_{2n-1}\\}$与$\\{a_{2n}\\}$都是等差数列}{$a_n=pn+q$, $p,q$是常数}{$\\{2a_{n}+1\\}$是等差数列}", "objs": [], "tags": [ "第四单元" @@ -44461,7 +44461,7 @@ }, "001755": { "id": "001755", - "content": "等差数列的首项为$\\dfrac{1}{5}$, 若从第$10$项起各项均大于$1$, 则此数列的公差$d$的取值范围为\\blank{30}.\n\\fourch{$\\dfrac{4}{45}\\le d<\\dfrac{1}{10}$}{$\\dfrac{4}{45}\\le d\\le \\dfrac{1}{10}$}{$\\dfrac{4}{45}|z_2|$}{不能确定}", + "content": "当$0|z_2|$}{不能确定}", "objs": [ "K0514001B" ], @@ -50969,7 +50969,7 @@ }, "002014": { "id": "002014", - "content": "当$m$在实数范围内变动时, 复数$z=(m^2-8m+15)(1-\\mathrm{i})$所对应的点的轨迹是\\blank{50}.\n\\fourch{直线}{射线}{线段}{圆}", + "content": "当$m$在实数范围内变动时, 复数$z=(m^2-8m+15)(1-\\mathrm{i})$所对应的点的轨迹是\\bracket{20}.\n\\fourch{直线}{射线}{线段}{圆}", "objs": [ "K0513003B", "K0513005B" @@ -50996,7 +50996,7 @@ }, "002015": { "id": "002015", - "content": "复平面内, 若$|z-1+\\mathrm{i}|+|z-1-\\mathrm{i}|=2$, 则复数$z$的对应的点的轨迹是\\blank{50}.\n\\fourch{圆}{两条射线}{射线}{线段}", + "content": "复平面内, 若$|z-1+\\mathrm{i}|+|z-1-\\mathrm{i}|=2$, 则复数$z$的对应的点的轨迹是\\bracket{20}.\n\\fourch{圆}{两条射线}{射线}{线段}", "objs": [ "K0514007B" ], @@ -51211,7 +51211,7 @@ }, "002023": { "id": "002023", - "content": "``$z_1$与$z_2$是共轭复数''是``$z_1+z_2\\in \\mathbf{R}$且$z_1z_2\\in \\mathbf{R}$''的\\blank{50}条件.\n\\fourch{充分非必要}{必要非充分}{充分必要}{既不充分又不必要}", + "content": "``$z_1$与$z_2$是共轭复数''是``$z_1+z_2\\in \\mathbf{R}$且$z_1z_2\\in \\mathbf{R}$''的\\bracket{20}条件.\n\\fourch{充分非必要}{必要非充分}{充分必要}{既不充分又不必要}", "objs": [ "K0512003B", "K0512005B" @@ -51238,7 +51238,7 @@ }, "002024": { "id": "002024", - "content": "若$z_1$与$z_2$互为共轭的虚数, 则满足$|z-z_1|^2-|z_2-z_1|^2=|z-z_2|^2$的复数$z$在复平面内所对应的点的轨迹是\\blank{50}.\n\\twoch{一条垂直于实轴的直线}{一条垂直于虚轴的直线}{线段}{圆}", + "content": "若$z_1$与$z_2$互为共轭的虚数, 则满足$|z-z_1|^2-|z_2-z_1|^2=|z-z_2|^2$的复数$z$在复平面内所对应的点的轨迹是\\bracket{20}.\n\\twoch{一条垂直于实轴的直线}{一条垂直于虚轴的直线}{线段}{圆}", "objs": [ "K0511005B", "K0514003B", @@ -51736,7 +51736,7 @@ }, "002043": { "id": "002043", - "content": "已知复数$z=a+b\\mathrm{i}(a,b\\in \\mathbf{R})$所对应的点在第四象限, 则$\\arg z=$\\blank{50}.\n\\fourch{$\\arcsin \\dfrac{b}{\\sqrt{a^2+b^2}}$}{$\\arcsin \\dfrac{a}{\\sqrt{a^2+b^2}}$}{$\\arctan \\dfrac{b}{a}$}{$2\\pi+\\arctan\\dfrac{b}{a}$}", + "content": "已知复数$z=a+b\\mathrm{i}(a,b\\in \\mathbf{R})$所对应的点在第四象限, 则$\\arg z=$\\bracket{20}.\n\\fourch{$\\arcsin \\dfrac{b}{\\sqrt{a^2+b^2}}$}{$\\arcsin \\dfrac{a}{\\sqrt{a^2+b^2}}$}{$\\arctan \\dfrac{b}{a}$}{$2\\pi+\\arctan\\dfrac{b}{a}$}", "objs": [], "tags": [ "第三单元", @@ -52384,7 +52384,7 @@ }, "002069": { "id": "002069", - "content": "已知非零复数$z$满足$0<\\arg z<2\\pi$, 则下列各式中, 辐角主值一定相等的两个复数是\\blank{50}.\n\\fourch{$z$和$\\bar{z}$}{$2z$和$z^2$}{$-z$和$z^{-1}$}{$\\bar{z}$和$1/z$}", + "content": "已知非零复数$z$满足$0<\\arg z<2\\pi$, 则下列各式中, 辐角主值一定相等的两个复数是\\bracket{20}.\n\\fourch{$z$和$\\bar{z}$}{$2z$和$z^2$}{$-z$和$z^{-1}$}{$\\bar{z}$和$1/z$}", "objs": [], "tags": [ "第五单元" @@ -53090,7 +53090,7 @@ }, "002097": { "id": "002097", - "content": "点$P(a,b)$在曲线$F(x,y)=0$上是$F(a,b)=0$的\\blank{50}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "content": "点$P(a,b)$在曲线$F(x,y)=0$上是$F(a,b)=0$的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", "objs": [], "tags": [ "第七单元" @@ -55180,7 +55180,7 @@ }, "002182": { "id": "002182", - "content": "[不定项选择]\n已知直线$l:f(x,y)=0$与直线$l$外一点$P(x_0,y_0)$, 那么曲线$f(x,y)-f(x_0,y_0)=0$可能为\\blank{50}.\n\\twoch{过$P$且与$l$平行的直线}{两条直线}{直线$l$}{与$l$相交的直线}", + "content": "[不定项选择]\n已知直线$l:f(x,y)=0$与直线$l$外一点$P(x_0,y_0)$, 那么曲线$f(x,y)-f(x_0,y_0)=0$可能为\\bracket{20}.\n\\twoch{过$P$且与$l$平行的直线}{两条直线}{直线$l$}{与$l$相交的直线}", "objs": [], "tags": [ "第七单元" @@ -55446,7 +55446,7 @@ }, "002193": { "id": "002193", - "content": "方程$4x^2-y^2+4x+2y=0$表示的曲线是\\blank{50}.\n\\twoch{一个点}{两条互相平行的直线}{两条互相垂直的直线}{两条相交但不垂直的直线}", + "content": "方程$4x^2-y^2+4x+2y=0$表示的曲线是\\bracket{20}.\n\\twoch{一个点}{两条互相平行的直线}{两条互相垂直的直线}{两条相交但不垂直的直线}", "objs": [], "tags": [ "第七单元" @@ -56761,7 +56761,7 @@ }, "002247": { "id": "002247", - "content": "``$A=C\\neq0, B=0$''是``$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$表示圆的方程''的\\blank{40}.\n\\twoch{充要条件}{充分非必要条件}{必要非充分条件}{既非充分又非必要条件}", + "content": "``$A=C\\neq0, B=0$''是``$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$表示圆的方程''的\\bracket{20}.\n\\twoch{充要条件}{充分非必要条件}{必要非充分条件}{既非充分又非必要条件}", "objs": [], "tags": [ "第七单元" @@ -56787,7 +56787,7 @@ }, "002248": { "id": "002248", - "content": "方程$x^4-y^4-4x^2+4y^2=0$所表示的曲线是\\blank{40}.\n\\twoch{两条相交直线}{两条相交直线和两条平行直线}{两条平行直线和一个圆}{两条相交直线和一个圆}", + "content": "方程$x^4-y^4-4x^2+4y^2=0$所表示的曲线是\\bracket{20}.\n\\twoch{两条相交直线}{两条相交直线和两条平行直线}{两条平行直线和一个圆}{两条相交直线和一个圆}", "objs": [], "tags": [ "第七单元" @@ -56811,7 +56811,7 @@ }, "002249": { "id": "002249", - "content": "方程$|x|-1=\\sqrt{1-(y-1)^2}$所表示的曲线是\\blank{40}.\n\\fourch{一个圆}{两个圆}{半个圆}{两个半圆}", + "content": "方程$|x|-1=\\sqrt{1-(y-1)^2}$所表示的曲线是\\bracket{20}.\n\\fourch{一个圆}{两个圆}{半个圆}{两个半圆}", "objs": [], "tags": [ "第七单元" @@ -56933,7 +56933,7 @@ }, "002254": { "id": "002254", - "content": "已知圆$x^2+y^2+mx+ny+p=0$与$x$轴相切于原点, 则$m,n,p$应满足\\blank{40}.\n\\twoch{$mn\\ne 0$且$p=0$}{$m\\ne 0$且$n^2+p^2=0$}{$n\\ne 0$且$m^2+p^2=0$}{$p\\ne 0$且$m^2+n^2=0$}", + "content": "已知圆$x^2+y^2+mx+ny+p=0$与$x$轴相切于原点, 则$m,n,p$应满足\\bracket{20}.\n\\twoch{$mn\\ne 0$且$p=0$}{$m\\ne 0$且$n^2+p^2=0$}{$n\\ne 0$且$m^2+p^2=0$}{$p\\ne 0$且$m^2+n^2=0$}", "objs": [], "tags": [ "第七单元" @@ -57299,7 +57299,7 @@ }, "002269": { "id": "002269", - "content": "已知点$P(x_0,y_0)$在圆$x^2+y^2=r^2$外, 则直线$x_0x+y_0y=r^2$与该圆的位置关系为\\blank{40}.\n\\fourch{相切}{相离}{相交}{不确定}", + "content": "已知点$P(x_0,y_0)$在圆$x^2+y^2=r^2$外, 则直线$x_0x+y_0y=r^2$与该圆的位置关系为\\bracket{20}.\n\\fourch{相切}{相离}{相交}{不确定}", "objs": [], "tags": [ "第七单元" @@ -57323,7 +57323,7 @@ }, "002270": { "id": "002270", - "content": "直线$ax=by$与圆$x^2+y^2-ax+by=0$的位置关系为\\blank{40}.\n\\fourch{相切}{相离}{相交}{不确定}", + "content": "直线$ax=by$与圆$x^2+y^2-ax+by=0$的位置关系为\\bracket{20}.\n\\fourch{相切}{相离}{相交}{不确定}", "objs": [], "tags": [ "第七单元" @@ -57790,7 +57790,7 @@ }, "002289": { "id": "002289", - "content": "已知实数$a,b,c$满足$3(a^2+b^2)=4c^2(c\\ne 0)$, 则直线$ax+by+c=0$与圆$x^2+y^2=1$的关系是\\blank{50}.\n\\fourch{相交}{相切}{相离}{不确定}", + "content": "已知实数$a,b,c$满足$3(a^2+b^2)=4c^2(c\\ne 0)$, 则直线$ax+by+c=0$与圆$x^2+y^2=1$的关系是\\bracket{20}.\n\\fourch{相交}{相切}{相离}{不确定}", "objs": [], "tags": [ "第七单元" @@ -57814,7 +57814,7 @@ }, "002290": { "id": "002290", - "content": "圆$x^2+y^2-2x=3$与直线$y=ax+1$的交点个数是\\blank{50}.\n\\fourch{$0$}{$1$}{$2$}{随$a$的不同而改变}%2 C", + "content": "圆$x^2+y^2-2x=3$与直线$y=ax+1$的交点个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{随$a$的不同而改变}%2 C", "objs": [], "tags": [ "第七单元" @@ -59398,7 +59398,7 @@ }, "002363": { "id": "002363", - "content": "与两圆$x^2+y^2=1$和$x^2+y^2-8x+7=0$都相切的圆的圆心轨迹是\\blank{50}.\n\\twoch{两个椭圆}{两条双曲线}{一条双曲线和一条直线}{一个椭圆和一条双曲线}", + "content": "与两圆$x^2+y^2=1$和$x^2+y^2-8x+7=0$都相切的圆的圆心轨迹是\\bracket{20}.\n\\twoch{两个椭圆}{两条双曲线}{一条双曲线和一条直线}{一个椭圆和一条双曲线}", "objs": [], "tags": [ "第七单元" @@ -59503,7 +59503,7 @@ }, "002368": { "id": "002368", - "content": "双曲线与其共轭双曲线有共同的\\blank{30}.\n\\fourch{焦点}{准线}{离心率}{渐近线}", + "content": "双曲线与其共轭双曲线有共同的\\bracket{20}.\n\\fourch{焦点}{准线}{离心率}{渐近线}", "objs": [], "tags": [ "第七单元" @@ -60033,7 +60033,7 @@ }, "002393": { "id": "002393", - "content": "若$A$是直线$l$外的一定点, 则过$A$且与$l$相切的圆的圆心轨迹是\\blank{30}.\n\\fourch{圆}{双曲线一支}{抛物线}{以上都不是}", + "content": "若$A$是直线$l$外的一定点, 则过$A$且与$l$相切的圆的圆心轨迹是\\bracket{20}.\n\\fourch{圆}{双曲线一支}{抛物线}{以上都不是}", "objs": [], "tags": [ "第七单元" @@ -60056,7 +60056,7 @@ }, "002394": { "id": "002394", - "content": "若$A$是直线$l$上的一定点, 则过$A$且与$l$相切的圆的圆心轨迹是\\blank{30}.\n\\fourch{圆}{双曲线一支}{抛物线}{以上都不是}", + "content": "若$A$是直线$l$上的一定点, 则过$A$且与$l$相切的圆的圆心轨迹是\\bracket{20}.\n\\fourch{圆}{双曲线一支}{抛物线}{以上都不是}", "objs": [], "tags": [ "第七单元" @@ -60702,7 +60702,7 @@ }, "002424": { "id": "002424", - "content": "设抛物线$y=ax^2 \\ (a>0)$与直线$y=kx+b$相交于两点, 它们的横坐标为$x_1,x_2$, 而$x_3$是直线与$x$轴交点的横坐标, 那么$x_1,x_2,x_3$的关系是\\blank{30}.\n\\twoch{$x_3=x_1+x_2$}{$x_3=\\dfrac{1}{x_1}+\\dfrac{1}{x_2}$}{$x_1x_2=x_2x_3+x_3x_1$}{$x_3=\\sqrt{x_1x_2}$}", + "content": "设抛物线$y=ax^2 \\ (a>0)$与直线$y=kx+b$相交于两点, 它们的横坐标为$x_1,x_2$, 而$x_3$是直线与$x$轴交点的横坐标, 那么$x_1,x_2,x_3$的关系是\\bracket{20}.\n\\twoch{$x_3=x_1+x_2$}{$x_3=\\dfrac{1}{x_1}+\\dfrac{1}{x_2}$}{$x_1x_2=x_2x_3+x_3x_1$}{$x_3=\\sqrt{x_1x_2}$}", "objs": [], "tags": [ "第七单元" @@ -61434,7 +61434,7 @@ }, "002455": { "id": "002455", - "content": "与普通方程$xy=1$表示相同曲线的参数方程($t$为参数)是\\blank{50}.\n\\fourch{$\\left\\{\\begin{array}{l}x=t^2,\\\\y=t^{-2},\\end{array}\\right.$}\n{$\\left\\{\\begin{array}{l}x=\\sin t,\\\\y=\\csc t,\\end{array}\\right.$}\n{$\\left\\{\\begin{array}{l}x=\\sec t,\\\\y=\\cos t,\\end{array}\\right.$}\n{$\\left\\{\\begin{array}{l}x=\\tan t,\\\\y=\\cot t,\\end{array}\\right.$}", + "content": "与普通方程$xy=1$表示相同曲线的参数方程($t$为参数)是\\bracket{20}.\n\\fourch{$\\left\\{\\begin{array}{l}x=t^2,\\\\y=t^{-2},\\end{array}\\right.$}\n{$\\left\\{\\begin{array}{l}x=\\sin t,\\\\y=\\csc t,\\end{array}\\right.$}\n{$\\left\\{\\begin{array}{l}x=\\sec t,\\\\y=\\cos t,\\end{array}\\right.$}\n{$\\left\\{\\begin{array}{l}x=\\tan t,\\\\y=\\cot t,\\end{array}\\right.$}", "objs": [], "tags": [ "第七单元" @@ -61458,7 +61458,7 @@ }, "002456": { "id": "002456", - "content": "若曲线的参数方程为$\\left\\{\\begin{array}{l}x=1+\\cos 2\\theta,\\\\y=\\sin^2\\theta,\\end{array}\\right.$($\\theta$为参数), 则该曲线是\\blank{50}.\n\\twoch{直线$x+2y-2=0$}{以$(2,0)$为端点的一条射线}{圆$(x-1)^2+y^2=1$}{以$(2,0)$和$(0,1)$为端点的线段}", + "content": "若曲线的参数方程为$\\left\\{\\begin{array}{l}x=1+\\cos 2\\theta,\\\\y=\\sin^2\\theta,\\end{array}\\right.$($\\theta$为参数), 则该曲线是\\bracket{20}.\n\\twoch{直线$x+2y-2=0$}{以$(2,0)$为端点的一条射线}{圆$(x-1)^2+y^2=1$}{以$(2,0)$和$(0,1)$为端点的线段}", "objs": [], "tags": [ "第七单元" @@ -62114,7 +62114,7 @@ }, "002483": { "id": "002483", - "content": "极坐标系中, 若等边三角形$ABC$的顶点$A,B,C$按顺时针排列, 且$A,B$的极坐标分别为$A(2,\\pi/4)$, $B(2,5\\pi/4)$, 则顶点$C$的极坐标可能是\\blank{50}.\n\\fourch{$(4,3\\pi/4)$}{$(2\\sqrt{3},3\\pi/4)$}{$(2\\sqrt{3},\\pi)$}{$(3,\\pi)$}", + "content": "极坐标系中, 若等边三角形$ABC$的顶点$A,B,C$按顺时针排列, 且$A,B$的极坐标分别为$A(2,\\pi/4)$, $B(2,5\\pi/4)$, 则顶点$C$的极坐标可能是\\bracket{20}.\n\\fourch{$(4,3\\pi/4)$}{$(2\\sqrt{3},3\\pi/4)$}{$(2\\sqrt{3},\\pi)$}{$(3,\\pi)$}", "objs": [], "tags": [ "暂无对应" @@ -62138,7 +62138,7 @@ }, "002484": { "id": "002484", - "content": "直角坐标为$(-3,4)$的点的极坐标可能是\\blank{50}.\n\\fourch{$(5,\\arctan(-4/3))$}{$(5,\\arcsin(4/5))$}{$(-5,-\\arccos(3/5))$}{$(-5,\\arccos(-3/5))$}", + "content": "直角坐标为$(-3,4)$的点的极坐标可能是\\bracket{20}.\n\\fourch{$(5,\\arctan(-4/3))$}{$(5,\\arcsin(4/5))$}{$(-5,-\\arccos(3/5))$}{$(-5,\\arccos(-3/5))$}", "objs": [], "tags": [ "暂无对应" @@ -62186,7 +62186,7 @@ }, "002486": { "id": "002486", - "content": "极坐标系中, 已知两点$P(\\rho_1,\\theta_1)$与$Q(\\rho_2,\\theta_2)$满足$\\rho_1+\\rho_2=\\theta_1+\\theta_2=0$, 则$P,Q$两点\\blank{50}\n\\twoch{重合}{关于极点对称}{关于极轴对称}{关于直线$\\theta=\\pi/2(\\rho\\in \\mathbf{R})$对称}", + "content": "极坐标系中, 已知两点$P(\\rho_1,\\theta_1)$与$Q(\\rho_2,\\theta_2)$满足$\\rho_1+\\rho_2=\\theta_1+\\theta_2=0$, 则$P,Q$两点\\bracket{20}\n\\twoch{重合}{关于极点对称}{关于极轴对称}{关于直线$\\theta=\\pi/2(\\rho\\in \\mathbf{R})$对称}", "objs": [], "tags": [ "暂无对应" @@ -62336,7 +62336,7 @@ }, "002492": { "id": "002492", - "content": "已知曲线$C$与曲线$\\rho=5\\sqrt{3}\\cos\\theta-5\\sin\\theta$关于极轴对称, 则曲线$C$的方程是\\blank{50}.\n\\twoch{$\\rho=-10\\cos(\\theta-\\pi/6)$}{$\\rho=10\\cos(\\theta-\\pi/6)$}{$\\rho=-10\\cos(\\theta+\\pi/6)$}{$\\rho=10\\cos(\\theta+\\pi/6)$}", + "content": "已知曲线$C$与曲线$\\rho=5\\sqrt{3}\\cos\\theta-5\\sin\\theta$关于极轴对称, 则曲线$C$的方程是\\bracket{20}.\n\\twoch{$\\rho=-10\\cos(\\theta-\\pi/6)$}{$\\rho=10\\cos(\\theta-\\pi/6)$}{$\\rho=-10\\cos(\\theta+\\pi/6)$}{$\\rho=10\\cos(\\theta+\\pi/6)$}", "objs": [], "tags": [ "暂无对应" @@ -70656,7 +70656,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\begin{cases}\n -5x^2+20x, & 1\\le x<4,\\\\ \\dfrac{125}2-\\dfrac{90}x-10x, & x\\ge 4.\n\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -70703,7 +70703,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=-(\\dfrac \\pi 2+2)x^2+lx, \\ x\\in (0,\\dfrac l{\\pi+2})$", "solution": "", "duration": -1, "usages": [], @@ -71256,7 +71256,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -71947,7 +71947,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $f(6)=-2a$, $f(300)=-100a$.", "solution": "", "duration": -1, "usages": [], @@ -72487,7 +72487,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a=4$, $b=0$; (2) 证明略.", "solution": "", "duration": -1, "usages": [], @@ -74114,7 +74114,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(3,+\\infty)$; (2) $[-5,1]$.", "solution": "", "duration": -1, "usages": [], @@ -74502,7 +74502,7 @@ }, "002987": { "id": "002987", - "content": "函数$f(x)=ax^2+bx+c$ 与函数$g(x)=cx^2+bx+a$($ac\\ne 0,\\ a\\ne c)$的值域分别为$M$、$N$, 则下列结论正确的是\\blank{50}.\n\\fourch{$M=N$}{$M\\subseteq N$}{$M\\supseteq N$}{$M\\cap N\\ne \\varnothing$}", + "content": "函数$f(x)=ax^2+bx+c$ 与函数$g(x)=cx^2+bx+a$($ac\\ne 0,\\ a\\ne c)$的值域分别为$M$、$N$, 则下列结论正确的是\\bracket{20}.\n\\fourch{$M=N$}{$M\\subseteq N$}{$M\\supseteq N$}{$M\\cap N\\ne \\varnothing$}", "objs": [ "K0215005B", "K0215001B", @@ -76201,7 +76201,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$k\\pi-\\dfrac\\pi 6, \\ k\\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [ @@ -76367,7 +76367,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$2\\alpha$的终边在第三、四象限或$y$轴负半轴, $\\dfrac{\\alpha}2$的终边在第一、三象限, $\\dfrac{\\alpha}3$的终边在第一、二、四象限", "solution": "", "duration": -1, "usages": [ @@ -76403,7 +76403,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 图略, $\\{\\alpha|\\dfrac\\pi 3+2k\\pi <\\alpha<\\dfrac{2\\pi}3+2k\\pi, \\ k\\in \\mathbf{Z}\\}$; (2) 图略, $\\{\\alpha|\\dfrac{2\\pi}3+2k\\pi<\\alpha<\\dfrac{4\\pi}3+2k\\pi, \\ k\\in \\mathbf{Z}\\}$; (3) 图略, $\\{\\alpha|\\dfrac\\pi 2+k\\pi<\\alpha<\\dfrac{3\\pi}4+k\\pi, \\ k\\in \\mathbf{Z}\\}$.", "solution": "", "duration": -1, "usages": [ @@ -77026,7 +77026,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -77062,7 +77062,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sin(\\alpha+\\dfrac{5\\pi}3)$", "solution": "", "duration": -1, "usages": [ @@ -77098,7 +77098,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{15}}4$", "solution": "", "duration": -1, "usages": [ @@ -77134,7 +77134,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{2}}{10}$", "solution": "", "duration": -1, "usages": [ @@ -77193,7 +77193,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 5{14}$", "solution": "", "duration": -1, "usages": [ @@ -77277,7 +77277,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{11\\pi}4$", "solution": "", "duration": -1, "usages": [ @@ -77336,7 +77336,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{59}{72}$", "solution": "", "duration": -1, "usages": [ @@ -77424,7 +77424,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{7\\pi}4$", "solution": "", "duration": -1, "usages": [], @@ -77468,7 +77468,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\dfrac 34,\\dfrac 32)\\cup (\\dfrac 32,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -77602,7 +77602,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{24}{25}$", "solution": "", "duration": -1, "usages": [ @@ -77638,7 +77638,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 14$", "solution": "", "duration": -1, "usages": [ @@ -77890,7 +77890,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -77973,7 +77973,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $2R^2\\sin A\\sin B\\sin C$; (2) $\\dfrac{abc}{4R}$; (3) $pr$.", "solution": "", "duration": -1, "usages": [], @@ -78061,7 +78061,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $\\dfrac{5\\pi}{6}$; (2) $\\dfrac{5\\pi}{6}$或$\\dfrac{\\pi}6$.", "solution": "", "duration": -1, "usages": [], @@ -78107,7 +78107,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -78131,7 +78131,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\sqrt{3},\\sqrt{5})$", "solution": "", "duration": -1, "usages": [], @@ -78198,7 +78198,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "长约为$445$米.", "solution": "", "duration": -1, "usages": [], @@ -78221,7 +78221,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -78244,7 +78244,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\sqrt{3}}3$", "solution": "", "duration": -1, "usages": [], @@ -78314,7 +78314,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{15}2$", "solution": "", "duration": -1, "usages": [], @@ -78427,7 +78427,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{x|\\dfrac\\pi 2+2k\\pi\\le x\\le \\dfrac{3\\pi}2+2k\\pi, \\ k\\in \\mathbf{Z}\\}$", "solution": "", "duration": -1, "usages": [], @@ -78459,7 +78459,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-1,2]$", "solution": "", "duration": -1, "usages": [], @@ -78594,7 +78594,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{x|2k\\pib$, 则下列不等式一定成立的是\\blank{30}.\n\\fourch{$a+c\\ge b-c$}{$ac>bc$}{$\\dfrac{c^2}{a-b}>0$}{$(a-b)c^2\\ge 0$}", + "content": "若$a,b,c\\in \\mathbf{R}$, 且$a>b$, 则下列不等式一定成立的是\\bracket{20}.\n\\fourch{$a+c\\ge b-c$}{$ac>bc$}{$\\dfrac{c^2}{a-b}>0$}{$(a-b)c^2\\ge 0$}", "objs": [ "K0111003B" ], @@ -91723,7 +91723,7 @@ }, "003744": { "id": "003744", - "content": "我们规定``渐近线''的概念: 已知曲线$C$, 如果存在有一条直线, 当曲线$C$上任一点$M$沿曲线运动时$M$可无限趋近于该直线但永远达不到, 那么这条直线称为这条曲线的``渐近线''. 下列函数\n\\textcircled{1} $f(x)=x^2+2x-3$, \\textcircled{2} $g(x)=2^x+1$, \\textcircled{3} $h(x)=\\log_2(x-1)$, \\textcircled{4} $t(x)=\\dfrac{2x+1}{x-1}$, \\textcircled{5} $u(x)=\\dfrac{x^2+2}{x}$, 其中有``渐近线''的个数为\\blank{30}.\n\\fourch{$2$}{$3$}{$4$}{$5$}", + "content": "我们规定``渐近线''的概念: 已知曲线$C$, 如果存在有一条直线, 当曲线$C$上任一点$M$沿曲线运动时$M$可无限趋近于该直线但永远达不到, 那么这条直线称为这条曲线的``渐近线''. 下列函数\n\\textcircled{1} $f(x)=x^2+2x-3$, \\textcircled{2} $g(x)=2^x+1$, \\textcircled{3} $h(x)=\\log_2(x-1)$, \\textcircled{4} $t(x)=\\dfrac{2x+1}{x-1}$, \\textcircled{5} $u(x)=\\dfrac{x^2+2}{x}$, 其中有``渐近线''的个数为\\bracket{20}.\n\\fourch{$2$}{$3$}{$4$}{$5$}", "objs": [], "tags": [ "第七单元" @@ -91973,7 +91973,7 @@ }, "003755": { "id": "003755", - "content": "过点$(1,0)$且与直线$x-2y-2=0$的法向量垂直的直线方程是\\blank{30}.\n\\twoch{$x-2y+1=0$}{$2x+y-2=0$}{$x+2y-1=0$}{$x-2y-1=0$}", + "content": "过点$(1,0)$且与直线$x-2y-2=0$的法向量垂直的直线方程是\\bracket{20}.\n\\twoch{$x-2y+1=0$}{$2x+y-2=0$}{$x+2y-1=0$}{$x-2y-1=0$}", "objs": [], "tags": [ "第七单元" @@ -91994,7 +91994,7 @@ }, "003756": { "id": "003756", - "content": "(理科)在极坐标中, 与点$\\left(2,\\dfrac{\\pi}{3}\\right)$关于极点对称的点的一个极坐标是\\blank{30}.\n\\fourch{$\\left(-2,-\\dfrac{\\pi}{3}\\right)$}{$\\left(2,-\\dfrac{\\pi}{3}\\right)$}{$\\left(2,-\\dfrac{2\\pi}{3}\\right)$}{$\\left(-2,\\dfrac{4\\pi}{3}\\right)$}\\\\\n(文科)如果实数$x,y$满足条件$\\begin{cases}\nx-y+1\\ge 0,\\\\y+1\\ge 0,\\\\x+y+1\\le 0,\n\\end{cases}$ 那么$2x-y$的最大值为\\blank{30}.\n\\fourch{$2$}{$1$}{$-2$}{$-3$}", + "content": "(理科)在极坐标中, 与点$\\left(2,\\dfrac{\\pi}{3}\\right)$关于极点对称的点的一个极坐标是\\bracket{20}.\n\\fourch{$\\left(-2,-\\dfrac{\\pi}{3}\\right)$}{$\\left(2,-\\dfrac{\\pi}{3}\\right)$}{$\\left(2,-\\dfrac{2\\pi}{3}\\right)$}{$\\left(-2,\\dfrac{4\\pi}{3}\\right)$}\\\\\n(文科)如果实数$x,y$满足条件$\\begin{cases}\nx-y+1\\ge 0,\\\\y+1\\ge 0,\\\\x+y+1\\le 0,\n\\end{cases}$ 那么$2x-y$的最大值为\\bracket{20}.\n\\fourch{$2$}{$1$}{$-2$}{$-3$}", "objs": [], "tags": [ "第七单元" @@ -92015,7 +92015,7 @@ }, "003757": { "id": "003757", - "content": "设函数$f(x)=x^3+\\dfrac{2^x-1}{2^x+1}$, 已知$a\\in (-1,1)$, $b\\in (-1,1)$. 则$a+b\\ge 0$是$f(a)+f(b)\\ge 0$的\\blank{30}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分也不必要条件}", + "content": "设函数$f(x)=x^3+\\dfrac{2^x-1}{2^x+1}$, 已知$a\\in (-1,1)$, $b\\in (-1,1)$. 则$a+b\\ge 0$是$f(a)+f(b)\\ge 0$的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分也不必要条件}", "objs": [ "K0106003B" ], @@ -92307,7 +92307,7 @@ }, "003770": { "id": "003770", - "content": "函数$f(x)=2^x+x^3-2$在区间$(0,1)$内的零点的个数是\\blank{30}.\n\\fourch{$0$}{$1$}{$2$}{$3$}", + "content": "函数$f(x)=2^x+x^3-2$在区间$(0,1)$内的零点的个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{$3$}", "objs": [ "K0223001B", "K0224001B" @@ -92331,7 +92331,7 @@ }, "003771": { "id": "003771", - "content": "设$\\overrightarrow{a},\\overrightarrow{b}$都是非零向量, 下列四个条件中, 使$\\dfrac{\\overrightarrow{a}}{|\\overrightarrow{a}|}=\\dfrac{\\overrightarrow{b}}{|\\overrightarrow{b}|}$成立的充分条件是\\blank{30}.\n\\twoch{$|\\overrightarrow{a}|=|\\overrightarrow{b}|$且$\\overrightarrow{a}\\parallel \\overrightarrow{b}$}{$\\overrightarrow{a}=-\\overrightarrow{b}$}{$\\overrightarrow{a}\\parallel\\overrightarrow{b}$}{$\\overrightarrow{a}=2\\overrightarrow{b}$}", + "content": "设$\\overrightarrow{a},\\overrightarrow{b}$都是非零向量, 下列四个条件中, 使$\\dfrac{\\overrightarrow{a}}{|\\overrightarrow{a}|}=\\dfrac{\\overrightarrow{b}}{|\\overrightarrow{b}|}$成立的充分条件是\\bracket{20}.\n\\twoch{$|\\overrightarrow{a}|=|\\overrightarrow{b}|$且$\\overrightarrow{a}\\parallel \\overrightarrow{b}$}{$\\overrightarrow{a}=-\\overrightarrow{b}$}{$\\overrightarrow{a}\\parallel\\overrightarrow{b}$}{$\\overrightarrow{a}=2\\overrightarrow{b}$}", "objs": [], "tags": [ "第五单元" @@ -92352,7 +92352,7 @@ }, "003772": { "id": "003772", - "content": "定义在$(-\\infty,0)\\cup (0,+\\infty)$上的函数$f(x)$, 如果对于任意给定的等比数列$\\{a_n\\}$, $\\{f(a_n)\\}$仍是等比数列, 则称$f(x)$为``保等比数列函数''. 现有定义在$(-\\infty,0)\\cup (0,+\\infty)$上的如下函数: \\textcircled{1} $f(x)=x^2$; \\textcircled{2} $f(x)=2^x$; \\textcircled{3} $f(x)=\\sqrt{|x|}$; \\textcircled{4} $f(x)=\\ln|x|$. 则其中是``保等比数列函数''的$f(x)$的序号为\\blank{30}.\n\\fourch{\\textcircled{1}\\textcircled{2}}{\\textcircled{3}\\textcircled{4}}{\\textcircled{1}\\textcircled{3}}{\\textcircled{2}\\textcircled{4}}", + "content": "定义在$(-\\infty,0)\\cup (0,+\\infty)$上的函数$f(x)$, 如果对于任意给定的等比数列$\\{a_n\\}$, $\\{f(a_n)\\}$仍是等比数列, 则称$f(x)$为``保等比数列函数''. 现有定义在$(-\\infty,0)\\cup (0,+\\infty)$上的如下函数: \\textcircled{1} $f(x)=x^2$; \\textcircled{2} $f(x)=2^x$; \\textcircled{3} $f(x)=\\sqrt{|x|}$; \\textcircled{4} $f(x)=\\ln|x|$. 则其中是``保等比数列函数''的$f(x)$的序号为\\bracket{20}.\n\\fourch{\\textcircled{1}\\textcircled{2}}{\\textcircled{3}\\textcircled{4}}{\\textcircled{1}\\textcircled{3}}{\\textcircled{2}\\textcircled{4}}", "objs": [ "KNONE" ], @@ -92645,7 +92645,7 @@ }, "003785": { "id": "003785", - "content": "已知函数$f(x)=2\\sin\\left(\\dfrac x2+\\dfrac \\pi 3\\right)$, 若对任意的$x\\in \\mathbf{R}$都有$f(x_1)\\le f(x)\\le f(x_2)$, 则$|x_1-x_2|$的最小值为\\blank{30}.\n\\fourch{$\\dfrac \\pi 3$}{$\\dfrac{2\\pi}{3}$}{$2\\pi$}{$4\\pi$}", + "content": "已知函数$f(x)=2\\sin\\left(\\dfrac x2+\\dfrac \\pi 3\\right)$, 若对任意的$x\\in \\mathbf{R}$都有$f(x_1)\\le f(x)\\le f(x_2)$, 则$|x_1-x_2|$的最小值为\\bracket{20}.\n\\fourch{$\\dfrac \\pi 3$}{$\\dfrac{2\\pi}{3}$}{$2\\pi$}{$4\\pi$}", "objs": [], "tags": [ "第三单元" @@ -92666,7 +92666,7 @@ }, "003786": { "id": "003786", - "content": "若数列$\\{b_n\\}$为等比数列, 其前$n$项的和为$S_n$, 若对任意$n\\in \\mathbf{N}^*$, 点$(n,S_n)$均在函数$y=bx+r$($b>0, \\ b\\ne 1, \\ b,r$为常数)的图像上, 则$r=$\\blank{30}.\n\\fourch{$0$}{$-1$}{$1$}{$2$}", + "content": "若数列$\\{b_n\\}$为等比数列, 其前$n$项的和为$S_n$, 若对任意$n\\in \\mathbf{N}^*$, 点$(n,S_n)$均在函数$y=bx+r$($b>0, \\ b\\ne 1, \\ b,r$为常数)的图像上, 则$r=$\\bracket{20}.\n\\fourch{$0$}{$-1$}{$1$}{$2$}", "objs": [], "tags": [ "第四单元" @@ -92687,7 +92687,7 @@ }, "003787": { "id": "003787", - "content": "``顺数''是指在一个整数中, 每一位数字比其左边的一位数字大(除首位数字外), 如$24567$就是一个五位``顺数''. 任取一个两位``顺数'', 该数大于$56$的概率为\\blank{30}.\n\\fourch{$\\dfrac 13$}{$\\dfrac 14$}{$\\dfrac {7}{12}$}{$\\dfrac{5}{16}$}", + "content": "``顺数''是指在一个整数中, 每一位数字比其左边的一位数字大(除首位数字外), 如$24567$就是一个五位``顺数''. 任取一个两位``顺数'', 该数大于$56$的概率为\\bracket{20}.\n\\fourch{$\\dfrac 13$}{$\\dfrac 14$}{$\\dfrac {7}{12}$}{$\\dfrac{5}{16}$}", "objs": [], "tags": [ "第八单元" @@ -92970,7 +92970,7 @@ }, "003800": { "id": "003800", - "content": "下列命题中正确的是\\blank{30}.\n\\twoch{若$ac>bc$, 则$a>b$}{若$a^2>b^2$, 则$a>b$}{若$\\dfrac 1a>\\dfrac 1b$, 则$abc$, 则$a>b$}{若$a^2>b^2$, 则$a>b$}{若$\\dfrac 1a>\\dfrac 1b$, 则$aa_8S_9$}{$a_9S_8a_8S_9$}{$a_9S_8\\bar{x}_{\\text{乙}}$, 乙比甲成绩稳定, 应该选乙参加比赛}{$\\bar{x}_{\\text{甲}}>\\bar{x}_{\\text{乙}}$, 甲比乙成绩稳定, 应该选甲参加比赛}{$\\bar{x}_{\\text{甲}}<\\bar{x}_{\\text{乙}}$, 甲比乙成绩稳定, 应该选甲参加比赛}{$\\bar{x}_{\\text{甲}}<\\bar{x}_{\\text{乙}}$, 乙比甲成绩稳定, 应该选乙参加比赛}", + "content": "为了从甲乙两人中选一人参加数学竞赛,老师将两人最近的$6$次数学测试的分数进行统计, 甲乙两人的得分情况如下表所示, \n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\t\\hline\n\t甲 & $72$ & $78$ & $79$ & $85$ & $86$ & $92$\\\\ \\hline\n\t乙 & $78$ & $86$ & $88$ & $88$ & $91$ & $93$\\\\ \\hline\n\\end{tabular}\n\\end{center}\n若甲乙两人的平均成绩分别是$\\bar{x}_{\\text{甲}}$, $\\bar{x}_{\\text{乙}}$, 则下列说法正确的是\\bracket{20}.\n\\twoch{$\\bar{x}_{\\text{甲}}>\\bar{x}_{\\text{乙}}$, 乙比甲成绩稳定, 应该选乙参加比赛}{$\\bar{x}_{\\text{甲}}>\\bar{x}_{\\text{乙}}$, 甲比乙成绩稳定, 应该选甲参加比赛}{$\\bar{x}_{\\text{甲}}<\\bar{x}_{\\text{乙}}$, 甲比乙成绩稳定, 应该选甲参加比赛}{$\\bar{x}_{\\text{甲}}<\\bar{x}_{\\text{乙}}$, 乙比甲成绩稳定, 应该选乙参加比赛}", "objs": [], "tags": [ "第九单元" @@ -93968,7 +93968,7 @@ }, "003846": { "id": "003846", - "content": "已知$m,n$是两条不同直线, $\\alpha,\\beta,\\gamma$是三个不同平面, 下列命题中正确的是\\blank{30}.\n\\twoch{$m\\parallel \\alpha$, $n\\parallel \\alpha$, 则$m\\parallel n$}{若$m\\parallel \\alpha$, $m\\parallel \\beta$, 则$\\alpha\\parallel \\beta$}{若$\\alpha\\perp \\gamma$, $\\beta\\perp \\gamma$, 则$\\alpha\\parallel \\beta$}{若$m\\perp \\alpha$, $n\\perp \\alpha$, 则$m\\parallel n$}", + "content": "已知$m,n$是两条不同直线, $\\alpha,\\beta,\\gamma$是三个不同平面, 下列命题中正确的是\\bracket{20}.\n\\twoch{$m\\parallel \\alpha$, $n\\parallel \\alpha$, 则$m\\parallel n$}{若$m\\parallel \\alpha$, $m\\parallel \\beta$, 则$\\alpha\\parallel \\beta$}{若$\\alpha\\perp \\gamma$, $\\beta\\perp \\gamma$, 则$\\alpha\\parallel \\beta$}{若$m\\perp \\alpha$, $n\\perp \\alpha$, 则$m\\parallel n$}", "objs": [], "tags": [ "第六单元" @@ -93989,7 +93989,7 @@ }, "003847": { "id": "003847", - "content": "平面四边形$ABCD$中, $\\overrightarrow{AB}+\\overrightarrow{CD}=\\overrightarrow{0}$, $(\\overrightarrow{AB}-\\overrightarrow{AD})\\cdot \\overrightarrow{AC}=0$, 则四边形$ABCD$是\\blank{30}.\n\\fourch{矩形}{菱形}{等腰梯形}{直角梯形}", + "content": "平面四边形$ABCD$中, $\\overrightarrow{AB}+\\overrightarrow{CD}=\\overrightarrow{0}$, $(\\overrightarrow{AB}-\\overrightarrow{AD})\\cdot \\overrightarrow{AC}=0$, 则四边形$ABCD$是\\bracket{20}.\n\\fourch{矩形}{菱形}{等腰梯形}{直角梯形}", "objs": [], "tags": [ "第五单元" @@ -94264,7 +94264,7 @@ }, "003860": { "id": "003860", - "content": "若集合$M=\\{y|y=x^2-1, \\ x\\in \\mathbf{R}\\}$, 集合$N=\\{x|y=\\sqrt{3-x}, \\ x\\in \\mathbf{R}\\}$, 则$M\\cap N=$\\blank{30}.\n\\fourch{$\\{(-\\sqrt{2},1),(\\sqrt{2},1)\\}$}{$\\{t|0\\le t\\le \\sqrt{3}\\}$}{$\\{t|-1\\le t\\le 3\\}$}{$\\{t|-\\infty=stealth]\n\t\\fill [gray] (0,0)--(0.65,0)--(0.65,1.3)--cycle;\n\t\\draw [->] (-0.5,0)--(0,0) node [below left] {$O$} --(3,0) node [below] {$x$};\n\t\\draw [->] (0,-0.5)--(0,2.5) node [left] {$y$};\n\t\\draw (0,0)--(1,2) node [above] {$A$}--(2,2) node [above] {$B$}--(2,0) node [above right] {$C$};\n\t\\draw (0.65,-0.5)--(0.65,2.5) node [right] {$l$};\n\t\\draw [dashed] (0,2) node [left] {$2$} --(1,2)--(1,0) node [below] {$1$};\n\t\\draw (2,0) node [below] {$2$};\n\t\n\t\\end{tikzpicture}\n\\end{center}\n则函数$S=f(t)$的图像大致为\\blank{30}.\n\\fourch{\\begin{tikzpicture}[>=stealth]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw (0,0)--(0.6,0.6)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,0.6)--(0,0.6);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[>=stealth]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw (0,0)--(0.6,1.2)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,1.2)--(0,1.2);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[>=stealth,samples=200]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw [domain=0:1] plot ({\\x*0.6},{\\x*\\x*0.6});\n\t\\draw (0.6,0.6)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,0.6)--(0,0.6);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[>=stealth,samples=200]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw [domain=0:1] plot ({\\x*0.6},{2*\\x*\\x*0.6});\n\t\\draw (0.6,1.2)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,1.2)--(0,1.2);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}", + "content": "如图, 直角梯形$OABC$中, $AB\\parallel OC$, $AB=1$, $OC=BC=2$, 直线$l: x=t$截此梯形所得位于$l$左方图形面积为$S$, \n\\begin{center}\n\t\\begin{tikzpicture}[samples=200,>=stealth]\n\t\\fill [gray] (0,0)--(0.65,0)--(0.65,1.3)--cycle;\n\t\\draw [->] (-0.5,0)--(0,0) node [below left] {$O$} --(3,0) node [below] {$x$};\n\t\\draw [->] (0,-0.5)--(0,2.5) node [left] {$y$};\n\t\\draw (0,0)--(1,2) node [above] {$A$}--(2,2) node [above] {$B$}--(2,0) node [above right] {$C$};\n\t\\draw (0.65,-0.5)--(0.65,2.5) node [right] {$l$};\n\t\\draw [dashed] (0,2) node [left] {$2$} --(1,2)--(1,0) node [below] {$1$};\n\t\\draw (2,0) node [below] {$2$};\n\t\n\t\\end{tikzpicture}\n\\end{center}\n则函数$S=f(t)$的图像大致为\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=stealth]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw (0,0)--(0.6,0.6)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,0.6)--(0,0.6);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[>=stealth]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw (0,0)--(0.6,1.2)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,1.2)--(0,1.2);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[>=stealth,samples=200]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw [domain=0:1] plot ({\\x*0.6},{\\x*\\x*0.6});\n\t\\draw (0.6,0.6)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,0.6)--(0,0.6);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[>=stealth,samples=200]\n\t\\draw [->] (-0.3,0)--(0,0) node [below left] {$O$} --(1.8,0) node [below] {$t$};\n\t\\draw [->] (0,-0.3)--(0,2.1) node [left] {$S$};\n\t\\draw (0.6,0) node [below] {$1$}--(0.6,0.1);\n\t\\draw (1.2,0) node [below] {$2$}--(1.2,0.1);\n\t\\draw (0,0.6) node [left] {$1$}--(0.1,0.6);\n\t\\draw (0,1.2) node [left] {$2$}--(0.1,1.2);\n\t\\draw (0,1.8) node [left] {$3$}--(0.1,1.8);\n\t\\draw [domain=0:1] plot ({\\x*0.6},{2*\\x*\\x*0.6});\n\t\\draw (0.6,1.2)--(1.2,1.8);\n\t\\draw [dashed] (0.6,0)--(0.6,1.2)--(0,1.2);\n\t\\draw [dashed] (1.2,0)--(1.2,1.8)--(0,1.8);\n\t\\end{tikzpicture}}", "objs": [ "K0216001B", "K0216003B", @@ -94593,7 +94593,7 @@ }, "003875": { "id": "003875", - "content": "在长方体$ABCD-A_1B_1C_1D_1$中, $B_1C$和$C_1D$与底面所成的角分别为$60^\\circ$和$45^\\circ$, 则异面直线$B_1C$和$C_1D$所成的角的余弦值为\\blank{30}.\n\\fourch{$\\dfrac{\\sqrt{3}}6$}{$\\dfrac{\\sqrt{2}}{6}$}{$\\dfrac{\\sqrt{6}}{3}$}{$\\dfrac{\\sqrt{6}}{4}$}", + "content": "在长方体$ABCD-A_1B_1C_1D_1$中, $B_1C$和$C_1D$与底面所成的角分别为$60^\\circ$和$45^\\circ$, 则异面直线$B_1C$和$C_1D$所成的角的余弦值为\\bracket{20}.\n\\fourch{$\\dfrac{\\sqrt{3}}6$}{$\\dfrac{\\sqrt{2}}{6}$}{$\\dfrac{\\sqrt{6}}{3}$}{$\\dfrac{\\sqrt{6}}{4}$}", "objs": [], "tags": [ "第六单元" @@ -94614,7 +94614,7 @@ }, "003876": { "id": "003876", - "content": "(理科)甲、乙、丙、丁与小强一起比赛象棋, 每两人都要比赛一盘, 到现在为止, 甲已经赛了$4$盘, 乙赛了$3$盘, 丙赛了$2$盘, 丁赛了$1$盘, 则小强已经赛了\\blank{30}.\n\\fourch{$4$盘}{$3$盘}{$2$盘}{$1$盘}\\\\\n(文科)``$-2\\le a\\le 2$''是``实系数一元二次方程$x^2+ax+1=0$有虚根''的\\blank{30}.\n\\fourch{充要条件}{必要不充分条件}{充分不必要条件}{既不充分也不必要条件}", + "content": "(理科)甲、乙、丙、丁与小强一起比赛象棋, 每两人都要比赛一盘, 到现在为止, 甲已经赛了$4$盘, 乙赛了$3$盘, 丙赛了$2$盘, 丁赛了$1$盘, 则小强已经赛了\\bracket{20}.\n\\fourch{$4$盘}{$3$盘}{$2$盘}{$1$盘}\\\\\n(文科)``$-2\\le a\\le 2$''是``实系数一元二次方程$x^2+ax+1=0$有虚根''的\\bracket{20}.\n\\fourch{充要条件}{必要不充分条件}{充分不必要条件}{既不充分也不必要条件}", "objs": [], "tags": [ "第八单元" @@ -94635,7 +94635,7 @@ }, "003877": { "id": "003877", - "content": "已知点$P(x,y)$是直线$kx+y+4=0 \\ (k>0)$上一动点, $PA,PB$是圆$C:x^2+y^2-2y=0$的两条切线, $A,B$是切点, 若四边形$PACB$($C$为圆心)面积的最小值为$2$, 则$k$的值为\\blank{30}.\n\\fourch{$2$}{$\\dfrac{\\sqrt{21}}{2}$}{$2\\sqrt{2}$}{$3$}", + "content": "已知点$P(x,y)$是直线$kx+y+4=0 \\ (k>0)$上一动点, $PA,PB$是圆$C:x^2+y^2-2y=0$的两条切线, $A,B$是切点, 若四边形$PACB$($C$为圆心)面积的最小值为$2$, 则$k$的值为\\bracket{20}.\n\\fourch{$2$}{$\\dfrac{\\sqrt{21}}{2}$}{$2\\sqrt{2}$}{$3$}", "objs": [], "tags": [ "第七单元" @@ -94917,7 +94917,7 @@ }, "003890": { "id": "003890", - "content": "直线$\\begin{vmatrix}\nx & 0 & 1\\\\-1 & 2 & -1\\\\y & 1 & 1\n\\end{vmatrix}=0$的一个法向量是\\blank{30}.\n\\fourch{$(2,3)$}{$(3,-2)$}{$(-2,3)$}{$(3,2)$}", + "content": "直线$\\begin{vmatrix}\nx & 0 & 1\\\\-1 & 2 & -1\\\\y & 1 & 1\n\\end{vmatrix}=0$的一个法向量是\\bracket{20}.\n\\fourch{$(2,3)$}{$(3,-2)$}{$(-2,3)$}{$(3,2)$}", "objs": [], "tags": [ "暂无对应" @@ -94938,7 +94938,7 @@ }, "003891": { "id": "003891", - "content": "已知平面$\\alpha,\\beta$和直线$m$, 给出条件: \\textcircled{1} $m\\parallel \\alpha$; \\textcircled{2} $m\\perp \\alpha$; \\textcircled{3} $m\\subseteq \\alpha$; \\textcircled{4} $\\alpha\\perp \\beta$; \\textcircled{5} $\\alpha\\parallel\\beta$. 由给出的两个条件能推导出$m\\parallel \\beta$的是\\blank{30}.\n\\fourch{\\textcircled{1}\\textcircled{4}}{\\textcircled{1}\\textcircled{5}}{\\textcircled{2}\\textcircled{4}}{\\textcircled{3}\\textcircled{5}}", + "content": "已知平面$\\alpha,\\beta$和直线$m$, 给出条件: \\textcircled{1} $m\\parallel \\alpha$; \\textcircled{2} $m\\perp \\alpha$; \\textcircled{3} $m\\subseteq \\alpha$; \\textcircled{4} $\\alpha\\perp \\beta$; \\textcircled{5} $\\alpha\\parallel\\beta$. 由给出的两个条件能推导出$m\\parallel \\beta$的是\\bracket{20}.\n\\fourch{\\textcircled{1}\\textcircled{4}}{\\textcircled{1}\\textcircled{5}}{\\textcircled{2}\\textcircled{4}}{\\textcircled{3}\\textcircled{5}}", "objs": [], "tags": [ "第六单元" @@ -94959,7 +94959,7 @@ }, "003892": { "id": "003892", - "content": "已知函数$f(x)$是定义在$(-\\infty,0)\\cup (0,+\\infty)$上的偶函数, 当$x>0$时, $f(x)=\\begin{cases}\n2^{|x-1|}-1, & 02,\n\\end{cases}$ 则函数$g(x)=4f(x)-1$的零点的个数为\\blank{30}.\n\\fourch{$4$}{$6$}{$8$}{$10$}", + "content": "已知函数$f(x)$是定义在$(-\\infty,0)\\cup (0,+\\infty)$上的偶函数, 当$x>0$时, $f(x)=\\begin{cases}\n2^{|x-1|}-1, & 02,\n\\end{cases}$ 则函数$g(x)=4f(x)-1$的零点的个数为\\bracket{20}.\n\\fourch{$4$}{$6$}{$8$}{$10$}", "objs": [ "K0216005B", "K0223001B" @@ -95247,7 +95247,7 @@ }, "003905": { "id": "003905", - "content": "已知条件$p: |x+1|>2$, 条件$q: x>a$, 且$\\bar{p}$是$\\bar{q}$的充分不必要条件, 则$a$的取值范围可以是\\blank{30}.\n\\fourch{$a\\ge 1$}{$a\\le 1$}{$a\\ge -1$}{$a\\le -3$}", + "content": "已知条件$p: |x+1|>2$, 条件$q: x>a$, 且$\\bar{p}$是$\\bar{q}$的充分不必要条件, 则$a$的取值范围可以是\\bracket{20}.\n\\fourch{$a\\ge 1$}{$a\\le 1$}{$a\\ge -1$}{$a\\le -3$}", "objs": [ "K0106003B" ], @@ -95270,7 +95270,7 @@ }, "003906": { "id": "003906", - "content": "已知$\\{a_n\\}$是以$a \\ (a>0)$为首项以$q \\ (-10)$为首项以$q \\ (-1=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [above left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:75] plot ({\\x/90},{ln(cos(\\x))});\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[samples=200,>=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [above left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:0] plot ({\\x/90},{ln(cos(\\x))});\n\t\\draw [domain=0:75] plot ({\\x/90},{-ln(cos(\\x))});\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[samples=200,>=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [below left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:0] plot ({\\x/90},{-ln(cos(\\x))});\n\t\\draw [domain=0:75] plot ({\\x/90},{ln(cos(\\x))});\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[samples=200,>=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [below left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:75] plot ({\\x/90},{-ln(cos(\\x))});\n\t\\end{tikzpicture}}", + "content": "函数$y=\\ln(\\cos x) \\ \\left(-\\dfrac{\\pi}{2}=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [above left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:75] plot ({\\x/90},{ln(cos(\\x))});\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[samples=200,>=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [above left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:0] plot ({\\x/90},{ln(cos(\\x))});\n\t\\draw [domain=0:75] plot ({\\x/90},{-ln(cos(\\x))});\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[samples=200,>=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [below left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:0] plot ({\\x/90},{-ln(cos(\\x))});\n\t\\draw [domain=0:75] plot ({\\x/90},{ln(cos(\\x))});\n\t\\end{tikzpicture}}{\\begin{tikzpicture}[samples=200,>=stealth]\n\t\\draw [->](-1.5,0)--(0,0) node [below left] {$O$}--(1.5,0) node [below] {$x$};\n\t\\draw [->](0,-1.5)--(0,1.5) node [left] {$y$};\n\t\\draw [dashed] (-1,-1.5)--(-1,1.5) (1,-1.5)--(1,1.5);\n\t\\draw (-1,0) node [below left] {$-\\dfrac{\\pi}{2}$};\n\t\\draw (1,0) node [below right] {$\\dfrac{\\pi}{2}$};\n\t\\draw [domain=-75:75] plot ({\\x/90},{-ln(cos(\\x))});\n\t\\end{tikzpicture}}", "objs": [ "K0216003B" ], @@ -95947,7 +95947,7 @@ }, "003937": { "id": "003937", - "content": "在实数集$\\mathbf{R}$上定义运算$\\otimes: x\\otimes y=2x^2+y^2+1-y$, 则满足$x\\otimes y=y\\otimes x$的实数对$(x,y)$在平面直角坐标系中对应点的轨迹为\\blank{30}.\n\\fourch{双曲线}{一条直线}{两条直线}{以上都不对}", + "content": "在实数集$\\mathbf{R}$上定义运算$\\otimes: x\\otimes y=2x^2+y^2+1-y$, 则满足$x\\otimes y=y\\otimes x$的实数对$(x,y)$在平面直角坐标系中对应点的轨迹为\\bracket{20}.\n\\fourch{双曲线}{一条直线}{两条直线}{以上都不对}", "objs": [], "tags": [ "第七单元" @@ -96226,7 +96226,7 @@ }, "003950": { "id": "003950", - "content": "若$m,n$为两条不同的直线, $\\alpha,\\beta$为两个不同的平面, 则以下命题正确的是\\blank{30}.\n\\twoch{若$m\\parallel \\alpha$, $n\\parallel\\alpha$, 则$m\\parallel n$}{若$m\\parallel \\beta$, $\\alpha\\parallel\\beta$, 则$m\\parallel\\alpha$}{若$m\\parallel n$, $m\\perp \\alpha$, 则$n\\perp \\alpha$}{若$\\alpha\\cap\\beta=m$, $m\\perp n$, 则$n\\perp\\alpha$}", + "content": "若$m,n$为两条不同的直线, $\\alpha,\\beta$为两个不同的平面, 则以下命题正确的是\\bracket{20}.\n\\twoch{若$m\\parallel \\alpha$, $n\\parallel\\alpha$, 则$m\\parallel n$}{若$m\\parallel \\beta$, $\\alpha\\parallel\\beta$, 则$m\\parallel\\alpha$}{若$m\\parallel n$, $m\\perp \\alpha$, 则$n\\perp \\alpha$}{若$\\alpha\\cap\\beta=m$, $m\\perp n$, 则$n\\perp\\alpha$}", "objs": [], "tags": [ "第六单元" @@ -96247,7 +96247,7 @@ }, "003951": { "id": "003951", - "content": "双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$的左焦点为$F_1$, 顶点为$A_1,A_2$, $P$是该双曲线右支上任意一点, 则分别以线段$PF_1,A_1A_2$为直径的两圆一定\\blank{30}.\n\\fourch{相交}{内切}{外切}{相离}", + "content": "双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$的左焦点为$F_1$, 顶点为$A_1,A_2$, $P$是该双曲线右支上任意一点, 则分别以线段$PF_1,A_1A_2$为直径的两圆一定\\bracket{20}.\n\\fourch{相交}{内切}{外切}{相离}", "objs": [], "tags": [ "第七单元" @@ -96268,7 +96268,7 @@ }, "003952": { "id": "003952", - "content": "方程$x^2+\\sqrt{2}x-1=0$的解可视为函数$y=x+\\sqrt{2}$的图像与函数$y=\\dfrac 1x$的图像交点的横坐标, 若$x^4+ax-4=0$的各个实根$x_1,x_2,\\cdots,x_k \\ (k\\le 4)$所对应的点$\\left(x_i,\\dfrac{4}{x_i}\\right) \\ (i=1,2,\\cdots,k)$均在直线$y=x$的同侧, 则实数$a$的取值范围是\\blank{30}.\n\\fourch{$(-\\infty,-6)$}{$(6,+\\infty)$}{$[-6,6]$}{$(-\\infty,-6)\\cup (6,+\\infty)$}", + "content": "方程$x^2+\\sqrt{2}x-1=0$的解可视为函数$y=x+\\sqrt{2}$的图像与函数$y=\\dfrac 1x$的图像交点的横坐标, 若$x^4+ax-4=0$的各个实根$x_1,x_2,\\cdots,x_k \\ (k\\le 4)$所对应的点$\\left(x_i,\\dfrac{4}{x_i}\\right) \\ (i=1,2,\\cdots,k)$均在直线$y=x$的同侧, 则实数$a$的取值范围是\\bracket{20}.\n\\fourch{$(-\\infty,-6)$}{$(6,+\\infty)$}{$[-6,6]$}{$(-\\infty,-6)\\cup (6,+\\infty)$}", "objs": [], "tags": [ "第七单元" @@ -96428,7 +96428,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{11\\pi}6$", "solution": "", "duration": -1, "usages": [ @@ -96563,7 +96563,7 @@ }, "003965": { "id": "003965", - "content": "(文科)已知非零实数$a,b$满足$a>b$. 则下列不等式中成立的是\\blank{30}.\n\\fourch{$a^2>b^2$}{$\\dfrac 1a<\\dfrac 1b$}{$a^2b>ab^2$}{$\\dfrac{a}{b^2}>\\dfrac{b}{a^2}$}\\\\\n(理科)对任意的实数$\\alpha,\\beta$, 下列等式恒成立的是\\blank{30}.\n\\twoch{$2\\sin\\alpha\\cdot\\cos\\beta=\\sin(\\alpha+\\beta)+\\sin(\\alpha-\\beta)$}{$2\\cos\\alpha\\cdot\\sin\\beta=\\sin(\\alpha+\\beta)+\\cos(\\alpha-\\beta)$}{$\\cos\\alpha+\\cos\\beta=2\\sin\\dfrac{\\alpha+\\beta}{2}\\cdot\\sin\\dfrac{\\alpha-\\beta}{2}$}{$\\cos\\alpha-\\cos\\beta=2\\cos\\dfrac{\\alpha+\\beta}{2}\\cdot\\cos\\dfrac{\\alpha-\\beta}{2}$}", + "content": "(文科)已知非零实数$a,b$满足$a>b$. 则下列不等式中成立的是\\bracket{20}.\n\\fourch{$a^2>b^2$}{$\\dfrac 1a<\\dfrac 1b$}{$a^2b>ab^2$}{$\\dfrac{a}{b^2}>\\dfrac{b}{a^2}$}\\\\\n(理科)对任意的实数$\\alpha,\\beta$, 下列等式恒成立的是\\bracket{20}.\n\\twoch{$2\\sin\\alpha\\cdot\\cos\\beta=\\sin(\\alpha+\\beta)+\\sin(\\alpha-\\beta)$}{$2\\cos\\alpha\\cdot\\sin\\beta=\\sin(\\alpha+\\beta)+\\cos(\\alpha-\\beta)$}{$\\cos\\alpha+\\cos\\beta=2\\sin\\dfrac{\\alpha+\\beta}{2}\\cdot\\sin\\dfrac{\\alpha-\\beta}{2}$}{$\\cos\\alpha-\\cos\\beta=2\\cos\\dfrac{\\alpha+\\beta}{2}\\cdot\\cos\\dfrac{\\alpha-\\beta}{2}$}", "objs": [ "K0111003B", "K0313002B", @@ -96588,7 +96588,7 @@ }, "003966": { "id": "003966", - "content": "(理科)已知函数$f(x)$是定义在$\\mathbf{R}$上的单调递减函数且为奇函数, 数列$\\{a_n\\}$是等差数列, $a_{1007}>0$, 则$f(a_1)+f(a_2)+f(a_3)+\\cdots+f(a_{2012})+f(a_{2013})$的值\\blank{30}.\n\\fourch{恒为正数}{恒为负数}{恒为$0$}{可正可负}", + "content": "(理科)已知函数$f(x)$是定义在$\\mathbf{R}$上的单调递减函数且为奇函数, 数列$\\{a_n\\}$是等差数列, $a_{1007}>0$, 则$f(a_1)+f(a_2)+f(a_3)+\\cdots+f(a_{2012})+f(a_{2013})$的值\\bracket{20}.\n\\fourch{恒为正数}{恒为负数}{恒为$0$}{可正可负}", "objs": [], "tags": [ "第二单元" @@ -96609,7 +96609,7 @@ }, "003967": { "id": "003967", - "content": "已知$A,B$为平面内两定点, 过该平面内动点$M$作直线$AB$的垂线, 垂足为$N$. 若$\\overrightarrow{MN}^2=\\lambda \\overrightarrow{AN}\\cdot\\overrightarrow{NB}$, 其中$\\lambda$为常数, 则动点$M$的轨迹不可能是\\blank{50}.\n\\fourch{圆}{椭圆}{抛物线}{双曲线}", + "content": "已知$A,B$为平面内两定点, 过该平面内动点$M$作直线$AB$的垂线, 垂足为$N$. 若$\\overrightarrow{MN}^2=\\lambda \\overrightarrow{AN}\\cdot\\overrightarrow{NB}$, 其中$\\lambda$为常数, 则动点$M$的轨迹不可能是\\bracket{20}.\n\\fourch{圆}{椭圆}{抛物线}{双曲线}", "objs": [], "tags": [ "第五单元" @@ -96885,7 +96885,7 @@ }, "003980": { "id": "003980", - "content": "(理科)在极坐标系中, ``点$P$是极点''是``点$P$的极坐标是$(0,0)$''成立的\\blank{30}.\n\\fourch{充分不必要条件}{必要不充分条件}{充要条件}{既不充分也不必要条件}\\\\\n(文科)$\\overrightarrow a,\\overrightarrow b$为非零向量, ``函数$f(x)=(x\\overrightarrow a+\\overrightarrow b)^2$为偶函数''是``$\\overrightarrow a\\perp \\overrightarrow b$''的\\blank{30}.\n\\fourch{充分不必要条件}{必要不充分条件}{充要条件}{既不充分也不必要条件}", + "content": "(理科)在极坐标系中, ``点$P$是极点''是``点$P$的极坐标是$(0,0)$''成立的\\bracket{20}.\n\\fourch{充分不必要条件}{必要不充分条件}{充要条件}{既不充分也不必要条件}\\\\\n(文科)$\\overrightarrow a,\\overrightarrow b$为非零向量, ``函数$f(x)=(x\\overrightarrow a+\\overrightarrow b)^2$为偶函数''是``$\\overrightarrow a\\perp \\overrightarrow b$''的\\bracket{20}.\n\\fourch{充分不必要条件}{必要不充分条件}{充要条件}{既不充分也不必要条件}", "objs": [ "K0106003B", "K0504006B", @@ -96915,7 +96915,7 @@ }, "003981": { "id": "003981", - "content": "(理科)在方程为$\\begin{cases}\nx=\\sin 2\\theta,\\\\ y=\\sin\\theta+\\cos\\theta\n\\end{cases}$的曲线上的点是\\blank{30}.\n\\fourch{$(2,\\sqrt{3})$}{$(1,\\sqrt{3})$}{$\\left(-\\dfrac 34,\\dfrac 12\\right)$}{$\\left(\\dfrac 12,-\\sqrt{2}\\right)$}\\\\\n(文科)若函数$y=f(x)$存在反函数, 则方程$f(x)=c$($c$为常数)\\blank{30}.\n\\fourch{有且只有一个实根}{至少有一个实根}{至多有一个实根}{没有实数根}", + "content": "(理科)在方程为$\\begin{cases}\nx=\\sin 2\\theta,\\\\ y=\\sin\\theta+\\cos\\theta\n\\end{cases}$的曲线上的点是\\bracket{20}.\n\\fourch{$(2,\\sqrt{3})$}{$(1,\\sqrt{3})$}{$\\left(-\\dfrac 34,\\dfrac 12\\right)$}{$\\left(\\dfrac 12,-\\sqrt{2}\\right)$}\\\\\n(文科)若函数$y=f(x)$存在反函数, 则方程$f(x)=c$($c$为常数)\\bracket{20}.\n\\fourch{有且只有一个实根}{至少有一个实根}{至多有一个实根}{没有实数根}", "objs": [], "tags": [ "第二单元", @@ -96937,7 +96937,7 @@ }, "003982": { "id": "003982", - "content": "设$M$是球$O$半径$OP$的中点, 分别过$M,O$作垂直于$OP$的平面, 截球面得两个圆, 则这两个圆的面积比值为\\blank{30}.\n\\fourch{$\\dfrac 14$}{$\\dfrac 12$}{$\\dfrac 23$}{$\\dfrac 34$}", + "content": "设$M$是球$O$半径$OP$的中点, 分别过$M,O$作垂直于$OP$的平面, 截球面得两个圆, 则这两个圆的面积比值为\\bracket{20}.\n\\fourch{$\\dfrac 14$}{$\\dfrac 12$}{$\\dfrac 23$}{$\\dfrac 34$}", "objs": [], "tags": [ "第六单元" @@ -97214,7 +97214,7 @@ }, "003995": { "id": "003995", - "content": "对于两条不相交的空间直线$a$和$b$, 一定存在平面$\\alpha$, 使得\\blank{30}.\n\\twoch{直线$a,b$均在平面$\\alpha$内}{直线$a$在平面$\\alpha$内, $b$与平面$\\alpha$平行}{直线$a,b$都垂直于平面$\\alpha$}{直线$a$在平面$\\alpha$内, $b$与平面$\\alpha$垂直}", + "content": "对于两条不相交的空间直线$a$和$b$, 一定存在平面$\\alpha$, 使得\\bracket{20}.\n\\twoch{直线$a,b$均在平面$\\alpha$内}{直线$a$在平面$\\alpha$内, $b$与平面$\\alpha$平行}{直线$a,b$都垂直于平面$\\alpha$}{直线$a$在平面$\\alpha$内, $b$与平面$\\alpha$垂直}", "objs": [], "tags": [ "第七单元" @@ -97235,7 +97235,7 @@ }, "003996": { "id": "003996", - "content": "过球面上两点作球的大圆, 可能的个数是\\blank{30}.\n\\fourch{有且只有一个}{一个或无穷多个}{无数个}{以上结论都不正确}", + "content": "过球面上两点作球的大圆, 可能的个数是\\bracket{20}.\n\\fourch{有且只有一个}{一个或无穷多个}{无数个}{以上结论都不正确}", "objs": [], "tags": [ "第六单元" @@ -97256,7 +97256,7 @@ }, "003997": { "id": "003997", - "content": "如果$\\left(3x^2-\\dfrac{2}{x^3}\\right)^n$的展开式中含有非零常数项, 那么正整数$n$的最小值为\\blank{30}.\n\\fourch{$10$}{$6$}{$5$}{$3$}", + "content": "如果$\\left(3x^2-\\dfrac{2}{x^3}\\right)^n$的展开式中含有非零常数项, 那么正整数$n$的最小值为\\bracket{20}.\n\\fourch{$10$}{$6$}{$5$}{$3$}", "objs": [], "tags": [ "第八单元" @@ -100756,7 +100756,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $S=1200\\sqrt{3}\\sin(2\\theta+\\dfrac\\pi 6)-600\\sqrt{3}, \\ \\theta \\in (0,\\dfrac \\pi 3)$; (2) $S$的最大值为$600\\sqrt{3}$(平方米), 相应的$\\theta$的值为$\\dfrac{\\pi}6$.", "solution": "", "duration": -1, "usages": [ @@ -101848,7 +101848,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\log_2 \\dfrac 43$; (2) $[3-\\sqrt{5},3+\\sqrt{5}]$; (3) $1$.", "solution": "", "duration": -1, "usages": [ @@ -106781,7 +106781,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -107465,7 +107465,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,0]\\cup [4,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -109484,7 +109484,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 34$", "solution": "", "duration": -1, "usages": [ @@ -110877,7 +110877,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\cos(\\alpha-\\beta)=\\dfrac 45$; (2) $\\cos\\alpha=\\dfrac 35$, $\\cos\\beta = \\dfrac 45$.", "solution": "", "duration": -1, "usages": [ @@ -112755,7 +112755,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-x^2+x$", "solution": "", "duration": -1, "usages": [ @@ -113257,7 +113257,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 45$", "solution": "", "duration": -1, "usages": [ @@ -114022,7 +114022,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{3\\sqrt{5}}5+3$", "solution": "", "duration": -1, "usages": [ @@ -114221,7 +114221,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-1$; (2) $1$; (3) $[8,9)$.", "solution": "", "duration": -1, "usages": [ @@ -117075,7 +117075,7 @@ "tags": [ "第一单元" ], - "genre": "选择题", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -124004,7 +124004,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -126670,7 +126670,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -130645,7 +130645,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$y=a(\\dfrac{4900}v+0.01v), \\ v\\in (0,+\\infty)$; 总耗费最小时, 飞行速度为$700$千米$/$时.", "solution": "", "duration": -1, "usages": [], @@ -135844,7 +135844,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -136085,7 +136085,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1)\\cup (1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -143306,7 +143306,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -143384,7 +143384,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{x|x=2k\\pi-\\dfrac\\pi 3, \\ k\\in \\mathbf{Z}\\}$", "solution": "", "duration": -1, "usages": [ @@ -143443,7 +143443,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -144511,7 +144511,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -144610,7 +144610,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -145564,7 +145564,7 @@ }, "006000": { "id": "006000", - "content": "函数$y=\\lg (1-\\sin x)-\\lg (1+\\sin x)$(.)\n\\twoch{是奇函数, 但非偶函数}{是偶函数, 但非奇函数}{既不是奇函数, 也不是偶函数}{奇偶性无法确定}", + "content": "函数$y=\\lg (1-\\sin x)-\\lg (1+\\sin x)$\\bracket{20}.\n\\twoch{是奇函数, 但非偶函数}{是偶函数, 但非奇函数}{既不是奇函数, 也不是偶函数}{奇偶性无法确定}", "objs": [], "tags": [ "第三单元" @@ -148032,7 +148032,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{33}{65}$", "solution": "", "duration": -1, "usages": [ @@ -148290,7 +148290,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{13}3$", "solution": "", "duration": -1, "usages": [], @@ -148357,7 +148357,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -148548,7 +148548,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$2-\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -148750,7 +148750,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 35$", "solution": "", "duration": -1, "usages": [ @@ -149125,7 +149125,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$p-q+1=0$且$p^2\\ge 4q$($q\\ne 1$可写可不写)", "solution": "", "duration": -1, "usages": [], @@ -149194,7 +149194,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -149447,7 +149447,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -149722,7 +149722,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{17}{4}$", "solution": "", "duration": -1, "usages": [], @@ -150234,7 +150234,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{13}{144}$", "solution": "", "duration": -1, "usages": [], @@ -151772,7 +151772,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -151829,7 +151829,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -155650,7 +155650,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$x=\\pi+\\arcsin \\dfrac 13$", "solution": "因为$\\sin (\\pi -x)=\\sin x=-\\dfrac 13$, 且由$\\pi =latex,scale = 0.5]\n\\draw [->] (-1,0) -- (15,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:720] plot ({\\x/180*pi},{2*sin(\\x/2)});\n\\draw [dashed] (pi,0) node [below] {$\\pi$} -- (pi,2) -- (0,2) node [left] {$2$};\n\\draw [dashed] ({3*pi},0) node [above] {$3\\pi$} -- ({3*pi},-2) -- (0,-2) node [left] {$-2$};\n\\draw ({4*pi},0) node [above] {$4\\pi$} ({2*pi},0) node [below left] {$2\\pi$};\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [], @@ -196710,7 +196710,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{x|x=-\\dfrac \\pi 4+k\\pi, \\ k\\in \\mathbf{Z}\\}$", "solution": "", "duration": -1, "usages": [ @@ -215439,7 +215439,7 @@ }, "009180": { "id": "009180", - "content": "若$O_1$为正方体$ABCD-A_1B_1C_1D_1$的面$A_1B_1C_1D_1$的中心, 则直线$BC_1$与对角面$BB_1D_1D$所成的角等于\n\\fourch{$\\angle C_1BD_1$}{$\\angle C_1BO_1$ }{$\\angle C_1BB_1$ }{$\\angle C_1BD$}", + "content": "若$O_1$为正方体$ABCD-A_1B_1C_1D_1$的面$A_1B_1C_1D_1$的中心, 则直线$BC_1$与对角面$BB_1D_1D$所成的角等于\\bracket{20}.\n\\fourch{$\\angle C_1BD_1$}{$\\angle C_1BO_1$ }{$\\angle C_1BB_1$ }{$\\angle C_1BD$}", "objs": [], "tags": [ "第六单元" @@ -223533,7 +223533,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -223854,7 +223854,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$(4,-3)$", "solution": "", "duration": -1, "usages": [ @@ -223891,7 +223891,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $x=2k\\pi-\\dfrac \\pi 3$或$2k\\pi-\\dfrac{2\\pi}3, \\ k\\in \\mathbf{Z}$; (2) $x=2k\\pi\\pm \\dfrac{2\\pi}3, \\ k\\in \\mathbf{Z}$; (3) $x=k\\pi-\\dfrac \\pi 3, \\ k\\in \\mathbf{Z}$.", "solution": "", "duration": -1, "usages": [ @@ -236558,7 +236558,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}", "solution": "", "duration": -1, "usages": [], @@ -236631,7 +236631,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,1)$", "solution": "", "duration": -1, "usages": [], @@ -238405,7 +238405,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-$; (2) $-$; (3) $+$.", "solution": "", "duration": -1, "usages": [ @@ -238506,7 +238506,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$(\\sin\\alpha,\\cos\\alpha)=(\\dfrac{\\sqrt{5}}5,-\\dfrac{2\\sqrt{5}}5)$或$(-\\dfrac{\\sqrt{5}}5,\\dfrac{2\\sqrt{5}}5)$", "solution": "", "duration": -1, "usages": [ @@ -238658,7 +238658,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $0$; (2) $\\sin\\alpha$; (3) $\\cot\\alpha$; (4) $-\\tan\\alpha$", "solution": "", "duration": -1, "usages": [ @@ -238718,7 +238718,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$60^\\circ$或$150^\\circ$", "solution": "", "duration": -1, "usages": [ @@ -238822,7 +238822,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\alpha+\\beta=2k\\pi, \\ k\\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [ @@ -238946,7 +238946,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{2}{\\cos\\alpha}$", "solution": "", "duration": -1, "usages": [ @@ -238984,7 +238984,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\sin\\alpha=\\dfrac 45$, $\\cos\\alpha=-\\dfrac 35$.", "solution": "", "duration": -1, "usages": [ @@ -239787,7 +239787,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $x=\\arcsin \\dfrac 25$或$\\pi-\\arcsin \\dfrac 25$; (2) $x=\\pi\\pm \\arccos\\dfrac 23$; (3) $x=-\\arctan \\dfrac 12+k\\pi, \\ k\\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [ @@ -243422,7 +243422,7 @@ }, "010438": { "id": "010438", - "content": "若平面$\\alpha$与平面$\\beta$、$\\gamma$都相交, 则这三个平面的交线可能有几条? \n\\fourch{$1$条或$2$条}{$2$条或$3$条}{$1$条或$3$条}{$1$条或$2$条或$3$条}", + "content": "若平面$\\alpha$与平面$\\beta$、$\\gamma$都相交, 则这三个平面的交线可能有\\bracket{20}条. \n\\fourch{$1$条或$2$条}{$2$条或$3$条}{$1$条或$3$条}{$1$条或$2$条或$3$条}", "objs": [], "tags": [ "第六单元" @@ -268062,7 +268062,7 @@ }, "011551": { "id": "011551", - "content": "已知点$M(a,b)$与点$N(0,-1)$在直线的两侧, 给出以下结论:\n\\textcircled{1} $3a-4b+5>0$;\\\\\n\\textcircled{2} 当$a>0$时, $a+b$有最小值, 无最大值;\\\\\n\\textcircled{3} $a^2+b^2>1$;\\\\\n\\textcircled{4} 当$a>0$且$a\\ne 1$时, $\\dfrac{b+1}{a-1}$的取值范围是$(-\\infty,-\\dfrac 94)\\cup (\\dfrac 34,+\\infty)$;\\\\\n正确的个数是\n\\fourch{$1$}{$2$}{$3$}{$4$}", + "content": "已知点$M(a,b)$与点$N(0,-1)$在直线的两侧, 给出以下结论:\n\\textcircled{1} $3a-4b+5>0$;\\\\\n\\textcircled{2} 当$a>0$时, $a+b$有最小值, 无最大值;\\\\\n\\textcircled{3} $a^2+b^2>1$;\\\\\n\\textcircled{4} 当$a>0$且$a\\ne 1$时, $\\dfrac{b+1}{a-1}$的取值范围是$(-\\infty,-\\dfrac 94)\\cup (\\dfrac 34,+\\infty)$;\\\\\n正确的个数是\\bracket{20}.\n\\fourch{$1$}{$2$}{$3$}{$4$}", "objs": [], "tags": [ "" @@ -282942,7 +282942,7 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2197.2\\text{m}/\\text{s}$; (2) $53.6$倍.", "solution": "", "duration": -1, "usages": [], @@ -282965,7 +282965,7 @@ "" ], "genre": "解答题", - "ans": "", + "ans": "(1) $19$万元; (2) 当促销费为$7$万元时, 该网店售出商品的总利润最大, 此时商品的剩余量为$0.25$万件.", "solution": "", "duration": -1, "usages": [], @@ -283124,7 +283124,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{5\\pi}{6}$, $10$, 钝, $\\dfrac{\\pi}{24}$", "solution": "", "duration": -1, "usages": [