From d08723e04e2e4f4222783c779ee0d1d0e8841da1 Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Thu, 16 Mar 2023 11:56:49 +0800 Subject: [PATCH] 20230316 noon --- 工具/修改题目数据库.ipynb | 6 +- 工具/寻找tex文件中未赋答案的题目.ipynb | 334 +------------- 工具/批量添加题库字段数据.ipynb | 243 +++------- 工具/文本文件/metadata.txt | 605 +++++-------------------- 题库0.3/Problems.json | 344 +++++++------- 5 files changed, 363 insertions(+), 1169 deletions(-) diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb index 84f0ee86..92ab8f7f 100644 --- a/工具/修改题目数据库.ipynb +++ b/工具/修改题目数据库.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 4, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -19,7 +19,7 @@ "source": [ "import os,re,json\n", "\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n", - "problems = \"14762\"\n", + "problems = \"31310\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", 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 7444eb94..6f096bbf 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 @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -134,339 +134,9 @@ "07_三角函数.tex\n", "08_平面向量与复数.tex\n", "09_立体几何综合.tex\n", - "013175\n", - "\n", - "\n", - "013178\n", - "\n", - "\n", - "031234\n", - "\n", - "\n", - "014028\n", - "\n", - "\n", - "014419\n", - "\n", - "\n", - "014426\n", - "\n", - "\n", - "014354\n", - "\n", - "\n", - "014410\n", - "\n", - "\n", - "013180\n", - "\n", - "\n", - "014042\n", - "\n", - "\n", - "014415\n", - "\n", - "\n", - "014044\n", - "\n", - "\n", - "014432\n", - "\n", - "\n", - "014049\n", - "\n", - "\n", - "014454\n", - "\n", - "\n", - "013187\n", - "\n", - "\n", - "014346\n", - "\n", - "\n", - "014427\n", - "\n", - "\n", - "014051\n", - "\n", - "\n", - "014056\n", - "\n", - "\n", - "014412\n", - "\n", - "\n", - "013183\n", - "\n", - "\n", - "014423\n", - "\n", - "\n", - "014435\n", - "\n", - "\n", - "031235\n", - "\n", - "\n", - "014359\n", - "\n", - "\n", - "014055\n", - "\n", - "\n", - "014352\n", - "\n", - "\n", - "014053\n", - "\n", - "\n", - "014037\n", - "\n", - "\n", "10_空间向量与应用.tex\n", - "014040\n", - "\n", - "\n", - "014039\n", - "\n", - "\n", - "014448\n", - "\n", - "\n", - "014436\n", - "\n", - "\n", - "014437\n", - "\n", - "\n", - "014451\n", - "\n", - "\n", - "014047\n", - "\n", - "\n", - "014452\n", - "\n", - "\n", - "014349\n", - "\n", - "\n", - "014455\n", - "\n", - "\n", - "014440\n", - "\n", - "\n", - "014439\n", - "\n", - "\n", - "014041\n", - "\n", - "\n", - "014045\n", - "\n", - "\n", - "014438\n", - "\n", - "\n", - "014441\n", - "\n", - "\n", - "014050\n", - "\n", - "\n", - "014348\n", - "\n", - "\n", - "014443\n", - "\n", - "\n", - "014360\n", - "\n", - "\n", "11_直线与圆.tex\n", - "014367\n", - "\n", - "\n", - "013058\n", - "\n", - "\n", - "013059\n", - "\n", - "\n", - "013969\n", - "\n", - "\n", - "031227\n", - "\n", - "\n", - "013060\n", - "\n", - "\n", - "013073\n", - "\n", - "\n", - "013074\n", - "\n", - "\n", - "013972\n", - "\n", - "\n", - "013062\n", - "\n", - "\n", - "013974\n", - "\n", - "\n", - "014377\n", - "\n", - "\n", - "014364\n", - "\n", - "\n", - "013066\n", - "\n", - "\n", - "013976\n", - "\n", - "\n", - "013970\n", - "\n", - "\n", - "013070\n", - "\n", - "\n", - "013071\n", - "\n", - "\n", - "014369\n", - "\n", - "\n", - "014373\n", - "\n", - "\n", - "013104\n", - "\n", - "\n", - "013069\n", - "\n", - "\n", - "013105\n", - "\n", - "\n", - "013063\n", - "\n", - "\n", - "031228\n", - "\n", - "\n", - "013076\n", - "\n", - "\n", - "031229\n", - "\n", - "\n", - "013077\n", - "\n", - "\n", - "013101\n", - "\n", - "\n", - "014366\n", - "\n", - "\n", "12_圆锥曲线.tex\n", - "013079\n", - "\n", - "\n", - "013090\n", - "\n", - "\n", - "013120\n", - "\n", - "\n", - "013081\n", - "\n", - "\n", - "013137\n", - "\n", - "\n", - "013084\n", - "\n", - "\n", - "013085\n", - "\n", - "\n", - "031230\n", - "\n", - "\n", - "013096\n", - "\n", - "\n", - "013097\n", - "\n", - "\n", - "013099\n", - "\n", - "\n", - "013130\n", - "\n", - "\n", - "013981\n", - "\n", - "\n", - "013134\n", - "\n", - "\n", - "013146\n", - "\n", - "\n", - "013102\n", - "\n", - "\n", - "013093\n", - "\n", - "\n", - "013139\n", - "\n", - "\n", - "013114\n", - "\n", - "\n", - "013082\n", - "\n", - "\n", - "013083\n", - "\n", - "\n", - "031231\n", - "\n", - "\n", - "013095\n", - "\n", - "\n", - "031232\n", - "\n", - "\n", - "013988\n", - "\n", - "\n", - "013131\n", - "\n", - "\n", - "013128\n", - "\n", - "\n", - "014464\n", - "\n", - "\n", - "013990\n", - "\n", - "\n", - "003629\n", - "\n", - "\n", "13_解析几何综合.tex\n", "013997\n", "\n", @@ -731,6 +401,8 @@ "高三下学期月考01.tex\n", "高三下学期测验01.tex\n", "高三下学期测验02.tex\n", + "高三下学期测验03.tex\n", + "高三下学期测验05.tex\n", "高三下学期周末卷01.tex\n", "高三下学期周末卷02.tex\n", "高三下学期周末卷03.tex\n", 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 ae8b5244..c20ec519 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 @@ -2,193 +2,74 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.667\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.788\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.939\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.818\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.970\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.818\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.879\t0.697\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.727\t0.424\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.364\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.212\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.515\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.667\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.606\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.545\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三10班\t0.242\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.600\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.500\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.650\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.950\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t1.000\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.700\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.950\t0.550\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.850\t0.450\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.200\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.100\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.500\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.750\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.600\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.450\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三11班\t0.200\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.556\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.667\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.667\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.778\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.889\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.667\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.944\t0.778\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.833\t0.611\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.389\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.167\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.722\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.833\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.611\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.667\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三12班\t0.556\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.722\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.833\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.944\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t1.000\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.944\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t1.000\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t1.000\t0.889\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t1.000\t0.833\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.722\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.444\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.889\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.889\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.889\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.833\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三01班\t0.778\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.625\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.906\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t1.000\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.906\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.781\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.875\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.906\t0.656\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.969\t0.719\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.438\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.469\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.625\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.688\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.781\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.688\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三02班\t0.625\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.640\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.800\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.840\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.960\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.800\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.880\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.680\t0.440\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.880\t0.760\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.560\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.480\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.680\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.800\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.680\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.840\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三03班\t0.640\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.667\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.722\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.889\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.889\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.889\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.667\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.556\t0.333\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t1.000\t0.500\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.167\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.278\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.722\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.778\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.667\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.611\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三04班\t0.500\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.789\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.868\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.921\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.921\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.895\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.921\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.974\t0.816\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.789\t0.474\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.447\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.342\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.816\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.763\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.789\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.553\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三05班\t0.658\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.625\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.750\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.969\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.844\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.875\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.750\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.656\t0.750\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.844\t0.531\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.281\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.156\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.812\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.812\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.656\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.531\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三06班\t0.531\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.448\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.483\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.621\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.966\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.897\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.828\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.690\t0.828\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.862\t0.655\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.379\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.207\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.690\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.759\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.552\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.828\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三07班\t0.379\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.760\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.760\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.840\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.960\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.800\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.920\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t1.000\t0.720\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t1.000\t0.560\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.440\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.320\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.800\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.800\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.600\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.560\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三08班\t0.640\n", - "题号: 013187 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.800\n", - "题号: 014346 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.750\n", - "题号: 014427 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.850\n", - "题号: 014051 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.800\n", - "题号: 014056 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.950\n", - "题号: 014412 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.650\n", - "题号: 013183 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.950\t0.550\n", - "题号: 014423 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t1.000\t0.550\n", - "题号: 014435 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.150\n", - "题号: 031235 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.100\n", - "题号: 014359 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.500\n", - "题号: 014055 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.600\n", - "题号: 014352 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.650\n", - "题号: 014053 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.700\n", - "题号: 014037 , 字段: usages 中已添加数据: 20230314\t2023届高三09班\t0.300\n" + "题号: 004353 , 字段: ans 中已修改数据: $[1,2)$\n", + "题号: 004270 , 字段: ans 中已修改数据: $(-3,1]$\n", + "题号: 004254 , 字段: ans 中已修改数据: $3$\n", + "题号: 004145 , 字段: ans 中已修改数据: $1$\n", + "题号: 004083 , 字段: ans 中已修改数据: $3$\n", + "题号: 004232 , 字段: ans 中已修改数据: $\\dfrac{34}{35}$\n", + "题号: 004216 , 字段: ans 中已修改数据: $4$\n", + "题号: 004149 , 字段: ans 中已修改数据: $[-\\dfrac 12,1]$\n", + "题号: 004172 , 字段: ans 中已修改数据: $\\dfrac 12$\n", + "题号: 004089 , 字段: ans 中已修改数据: $-1$与$\\dfrac 12$\n", + "题号: 004415 , 字段: ans 中已修改数据: $1$\n", + "题号: 004135 , 字段: ans 中已修改数据: D\n", + "题号: 004136 , 字段: ans 中已修改数据: C\n", + "题号: 031282 , 字段: ans 中已修改数据: A\n", + "题号: 004159 , 字段: ans 中已修改数据: (1) $2$; (2) $\\arctan\\dfrac{\\sqrt{2}}4$\n", + "题号: 004442 , 字段: ans 中已修改数据: (1) $\\dfrac{\\pi}{12}$或$\\dfrac\\pi 4$; (2) $\\omega = \\dfrac 23$, 单调递增区间为$[0,\\dfrac\\pi 2]$\n", + "题号: 004721 , 字段: ans 中已修改数据: (1) $8\\sqrt{3}-8$; (2) 当$A$在弧$\\overset\\frown{MN}$的四等分点(更靠近$M$)处时, 矩形$ABCD$的面积最大, 最大面积为$16\\sqrt{2}-16$\n", + "题号: 004246 , 字段: ans 中已修改数据: (1) $[0,\\arctan\\dfrac 32)\\cup (\\dfrac{3\\pi}4,\\pi)$; (2) $\\dfrac 83\\pi+\\sqrt{3}$; (3) 曲线$C$的方程为$x^2=\\begin{cases} 24-8y, & y\\ge 0, \\\\ 24+12y, & y\\le 0,\\end{cases}$ $a$的取值范围为$(6,24)$\n", + "题号: 004352 , 字段: ans 中已修改数据: (1) $-5,-3,-1,1,3,5,7$; (2) $a_n=\\begin{cases}\\dfrac {n+1}2, & n=2k-1,\\\\ 1-\\dfrac n 2, & n = 2k \\end{cases}$($k$为正整数); (3) 证明略\n", + "题号: 031311 , 字段: ans 中已修改数据: $\\{4,5\\}$\n", + "题号: 031312 , 字段: ans 中已修改数据: $(1,11)$\n", + "题号: 031313 , 字段: ans 中已修改数据: $-\\dfrac 35+\\dfrac 45\\mathrm{i}$\n", + "题号: 031314 , 字段: ans 中已修改数据: $1$\n", + "题号: 031315 , 字段: ans 中已修改数据: $2\\sqrt{3}$\n", + "题号: 031316 , 字段: ans 中已修改数据: $2$\n", + "题号: 031317 , 字段: ans 中已修改数据: $(-\\dfrac 15,\\dfrac 25)$\n", + "题号: 031318 , 字段: ans 中已修改数据: $(1,5)$\n", + "题号: 031319 , 字段: ans 中已修改数据: $\\dfrac 1{4046}$\n", + "题号: 031320 , 字段: ans 中已修改数据: $\\dfrac 3{392}$\n", + "题号: 031321 , 字段: ans 中已修改数据: $(-6,\\dfrac{19}{54})$\n", + "题号: 031322 , 字段: ans 中已修改数据: $2$\n", + "题号: 031323 , 字段: ans 中已修改数据: A\n", + "题号: 031324 , 字段: ans 中已修改数据: B\n", + "题号: 031325 , 字段: ans 中已修改数据: B\n", + "题号: 031326 , 字段: ans 中已修改数据: D\n", + "题号: 031327 , 字段: ans 中已修改数据: (1) $\\arctan 35$; (2) $3\\sqrt{2}$\n", + "题号: 031328 , 字段: ans 中已修改数据: (1) $33.7$岁; (2) $\\chi^2\\approx 87.366>3.841$, 所以有骑行绿道与万元级运动自行车购买意愿有关\n", + "题号: 031329 , 字段: ans 中已修改数据: (1) 约为$65.7\\text{cm}^2$; (2) 参考改进建议: \\textcircled{1} 雨伞不遮挡视线; \\textcircled{2} 伞面为弧形，改进模型将伞设为一段圆弧; \\textcircled{3} 考虑伞柄可以伸缩; \\textcircled{4} 人体改进为立体模型; \\textcircled{5} 考虑风速、风向; \\textcircled{6} 考虑撑伞的省力、稳定等.\n", + "题号: 031330 , 字段: ans 中已修改数据: (1) $\\dfrac 12$; (2) 证明略; (3) $\\dfrac 49x^2+\\dfrac 45 y^2=1$($y>0$)\n", + "题号: 031331 , 字段: ans 中已修改数据: (1) $a=-1$; (2) 当$a\\ge 0$时, $f(x)$在$(0,+\\infty)$上是严格增函数; 当$a<0$时, $f(x)$在$(0,-\\dfrac 1a]$上是严格增函数, 在$[-\\dfrac 1a,+\\infty)$上是严格减函数; (3) (i) $(-\\dfrac 1{\\mathrm{e}},0)$; (ii) $(\\dfrac 12,+\\infty)$\n", + "题号: 014743 , 字段: ans 中已修改数据: $\\pi$\n", + "题号: 014744 , 字段: ans 中已修改数据: $1$\n", + "题号: 014745 , 字段: ans 中已修改数据: $9$\n", + "题号: 014746 , 字段: ans 中已修改数据: $80$\n", + "题号: 014747 , 字段: ans 中已修改数据: $3$\n", + "题号: 014748 , 字段: ans 中已修改数据: $0.3$\n", + "题号: 014749 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{3}}3\\pi$\n", + "题号: 014750 , 字段: ans 中已修改数据: $9$\n", + "题号: 014751 , 字段: ans 中已修改数据: $8$\n", + "题号: 014752 , 字段: ans 中已修改数据: $1$\n", + "题号: 014753 , 字段: ans 中已修改数据: $[16-\\sqrt{2},16+\\sqrt{2}]$\n", + "题号: 014754 , 字段: ans 中已修改数据: $10-4\\sqrt{7}$\n", + "题号: 014755 , 字段: ans 中已修改数据: D\n", + "题号: 014756 , 字段: ans 中已修改数据: A\n", + "题号: 014757 , 字段: ans 中已修改数据: B\n", + "题号: 014758 , 字段: ans 中已修改数据: B\n", + "题号: 014759 , 字段: ans 中已修改数据: (1) $\\dfrac\\pi 3$; (2) 最大值为$6$\n", + "题号: 014760 , 字段: ans 中已修改数据: (1) $\\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\\arcsin\\dfrac{\\sqrt{6}}3$\n", + "题号: 014761 , 字段: ans 中已修改数据: (1) 证明略; $a_n=5^{n-1}+1$; (2) $999$\n", + "题号: 014762 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}4+\\dfrac{y^2}3=1$; (2) $4$; (3) $8$\n", + "题号: 014763 , 字段: ans 中已修改数据: (1) $0$是极大值点, $2$是极小值点; (2) $[\\dfrac 72-\\ln 4,+\\infty)$; (3) 证明略\n" ] } ], diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 7bfe66e5..58a89c0c 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,542 +1,183 @@ -usages +ans +004353 +$[1,2)$ -013187 -20230314 2023届高三10班 0.667 +004270 +$(-3,1]$ -014346 -20230314 2023届高三10班 0.788 +004254 +$3$ -014427 -20230314 2023届高三10班 0.939 +004145 +$1$ -014051 -20230314 2023届高三10班 0.818 +004083 +$3$ -014056 -20230314 2023届高三10班 0.970 +004232 +$\dfrac{34}{35}$ -014412 -20230314 2023届高三10班 0.818 +004216 +$4$ -013183 -20230314 2023届高三10班 0.879 0.697 +004149 +$[-\dfrac 12,1]$ -014423 -20230314 2023届高三10班 0.727 0.424 +004172 +$\dfrac 12$ -014435 -20230314 2023届高三10班 0.364 +004089 +$-1$与$\dfrac 12$ -031235 -20230314 2023届高三10班 0.212 +004415 +$1$ -014359 -20230314 2023届高三10班 0.515 +004135 +D -014055 -20230314 2023届高三10班 0.667 +004136 +C -014352 -20230314 2023届高三10班 0.606 +031282 +A -014053 -20230314 2023届高三10班 0.545 +004159 +(1) $2$; (2) $\arctan\dfrac{\sqrt{2}}4$ -014037 -20230314 2023届高三10班 0.242 +004442 +(1) $\dfrac{\pi}{12}$或$\dfrac\pi 4$; (2) $\omega = \dfrac 23$, 单调递增区间为$[0,\dfrac\pi 2]$ -013187 -20230314 2023届高三11班 0.600 +004721 +(1) $8\sqrt{3}-8$; (2) 当$A$在弧$\overset\frown{MN}$的四等分点(更靠近$M$)处时, 矩形$ABCD$的面积最大, 最大面积为$16\sqrt{2}-16$ -014346 -20230314 2023届高三11班 0.500 +004246 +(1) $[0,\arctan\dfrac 32)\cup (\dfrac{3\pi}4,\pi)$; (2) $\dfrac 83\pi+\sqrt{3}$; (3) 曲线$C$的方程为$x^2=\begin{cases} 24-8y, & y\ge 0, \\ 24+12y, & y\le 0,\end{cases}$ $a$的取值范围为$(6,24)$ -014427 -20230314 2023届高三11班 0.650 +004352 +(1) $-5,-3,-1,1,3,5,7$; (2) $a_n=\begin{cases}\dfrac {n+1}2, & n=2k-1,\\ 1-\dfrac n 2, & n = 2k \end{cases}$($k$为正整数); (3) 证明略 -014051 -20230314 2023届高三11班 0.950 +031311 +$\{4,5\}$ -014056 -20230314 2023届高三11班 1.000 +031312 +$(1,11)$ -014412 -20230314 2023届高三11班 0.700 +031313 +$-\dfrac 35+\dfrac 45\mathrm{i}$ -013183 -20230314 2023届高三11班 0.950 0.550 +031314 +$1$ -014423 -20230314 2023届高三11班 0.850 0.450 +031315 +$2\sqrt{3}$ -014435 -20230314 2023届高三11班 0.200 +031316 +$2$ -031235 -20230314 2023届高三11班 0.100 +031317 +$(-\dfrac 15,\dfrac 25)$ -014359 -20230314 2023届高三11班 0.500 +031318 +$(1,5)$ -014055 -20230314 2023届高三11班 0.750 +031319 +$\dfrac 1{4046}$ -014352 -20230314 2023届高三11班 0.600 +031320 +$\dfrac 3{392}$ -014053 -20230314 2023届高三11班 0.450 +031321 +$(-6,\dfrac{19}{54})$ -014037 -20230314 2023届高三11班 0.200 +031322 +$2$ -013187 -20230314 2023届高三12班 0.556 +031323 +A -014346 -20230314 2023届高三12班 0.667 +031324 +B -014427 -20230314 2023届高三12班 0.667 +031325 +B -014051 -20230314 2023届高三12班 0.778 +031326 +D -014056 -20230314 2023届高三12班 0.889 +031327 +(1) $\arctan 35$; (2) $3\sqrt{2}$ -014412 -20230314 2023届高三12班 0.667 +031328 +(1) $33.7$岁; (2) $\chi^2\approx 87.366>3.841$, 所以有骑行绿道与万元级运动自行车购买意愿有关 -013183 -20230314 2023届高三12班 0.944 0.778 +031329 +(1) 约为$65.7\text{cm}^2$; (2) 参考改进建议: \textcircled{1} 雨伞不遮挡视线; \textcircled{2} 伞面为弧形，改进模型将伞设为一段圆弧; \textcircled{3} 考虑伞柄可以伸缩; \textcircled{4} 人体改进为立体模型; \textcircled{5} 考虑风速、风向; \textcircled{6} 考虑撑伞的省力、稳定等. -014423 -20230314 2023届高三12班 0.833 0.611 +031330 +(1) $\dfrac 12$; (2) 证明略; (3) $\dfrac 49x^2+\dfrac 45 y^2=1$($y>0$) -014435 -20230314 2023届高三12班 0.389 +031331 +(1) $a=-1$; (2) 当$a\ge 0$时, $f(x)$在$(0,+\infty)$上是严格增函数; 当$a<0$时, $f(x)$在$(0,-\dfrac 1a]$上是严格增函数, 在$[-\dfrac 1a,+\infty)$上是严格减函数; (3) (i) $(-\dfrac 1{\mathrm{e}},0)$; (ii) $(\dfrac 12,+\infty)$ -031235 -20230314 2023届高三12班 0.167 +014743 +$\pi$ -014359 -20230314 2023届高三12班 0.722 +014744 +$1$ -014055 -20230314 2023届高三12班 0.833 +014745 +$9$ -014352 -20230314 2023届高三12班 0.611 +014746 +$80$ -014053 -20230314 2023届高三12班 0.667 +014747 +$3$ -014037 -20230314 2023届高三12班 0.556 +014748 +$0.3$ -013187 -20230314 2023届高三01班 0.722 +014749 +$\dfrac{\sqrt{3}}3\pi$ -014346 -20230314 2023届高三01班 0.833 +014750 +$9$ -014427 -20230314 2023届高三01班 0.944 +014751 +$8$ -014051 -20230314 2023届高三01班 1.000 +014752 +$1$ -014056 -20230314 2023届高三01班 0.944 +014753 +$[16-\sqrt{2},16+\sqrt{2}]$ -014412 -20230314 2023届高三01班 1.000 +014754 +$10-4\sqrt{7}$ -013183 -20230314 2023届高三01班 1.000 0.889 +014755 +D -014423 -20230314 2023届高三01班 1.000 0.833 +014756 +A -014435 -20230314 2023届高三01班 0.722 +014757 +B -031235 -20230314 2023届高三01班 0.444 +014758 +B -014359 -20230314 2023届高三01班 0.889 +014759 +(1) $\dfrac\pi 3$; (2) 最大值为$6$ -014055 -20230314 2023届高三01班 0.889 +014760 +(1) $\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\arcsin\dfrac{\sqrt{6}}3$ -014352 -20230314 2023届高三01班 0.889 +014761 +(1) 证明略; $a_n=5^{n-1}+1$; (2) $999$ -014053 -20230314 2023届高三01班 0.833 - -014037 -20230314 2023届高三01班 0.778 - -013187 -20230314 2023届高三02班 0.625 - -014346 -20230314 2023届高三02班 0.906 - -014427 -20230314 2023届高三02班 1.000 - -014051 -20230314 2023届高三02班 0.906 - -014056 -20230314 2023届高三02班 0.781 - -014412 -20230314 2023届高三02班 0.875 - -013183 -20230314 2023届高三02班 0.906 0.656 - -014423 -20230314 2023届高三02班 0.969 0.719 - -014435 -20230314 2023届高三02班 0.438 - -031235 -20230314 2023届高三02班 0.469 - -014359 -20230314 2023届高三02班 0.625 - -014055 -20230314 2023届高三02班 0.688 - -014352 -20230314 2023届高三02班 0.781 - -014053 -20230314 2023届高三02班 0.688 - -014037 -20230314 2023届高三02班 0.625 - -013187 -20230314 2023届高三03班 0.640 - -014346 -20230314 2023届高三03班 0.800 - -014427 -20230314 2023届高三03班 0.840 - -014051 -20230314 2023届高三03班 0.960 - -014056 -20230314 2023届高三03班 0.800 - -014412 -20230314 2023届高三03班 0.880 - -013183 -20230314 2023届高三03班 0.680 0.440 - -014423 -20230314 2023届高三03班 0.880 0.760 - -014435 -20230314 2023届高三03班 0.560 - -031235 -20230314 2023届高三03班 0.480 - -014359 -20230314 2023届高三03班 0.680 - -014055 -20230314 2023届高三03班 0.800 - -014352 -20230314 2023届高三03班 0.680 - -014053 -20230314 2023届高三03班 0.840 - -014037 -20230314 2023届高三03班 0.640 - -013187 -20230314 2023届高三04班 0.667 - -014346 -20230314 2023届高三04班 0.722 - -014427 -20230314 2023届高三04班 0.889 - -014051 -20230314 2023届高三04班 0.889 - -014056 -20230314 2023届高三04班 0.889 - -014412 -20230314 2023届高三04班 0.667 - -013183 -20230314 2023届高三04班 0.556 0.333 - -014423 -20230314 2023届高三04班 1.000 0.500 - -014435 -20230314 2023届高三04班 0.167 - -031235 -20230314 2023届高三04班 0.278 - -014359 -20230314 2023届高三04班 0.722 - -014055 -20230314 2023届高三04班 0.778 - -014352 -20230314 2023届高三04班 0.667 - -014053 -20230314 2023届高三04班 0.611 - -014037 -20230314 2023届高三04班 0.500 - -013187 -20230314 2023届高三05班 0.789 - -014346 -20230314 2023届高三05班 0.868 - -014427 -20230314 2023届高三05班 0.921 - -014051 -20230314 2023届高三05班 0.921 - -014056 -20230314 2023届高三05班 0.895 - -014412 -20230314 2023届高三05班 0.921 - -013183 -20230314 2023届高三05班 0.974 0.816 - -014423 -20230314 2023届高三05班 0.789 0.474 - -014435 -20230314 2023届高三05班 0.447 - -031235 -20230314 2023届高三05班 0.342 - -014359 -20230314 2023届高三05班 0.816 - -014055 -20230314 2023届高三05班 0.763 - -014352 -20230314 2023届高三05班 0.789 - -014053 -20230314 2023届高三05班 0.553 - -014037 -20230314 2023届高三05班 0.658 - -013187 -20230314 2023届高三06班 0.625 - -014346 -20230314 2023届高三06班 0.750 - -014427 -20230314 2023届高三06班 0.969 - -014051 -20230314 2023届高三06班 0.844 - -014056 -20230314 2023届高三06班 0.875 - -014412 -20230314 2023届高三06班 0.750 - -013183 -20230314 2023届高三06班 0.656 0.750 - -014423 -20230314 2023届高三06班 0.844 0.531 - -014435 -20230314 2023届高三06班 0.281 - -031235 -20230314 2023届高三06班 0.156 - -014359 -20230314 2023届高三06班 0.812 - -014055 -20230314 2023届高三06班 0.812 - -014352 -20230314 2023届高三06班 0.656 - -014053 -20230314 2023届高三06班 0.531 - -014037 -20230314 2023届高三06班 0.531 - -013187 -20230314 2023届高三07班 0.448 - -014346 -20230314 2023届高三07班 0.483 - -014427 -20230314 2023届高三07班 0.621 - -014051 -20230314 2023届高三07班 0.966 - -014056 -20230314 2023届高三07班 0.897 - -014412 -20230314 2023届高三07班 0.828 - -013183 -20230314 2023届高三07班 0.690 0.828 - -014423 -20230314 2023届高三07班 0.862 0.655 - -014435 -20230314 2023届高三07班 0.379 - -031235 -20230314 2023届高三07班 0.207 - -014359 -20230314 2023届高三07班 0.690 - -014055 -20230314 2023届高三07班 0.759 - -014352 -20230314 2023届高三07班 0.552 - -014053 -20230314 2023届高三07班 0.828 - -014037 -20230314 2023届高三07班 0.379 - -013187 -20230314 2023届高三08班 0.760 - -014346 -20230314 2023届高三08班 0.760 - -014427 -20230314 2023届高三08班 0.840 - -014051 -20230314 2023届高三08班 0.960 - -014056 -20230314 2023届高三08班 0.800 - -014412 -20230314 2023届高三08班 0.920 - -013183 -20230314 2023届高三08班 1.000 0.720 - -014423 -20230314 2023届高三08班 1.000 0.560 - -014435 -20230314 2023届高三08班 0.440 - -031235 -20230314 2023届高三08班 0.320 - -014359 -20230314 2023届高三08班 0.800 - -014055 -20230314 2023届高三08班 0.800 - -014352 -20230314 2023届高三08班 0.600 - -014053 -20230314 2023届高三08班 0.560 - -014037 -20230314 2023届高三08班 0.640 - -013187 -20230314 2023届高三09班 0.800 - -014346 -20230314 2023届高三09班 0.750 - -014427 -20230314 2023届高三09班 0.850 - -014051 -20230314 2023届高三09班 0.800 - -014056 -20230314 2023届高三09班 0.950 - -014412 -20230314 2023届高三09班 0.650 - -013183 -20230314 2023届高三09班 0.950 0.550 - -014423 -20230314 2023届高三09班 1.000 0.550 - -014435 -20230314 2023届高三09班 0.150 - -031235 -20230314 2023届高三09班 0.100 - -014359 -20230314 2023届高三09班 0.500 - -014055 -20230314 2023届高三09班 0.600 - -014352 -20230314 2023届高三09班 0.650 - -014053 -20230314 2023届高三09班 0.700 - -014037 -20230314 2023届高三09班 0.300 +014762 +(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$; (2) $4$; (3) $8$ +014763 +(1) $0$是极大值点, $2$是极小值点; (2) $[\dfrac 72-\ln 4,+\infty)$; (3) 证明略 \ No newline at end of file diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index d1ecd26a..e0ed1a44 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -98306,7 +98306,7 @@ "双曲线" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2$; (2) $\\arccos\\dfrac{11}{16}$; (3) $\\overrightarrow{OM}\\cdot \\overrightarrow{ON}=4+b^2$, 取值范围为$(6+2\\sqrt{5},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -109432,7 +109432,7 @@ "双曲线" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -109601,7 +109601,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$与$\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -110932,7 +110932,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -110958,7 +110958,7 @@ "第六单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -111228,7 +111228,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -111334,7 +111334,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-\\dfrac 12,1]$", "solution": "", "duration": -1, "usages": [ @@ -111622,7 +111622,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2$; (2) $\\arctan\\dfrac{\\sqrt{2}}4$", "solution": "", "duration": -1, "usages": [ @@ -111990,7 +111990,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -113151,7 +113151,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -113595,7 +113595,7 @@ "概率" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{34}{35}$", "solution": "", "duration": -1, "usages": [ @@ -113970,7 +113970,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[0,\\arctan\\dfrac 32)\\cup (\\dfrac{3\\pi}4,\\pi)$; (2) $\\dfrac 83\\pi+\\sqrt{3}$; (3) 曲线$C$的方程为$x^2=\\begin{cases} 24-8y, & y\\ge 0, \\\\ 24+12y, & y\\le 0,\\end{cases}$ $a$的取值范围为$(6,24)$", "solution": "", "duration": -1, "usages": [ @@ -114238,7 +114238,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -114648,7 +114648,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-3,1]$", "solution": "", "duration": -1, "usages": [ @@ -116878,7 +116878,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-5,-3,-1,1,3,5,7$; (2) $a_n=\\begin{cases}\\dfrac {n+1}2, & n=2k-1,\\\\ 1-\\dfrac n 2, & n = 2k \\end{cases}$($k$为正整数); (3) 证明略", "solution": "", "duration": -1, "usages": [ @@ -116903,7 +116903,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$[1,2)$", "solution": "", "duration": -1, "usages": [ @@ -118619,7 +118619,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -119353,7 +119353,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{\\pi}{12}$或$\\dfrac\\pi 4$; (2) $\\omega = \\dfrac 23$, 单调递增区间为$[0,\\dfrac\\pi 2]$", "solution": "", "duration": -1, "usages": [ @@ -127166,7 +127166,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $8\\sqrt{3}-8$; (2) 当$A$在弧$\\overset\\frown{MN}$的四等分点(更靠近$M$)处时, 矩形$ABCD$的面积最大, 最大面积为$16\\sqrt{2}-16$", "solution": "", "duration": -1, "usages": [ @@ -323832,7 +323832,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$a=3$", "solution": "", "duration": -1, "usages": [ @@ -323866,7 +323866,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pi-\\arctan\\dfrac ab$", "solution": "", "duration": -1, "usages": [ @@ -323900,7 +323900,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$[0,\\dfrac\\pi 4]\\cup (\\dfrac \\pi 2,\\pi)$", "solution": "", "duration": -1, "usages": [ @@ -323955,7 +323955,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -323989,7 +323989,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$4-\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -324052,7 +324052,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $l_1$不是$M$中的直线, $l_2$是$M$中的直线; (2) $D$不是$S$中的点, $E$是$S$中的点; (3) $y^2=x$", "solution": "", "duration": -1, "usages": [ @@ -324128,7 +324128,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{-3,2,-1\\}$", "solution": "", "duration": -1, "usages": [], @@ -324149,7 +324149,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(2,-4)$", "solution": "", "duration": -1, "usages": [], @@ -324170,7 +324170,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 43$", "solution": "", "duration": -1, "usages": [], @@ -324212,7 +324212,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$23x-20y+20=0$", "solution": "", "duration": -1, "usages": [ @@ -324246,7 +324246,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 3$", "solution": "", "duration": -1, "usages": [ @@ -324301,7 +324301,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -324322,7 +324322,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $45^\\circ$; (2) $3x+7y-13=0$或$7x-3y-11=0$", "solution": "", "duration": -1, "usages": [], @@ -324364,7 +324364,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pm 4$", "solution": "", "duration": -1, "usages": [], @@ -324406,7 +324406,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x^2}2-\\dfrac{y^2}6=1$", "solution": "", "duration": -1, "usages": [], @@ -324427,7 +324427,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$11$", "solution": "", "duration": -1, "usages": [], @@ -324448,7 +324448,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "相切", "solution": "", "duration": -1, "usages": [], @@ -324469,7 +324469,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(2x-1)^2+(4y-1)^2=1$", "solution": "", "duration": -1, "usages": [], @@ -324490,7 +324490,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{h_1}{\\tan\\theta_1}+\\dfrac{h_2}{\\tan\\theta_2}\\le 2a$", "solution": "", "duration": -1, "usages": [], @@ -324597,7 +324597,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$y=-\\dfrac 1{32}$", "solution": "", "duration": -1, "usages": [], @@ -324660,7 +324660,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [], @@ -324702,7 +324702,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$y=\\pm \\sqrt{2} x$", "solution": "", "duration": -1, "usages": [], @@ -324723,7 +324723,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x^2}{9/4}-\\dfrac{y^2}{187/4}=1$($x>0$)", "solution": "", "duration": -1, "usages": [], @@ -324744,7 +324744,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac\\pi 4,\\pi)$", "solution": "", "duration": -1, "usages": [], @@ -324786,7 +324786,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -324830,7 +324830,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $2$; (2) 恒等于$4$, 是定值", "solution": "", "duration": -1, "usages": [], @@ -324851,7 +324851,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$y^2=8x$", "solution": "", "duration": -1, "usages": [], @@ -324893,7 +324893,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$x^2+y^2=25$", "solution": "", "duration": -1, "usages": [], @@ -324914,7 +324914,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(2,3)$", "solution": "", "duration": -1, "usages": [], @@ -325103,7 +325103,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$22$", "solution": "", "duration": -1, "usages": [], @@ -325229,7 +325229,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [], @@ -325397,7 +325397,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{4}{3}\\sqrt{6}$", "solution": "", "duration": -1, "usages": [], @@ -325439,7 +325439,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x^2}4+y^2=1$或$x^2+\\dfrac{y^2}{4}=1$", "solution": "", "duration": -1, "usages": [], @@ -325460,7 +325460,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [], @@ -325523,7 +325523,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(\\pm \\sqrt{3},0)$; (2) 最大值为$5$, 最小值为$\\dfrac{\\sqrt{2}}2$; (3) $(1,1+\\sqrt{2}]$", "solution": "", "duration": -1, "usages": [], @@ -325586,7 +325586,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x^2}{16}-\\dfrac{y^2}{9}=1$($x>0$)", "solution": "", "duration": -1, "usages": [], @@ -325628,7 +325628,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -325777,7 +325777,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $x^2-\\dfrac{y^2}3=1$; (2) $\\lambda$存在, $\\lambda=2$", "solution": "", "duration": -1, "usages": [], @@ -326473,7 +326473,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$36\\pi$", "solution": "", "duration": -1, "usages": [ @@ -326549,7 +326549,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{4}\\textcircled{5}", "solution": "", "duration": -1, "usages": [ @@ -326606,7 +326606,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 23 c\\sqrt{a^2-c^2-1}$", "solution": "", "duration": -1, "usages": [ @@ -326682,7 +326682,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $17-12\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -326779,7 +326779,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}\\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -343846,7 +343846,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,-2)$", "solution": "", "duration": -1, "usages": [ @@ -343880,7 +343880,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [], @@ -343922,7 +343922,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(x-1)^2+y^2=2$", "solution": "", "duration": -1, "usages": [ @@ -343977,7 +343977,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$4.4$", "solution": "", "duration": -1, "usages": [ @@ -344034,7 +344034,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $150$米; (2) ($OM\\in [10,35]$)当$OM$的长为$10$米时, 圆形保护区的面积最大", "solution": "", "duration": -1, "usages": [ @@ -344152,7 +344152,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "$(0,1]$(单位: $\\text{cm}$)", "solution": "", "duration": -1, "usages": [], @@ -344299,7 +344299,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x^2}{4}-\\dfrac{y^2}{5}=1$($x>0$)", "solution": "", "duration": -1, "usages": [], @@ -344341,7 +344341,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $5$; (2) $\\lambda = \\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -345142,7 +345142,7 @@ "第六单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -345344,7 +345344,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 23 c\\sqrt{a^2-c^2-1}$", "solution": "", "duration": -1, "usages": [ @@ -345399,7 +345399,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,0,-1)$", "solution": "", "duration": -1, "usages": [ @@ -345432,7 +345432,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\arccos\\dfrac{\\sqrt{6}}3$", "solution": "", "duration": -1, "usages": [ @@ -345465,7 +345465,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$或$71$", "solution": "", "duration": -1, "usages": [], @@ -345486,7 +345486,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "$4+2\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -345541,7 +345541,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 92+\\dfrac{\\sqrt{5}}2+\\sqrt{3}$; (2) $\\dfrac{8\\sqrt{2}}3\\pi$; (3) $\\dfrac{2\\sqrt{5}}5$", "solution": "", "duration": -1, "usages": [ @@ -345575,7 +345575,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 35$", "solution": "", "duration": -1, "usages": [], @@ -345617,7 +345617,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $E$是棱$AB$的中点", "solution": "", "duration": -1, "usages": [ @@ -345671,7 +345671,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$1+\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -345705,7 +345705,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{11}8$", "solution": "", "duration": -1, "usages": [], @@ -345726,7 +345726,7 @@ "第六单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -345781,7 +345781,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\sqrt{6}\\pi$", "solution": "", "duration": -1, "usages": [ @@ -345836,7 +345836,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -345870,7 +345870,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$1:4$", "solution": "", "duration": -1, "usages": [ @@ -352440,7 +352440,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\pi$", "solution": "", "duration": -1, "usages": [ @@ -352491,7 +352491,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\arccos \\dfrac{\\sqrt{10}}{10}$; (3) $\\dfrac 13$", "solution": "", "duration": -1, "usages": [], @@ -352510,7 +352510,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac{5\\pi}6$; (3) 存在($M$满足$\\overrightarrow{OM}=(4-\\sqrt{10})\\overrightarrow{OA}+(\\sqrt{10}-3)\\overrightarrow{OP}$)", "solution": "", "duration": -1, "usages": [ @@ -352579,7 +352579,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -352630,7 +352630,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -352738,7 +352738,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$5\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -352770,7 +352770,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac\\pi 6$", "solution": "", "duration": -1, "usages": [], @@ -352846,7 +352846,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $1$; (2) $m=-1$, 距离为$\\sqrt{2}$; (3) $x+1=0$或$3x-4y+11=0$", "solution": "", "duration": -1, "usages": [ @@ -352899,7 +352899,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $x-y-1=0$或$7x+2y-23=0$; (2) 弦$PQ$最短时, 所在直线的方程为$x+y-3=0$; 弦$PQ$最长时, 所在直线的方程为$x-y+3=0$; (3) 当$a=2$时, 两圆内切; 当$a\\in (2-2\\sqrt{2},2)\\cup (2,2+2\\sqrt{2})$时, 两圆相交; 当$a=2\\pm 2\\sqrt{2}$时, 两圆外切; 当$a\\in (-\\infty,2-2\\sqrt{2})\\cup (2+2\\sqrt{2},+\\infty)$时, 两圆外离", "solution": "", "duration": -1, "usages": [], @@ -352918,7 +352918,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,\\dfrac 12)$", "solution": "", "duration": -1, "usages": [ @@ -352969,7 +352969,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[0,\\dfrac\\pi 4]\\cup (\\dfrac {3\\pi}4,\\pi)$", "solution": "", "duration": -1, "usages": [], @@ -353045,7 +353045,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-1$或$-11$", "solution": "", "duration": -1, "usages": [], @@ -353121,7 +353121,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(1,2]$", "solution": "", "duration": -1, "usages": [ @@ -353873,7 +353873,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{17}$", "solution": "", "duration": -1, "usages": [ @@ -353924,7 +353924,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -353994,7 +353994,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 32$; (2) 存在, $\\angle BOD=\\dfrac\\pi 6$", "solution": "", "duration": -1, "usages": [ @@ -354083,7 +354083,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{21\\sqrt{2}}{32}$", "solution": "", "duration": -1, "usages": [ @@ -354172,7 +354172,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{15}2\\sqrt{3}$; (2) $3375\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -354242,7 +354242,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{10}3\\pi$", "solution": "", "duration": -1, "usages": [ @@ -354274,7 +354274,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -354382,7 +354382,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [ @@ -354452,7 +354452,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$[\\dfrac{27}4,\\dfrac{64}3]$", "solution": "", "duration": -1, "usages": [ @@ -354484,7 +354484,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -354515,7 +354515,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(1,1,2)$", "solution": "", "duration": -1, "usages": [ @@ -354546,7 +354546,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [], @@ -354565,7 +354565,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2$或$-\\dfrac 52$", "solution": "", "duration": -1, "usages": [], @@ -354584,7 +354584,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(2,-2,1)$", "solution": "", "duration": -1, "usages": [], @@ -354603,7 +354603,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\overrightarrow{BE}=\\dfrac 12\\overrightarrow{a}-\\overrightarrow{b}$, $\\overrightarrow{DF}=\\dfrac 12\\overrightarrow{b}+\\dfrac 12\\overrightarrow{c}$; (2) $\\pi-\\arccos \\dfrac 23$", "solution": "", "duration": -1, "usages": [], @@ -354641,7 +354641,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 存在, $\\lambda=1\\pm \\dfrac{\\sqrt{2}}2$", "solution": "", "duration": -1, "usages": [], @@ -354736,7 +354736,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-4,3,2)$", "solution": "", "duration": -1, "usages": [ @@ -354805,7 +354805,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{30}$", "solution": "", "duration": -1, "usages": [ @@ -354836,7 +354836,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac 72,0,\\dfrac 72)$", "solution": "", "duration": -1, "usages": [ @@ -354886,7 +354886,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[0,8]$", "solution": "", "duration": -1, "usages": [ @@ -354918,7 +354918,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $\\dfrac{2\\sqrt{42}}7$; (3) 存在, $A_1E=1$", "solution": "", "duration": -1, "usages": [ @@ -355101,7 +355101,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\sqrt{2}$; (2) $y=x+1$", "solution": "", "duration": -1, "usages": [], @@ -360402,7 +360402,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$\\pi$", "solution": "", "duration": -1, "usages": [], @@ -360421,7 +360421,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -360440,7 +360440,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [], @@ -360459,7 +360459,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$80$", "solution": "", "duration": -1, "usages": [], @@ -360478,7 +360478,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -360497,7 +360497,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$0.3$", "solution": "", "duration": -1, "usages": [], @@ -360516,7 +360516,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$\\dfrac{\\sqrt{3}}3\\pi$", "solution": "", "duration": -1, "usages": [], @@ -360535,7 +360535,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [], @@ -360554,7 +360554,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [], @@ -360573,7 +360573,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -360592,7 +360592,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$[16-\\sqrt{2},16+\\sqrt{2}]$", "solution": "", "duration": -1, "usages": [], @@ -360611,7 +360611,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$10-4\\sqrt{7}$", "solution": "", "duration": -1, "usages": [], @@ -360630,7 +360630,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -360649,7 +360649,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -360668,7 +360668,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -360687,7 +360687,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -360706,7 +360706,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $\\dfrac\\pi 3$; (2) 最大值为$6$", "solution": "", "duration": -1, "usages": [], @@ -360725,7 +360725,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $\\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\\arcsin\\dfrac{\\sqrt{6}}3$", "solution": "", "duration": -1, "usages": [], @@ -360744,7 +360744,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) 证明略; $a_n=5^{n-1}+1$; (2) $999$", "solution": "", "duration": -1, "usages": [], @@ -360763,7 +360763,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $\\dfrac{x^2}4+\\dfrac{y^2}3=1$; (2) $4$; (3) $8$", "solution": "", "duration": -1, "usages": [], @@ -360782,7 +360782,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $0$是极大值点, $2$是极小值点; (2) $[\\dfrac 72-\\ln 4,+\\infty)$; (3) 证明略", "solution": "", "duration": -1, "usages": [], @@ -438044,7 +438044,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$x^2+y^2-8x-2y+12=0$, $(x+1)^2+y^2=4$", "solution": "", "duration": -1, "usages": [ @@ -438081,7 +438081,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$2x+3y-8=0$", "solution": "", "duration": -1, "usages": [], @@ -438105,7 +438105,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-5\\sqrt{2},1]$", "solution": "", "duration": -1, "usages": [], @@ -438129,7 +438129,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$y^2=16x$($x\\ne 0$)", "solution": "", "duration": -1, "usages": [], @@ -438153,7 +438153,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$y=\\dfrac{x^2}4-3$($x<-4$或$x>4$)", "solution": "", "duration": -1, "usages": [], @@ -438177,7 +438177,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{5}$", "solution": "", "duration": -1, "usages": [], @@ -438225,7 +438225,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 23\\sqrt{6}$", "solution": "", "duration": -1, "usages": [ @@ -438262,7 +438262,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{2-\\dfrac{\\sqrt{2}}2}R$", "solution": "", "duration": -1, "usages": [ @@ -439513,7 +439513,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -440407,7 +440407,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -440429,7 +440429,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$\\{4,5\\}$", "solution": "", "duration": -1, "usages": [], @@ -440448,7 +440448,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$(1,11)$", "solution": "", "duration": -1, "usages": [], @@ -440467,7 +440467,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$-\\dfrac 35+\\dfrac 45\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -440486,7 +440486,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -440505,7 +440505,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$2\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -440524,7 +440524,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -440543,7 +440543,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$(-\\dfrac 15,\\dfrac 25)$", "solution": "", "duration": -1, "usages": [], @@ -440562,7 +440562,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$(1,5)$", "solution": "", "duration": -1, "usages": [], @@ -440581,7 +440581,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$\\dfrac 1{4046}$", "solution": "", "duration": -1, "usages": [], @@ -440600,7 +440600,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$\\dfrac 3{392}$", "solution": "", "duration": -1, "usages": [], @@ -440619,7 +440619,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$(-6,\\dfrac{19}{54})$", "solution": "", "duration": -1, "usages": [], @@ -440638,7 +440638,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -440657,7 +440657,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -440676,7 +440676,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -440695,7 +440695,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -440714,7 +440714,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -440733,7 +440733,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $\\arctan 35$; (2) $3\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -440752,7 +440752,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $33.7$岁; (2) $\\chi^2\\approx 87.366>3.841$, 所以有骑行绿道与万元级运动自行车购买意愿有关", "solution": "", "duration": -1, "usages": [], @@ -440771,7 +440771,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) 约为$65.7\\text{cm}^2$; (2) 参考改进建议: \\textcircled{1} 雨伞不遮挡视线; \\textcircled{2} 伞面为弧形，改进模型将伞设为一段圆弧; \\textcircled{3} 考虑伞柄可以伸缩; \\textcircled{4} 人体改进为立体模型; \\textcircled{5} 考虑风速、风向; \\textcircled{6} 考虑撑伞的省力、稳定等.", "solution": "", "duration": -1, "usages": [], @@ -440790,7 +440790,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $\\dfrac 12$; (2) 证明略; (3) $\\dfrac 49x^2+\\dfrac 45 y^2=1$($y>0$)", "solution": "", "duration": -1, "usages": [], @@ -440809,7 +440809,7 @@ "objs": [], "tags": [], "genre": "", - "ans": "", + "ans": "(1) $a=-1$; (2) 当$a\\ge 0$时, $f(x)$在$(0,+\\infty)$上是严格增函数; 当$a<0$时, $f(x)$在$(0,-\\dfrac 1a]$上是严格增函数, 在$[-\\dfrac 1a,+\\infty)$上是严格减函数; (3) (i) $(-\\dfrac 1{\\mathrm{e}},0)$; (ii) $(\\dfrac 12,+\\infty)$", "solution": "", "duration": -1, "usages": [],