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 dd951c8c..bc742ac6 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": 27, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 27, + "execution_count": 5, "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 = \"536,542,543\"\n", + "problems = \"4129\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", @@ -51,7 +51,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -75,7 +75,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -94,7 +94,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/关键字筛选题号.ipynb b/工具/关键字筛选题号.ipynb index b2f368f3..5460d16d 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 8, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -21,7 +21,7 @@ "\n", "\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n", "keywords_dict_table = [\n", - " {\"origin\":[\"百分百\"],\"tags\":[r\"第九单元\"]}\n", + " {\"origin\":[\"高考\"],\"origin2\":[\"20\"],\"origin_not\":[\"冲刺\"],\"tags\":[\"第九单元\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\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 5a7c03fb..7b17a3ec 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": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -99,6 +99,16 @@ "赋能15.tex\n", "赋能16.tex\n", "赋能17.tex\n", + "赋能18.tex\n", + "赋能19.tex\n", + "011263\n", + "\n", + "\n", + "011266\n", + "\n", + "\n", + "赋能20.tex\n", + "赋能21.tex\n", "2017届上海春季高考.tex\n", "2018届上海春季高考.tex\n", "2019届上海春季高考.tex\n", @@ -979,7 +989,7 @@ "013990\n", "\n", "\n", - "014499\n", + "003629\n", "\n", "\n", "13_解析几何综合.tex\n", @@ -1073,7 +1083,69 @@ "014019\n", "\n", "\n", + "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", + "004292\n", + "\n", + "\n", + "004143\n", + "\n", + "\n", + "004190\n", + "\n", + "\n", + "004169\n", + "\n", + "\n", + "031241\n", + "\n", + "\n", + "004128\n", + "\n", + "\n", + "004189\n", + "\n", + "\n", + "004129\n", + "\n", + "\n", + "031242\n", + "\n", + "\n", + "004130\n", + "\n", + "\n", + "004233\n", + "\n", + "\n", + "004174\n", + "\n", + "\n", + "012437\n", + "\n", + "\n", + "014087\n", + "\n", + "\n", + "012346\n", + "\n", + "\n", + "020958\n", + "\n", + "\n", + "004657\n", + "\n", + "\n", + "011218\n", + "\n", + "\n", + "004508\n", + "\n", + "\n", + "011388\n", + "\n", + "\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", @@ -1126,7 +1198,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -1145,7 +1217,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index c67f1bff..28b191ff 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -11,8 +11,8 @@ "text": [ "首个空闲id: 14628 , 直至 020000\n", "首个空闲id: 22048 , 直至 030000\n", - "首个空闲id: 31244 , 直至 040000\n", - "首个空闲id: 40057 , 直至 999999\n" + "首个空闲id: 31266 , 直至 040000\n", + "首个空闲id: 40083 , 直至 999999\n" ] } ], @@ -46,7 +46,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -65,7 +65,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, 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 f903e0b0..ac063139 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 +2,29 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.944\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.833\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.806\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.917\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.444\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.722\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.889\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.944\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.806\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.611\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.389\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.750\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.389\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t1.000\t0.556\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三10班\t0.806\t0.250\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.857\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.857\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.857\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.905\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.571\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.667\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.905\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.857\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.667\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.571\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.381\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.476\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.524\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.048\t0.238\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三11班\t0.762\t0.238\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t1.000\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.955\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.909\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.818\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.364\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.682\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t1.000\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t1.000\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.818\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.818\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.591\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.545\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.682\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.909\t0.636\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三12班\t0.864\t0.227\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t1.000\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.852\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.926\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t1.000\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.963\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.852\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.963\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t1.000\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.926\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.926\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.926\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.963\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.741\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t1.000\t0.741\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三01班\t0.889\t0.852\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.938\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.844\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.875\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.875\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.812\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.875\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.906\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t1.000\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.906\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.812\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.688\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.719\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.719\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.688\t0.594\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三02班\t0.656\t0.594\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.923\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.769\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.808\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.923\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.923\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.692\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.923\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.923\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.923\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.962\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.462\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.692\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.346\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.923\t0.654\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三03班\t0.808\t0.500\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.967\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.833\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.833\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.933\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.867\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.600\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.900\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.933\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.833\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.833\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.800\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.800\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.567\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.900\t0.567\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三04班\t0.467\t0.433\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.975\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.875\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.900\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.850\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.750\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.800\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.900\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.925\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.825\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.775\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.600\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.850\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.650\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.650\t0.375\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三05班\t0.050\t0.400\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.921\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.947\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.947\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.947\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.868\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.737\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.974\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.974\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.816\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.868\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.684\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.868\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.737\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.921\t0.579\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三06班\t0.895\t0.737\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.938\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.750\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.656\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.750\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.375\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.625\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.969\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.969\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.719\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.469\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.531\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.719\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.344\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.906\t0.438\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三07班\t0.594\t0.344\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.966\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.966\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.862\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.862\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.828\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t1.000\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.931\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t1.000\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.724\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.724\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.621\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.793\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.414\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.931\t0.690\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三08班\t0.724\t0.414\n", - "题号: 012881 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.935\n", - "题号: 012882 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.968\n", - "题号: 012883 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.677\n", - "题号: 012884 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.839\n", - "题号: 012885 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.419\n", - "题号: 012887 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.645\n", - "题号: 012905 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.935\n", - "题号: 012906 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.968\n", - "题号: 012907 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.645\n", - "题号: 012908 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.677\n", - "题号: 012912 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.742\n", - "题号: 012913 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.806\n", - "题号: 012901 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.484\n", - "题号: 012902 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.871\t0.290\n", - "题号: 012903 , 字段: usages 中已添加数据: 20230224\t2023届高三09班\t0.903\t0.452\n" + "题号: 003675 , 字段: ans 中已修改数据: $(-\\infty,0)$\n", + "题号: 031239 , 字段: ans 中已修改数据: $\\dfrac 23$\n", + "题号: 031240 , 字段: ans 中已修改数据: $\\dfrac{2\\pi}3$\n", + "题号: 031237 , 字段: ans 中已修改数据: $\\dfrac 35$\n", + "题号: 004256 , 字段: ans 中已修改数据: $(-\\infty,-1]\\cup [0,+\\infty)$\n", + "题号: 004499 , 字段: ans 中已修改数据: $0217$\n", + "题号: 004132 , 字段: ans 中已修改数据: $[-3,1]$\n", + "题号: 004217 , 字段: ans 中已修改数据: $36$\n", + "题号: 008972 , 字段: ans 中已修改数据: B\n", + "题号: 009082 , 字段: ans 中已修改数据: D\n", + "题号: 012445 , 字段: ans 中已修改数据: B\n", + "题号: 030691 , 字段: ans 中已修改数据: B\n", + "题号: 011301 , 字段: ans 中已修改数据: (1) $c=8$; (2) $6\\sqrt{6}$\n", + "题号: 003691 , 字段: ans 中已修改数据: (1) $935$辆; (2) 因$8782>8736$, 故第$42$个月底单车保有量超过了容纳量\n", + "题号: 011450 , 字段: ans 中已修改数据: (1) $x=\\dfrac{\\sqrt{2}}2$或$x=-\\dfrac{\\sqrt{2}}2$; (2) $x_1^2+x_2^2=1$, $y_1^2+y_2^2=2$; (3) 不存在, 证明略.\n", + "题号: 031236 , 字段: ans 中已修改数据: (1) $y=x$; (2) $g'(x)=\\mathrm{e}^x(\\ln (x+1)+\\dfrac 1{x+1}+\\dfrac{x}{(x+1)^2})$, 故$g(x)$在$[1,+\\infty)$上是严格增函数; (3) 证明略.\n" ] } ], @@ -286,7 +122,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -305,7 +141,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index ba83744d..dc6031e0 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,542 +1,48 @@ -usages +ans +003675 +$(-\infty,0)$ -012881 -20230224 2023届高三10班 0.944 +031239 +$\dfrac 23$ -012882 -20230224 2023届高三10班 0.833 +031240 +$\dfrac{2\pi}3$ -012883 -20230224 2023届高三10班 0.806 +031237 +$\dfrac 35$ -012884 -20230224 2023届高三10班 0.917 +004256 +$(-\infty,-1]\cup [0,+\infty)$ -012885 -20230224 2023届高三10班 0.444 +004499 +$0217$ -012887 -20230224 2023届高三10班 0.722 +004132 +$[-3,1]$ -012905 -20230224 2023届高三10班 0.889 +004217 +$36$ -012906 -20230224 2023届高三10班 0.944 +008972 +B -012907 -20230224 2023届高三10班 0.806 +009082 +D -012908 -20230224 2023届高三10班 0.611 +012445 +B -012912 -20230224 2023届高三10班 0.389 +030691 +B -012913 -20230224 2023届高三10班 0.750 +011301 +(1) $c=8$; (2) $6\sqrt{6}$ -012901 -20230224 2023届高三10班 0.389 +003691 +(1) $935$辆; (2) 因$8782>8736$, 故第$42$个月底单车保有量超过了容纳量 -012902 -20230224 2023届高三10班 1.000 0.556 - -012903 -20230224 2023届高三10班 0.806 0.250 - -012881 -20230224 2023届高三11班 0.857 - -012882 -20230224 2023届高三11班 0.857 - -012883 -20230224 2023届高三11班 0.857 - -012884 -20230224 2023届高三11班 0.905 - -012885 -20230224 2023届高三11班 0.571 - -012887 -20230224 2023届高三11班 0.667 - -012905 -20230224 2023届高三11班 0.905 - -012906 -20230224 2023届高三11班 0.857 - -012907 -20230224 2023届高三11班 0.667 - -012908 -20230224 2023届高三11班 0.571 - -012912 -20230224 2023届高三11班 0.381 - -012913 -20230224 2023届高三11班 0.476 - -012901 -20230224 2023届高三11班 0.524 - -012902 -20230224 2023届高三11班 0.048 0.238 - -012903 -20230224 2023届高三11班 0.762 0.238 - -012881 -20230224 2023届高三12班 1.000 - -012882 -20230224 2023届高三12班 0.955 - -012883 -20230224 2023届高三12班 0.909 - -012884 -20230224 2023届高三12班 0.818 - -012885 -20230224 2023届高三12班 0.364 - -012887 -20230224 2023届高三12班 0.682 - -012905 -20230224 2023届高三12班 1.000 - -012906 -20230224 2023届高三12班 1.000 - -012907 -20230224 2023届高三12班 0.818 - -012908 -20230224 2023届高三12班 0.818 - -012912 -20230224 2023届高三12班 0.591 - 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-012903 -20230224 2023届高三07班 0.594 0.344 - -012881 -20230224 2023届高三08班 0.966 - -012882 -20230224 2023届高三08班 0.966 - -012883 -20230224 2023届高三08班 0.862 - -012884 -20230224 2023届高三08班 0.862 - -012885 -20230224 2023届高三08班 0.828 - -012887 -20230224 2023届高三08班 1.000 - -012905 -20230224 2023届高三08班 0.931 - -012906 -20230224 2023届高三08班 1.000 - -012907 -20230224 2023届高三08班 0.724 - -012908 -20230224 2023届高三08班 0.724 - -012912 -20230224 2023届高三08班 0.621 - -012913 -20230224 2023届高三08班 0.793 - -012901 -20230224 2023届高三08班 0.414 - -012902 -20230224 2023届高三08班 0.931 0.690 - -012903 -20230224 2023届高三08班 0.724 0.414 - -012881 -20230224 2023届高三09班 0.935 - -012882 -20230224 2023届高三09班 0.968 - -012883 -20230224 2023届高三09班 0.677 - -012884 -20230224 2023届高三09班 0.839 - -012885 -20230224 2023届高三09班 0.419 - -012887 -20230224 2023届高三09班 0.645 - -012905 -20230224 2023届高三09班 0.935 - -012906 -20230224 2023届高三09班 0.968 - -012907 -20230224 2023届高三09班 0.645 - -012908 -20230224 2023届高三09班 0.677 - -012912 -20230224 2023届高三09班 0.742 - -012913 -20230224 2023届高三09班 0.806 - -012901 -20230224 2023届高三09班 0.484 - -012902 -20230224 2023届高三09班 0.871 0.290 - -012903 -20230224 2023届高三09班 0.903 0.452 +011450 +(1) $x=\dfrac{\sqrt{2}}2$或$x=-\dfrac{\sqrt{2}}2$; (2) $x_1^2+x_2^2=1$, $y_1^2+y_2^2=2$; (3) 不存在, 证明略. +031236 +(1) $y=x$; (2) $g'(x)=\mathrm{e}^x(\ln (x+1)+\dfrac 1{x+1}+\dfrac{x}{(x+1)^2})$, 故$g(x)$在$[1,+\infty)$上是严格增函数; (3) 证明略. \ No newline at end of file diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index 84b3b735..bac875fd 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1 +1 @@ -003767,003803,003842,003845,003920,003960,013289,013298,013338,013349,013373,013385,013397,013403,013410,013417,013425,013448,013462,013488,013501,013540,013546,013570,013585,013601,013614,013631,013638,013664,013676,013684 \ No newline at end of file +003617,011704,011719,012385,012745,012752 \ No newline at end of file diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index cf079b24..45ca827b 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -2,49 +2,28 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 31244\n", - "raworigin = \"2023年教育部命题四省联考\"\n", - "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\四省.tex\"\n", + "starting_id = 31266\n", + "raworigin = \"自拟题目\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", "editor = \"20230224\\t王伟叶\"\n", - "indexed = True\n" + "indexed = False\n" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "添加题号031244, 来源: 2023年教育部命题四省联考试题1\n", - "添加题号031245, 来源: 2023年教育部命题四省联考试题2\n", - "添加题号031246, 来源: 2023年教育部命题四省联考试题3\n", - "添加题号031247, 来源: 2023年教育部命题四省联考试题4\n", - "添加题号031248, 来源: 2023年教育部命题四省联考试题5\n", - "添加题号031249, 来源: 2023年教育部命题四省联考试题6\n", - "添加题号031250, 来源: 2023年教育部命题四省联考试题7\n", - "添加题号031251, 来源: 2023年教育部命题四省联考试题8\n", - "添加题号031252, 来源: 2023年教育部命题四省联考试题9\n", - "添加题号031253, 来源: 2023年教育部命题四省联考试题10\n", - "添加题号031254, 来源: 2023年教育部命题四省联考试题11\n", - "添加题号031255, 来源: 2023年教育部命题四省联考试题12\n", - "添加题号031256, 来源: 2023年教育部命题四省联考试题13\n", - "添加题号031257, 来源: 2023年教育部命题四省联考试题14\n", - "添加题号031258, 来源: 2023年教育部命题四省联考试题15\n", - "添加题号031259, 来源: 2023年教育部命题四省联考试题16\n", - "添加题号031260, 来源: 2023年教育部命题四省联考试题17\n", - "添加题号031261, 来源: 2023年教育部命题四省联考试题18\n", - "添加题号031262, 来源: 2023年教育部命题四省联考试题19\n", - "添加题号031263, 来源: 2023年教育部命题四省联考试题20\n", - "添加题号031264, 来源: 2023年教育部命题四省联考试题21\n", - "添加题号031265, 来源: 2023年教育部命题四省联考试题22\n" + "添加题号031266, 来源: 自拟题目\n" ] } ], @@ -149,7 +128,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -168,7 +147,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index 0a424239..ac46fa85 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -15,9 +15,9 @@ "题块 2 处理完毕.\n", "正在处理题块 3 .\n", "题块 3 处理完毕.\n", - "开始编译教师版本pdf文件: 临时文件/高三下学期测验02_教师_20230222.tex\n", + "开始编译教师版本pdf文件: 临时文件/高三下学期月考01_教师_20230224.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/高三下学期测验02_学生_20230222.tex\n", + "开始编译学生版本pdf文件: 临时文件/高三下学期月考01_学生_20230224.tex\n", "0\n" ] } @@ -35,7 +35,7 @@ "\"\"\"---设置题块编号---\"\"\"\n", "\n", "problems = [\n", - "\"4292,4143,4190,4169,31241,4128,4189,4129,31242,4130,4233,4174\",\"12021,12437,14087,12346\",\"20958,4657,11218,4508,11388\"\n", + "\"3675,12165,4252,31239,31238,31266,31240,31237,4256,4499,4132,4217\",\"8972,9082,12445,30691\",\"10000,11301,3691,11450,31236\"\n", "]\n", "\n", "\"\"\"---设置结束---\"\"\"\n", @@ -49,7 +49,7 @@ "elif paper_type == 2:\n", " enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n", " template_file = \"模板文件/测验周末卷模板.txt\" #设置模板文件名\n", - " exec_list = [(\"标题替换\",\"高三下学期测验02\")] #设置讲义标题\n", + " exec_list = [(\"标题替换\",\"高三下学期月考01\")] #设置讲义标题\n", " destination_file = \"临时文件/\"+exec_list[0][1] # 设置输出文件名\n", "elif paper_type == 3:\n", " enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n", @@ -204,7 +204,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -223,7 +223,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb index f6edabb2..b4c81cb1 100644 --- a/工具/识别题库中尚未标注的题目类型.ipynb +++ b/工具/识别题库中尚未标注的题目类型.ipynb @@ -2,149 +2,9 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "014532 填空题\n", - "014533 填空题\n", - "014534 解答题\n", - "014535 填空题\n", - "014536 解答题\n", - "014537 解答题\n", - "014538 解答题\n", - "014539 填空题\n", - "014540 解答题\n", - "014541 填空题\n", - "014542 解答题\n", - "014543 填空题\n", - "014544 填空题\n", - "014545 填空题\n", - "014546 选择题\n", - "014547 填空题\n", - "014548 解答题\n", - "014549 解答题\n", - "014550 填空题\n", - "014551 填空题\n", - "014552 解答题\n", - "014553 填空题\n", - "014554 填空题\n", - "014555 解答题\n", - "014556 解答题\n", - "014557 解答题\n", - "014558 填空题\n", - "014559 填空题\n", - "014560 选择题\n", - "014561 填空题\n", - "014562 填空题\n", - "014563 填空题\n", - "014564 填空题\n", - "014565 填空题\n", - "014566 解答题\n", - "014567 解答题\n", - "014568 选择题\n", - "014569 解答题\n", - "014570 填空题\n", - "014571 填空题\n", - "014572 填空题\n", - "014573 填空题\n", - "014574 填空题\n", - "014575 填空题\n", - "014576 填空题\n", - "014577 填空题\n", - "014578 解答题\n", - "014579 填空题\n", - "014580 填空题\n", - "014581 填空题\n", - "014582 填空题\n", - "014583 填空题\n", - "014584 填空题\n", - "014585 填空题\n", - "014586 填空题\n", - "014587 填空题\n", - "014588 解答题\n", - "014589 填空题\n", - "014590 解答题\n", - "014591 填空题\n", - "014592 填空题\n", - "014593 填空题\n", - "014594 填空题\n", - "014595 解答题\n", - "014596 解答题\n", - "014597 解答题\n", - "014598 填空题\n", - "014599 填空题\n", - "014600 解答题\n", - "014601 填空题\n", - "014602 填空题\n", - "014603 填空题\n", - "014604 填空题\n", - "014605 填空题\n", - "014606 填空题\n", - "014607 填空题\n", - "014608 解答题\n", - "014609 填空题\n", - "014610 选择题\n", - "014611 填空题\n", - "014612 填空题\n", - "014613 填空题\n", - "014614 填空题\n", - "014615 填空题\n", - "014616 填空题\n", - "014617 填空题\n", - "014618 填空题\n", - "014619 填空题\n", - "014620 填空题\n", - "014621 填空题\n", - "014622 填空题\n", - "014623 填空题\n", - "014624 解答题\n", - "014625 解答题\n", - "014626 填空题\n", - "014627 解答题\n", - "031236 解答题\n", - "040001 选择题\n", - "040002 填空题\n", - "040003 选择题\n", - "040004 填空题\n", - "040005 填空题\n", - "040006 填空题\n", - "040007 填空题\n", - "040008 填空题\n", - "040009 填空题\n", - "040010 填空题\n", - "040011 填空题\n", - "040012 填空题\n", - "040013 填空题\n", - "040014 填空题\n", - "040015 解答题\n", - "040016 解答题\n", - "040017 解答题\n", - "040018 填空题\n", - "040019 填空题\n", - "040020 填空题\n", - "040021 填空题\n", - "040022 填空题\n", - "040023 填空题\n", - "040024 填空题\n", - "040025 填空题\n", - "040026 填空题\n", - "040027 填空题\n", - "040028 填空题\n", - "040029 填空题\n", - "040030 填空题\n", - "040031 填空题\n", - "040032 填空题\n", - "040033 填空题\n", - "040034 解答题\n", - "040035 解答题\n", - "040036 解答题\n" - ] - } - ], + "outputs": [], "source": [ "import os,re,json\n", "\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 04cc60fc..c9c537ea 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": 9, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/提高课第九单元备选_教师用_20230222.tex\n", + "开始编译教师版本pdf文件: 临时文件/错题修改_教师用_20230225.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/提高课第九单元备选_学生用_20230222.tex\n", + "开始编译学生版本pdf文件: 临时文件/错题修改_学生用_20230225.tex\n", "0\n" ] } @@ -26,7 +26,7 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n", "problems = r\"\"\"\n", - "a\n", + "14221\n", "\n", "\n", "\"\"\"\n", @@ -34,7 +34,7 @@ "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/提高课第九单元备选\"\n", + "filename = \"临时文件/错题修改\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 17f808aa..cdd09f6c 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -99391,7 +99391,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,0)$", "solution": "", "duration": -1, "usages": [], @@ -99809,7 +99809,7 @@ }, "003691": { "id": "003691", - "content": "根据预测, 某地第$n \\ (n\\in \\mathbf{N}^*)$个月共享单车的投放量和损失量分别为$a_n$和$b_n$(单位: 辆), 其中$a_n=\\begin{cases}\n5n^4+15, & 1\\le n\\le 3,\\\\ -10n+470, & n \\ge 4,\n\\end{cases}$ $b_n=n+5$, 第$n$个月底的共享单车的保有量是前$n$个月的累计投放量与累计损失量的差.\\\\\n(1) 求该地区第$4$个月底的共享单车的保有量;\\\\\n(2) 已知该地共享单车停放点第$n$个月底的单车容纳量$S_n=-4(n-46)^2+8800$(单位: 辆). 设在某月底, 共享单车保有量达到最大, 问该保有量是否超出了此时停放点的单车容纳量?", + "content": "根据预测, 某地第$n$($n\\in \\mathbf{N}$, $n\\ge 1$)个月共享单车的投放量和损失量分别为$a_n$和$b_n$(单位: 辆), 其中$a_n=\\begin{cases}\n5n^4+15, & 1\\le n\\le 3,\\\\ -10n+470, & n \\ge 4,\n\\end{cases}$ $b_n=n+5$, 第$n$个月底的共享单车的保有量是前$n$个月的累计投放量与累计损失量的差.\\\\\n(1) 求该地区第$4$个月底的共享单车的保有量;\\\\\n(2) 已知该地共享单车停放点第$n$个月底的单车容纳量$S_n=-4(n-46)^2+8800$(单位: 辆). 设在某月底, 共享单车保有量达到最大, 问该保有量是否超出了此时停放点的单车容纳量?", "objs": [ "K0406005X" ], @@ -99817,7 +99817,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $935$辆; (2) 因$8782>8736$, 故第$42$个月底单车保有量超过了容纳量", "solution": "", "duration": -1, "usages": [], @@ -110588,7 +110588,7 @@ }, "004129": { "id": "004129", - "content": "设椭圆$\\Gamma:\\dfrac{x^2}{a^2}+y^2=1$($a>1$)的左顶点为$A$, 过点$A$的直线$l$与$\\Gamma$相交于另一点$B$, 与$y$轴相交于点$C$. 若$|OA|=|OC|$, $|AB|=|AC|$, 则$a=$\\blank{50}.", + "content": "设椭圆$\\Gamma:\\dfrac{x^2}{a^2}+y^2=1$($a>1$)的左顶点为$A$, 过点$A$的直线$l$与$\\Gamma$相交于另一点$B$, 与$y$轴相交于点$C$. 若$|OA|=|OC|$, $|AB|=|BC|$, 则$a=$\\blank{50}.", "objs": [ "K0715003X" ], @@ -110676,7 +110676,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-3,1]$", "solution": "", "duration": -1, "usages": [ @@ -112936,7 +112936,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$36$", "solution": "", "duration": -1, "usages": [ @@ -114012,7 +114012,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1]\\cup [0,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -120893,7 +120893,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$0217$", "solution": "", "duration": -1, "usages": [ @@ -226726,7 +226726,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -229134,7 +229134,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -282132,7 +282132,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $c=8$; (2) $6\\sqrt{6}$", "solution": "", "duration": -1, "usages": [], @@ -285459,13 +285459,13 @@ }, "011450": { "id": "011450", - "content": "已知动直线$l$与椭圆C:$x^2+\\dfrac{y^2}2=1$交于$P(x_1,y_1)$、$Q(x_2,y_2)$两不同点, 且$\\triangle OPQ$的面积$S_{\\triangle OPQ}=\\dfrac{\\sqrt 2}2$, 其中$O$为坐标原点.\\\\\n(1) 若动直线$l$垂直于$x$轴, 求直线$l$的方程;\\\\\n(2) 证明$x_1^2+x_2^2$和$y_1^2+y_2^2$均为定值;\\\\\n(3) 椭圆$C$上是否存在点$D,E,G$, 使得三角形面积$S_{\\triangle ODE}=S_{\\triangle ODG}=S_{\\triangle OEG}=\\dfrac{\\sqrt 2}2$? 若存在, 判断$\\triangle DEG$的形状; 若不存在, 请说明理由.", + "content": "已知动直线$l$与椭圆$C: x^2+\\dfrac{y^2}2=1$交于$P(x_1,y_1)$、$Q(x_2,y_2)$两不同点, 且$\\triangle OPQ$的面积$S_{\\triangle OPQ}=\\dfrac{\\sqrt 2}2$, 其中$O$为坐标原点.\\\\\n(1) 若动直线$l$垂直于$x$轴, 求直线$l$的方程;\\\\\n(2) 证明$x_1^2+x_2^2$和$y_1^2+y_2^2$均为定值;\\\\\n(3) 椭圆$C$上是否存在点$D,E,G$, 使得三角形面积$S_{\\triangle ODE}=S_{\\triangle ODG}=S_{\\triangle OEG}=\\dfrac{\\sqrt 2}2$? 若存在, 判断$\\triangle DEG$的形状; 若不存在, 请说明理由.", "objs": [], "tags": [ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $x=\\dfrac{\\sqrt{2}}2$或$x=-\\dfrac{\\sqrt{2}}2$; (2) $x_1^2+x_2^2=1$, $y_1^2+y_2^2=2$; (3) 不存在, 证明略.", "solution": "", "duration": -1, "usages": [], @@ -308884,7 +308884,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -347523,7 +347523,7 @@ }, "014221": { "id": "014221", - "content": "已知$\\cos (2 \\alpha-\\beta)=-\\dfrac{11}{14}$, $\\sin (\\alpha-2 \\beta)=\\dfrac{4 \\sqrt{3}}{7}$, $0<\\beta<\\dfrac{\\pi}{4}<\\alpha<\\dfrac{\\pi}{2}$, 求$\\alpha+\\beta$的值.", + "content": "已知$\\cos (2 \\alpha-\\beta)=-\\dfrac{2\\sqrt{7}}{7}$, $\\sin (\\alpha-2 \\beta)=\\dfrac{\\sqrt{21}}{14}$, $0<\\beta<\\dfrac{\\pi}{4}<\\alpha<\\dfrac{\\pi}{2}$, 求$\\alpha+\\beta$的值.", "objs": [], "tags": [], "genre": "解答题", @@ -347533,7 +347533,8 @@ "usages": [], "origin": "2023年空中课堂高三复习课08", "edit": [ - "20230131\t王伟叶" + "20230131\t王伟叶", + "20230225\t周双" ], "same": [], "related": [], @@ -419928,7 +419929,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -431895,7 +431896,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $y=x$; (2) $g'(x)=\\mathrm{e}^x(\\ln (x+1)+\\dfrac 1{x+1}+\\dfrac{x}{(x+1)^2})$, 故$g(x)$在$[1,+\\infty)$上是严格增函数; (3) 证明略.", "solution": "", "duration": -1, "usages": [], @@ -431920,7 +431921,7 @@ "概率" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 35$", "solution": "", "duration": -1, "usages": [], @@ -431971,7 +431972,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 23$", "solution": "", "duration": -1, "usages": [], @@ -431996,7 +431997,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\pi}3$", "solution": "", "duration": -1, "usages": [], @@ -432091,7 +432092,7 @@ "content": "设$z=1+\\mathrm{i}$, 则$z^2-\\mathrm{i}=$\\bracket{20}.\n\\fourch{$\\mathrm{i}$}{$-\\mathrm{i}$}{$1$}{$-1$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -432110,7 +432111,7 @@ "content": "设集合$A=\\{2,3, a^2-2 a-3\\}$, $B=\\{0,3\\}$, $C=\\{2, a\\}$. 若$B \\subseteq A$, $A \\cap C=\\{2\\}$, 则$a=$\\bracket{20}.\n\\fourch{$-3$}{$-1$}{$1$}{$3$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -432129,7 +432130,7 @@ "content": "甲、乙、丙、丁四名教师带领学生参加校园植树活动, 教师随机分成三组, 每组至少一人, 则甲、乙在同一组的概率为\\bracket{20}.\n\\fourch{$\\dfrac{1}{6}$}{$\\dfrac{1}{4}$}{$\\dfrac{1}{3}$}{$\\dfrac{1}{2}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -432148,7 +432149,7 @@ "content": "平面向量$\\overrightarrow{a}$与$\\overrightarrow{b}$相互垂直, 已知$\\overrightarrow{a}=(6,-8)$, $|\\overrightarrow{b}|=5$, 且$\\overrightarrow{b}$与向量$(1,0)$的夹角是钝角, 则$\\overrightarrow{b}=$\\bracket{20}.\n\\fourch{$(-3,-4)$}{$(4,3)$}{$(-4,3)$}{$(-4,-3)$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -432167,7 +432168,7 @@ "content": "已知点$A, B, C$为椭圆$D$的三个顶点, 若$\\triangle ABC$是正三角形, 则$D$的离心率是\\bracket{20}.\n\\fourch{$\\dfrac{1}{2}$}{$\\dfrac{2}{3}$}{$\\dfrac{\\sqrt{6}}{3}$}{$\\dfrac{\\sqrt{3}}{2}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -432186,7 +432187,7 @@ "content": "三棱锥$A-BCD$中, $AC \\perp$平面$BCD$, $BD \\perp CD$. 若$AB=3, BD=1$, 则该三棱锥体积的最大值为\\bracket{20}.\n\\fourch{$2$}{$\\dfrac{4}{3}$}{$1$}{$\\dfrac{2}{3}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -432205,7 +432206,7 @@ "content": "设函数$f(x), g(x)$在$\\mathbf{R}$的导函数存在, 且$f'(x)g(x)$}{$f(x)+g(a)=latex,scale = 3]\n\\draw (0,0,0) node [left] {$O$} coordinate (O);\n\\draw ({sqrt(2)/2},0,{sqrt(2)/2}) node [below] {$A$} coordinate (A);\n\\draw ({sqrt(6)/4},{1/2},{sqrt(6)/4}) node [below right] {$C$} coordinate (C);\n\\draw ({sqrt(6)/4},0,{sqrt(6)/4}) node [above left] {$K$} coordinate (K);\n\\draw ({sqrt(6)/4},0,0) node [above right] {$N$} coordinate (N);\n\\draw ($(N)+(C)-(K)$) node [above] {$M$} coordinate (M);\n\\draw (1,0,0) node [right] {$B$} coordinate (B);\n\\draw ($(O)!{4/sqrt(10)}!(M)$) node [right] {$D$} coordinate (D);\n\\draw (O)--(A)(O)--(C)(O)--(D)(K)--(C)--(M);\n\\draw [dashed] (O)--(B)(M)--(N)--(K)(O)--++(0,1,0)(O)--++(0,0,1);\n\\draw [domain = 0:45] plot ({cos(\\x)},0,{sin(\\x)});\n\\draw [dashed, domain = 45:90] plot ({cos(\\x)},0,{sin(\\x)});\n\\draw [domain = 0:{acos(sqrt(6)/sqrt(10))}] plot ({cos(\\x)},{sin(\\x)},0);\n\\draw [dashed,domain = {acos(sqrt(6)/sqrt(10))}:90] plot ({cos(\\x)},{sin(\\x)},0);\n\\draw [dashed, domain = 0:90] plot (0,{cos(\\x)},{sin(\\x)});\n\\draw [domain = 0:30] plot ({sqrt(2)/2*cos(\\x)},{sin(\\x)},{sqrt(2)/2*cos(\\x)});\n\\draw [dashed, domain = 30:90] plot ({sqrt(2)/2*cos(\\x)},{sin(\\x)},{sqrt(2)/2*cos(\\x)});\n\\draw [domain = 0:{acos(sqrt(10)/4)}] plot ({sqrt(6)/sqrt(10)*cos(\\x)},{2/sqrt(10)*cos(\\x)},{sin(\\x)});\n\\draw [dashed, domain = {acos(sqrt(10)/4)}:90] plot ({sqrt(6)/sqrt(10)*cos(\\x)},{2/sqrt(10)*cos(\\x)},{sin(\\x)});\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -432319,7 +432320,7 @@ "content": "某工厂生产的产品的质量指标服从正态分布$N(100, \\sigma^2)$. 质量指标介于$99$至$101$之间''的产品为良品, 为使这种产品的良品率达到$95.45 \\%$, 则需调整生产工艺, 使得$\\sigma$至多为\\blank{50}. (若$X \\sim N(\\mu, \\sigma^2)$, 则$P\\{|X-\\mu|<2 \\sigma\\}=0.9545$)", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -432338,7 +432339,7 @@ "content": "若$P, Q$分别是抛物线$x^2=y$与圆$(x-3)^2+y^2=1$上的点, 则$|PQ|$的最小值为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -432357,7 +432358,7 @@ "content": "数学家祖冲之曾给出圆周率$\\pi$的两个近似值: ``约率''$\\dfrac{22}{7}$与``密率''$\\dfrac{355}{113}$、它们可用``调日法''得到: 称小于$3.1415926$的近似值为弱率, 大于$3.1415927$的近似值为强率. 由$\\dfrac{3}{1}<\\pi<\\dfrac{4}{1}$, 取$3$为弱率, $4$为强率, 得$a_1=\\dfrac{3+4}{1+1}=\\dfrac{7}{2}$, 故$a_1$为强率, 与上一次的弱率$3$计算得$a_2=\\dfrac{3+7}{1+2}=\\dfrac{10}{3}$, 故$a_2$为强率, 继续计算, $\\cdots \\cdots$. 若某次得到的近似值为强率, 与上一次的弱率继续计算得到新的近似值; 若某次得到的近似值为弱率, 与上一次的强率继续计算得到新的近似值, 依此类推. 已知$a_m=\\dfrac{22}{7}$, 则$m=$\\blank{50}; $a_{8}=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -432376,7 +432377,7 @@ "content": "如图为一个开关阵列, 每个开关只有``开''和``关''两种状态, 按其中一个开关$1$次, 将导致自身和所有相邻的开关改变状态. 例如, 按$(2,2)$将导致$(1,2),(2,1),(2,2),(2,3),(3,2)$改变状态. 如果要求只改变$(1,1)$的状态, 则需按开关的最少次数为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline$(1,1)$&$(1,2)$&$(1,3)$\\\\\n\\hline$(2,1)$&$(2,2)$&$(2,3)$\\\\\n\\hline$(3,1)$&$(3,2)$&$(3,3)$\\\\\n\\hline\n\\end{tabular}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -432395,7 +432396,7 @@ "content": "如图, 四边形$ABCD$是圆柱底面的内接四边形, $AC$是圆柱的底面直径, $PC$是圆柱的母线, $E$是$AC$与$BD$的交点, $AB=AD$, $\\angle BAD=60^{\\circ}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-2,0) arc (180:360:2 and 0.5);\n\\draw [dashed] (-2,0) arc (180:0:2 and 0.5);\n\\draw (0,4) ellipse (2 and 0.5);\n\\draw (-2,0) -- (-2,4) (2,0) -- (2,4);\n\\draw (150:2 and 0.5) node [above] {$B$} coordinate (B);\n\\draw (30:2 and 0.5) node [below] {$D$} coordinate (D);\n\\draw (80:2 and 0.5) node [above right] {$C$} coordinate (C);\n\\draw (260:2 and 0.5) node [below] {$A$} coordinate (A);\n\\draw (C)++(0,4) node [above] {$P$} coordinate (P);\n\\draw ($(P)!0.25!(A)$) node [left] {$F$} coordinate (F);\n\\draw [dashed] (P)--(A)(P)--(B)(P)--(C)(P)--(D)(A)--(C)(B)--(D)(C)--(F)(D)--(F)(A)--(B)--(C)--(D)--cycle;\n\\path [name path = AC] (A)--(C);\n\\path [name path = BD] (B)--(D);\n\\path [name intersections = {of = AC and BD, by = E}];\n\\draw (E) node [below right] {$E$};\n\\end{tikzpicture}\n\\end{center}\n(1) 记圆柱的体积为$V_1$, 四棱锥$P-ABCD$的体积为$V_2$, 求$\\dfrac{V_1}{V_2}$;\\\\\n(2) 设点$F$在线段$AP$上, $PA=4PF$, $PC=4CE$, 求二面角$F-CD-P$的余弦值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -432407,14 +432408,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031261": { "id": "031261", "content": "已知函数$f(x)=\\sin (\\omega x+\\varphi)$在区间$(\\dfrac{\\pi}{6}, \\dfrac{\\pi}{2})$单调, 其中$\\omega$为正整数, $|\\varphi|<\\dfrac{\\pi}{2}$, 且$f(\\dfrac{\\pi}{2})=f(\\dfrac{2 \\pi}{3})$.\\\\\n(1) 求$y=f(x)$图像的一条对称轴;\\\\\n(2) 若$f(\\dfrac{\\pi}{6})=\\dfrac{\\sqrt{3}}{2}$, 求$\\varphi$.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -432426,14 +432427,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031262": { "id": "031262", "content": "记数列$\\{a_n\\}$的前$n$项和为$T_n$, 且$a_1=1$, $a_n=T_{n-1}$($n \\geq 2$).\\\\\n(1) 求数列$\\{a_n\\}$的通项公式:\\\\\n(2) 设$m$为整数, 且对任意$n \\in \\mathbf{N}$, $n \\ge 1$, $m \\geq \\dfrac{1}{a_1}+\\dfrac{2}{a_2}+\\cdots+\\dfrac{n}{a_n}$, 求$m$的最小值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -432445,14 +432446,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031263": { "id": "031263", "content": "一个池塘里的鱼的数目记为$N$, 从池塘里捞出$200$尾鱼, 并给鱼作上标识, 然后把鱼放回池塘里, 过一小段时间后再从池塘里拱出$500$尾鱼, $X$表示捞出的$500$尾鱼中有标识的鱼的数目.\\\\\n(1) 若$N=5000$, 求$X$的数学期望;\\\\\n(2) 已知捞出的$500$尾鱼中$15$尾有标识, 试给出$N$的估计值(以使得$P(X=15)$取大的$N$的值作为$N$的估计值).", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -432464,14 +432465,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031264": { "id": "031264", "content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)过点$A(4 \\sqrt{2}, 3)$, 且焦距为$10$.\\\\\n(1) 求$C$的方程;\\\\\n(2) 已知点$B(4 \\sqrt{2},-3)$, $D(2 \\sqrt{2}, 0)$, $E$为线段$AB$上一点, 且直线$DE$交$C$于$G$, $H$两点. 证明: $\\dfrac{|GD|}{|GE|}=\\dfrac{|HD|}{|HE|}$.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -432483,14 +432484,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031265": { "id": "031265", "content": "椭圆曲线加密算法运用于区块链.\\\\\n椭圆曲线$C=\\{(x, y) | y^2=x^3+a x+b,\\ 4 a^3+27 b^2 \\neq 0\\}$, $P \\in C$关于$x$轴的对称点记为 $\\tilde{C}$. $C$在点$P(x, y)$($y \\neq 0$)处的切线是指曲线$y=\\pm \\sqrt{x^3+a x+b}$在点$P$处的切线. 定义``$\\oplus$\" 运算满足:\\\\\n\\textcircled{1} 若$P \\in C$, $Q \\in C$, 且直线$PQ$与$C$有第三个交点$R$, 则$P \\oplus Q=\\tilde{R}$;\\\\\n\\textcircled{2} 若$P \\in C$, $Q \\in C$, 且$PQ$为$C$的切线, 切点为$P$, 则$P \\oplus Q=\\tilde{P}$;\\\\\n\\textcircled{3} 若$P \\in C$, 规定$P \\oplus \\tilde{P}=0^{\\circ}$, 且$P \\oplus 0^{\\circ}=0^{\\circ} \\oplus P=P$.\\\\\n(1) 当$4 a^3+27 b^2=0$时, 讨论函数$h(x)=x^3+a x+b$零点的个数;\\\\\n(2) 已知``$\\oplus$''运算满足交换律、结合律, 若$P \\in C$, $Q \\in C$, 且$PQ$为$C$的切线, 切点为$P$, 证明: $P \\oplus P=\\tilde{Q}$;\\\\(3) 已知$P(x_1, y_1) \\in C$, $Q(x_2, y_2) \\in C$, 且直线$PQ$与$C$有第三个交点, 求$P \\oplus Q$的坐标.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -432502,6 +432503,25 @@ "same": [], "related": [], "remark": "", + "space": "12ex" + }, + "031266": { + "id": "031266", + "content": "已知$18$个整数的中位数为$5$, 第$75$百分位数也为$5$, 那么这$18$个数中, $5$的个数的最小可能值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$6$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", "space": "" }, "040001": { @@ -433193,7 +433213,7 @@ "content": "已知点$M$的极坐标是$(-2,-\\dfrac{\\pi}{6})$, 它关于极轴的对称点坐标是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433212,7 +433232,7 @@ "content": "在极坐标系中, 若点$A(1, \\dfrac{3 \\pi}{4})$、$B(2, \\dfrac{\\pi}{4})$, 则$A$、$B$两点间的距离为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433231,7 +433251,7 @@ "content": "若点$M$的直角坐标为$(-3,-3 \\sqrt{3})$, 若$\\rho>0$, $0 \\leq \\theta<2 \\pi$, 则点$M$的极坐标是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433250,7 +433270,7 @@ "content": "极坐标系中, 若点$A$的极坐标是$(3, \\dfrac{\\pi}{6})$, 则:\\\\\n(1) 点$A$关于极轴对称的点极坐标是\\blank{50};\\\\\n(2) 点$A$关于极点对称的点极坐标是\\blank{50};\\\\\n(3) 点$A$关于直线$\\theta=\\dfrac{\\pi}{2}$的对称点的极坐标是\\blank{50}.(规定$\\rho>0$, $\\theta \\in[0,2 \\pi)$)", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433269,7 +433289,7 @@ "content": "若直线$l$的极坐标方程为$2 \\rho \\sin (\\theta-\\dfrac{\\pi}{4})=\\sqrt{2}$, 点$A$的极坐标为$(2 \\sqrt{2}, \\dfrac{7 \\pi}{4})$, 则点$A$到直线$l$的距离为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433288,7 +433308,7 @@ "content": "若曲线$C$的极坐标方程为$\\rho=3 \\sin \\theta$, 则曲线$C$的直角坐标方程为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433307,7 +433327,7 @@ "content": "在极坐标系中, 圆$\\rho=8 \\sin \\theta$上的点到直线$\\theta=\\dfrac{\\pi}{3}$($\\rho \\in \\mathbf{R}$)距离的最大值是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433326,7 +433346,7 @@ "content": "若双曲线的渐近线方程为$y=\\pm 3 x$, 它的一个焦点是$(\\sqrt{10}, 0)$, 则双曲线的方程是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433345,7 +433365,7 @@ "content": "已知椭圆$\\dfrac{x^2}{16}+\\dfrac{y^2}{7}=1$的右焦点为$F$, 过原点$O$作直线交椭圆于$A$、$B$两点, 点$A$在$x$轴的上方. 若三角形$ABF$的面积为$2$, 则点$A(p, q)$的纵坐标$q=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433364,7 +433384,7 @@ "content": "直线$y=x+3$与曲线$\\dfrac{y^2}{9}-\\dfrac{x|x|}{4}=1$公共点的个数是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433383,7 +433403,7 @@ "content": "若实数$x$、$y$满足$\\dfrac{y}{2}=\\sqrt{1-x^2}$, 则$y-2 x$的取值范围为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433402,7 +433422,7 @@ "content": "直线$y=k(x-3)$($k \\in \\mathbf{R}$)与双曲线$\\dfrac{x^2}{m}-\\dfrac{y^2}{27}=1$, 某学生作如下变形: 由$\\begin{cases}y=k(x-3), \\\\ \\dfrac{x^2}{m}-\\dfrac{y^2}{27}=1,\\end{cases}$消去$y$后得到形如: $a x^2+b x+c=0$的方程, 当$a=0$时该方程恒有一解; 当$a \\neq 0$时$\\Delta=b^2-4 a c \\geq 0$对$k \\in \\mathbf{R}$恒成立, 假设该学生的演算过程是正确的, 根据该学生的演算过程提供的信息, 则实数$m$的取值范围为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -433421,7 +433441,7 @@ "content": "若点$A(-2,-\\dfrac{\\pi}{2})$、$B(\\sqrt{2}, \\dfrac{3 \\pi}{4})$、$0(0,0)$, 则$\\triangle ABO$为\\bracket{20}.\n\\fourch{正三角形}{直角三角形}{锐角等腰三角形}{直角等腰三角形}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -433440,7 +433460,7 @@ "content": "已知动点$P(x, y)$满足$13 \\sqrt{(x+2)^2+(y-3)^2}=|12 x+5 y-1|$, 则$P$点的轨迹是\\bracket{20}.\n\\fourch{两条相交直线}{拋物线}{双曲线}{椭圆}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -433459,7 +433479,7 @@ "content": "若动点$(x, y)$在曲线$\\dfrac{x^2}{4}+\\dfrac{y^2}{b^2}=1(0=latex,scale = 0.3]\n\\draw [->] (-8,0) -- (8,0) node [below] {$x$};\n\\draw [->] (0,-6) -- (0,6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\filldraw (2,0) circle (0.06) node [below] {$M$} coordinate (M);\n\\filldraw (4,0) circle (0.06) node [below] {$F$} coordinate (F);\n\\draw (-6,0) node [below left] {$A$} coordinate (A);\n\\draw (6,0) node [below right] {$B$} coordinate (B);\n\\draw (1.5,{sqrt(18.75)}) node [above] {$P$} coordinate (P);\n\\draw (A)--(P)--(F);\n\\draw (0,0) ellipse (6 and {sqrt(20)});\n\\end{tikzpicture}\n\\end{center}\n(1) 求点$P$的坐标;\\\\\n(2) 设$\\mathrm{M}$是椭圆长轴$\\mathrm{AB}$上的一点, $\\mathrm{M}$到直线$\\mathrm{A} P$的距离等于$|MB|$, 求椭圆上的点到点$\\mathrm{M}$的距离$d$的最小值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -433528,14 +433548,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "040055": { "id": "040055", "content": "已知抛物线$y^2=2 p x$($p>0$), $a$是实数. 过动点$M(a, 0)$且斜率为$1$的直线$l$与该抛物线交于不同两点$A$、$B$, 且$|AB| \\leq 2 p$.\\\\\n(1) 求$a$的取值范围;\\\\\n(2) 若线段$AB$的垂直平分线交$x$轴于点$N$, 求三角形$NAB$面积的最大值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -433547,14 +433567,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "040056": { "id": "040056", "content": "已知双曲线$\\Gamma: \\dfrac{x^2}{2}-\\dfrac{y^2}{4}=1$的右顶点为$A$, 点$B$的坐标为$(1, \\sqrt{2})$.\\\\\n(1) 设双曲线$\\Gamma$的两条渐近线的夹角为$\\theta$, 求$\\cos \\theta$;\\\\\n(2) 设点$D$是双曲线$\\Gamma$上的动点, 若点$N$满足$\\overrightarrow{BN}=\\overrightarrow{ND}$, 求点$N$的轨迹方程;\\\\\n(3) 过点$B$的动直线$l$交双曲线$\\Gamma$于$P$、$Q$两个不同的点, $M$为线段$PQ$的中点, 求直线$AM$的斜率的取值范围.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -433566,6 +433586,500 @@ "same": [], "related": [], "remark": "", + "space": "12ex" + }, + "040057": { + "id": "040057", + "content": "若$\\alpha$是锐角, $\\sin \\alpha=\\dfrac{3}{4}$, 则$\\cos \\alpha+\\tan \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", "space": "" + }, + "040058": { + "id": "040058", + "content": "若$\\alpha \\in(2 k \\pi+\\dfrac{\\pi}{2}, 2 k \\pi+\\pi)$, $k \\in \\mathbf{Z}$, $|\\cos \\alpha|=\\dfrac{5}{13}$, 则$\\sin \\alpha+\\cot \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040059": { + "id": "040059", + "content": "若$\\tan \\alpha=3$, 则$\\dfrac{\\sin \\alpha+\\cos \\alpha}{\\sin \\alpha-\\cos \\alpha}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040060": { + "id": "040060", + "content": "设$m$是常数, 且$-1-\\dfrac{2 \\pi}{3}$. 当$a=\\dfrac{1}{2}$时, 方程$\\cos x=a$在$[-\\dfrac{2 \\pi}{3}, m]$内恰有一个$x$, 则$m$的取值范围为\\blank{50};\\\\\n(3) 常数$a$使得: 对于任意常数$m>-\\dfrac{2 \\pi}{3}$, 方程$\\cos x=a$在$[-\\dfrac{2 \\pi}{3}, m]$内总是至少有一个$x$存在, 则$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040072": { + "id": "040072", + "content": "设$\\dfrac{3 \\pi}{2}<\\alpha<2 \\pi$, 化简:\\\\\n(1) $\\sqrt{\\tan ^2 \\alpha+\\cot ^2 \\alpha+2}$;\\\\\n(2) $\\sqrt{\\dfrac{1}{1-\\cos \\alpha}+\\dfrac{1}{1+\\cos \\alpha}}(\\dfrac{3 \\pi}{2}<\\alpha<2 \\pi)$;\\\\\n(3) $\\tan (\\dfrac{9 \\pi}{4}+\\theta) \\tan (\\dfrac{3 \\pi}{4}+\\theta)$;\\\\\n(4) $\\dfrac{1+\\sin (\\pi-x)}{\\cos (\\pi-x)}-\\dfrac{\\cos (\\pi+x)}{1+\\sin (\\pi+x)}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040073": { + "id": "040073", + "content": "证明下列恒等式:\\\\\n(1) $(\\sin \\alpha+\\cos \\alpha)^2=1+2 \\sin \\alpha \\cos \\alpha$;\\\\\n(2) $(\\sin \\alpha-\\cos \\alpha)^2=1-2 \\sin \\alpha \\cos \\alpha$;\\\\\n(3) $(\\sin \\alpha+\\cos \\alpha)^2+(\\sin \\alpha-\\cos \\alpha)^2=2$;\\\\\n(4) $(\\sin \\alpha+\\cos \\alpha)^2-(\\sin \\alpha-\\cos \\alpha)^2=4 \\sin \\alpha \\cos \\alpha$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040074": { + "id": "040074", + "content": "已知$\\sin \\alpha$、$\\cos \\alpha$是方程$8 x^2+6 k x+2 k+1=0$的两个实数根, 求$k$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040075": { + "id": "040075", + "content": "已知数列$\\{a_n\\}$满足$a_1=1$, $a_n=\\dfrac{a_{n-1}}{3 a_{n-1}+1}$, 那么它的通项公式是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040076": { + "id": "040076", + "content": "已知数列$\\{a_n\\}$满足$a_1=1$, $a_{n-1} a_n=a_{n-1}-a_n$, 那么它的通项公式是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040077": { + "id": "040077", + "content": "已知数列$\\{a_n\\}$满足$a_1=1$, $a_n=5 a_{n-1}+5^n$, 那么它的通项公式是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040078": { + "id": "040078", + "content": "已知数列$\\{a_n\\}$满足$a_1=1$且$a_{n+1}=2 a_n+3$, 则$a_n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040079": { + "id": "040079", + "content": "已知数列$\\{a_n\\}$满足: $a_1=1$, $a_{n+1}-a_n \\in\\{a_1, a_2, \\cdots, a_n\\}$($n \\geq 1$), 记数列$\\{a_n\\}$的前$n$项和为$S_n$, 若对所有满足条件的数列$\\{a_n\\}$, $S_{10}$的最大值为$M$. 最小值为$m$, 则$M+m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040080": { + "id": "040080", + "content": "数列$\\{a_n\\}$中, $a_n=\\begin{cases}2^n, & n=2 k-1, \\\\ 2 n, & n=2 k\\end{cases}$($k \\geq 1$). 求$\\{a_n\\}$的前$n$项和$S_n$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040081": { + "id": "040081", + "content": "在数列$\\{a_n\\}$中, 已知$a_1=1$, 当$n \\geq 1$时$a_{n+1}>a_n$, 且满足$(a_{n+1}+a_n-1)^2=4 a_{n+1} a_n$, 设$b_n=\\sqrt{a_n}$.\\\\\n(1) 求证: 数列$\\{b_n\\}$是等差数列;\\\\\n(2) 求数列$\\{a_n\\}$的通项公式.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040082": { + "id": "040082", + "content": "数列$\\{a_n\\}$中, $a_n=2 n-1$, $n$为正整数.\\\\\n(1) 是否存在等差数列$\\{b_n\\}$, 其前$n$项和$S_n$满足$\\{x | x=S_n, n$为正整数$\\} \\subseteq\\{x | x=a_n, n$为正整数$\\}$? 若存在, 找出一个这样的等差数列$\\{b_n\\}$; 若不存在, 说明理由;\\\\\n(2) 是否存在等比数列$\\{c_n\\}$, 其前$n$项和$T_n$满足$\\{x | x=T_n, n$为正整数$\\} \\subseteq\\{x | x=a_n, n$为正整数$\\}$? 若存在, 找出一个这样的等比数列$\\{c_n\\}$; 若不存在, 说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷02", + "edit": [ + "20230224\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" } } \ No newline at end of file