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 40c58a52..efaee5c0 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": 2, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 2, + "execution_count": 1, "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 = \"14764:14783\"\n", + "problems = \"031244,031245,031246,031247,031248,031249,031250,031251,031252,031253,031254,031255,031256,031257,031258,031259,031260,031261,031262,031263,031264,031265,031311,031312,031313,031314,031315,031316,031317,031318,031319,031320,031321,031322,031323,031324,031325,031326,031327,031328,031329,031330,031331\"\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": 2, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ 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 9adae067..2b305e84 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -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", - " {\"content\":[r\"双曲线\"],\"content2\":[r\"部分\"]}\n", + " {\"origin\":[r\"素养\"]}\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 ca876bfd..63a8ac36 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 @@ -103,7 +103,31 @@ "赋能19.tex\n", "赋能20.tex\n", "赋能21.tex\n", - "031243\n", + "赋能22.tex\n", + "030600\n", + "\n", + "\n", + "赋能23.tex\n", + "赋能24.tex\n", + "赋能25.tex\n", + "赋能26.tex\n", + "001748\n", + "\n", + "\n", + "赋能27.tex\n", + "003839\n", + "\n", + "\n", + "赋能28.tex\n", + "004537\n", + "\n", + "\n", + "赋能29.tex\n", + "010525\n", + "\n", + "\n", + "赋能30.tex\n", + "013307\n", "\n", "\n", "2017届上海春季高考.tex\n", @@ -401,6 +425,79 @@ "012938\n", "\n", "\n", + "16_导数及其应用.tex\n", + "040202\n", + "\n", + "\n", + "040205\n", + "\n", + "\n", + "021376\n", + "\n", + "\n", + "021396\n", + "\n", + "\n", + "013633\n", + "\n", + "\n", + "031354\n", + "\n", + "\n", + "030416\n", + "\n", + "\n", + "031353\n", + "\n", + "\n", + "013297\n", + "\n", + "\n", + "030400\n", + "\n", + "\n", + "021429\n", + "\n", + "\n", + "030424\n", + "\n", + "\n", + "021428\n", + "\n", + "\n", + "021365\n", + "\n", + "\n", + "013334\n", + "\n", + "\n", + "021395\n", + "\n", + "\n", + "021418\n", + "\n", + "\n", + "031355\n", + "\n", + "\n", + "031356\n", + "\n", + "\n", + "030420\n", + "\n", + "\n", + "021431\n", + "\n", + "\n", + "013508\n", + "\n", + "\n", + "040222\n", + "\n", + "\n", + "030426\n", + "\n", + "\n", "17_计数原理与二项式定理.tex\n", "013222\n", "\n", @@ -577,6 +674,76 @@ "014600\n", "\n", "\n", + "19_统计.tex\n", + "013220\n", + "\n", + "\n", + "014092\n", + "\n", + "\n", + "014629\n", + "\n", + "\n", + "014631\n", + "\n", + "\n", + "014632\n", + "\n", + "\n", + "014635\n", + "\n", + "\n", + "014641\n", + "\n", + "\n", + "014637\n", + "\n", + "\n", + "014638\n", + "\n", + "\n", + "014634\n", + "\n", + "\n", + "014633\n", + "\n", + "\n", + "013235\n", + "\n", + "\n", + "013218\n", + "\n", + "\n", + "013237\n", + "\n", + "\n", + "014640\n", + "\n", + "\n", + "014642\n", + "\n", + "\n", + "014643\n", + "\n", + "\n", + "014636\n", + "\n", + "\n", + "014088\n", + "\n", + "\n", + "014085\n", + "\n", + "\n", + "014644\n", + "\n", + "\n", + "014645\n", + "\n", + "\n", + "014646\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", 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 70364c1a..4847e930 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 @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "首个空闲id: 14764 , 直至 020000\n", + "首个空闲id: 14784 , 直至 020000\n", "首个空闲id: 22106 , 直至 030000\n", - "首个空闲id: 31361 , 直至 040000\n", + "首个空闲id: 31382 , 直至 040000\n", "首个空闲id: 40336 , 直至 999999\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 c18ba8b6..64724073 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 @@ -2,181 +2,34 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t1.000\t0.943\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t1.000\t0.886\t0.886\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.686\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.800\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.714\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.886\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.886\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.914\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.314\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.429\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.771\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.943\t0.714\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.514\t0.714\t0.314\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三10班\t0.857\t0.829\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t1.000\t0.700\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t1.000\t0.950\t0.850\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.650\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.800\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.600\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.900\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.950\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t1.000\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.350\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.250\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.850\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t1.000\t0.900\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.700\t0.850\t0.150\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三11班\t0.800\t0.550\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t1.000\t1.000\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t1.000\t0.857\t0.857\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.857\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.667\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.571\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.952\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.905\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.905\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.429\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.667\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.714\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t1.000\t0.762\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.809\t0.762\t0.286\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三12班\t0.809\t0.809\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t1.000\t1.000\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t1.000\t0.964\t1.000\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.964\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.929\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.857\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.964\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t1.000\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t1.000\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.643\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.821\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.964\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.964\t0.893\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.679\t0.964\t0.536\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三01班\t0.893\t0.929\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t1.000\t0.781\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t1.000\t0.938\t0.906\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.719\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.906\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.844\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.750\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.969\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.906\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.438\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.812\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.875\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t1.000\t0.219\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.500\t0.812\t0.500\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三02班\t0.656\t0.562\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t1.000\t1.000\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.917\t0.917\t0.917\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.750\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.708\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.792\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.792\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.958\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t1.000\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.500\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.792\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t1.000\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.958\t0.708\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.417\t0.917\t0.375\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三03班\t0.833\t0.958\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t1.000\t0.880\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.960\t0.880\t0.920\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.760\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.880\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.680\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.600\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.960\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.880\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.400\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.680\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.760\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.920\t0.440\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.360\t0.520\t0.320\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三04班\t0.800\t0.400\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t1.000\t0.944\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.972\t0.917\t0.917\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.861\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.889\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.806\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.889\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.972\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.972\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.472\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.583\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.833\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.917\t0.861\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.583\t0.778\t0.389\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三05班\t0.944\t0.861\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.971\t0.943\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.943\t0.800\t0.914\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.771\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.914\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.886\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.943\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t1.000\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.971\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.543\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.829\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.886\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t1.000\t0.943\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.400\t0.943\t0.229\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三06班\t0.886\t0.914\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.964\t0.821\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t1.000\t0.893\t0.893\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.571\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.607\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.679\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.857\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.893\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t1.000\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.321\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.464\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.714\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.929\t0.714\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.714\t0.714\t0.179\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三07班\t0.964\t0.250\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.962\t0.962\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t1.000\t0.885\t0.846\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.808\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.769\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.692\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.769\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.962\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.885\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.462\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.538\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.769\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t1.000\t0.615\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.269\t0.692\t0.231\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三08班\t0.808\t0.269\n", - "题号: 014532 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.893\t0.857\n", - "题号: 014533 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.964\t0.786\t0.786\n", - "题号: 012920 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.786\n", - "题号: 014534 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.714\n", - "题号: 013926 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.643\n", - "题号: 013921 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.786\n", - "题号: 012967 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.893\n", - "题号: 012968 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.857\n", - "题号: 012933 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.286\n", - "题号: 013923 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.321\n", - "题号: 014546 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.714\n", - "题号: 014540 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.929\t0.786\n", - "题号: 013007 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.679\t0.571\t0.214\n", - "题号: 014538 , 字段: usages 中已添加数据: 20230321\t2023届高三09班\t0.893\t0.607\n" + "题号: 031361 , 字段: ans 中已修改数据: $\\sqrt{2}$\n", + "题号: 031362 , 字段: ans 中已修改数据: $66$\n", + "题号: 031363 , 字段: ans 中已修改数据: $-1$\n", + "题号: 031364 , 字段: ans 中已修改数据: $8.5$\n", + "题号: 031365 , 字段: ans 中已修改数据: $160$\n", + "题号: 031366 , 字段: ans 中已修改数据: $\\dfrac{8\\sqrt{3}}3\\pi$\n", + "题号: 031367 , 字段: ans 中已修改数据: $10\\sqrt{3}$\n", + "题号: 031368 , 字段: ans 中已修改数据: $-3$\n", + "题号: 031369 , 字段: ans 中已修改数据: $\\dfrac 45$\n", + "题号: 031370 , 字段: ans 中已修改数据: $\\dfrac{4\\pi}3$\n", + "题号: 031371 , 字段: ans 中已修改数据: $[-\\dfrac{13}4,3]$\n", + "题号: 031372 , 字段: ans 中已修改数据: $[\\dfrac 52,3]$\n", + "题号: 031373 , 字段: ans 中已修改数据: B\n", + "题号: 031374 , 字段: ans 中已修改数据: A\n", + "题号: 031375 , 字段: ans 中已修改数据: B\n", + "题号: 031376 , 字段: ans 中已修改数据: D\n", + "题号: 031377 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arcsin \\dfrac{\\sqrt{15}}5$\n", + "题号: 031378 , 字段: ans 中已修改数据: (1) 当$a=0$时, $f_a(x)$是偶函数, 当$a\\ne 0$时, $f_a(x)$既不是奇函数又不是偶函数; (2) $[0,4]$\n", + "题号: 031379 , 字段: ans 中已修改数据: (1) $[arcsin \\dfrac 13,\\dfrac{\\pi}6]$; (2) 约为$29.3^\\circ$\n", + "题号: 031380 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{4}-\\dfrac{y^2}{4}=1$; (2) $k_1k_2=1$; (3) $(\\dfrac 12,1)\\cup (1,2)$\n", + "题号: 031381 , 字段: ans 中已修改数据: (1) $P_2=9$, $S_2=38$; (2) $14a+27b+14c$; (3) 存在, 满足的条件为$\\begin{cases} a+c=0, \\\\ b\\ne 0,\\end{cases}$或$\\begin{cases} a+2b+c=0, \\\\ b\\ne 0.\\end{cases}$\n" ] } ], diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 1da7e258..ba519421 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,506 +1,63 @@ -usages +ans +31361 +$\sqrt{2}$ -014532 -20230321 2023届高三10班 1.000 0.943 +31362 +$66$ -014533 -20230321 2023届高三10班 1.000 0.886 0.886 +31363 +$-1$ -012920 -20230321 2023届高三10班 0.686 +31364 +$8.5$ -014534 -20230321 2023届高三10班 0.800 +31365 +$160$ -013926 -20230321 2023届高三10班 0.714 +31366 +$\dfrac{8\sqrt{3}}3\pi$ -013921 -20230321 2023届高三10班 0.886 +31367 +$10\sqrt{3}$ -012967 -20230321 2023届高三10班 0.886 +31368 +$-3$ -012968 -20230321 2023届高三10班 0.914 +31369 +$\dfrac 45$ -012933 -20230321 2023届高三10班 0.314 +31370 +$\dfrac{4\pi}3$ -013923 -20230321 2023届高三10班 0.429 +31371 +$[-\dfrac{13}4,3]$ -014546 -20230321 2023届高三10班 0.771 +31372 +$[\dfrac 52,3]$ -014540 -20230321 2023届高三10班 0.943 0.714 +31373 +B -013007 -20230321 2023届高三10班 0.514 0.714 0.314 +31374 +A -014538 -20230321 2023届高三10班 0.857 0.829 +31375 +B -014532 -20230321 2023届高三11班 1.000 0.700 +31376 +D -014533 -20230321 2023届高三11班 1.000 0.950 0.850 +31377 +(1) 证明略; (2) $\arcsin \dfrac{\sqrt{15}}5$ -012920 -20230321 2023届高三11班 0.650 +31378 +(1) 当$a=0$时, $f_a(x)$是偶函数, 当$a\ne 0$时, $f_a(x)$既不是奇函数又不是偶函数; (2) $[0,4]$ -014534 -20230321 2023届高三11班 0.800 +31379 +(1) $[arcsin \dfrac 13,\dfrac{\pi}6]$; (2) 约为$29.3^\circ$ -013926 -20230321 2023届高三11班 0.600 - -013921 -20230321 2023届高三11班 0.900 - -012967 -20230321 2023届高三11班 0.950 - -012968 -20230321 2023届高三11班 1.000 - -012933 -20230321 2023届高三11班 0.350 - -013923 -20230321 2023届高三11班 0.250 - -014546 -20230321 2023届高三11班 0.850 - -014540 -20230321 2023届高三11班 1.000 0.900 - -013007 -20230321 2023届高三11班 0.700 0.850 0.150 - -014538 -20230321 2023届高三11班 0.800 0.550 - -014532 -20230321 2023届高三12班 1.000 1.000 - -014533 -20230321 2023届高三12班 1.000 0.857 0.857 - -012920 -20230321 2023届高三12班 0.857 - -014534 -20230321 2023届高三12班 0.667 - -013926 -20230321 2023届高三12班 0.571 - -013921 -20230321 2023届高三12班 0.952 - -012967 -20230321 2023届高三12班 0.905 - -012968 -20230321 2023届高三12班 0.905 - -012933 -20230321 2023届高三12班 0.429 - -013923 -20230321 2023届高三12班 0.667 - -014546 -20230321 2023届高三12班 0.714 - -014540 -20230321 2023届高三12班 1.000 0.762 - -013007 -20230321 2023届高三12班 0.809 0.762 0.286 - -014538 -20230321 2023届高三12班 0.809 0.809 - -014532 -20230321 2023届高三01班 1.000 1.000 - -014533 -20230321 2023届高三01班 1.000 0.964 1.000 - -012920 -20230321 2023届高三01班 0.964 - -014534 -20230321 2023届高三01班 0.929 - -013926 -20230321 2023届高三01班 0.857 - -013921 -20230321 2023届高三01班 0.964 - -012967 -20230321 2023届高三01班 1.000 - -012968 -20230321 2023届高三01班 1.000 - -012933 -20230321 2023届高三01班 0.643 - -013923 -20230321 2023届高三01班 0.821 - -014546 -20230321 2023届高三01班 0.964 - -014540 -20230321 2023届高三01班 0.964 0.893 - -013007 -20230321 2023届高三01班 0.679 0.964 0.536 - -014538 -20230321 2023届高三01班 0.893 0.929 - -014532 -20230321 2023届高三02班 1.000 0.781 - -014533 -20230321 2023届高三02班 1.000 0.938 0.906 - -012920 -20230321 2023届高三02班 0.719 - -014534 -20230321 2023届高三02班 0.906 - -013926 -20230321 2023届高三02班 0.844 - -013921 -20230321 2023届高三02班 0.750 - -012967 -20230321 2023届高三02班 0.969 - -012968 -20230321 2023届高三02班 0.906 - -012933 -20230321 2023届高三02班 0.438 - -013923 -20230321 2023届高三02班 0.812 - -014546 -20230321 2023届高三02班 0.875 - -014540 -20230321 2023届高三02班 1.000 0.219 - -013007 -20230321 2023届高三02班 0.500 0.812 0.500 - -014538 -20230321 2023届高三02班 0.656 0.562 - -014532 -20230321 2023届高三03班 1.000 1.000 - -014533 -20230321 2023届高三03班 0.917 0.917 0.917 - -012920 -20230321 2023届高三03班 0.750 - -014534 -20230321 2023届高三03班 0.708 - -013926 -20230321 2023届高三03班 0.792 - -013921 -20230321 2023届高三03班 0.792 - -012967 -20230321 2023届高三03班 0.958 - -012968 -20230321 2023届高三03班 1.000 - -012933 -20230321 2023届高三03班 0.500 - -013923 -20230321 2023届高三03班 0.792 - -014546 -20230321 2023届高三03班 1.000 - -014540 -20230321 2023届高三03班 0.958 0.708 - -013007 -20230321 2023届高三03班 0.417 0.917 0.375 - -014538 -20230321 2023届高三03班 0.833 0.958 - -014532 -20230321 2023届高三04班 1.000 0.880 - -014533 -20230321 2023届高三04班 0.960 0.880 0.920 - -012920 -20230321 2023届高三04班 0.760 - -014534 -20230321 2023届高三04班 0.880 - -013926 -20230321 2023届高三04班 0.680 - -013921 -20230321 2023届高三04班 0.600 - -012967 -20230321 2023届高三04班 0.960 - -012968 -20230321 2023届高三04班 0.880 - -012933 -20230321 2023届高三04班 0.400 - -013923 -20230321 2023届高三04班 0.680 - -014546 -20230321 2023届高三04班 0.760 - -014540 -20230321 2023届高三04班 0.920 0.440 - -013007 -20230321 2023届高三04班 0.360 0.520 0.320 - -014538 -20230321 2023届高三04班 0.800 0.400 - -014532 -20230321 2023届高三05班 1.000 0.944 - -014533 -20230321 2023届高三05班 0.972 0.917 0.917 - -012920 -20230321 2023届高三05班 0.861 - -014534 -20230321 2023届高三05班 0.889 - -013926 -20230321 2023届高三05班 0.806 - -013921 -20230321 2023届高三05班 0.889 - -012967 -20230321 2023届高三05班 0.972 - -012968 -20230321 2023届高三05班 0.972 - -012933 -20230321 2023届高三05班 0.472 - -013923 -20230321 2023届高三05班 0.583 - -014546 -20230321 2023届高三05班 0.833 - -014540 -20230321 2023届高三05班 0.917 0.861 - -013007 -20230321 2023届高三05班 0.583 0.778 0.389 - -014538 -20230321 2023届高三05班 0.944 0.861 - -014532 -20230321 2023届高三06班 0.971 0.943 - -014533 -20230321 2023届高三06班 0.943 0.800 0.914 - -012920 -20230321 2023届高三06班 0.771 - -014534 -20230321 2023届高三06班 0.914 - -013926 -20230321 2023届高三06班 0.886 - -013921 -20230321 2023届高三06班 0.943 - -012967 -20230321 2023届高三06班 1.000 - -012968 -20230321 2023届高三06班 0.971 - -012933 -20230321 2023届高三06班 0.543 - -013923 -20230321 2023届高三06班 0.829 - -014546 -20230321 2023届高三06班 0.886 - -014540 -20230321 2023届高三06班 1.000 0.943 - -013007 -20230321 2023届高三06班 0.400 0.943 0.229 - -014538 -20230321 2023届高三06班 0.886 0.914 - -014532 -20230321 2023届高三07班 0.964 0.821 - -014533 -20230321 2023届高三07班 1.000 0.893 0.893 - -012920 -20230321 2023届高三07班 0.571 - -014534 -20230321 2023届高三07班 0.607 - -013926 -20230321 2023届高三07班 0.679 - -013921 -20230321 2023届高三07班 0.857 - -012967 -20230321 2023届高三07班 0.893 - -012968 -20230321 2023届高三07班 1.000 - -012933 -20230321 2023届高三07班 0.321 - -013923 -20230321 2023届高三07班 0.464 - -014546 -20230321 2023届高三07班 0.714 - -014540 -20230321 2023届高三07班 0.929 0.714 - -013007 -20230321 2023届高三07班 0.714 0.714 0.179 - -014538 -20230321 2023届高三07班 0.964 0.250 - -014532 -20230321 2023届高三08班 0.962 0.962 - -014533 -20230321 2023届高三08班 1.000 0.885 0.846 - -012920 -20230321 2023届高三08班 0.808 - -014534 -20230321 2023届高三08班 0.769 - -013926 -20230321 2023届高三08班 0.692 - -013921 -20230321 2023届高三08班 0.769 - -012967 -20230321 2023届高三08班 0.962 - -012968 -20230321 2023届高三08班 0.885 - -012933 -20230321 2023届高三08班 0.462 - -013923 -20230321 2023届高三08班 0.538 - -014546 -20230321 2023届高三08班 0.769 - -014540 -20230321 2023届高三08班 1.000 0.615 - -013007 -20230321 2023届高三08班 0.269 0.692 0.231 - -014538 -20230321 2023届高三08班 0.808 0.269 - -014532 -20230321 2023届高三09班 0.893 0.857 - -014533 -20230321 2023届高三09班 0.964 0.786 0.786 - -012920 -20230321 2023届高三09班 0.786 - -014534 -20230321 2023届高三09班 0.714 - -013926 -20230321 2023届高三09班 0.643 - -013921 -20230321 2023届高三09班 0.786 - -012967 -20230321 2023届高三09班 0.893 - -012968 -20230321 2023届高三09班 0.857 - -012933 -20230321 2023届高三09班 0.286 - -013923 -20230321 2023届高三09班 0.321 - -014546 -20230321 2023届高三09班 0.714 - -014540 -20230321 2023届高三09班 0.929 0.786 - -013007 -20230321 2023届高三09班 0.679 0.571 0.214 - -014538 -20230321 2023届高三09班 0.893 0.607 +31380 +(1) $\dfrac{x^2}{4}-\dfrac{y^2}{4}=1$; (2) $k_1k_2=1$; (3) $(\dfrac 12,1)\cup (1,2)$ +31381 +(1) $P_2=9$, $S_2=38$; (2) $14a+27b+14c$; (3) 存在, 满足的条件为$\begin{cases} a+c=0, \\ b\ne 0,\end{cases}$或$\begin{cases} a+2b+c=0, \\ b\ne 0.\end{cases}$ 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 94677037..b2bf58bd 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 @@ -004221,012238,013537,014499,014506 \ No newline at end of file +031332,031333,031334,031335,031336,031337,031338,031339,031340,031341,031342,031343,031344,031345,031346,031347,031348,031349,031350,031351,031352 \ 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 c063af0e..d7ac84f4 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 @@ -7,11 +7,11 @@ "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 14764\n", - "raworigin = \"2023年空中课堂高三复习课\"\n", + "starting_id = 31361\n", + "raworigin = \"2023届四校联考(复兴奉贤松二金山)\"\n", "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目9.tex\"\n", "editor = \"20230326\\t王伟叶\"\n", - "indexed = False\n" + "indexed = True\n" ] }, { @@ -23,26 +23,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "添加题号014764, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014765, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014766, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014767, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014768, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014769, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014770, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014771, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014772, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014773, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014774, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014775, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014776, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014777, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014778, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014779, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014780, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014781, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014782, 来源: 2023年空中课堂高三复习课24\n", - "添加题号014783, 来源: 2023年空中课堂高三复习课24\n" + "添加题号031361, 来源: 2023届四校联考(复兴奉贤松二金山)试题1\n", + "添加题号031362, 来源: 2023届四校联考(复兴奉贤松二金山)试题2\n", + "添加题号031363, 来源: 2023届四校联考(复兴奉贤松二金山)试题3\n", + "添加题号031364, 来源: 2023届四校联考(复兴奉贤松二金山)试题4\n", + "添加题号031365, 来源: 2023届四校联考(复兴奉贤松二金山)试题5\n", + "添加题号031366, 来源: 2023届四校联考(复兴奉贤松二金山)试题6\n", + "添加题号031367, 来源: 2023届四校联考(复兴奉贤松二金山)试题7\n", + "添加题号031368, 来源: 2023届四校联考(复兴奉贤松二金山)试题8\n", + "添加题号031369, 来源: 2023届四校联考(复兴奉贤松二金山)试题9\n", + "添加题号031370, 来源: 2023届四校联考(复兴奉贤松二金山)试题10\n", + "添加题号031371, 来源: 2023届四校联考(复兴奉贤松二金山)试题11\n", + "添加题号031372, 来源: 2023届四校联考(复兴奉贤松二金山)试题12\n", + "添加题号031373, 来源: 2023届四校联考(复兴奉贤松二金山)试题13\n", + "添加题号031374, 来源: 2023届四校联考(复兴奉贤松二金山)试题14\n", + "添加题号031375, 来源: 2023届四校联考(复兴奉贤松二金山)试题15\n", + "添加题号031376, 来源: 2023届四校联考(复兴奉贤松二金山)试题16\n", + "添加题号031377, 来源: 2023届四校联考(复兴奉贤松二金山)试题17\n", + "添加题号031378, 来源: 2023届四校联考(复兴奉贤松二金山)试题18\n", + "添加题号031379, 来源: 2023届四校联考(复兴奉贤松二金山)试题19\n", + "添加题号031380, 来源: 2023届四校联考(复兴奉贤松二金山)试题20\n", + "添加题号031381, 来源: 2023届四校联考(复兴奉贤松二金山)试题21\n" ] } ], 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 31107fe8..3750eb69 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 @@ -9,26 +9,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "014764 填空题\n", - "014765 填空题\n", - "014766 填空题\n", - "014767 填空题\n", - "014768 选择题\n", - "014769 解答题\n", - "014770 解答题\n", - "014771 解答题\n", - "014772 填空题\n", - "014773 填空题\n", - "014774 填空题\n", - "014775 解答题\n", - "014776 填空题\n", - "014777 填空题\n", - "014778 填空题\n", - "014779 填空题\n", - "014780 填空题\n", - "014781 选择题\n", - "014782 填空题\n", - "014783 解答题\n" + "031361 填空题\n", + "031362 填空题\n", + "031363 填空题\n", + "031364 填空题\n", + "031365 填空题\n", + "031366 填空题\n", + "031367 填空题\n", + "031368 填空题\n", + "031369 填空题\n", + "031370 填空题\n", + "031371 填空题\n", + "031372 填空题\n", + "031373 选择题\n", + "031374 选择题\n", + "031375 选择题\n", + "031376 选择题\n", + "031377 解答题\n", + "031378 解答题\n", + "031379 解答题\n", + "031380 解答题\n", + "031381 解答题\n" ] } ], diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index d9937264..f2bd61fa 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -362395,7 +362395,7 @@ }, "014769": { "id": "014769", - "content": "现有一张半径为$2$米的圆形铁皮, 从中裁剪出一块扇形铁皮 (如图$1$中阴影部分), 并卷成一个深度为$h$米的圆锥筒 (如图$2$) 的容器. 当圆锥筒容器的深度$h$为多少米时, 其容积最大? 容积的最大值为多少立方米? (铁皮厚度忽略不计)\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) circle (2);\n\\draw (0,0) --++ (30:2) (0,0) --++ (150:2);\n\\draw (0,-2) node [below] {图$1$};\n\\draw (4,-2) --++ (1.5,3) node [midway, below right] {$2$} (4,-2) --++ (-1.5,3);\n\\draw (4,1) ellipse (1.5 and 0.5);\n\\draw (4,-2) -- (4,1) node [midway, left] {$h$} --++ (1.5,0) node [midway, above] {$r$};\n\\draw (4,-2) node [below] {图$2$};\n\\end{tikzpicture}\n\\end{center}", + "content": "现有一张半径为$2$米的圆形铁皮, 从中裁剪出一块扇形铁皮 (如图$1$), 并卷成一个深度为$h$米的圆锥筒 (如图$2$) 的容器. 当圆锥筒容器的深度$h$为多少米时, 其容积最大? 容积的最大值为多少立方米? (铁皮厚度忽略不计)\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) circle (2);\n\\draw (0,0) --++ (30:2) (0,0) --++ (150:2);\n\\draw (0,-2) node [below] {图$1$};\n\\draw (4,-2) --++ (1.5,3) node [midway, below right] {$2$} (4,-2) --++ (-1.5,3);\n\\draw (4,1) ellipse (1.5 and 0.5);\n\\draw (4,-2) -- (4,1) node [midway, left] {$h$} --++ (1.5,0) node [midway, above] {$r$};\n\\draw (4,-2) node [below] {图$2$};\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], "genre": "解答题", @@ -362414,7 +362414,7 @@ }, "014770": { "id": "014770", - "content": "已知$f(x)=2 x^4-x$.\\\\\n(1) 求曲线$y=f(x)$在点$A(1,1)$处的切线$l$的方程;\\\\\n(2) 证明: 曲线$y=f(x)$上除切点$A(1,1)$外, 其余点都在该切线$l$的上方.", + "content": "已知$f(x)=2 x^4-x$.\\\\\n(1) 求曲线$y=f(x)$在点$A(1,1)$处的切线$l$的方程;\\\\\n(2) 证明: 曲线$y=f(x)$上除切点$A(1,1)$外, 其余点都在(1)中切线$l$的上方.", "objs": [], "tags": [], "genre": "解答题", @@ -443527,7 +443527,7 @@ "20230321\t2023届高三08班\t0.871", "20230321\t2023届高三09班\t0.933" ], - "origin": "23届四校联考试题1", + "origin": "23届四校联考(南模大同控江曹二)试题1", "edit": [ "20230315\t王伟叶" ], @@ -443559,7 +443559,7 @@ "20230321\t2023届高三08班\t0.871", "20230321\t2023届高三09班\t0.867" ], - "origin": "23届四校联考试题2", + "origin": "23届四校联考(南模大同控江曹二)试题2", "edit": [ "20230315\t王伟叶" ], @@ -443591,7 +443591,7 @@ "20230321\t2023届高三08班\t1.000", "20230321\t2023届高三09班\t1.000" ], - "origin": "23届四校联考试题3", + "origin": "23届四校联考(南模大同控江曹二)试题3", "edit": [ "20230315\t王伟叶" ], @@ -443623,7 +443623,7 @@ "20230321\t2023届高三08班\t0.903", "20230321\t2023届高三09班\t0.767" ], - "origin": "23届四校联考试题4", + "origin": "23届四校联考(南模大同控江曹二)试题4", "edit": [ "20230315\t王伟叶" ], @@ -443655,7 +443655,7 @@ "20230321\t2023届高三08班\t0.839", "20230321\t2023届高三09班\t0.967" ], - "origin": "23届四校联考试题5", + "origin": "23届四校联考(南模大同控江曹二)试题5", "edit": [ "20230315\t王伟叶" ], @@ -443687,7 +443687,7 @@ "20230321\t2023届高三08班\t0.968", "20230321\t2023届高三09班\t0.833" ], - "origin": "23届四校联考试题6", + "origin": "23届四校联考(南模大同控江曹二)试题6", "edit": [ "20230315\t王伟叶" ], @@ -443719,7 +443719,7 @@ "20230321\t2023届高三08班\t0.548", "20230321\t2023届高三09班\t0.633" ], - "origin": "23届四校联考试题7", + "origin": "23届四校联考(南模大同控江曹二)试题7", "edit": [ "20230315\t王伟叶" ], @@ -443751,7 +443751,7 @@ "20230321\t2023届高三08班\t0.258", "20230321\t2023届高三09班\t0.100" ], - "origin": "23届四校联考试题8", + "origin": "23届四校联考(南模大同控江曹二)试题8", "edit": [ "20230315\t王伟叶" ], @@ -443783,7 +443783,7 @@ "20230321\t2023届高三08班\t0.161", "20230321\t2023届高三09班\t0.000" ], - "origin": "23届四校联考试题9", + "origin": "23届四校联考(南模大同控江曹二)试题9", "edit": [ "20230315\t王伟叶" ], @@ -443815,7 +443815,7 @@ "20230321\t2023届高三08班\t0.258", "20230321\t2023届高三09班\t0.367" ], - "origin": "23届四校联考试题10", + "origin": "23届四校联考(南模大同控江曹二)试题10", "edit": [ "20230315\t王伟叶" ], @@ -443847,7 +443847,7 @@ "20230321\t2023届高三08班\t0.419", "20230321\t2023届高三09班\t0.233" ], - "origin": "23届四校联考试题11", + "origin": "23届四校联考(南模大同控江曹二)试题11", "edit": [ "20230315\t王伟叶" ], @@ -443879,7 +443879,7 @@ "20230321\t2023届高三08班\t0.194", "20230321\t2023届高三09班\t0.133" ], - "origin": "23届四校联考试题12", + "origin": "23届四校联考(南模大同控江曹二)试题12", "edit": [ "20230315\t王伟叶" ], @@ -443911,7 +443911,7 @@ "20230321\t2023届高三08班\t0.677", "20230321\t2023届高三09班\t0.900" ], - "origin": "23届四校联考试题13", + "origin": "23届四校联考(南模大同控江曹二)试题13", "edit": [ "20230315\t王伟叶" ], @@ -443943,7 +443943,7 @@ "20230321\t2023届高三08班\t0.871", "20230321\t2023届高三09班\t0.900" ], - "origin": "23届四校联考试题14", + "origin": "23届四校联考(南模大同控江曹二)试题14", "edit": [ "20230315\t王伟叶" ], @@ -443975,7 +443975,7 @@ "20230321\t2023届高三08班\t0.710", "20230321\t2023届高三09班\t0.767" ], - "origin": "23届四校联考试题15", + "origin": "23届四校联考(南模大同控江曹二)试题15", "edit": [ "20230315\t王伟叶" ], @@ -444007,7 +444007,7 @@ "20230321\t2023届高三08班\t0.742", "20230321\t2023届高三09班\t0.633" ], - "origin": "23届四校联考试题16", + "origin": "23届四校联考(南模大同控江曹二)试题16", "edit": [ "20230315\t王伟叶" ], @@ -444039,7 +444039,7 @@ "20230321\t2023届高三08班\t0.979\t0.879", "20230321\t2023届高三09班\t0.961\t0.867" ], - "origin": "23届四校联考试题17", + "origin": "23届四校联考(南模大同控江曹二)试题17", "edit": [ "20230315\t王伟叶" ], @@ -444071,7 +444071,7 @@ "20230321\t2023届高三08班\t0.909\t0.673", "20230321\t2023届高三09班\t0.911\t0.575" ], - "origin": "23届四校联考试题18", + "origin": "23届四校联考(南模大同控江曹二)试题18", "edit": [ "20230315\t王伟叶" ], @@ -444103,7 +444103,7 @@ "20230321\t2023届高三08班\t0.429\t0.903", "20230321\t2023届高三09班\t0.170\t0.617" ], - "origin": "23届四校联考试题19", + "origin": "23届四校联考(南模大同控江曹二)试题19", "edit": [ "20230315\t王伟叶" ], @@ -444135,7 +444135,7 @@ "20230321\t2023届高三08班\t0.935\t0.430\t0.065", "20230321\t2023届高三09班\t0.933\t0.294\t0.000" ], - "origin": "23届四校联考试题20", + "origin": "23届四校联考(南模大同控江曹二)试题20", "edit": [ "20230315\t王伟叶" ], @@ -444167,7 +444167,7 @@ "20230321\t2023届高三08班\t0.516\t0.398\t0.024", "20230321\t2023届高三09班\t0.858\t0.272\t0.042" ], - "origin": "23届四校联考试题21", + "origin": "23届四校联考(南模大同控江曹二)试题21", "edit": [ "20230315\t王伟叶" ], @@ -444767,6 +444767,405 @@ "remark": "", "space": "" }, + "031361": { + "id": "031361", + "content": "已知复数$z$满足$z(1+\\mathrm{i})=2 \\mathrm{i}$, $i$为虚数单位, 则$|z|$值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\sqrt{2}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题1", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031362": { + "id": "031362", + "content": "在等差数列$\\{a_n\\}$中, $2 a_9-a_{12}=6$, 则数列$\\{a_n\\}$的前$11$项和$S_{11}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$66$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题2", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031363": { + "id": "031363", + "content": "已知向量$\\overrightarrow {a}$和$\\overrightarrow {b}$满足$\\overrightarrow {a}=(1,2)$, $\\overrightarrow {b}=(-2,0)$, 则$\\overrightarrow {a}$在$\\overrightarrow {b}$方向上的数量投影为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$-1$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题3", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031364": { + "id": "031364", + "content": "某单位为了解该单位党员开展学习党史知识活动情况, 随机抽取了部分党员, 对他们一周的党史学习时间进行了统计, 统计数据如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 党史学习时间 (小时) & 7 & 8 & 9 & 10 & 11 \\\\\n\\hline 党员人数 & 6 & 10 & 9 & 8 & 7 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n则该单位党员一周学习党史时间的第$40$百分位数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$8.5$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题4", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031365": { + "id": "031365", + "content": "二项式$(2 x+\\dfrac{1}{\\sqrt[3]{x}})^6$的展开式中, 含$x^2$的项的系数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$160$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题5", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031366": { + "id": "031366", + "content": "已知圆锥的底面半径为$2$, 底面圆心到某条母线的距离为$1$, 则该圆锥的侧面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac{8\\sqrt{3}}3\\pi$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题6", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031367": { + "id": "031367", + "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$所对的边分別为$a$、$b$、$c$, 且$a=5$, $b=7$, $B=60^{\\circ}$, 则$\\triangle ABC$的面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$10\\sqrt{3}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题7", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031368": { + "id": "031368", + "content": "若$x=1$是函数$f(x)=\\dfrac{1}{3} x^3+(a+1) x^2-(a^2+3 a-3) x$的极大值点, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$-3$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题8", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031369": { + "id": "031369", + "content": "非空集合$A$中所有元素乘积记为$T(A)$. 已知集合$M=\\{1,4,5,8\\}$, 从集合$M$的所有非空子集中任选一个子集$A$, 则$T(A)$为偶数的概率是\\blank{50}(结果用最简分数表示).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac 45$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题9", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031370": { + "id": "031370", + "content": "已知函数$f(x)=\\sin (2 x+\\dfrac{\\pi}{6})$($0 \\leq x \\leq \\pi$), 且$f(\\alpha)=f(\\beta)=\\dfrac{1}{3}$($\\alpha \\neq \\beta$), 则$\\alpha+\\beta=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac{4\\pi}3$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题10", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031371": { + "id": "031371", + "content": "已知函数$f(x)=\\begin{cases}x+2, x1$''是``$a^3>1$''的\\bracket{20}条件.\n\\fourch{充分非必要}{必要非充分}{充要}{既非充分也非必要}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "B", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题13", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031374": { + "id": "031374", + "content": "已知盒中装有形状完全相同的$4$个黑球与$2$个白球, 现从中有放回的摸取$4$次, 每次都是从盒子中随机摸出$1$个球, 设摸得白球个数为$X$, 则$E[X]$为\\bracket{20}.\n\\fourch{$\\dfrac{4}{3}$}{$\\dfrac{5}{3}$}{$2$}{$\\dfrac{4}{9}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "A", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题14", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031375": { + "id": "031375", + "content": "《九章算术》中所述``羡除'', 是指如图所示五面体$ABCDEF$, 其中$AB\\parallel DC\\parallel EF$, ``羡除''形似``楔体''. ``广''是指``羡除''的三条平行侧棱之长$a$、$b$、$c$,``深''是指一条侧棱到另两条侧棱所在平面的距离$m$, ``袤''是指这两条侧棱所在平行直线之问的距离$n$(如图). 羡除的体积公式为$V=\\dfrac{(a+b+c) m n}{6}$, 过线段$AD, BC$的中点$G, H$及直线$EF$作该羡除的一个截面$\\alpha$, 已知$\\alpha$刚好将羡除分成体积比为$5: 4$的两部分. 若$AB=4$, $DC=2$, 则$EF$的长为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$D$} coordinate (D);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (-1.5,0,2) node [left] {$A$} coordinate (A);\n\\draw (2.5,0,2) node [right] {$B$} coordinate (B);\n\\draw (0,2,0.5) node [above] {$E$} coordinate (E);\n\\draw (2,2,0.5) node [above] {$F$} coordinate (F);\n\\draw (A)--(B)--(C)--(F)--(E)--cycle(B)--(F);\n\\draw [dashed] (E)--(D)--(A)(D)--(C);\n\\draw [dashed] (E) ++ (1,0,0) --++ (0,-2,0) node [midway, right] {$m$} coordinate (G);\n\\draw [dashed] (G) ++ (0,0,1.5) --++ (0,0,-2) node [midway, right] {$n$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$2$}{$3$}{$4$}{$6$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "B", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题15", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031376": { + "id": "031376", + "content": "考虑这样的等腰三角形: 它的三个顶点都在椭圆$\\Gamma: \\dfrac{x^2}{9}+y^2=1$上, 且其中恰有两个顶点为$\\Gamma$的顶点. 这样的等腰三角形的个数为\\bracket{20}\n\\fourch{$8$}{$12$}{$16$}{$20$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "D", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题16", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031377": { + "id": "031377", + "content": "如图, $AB$是圆柱底面圆的一条直径, $AB=2, PA$是圆柱的母线, $PA=3$, 点$C$是圆柱底面圆周上的点, $\\angle ABC=30^{\\circ}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (1,3) ellipse (1 and 0.25);\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0) node [right] {$B$} coordinate (B);\n\\draw (1,0) ++ (-120:1 and 0.25) node [below] {$C$} coordinate (C);\n\\draw (A) ++ (0,1) node [left] {$E$} coordinate (E);\n\\draw (A) ++ (0,3) node [left] {$P$} coordinate (P);\n\\draw (A) arc (180:360:1 and 0.25);\n\\draw [dashed] (A) arc (180:0:1 and 0.25);\n\\draw (A)--(P)(B)--++(0,3);\n\\draw [dashed] (P)--(B)(P)--(C)(E)--(B)(E)--(C)(A)--(B)--(C)--cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $BC \\perp$平面$PAC$;\\\\\n(2) 若点$E$在$PA$上且$EA=\\dfrac{1}{3} PA$, 求$BE$与平面$PAC$所成角的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 证明略; (2) $\\arcsin \\dfrac{\\sqrt{15}}5$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题17", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031378": { + "id": "031378", + "content": "已知$f_a(x)=|x|+|x-a|$, 其中$a \\in \\mathbf{R}$.\\\\\n(1) 判断函数$y=f_a(x)$的奇偶性, 并说明理由;\\\\\n(2) 当$a=4$时, 对任意非零实数$c$, 不等式$f_a(t) \\leq 2|c+\\dfrac{1}{c}|$均成立, 求实数$t$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 当$a=0$时, $f_a(x)$是偶函数, 当$a\\ne 0$时, $f_a(x)$既不是奇函数又不是偶函数; (2) $[0,4]$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题18", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031379": { + "id": "031379", + "content": "某公园为了美化环境和方便顾客, 计划建造一座圆弧形拱桥, 已知该桥的剖面如图所示, 共包括一段圆弧形桥面$ACB$和两段长度相等的直线型桥面$AD, BE$, 拱桥$ACB$所在圆的半径为$3$米, 圆心$O$在$DE$上, 且$AD$和$BE$所在直线与圆$O$分别在连结点$A$和$B$处相切. 根据空间限制及桥面坡度的限制, 桥面跨度$DE$的长要苴不大于$18$米, 不小于$12$米. 己知直线型桥面的修建费用是每米$0.6$万元, 弧形桥面的修建费用是每米$2.5$万元. 设$\\angle ADO=\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (0,1) node [above] {$C$} coordinate (C);\n\\draw (70:1) node [above right] {$B$} coordinate (B);\n\\draw (110:1) node [above left] {$A$} coordinate (A);\n\\draw ({-1/cos(70)},0) node [below] {$D$} coordinate (D);\n\\draw ({1/cos(70)},0) node [below] {$E$} coordinate (E);\n\\draw (B)--(E)(A)--(D)(B) arc (70:110:1);\n\\draw [dashed] (-4,0) -- (4,0) (B) arc (70:-250:1);\n\\filldraw (O) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n(1) 若桥面(线段$AD, BE$和弧$ACB$)的修建总费用为$W$万元, 求$W$关于\n$\\theta$的函数表达式, 并写出$\\theta$的取值范围;\\\\\n(2) 当$\\theta$为何值时, 桥面修建总费用$W$最低?(角$\\theta$的取值精确到$0.1^{\\circ}$)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $[arcsin \\dfrac 13,\\dfrac{\\pi}6]$; (2) 约为$29.3^\\circ$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题19", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031380": { + "id": "031380", + "content": "如图, 已知椭圆$\\Gamma_1: \\dfrac{x^2}{8}+\\dfrac{y^2}{4}=1$的两个焦点为$F_1, F_2$, 且$F_1, F_2$为双曲线$\\Gamma_2$的顶点, 双曲线$\\Gamma_2$的一条浙近线方程为$y=-x$, 设$P$为该双曲线$\\Gamma_2$上异于顶点的任意一点, 直线$PF_1, PF_2$的斜率分别的$k_1, k_2$, 且直线$PF_1$和$PF_2$与椭圆$\\Gamma_1$的交点分别为$A, B$和$C, D$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\path [name path = elli, draw] (0,0) ellipse ({2*sqrt(2)} and 2);\n\\filldraw (-2,0) node [below right] {$F_1$} coordinate (F_1) circle (0.03) (2,0) node [below right] {$F_2$} coordinate (F_2) circle (0.03);\n\\draw [domain = -3:3, samples = 100] plot ({sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = -3:3, samples = 100] plot ({-sqrt(\\x*\\x+4)},\\x);\n\\draw (3,{sqrt(5)}) node [above] {$P$} coordinate (P);\n\\path [name path = l1] (P) -- ($(P)!1.3!(F_1)$);\n\\path [name path = l2] (P) -- ($(P)!1.9!(F_2)$);\n\\path [name intersections = {of = elli and l1, by = {A,B}}];\n\\draw (P) -- (A) node [above] {$A$} -- (B) node [below left] {$B$};\n\\path [name intersections = {of = elli and l2, by = {C,D}}];\n\\draw (P) -- (C) node [right] {$C$} -- (D) node [below] {$D$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求双曲线$\\Gamma_2$的标准方程;\\\\\n(2) 证明: 直线$PF_1, PF_2$的斜率之积$k_1 \\cdot k_2$为定值;\\\\\n(3) 求$\\dfrac{|AB|}{|CD|}$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $\\dfrac{x^2}{4}-\\dfrac{y^2}{4}=1$; (2) $k_1k_2=1$; (3) $(\\dfrac 12,1)\\cup (1,2)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题20", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031381": { + "id": "031381", + "content": "在一个有穷数列的每相邻两项之间插入这两项的和, 形成新的数列, 我们把这样的操作称为该数列的一次``和扩充''. 如数列$1,2$第$1$次``和扩充''后得到数列$1,3,2$, 第$2$次``和扩充''后得到数列$1,4,3,5,2$. 设数列$a, b, c$经过第$n$次``和扩充''后所得数列的项数记为$P_n$, 所有项的和记为$S_n$.\\\\\n(1) 若$a=1$, $b=2$, $c=3$, 求$P_2, S_2$;\\\\\n(2) 设满足$P_n \\geq 2023$的$n$的最小值为$n_0$, 求$n_0$及$S_{[\\frac{n_0}{3}]}$(其中$[x]$是指不超过$x$的最大整数, 如$[1.2]=1$, $[-2.6]=-3)$;\\\\\n(3) 是否存在实数$a, b, c$, 使得数列$\\{S_n\\}$为等比数列? 若存在, 求$a, b, c$满足的条件; 若不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $P_2=9$, $S_2=38$; (2) $14a+27b+14c$; (3) 存在, 满足的条件为$\\begin{cases} a+c=0, \\\\ b\\ne 0,\\end{cases}$或$\\begin{cases} a+2b+c=0, \\\\ b\\ne 0.\\end{cases}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届四校联考(复兴奉贤松二金山)试题21", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "040001": { "id": "040001", "content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",