From d42b1b1f278d0cb033df7407c86424bab88c260d Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Thu, 30 Mar 2023 10:52:00 +0800 Subject: [PATCH] 20230330 AM --- 工具/修改题目数据库.ipynb | 6 +- 工具/关键字筛选题号.ipynb | 6 +- 工具/寻找tex文件中未赋答案的题目.ipynb | 577 +------------------------ 工具/批量添加题库字段数据.ipynb | 207 ++++----- 工具/批量题号选题pdf生成.ipynb | 71 +-- 工具/文本文件/metadata.txt | 485 ++++++++------------- 工具/文本文件/题号筛选.txt | 2 +- 工具/试卷答案生成.ipynb | 2 +- 文本处理工具/表格整理.ipynb | 4 +- 题库0.3/Problems.json | 382 ++++++++-------- 10 files changed, 512 insertions(+), 1230 deletions(-) diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb index 8feb0edc..3708daa4 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": 3, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 3, + "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 = \"31321\"\n", + "problems = \"12612\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", 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 4bb9809e..fbb77541 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": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 5, + "execution_count": 4, "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", - " {\"usages\":[r\"2025届高一1[12][^\\n]*0\\.[0123456]\\d{2}\"]}\n", + " {\"usages\":[r\"2023届高三02[^\\n]*0\\.[34567]\\d{2}\"],\"tags\":[\"第[八九]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 63a8ac36..72a77e7d 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": 4, "metadata": {}, "outputs": [ { @@ -165,585 +165,12 @@ "11_直线与圆.tex\n", "12_圆锥曲线.tex\n", "13_解析几何综合.tex\n", - "013997\n", - "\n", - "\n", - "013116\n", - "\n", - "\n", - "013118\n", - "\n", - "\n", - "013119\n", - "\n", - "\n", - "013143\n", - "\n", - "\n", - "013108\n", - "\n", - "\n", - "014478\n", - "\n", - "\n", - "013992\n", - "\n", - "\n", - "013989\n", - "\n", - "\n", - "014503\n", - "\n", - "\n", - "014505\n", - "\n", - "\n", - "013982\n", - "\n", - "\n", - "013112\n", - "\n", - "\n", - "014020\n", - "\n", - "\n", - "014483\n", - "\n", - "\n", - "013979\n", - "\n", - "\n", - "013136\n", - "\n", - "\n", - "014459\n", - "\n", - "\n", - "014491\n", - "\n", - "\n", - "014479\n", - "\n", - "\n", - "013121\n", - "\n", - "\n", - 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"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", - "\n", - "013228\n", - "\n", - "\n", - "013232\n", - "\n", - "\n", - "013236\n", - "\n", - "\n", - "014074\n", - "\n", - "\n", - "014570\n", - "\n", - "\n", - "014583\n", - "\n", - "\n", - "013223\n", - "\n", - 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"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", @@ -816,7 +243,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15" + "version": "3.8.15" }, "orig_nbformat": 4, "vscode": { 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 7d691c38..581ece29 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 @@ -2,133 +2,98 @@ "cells": [ { "cell_type": "code", - "execution_count": 11, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t1.000\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.857\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.381\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.809\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.762\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.714\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.952\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.857\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.857\t0.905\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.952\t0.857\t0.714\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.381\t0.619\t0.238\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三11班\t0.762\t0.667\t0.714\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.944\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.889\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.333\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t1.000\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.778\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.611\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.833\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.944\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.889\t0.833\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t1.000\t0.833\t0.722\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.611\t0.667\t0.278\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三12班\t0.833\t0.722\t0.889\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.964\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.893\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.429\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.964\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.750\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.607\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t1.000\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.893\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t1.000\t0.964\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.714\t0.929\t0.750\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.357\t0.107\t0.857\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三01班\t0.643\t0.393\t0.786\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.967\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.767\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.533\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.967\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.833\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.800\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.967\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.967\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.900\t0.867\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.933\t0.967\t0.933\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.767\t0.500\t0.800\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三02班\t0.833\t0.600\t0.967\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.957\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.696\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.478\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.783\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.739\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.696\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t1.000\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.957\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.957\t0.913\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.652\t1.000\t0.870\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.087\t0.130\t0.130\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三04班\t0.652\t0.522\t0.957\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.914\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.800\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.514\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.943\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.886\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.571\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.971\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.971\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.886\t0.857\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.943\t1.000\t0.829\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.371\t0.314\t0.200\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三05班\t0.629\t0.543\t0.886\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.973\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.865\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.595\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.973\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.757\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.703\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.946\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.865\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t1.000\t0.838\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.378\t1.000\t0.703\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.351\t0.081\t1.000\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三06班\t0.703\t0.568\t0.892\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t1.000\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.913\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.522\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.826\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.696\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.696\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.913\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.957\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t1.000\t0.957\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.826\t1.000\t0.826\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.435\t0.087\t0.043\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三07班\t0.826\t0.826\t0.957\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t1.000\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.783\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.478\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.913\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.783\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.696\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.957\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.913\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.957\t1.000\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.957\t0.913\t0.696\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.217\t0.261\t0.087\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三08班\t0.522\t0.304\t0.826\n", - "题号: 013220 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.963\n", - "题号: 014092 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.852\n", - "题号: 014629 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.518\n", - "题号: 014631 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.889\n", - "题号: 014632 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.704\n", - "题号: 014635 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.444\n", - "题号: 014641 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t1.000\n", - "题号: 014087 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.815\n", - "题号: 014637 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t1.000\t0.926\n", - "题号: 014638 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.556\t0.815\t0.593\n", - "题号: 014634 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.222\t0.333\t0.111\n", - "题号: 014633 , 字段: usages 中已添加数据: 20230329\t2023届高三09班\t0.444\t0.518\t0.593\n" + "题号: 013217 , 字段: ans 中已修改数据: $\\dfrac 16$\n", + "题号: 014083 , 字段: ans 中已修改数据: $\\dfrac{27}{100}$\n", + "题号: 014090 , 字段: ans 中已修改数据: $\\dfrac 13$\n", + "题号: 014577 , 字段: ans 中已修改数据: $\\dfrac{13}{21}$\n", + "题号: 014585 , 字段: ans 中已修改数据: $\\dfrac{6}{25}$\n", + "题号: 014591 , 字段: ans 中已修改数据: $\\dfrac{9}{10}$\n", + "题号: 014593 , 字段: ans 中已修改数据: $\\dfrac 13$\n", + "题号: 014601 , 字段: ans 中已修改数据: $\\dfrac 2{55}$\n", + "题号: 014599 , 字段: ans 中已修改数据: $\\dfrac{41}{70}$\n", + "题号: 014603 , 字段: ans 中已修改数据: $(0,0.7)$\n", + "题号: 014598 , 字段: ans 中已修改数据: $9$\n", + "题号: 014594 , 字段: ans 中已修改数据: $0.14$\n", + "题号: 014094 , 字段: ans 中已修改数据: (1) $\\dfrac 15$; (2) $\\dfrac 35$; (3) $\\dfrac 9{10}$\n", + "题号: 014597 , 字段: ans 中已修改数据: (1) $0.6$; (2) $X\\sim \\begin{pmatrix}0 & 10 & 20 & 30 \\\\ 0.16 & 0.44 & 0.34 & 0.06\\end{pmatrix}$, $E[X]=13$\n", + "题号: 014608 , 字段: ans 中已修改数据: $P_n=\\dfrac 12(1+(-\\dfrac 13)^{n-1})$\n", + "题号: 014081 , 字段: ans 中已修改数据: $\\dfrac 45$\n", + "题号: 014086 , 字段: ans 中已修改数据: $\\dfrac{9}{50}$\n", + "题号: 014091 , 字段: ans 中已修改数据: $\\dfrac{31}{120}$\n", + "题号: 014580 , 字段: ans 中已修改数据: $\\dfrac 12$\n", + "题号: 013234 , 字段: ans 中已修改数据: $\\dfrac{1}{168}$\n", + "题号: 014592 , 字段: ans 中已修改数据: $\\dfrac{95}{99}$\n", + "题号: 014602 , 字段: ans 中已修改数据: $\\dfrac 49$\n", + "题号: 014605 , 字段: ans 中已修改数据: $0.66$\n", + "题号: 014606 , 字段: ans 中已修改数据: $\\dfrac 43$\n", + "题号: 014604 , 字段: ans 中已修改数据: $0.1$\n", + "题号: 014607 , 字段: ans 中已修改数据: $5$\n", + "题号: 014595 , 字段: ans 中已修改数据: (1) $\\dfrac 3{16}$; (2) $\\dfrac 12$\n", + "题号: 014596 , 字段: ans 中已修改数据: $0.03$\n", + "题号: 014600 , 字段: ans 中已修改数据: (1) $\\dfrac{12}{25}$; (2) $\\dfrac 9{25}$\n", + "题号: 013220 , 字段: ans 中已修改数据: $m>n$\n", + "题号: 014092 , 字段: ans 中已修改数据: $63$\n", + "题号: 014629 , 字段: ans 中已修改数据: $447$\n", + "题号: 014631 , 字段: ans 中已修改数据: B\n", + "题号: 014632 , 字段: ans 中已修改数据: 无关\n", + "题号: 014635 , 字段: ans 中已修改数据: \\textcircled{1}\\textcircled{2}\\textcircled{4}\n", + "题号: 014641 , 字段: ans 中已修改数据: $7$\n", + "题号: 014637 , 字段: ans 中已修改数据: (1) $a=0.3$, $b=0.1$; (2) 甲离子残留百分比的平均值约为$4.05$($\\%$), 乙离子残留百分比的平均值约为$6$($\\%$)\n", + "题号: 014638 , 字段: ans 中已修改数据: (1) 图略, 有明显的正相关关系; (2) $r\\approx 0.97$, 相关性明显, 为正相关; (3) 拟合直线为$y=1.0173x+0.1909$, 当产品加工前含水率为$19\\%$时, 加工后含水率估计为$19.5\\%$\n", + "题号: 014634 , 字段: ans 中已修改数据: (1) 图略; (2) \\begin{tabular}{|c||c|c||c|c|c|}\n", + "\\hline\n", + "学历 & 均值 & 中位数 & 极差 & 方差 & 标准差 \\\\ \\hline\n", + "专科 & $14.13$ & $14.66$ & $9.94$ & $4.52$ & $2.13$ \\\\ \\hline\n", + "本科 & $20.05$ & $19.75$ & $26.73$ & $45.84$ & $6.77$ \\\\ \\hline\n", + "研究生 & $5.20$ & $4.54$ & $17.39$ & $14.03$ & $3.75$ \\\\ \\hline\n", + "\\end{tabular} (3) 专科与本科的相关系数约为$0.68$, 有较强的正相关性; 专科与研究生的相关系数约为$0.41$, 有较弱的正相关性; 本科与研究生的相关性约为$0.90$, 有很强的正相关性\n", + "题号: 014633 , 字段: ans 中已修改数据: (1) 女性样本离散程度较高, 男性样本数据的第$80$百分位数为$2.7$($\\%$); (2) $a=8$, 平均数约为$6.3$, 方差约为$41.3$; (3) 男性$2625$人, 女性$2375$人\n", + "题号: 013235 , 字段: ans 中已修改数据: \\textcircled{3}\n", + "题号: 013218 , 字段: ans 中已修改数据: $50$\n", + "题号: 013237 , 字段: ans 中已修改数据: $8$或$10$或$11$\n", + "题号: 014640 , 字段: ans 中已修改数据: \\textcircled{1}\\textcircled{4}\n", + "题号: 014642 , 字段: ans 中已修改数据: $27.6\\times 10^3$\n", + "题号: 014643 , 字段: ans 中已修改数据: $3$; $30$\n", + "题号: 014636 , 字段: ans 中已修改数据: C\n", + "题号: 014088 , 字段: ans 中已修改数据: B\n", + "题号: 014085 , 字段: ans 中已修改数据: (1) $400$; (2) $4$; (3) $0.7$\n", + "题号: 014644 , 字段: ans 中已修改数据: (1) 横截面积的平均值约为$0.06\\text{m}^2$; 材积量的平均值约为$0.39\\text{m}^3$; (2) $r\\approx 0.97$; (3) 比例系数的估计值$\\hat{k}=\\dfrac{\\displaystyle\\sum_{i=1}^{10}x_iy_i}{\\displaystyle\\sum_{i=1}^{10}x_i^2}$, 约为$1210.9\\text{m}^3$\n", + "题号: 014645 , 字段: ans 中已修改数据: (1) $\\chi^2=24$, 认为有关; (2) 证明略; (3) $R$的估计值为$6$\n", + "题号: 014646 , 字段: ans 中已修改数据: (1) $X\\sim \\begin{pmatrix} 155 & 165 & 175 & 185 & 195 & 205 \\\\ 0.22 & 0.27 & 0.25 & 0.15 & 0.1 & 0.01\\end{pmatrix}$, $E[X]=171.7$($\\text{cm}$); (2) $0.0312$; (3) $27.25$\n", + "题号: 012942 , 字段: ans 中已修改数据: $\\begin{cases} 2, & n=1, \\\\ 2^{n-1} & n\\ge 2\\end{cases}$\n", + "题号: 012941 , 字段: ans 中已修改数据: $\\dfrac{2}{19}$\n", + "题号: 012976 , 字段: ans 中已修改数据: $2^{\\frac{n(n-1)}{2}}$\n", + "题号: 012923 , 字段: ans 中已修改数据: $3018$\n", + "题号: 013002 , 字段: ans 中已修改数据: $2999$\n", + "题号: 014550 , 字段: ans 中已修改数据: $(-\\infty,3)$\n", + "题号: 012966 , 字段: ans 中已修改数据: $8$\n", + "题号: 013005 , 字段: ans 中已修改数据: $2^{n+1}$\n", + "题号: 013935 , 字段: ans 中已修改数据: $\\dfrac{2\\sqrt{3}}3$\n", + "题号: 012978 , 字段: ans 中已修改数据: $33$\n", + "题号: 012932 , 字段: ans 中已修改数据: $\\dfrac{n}{n+1}$\n", + "题号: 012947 , 字段: ans 中已修改数据: $\\begin{cases} 2, & n=1, \\\\ -\\dfrac{1}{3^{n-1}} & n\\ge 2\\end{cases}$\n", + "题号: 012971 , 字段: ans 中已修改数据: (1) 最大项为$a_{10}-b_{10}=8976$; (2) $\\{1,2,3,\\cdots,13\\}$\n", + "题号: 013960 , 字段: ans 中已修改数据: (1) $a_n=2^n+1$; (2) 证明略; (3) 证明略\n", + "题号: 013000 , 字段: ans 中已修改数据: $\\dfrac 34-\\dfrac{2n+3}{2(n^2+3n+2)}$\n", + "题号: 012956 , 字段: ans 中已修改数据: $\\begin{cases} 4, & n=1, \\\\ 2 & n\\ge 2\\end{cases}$\n", + "题号: 014553 , 字段: ans 中已修改数据: $3$\n", + "题号: 012959 , 字段: ans 中已修改数据: $\\begin{cases} 1, & n=1, \\\\ 2^{n-2} & n\\ge 2\\end{cases}$\n", + "题号: 012977 , 字段: ans 中已修改数据: $0$; $-\\dfrac{63}{256}$\n", + "题号: 012982 , 字段: ans 中已修改数据: $4$或$5$或$32$\n", + "题号: 013955 , 字段: ans 中已修改数据: $9$\n", + "题号: 013944 , 字段: ans 中已修改数据: $(-\\infty,-2]\\cup [2,+\\infty)$\n", + "题号: 012936 , 字段: ans 中已修改数据: $1830$\n", + "题号: 014560 , 字段: ans 中已修改数据: B\n", + "题号: 013006 , 字段: ans 中已修改数据: (1) $\\{f(n)\\}$是严格增数列, 证明略; (2) $(-\\infty,0)\\cup (0,1)$\n", + "题号: 012983 , 字段: ans 中已修改数据: (1) $(a_1,a_2)=(0,0)$或$(1-\\sqrt{2},2-\\sqrt{2})$或$(1+\\sqrt{2},2+\\sqrt{2})$; (2) 当$n=7$时$T_n$最大, $T_7=7-\\dfrac{21}{2}\\lg 2$\n", + "题号: 012938 , 字段: ans 中已修改数据: (1) $b_n=\\begin{cases} 2^{\\frac 32 n}, & n=2k, \\\\ 2^{\\frac{3n-1}2} & n=2k-1\\end{cases}$($k$为正整数); (2) $S_n=\\begin{cases} \\dfrac{10}{7}\\cdot 2^{\\frac 32 n}-\\dfrac{10}{7}, & n=2k, \\\\ \\dfrac{3}{7}\\cdot 2^{\\frac{3n-1}2}-\\dfrac{10}{7} & n=2k-1\\end{cases}$($k$为正整数)\n" ] } ], diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb index dc669473..e5061b9e 100644 --- a/工具/批量题号选题pdf生成.ipynb +++ b/工具/批量题号选题pdf生成.ipynb @@ -9,9 +9,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/2022学年下学期高一高二材料_教师用_20230330.tex\n", + "开始编译教师版本pdf文件: 临时文件/高三二模前易错题_教师用_20230330.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/2022学年下学期高一高二材料_学生用_20230330.tex\n", + "开始编译学生版本pdf文件: 临时文件/高三二模前易错题_学生用_20230330.tex\n", "0\n" ] } @@ -29,43 +29,50 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#字典字段为文件名, 之后为内容的题号\n", "problems_dict = {\n", - "\"2024届高二下学期周末卷01\":\"40001:40017\",\n", - "\"2025届高一下学期周末卷01\":\"40018:40036\",\n", - "\"2024届高二下学期周末卷02\":\"40037:40056\",\n", - "\"2025届高一下学期周末卷02\":\"40057:40082\",\n", - "\"2025届高一下学期周末卷03\":\"40083:40104\",\n", - "\"2025届高一下学期周末卷03小测\":\"40105:40112\",\n", - "\"2025届高一下学期周末卷04旧版\":\"40113:40130\",\n", - "\"2025届高一下学期周末卷04小测\":\"40131:40139\",\n", - "\"2024届高二下学期周末卷03\":\"40140:40160\",\n", - "\"2024届高二上学期期末考试\":\"31267:31287\",\n", - "\"2025届高一上学期期末考试\":\"31288:31308\",\n", - "\"2024届高二下学期周末卷04\":\"40161:40180\",\n", - "\"2025届高一下学期周末卷04\":\"40181:40201\",\n", - "\"2024届高二下学期周末卷05\":\"40202:40225\",\n", - "\"2025届高一下学期周末卷05\":\"40226:40245\",\n", - "\"2024届空间向量校本作业\":\"22048:22083\",\n", - "\"2024届二项式定理校本作业\":\"22084:22105\",\n", - "\"2025届高一下学期周末卷05小测\":\"40246:40255\",\n", - "\"2025届高一下学期周末卷06\":\"40256:40273\",\n", - "\"2025届高一下学期周末卷06小测\":\"40274:40282\",\n", - "\"2025届高一下学期期中复习一(集合逻辑不等式)\":\"40283:40298\",\n", - "\"2024届高二下学期周末卷06\":\"40299:40316\",\n", - "\"2024届高二下学期周末卷07\":\"40317:40335\",\n", - "\"2025届高一下学期测验01\":\"40336:40349\",\n", - "\"2025届高一下学期测验02\":\"40350:40367\",\n", - "\"2025届高一下学期期中复习二(幂指对函数)\":\"40368:40386\",\n", - "\"2025届高一下学期周末卷02小测\":\"40387:40395\",\n", - "\"2025届高一下学期周末卷07\":\"40396:40413\"\n", - "\n", + "\"函数易错题\":\"000060,000087,000092,000342,000361,000655,000734,000778,000795,001211,001218,001221,001227,001253,001262,001270,001277,001287,001308,001309,001312,001325,001328,001329,001339,001340,001343,001352,002831,002838,002851,002856,002859,002888,002894,002895,002898,002905,002918,002959,002966,002968,002975,003013,003648,003747,003828,003884,004009,004067,004089,004116,004153,004157,004217,004224,004247,004256,004265,004320,004359,004370,004424,004435,004440,004444,004457,004463,004464,004466,004486,004509,004636,004702,004721,004763,005016,005086,005123,005569,005592,005650,005678,007939,007950,009488,009517,009522,009922,010196,010197,010796,010797,010807,010813,010933,010938,010943,010953,010955,011060,011066,011067,011079,011081,011087,011131,011143,011144,011148,011152,011153,011218,011999,012023,012063,012064,012074,012092,012104,012114,012116,012172,012178,012179,012181,012192,012235,012242,012277,012536,012543,012549,012612,012717,012733,012738,012764,012796,012830,012839,012842,012843,012848,012851,012855,012856,012859,012872,012891,012892,012893,012901,012902,012903,012912,012913,012915,013721,013747,013750,013800,013840,013841,013842,013844,014170,014180,014190,014191,014192,014203,014262,021428,021429,030041,030043,030046,030047,030048,030050,030051,030060,030103,030291,030321,030327,030337,030343,030356,030369,030374,030377,030381,030382,030388,030391,030398,030402,030406,030410,030411,030416,030420,030424,030426,030438,030439,030446,030504,030691,031215,031219,031220,031221,031236,031241,031321,031331,031355,031356\",\n", + "\"数列易错题\":\"000320,000321,000322,000403,001741,001769,001781,001783,001788,001809,001810,001839,003210,003219,003239,003253,003281,003283,003298,003309,003310,003312,004128,004352,004472,004476,006717,006760,006793,006911,008456,010773,010777,010787,010942,010964,011059,011090,011109,011388,012067,012073,012094,012112,012116,012181,012202,012220,012239,012540,012547,012715,012729,012735,012920,012933,012965,012969,012972,012979,013007,013921,013925,014092,014532,014538,030072,030281,030426,030473,030478,030496,030499,030502\",\n", + "\"解析几何易错题\":\"000248,000267,000271,000274,000282,000337,000360,000363,000464,000493,000501,000625,000669,000804,000960,002141,002162,002183,002252,002262,002268,002270,002278,002314,002329,002342,002372,002391,002403,002418,002426,002434,002435,003421,003431,003437,003438,003629,003893,004213,004246,004504,004550,008757,008760,008854,008865,008866,008873,008912,008937,008952,008956,009784,009823,010630,010631,010673,010951,010958,010963,011099,011106,011110,011450,012115,012180,012193,012197,012199,012200,012213,012218,012243,012255,012263,012276,012548,012716,012728,012730,012737,012915,013058,013060,013063,013066,013069,013073,013077,013081,013090,013096,013097,013099,013101,013112,013114,013118,013128,013130,013134,013139,013841,013903,013970,013974,013976,013981,013982,013988,013990,013992,013999,014019,014020,014364,014366,014478,014503,014505,030026,030484,030501,031228,031229,031231,031233,031317,031322,031323,031330\",\n", + "\"概率统计易错题\":\"000219,000223,000230,000233,000332,000340,000345,000359,000373,000401,000412,000462,000491,000654,000704,002537,002563,002586,002602,002605,002662,002664,003567,003574,003581,003585,003640,003666,004030,004068,004257,004499,004575,004578,004584,004586,004590,004595,004598,004599,004600,004601,004607,004611,004616,004617,004618,007361,007423,007432,007455,007476,007502,007506,007527,007528,007535,007539,007630,007631,007641,007643,007660,007673,009355,009357,009744,009745,010011,010013,010540,010554,010558,010868,010905,010918,010922,010929,010950,011137,011229,011993,012105,012254,012705,013221,013232,013711,014070,014079,014080,014087,014091,014096,030187,030188,030189,030191,030193,030194,030196,030209,030227,030253,030261,030268,030270,030275,030495,030499,030520,030524,030525,030530,030531,030532,030535,030538,030540,030552,030579,030580,030582,030588,030593,031158,031160,031163,031196,031201,031202,031203,031237,031238,031320,031328\"\n", "}\n", + "# problems_dict = {\n", + "# \"2024届高二下学期周末卷01\":\"40001:40017\",\n", + "# \"2025届高一下学期周末卷01\":\"40018:40036\",\n", + "# \"2024届高二下学期周末卷02\":\"40037:40056\",\n", + "# \"2025届高一下学期周末卷02\":\"40057:40082\",\n", + "# \"2025届高一下学期周末卷03\":\"40083:40104\",\n", + "# \"2025届高一下学期周末卷03小测\":\"40105:40112\",\n", + "# \"2025届高一下学期周末卷04旧版\":\"40113:40130\",\n", + "# \"2025届高一下学期周末卷04小测\":\"40131:40139\",\n", + "# \"2024届高二下学期周末卷03\":\"40140:40160\",\n", + "# \"2024届高二上学期期末考试\":\"31267:31287\",\n", + "# \"2025届高一上学期期末考试\":\"31288:31308\",\n", + "# \"2024届高二下学期周末卷04\":\"40161:40180\",\n", + "# \"2025届高一下学期周末卷04\":\"40181:40201\",\n", + "# \"2024届高二下学期周末卷05\":\"40202:40225\",\n", + "# \"2025届高一下学期周末卷05\":\"40226:40245\",\n", + "# \"2024届空间向量校本作业\":\"22048:22083\",\n", + "# \"2024届二项式定理校本作业\":\"22084:22105\",\n", + "# \"2025届高一下学期周末卷05小测\":\"40246:40255\",\n", + "# \"2025届高一下学期周末卷06\":\"40256:40273\",\n", + "# \"2025届高一下学期周末卷06小测\":\"40274:40282\",\n", + "# \"2025届高一下学期期中复习一(集合逻辑不等式)\":\"40283:40298\",\n", + "# \"2024届高二下学期周末卷06\":\"40299:40316\",\n", + "# \"2024届高二下学期周末卷07\":\"40317:40335\",\n", + "# \"2025届高一下学期测验01\":\"40336:40349\",\n", + "# \"2025届高一下学期测验02\":\"40350:40367\",\n", + "# \"2025届高一下学期期中复习二(幂指对函数)\":\"40368:40386\",\n", + "# \"2025届高一下学期周末卷02小测\":\"40387:40395\",\n", + "# \"2025届高一下学期周末卷07\":\"40396:40413\"\n", + "\n", + "# }\n", "\n", "\"\"\"---设置题目列表结束---\"\"\"\n", "\n", "\"\"\"---设置文件保存路径---\"\"\"\n", "#目录和文件的分隔务必用/\n", "directory = \"临时文件/\"\n", - "filename = \"2022学年下学期高一高二材料\"\n", + "filename = \"高三二模前易错题\"\n", + "# filename = \"2022学年下学期高一高二材料\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "if directory[-1] != \"/\":\n", " directory += \"/\"\n", diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index db2c2cba..a986cb4a 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,362 +1,245 @@ -usages + +ans + +013217 +$\dfrac 16$ + +014083 +$\dfrac{27}{100}$ + +014090 +$\dfrac 13$ + +014577 +$\dfrac{13}{21}$ + +014585 +$\dfrac{6}{25}$ + +014591 +$\dfrac{9}{10}$ + +014593 +$\dfrac 13$ + +014601 +$\dfrac 2{55}$ + +014599 +$\dfrac{41}{70}$ + +014603 +$(0,0.7)$ + +014598 +$9$ + +014594 +$0.14$ + +014094 +(1) $\dfrac 15$; (2) $\dfrac 35$; (3) $\dfrac 9{10}$ + +014597 +(1) $0.6$; (2) $X\sim \begin{pmatrix}0 & 10 & 20 & 30 \\ 0.16 & 0.44 & 0.34 & 0.06\end{pmatrix}$, $E[X]=13$ + +014608 +$P_n=\dfrac 12(1+(-\dfrac 13)^{n-1})$ + +014081 +$\dfrac 45$ + +014086 +$\dfrac{9}{50}$ + +014091 +$\dfrac{31}{120}$ + +014580 +$\dfrac 12$ + +013234 +$\dfrac{1}{168}$ + +014592 +$\dfrac{95}{99}$ + +014602 +$\dfrac 49$ + +014605 +$0.66$ + +014606 +$\dfrac 43$ + +014604 +$0.1$ + +014607 +$5$ + +014595 +(1) $\dfrac 3{16}$; (2) $\dfrac 12$ + +014596 +$0.03$ + +014600 +(1) $\dfrac{12}{25}$; (2) $\dfrac 9{25}$ 013220 -20230329 2023届高三11班 1.000 +$m>n$ 014092 -20230329 2023届高三11班 0.857 +$63$ 014629 -20230329 2023届高三11班 0.381 +$447$ 014631 -20230329 2023届高三11班 0.809 +B 014632 -20230329 2023届高三11班 0.762 +无关 014635 -20230329 2023届高三11班 0.714 +\textcircled{1}\textcircled{2}\textcircled{4} 014641 -20230329 2023届高三11班 0.952 - -014087 -20230329 2023届高三11班 0.857 +$7$ 014637 -20230329 2023届高三11班 0.857 0.905 +(1) $a=0.3$, $b=0.1$; (2) 甲离子残留百分比的平均值约为$4.05$($\%$), 乙离子残留百分比的平均值约为$6$($\%$) 014638 -20230329 2023届高三11班 0.952 0.857 0.714 +(1) 图略, 有明显的正相关关系; (2) $r\approx 0.97$, 相关性明显, 为正相关; (3) 拟合直线为$y=1.0173x+0.1909$, 当产品加工前含水率为$19\%$时, 加工后含水率估计为$19.5\%$ 014634 -20230329 2023届高三11班 0.381 0.619 0.238 +(1) 图略; (2) \begin{tabular}{|c||c|c||c|c|c|} +\hline +学历 & 均值 & 中位数 & 极差 & 方差 & 标准差 \\ \hline +专科 & $14.13$ & $14.66$ & $9.94$ & $4.52$ & $2.13$ \\ \hline +本科 & $20.05$ & $19.75$ & $26.73$ & $45.84$ & $6.77$ \\ \hline +研究生 & $5.20$ & $4.54$ & $17.39$ & $14.03$ & $3.75$ \\ \hline +\end{tabular} (3) 专科与本科的相关系数约为$0.68$, 有较强的正相关性; 专科与研究生的相关系数约为$0.41$, 有较弱的正相关性; 本科与研究生的相关性约为$0.90$, 有很强的正相关性 014633 -20230329 2023届高三11班 0.762 0.667 0.714 +(1) 女性样本离散程度较高, 男性样本数据的第$80$百分位数为$2.7$($\%$); (2) $a=8$, 平均数约为$6.3$, 方差约为$41.3$; (3) 男性$2625$人, 女性$2375$人 -013220 -20230329 2023届高三12班 0.944 +013235 +\textcircled{3} -014092 -20230329 2023届高三12班 0.889 +013218 +$50$ -014629 -20230329 2023届高三12班 0.333 +013237 +$8$或$10$或$11$ -014631 -20230329 2023届高三12班 1.000 +014640 +\textcircled{1}\textcircled{4} -014632 -20230329 2023届高三12班 0.778 +014642 +$27.6\times 10^3$ -014635 -20230329 2023届高三12班 0.611 +014643 +$3$; $30$ -014641 -20230329 2023届高三12班 0.833 +014636 +C -014087 -20230329 2023届高三12班 0.944 +014088 +B -014637 -20230329 2023届高三12班 0.889 0.833 +014085 +(1) $400$; (2) $4$; (3) $0.7$ -014638 -20230329 2023届高三12班 1.000 0.833 0.722 +014644 +(1) 横截面积的平均值约为$0.06\text{m}^2$; 材积量的平均值约为$0.39\text{m}^3$; (2) $r\approx 0.97$; (3) 比例系数的估计值$\hat{k}=\dfrac{\displaystyle\sum_{i=1}^{10}x_iy_i}{\displaystyle\sum_{i=1}^{10}x_i^2}$, 约为$1210.9\text{m}^3$ -014634 -20230329 2023届高三12班 0.611 0.667 0.278 +014645 +(1) $\chi^2=24$, 认为有关; (2) 证明略; (3) $R$的估计值为$6$ -014633 -20230329 2023届高三12班 0.833 0.722 0.889 +014646 +(1) $X\sim \begin{pmatrix} 155 & 165 & 175 & 185 & 195 & 205 \\ 0.22 & 0.27 & 0.25 & 0.15 & 0.1 & 0.01\end{pmatrix}$, $E[X]=171.7$($\text{cm}$); (2) $0.0312$; (3) $27.25$ -013220 -20230329 2023届高三01班 0.964 +012942 +$\begin{cases} 2, & n=1, \\ 2^{n-1} & n\ge 2\end{cases}$ -014092 -20230329 2023届高三01班 0.893 +012941 +$\dfrac{2}{19}$ -014629 -20230329 2023届高三01班 0.429 +012976 +$2^{\frac{n(n-1)}{2}}$ -014631 -20230329 2023届高三01班 0.964 +012923 +$3018$ -014632 -20230329 2023届高三01班 0.750 +013002 +$2999$ -014635 -20230329 2023届高三01班 0.607 +014550 +$(-\infty,3)$ -014641 -20230329 2023届高三01班 1.000 +012966 +$8$ -014087 -20230329 2023届高三01班 0.893 +013005 +$2^{n+1}$ -014637 -20230329 2023届高三01班 1.000 0.964 +013935 +$\dfrac{2\sqrt{3}}3$ -014638 -20230329 2023届高三01班 0.714 0.929 0.750 +012978 +$33$ -014634 -20230329 2023届高三01班 0.357 0.107 0.857 +012932 +$\dfrac{n}{n+1}$ -014633 -20230329 2023届高三01班 0.643 0.393 0.786 +012947 +$\begin{cases} 2, & n=1, \\ -\dfrac{1}{3^{n-1}} & n\ge 2\end{cases}$ -013220 -20230329 2023届高三02班 0.967 +012971 +(1) 最大项为$a_{10}-b_{10}=8976$; (2) $\{1,2,3,\cdots,13\}$ -014092 -20230329 2023届高三02班 0.767 +013960 +(1) $a_n=2^n+1$; (2) 证明略; (3) 证明略 -014629 -20230329 2023届高三02班 0.533 +013000 +$\dfrac 34-\dfrac{2n+3}{2(n^2+3n+2)}$ -014631 -20230329 2023届高三02班 0.967 +012956 +$\begin{cases} 4, & n=1, \\ 2 & n\ge 2\end{cases}$ -014632 -20230329 2023届高三02班 0.833 +014553 +$3$ -014635 -20230329 2023届高三02班 0.800 +012959 +$\begin{cases} 1, & n=1, \\ 2^{n-2} & n\ge 2\end{cases}$ -014641 -20230329 2023届高三02班 0.967 +012977 +$0$; $-\dfrac{63}{256}$ -014087 -20230329 2023届高三02班 0.967 +012982 +$4$或$5$或$32$ -014637 -20230329 2023届高三02班 0.900 0.867 +013955 +$9$ -014638 -20230329 2023届高三02班 0.933 0.967 0.933 +013944 +$(-\infty,-2]\cup [2,+\infty)$ -014634 -20230329 2023届高三02班 0.767 0.500 0.800 +012936 +$1830$ -014633 -20230329 2023届高三02班 0.833 0.600 0.967 +014560 +B -013220 -20230329 2023届高三04班 0.957 +013006 +(1) $\{f(n)\}$是严格增数列, 证明略; (2) $(-\infty,0)\cup (0,1)$ -014092 -20230329 2023届高三04班 0.696 - -014629 -20230329 2023届高三04班 0.478 - -014631 -20230329 2023届高三04班 0.783 - -014632 -20230329 2023届高三04班 0.739 - -014635 -20230329 2023届高三04班 0.696 - -014641 -20230329 2023届高三04班 1.000 - -014087 -20230329 2023届高三04班 0.957 - -014637 -20230329 2023届高三04班 0.957 0.913 - -014638 -20230329 2023届高三04班 0.652 1.000 0.870 - -014634 -20230329 2023届高三04班 0.087 0.130 0.130 - -014633 -20230329 2023届高三04班 0.652 0.522 0.957 - -013220 -20230329 2023届高三05班 0.914 - -014092 -20230329 2023届高三05班 0.800 - -014629 -20230329 2023届高三05班 0.514 - -014631 -20230329 2023届高三05班 0.943 - -014632 -20230329 2023届高三05班 0.886 - -014635 -20230329 2023届高三05班 0.571 - -014641 -20230329 2023届高三05班 0.971 - -014087 -20230329 2023届高三05班 0.971 - -014637 -20230329 2023届高三05班 0.886 0.857 - -014638 -20230329 2023届高三05班 0.943 1.000 0.829 - -014634 -20230329 2023届高三05班 0.371 0.314 0.200 - -014633 -20230329 2023届高三05班 0.629 0.543 0.886 - -013220 -20230329 2023届高三06班 0.973 - -014092 -20230329 2023届高三06班 0.865 - -014629 -20230329 2023届高三06班 0.595 - -014631 -20230329 2023届高三06班 0.973 - -014632 -20230329 2023届高三06班 0.757 - -014635 -20230329 2023届高三06班 0.703 - -014641 -20230329 2023届高三06班 0.946 - -014087 -20230329 2023届高三06班 0.865 - -014637 -20230329 2023届高三06班 1.000 0.838 - -014638 -20230329 2023届高三06班 0.378 1.000 0.703 - -014634 -20230329 2023届高三06班 0.351 0.081 1.000 - -014633 -20230329 2023届高三06班 0.703 0.568 0.892 - -013220 -20230329 2023届高三07班 1.000 - -014092 -20230329 2023届高三07班 0.913 - -014629 -20230329 2023届高三07班 0.522 - -014631 -20230329 2023届高三07班 0.826 - -014632 -20230329 2023届高三07班 0.696 - -014635 -20230329 2023届高三07班 0.696 - -014641 -20230329 2023届高三07班 0.913 - -014087 -20230329 2023届高三07班 0.957 - -014637 -20230329 2023届高三07班 1.000 0.957 - -014638 -20230329 2023届高三07班 0.826 1.000 0.826 - -014634 -20230329 2023届高三07班 0.435 0.087 0.043 - -014633 -20230329 2023届高三07班 0.826 0.826 0.957 - -013220 -20230329 2023届高三08班 1.000 - -014092 -20230329 2023届高三08班 0.783 - -014629 -20230329 2023届高三08班 0.478 - -014631 -20230329 2023届高三08班 0.913 - -014632 -20230329 2023届高三08班 0.783 - -014635 -20230329 2023届高三08班 0.696 - -014641 -20230329 2023届高三08班 0.957 - -014087 -20230329 2023届高三08班 0.913 - -014637 -20230329 2023届高三08班 0.957 1.000 - -014638 -20230329 2023届高三08班 0.957 0.913 0.696 - -014634 -20230329 2023届高三08班 0.217 0.261 0.087 - -014633 -20230329 2023届高三08班 0.522 0.304 0.826 - -013220 -20230329 2023届高三09班 0.963 - -014092 -20230329 2023届高三09班 0.852 - -014629 -20230329 2023届高三09班 0.518 - -014631 -20230329 2023届高三09班 0.889 - -014632 -20230329 2023届高三09班 0.704 - -014635 -20230329 2023届高三09班 0.444 - -014641 -20230329 2023届高三09班 1.000 - -014087 -20230329 2023届高三09班 0.815 - -014637 -20230329 2023届高三09班 1.000 0.926 - -014638 -20230329 2023届高三09班 0.556 0.815 0.593 - -014634 -20230329 2023届高三09班 0.222 0.333 0.111 - -014633 -20230329 2023届高三09班 0.444 0.518 0.593 +012983 +(1) $(a_1,a_2)=(0,0)$或$(1-\sqrt{2},2-\sqrt{2})$或$(1+\sqrt{2},2+\sqrt{2})$; (2) 当$n=7$时$T_n$最大, $T_7=7-\dfrac{21}{2}\lg 2$ +012938 +(1) $b_n=\begin{cases} 2^{\frac 32 n}, & n=2k, \\ 2^{\frac{3n-1}2} & n=2k-1\end{cases}$($k$为正整数); (2) $S_n=\begin{cases} \dfrac{10}{7}\cdot 2^{\frac 32 n}-\dfrac{10}{7}, & n=2k, \\ \dfrac{3}{7}\cdot 2^{\frac{3n-1}2}-\dfrac{10}{7} & n=2k-1\end{cases}$($k$为正整数) \ 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 4f5a8da7..c5136bf6 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 @@ -000321,000322,000403,001769,001781,001788,001809,001810,003210,003219,003239,003253,003281,003298,003309,003310,003312,004128,004472,004476,006717,006760,006793,006911,008456,010773,010777,010787,011059,011109,012067,012239,012729,012920,012933,013007,013921,014538,030072,030281,030473,030478,030496 \ No newline at end of file +000219,000223,000230,000233,000332,000340,000345,000359,000373,000401,000412,000462,000491,000654,000704,002537,002563,002586,002602,002605,002662,002664,003567,003574,003581,003585,003640,003666,004030,004068,004257,004499,004575,004578,004584,004586,004590,004595,004598,004599,004600,004601,004607,004611,004616,004617,004618,007361,007423,007432,007455,007476,007502,007506,007527,007528,007535,007539,007630,007631,007641,007643,007660,007673,009355,009357,009744,009745,010011,010013,010540,010554,010558,010868,010905,010918,010922,010929,010950,011137,011229,011993,012105,012254,012705,013221,013232,013711,014070,014079,014080,014087,014091,014096,030187,030188,030189,030191,030193,030194,030196,030209,030227,030253,030261,030268,030270,030275,030495,030499,030520,030524,030525,030530,030531,030532,030535,030538,030540,030552,030579,030580,030582,030588,030593,031158,031160,031163,031196,031201,031202,031203,031237,031238,031320,031328 \ No newline at end of file diff --git a/工具/试卷答案生成.ipynb b/工具/试卷答案生成.ipynb index 54dc42a0..d7109e8f 100644 --- a/工具/试卷答案生成.ipynb +++ b/工具/试卷答案生成.ipynb @@ -83,7 +83,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15" + "version": "3.8.15" }, "orig_nbformat": 4, "vscode": { diff --git a/文本处理工具/表格整理.ipynb b/文本处理工具/表格整理.ipynb index d652d6ee..f76159dd 100644 --- a/文本处理工具/表格整理.ipynb +++ b/文本处理工具/表格整理.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -82,7 +82,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15" + "version": "3.8.15" }, "orig_nbformat": 4, "vscode": { diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index eb6a82c1..7ab7b090 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -321431,7 +321431,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$60$", "solution": "", "duration": -1, "usages": [ @@ -321507,7 +321507,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$3018$", "solution": "", "duration": -1, "usages": [], @@ -321591,7 +321591,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -321625,7 +321625,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pm 2\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -321722,7 +321722,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{n}{n+1}$", "solution": "", "duration": -1, "usages": [], @@ -321743,7 +321743,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2^{2n-1}+1}3$", "solution": "", "duration": -1, "usages": [ @@ -321819,7 +321819,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$1830$", "solution": "", "duration": -1, "usages": [], @@ -321861,7 +321861,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $b_n=\\begin{cases} 2^{\\frac 32 n}, & n=2k, \\\\ 2^{\\frac{3n-1}2} & n=2k-1\\end{cases}$($k$为正整数); (2) $S_n=\\begin{cases} \\dfrac{10}{7}\\cdot 2^{\\frac 32 n}-\\dfrac{10}{7}, & n=2k, \\\\ \\dfrac{3}{7}\\cdot 2^{\\frac{3n-1}2}-\\dfrac{10}{7} & n=2k-1\\end{cases}$($k$为正整数)", "solution": "", "duration": -1, "usages": [], @@ -321924,7 +321924,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2}{19}$", "solution": "", "duration": -1, "usages": [], @@ -321945,7 +321945,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\begin{cases} 2, & n=1, \\\\ 2^{n-1} & n\\ge 2\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -322050,7 +322050,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\begin{cases} 2, & n=1, \\\\ -\\dfrac{1}{3^{n-1}} & n\\ge 2\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -322134,7 +322134,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -322189,7 +322189,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2^{n+1}-3$", "solution": "", "duration": -1, "usages": [ @@ -322244,7 +322244,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,1)\\cup (1,2)$", "solution": "", "duration": -1, "usages": [ @@ -322278,7 +322278,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\begin{cases} 4, & n=1, \\\\ 2 & n\\ge 2\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -322341,7 +322341,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\begin{cases} 1, & n=1, \\\\ 2^{n-2} & n\\ge 2\\end{cases}$", "solution": "", "duration": -1, "usages": [], @@ -322468,7 +322468,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1]\\cup [3,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -322502,7 +322502,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [], @@ -322523,7 +322523,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$(12,14)$", "solution": "", "duration": -1, "usages": [ @@ -322557,7 +322557,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -322591,7 +322591,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 32$", "solution": "", "duration": -1, "usages": [ @@ -322646,7 +322646,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 最大项为$a_{10}-b_{10}=8976$; (2) $\\{1,2,3,\\cdots,13\\}$", "solution": "", "duration": -1, "usages": [], @@ -322667,7 +322667,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 如$d=1$(正奇数都可以); (2) 是的, 证明略", "solution": "", "duration": -1, "usages": [ @@ -322764,7 +322764,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2^{\\frac{n(n-1)}{2}}$", "solution": "", "duration": -1, "usages": [], @@ -322785,7 +322785,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$0$; $-\\dfrac{63}{256}$", "solution": "", "duration": -1, "usages": [], @@ -322806,7 +322806,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$33$", "solution": "", "duration": -1, "usages": [], @@ -322827,7 +322827,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -322882,7 +322882,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$9^{2m-1}-9^{m-1}$", "solution": "", "duration": -1, "usages": [ @@ -322916,7 +322916,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$或$5$或$32$", "solution": "", "duration": -1, "usages": [], @@ -322937,7 +322937,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(a_1,a_2)=(0,0)$或$(1-\\sqrt{2},2-\\sqrt{2})$或$(1+\\sqrt{2},2+\\sqrt{2})$; (2) 当$n=7$时$T_n$最大, $T_7=7-\\dfrac{21}{2}\\lg 2$", "solution": "", "duration": -1, "usages": [], @@ -323294,7 +323294,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 34-\\dfrac{2n+3}{2(n^2+3n+2)}$", "solution": "", "duration": -1, "usages": [], @@ -323336,7 +323336,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2999$", "solution": "", "duration": -1, "usages": [], @@ -323399,7 +323399,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2^{n+1}$", "solution": "", "duration": -1, "usages": [], @@ -323420,7 +323420,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{f(n)\\}$是严格增数列, 证明略; (2) $(-\\infty,0)\\cup (0,1)$", "solution": "", "duration": -1, "usages": [], @@ -323441,7 +323441,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) $a_n=n-2+\\dfrac{3}{2^n}$; (3) $\\lambda$存在, $\\lambda=\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -326281,7 +326281,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -326377,7 +326377,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "存在, 坐标为$(-\\dfrac{10}3,0)$", "solution": "", "duration": -1, "usages": [ @@ -326485,7 +326485,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -326539,7 +326539,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$[\\sqrt{2},2)$", "solution": "", "duration": -1, "usages": [ @@ -326572,7 +326572,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{16}3$", "solution": "", "duration": -1, "usages": [ @@ -326639,7 +326639,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -326715,7 +326715,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,-3-2\\sqrt{2})\\cup (3,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -327030,7 +327030,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{8\\sqrt{3}}3$", "solution": "", "duration": -1, "usages": [ @@ -327215,7 +327215,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [ @@ -329017,7 +329017,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 16$", "solution": "", "duration": -1, "usages": [ @@ -329049,7 +329049,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$50$", "solution": "", "duration": -1, "usages": [], @@ -329091,7 +329091,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$m>n$", "solution": "", "duration": -1, "usages": [ @@ -329123,7 +329123,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$12$", "solution": "", "duration": -1, "usages": [ @@ -329157,7 +329157,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$66$", "solution": "", "duration": -1, "usages": [ @@ -329189,7 +329189,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$10$", "solution": "", "duration": -1, "usages": [ @@ -329221,7 +329221,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$12$", "solution": "", "duration": -1, "usages": [ @@ -329319,7 +329319,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$720$", "solution": "", "duration": -1, "usages": [ @@ -329351,7 +329351,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$70$", "solution": "", "duration": -1, "usages": [ @@ -329427,7 +329427,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$或$4$", "solution": "", "duration": -1, "usages": [ @@ -329480,7 +329480,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{168}$", "solution": "", "duration": -1, "usages": [ @@ -329511,7 +329511,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}", "solution": "", "duration": -1, "usages": [], @@ -329532,7 +329532,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$96$", "solution": "", "duration": -1, "usages": [ @@ -329564,7 +329564,7 @@ "第九单元" ], "genre": "填空题", - "ans": "", + "ans": "$8$或$10$或$11$", "solution": "", "duration": -1, "usages": [], @@ -330826,7 +330826,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -331617,7 +331617,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -335285,7 +335285,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -337927,7 +337927,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -344493,7 +344493,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$3^{n-1}$", "solution": "", "duration": -1, "usages": [ @@ -344548,7 +344548,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [ @@ -344603,7 +344603,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$n\\cdot (\\dfrac 12)^{n-1}$", "solution": "", "duration": -1, "usages": [ @@ -344658,7 +344658,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -344692,7 +344692,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{2015}$", "solution": "", "duration": -1, "usages": [ @@ -344894,7 +344894,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\sqrt{3}}3$", "solution": "", "duration": -1, "usages": [], @@ -345084,7 +345084,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-2]\\cup [2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -345252,7 +345252,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a_n=10-2n$; (2) $S_n=\\begin{cases}-n^2+9n, & n=1,2,3,4,5, \\\\ n^2-9n+40, & n=6,7,8,\\cdots.\\end{cases}$ (3) 存在, 整数$m$的最大值为$7$", "solution": "", "duration": -1, "usages": [ @@ -345328,7 +345328,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [], @@ -345434,7 +345434,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a_n=2^n+1$; (2) 证明略; (3) 证明略", "solution": "", "duration": -1, "usages": [], @@ -345905,7 +345905,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "点$C$", "solution": "", "duration": -1, "usages": [ @@ -345994,7 +345994,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$a-6$", "solution": "", "duration": -1, "usages": [ @@ -346165,7 +346165,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{x^2}3+\\dfrac{y^2}2=1$", "solution": "", "duration": -1, "usages": [ @@ -346252,7 +346252,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -346369,7 +346369,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [ @@ -346423,7 +346423,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$或$-2$", "solution": "", "duration": -1, "usages": [ @@ -346711,7 +346711,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-1,0)$", "solution": "", "duration": -1, "usages": [ @@ -346766,7 +346766,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) (如)不经过原点的直线$l$与抛物线$x^2=2py$交于$A(x_A,y_A)$与$B(x_B,y_B)$两点, 直线$l$与$x$轴相交于点$C(x_C,y_C)$, 则$\\dfrac{1}{x_A}+\\dfrac{1}{x_B}=\\dfrac{1}{x_C}$, 证明略", "solution": "", "duration": -1, "usages": [ @@ -346885,7 +346885,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}9+\\dfrac{y^2}4=1$; (2) $k=\\dfrac 12$或$\\dfrac{11}{28}$", "solution": "", "duration": -1, "usages": [ @@ -346919,7 +346919,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y^2=4x$; (2) $(-\\infty,-3)\\cup (-3,0)\\cup (0,1)$; (3) 定值为$2$, 证明略", "solution": "", "duration": -1, "usages": [ @@ -348173,7 +348173,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $294$; (2) $42$; (3) $24$", "solution": "", "duration": -1, "usages": [ @@ -348207,7 +348207,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $88$; (2) $45321$; (3) $3999960$", "solution": "", "duration": -1, "usages": [ @@ -348283,7 +348283,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$7$", "solution": "", "duration": -1, "usages": [ @@ -348315,7 +348315,7 @@ "第八单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -348347,7 +348347,7 @@ "第八单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -348423,7 +348423,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a_1=0$, $a_2=8$, $a_3=56$; (2) 证明略; (3) 存在, $a=1$, $b=-1$", "solution": "", "duration": -1, "usages": [ @@ -348455,7 +348455,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-11628$; (2) 前一个性质不能推广, 后一个性质能推广, 证明略; (3) 证明略", "solution": "", "duration": -1, "usages": [ @@ -348489,7 +348489,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 45$", "solution": "", "duration": -1, "usages": [ @@ -348541,7 +348541,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{27}{100}$", "solution": "", "duration": -1, "usages": [ @@ -348595,7 +348595,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $400$; (2) $4$; (3) $0.7$", "solution": "", "duration": -1, "usages": [], @@ -348616,7 +348616,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{9}{50}$", "solution": "", "duration": -1, "usages": [ @@ -348690,7 +348690,7 @@ "第九单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -348732,7 +348732,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 13$", "solution": "", "duration": -1, "usages": [ @@ -348764,7 +348764,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{31}{120}$", "solution": "", "duration": -1, "usages": [ @@ -348795,7 +348795,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$63$", "solution": "", "duration": -1, "usages": [ @@ -348848,7 +348848,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 15$; (2) $\\dfrac 35$; (3) $\\dfrac 9{10}$", "solution": "", "duration": -1, "usages": [ @@ -348901,7 +348901,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [ @@ -357541,7 +357541,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\pi}3$", "solution": "", "duration": -1, "usages": [ @@ -357931,7 +357931,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$x=0$或$y=-1$或$y=-\\dfrac 12 x-1$", "solution": "", "duration": -1, "usages": [ @@ -357962,7 +357962,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{11\\sqrt{2}}8$", "solution": "", "duration": -1, "usages": [ @@ -358053,7 +358053,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}2+y^2=1$; (2) $y=\\pm\\sqrt{2}(x-1)$; (3) $(\\dfrac{\\sqrt{6}}3,0)$", "solution": "", "duration": -1, "usages": [ @@ -358103,7 +358103,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -358230,7 +358230,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\dfrac 12,\\dfrac 12)$", "solution": "", "duration": -1, "usages": [ @@ -358473,7 +358473,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$3.6$", "solution": "", "duration": -1, "usages": [ @@ -358525,7 +358525,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-1,0)$", "solution": "", "duration": -1, "usages": [ @@ -358556,7 +358556,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -358626,7 +358626,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -359078,7 +359078,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$17$; $135$", "solution": "", "duration": -1, "usages": [ @@ -359112,7 +359112,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$; $\\dfrac{255}{16}$; $16$", "solution": "", "duration": -1, "usages": [ @@ -359146,7 +359146,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2$", "solution": "", "duration": -1, "usages": [ @@ -359178,7 +359178,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-2d$", "solution": "", "duration": -1, "usages": [ @@ -359210,7 +359210,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 有最小项, 第$15$项最小", "solution": "", "duration": -1, "usages": [ @@ -359263,7 +359263,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 约$39.2$吨; (2) 在$2025$年, 该地区通过环保方式处理的垃圾量首次超过这一年产生的生活垃圾量的$50\\%$", "solution": "", "duration": -1, "usages": [ @@ -359316,7 +359316,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $3$; (2) $18$, $19$或$20$", "solution": "", "duration": -1, "usages": [ @@ -359445,7 +359445,7 @@ "第四单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -359534,7 +359534,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,3)$", "solution": "", "duration": -1, "usages": [], @@ -359591,7 +359591,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -359724,7 +359724,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -359914,7 +359914,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $11$; (2) $30$", "solution": "", "duration": -1, "usages": [ @@ -360001,7 +360001,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $96$; (2) $60$", "solution": "", "duration": -1, "usages": [ @@ -360033,7 +360033,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $604800$; (2) $4656$", "solution": "", "duration": -1, "usages": [ @@ -360084,7 +360084,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{13}{21}$", "solution": "", "duration": -1, "usages": [ @@ -360114,7 +360114,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $448$; (2) $6561$; (3) 最大项为$a_10$($=3075072$)", "solution": "", "duration": -1, "usages": [ @@ -360144,7 +360144,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$81$", "solution": "", "duration": -1, "usages": [ @@ -360174,7 +360174,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -360203,7 +360203,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$60$", "solution": "", "duration": -1, "usages": [ @@ -360235,7 +360235,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$24$", "solution": "", "duration": -1, "usages": [ @@ -360267,7 +360267,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$或$4$", "solution": "", "duration": -1, "usages": [ @@ -360297,7 +360297,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$420$", "solution": "", "duration": -1, "usages": [ @@ -360329,7 +360329,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{6}{25}$", "solution": "", "duration": -1, "usages": [ @@ -360359,7 +360359,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [ @@ -360391,7 +360391,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$48$", "solution": "", "duration": -1, "usages": [ @@ -360423,7 +360423,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $120960$; (2) $604800$; (3) $132$", "solution": "", "duration": -1, "usages": [ @@ -360453,7 +360453,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$120$", "solution": "", "duration": -1, "usages": [ @@ -360502,7 +360502,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{9}{10}$", "solution": "", "duration": -1, "usages": [ @@ -360532,7 +360532,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{95}{99}$", "solution": "", "duration": -1, "usages": [ @@ -360561,7 +360561,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 13$", "solution": "", "duration": -1, "usages": [ @@ -360591,7 +360591,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0.14$", "solution": "", "duration": -1, "usages": [ @@ -360621,7 +360621,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 3{16}$; (2) $\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -360650,7 +360650,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$0.03$", "solution": "", "duration": -1, "usages": [ @@ -360679,7 +360679,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $0.6$; (2) $X\\sim \\begin{pmatrix}0 & 10 & 20 & 30 \\\\ 0.16 & 0.44 & 0.34 & 0.06\\end{pmatrix}$, $E[X]=13$", "solution": "", "duration": -1, "usages": [ @@ -360709,7 +360709,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [ @@ -360739,7 +360739,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{41}{70}$", "solution": "", "duration": -1, "usages": [ @@ -360769,7 +360769,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{12}{25}$; (2) $\\dfrac 9{25}$", "solution": "", "duration": -1, "usages": [ @@ -360798,7 +360798,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 2{55}$", "solution": "", "duration": -1, "usages": [ @@ -360828,7 +360828,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 49$", "solution": "", "duration": -1, "usages": [ @@ -360857,7 +360857,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(0,0.7)$", "solution": "", "duration": -1, "usages": [ @@ -360887,7 +360887,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0.1$", "solution": "", "duration": -1, "usages": [ @@ -360916,7 +360916,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0.66$", "solution": "", "duration": -1, "usages": [ @@ -360945,7 +360945,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 43$", "solution": "", "duration": -1, "usages": [ @@ -360974,7 +360974,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [ @@ -361003,7 +361003,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$P_n=\\dfrac 12(1+(-\\dfrac 13)^{n-1})$", "solution": "", "duration": -1, "usages": [ @@ -361413,7 +361413,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$447$", "solution": "", "duration": -1, "usages": [ @@ -361462,7 +361462,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -361492,7 +361492,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "无关", "solution": "", "duration": -1, "usages": [ @@ -361522,7 +361522,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 女性样本离散程度较高, 男性样本数据的第$80$百分位数为$2.7$($\\%$); (2) $a=8$, 平均数约为$6.3$, 方差约为$41.3$; (3) 男性$2625$人, 女性$2375$人", "solution": "", "duration": -1, "usages": [ @@ -361552,7 +361552,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 图略; (2) \\begin{tabular}{|c||c|c||c|c|c|}\n\\hline\n学历 & 均值 & 中位数 & 极差 & 方差 & 标准差 \\\\ \\hline\n专科 & $14.13$ & $14.66$ & $9.94$ & $4.52$ & $2.13$ \\\\ \\hline\n本科 & $20.05$ & $19.75$ & $26.73$ & $45.84$ & $6.77$ \\\\ \\hline\n研究生 & $5.20$ & $4.54$ & $17.39$ & $14.03$ & $3.75$ \\\\ \\hline\n\\end{tabular} (3) 专科与本科的相关系数约为$0.68$, 有较强的正相关性; 专科与研究生的相关系数约为$0.41$, 有较弱的正相关性; 本科与研究生的相关性约为$0.90$, 有很强的正相关性", "solution": "", "duration": -1, "usages": [ @@ -361582,7 +361582,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -361612,7 +361612,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -361631,7 +361631,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $a=0.3$, $b=0.1$; (2) 甲离子残留百分比的平均值约为$4.05$($\\%$), 乙离子残留百分比的平均值约为$6$($\\%$)", "solution": "", "duration": -1, "usages": [ @@ -361661,7 +361661,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 图略, 有明显的正相关关系; (2) $r\\approx 0.97$, 相关性明显, 为正相关; (3) 拟合直线为$y=1.0173x+0.1909$, 当产品加工前含水率为$19\\%$时, 加工后含水率估计为$19.5\\%$", "solution": "", "duration": -1, "usages": [ @@ -361710,7 +361710,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -361729,7 +361729,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$7$", "solution": "", "duration": -1, "usages": [ @@ -361759,7 +361759,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$27.6\\times 10^3$", "solution": "", "duration": -1, "usages": [], @@ -361778,7 +361778,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$; $30$", "solution": "", "duration": -1, "usages": [], @@ -361797,7 +361797,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 横截面积的平均值约为$0.06\\text{m}^2$; 材积量的平均值约为$0.39\\text{m}^3$; (2) $r\\approx 0.97$; (3) 比例系数的估计值$\\hat{k}=\\dfrac{\\displaystyle\\sum_{i=1}^{10}x_iy_i}{\\displaystyle\\sum_{i=1}^{10}x_i^2}$, 约为$1210.9\\text{m}^3$", "solution": "", "duration": -1, "usages": [], @@ -361816,7 +361816,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\chi^2=24$, 认为有关; (2) 证明略; (3) $R$的估计值为$6$", "solution": "", "duration": -1, "usages": [], @@ -361835,7 +361835,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $X\\sim \\begin{pmatrix} 155 & 165 & 175 & 185 & 195 & 205 \\\\ 0.22 & 0.27 & 0.25 & 0.15 & 0.1 & 0.01\\end{pmatrix}$, $E[X]=171.7$($\\text{cm}$); (2) $0.0312$; (3) $27.25$", "solution": "", "duration": -1, "usages": [], @@ -397193,7 +397193,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -397448,7 +397448,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$1$; $4$", "solution": "", "duration": -1, "usages": [ @@ -397878,7 +397878,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{2}}2$", "solution": "", "duration": -1, "usages": [ @@ -397913,7 +397913,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -398411,7 +398411,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$18$", "solution": "", "duration": -1, "usages": [ @@ -398644,7 +398644,7 @@ "导数" ], "genre": "解答题", - "ans": "", + "ans": "(1) 当$a\\le 2$时, $f(x)$是定义域$(0,+\\infty)$上的严格减函数; 当$a>2$时, $f(x)$在$(0,\\dfrac{a-\\sqrt{a^2-4}}2]$上是严格减函数, 在$[\\dfrac{a-\\sqrt{a^2-4}}2,\\dfrac{a+\\sqrt{a^2-4}}2]$上是严格增函数; (2) 证明略", "solution": "", "duration": -1, "usages": [ @@ -398678,7 +398678,7 @@ "导数" ], "genre": "解答题", - "ans": "", + "ans": "(1) 最大值为$\\dfrac 1{\\mathrm{e}}$, 最小值为$-\\mathrm{e}$; (2) 最大值为$10$, 最小值为$-71$; (3) 最大值为$\\dfrac{\\pi}6+\\sqrt{3}$, 最小值为$\\dfrac{\\pi}2$; (4) 最大值为$\\sqrt{\\mathrm{e}}$, 最小值为$-\\dfrac 2{\\mathrm{e}}$", "solution": "", "duration": -1, "usages": [ @@ -398734,7 +398734,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -424617,7 +424617,7 @@ "导数" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -425096,7 +425096,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$(4,5)$", "solution": "", "duration": -1, "usages": [ @@ -425226,7 +425226,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$[-\\dfrac 18,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -425347,7 +425347,7 @@ "导数" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,\\dfrac 14)$; (2) $6\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -425409,7 +425409,7 @@ "导数" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[1,+\\infty)$; (2) 证明略", "solution": "", "duration": -1, "usages": [ @@ -444026,7 +444026,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$y=x-1$; $(x-3)^2+(y-2)^2=16$或$(x-11)^2+(y+6)^2=144$", "solution": "", "duration": -1, "usages": [ @@ -447416,7 +447416,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "(1) $[0,+\\infty)$; (2) $(-\\infty,-6]$; (3) $-6$; (4) $(-6,0)$", "solution": "", "duration": -1, "usages": [ @@ -447453,7 +447453,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$\\mathrm{e}^2$", "solution": "", "duration": -1, "usages": [ @@ -447490,7 +447490,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$2$或$-2$; $3$或$-29$", "solution": "", "duration": -1, "usages": [ @@ -447530,7 +447530,7 @@ "导数" ], "genre": "填空题", - "ans": "", + "ans": "$-2$; $[-3,-1]$", "solution": "", "duration": -1, "usages": [ @@ -452001,7 +452001,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $\\dfrac 12 x^{-\\frac 12}$; (2) $\\dfrac 13 x^{-\\frac 23}$; (3) $-\\dfrac 12 x^{-\\dfrac 32}$; (4) $2x-\\mathrm{e}^x$; (5) $\\dfrac 1x-\\sin x$; (6) $\\dfrac 12 x^{-\\frac 12}+\\cos x$; (7) $\\mathrm{e}^x(x^3+3x^2)$; (8) $1+\\ln x$; (9) $\\dfrac{\\sin x-x\\cos x}{\\sin^2 x}$; (10) $2\\mathrm{e}^{2x-1}$; (11) $2^x\\ln 2$; (12) $-(\\dfrac 13)^{x+1}\\ln 3$; (13) $\\dfrac{1}{x\\ln 10}$; (14) $\\dfrac{2}{2x-1}$; (15) $\\dfrac{2}{(2x-3)\\ln 3}$; (16) $\\cos (x-\\dfrac\\pi 3)$; (17) $-\\dfrac 13 \\sin(\\dfrac x 3+\\dfrac \\pi 4)$; (18) $\\dfrac{2}{\\cos^2(2x)}$", "solution": "", "duration": -1, "usages": [ @@ -452070,7 +452070,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $-9$; (2) $-6$", "solution": "", "duration": -1, "usages": [ @@ -452405,7 +452405,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [