diff --git a/工具/模板文件/日常选题讲义模板.tex b/工具/模板文件/日常选题讲义模板.tex
new file mode 100644
index 00000000..1e38f089
--- /dev/null
+++ b/工具/模板文件/日常选题讲义模板.tex
@@ -0,0 +1,76 @@
+\documentclass[10pt,a4paper,twoside]{article}
+\usepackage[UTF8, fontset = none, heading = true]{ctex}
+\setCJKmainfont[BoldFont=黑体,ItalicFont=楷体]{华文中宋}
+\usepackage{amssymb,amsmath,amsfonts,amsthm,mathrsfs,dsfont,graphicx}
+\usepackage{ifthen,indentfirst,enumerate,color,lastpage}
+\usepackage{tikz}
+\usepackage{multicol}
+\usepackage{makecell}
+\usepackage{longtable}
+\usepackage{diagbox}
+\usepackage[top=1in, bottom=1in,left=0.8in,right=0.8in]{geometry}
+\usepackage{fancyhdr}
+\fancyhf{}
+\fancyhead[LO]{学号\blank{50} \ 姓名\blank{80}}
+\chead{\notestitle}
+\rhead{--\ \thepage\ of \pageref{LastPage} \ --}
+\pagestyle{fancy}
+\ctexset{section={
+name={},
+number=\chinese{section},
+}}
+\CTEXsetup[format={\bfseries\raggedright}]{section}
+\usetikzlibrary{arrows,calc,intersections,patterns,decorations.pathreplacing,3d,angles,quotes,positioning,shapes.geometric}
+
+\renewcommand{\baselinestretch}{1.5}
+\newtheorem{defi}{定义~}
+\newtheorem{eg}{例~}
+\newtheorem{ex}{~}
+\newtheorem{rem}{注~}
+\newtheorem{thm}{定理~}
+\newtheorem{coro}{推论~}
+\newtheorem{axiom}{公理~}
+\newtheorem{prop}{性质~}
+\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
+\newcommand{\bracket}[1]{(\hbox to #1pt{})}
+\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
+A.~#1\\
+B.~#2\\
+C.~#3\\
+D.~#4
+\end{tabular}}
+\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
+A.~#1& B.~#2\\
+C.~#3& D.~#4
+\end{tabular}}
+\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
+(1)~#1& (2)~#2\\
+(3)~#3& (4)~#4
+\end{tabular}}
+\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
+A.~#1 &B.~#2& C.~#3& D.~#4
+\end{tabular}}
+\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
+(1)~#1 &(2)~#2& (3)~#3& (4)~#4
+\end{tabular}}
+
+
+% 修改标题处
+\newcommand{\notestitle}{标题文字待处理}
+
+\begin{document}
+\begin{center}
+{\bf\large \notestitle}
+\end{center}
+
+
+%\section{课前练习}
+
+\begin{enumerate}[1.]
+待替换1
+\end{enumerate}
+
+
+
+
+\end{document}
\ No newline at end of file
diff --git a/工具/模板文件/题目清单.synctex.gz b/工具/模板文件/题目清单.synctex.gz
deleted file mode 100644
index a7bb1e5d..00000000
Binary files a/工具/模板文件/题目清单.synctex.gz and /dev/null differ
diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb
index 07109d01..accf7ccb 100644
--- a/工具/添加关联题目.ipynb
+++ b/工具/添加关联题目.ipynb
@@ -2,15 +2,15 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 47,
    "metadata": {},
    "outputs": [],
    "source": [
     "import os,re,json,time\n",
     "\n",
     "\"\"\"---设置原题目id与新题目id---\"\"\"\n",
-    "old_id = \"8191\"\n",
-    "new_id = \"30028\"\n",
+    "old_id = \"3181\"\n",
+    "new_id = \"30068\"\n",
     "\"\"\"---设置完毕---\"\"\"\n",
     "\n",
     "old_id = old_id.zfill(6)\n",
@@ -50,7 +50,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3.9.7 ('base')",
+   "display_name": "Python 3.8.8 ('base')",
    "language": "python",
    "name": "python3"
   },
@@ -64,12 +64,12 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.7"
+   "version": "3.8.8"
   },
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
+    "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
    }
   }
  },
diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb
index ca652463..848a4987 100644
--- a/工具/讲义生成.ipynb
+++ b/工具/讲义生成.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -11,11 +11,9 @@
      "text": [
       "正在处理题块 1 .\n",
       "题块 1 处理完毕.\n",
-      "正在处理题块 2 .\n",
-      "题块 2 处理完毕.\n",
-      "开始编译教师版本pdf文件:  临时文件/19_复数的几何意义与实系数二次方程预选_教师_20220923.tex\n",
+      "开始编译教师版本pdf文件:  临时文件/国庆卷_教师_20220924.tex\n",
       "0\n",
-      "开始编译学生版本pdf文件:  临时文件/19_复数的几何意义与实系数二次方程预选_学生_20220923.tex\n",
+      "开始编译学生版本pdf文件:  临时文件/国庆卷_学生_20220924.tex\n",
       "0\n"
      ]
     }
@@ -28,29 +26,34 @@
     "\"\"\"---设置模式结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置模板文件名---\"\"\"\n",
-    "template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
+    "# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
     "# template_file = \"模板文件/测验周末卷模板.tex\"\n",
+    "template_file = \"模板文件/日常选题讲义模板.tex\"\n",
     "\"\"\"---设置模板文件名结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置其他预处理替换命令---\"\"\"\n",
     "#2023届第一轮讲义更换标题\n",
-    "exec_list = [(\"标题数字待处理\",\"19\"),(\"标题文字待处理\",\"复数的几何意义与实系数二次方程\")] \n",
-    "enumi_mode = 0\n",
+    "# exec_list = [(\"标题数字待处理\",\"19\"),(\"标题文字待处理\",\"复数的几何意义与实系数二次方程\")] \n",
+    "# enumi_mode = 0\n",
     "\n",
     "#2023届测验卷与周末卷\n",
     "# exec_list = [(\"标题替换\",\"周末卷03\")]\n",
     "# enumi_mode = 1\n",
+    "\n",
+    "#日常选题讲义\n",
+    "exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n",
+    "enumi_mode = 0\n",
+    "\n",
     "\"\"\"---其他预处理替换命令结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置目标文件名---\"\"\"\n",
-    "destination_file = \"临时文件/19_复数的几何意义与实系数二次方程预选\"\n",
+    "destination_file = \"临时文件/国庆卷\"\n",
     "\"\"\"---设置目标文件名结束---\"\"\"\n",
     "\n",
     "\n",
     "\"\"\"---设置题号数据---\"\"\"\n",
     "problems = [\n",
-    "\"788,422,637,2010,2020,902,2018,598,2015,3521,3524,3534,2057,3542,168,2085,2086,3541,3544\",\n",
-    "\"163,2012,3519,3520,3523,3522,3535,831,2016,2017,3528,7313,7314,3551,3758,4167,9032,172\"\n",
+    "\"30029:30068\"\n",
     "]\n",
     "\"\"\"---设置题号数据结束---\"\"\"\n",
     "\n",
@@ -194,7 +197,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3.9.7 ('base')",
+   "display_name": "Python 3.8.8 ('base')",
    "language": "python",
    "name": "python3"
   },
@@ -208,12 +211,12 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.7"
+   "version": "3.8.8"
   },
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
+    "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
    }
   }
  },
diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb
index 22fa49b4..6b96ba71 100644
--- a/工具/题号选题pdf生成.ipynb
+++ b/工具/题号选题pdf生成.ipynb
@@ -2,16 +2,16 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "开始编译教师版本pdf文件:  临时文件/题库_教师用_20220923.tex\n",
+      "开始编译教师版本pdf文件:  临时文件/国庆卷粗_教师用_20220924.tex\n",
       "0\n",
-      "开始编译学生版本pdf文件:  临时文件/题库_学生用_20220923.tex\n",
+      "开始编译学生版本pdf文件:  临时文件/国庆卷粗_学生用_20220924.tex\n",
       "0\n"
      ]
     }
@@ -26,13 +26,14 @@
     "\"\"\"---设置题目列表---\"\"\"\n",
     "#留空为编译全题库\n",
     "problems = r\"\"\"\n",
+    "30029:30068\n",
     "\n",
     "\"\"\"\n",
     "\"\"\"---设置题目列表结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置文件名---\"\"\"\n",
     "#目录和文件的分隔务必用/\n",
-    "filename = \"临时文件/题库\"\n",
+    "filename = \"临时文件/国庆卷粗\"\n",
     "\"\"\"---设置文件名结束---\"\"\"\n",
     "\n",
     "\n",
@@ -157,9 +158,7 @@
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": [
-    "\n"
-   ]
+   "source": []
   }
  ],
  "metadata": {
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index cf0ba549..00711da8 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -857,7 +857,9 @@
             "20220624\t王伟叶, 余利成"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030038"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -2132,7 +2134,9 @@
             "20220624\t王伟叶, 余利成"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030052"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -2253,7 +2257,9 @@
             "20220624\t王伟叶, 余利成"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030046"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -2854,7 +2860,9 @@
         "same": [
             "008210"
         ],
-        "related": [],
+        "related": [
+            "030063"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -13394,7 +13402,9 @@
             "20220624\t朱敏慧, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030039"
+        ],
         "remark": "",
         "space": ""
     },
@@ -19879,7 +19889,9 @@
             "20220624\t朱敏慧, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030043"
+        ],
         "remark": "",
         "space": ""
     },
@@ -25548,7 +25560,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030030"
+        ],
         "remark": "",
         "space": "8ex"
     },
@@ -26372,7 +26386,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030037"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -27332,7 +27348,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030033"
+        ],
         "remark": "",
         "space": ""
     },
@@ -27624,7 +27642,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030034"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -30867,7 +30887,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030047"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -30947,7 +30969,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030049"
+        ],
         "remark": "第(3)小题有学生未考虑定义域，有学生在化简过程中出现了分母为$x$.",
         "space": "12ex"
     },
@@ -31106,7 +31130,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030051"
+        ],
         "remark": "学生有些未想到求导, 瞎猜的答案.",
         "space": ""
     },
@@ -32079,7 +32105,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030045"
+        ],
         "remark": "",
         "space": ""
     },
@@ -32884,7 +32912,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030046"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -33774,7 +33804,8 @@
         ],
         "same": [],
         "related": [
-            "001331"
+            "001331",
+            "030042"
         ],
         "remark": "",
         "space": ""
@@ -33856,7 +33887,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030044"
+        ],
         "remark": "",
         "space": ""
     },
@@ -36040,7 +36073,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030057"
+        ],
         "remark": "",
         "space": ""
     },
@@ -40364,7 +40399,8 @@
         ],
         "same": [],
         "related": [
-            "001587"
+            "001587",
+            "030059"
         ],
         "remark": "",
         "space": ""
@@ -68652,7 +68688,7 @@
     },
     "002747": {
         "id": "002747",
-        "content": "已知$m$是实常数. 命题甲: 关于$x$的方程$x^2+x+m=0$有两个相异的负根; 命题乙: 关于$x$的方程$4x^2+x+m=0$无实根, 若这两个命题有且只有一个是真命题, 求实数$m$的取值范围.\n*",
+        "content": "已知$m$是实常数. 命题甲: 关于$x$的方程$x^2+x+m=0$有两个相异的负根; 命题乙: 关于$x$的方程$4x^2+x+m=0$无实根, 若这两个命题有且只有一个是真命题, 求实数$m$的取值范围.",
         "objs": [
             "K0107002B"
         ],
@@ -68672,7 +68708,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030032"
+        ],
         "remark": "",
         "space": "16ex"
     },
@@ -69359,7 +69397,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030040"
+        ],
         "remark": "",
         "space": ""
     },
@@ -70712,7 +70752,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030060"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -72304,7 +72346,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030048"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -78603,7 +78647,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030064"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -78626,7 +78672,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030065"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -78790,7 +78838,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030066"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -79067,7 +79117,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030067"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -79207,7 +79259,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030068"
+        ],
         "remark": "",
         "space": ""
     },
@@ -89515,7 +89569,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030050"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -96450,7 +96506,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030055"
+        ],
         "remark": "",
         "space": ""
     },
@@ -114033,7 +114091,9 @@
             "20220711\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030062"
+        ],
         "remark": "",
         "space": ""
     },
@@ -127746,7 +127806,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030036"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -137651,7 +137713,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030041"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -143406,7 +143470,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030054"
+        ],
         "remark": "",
         "space": ""
     },
@@ -151794,7 +151860,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030061"
+        ],
         "remark": "",
         "space": ""
     },
@@ -187997,7 +188065,9 @@
         "same": [
             "000089"
         ],
-        "related": [],
+        "related": [
+            "030053"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -223876,7 +223946,9 @@
             "20220730\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030058"
+        ],
         "remark": "",
         "space": "12ex"
     },
@@ -235875,7 +235947,8 @@
         ],
         "same": [],
         "related": [
-            "011853"
+            "011853",
+            "030035"
         ],
         "remark": "",
         "space": "12ex"
@@ -278392,7 +278465,9 @@
             "20220803\t伍杨超, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030029"
+        ],
         "remark": "",
         "space": "16ex"
     },
@@ -279566,7 +279641,9 @@
             "20220803\t伍杨超, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "030031"
+        ],
         "remark": "",
         "space": ""
     },
@@ -283149,7 +283226,8 @@
         ],
         "same": [],
         "related": [
-            "001387"
+            "001387",
+            "030056"
         ],
         "remark": "",
         "space": ""
@@ -283502,5 +283580,969 @@
         ],
         "remark": "",
         "space": ""
+    },
+    "030029": {
+        "id": "030029",
+        "content": "证明:集合$A=\\{x|x=14n-1, \\ n\\in\\mathbf{Z}\\}$是$B=\\{x|x=7n+6, \\ n\\in\\mathbf{Z}\\}$的真子集.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "解答题",
+        "ans": "证明略",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一校本作业必修第一章-20220924修改",
+        "edit": [
+            "20220803\t伍杨超, 王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020035"
+        ],
+        "remark": "",
+        "space": "16ex"
+    },
+    "030030": {
+        "id": "030030",
+        "content": "已知集合$A=\\{1,2\\}$, $B=\\{x|mx^2+2mx-1>0, x \\in\\mathbf{R}\\}$. 已知$A \\cap B=\\{2\\}$, 则实数$m$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1106-集合的运算-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001016"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030031": {
+        "id": "030031",
+        "content": "已知$x,y,z\\in \\mathbf{R}$, ``$x^2+y^2+z^2>0$''是``$x\\ne 0$或$y\\ne 0$或$z\\ne 0$''的\\bracket{20}.\n\\twoch{充分而不必要条件}{必要而不充分条件}{充要条件}{既不充分又不必要条件}",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "选择题",
+        "ans": "C",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一校本作业必修第一章-20220924修改",
+        "edit": [
+            "20220803\t伍杨超, 王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020081"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030032": {
+        "id": "030032",
+        "content": "已知$m$是实常数. 命题甲: 关于$x$的方程$x^2+x+2m=0$有两个相异的负根; 命题乙: 关于$x$的方程$4x^2+x+2m=0$无实根, 若这两个命题有且只有一个是真命题, 则实数$m$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "填空题",
+        "ans": "$(0,\\dfrac 1{32}]\\cup [\\dfrac 18,+\\infty)$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "002747"
+        ],
+        "remark": "",
+        "space": "16ex"
+    },
+    "030033": {
+        "id": "030033",
+        "content": "判断题: (如果正确请在题目前面的横线上写``\\checkmark'', 错误请在题目前面的横线上写``$\\times$'')\\\\ \n\\blank{30}(1) 若$a>b$, $c\\geq d$, 则$a+c>b+d$;\\\\ \n\\blank{30}(2) 若$a>b$, $c\\geq d$, 则$a+c\\geq b+d$;\\\\ \n\\blank{30}(3) 若$a\\ge b$, $c\\ge d$, 则$a+c\\ge b+d$.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1117-不等式的性质-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001085"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030034": {
+        "id": "030034",
+        "content": "利用绝对值的三角不等式$|a+b|\\le |a|+|b|$, 证明: 对任意$x,y\\in\\mathbf{R}$, $|x-y|\\ge ||x|-|y||$.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "解答题",
+        "ans": "证明略",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1119-含有绝对值的不等式基本性质-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001096"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030035": {
+        "id": "030035",
+        "content": "证明: $|x+2|-|3-x|\\ge -5$, 对所有实数$x$均成立, 并求等号成立时$x$的取值范围.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "解答题",
+        "ans": "证明略, 等号成立时$x$的取值范围为$(-\\infty,-2]$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材必修第一册习题-20220924修改",
+        "edit": [
+            "20220806\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "011853",
+            "010104"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030036": {
+        "id": "030036",
+        "content": "已知关于$x$的不等式$|x-4|+|x+3|<a$在实数集$\\mathbf{R}$上的解集不是空集, 则实数$a$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "填空题",
+        "ans": "$(7,+\\infty)$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "代数精编第二章不等式-20220924修改",
+        "edit": [
+            "20220720\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "005239"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030037": {
+        "id": "030037",
+        "content": "解关于$x$的方程: $ax-1=x-ab$.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "解答题",
+        "ans": "当$a\\ne 1$时, 解为$\\dfrac{1-ab}{a-1}$; 当$a=1$且$b\\ne 1$时, 解集为$\\varnothing$; 当$a=1$且$b=1$时, 解集为$\\mathbf{R}$.",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1113-一次方程与二次方程-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001049"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030038": {
+        "id": "030038",
+        "content": "设$a,b\\in \\mathbf{R}$, 已知关于$x$的不等式$(a+b)x+(b-2a)<0$的解集为$(1, +\\infty)$, 则不等式$(a-b)x+4b-a>0$的解集为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20220924修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "000035"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030039": {
+        "id": "030039",
+        "content": "不等式$\\dfrac1{|x-2|}\\ge 3 $的解集为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "填空题",
+        "ans": "$[\\dfrac 53,2)\\cup (2,\\dfrac 73]$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "赋能练习-20220924修改",
+        "edit": [
+            "20220624\t朱敏慧, 王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "000540"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030040": {
+        "id": "030040",
+        "content": "已知关于$x$的不等式$ax^2-bx+c>0$的解集是$(-\\dfrac 32,\\dfrac 12)$, 对于$a,b,c$有以下结论: \\textcircled{1} $a>0$; \\textcircled{2} $b>0$; \\textcircled{3} $c>0$; \\textcircled{4} $a+b+c>0$; \\textcircled{5} $a-b+c>0$. 其中正确的序号有\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "填空题",
+        "ans": "\\textcircled{2}\\textcircled{3}\\textcircled{4}",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "002775"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030041": {
+        "id": "030041",
+        "content": "已知三个个正数$a,b,c$满足$a^{\\lg bx}=b^{\\lg ax}$, 则$a,b,c$满足的条件为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "$a=b$或$c=1$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "代数精编第三章函数-20220924修改",
+        "edit": [
+            "20220720\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "005650"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030042": {
+        "id": "030042",
+        "content": "函数$y=\\log_2(x^2+x-2)$的递增区间是\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1155-对数函数-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001331",
+            "001325"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030043": {
+        "id": "030043",
+        "content": "若函数$f(x)={\\log_a}(x^2-4ax+1)\\ (a>0, \\ a\\ne 1)$没有最小值, 则$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "赋能练习-20220924修改",
+        "edit": [
+            "20220624\t朱敏慧, 王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "000795"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030044": {
+        "id": "030044",
+        "content": "不等式$\\log_{\\frac{1}{2}}(x^2+x+1)<\\log_{\\frac{1}{2}}(5x-2)$的解集为\\blank{80}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "$(\\dfrac 25,1)\\cup (3,+\\infty)$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1155-对数函数-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001328"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030045": {
+        "id": "030045",
+        "content": "已知函数$y=f(2x+1)$的定义域为$[0,3]$, 则函数$y=f(3x-1)$的定义域为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "$[\\dfrac 23,\\dfrac 83]$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1146-一次函数与分式线性函数-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001262"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030046": {
+        "id": "030046",
+        "content": "作出函数$y=(x^3-1)^2-1$的大致图像, 写出它的单调区间, 并证明你的结论.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20220924修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "000092"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030047": {
+        "id": "030047",
+        "content": "判断函数$y=(\\sqrt{x}+2)(2^x+1)$的单调性, 并证明.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "解答题",
+        "ans": "证明略",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1140-函数的运算复合与奇偶性单调性的关系-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001218"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030048": {
+        "id": "030048",
+        "content": "设常数$a\\in \\mathbf{R}$. 若$y=\\log_{\\frac 12}(x^2-2ax+12)$在$[-2,+\\infty)$上是严格减函数, 则$a$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "002895"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030049": {
+        "id": "030049",
+        "content": "判断函数$y=\\dfrac{\\sqrt{4x^2+1}+2x+1}{\\sqrt{4x^2+1}+2x-1}$的奇偶性, 并说明理由.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "解答题",
+        "ans": "(1) 奇函数, 证明略",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1141-更多奇偶性与单调性的练习-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001221"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030050": {
+        "id": "030050",
+        "content": "已知$f(x)=ax+\\dfrac{1}{x+1}, \\ a\\in \\mathbf{R}$. 若$y=f(x)$在$x\\in [3,4]$时有零点, 则$a$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "上海2019年秋季高考试题18-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003648"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030051": {
+        "id": "030051",
+        "content": "函数$y=x^3+\\dfrac{27}{x}, \\ x\\in [1,4]$的最大值为\\blank{50}, 最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t1142-函数的最值-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001227"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030052": {
+        "id": "030052",
+        "content": "已知函数$y=-x^2+2ax$, $x\\in [0, 1]$的最大值为$a+1$. 求实数$a$的值.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "解答题",
+        "ans": "$-1$或$2$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20220924修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "000087"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030053": {
+        "id": "030053",
+        "content": "已知$y=f(x)$是定义在$(-2,2)$上的奇函数, 在区间$[0,2)$上是严格增函数, 且$f(1-a)+f(1-a^2)<0$, 则实数$a$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "填空题",
+        "ans": "$(1,\\sqrt{3})$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "二期课改练习册高一第一学期-20220924修改",
+        "edit": [
+            "20220726\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "007939"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030054": {
+        "id": "030054",
+        "content": "直角坐标平面内, 终边过点$(1,\\sqrt{2})$的所有角组成的集合可表示成\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "$\\{x|x=2k\\pi+\\arctan \\sqrt{2}, \\ k\\in \\mathbf{Z}\\}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "代数精编第四章三角函数-20220924修改",
+        "edit": [
+            "20220720\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "005902"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030055": {
+        "id": "030055",
+        "content": "已知角$\\alpha$的终边上一点的坐标为$\\left(\\sin\\dfrac{3\\pi}{7},\\cos\\dfrac{3\\pi}{7}\\right)$, 则角$\\alpha$的最小正值为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "$\\dfrac{\\pi}{14}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016年双基百分百-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003959"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030056": {
+        "id": "030056",
+        "content": "四点三十分时, 时针和分针的夹角的弧度数为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t2104-弧度制与任意角[1]-20220912修改-20220924修改",
+        "edit": [
+            "20220912\t王伟叶\t朱敏慧",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001387",
+            "030015"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030057": {
+        "id": "030057",
+        "content": "已知$\\theta$是象限角, 化简下列各式.\\\\ \n(1) $\\dfrac{\\cos(-\\theta)\\sin(\\pi-\\theta)}{\\cos(\\theta-3\\pi)}+\\dfrac{\\sin(-2\\pi-\\theta)\\sin(\\theta+\\pi)}{\\sin(4\\pi-\\theta)}=$\\blank{50}.\\\\ \n(2) $\\sin\\left(\\dfrac{\\pi}{2}-\\theta\\right)+\\sin\\left(\\dfrac{5\\pi}{2}+\\theta\\right)\n-\\sin\\left(\\dfrac{3\\pi}{2}-\\theta\\right)+\\sin\\left(\\dfrac{3\\pi}{2}+\\theta\\right)=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t2108-诱导公式-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001412"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030058": {
+        "id": "030058",
+        "content": "已知点$A$的坐标为$(3, 4)$, 将$OA$绕坐标原点$O$逆时针旋转$\\dfrac\\pi 4$至$OA'$. 求点$A'$的坐标.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "新教材必修第二册课堂练习-20220924修改",
+        "edit": [
+            "20220730\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "009561"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030059": {
+        "id": "030059",
+        "content": "方程$\\sin x+4\\cos x=0$的解集为\\blank{150}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "$\\{x|x=-\\arctan 4+k\\pi, \\ k\\in \\mathbf{Z}\\}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2016届创新班作业\t2125-三角方程-20220924修改",
+        "edit": [
+            "20220625\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "001587",
+            "001586"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030060": {
+        "id": "030060",
+        "content": "如图, 用长为$l$的铁丝弯成中间为矩形, 两端为半圆形的空心框架, 若矩形一边长为$2x$, 试用解析式将此框架围成的面积$y$表示为$x$的函数.\n\\begin{center}\n    \\begin{tikzpicture}[>=latex]\n        \\draw (2,0) -- (2,1.5) arc (0:180:1) -- (0,0) arc (180:360:1) -- cycle;\n        \\draw [<->] (0,0.3) -- (2,0.3) node [midway, fill = white] {$2x$};\n    \\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "002830"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030061": {
+        "id": "030061",
+        "content": "下列各式中, 不正确的是\\bracket{20}.\n\\twoch{$\\sin \\alpha +\\sin \\beta =2\\sin \\dfrac{\\beta +\\alpha}2\\cos \\dfrac{\\beta -\\alpha}2$}{$\\sin \\alpha -\\sin \\beta =2\\cos \\dfrac{\\beta +\\alpha}2\\sin \\dfrac{\\alpha -\\beta}2$}{$\\cos \\alpha +\\cos \\beta =2\\cos \\dfrac{\\beta +\\alpha}2\\cos \\dfrac{\\beta -\\alpha}2$}{$\\cos \\alpha -\\cos \\beta =2\\sin \\dfrac{\\beta +\\alpha}2\\sin \\dfrac{\\alpha -\\beta}2$}",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "选择题",
+        "ans": "D",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "代数精编第五章三角恒等式与解三角形-20220924修改",
+        "edit": [
+            "20220720\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "006286"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030062": {
+        "id": "030062",
+        "content": "在$\\triangle ABC$中, $b=3,c=2$, $B-C=\\dfrac{\\pi}2$, 则$\\tan A=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三上期中区统考第12题-20220924修改",
+        "edit": [
+            "20220711\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "004672"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030063": {
+        "id": "030063",
+        "content": "在$\\triangle ABC$中, 已知$A=60^\\circ$, $b=6$. 若$a=2\\sqrt{7}$, 则$B=$\\blank{50}; 若$a=6$, 则$B=$\\blank{50}; 若$a=9$, 则$B=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "教材复习题-20220924修改",
+        "edit": [
+            "20220624\t王伟叶, 余利成",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "000116"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030064": {
+        "id": "030064",
+        "content": "函数$y=\\sqrt{\\cos x}+\\dfrac 1{\\sqrt{36-x^2}}$的定义域为\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003155"
+        ],
+        "remark": "",
+        "space": ""
+    },
+    "030065": {
+        "id": "030065",
+        "content": "求函数$y=\\sin x(\\sin x+\\sqrt{3}\\cos x)$的最大值与最小值.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003156"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030066": {
+        "id": "030066",
+        "content": "求函数$y=\\dfrac{\\cos^2 x-3}{1-\\sin x}$的最大值.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003163"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030067": {
+        "id": "030067",
+        "content": "已知函数$f(x)=(2\\sin(x+\\dfrac{\\pi}3)+\\sin x)\\cos x-\\sqrt 3\\sin^2 x$, 求$f(x)$的单调递减区间",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003175"
+        ],
+        "remark": "",
+        "space": "12ex"
+    },
+    "030068": {
+        "id": "030068",
+        "content": "设常数$a\\in \\mathbf{R}$. 若函数$y=\\sin 2x+a\\cos 2x$的图像关于直线$x=\\dfrac{\\pi}3$对称, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [
+            "第三单元"
+        ],
+        "genre": "填空题",
+        "ans": "$-\\dfrac{\\sqrt{3}}3$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20220924修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20220924\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "003181"
+        ],
+        "remark": "",
+        "space": ""
     }
 }
\ No newline at end of file