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 46ae1d54..b42d34d3 100644
--- a/工具/修改题目数据库.ipynb
+++ b/工具/修改题目数据库.ipynb
@@ -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 = \"30524\"\n",
+    "problems = \"30552\"\n",
     "\n",
     "def generate_number_set(string,dict):\n",
     "    string = re.sub(r\"[\\n\\s]\",\"\",string)\n",
diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb
index 0c5f8a5c..03ecf489 100644
--- a/工具/寻找阶段末尾空闲题号.ipynb
+++ b/工具/寻找阶段末尾空闲题号.ipynb
@@ -2,16 +2,16 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "首个空闲id: 12739 , 直至 020000\n",
+      "首个空闲id: 12760 , 直至 020000\n",
       "首个空闲id: 21441 , 直至 030000\n",
-      "首个空闲id: 31057 , 直至 999999\n"
+      "首个空闲id: 31158 , 直至 999999\n"
      ]
     }
    ],
@@ -45,7 +45,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "mathdept",
+   "display_name": "Python 3.8.15 ('mathdept')",
    "language": "python",
    "name": "python3"
   },
@@ -59,12 +59,12 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.15"
+   "version": "3.8.15"
   },
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
+    "hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2"
    }
   }
  },
diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb
index 3c09514a..27bdf884 100644
--- a/工具/添加题目到数据库.ipynb
+++ b/工具/添加题目到数据库.ipynb
@@ -7,10 +7,10 @@
    "outputs": [],
    "source": [
     "#修改起始id,出处,文件名\n",
-    "starting_id = 31057\n",
-    "origin = \"\"\n",
-    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n",
-    "editor = \"20230108\\t王伟叶\""
+    "starting_id = 12739\n",
+    "origin = \"2011届春季高考\"\n",
+    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目7.tex\"\n",
+    "editor = \"20230109\\t王伟叶\""
    ]
   },
   {
@@ -70,8 +70,8 @@
     "    pid = str(id).zfill(6)\n",
     "    if pid in pro_dict:\n",
     "        duplicate_flag = True\n",
-    "    NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n",
-    "    # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n",
+    "    # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n",
+    "    NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n",
     "    pro_dict[pid] = NewProblem\n",
     "    id += 1\n",
     "\n",
@@ -101,7 +101,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "mathdept",
+   "display_name": "Python 3.9.15 ('pythontest')",
    "language": "python",
    "name": "python3"
   },
@@ -120,7 +120,7 @@
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
+    "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
    }
   }
  },
diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb
index 7dc416cf..07eaf025 100644
--- a/工具/识别题库中尚未标注的题目类型.ipynb
+++ b/工具/识别题库中尚未标注的题目类型.ipynb
@@ -9,567 +9,27 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "030597 填空题\n",
-      "030598 填空题\n",
-      "030599 填空题\n",
-      "030600 填空题\n",
-      "030601 填空题\n",
-      "030602 填空题\n",
-      "030603 填空题\n",
-      "030604 填空题\n",
-      "030605 填空题\n",
-      "030606 填空题\n",
-      "030607 填空题\n",
-      "030608 填空题\n",
-      "030609 填空题\n",
-      "030610 填空题\n",
-      "030611 填空题\n",
-      "030612 填空题\n",
-      "030613 填空题\n",
-      "030614 填空题\n",
-      "030615 填空题\n",
-      "030616 填空题\n",
-      "030617 填空题\n",
-      "030618 填空题\n",
-      "030619 填空题\n",
-      "030620 填空题\n",
-      "030621 填空题\n",
-      "030622 填空题\n",
-      "030623 填空题\n",
-      "030624 填空题\n",
-      "030625 选择题\n",
-      "030626 选择题\n",
-      "030627 选择题\n",
-      "030628 选择题\n",
-      "030629 选择题\n",
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-      "030631 选择题\n",
-      "030632 选择题\n",
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-      "030634 选择题\n",
-      "030635 填空题\n",
-      "030636 选择题\n",
-      "030637 填空题\n",
-      "030638 填空题\n",
-      "030639 填空题\n",
-      "030640 选择题\n",
-      "030641 填空题\n",
-      "030642 填空题\n",
-      "030643 填空题\n",
-      "030644 选择题\n",
-      "030645 选择题\n",
-      "030646 填空题\n",
-      "030647 填空题\n",
-      "030648 填空题\n",
-      "030649 填空题\n",
-      "030650 填空题\n",
-      "030651 选择题\n",
-      "030652 选择题\n",
-      "030653 选择题\n",
-      "030654 选择题\n",
-      "030655 填空题\n",
-      "030656 填空题\n",
-      "030657 填空题\n",
-      "030658 填空题\n",
-      "030659 填空题\n",
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-      "030662 填空题\n",
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-      "030664 填空题\n",
-      "030665 填空题\n",
-      "030666 填空题\n",
-      "030667 选择题\n",
-      "030668 选择题\n",
-      "030669 解答题\n",
-      "030670 填空题\n",
-      "030671 选择题\n",
-      "030672 选择题\n",
-      "030673 选择题\n",
-      "030674 选择题\n",
-      "030675 选择题\n",
-      "030676 解答题\n",
-      "030677 解答题\n",
-      "030678 填空题\n",
-      "030679 填空题\n",
-      "030680 填空题\n",
-      "030681 填空题\n",
-      "030682 填空题\n",
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-      "030685 填空题\n",
-      "030686 填空题\n",
-      "030687 填空题\n",
-      "030688 填空题\n",
-      "030689 选择题\n",
-      "030690 选择题\n",
-      "030691 选择题\n",
-      "030692 选择题\n",
-      "030693 填空题\n",
-      "030694 填空题\n",
-      "030695 填空题\n",
-      "030696 填空题\n",
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-      "030698 填空题\n",
-      "030699 填空题\n",
-      "030700 填空题\n",
-      "030701 选择题\n",
-      "030702 填空题\n",
-      "030703 填空题\n",
-      "030704 解答题\n",
-      "030705 解答题\n",
-      "030706 解答题\n",
-      "030707 解答题\n",
-      "030708 解答题\n",
-      "030709 解答题\n",
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-      "030711 解答题\n",
-      "030712 解答题\n",
-      "030713 解答题\n",
-      "030714 解答题\n",
-      "030715 解答题\n",
-      "030716 填空题\n",
-      "030717 填空题\n",
-      "030718 填空题\n",
-      "030719 填空题\n",
-      "030720 填空题\n",
-      "030721 填空题\n",
-      "030722 选择题\n",
-      "030723 选择题\n",
-      "030724 解答题\n",
-      "030725 解答题\n",
-      "030726 解答题\n",
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-      "030728 选择题\n",
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-      "030730 解答题\n",
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-      "030755 选择题\n",
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-      "030765 选择题\n",
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-      "030769 解答题\n",
-      "030770 填空题\n",
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-      "030961 填空题\n",
-      "030962 填空题\n",
-      "030963 填空题\n",
-      "030964 填空题\n",
-      "030965 解答题\n",
-      "030966 填空题\n",
-      "030967 填空题\n",
-      "030968 填空题\n",
-      "030969 解答题\n",
-      "030970 填空题\n",
-      "030971 填空题\n",
-      "030972 填空题\n",
-      "030973 填空题\n",
-      "030974 填空题\n",
-      "030975 填空题\n",
-      "030976 填空题\n",
-      "030977 填空题\n",
-      "030978 填空题\n",
-      "030979 选择题\n",
-      "030980 选择题\n",
-      "030981 选择题\n",
-      "030982 填空题\n",
-      "030983 选择题\n",
-      "030984 填空题\n",
-      "030985 填空题\n",
-      "030986 填空题\n",
-      "030987 填空题\n",
-      "030988 填空题\n",
-      "030989 选择题\n",
-      "030990 选择题\n",
-      "030991 选择题\n",
-      "030992 选择题\n",
-      "030993 选择题\n",
-      "030994 选择题\n",
-      "030995 选择题\n",
-      "030996 选择题\n",
-      "030997 选择题\n",
-      "030998 选择题\n",
-      "030999 填空题\n",
-      "031000 填空题\n",
-      "031001 填空题\n",
-      "031002 选择题\n",
-      "031003 选择题\n",
-      "031004 选择题\n",
-      "031005 选择题\n",
-      "031006 选择题\n",
-      "031007 填空题\n",
-      "031008 填空题\n",
-      "031009 填空题\n",
-      "031010 填空题\n",
-      "031011 填空题\n",
-      "031012 填空题\n",
-      "031013 填空题\n",
-      "031014 填空题\n",
-      "031015 填空题\n",
-      "031016 填空题\n",
-      "031017 填空题\n",
-      "031018 填空题\n",
-      "031019 填空题\n",
-      "031020 填空题\n",
-      "031021 填空题\n",
-      "031022 填空题\n",
-      "031023 填空题\n",
-      "031024 填空题\n",
-      "031025 填空题\n",
-      "031026 解答题\n",
-      "031027 解答题\n",
-      "031028 解答题\n",
-      "031029 解答题\n",
-      "031030 解答题\n",
-      "031031 解答题\n",
-      "031032 解答题\n",
-      "031033 解答题\n",
-      "031034 解答题\n",
-      "031035 解答题\n",
-      "031036 解答题\n",
-      "031037 解答题\n",
-      "031038 解答题\n",
-      "031039 解答题\n",
-      "031040 解答题\n",
-      "031041 解答题\n",
-      "031042 解答题\n",
-      "031043 解答题\n",
-      "031044 解答题\n",
-      "031045 解答题\n",
-      "031046 解答题\n",
-      "031047 解答题\n",
-      "031048 解答题\n",
-      "031049 解答题\n",
-      "031050 解答题\n",
-      "031051 解答题\n",
-      "031052 解答题\n",
-      "031053 解答题\n",
-      "031054 解答题\n",
-      "031055 解答题\n",
-      "031056 解答题\n",
-      "031057 填空题\n",
-      "031058 填空题\n",
-      "031059 选择题\n",
-      "031060 填空题\n",
-      "031061 选择题\n",
-      "031062 填空题\n",
-      "031063 填空题\n",
-      "031064 填空题\n",
-      "031065 填空题\n",
-      "031066 填空题\n",
-      "031067 选择题\n",
-      "031068 选择题\n",
-      "031069 填空题\n",
-      "031070 填空题\n",
-      "031071 填空题\n",
-      "031072 填空题\n",
-      "031073 填空题\n",
-      "031074 填空题\n",
-      "031075 选择题\n",
-      "031076 选择题\n",
-      "031077 解答题\n",
-      "031078 解答题\n",
-      "031079 解答题\n",
-      "031080 解答题\n",
-      "031081 解答题\n",
-      "031082 解答题\n",
-      "031083 解答题\n",
-      "031084 解答题\n",
-      "031085 解答题\n",
-      "031086 解答题\n",
-      "031087 解答题\n",
-      "031088 解答题\n",
-      "031089 解答题\n",
-      "031090 解答题\n",
-      "031091 解答题\n",
-      "031092 解答题\n",
-      "031093 解答题\n",
-      "031094 解答题\n",
-      "031095 填空题\n",
-      "031096 填空题\n",
-      "031097 填空题\n",
-      "031098 填空题\n",
-      "031099 填空题\n",
-      "031100 填空题\n",
-      "031101 填空题\n",
-      "031102 填空题\n",
-      "031103 填空题\n",
-      "031104 填空题\n",
-      "031105 填空题\n",
-      "031106 选择题\n",
-      "031107 选择题\n",
-      "031108 选择题\n",
-      "031109 选择题\n",
-      "031110 解答题\n",
-      "031111 解答题\n",
-      "031112 解答题\n",
-      "031113 解答题\n",
-      "031114 解答题\n",
-      "031115 解答题\n",
-      "031116 解答题\n",
-      "031117 解答题\n",
-      "031118 填空题\n",
-      "031119 填空题\n",
-      "031120 填空题\n",
-      "031121 填空题\n",
-      "031122 填空题\n",
-      "031123 填空题\n",
-      "031124 填空题\n",
-      "031125 填空题\n",
-      "031126 填空题\n",
-      "031127 填空题\n",
-      "031128 填空题\n",
-      "031129 解答题\n",
-      "031130 解答题\n",
-      "031131 解答题\n",
-      "031132 解答题\n",
-      "031133 解答题\n",
-      "031134 填空题\n",
-      "031135 填空题\n",
-      "031136 填空题\n",
-      "031137 填空题\n",
-      "031138 填空题\n",
-      "031139 选择题\n",
-      "031140 选择题\n",
-      "031141 选择题\n",
-      "031142 选择题\n",
-      "031143 选择题\n",
-      "031144 选择题\n",
-      "031145 解答题\n",
-      "031146 填空题\n",
-      "031147 填空题\n",
-      "031148 填空题\n",
-      "031149 填空题\n",
-      "031150 填空题\n",
-      "031151 填空题\n",
-      "031152 填空题\n",
-      "031153 填空题\n",
-      "031154 填空题\n",
-      "031155 选择题\n",
-      "031156 选择题\n",
-      "031157 选择题\n"
+      "012739 填空题\n",
+      "012740 填空题\n",
+      "012741 填空题\n",
+      "012742 填空题\n",
+      "012743 填空题\n",
+      "012744 填空题\n",
+      "012745 填空题\n",
+      "012746 填空题\n",
+      "012747 填空题\n",
+      "012748 填空题\n",
+      "012749 填空题\n",
+      "012750 填空题\n",
+      "012751 选择题\n",
+      "012752 选择题\n",
+      "012753 选择题\n",
+      "012754 选择题\n",
+      "012755 解答题\n",
+      "012756 解答题\n",
+      "012757 解答题\n",
+      "012758 解答题\n",
+      "012759 解答题\n"
      ]
     }
    ],
@@ -611,7 +71,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "mathdept",
+   "display_name": "Python 3.9.15 ('pythontest')",
    "language": "python",
    "name": "python3"
   },
@@ -630,7 +90,7 @@
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
+    "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
    }
   }
  },
diff --git a/文本处理工具/剪贴板文本整理_word文件.ipynb b/文本处理工具/剪贴板文本整理_word文件.ipynb
index 819743fc..2345d154 100644
--- a/文本处理工具/剪贴板文本整理_word文件.ipynb
+++ b/文本处理工具/剪贴板文本整理_word文件.ipynb
@@ -522,7 +522,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "mathdept",
+   "display_name": "Python 3.9.15 ('pythontest')",
    "language": "python",
    "name": "python3"
   },
@@ -541,7 +541,7 @@
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
+    "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
    }
   }
  },
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 649aec91..980d8874 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -313927,6 +313927,405 @@
         "remark": "",
         "space": "12ex"
     },
+    "012739": {
+        "id": "012739",
+        "content": "已知集合$A=\\{1,2\\}$, $B=\\{1, a\\}$, 且$A=B$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题1",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012740": {
+        "id": "012740",
+        "content": "已知向量$\\overrightarrow a=(3,4)$, $\\overrightarrow b=(1,2)$, 则$\\overrightarrow a-2 \\overrightarrow b=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题2",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012741": {
+        "id": "012741",
+        "content": "若不等式$|x-1|\\leq 2$, 则$x$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题3",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012742": {
+        "id": "012742",
+        "content": "已知圆$C$的一般方程为$x^2+2 x+y^2=0$, 则圆$C$的半径为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题4",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012743": {
+        "id": "012743",
+        "content": "已知事件$A$发生的概率为$P(A)=0.5$, 则它的对立事件的概率$P(\\overline A)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题5",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012744": {
+        "id": "012744",
+        "content": "已知正实数$a$、$b$满足$a+4 b=1$, 则$a b$的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题6",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012745": {
+        "id": "012745",
+        "content": "某校抽取$100$名学生测身高, 其中身高最大值为$186 \\text{cm}$, 最小值$154 \\text{cm}$, 根据身高数据绘制频率组距分布直方图, 组距为 $5$, 且第一组下限为$153.5 \\text{cm}$, 则组数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题7",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012746": {
+        "id": "012746",
+        "content": "设$(1-2 x)^4=a_0+a_1 x+a_2 x^2+a_3 x^3+a_4 x^4$, 则$a_0+a_4=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题8",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012747": {
+        "id": "012747",
+        "content": "已知函数$f(x)=2^{-x}+1$, 且$g(x)=\\begin{cases}\\log_2(x+1), & x \\geq 0, \\\\f(-x), & x<0,\\end{cases}$ 则方程$g(x)=2$的解为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题9",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012748": {
+        "id": "012748",
+        "content": "在$4$名男生, $6$名女生中任选$3$人, 则恰有$1$名男生和$2$名女生的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题10",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012749": {
+        "id": "012749",
+        "content": "设$z_1$、$z_2 \\in \\mathbf{C}$且$z_1=\\mathrm{i} \\cdot \\overline{z_2}$, 满足$|z_1-1|=1$, 则$|z_1-z_2|$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题11",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012750": {
+        "id": "012750",
+        "content": "设$\\overrightarrow{OA}$、$\\overrightarrow{OB}$、$\\overrightarrow{OC}$为空间中三个单位向量, 且$\\overrightarrow{OA} \\perp \\overrightarrow{OB}$, $\\overrightarrow{OA} \\perp \\overrightarrow{OC}$, $\\overrightarrow{OB}$与$\\overrightarrow{OC}$夹角为$60^{\\circ}$, $P$为空间任意一点, 且$|\\overrightarrow{OP}|=1$, 满足$|\\overrightarrow{OP} \\cdot \\overrightarrow{OC}|\\leq|\\overrightarrow{OP} \\cdot \\overrightarrow{OB}|\\leq|\\overrightarrow{OP} \\cdot \\overrightarrow{OA}|$, 则$|\\overrightarrow{OP} \\cdot \\overrightarrow{OC}|$的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题12",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012751": {
+        "id": "012751",
+        "content": "下列函数是偶函数的是\\bracket{20}.\n\\fourch{$y=\\sin x$}{$y=\\cos x$}{$y=x^3$}{$y=2^x$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题13",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012752": {
+        "id": "012752",
+        "content": "根据下图判断, 下列选项错误的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i in {2017,2018,...,2021} {\\draw ({(\\i-2016)*2-1},0) node [below] {$\\i$年};};\n\\foreach \\i/\\j in {1/10000,2/20000,3/30000,4/40000,5/50000} {\\draw [gray] (10,\\i) -- (0,\\i) node [black,left] {$\\j$};}; \n\\foreach \\i/\\j/\\k in {1/1.312031/1.911751,2/1.366685/2.034308,3/1.372091/2.032591,4/1.372536/2.110311,5/1.571867/2.489168}\n{\\fill [white] ({2*\\i-1.5},0) --++ (0,\\j) --++ (1,0) --++ (0,{-\\j});\n\\fill [gray!50] ({2*\\i-1.5},\\j) --++ (0,\\k) --++ (1,0) --++ (0,{-\\k});\n\\draw ({2*\\i-1.5},0) --++ (0,\\j) --++ (1,0) --++ (0,{-\\j});\n\\draw ({2*\\i-1.5},\\j) --++ (0,\\k) --++ (1,0) --++ (0,{-\\k});\n};\n\\foreach \\i/\\j/\\k in {1/1.312031/13120.31,2/1.366685/13666.85,3/1.372091/13720.91,4/1.372536/13725.36,5/1.571867/15718.67}\n{\\draw ({2*\\i-1},{\\j/2}) node {\\tiny $\\k$};};\n\\foreach \\i/\\j/\\k/\\n in {1/1.312031/1.911751/19117.51,2/1.366685/2.034308/20343.08,3/1.372091/2.032591/20325.91,4/1.372536/2.110311/21103.11,5/1.571867/2.489168/24891.68}\n{\\draw ({2*\\i-1},{\\j+\\k/2}) node {\\tiny $\\n$};};\n\\filldraw [fill = gray!50] (10.5,3) rectangle (10.7,3.2) (10.9,3.1) node [right] {货物进口额};\n\\draw (10.5,2) rectangle (10.7,2.2) (10.9,2.1) node [right] {货物出口额};\n\\draw [->] (0,0) -- (10,0) node [below] {年份};\n\\draw [->] (0,0) -- (0,5.5) node [left] {亿元};\n\\draw (5,-1) node {2017-2021年上海市货物进出口总额};\n\\end{tikzpicture}\n\\end{center}\n\\onech{从 2018 年开始, 2021 的进出口总额增长率最大}{从 2018 年开始, 进出口总额逐年增大}{从 2018 年开始, 进口总额逐年增大}{从 2018 年开始, 2020 的进出口总额增长率最小}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题14",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012753": {
+        "id": "012753",
+        "content": "如图所示, 正方体$ABCD-A_1B_1C_1D_1$中, $P$是$A_1C_1$上的动点, 则下列直线中, 始终与直线$BP$异面的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw (A1) -- (C1);\n\\filldraw ($(A1)!0.4!(C1)$) circle (0.03) node [above] {$P$} coordinate (P);\n\\draw [dashed] (B) -- (P);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$DD_1$}{$AC$}{$AD_1$}{$B_1C$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题15",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012754": {
+        "id": "012754",
+        "content": "数列$\\{a_n\\}$的各项均为实数, $S_n$为其前$n$项和, 对任意$k>2022$($k \\in \\mathbf{N}$)都有$|S_k|>|S_{k+1}|$, 则下列各数列中, 可能使条件成立的数列是\\bracket{20}.\n\\onech{$a_1$、$a_3$、$a_5$、$\\cdots$、$a_{2 n-1}$为等差数列, $a_2$、$a_4$、$a_6$、$\\cdots$、$a_{2 n}$为等比数列}{$a_1$、$a_3$、$a_5$、$\\cdots$、$a_{2 n-1}$为等比数列, $a_2$、$a_4$、$a_6$、$\\cdots$、$a_{2 n}$为等差数列}{$a_1$、$a_2$、$a_3$、$\\cdots$、$a_{2022}$为等差数列, $a_{2023}$、$a_{2024}$、$\\cdots$、$a_n$为等比数列}{$a_1$、$a_2$、$a_3$、$\\cdots$、$a_{2022}$为等比数列, $a_{2023}$、$a_{2024}$、$\\cdots$、$a_n$为等差数列}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题16",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "012755": {
+        "id": "012755",
+        "content": "已知$PA \\perp$平面$ABC$, $AB \\perp AC$, $PA=AB=3$, $AC=4$, $M$为$BC$中点, 过点$M$分别作平行于平面$PAB$的直线交$AC$、$PC$于点$E$、$F$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (4,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,3,0) node [above] {$P$} coordinate (P);\n\\draw (0,0,3) node [left] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [below] {$M$} coordinate (M);\n\\draw ($(C)!0.5!(P)$) node [above] {$E$} coordinate (E);\n\\draw ($(A)!0.5!(C)$) node [above right] {$F$} coordinate (F);\n\\draw (P)--(B)--(C)--cycle (E)--(M);\n\\draw [dashed] (P)--(A)--(B) (E)--(F)--(M) (A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$PM$与平面$ABC$所成的角;\\\\\n(2) 证明: 平面$MEF\\parallel$平面$PAB$, 并求直线$ME$到平面$PAB$的距离.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题17",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "012756": {
+        "id": "012756",
+        "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$对应边为$a$、$b$、$c$, 其中$b=2$.\\\\\n(1) 若$A+C=\\dfrac{2 \\pi}3$, 且$a=2 c$, 求边长$c$的值;\\\\\n(2) 若$A-C=\\dfrac{\\pi}{12}$, $a=\\sqrt 2 c \\sin A$, 求$\\triangle ABC$的面积.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题18",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "012757": {
+        "id": "012757",
+        "content": "为了节能环保, 节约材料、定义建筑物的 ``体形系数'' 为$S=\\dfrac{F_0}{V_0}$, 其中$F_0$为建筑物暴露在空气中的面积 (单位: 平方米), $V_0$为建筑物的体积 (单位: 立方米).\\\\\n(1) 若有一圆柱形建筑物的底面半径为$R$, 高度为$H$, 求该建筑物的 ``体形系数'';(结果用含$R$、$H$的代数式表示)\\\\\n(2) 定义建筑物的 ``形状因子'' 为$f=\\dfrac{L^2}A$, 其中$A$为底面面积, $L$为建筑底面周长, 又定义$T$为总建筑面积, 即为每层建筑面积总和 (每层建筑面积为每一层的底面面积). 现有一垂直于底面的宿舍, 已知该宿舍的层高为$3$米, 有$n$层, 其 ``形状因子''$f=18$, 总建筑面积为$T=10000$平方米, 试求当该宿舍的层数$n$为多少时, ``体形系数''$S$最小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题19",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "012758": {
+        "id": "012758",
+        "content": "椭圆$\\Gamma: \\dfrac{x^2}{m^2}+\\dfrac{y^2}3=1$($m>0$, $m \\neq \\sqrt 3$).\\\\\n(1) 若$m=2$, 求椭圆$\\Gamma$的离心率;\\\\\n(2) 设$A_1$、$A_2$为椭圆$\\Gamma$的左右顶点, 椭圆$\\Gamma$上一点$E$的纵坐标为$1$, 且$\\overrightarrow{EA_1} \\cdot \\overrightarrow{EA_2}=-2$, 求$m$的值;\\\\\n(3) 过椭圆$\\Gamma$上一点$P$作斜率为$\\sqrt 3$的直线, 与双曲线$\\dfrac{y^2}{5 m^2}-\\dfrac{x^2}5=1$有一个公共点, 求$m$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题20",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "012759": {
+        "id": "012759",
+        "content": "设函数$f(x)=a x^3-(a+1) x^2+x$, $g(x)=k x+m$, 其中$a \\geq 0$, $k$、$m \\in \\mathbf{R}$, 若对任意$x \\in[0,1]$均有$f(x) \\leq g(x)$, 则称函数$y=g(x)$是函数$y=f(x)$的 ``控制函数''. 对于$x_0\\in [0,1]$以及定义域包含$[0,1]$上的函数$y=f(x)$, 若对所有$y=f(x)$的控制函数$y=g(x)$, $g(x_0)$有最小值, 就将该最小值定义为$\\overline f(x_0)$.\\\\\n(1) 若$a=2$, $g(x)=x$, 试问$y=g(x)$是否为函数$y=f(x)$的 ``控制函数'';\\\\\n(2) 若$a=0$, 使得直线$y=h(x)$是曲线$y=f(x)$在$x=\\dfrac 14$处的切线. 证明: 函数$y=h(x)$为函数$y=f(x)$的 ``控制函数'', 并求$\\overline f(\\dfrac 14)$的值;\\\\\n(3) 若曲线$y=f(x)$在$x=x_0$, $x_0 \\in(0,1)$处的切线过点$(1,0)$, 且$c \\in[x_0,1]$. 证明: 当且仅当$c=x_0$或$c=1$时, $\\overline f(c)=f(c)$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2023届春季高考试题21",
+        "edit": [
+            "20230109\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
     "020001": {
         "id": "020001",
         "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
@@ -360505,7 +360904,7 @@
     },
     "030552": {
         "id": "030552",
-        "content": "某城市高中数学统考, 假设考试成缋服从正态分布$N(75,8^2)$. 如果按照$16 \\%, 34 \\%, 34 \\%, 16 \\%$的比例将考试成绩分为A, B, C, D四个等级, 试确定各等级的分数线(精确到$1$分).",
+        "content": "某城市高中数学统考, 假设考试成绩服从正态分布$N(75,8^2)$. 如果按照$16 \\%, 34 \\%, 34 \\%, 16 \\%$的比例将考试成绩分为A, B, C, D四个等级, 试确定各等级的分数线(精确到$1$分).",
         "objs": [],
         "tags": [
             "第八单元"