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 192bfb2e..2cfafb51 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": 52,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
@@ -11,7 +11,7 @@
        "0"
       ]
      },
-     "execution_count": 52,
+     "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 = \"3637,11610,12444\"\n",
+    "problems = \"31267\"\n",
     "\n",
     "def generate_number_set(string,dict):\n",
     "    string = re.sub(r\"[\\n\\s]\",\"\",string)\n",
diff --git a/工具/分年级专用工具/小闲平台数据导入_2024届.ipynb b/工具/分年级专用工具/小闲平台数据导入_2024届.ipynb
index 57e93fd3..5aef980a 100644
--- a/工具/分年级专用工具/小闲平台数据导入_2024届.ipynb
+++ b/工具/分年级专用工具/小闲平台数据导入_2024届.ipynb
@@ -2,9 +2,40 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2024届高二10班\n",
+      "2024届高二10班 有效\n",
+      "2024届高二11班\n",
+      "2024届高二11班 有效\n",
+      "2024届高二12班\n",
+      "2024届高二12班 有效\n",
+      "2024届高二01班\n",
+      "2024届高二01班 有效\n",
+      "2024届高二02班\n",
+      "2024届高二02班 有效\n",
+      "2024届高二03班\n",
+      "2024届高二03班 有效\n",
+      "2024届高二04班\n",
+      "2024届高二04班 有效\n",
+      "2024届高二05班\n",
+      "2024届高二05班 有效\n",
+      "2024届高二06班\n",
+      "2024届高二06班 有效\n",
+      "2024届高二07班\n",
+      "2024届高二07班 有效\n",
+      "2024届高二08班\n",
+      "2024届高二08班 有效\n",
+      "2024届高二09班\n",
+      "2024届高二09班 有效\n"
+     ]
+    }
+   ],
    "source": [
     "import zipfile,os,re,time\n",
     "import pandas as pd\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 267b9379..337f6cdf 100644
--- a/工具/寻找阶段末尾空闲题号.ipynb
+++ b/工具/寻找阶段末尾空闲题号.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -11,8 +11,8 @@
      "text": [
       "首个空闲id: 14628 , 直至 020000\n",
       "首个空闲id: 22048 , 直至 030000\n",
-      "首个空闲id: 31267 , 直至 040000\n",
-      "首个空闲id: 40083 , 直至 999999\n"
+      "首个空闲id: 31309 , 直至 040000\n",
+      "首个空闲id: 40161 , 直至 999999\n"
      ]
     }
    ],
diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb
index d723eb0e..350d9ce5 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
@@ -2,93 +2,241 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t1.000\t0.975\t0.700\t0.750\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.875\t0.925\t0.925\t0.950\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.650\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.775\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t1.000\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.887\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.838\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.900\t0.750\t0.925\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.925\t0.775\t0.825\t0.650\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.975\t0.975\n",
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t1.000\t0.947\t0.711\t0.789\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.868\t0.974\t0.974\t0.895\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.474\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.789\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.895\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.921\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.882\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.895\t0.842\t0.947\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.921\t0.605\t0.789\t0.605\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.895\t0.829\n",
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.917\t0.861\t0.500\t0.472\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.833\t0.917\t0.889\t0.833\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.417\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.750\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.986\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.708\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.792\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.722\t0.444\t0.639\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.750\t0.583\t0.528\t0.444\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.639\t0.625\n",
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.914\t0.857\t0.571\t0.429\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.857\t0.800\t0.914\t0.743\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.629\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.743\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.829\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.700\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.514\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.686\t0.343\t0.943\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.714\t0.657\t0.514\t0.400\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.543\t0.429\n",
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.974\t0.923\t0.769\t0.718\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.949\t0.872\t0.872\t0.923\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.667\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.846\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.795\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.744\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.692\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.744\t0.615\t0.923\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.692\t0.718\t0.590\t0.410\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.577\t0.423\n",
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.879\t0.788\t0.394\t0.485\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.849\t0.879\t0.879\t0.727\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.697\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.606\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.864\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.803\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.742\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.667\t0.455\t0.879\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.727\t0.576\t0.424\t0.273\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.667\t0.515\n",
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t1.000\t0.939\t0.576\t0.424\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.697\t0.849\t0.849\t0.788\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.515\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.758\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.849\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.727\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.515\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.818\t0.576\t0.939\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.939\t0.636\t0.485\t0.515\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.773\t0.530\n",
-      "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t1.000\t0.892\t0.676\t0.595\n",
-      "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.919\t0.811\t0.973\t0.784\n",
-      "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.622\n",
-      "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.649\n",
-      "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.811\n",
-      "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.676\n",
-      "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.703\n",
-      "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.892\t0.622\t0.919\n",
-      "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.973\t0.703\t0.540\t0.568\n",
-      "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.878\t0.716\n"
+      "题号: 031276 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.857\n",
+      "题号: 031268 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.929\n",
+      "题号: 031269 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.821\n",
+      "题号: 031270 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.714\n",
+      "题号: 031271 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.750\n",
+      "题号: 031272 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.714\n",
+      "题号: 031273 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.607\n",
+      "题号: 031274 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.500\n",
+      "题号: 031275 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.464\n",
+      "题号: 031277 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.179\n",
+      "题号: 031278 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.000\n",
+      "题号: 031279 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.500\n",
+      "题号: 031280 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.786\n",
+      "题号: 031281 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.786\n",
+      "题号: 031282 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.786\n",
+      "题号: 031283 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.964\n",
+      "题号: 031284 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.686\n",
+      "题号: 031285 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.699\n",
+      "题号: 031287 , 字段: usages 中已添加数据: 20230302\t2024届高二10班\t0.155\n",
+      "题号: 031276 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.844\n",
+      "题号: 031268 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.969\n",
+      "题号: 031269 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.812\n",
+      "题号: 031270 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.906\n",
+      "题号: 031271 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.594\n",
+      "题号: 031272 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.875\n",
+      "题号: 031273 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.688\n",
+      "题号: 031274 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.625\n",
+      "题号: 031275 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.688\n",
+      "题号: 031277 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.281\n",
+      "题号: 031278 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.000\n",
+      "题号: 031279 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.781\n",
+      "题号: 031280 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.969\n",
+      "题号: 031281 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.719\n",
+      "题号: 031282 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.812\n",
+      "题号: 031283 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.893\n",
+      "题号: 031284 , 字段: usages 中已添加数据: 20230302\t2024届高二11班\t0.799\n",
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+      "题号: 031273 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.583\n",
+      "题号: 031274 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.750\n",
+      "题号: 031275 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.458\n",
+      "题号: 031277 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.375\n",
+      "题号: 031278 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.000\n",
+      "题号: 031279 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.708\n",
+      "题号: 031280 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t1.000\n",
+      "题号: 031281 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.917\n",
+      "题号: 031282 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.667\n",
+      "题号: 031283 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.917\n",
+      "题号: 031284 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.655\n",
+      "题号: 031285 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.688\n",
+      "题号: 031287 , 字段: usages 中已添加数据: 20230302\t2024届高二08班\t0.208\n",
+      "题号: 031276 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.864\n",
+      "题号: 031268 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.955\n",
+      "题号: 031269 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.864\n",
+      "题号: 031270 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.864\n",
+      "题号: 031271 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.773\n",
+      "题号: 031272 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.909\n",
+      "题号: 031273 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.545\n",
+      "题号: 031274 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.818\n",
+      "题号: 031275 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.455\n",
+      "题号: 031277 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.091\n",
+      "题号: 031278 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.000\n",
+      "题号: 031279 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.955\n",
+      "题号: 031280 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.909\n",
+      "题号: 031281 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.818\n",
+      "题号: 031282 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.955\n",
+      "题号: 031283 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.942\n",
+      "题号: 031284 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.828\n",
+      "题号: 031285 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.867\n",
+      "题号: 031287 , 字段: usages 中已添加数据: 20230302\t2024届高二09班\t0.197\n"
      ]
     }
    ],
diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt
index 61f80b63..98be3bee 100644
--- a/工具/文本文件/metadata.txt
+++ b/工具/文本文件/metadata.txt
@@ -1,74 +1,686 @@
 usages
 
-021529
-20230227	2025届高一11班	0.988	0.951	0.890	0.927	0.793	0.817	0.902
+31276
+20230302	2024届高二10班	0.857
 
-021530
-20230227	2025届高一11班	0.915	0.927	0.915	0.963
+31268
+20230302	2024届高二10班	0.929
 
-021531
-20230227	2025届高一11班	0.854	0.829	0.854	0.768
+31269
+20230302	2024届高二10班	0.821
 
-021529
-20230227	2025届高一12班	0.975	0.938	0.825	0.925	0.875	0.775	0.825
+31270
+20230302	2024届高二10班	0.714
 
-021530
-20230227	2025届高一12班	0.875	0.912	0.925	0.875
+31271
+20230302	2024届高二10班	0.750
 
-021531
-20230227	2025届高一12班	0.875	0.838	0.887	0.713
+31272
+20230302	2024届高二10班	0.714
 
-021529
-20230227	2025届高一01班	0.915	0.854	0.793	0.890	0.768	0.756	0.780
+31273
+20230302	2024届高二10班	0.607
 
-021530
-20230227	2025届高一01班	0.854	0.768	0.732	0.805
+31274
+20230302	2024届高二10班	0.500
 
-021531
-20230227	2025届高一01班	0.549	0.634	0.732	0.476
+31275
+20230302	2024届高二10班	0.464
 
-021529
-20230227	2025届高一04班	0.987	0.974	0.833	0.910	0.936	0.590	0.590
+31277
+20230302	2024届高二10班	0.179
 
-021530
-20230227	2025届高一04班	0.705	0.782	0.936	0.679
+31278
+20230302	2024届高二10班	0.000
 
-021531
-20230227	2025届高一04班	0.641	0.577	0.821	0.628
+31279
+20230302	2024届高二10班	0.500
 
-021529
-20230227	2025届高一05班	0.964	1.000	0.857	0.952	0.905	0.631	0.738
+31280
+20230302	2024届高二10班	0.786
 
-021530
-20230227	2025届高一05班	0.786	0.798	0.833	0.798
+31281
+20230302	2024届高二10班	0.786
 
-021531
-20230227	2025届高一05班	0.619	0.619	0.726	0.667
+31282
+20230302	2024届高二10班	0.786
 
-021529
-20230227	2025届高一06班	0.988	0.738	0.863	0.900	0.762	0.750	0.850
+31283
+20230302	2024届高二10班	0.964
 
-021530
-20230227	2025届高一06班	0.812	0.838	0.787	0.738
+31284
+20230302	2024届高二10班	0.686
 
-021531
-20230227	2025届高一06班	0.562	0.637	0.700	0.613
+31285
+20230302	2024届高二10班	0.699
 
-021529
-20230227	2025届高一08班	0.970	0.894	0.803	0.939	0.970	0.697	0.879
+31287
+20230302	2024届高二10班	0.155
 
-021530
-20230227	2025届高一08班	0.682	0.894	0.833	0.864
+31276
+20230302	2024届高二11班	0.844
 
-021531
-20230227	2025届高一08班	0.879	0.773	0.833	0.924
+31268
+20230302	2024届高二11班	0.969
 
-021529
-20230227	2025届高一09班	0.946	0.946	0.892	0.892	0.946	0.757	0.865
+31269
+20230302	2024届高二11班	0.812
 
-021530
-20230227	2025届高一09班	0.919	0.865	0.865	0.689
+31270
+20230302	2024届高二11班	0.906
 
-021531
-20230227	2025届高一09班	0.878	0.635	0.784	0.824
+31271
+20230302	2024届高二11班	0.594
+
+31272
+20230302	2024届高二11班	0.875
+
+31273
+20230302	2024届高二11班	0.688
+
+31274
+20230302	2024届高二11班	0.625
+
+31275
+20230302	2024届高二11班	0.688
+
+31277
+20230302	2024届高二11班	0.281
+
+31278
+20230302	2024届高二11班	0.000
+
+31279
+20230302	2024届高二11班	0.781
+
+31280
+20230302	2024届高二11班	0.969
+
+31281
+20230302	2024届高二11班	0.719
+
+31282
+20230302	2024届高二11班	0.812
+
+31283
+20230302	2024届高二11班	0.893
+
+31284
+20230302	2024届高二11班	0.799
+
+31285
+20230302	2024届高二11班	0.790
+
+31287
+20230302	2024届高二11班	0.309
+
+31276
+20230302	2024届高二12班	0.931
+
+31268
+20230302	2024届高二12班	0.966
+
+31269
+20230302	2024届高二12班	0.897
+
+31270
+20230302	2024届高二12班	0.724
+
+31271
+20230302	2024届高二12班	0.793
+
+31272
+20230302	2024届高二12班	0.966
+
+31273
+20230302	2024届高二12班	0.586
+
+31274
+20230302	2024届高二12班	0.724
+
+31275
+20230302	2024届高二12班	0.552
+
+31277
+20230302	2024届高二12班	0.621
+
+31278
+20230302	2024届高二12班	0.035
+
+31279
+20230302	2024届高二12班	0.690
+
+31280
+20230302	2024届高二12班	0.931
+
+31281
+20230302	2024届高二12班	0.862
+
+31282
+20230302	2024届高二12班	0.897
+
+31283
+20230302	2024届高二12班	0.929
+
+31284
+20230302	2024届高二12班	0.820
+
+31285
+20230302	2024届高二12班	0.690
+
+31287
+20230302	2024届高二12班	0.330
+
+31276
+20230302	2024届高二01班	0.921
+
+31268
+20230302	2024届高二01班	0.974
+
+31269
+20230302	2024届高二01班	0.974
+
+31270
+20230302	2024届高二01班	0.921
+
+31271
+20230302	2024届高二01班	0.895
+
+31272
+20230302	2024届高二01班	0.974
+
+31273
+20230302	2024届高二01班	0.947
+
+31274
+20230302	2024届高二01班	0.921
+
+31275
+20230302	2024届高二01班	0.789
+
+31277
+20230302	2024届高二01班	0.737
+
+31278
+20230302	2024届高二01班	0.105
+
+31279
+20230302	2024届高二01班	0.816
+
+31280
+20230302	2024届高二01班	1.000
+
+31281
+20230302	2024届高二01班	0.974
+
+31282
+20230302	2024届高二01班	0.974
+
+31283
+20230302	2024届高二01班	0.993
+
+31284
+20230302	2024届高二01班	0.917
+
+31285
+20230302	2024届高二01班	0.885
+
+31287
+20230302	2024届高二01班	0.547
+
+31276
+20230302	2024届高二02班	0.975
+
+31268
+20230302	2024届高二02班	1.000
+
+31269
+20230302	2024届高二02班	0.925
+
+31270
+20230302	2024届高二02班	0.875
+
+31271
+20230302	2024届高二02班	0.950
+
+31272
+20230302	2024届高二02班	0.900
+
+31273
+20230302	2024届高二02班	0.875
+
+31274
+20230302	2024届高二02班	0.925
+
+31275
+20230302	2024届高二02班	0.800
+
+31277
+20230302	2024届高二02班	0.575
+
+31278
+20230302	2024届高二02班	0.175
+
+31279
+20230302	2024届高二02班	0.825
+
+31280
+20230302	2024届高二02班	0.925
+
+31281
+20230302	2024届高二02班	0.900
+
+31282
+20230302	2024届高二02班	0.950
+
+31283
+20230302	2024届高二02班	0.968
+
+31284
+20230302	2024届高二02班	0.863
+
+31285
+20230302	2024届高二02班	0.905
+
+31287
+20230302	2024届高二02班	0.597
+
+31276
+20230302	2024届高二03班	0.971
+
+31268
+20230302	2024届高二03班	1.000
+
+31269
+20230302	2024届高二03班	0.853
+
+31270
+20230302	2024届高二03班	0.735
+
+31271
+20230302	2024届高二03班	0.676
+
+31272
+20230302	2024届高二03班	0.971
+
+31273
+20230302	2024届高二03班	0.765
+
+31274
+20230302	2024届高二03班	0.765
+
+31275
+20230302	2024届高二03班	0.676
+
+31277
+20230302	2024届高二03班	0.471
+
+31278
+20230302	2024届高二03班	0.059
+
+31279
+20230302	2024届高二03班	0.559
+
+31280
+20230302	2024届高二03班	0.971
+
+31281
+20230302	2024届高二03班	0.853
+
+31282
+20230302	2024届高二03班	0.971
+
+31283
+20230302	2024届高二03班	0.937
+
+31284
+20230302	2024届高二03班	0.813
+
+31285
+20230302	2024届高二03班	0.805
+
+31287
+20230302	2024届高二03班	0.328
+
+31276
+20230302	2024届高二04班	0.794
+
+31268
+20230302	2024届高二04班	0.971
+
+31269
+20230302	2024届高二04班	0.765
+
+31270
+20230302	2024届高二04班	0.824
+
+31271
+20230302	2024届高二04班	0.706
+
+31272
+20230302	2024届高二04班	0.941
+
+31273
+20230302	2024届高二04班	0.706
+
+31274
+20230302	2024届高二04班	0.735
+
+31275
+20230302	2024届高二04班	0.559
+
+31277
+20230302	2024届高二04班	0.412
+
+31278
+20230302	2024届高二04班	0.059
+
+31279
+20230302	2024届高二04班	0.794
+
+31280
+20230302	2024届高二04班	0.912
+
+31281
+20230302	2024届高二04班	0.853
+
+31282
+20230302	2024届高二04班	0.912
+
+31283
+20230302	2024届高二04班	0.933
+
+31284
+20230302	2024届高二04班	0.847
+
+31285
+20230302	2024届高二04班	0.681
+
+31287
+20230302	2024届高二04班	0.284
+
+31276
+20230302	2024届高二05班	0.935
+
+31268
+20230302	2024届高二05班	0.968
+
+31269
+20230302	2024届高二05班	0.968
+
+31270
+20230302	2024届高二05班	0.839
+
+31271
+20230302	2024届高二05班	0.774
+
+31272
+20230302	2024届高二05班	1.000
+
+31273
+20230302	2024届高二05班	0.677
+
+31274
+20230302	2024届高二05班	0.839
+
+31275
+20230302	2024届高二05班	0.806
+
+31277
+20230302	2024届高二05班	0.387
+
+31278
+20230302	2024届高二05班	0.000
+
+31279
+20230302	2024届高二05班	0.742
+
+31280
+20230302	2024届高二05班	0.935
+
+31281
+20230302	2024届高二05班	0.968
+
+31282
+20230302	2024届高二05班	0.903
+
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+20230302	2024届高二05班	0.963
+
+31284
+20230302	2024届高二05班	0.862
+
+31285
+20230302	2024届高二05班	0.827
+
+31287
+20230302	2024届高二05班	0.272
+
+31276
+20230302	2024届高二06班	0.881
+
+31268
+20230302	2024届高二06班	0.952
+
+31269
+20230302	2024届高二06班	0.881
+
+31270
+20230302	2024届高二06班	0.809
+
+31271
+20230302	2024届高二06班	0.691
+
+31272
+20230302	2024届高二06班	0.857
+
+31273
+20230302	2024届高二06班	0.738
+
+31274
+20230302	2024届高二06班	0.714
+
+31275
+20230302	2024届高二06班	0.524
+
+31277
+20230302	2024届高二06班	0.381
+
+31278
+20230302	2024届高二06班	0.048
+
+31279
+20230302	2024届高二06班	0.809
+
+31280
+20230302	2024届高二06班	0.976
+
+31281
+20230302	2024届高二06班	0.929
+
+31282
+20230302	2024届高二06班	0.905
+
+31283
+20230302	2024届高二06班	0.959
+
+31284
+20230302	2024届高二06班	0.804
+
+31285
+20230302	2024届高二06班	0.835
+
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+20230302	2024届高二06班	0.352
+
+31276
+20230302	2024届高二07班	0.907
+
+31268
+20230302	2024届高二07班	0.954
+
+31269
+20230302	2024届高二07班	0.930
+
+31270
+20230302	2024届高二07班	0.791
+
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+20230302	2024届高二07班	0.721
+
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+20230302	2024届高二07班	0.977
+
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+20230302	2024届高二07班	0.698
+
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+20230302	2024届高二07班	0.791
+
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+20230302	2024届高二07班	0.605
+
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+20230302	2024届高二07班	0.372
+
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+20230302	2024届高二07班	0.116
+
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+20230302	2024届高二07班	0.721
+
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+20230302	2024届高二07班	0.977
+
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+20230302	2024届高二07班	0.930
+
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+20230302	2024届高二07班	0.930
+
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+20230302	2024届高二07班	0.930
+
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+20230302	2024届高二07班	0.865
+
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+20230302	2024届高二07班	0.829
+
+31287
+20230302	2024届高二07班	0.397
+
+31276
+20230302	2024届高二08班	0.927
+
+31268
+20230302	2024届高二08班	0.917
+
+31269
+20230302	2024届高二08班	0.833
+
+31270
+20230302	2024届高二08班	0.583
+
+31271
+20230302	2024届高二08班	0.625
+
+31272
+20230302	2024届高二08班	0.917
+
+31273
+20230302	2024届高二08班	0.583
+
+31274
+20230302	2024届高二08班	0.750
+
+31275
+20230302	2024届高二08班	0.458
+
+31277
+20230302	2024届高二08班	0.375
+
+31278
+20230302	2024届高二08班	0.000
+
+31279
+20230302	2024届高二08班	0.708
+
+31280
+20230302	2024届高二08班	1.000
+
+31281
+20230302	2024届高二08班	0.917
+
+31282
+20230302	2024届高二08班	0.667
+
+31283
+20230302	2024届高二08班	0.917
+
+31284
+20230302	2024届高二08班	0.655
+
+31285
+20230302	2024届高二08班	0.688
+
+31287
+20230302	2024届高二08班	0.208
+
+31276
+20230302	2024届高二09班	0.864
+
+31268
+20230302	2024届高二09班	0.955
+
+31269
+20230302	2024届高二09班	0.864
+
+31270
+20230302	2024届高二09班	0.864
+
+31271
+20230302	2024届高二09班	0.773
+
+31272
+20230302	2024届高二09班	0.909
+
+31273
+20230302	2024届高二09班	0.545
+
+31274
+20230302	2024届高二09班	0.818
+
+31275
+20230302	2024届高二09班	0.455
+
+31277
+20230302	2024届高二09班	0.091
+
+31278
+20230302	2024届高二09班	0.000
+
+31279
+20230302	2024届高二09班	0.955
+
+31280
+20230302	2024届高二09班	0.909
+
+31281
+20230302	2024届高二09班	0.818
+
+31282
+20230302	2024届高二09班	0.955
+
+31283
+20230302	2024届高二09班	0.942
+
+31284
+20230302	2024届高二09班	0.828
+
+31285
+20230302	2024届高二09班	0.867
+
+31287
+20230302	2024届高二09班	0.197
 
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 00a38ab6..8fb73877 100644
--- a/工具/添加题目到数据库.ipynb
+++ b/工具/添加题目到数据库.ipynb
@@ -2,105 +2,48 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
     "#修改起始id,出处,文件名\n",
-    "starting_id = 40083\n",
+    "starting_id = 31288\n",
     "raworigin = \"\"\n",
     "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n",
-    "editor = \"20230302\\t王伟叶\"\n",
-    "indexed = False\n"
+    "editor = \"20230303\\t王伟叶\"\n",
+    "indexed = True\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "添加题号040083, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040084, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040085, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040086, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040087, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040088, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040089, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040090, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040091, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040092, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040093, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040094, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040095, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040096, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040097, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040098, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040099, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040100, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040101, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040102, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040103, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040104, 来源: 2025届高一下学期周末卷03\n",
-      "添加题号040105, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040106, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040107, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040108, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040109, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040110, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040111, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040112, 来源: 2025届高一下学期周末卷03小测\n",
-      "添加题号040113, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040114, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040115, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040116, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040117, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040118, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040119, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040120, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040121, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040122, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040123, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040124, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040125, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040126, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040127, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040128, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040129, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040130, 来源: 2025届高一下学期周末卷04\n",
-      "添加题号040131, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040132, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040133, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040134, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040135, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040136, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040137, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040138, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040139, 来源: 2025届高一下学期周末卷04小测\n",
-      "添加题号040140, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040141, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040142, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040143, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040144, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040145, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040146, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040147, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040148, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040149, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040150, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040151, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040152, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040153, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040154, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040155, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040156, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040157, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040158, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040159, 来源: 2024届高二下学期周末卷03\n",
-      "添加题号040160, 来源: 2024届高二下学期周末卷03\n"
+      "添加题号031288, 来源: 2025届高一上学期期末考试试题1\n",
+      "添加题号031289, 来源: 2025届高一上学期期末考试试题2\n",
+      "添加题号031290, 来源: 2025届高一上学期期末考试试题3\n",
+      "添加题号031291, 来源: 2025届高一上学期期末考试试题4\n",
+      "添加题号031292, 来源: 2025届高一上学期期末考试试题5\n",
+      "添加题号031293, 来源: 2025届高一上学期期末考试试题6\n",
+      "添加题号031294, 来源: 2025届高一上学期期末考试试题7\n",
+      "添加题号031295, 来源: 2025届高一上学期期末考试试题8\n",
+      "添加题号031296, 来源: 2025届高一上学期期末考试试题9\n",
+      "添加题号031297, 来源: 2025届高一上学期期末考试试题10\n",
+      "添加题号031298, 来源: 2025届高一上学期期末考试试题11\n",
+      "添加题号031299, 来源: 2025届高一上学期期末考试试题12\n",
+      "添加题号031300, 来源: 2025届高一上学期期末考试试题13\n",
+      "添加题号031301, 来源: 2025届高一上学期期末考试试题14\n",
+      "添加题号031302, 来源: 2025届高一上学期期末考试试题15\n",
+      "添加题号031303, 来源: 2025届高一上学期期末考试试题16\n",
+      "添加题号031304, 来源: 2025届高一上学期期末考试试题17\n",
+      "添加题号031305, 来源: 2025届高一上学期期末考试试题18\n",
+      "添加题号031306, 来源: 2025届高一上学期期末考试试题19\n",
+      "添加题号031307, 来源: 2025届高一上学期期末考试试题20\n",
+      "添加题号031308, 来源: 2025届高一上学期期末考试试题21\n"
      ]
     }
    ],
@@ -205,7 +148,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "pythontest",
+   "display_name": "mathdept",
    "language": "python",
    "name": "python3"
   },
@@ -224,7 +167,7 @@
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
+    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
    }
   }
  },
diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb
index b4c81cb1..f01c5e20 100644
--- a/工具/识别题库中尚未标注的题目类型.ipynb
+++ b/工具/识别题库中尚未标注的题目类型.ipynb
@@ -2,9 +2,136 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "031267 填空题\n",
+      "031268 填空题\n",
+      "031269 填空题\n",
+      "031270 填空题\n",
+      "031271 填空题\n",
+      "031272 填空题\n",
+      "031273 填空题\n",
+      "031274 填空题\n",
+      "031275 填空题\n",
+      "031276 填空题\n",
+      "031277 填空题\n",
+      "031278 填空题\n",
+      "031279 选择题\n",
+      "031280 选择题\n",
+      "031281 选择题\n",
+      "031282 选择题\n",
+      "031283 解答题\n",
+      "031284 解答题\n",
+      "031285 解答题\n",
+      "031286 解答题\n",
+      "031287 解答题\n",
+      "031288 填空题\n",
+      "031289 填空题\n",
+      "031290 填空题\n",
+      "031291 填空题\n",
+      "031292 填空题\n",
+      "031293 填空题\n",
+      "031294 填空题\n",
+      "031295 填空题\n",
+      "031296 填空题\n",
+      "031297 填空题\n",
+      "031298 填空题\n",
+      "031299 填空题\n",
+      "031300 选择题\n",
+      "031301 选择题\n",
+      "031302 选择题\n",
+      "031303 选择题\n",
+      "031304 解答题\n",
+      "031305 解答题\n",
+      "031306 解答题\n",
+      "031307 解答题\n",
+      "031308 解答题\n",
+      "040083 填空题\n",
+      "040084 填空题\n",
+      "040085 填空题\n",
+      "040086 填空题\n",
+      "040087 填空题\n",
+      "040088 填空题\n",
+      "040089 填空题\n",
+      "040090 填空题\n",
+      "040091 填空题\n",
+      "040092 填空题\n",
+      "040093 填空题\n",
+      "040094 填空题\n",
+      "040095 填空题\n",
+      "040096 填空题\n",
+      "040097 填空题\n",
+      "040098 选择题\n",
+      "040099 解答题\n",
+      "040100 解答题\n",
+      "040101 解答题\n",
+      "040102 解答题\n",
+      "040103 解答题\n",
+      "040104 解答题\n",
+      "040105 填空题\n",
+      "040106 填空题\n",
+      "040107 填空题\n",
+      "040108 填空题\n",
+      "040109 填空题\n",
+      "040110 解答题\n",
+      "040111 解答题\n",
+      "040112 解答题\n",
+      "040113 填空题\n",
+      "040114 填空题\n",
+      "040115 填空题\n",
+      "040116 填空题\n",
+      "040117 填空题\n",
+      "040118 填空题\n",
+      "040119 填空题\n",
+      "040120 填空题\n",
+      "040121 填空题\n",
+      "040122 填空题\n",
+      "040123 填空题\n",
+      "040124 填空题\n",
+      "040125 填空题\n",
+      "040126 填空题\n",
+      "040127 解答题\n",
+      "040128 解答题\n",
+      "040129 解答题\n",
+      "040130 解答题\n",
+      "040131 填空题\n",
+      "040132 填空题\n",
+      "040133 填空题\n",
+      "040134 填空题\n",
+      "040135 填空题\n",
+      "040136 填空题\n",
+      "040137 填空题\n",
+      "040138 解答题\n",
+      "040139 解答题\n",
+      "040140 填空题\n",
+      "040141 填空题\n",
+      "040142 填空题\n",
+      "040143 填空题\n",
+      "040144 填空题\n",
+      "040145 填空题\n",
+      "040146 填空题\n",
+      "040147 填空题\n",
+      "040148 填空题\n",
+      "040149 填空题\n",
+      "040150 填空题\n",
+      "040151 填空题\n",
+      "040152 填空题\n",
+      "040153 填空题\n",
+      "040154 填空题\n",
+      "040155 选择题\n",
+      "040156 选择题\n",
+      "040157 解答题\n",
+      "040158 解答题\n",
+      "040159 解答题\n",
+      "040160 解答题\n"
+     ]
+    }
+   ],
    "source": [
     "import os,re,json\n",
     "\n",
@@ -33,6 +160,26 @@
     "    f.write(database)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "''"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "\"aaa\"*0"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
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 a4f3f8d0..eeed1818 100644
--- a/工具/题号选题pdf生成.ipynb
+++ b/工具/题号选题pdf生成.ipynb
@@ -36,7 +36,9 @@
     "filename = \"临时文件/2023届劳模子女数学讲座_01_预备知识\"\n",
     "\"\"\"---设置文件名结束---\"\"\"\n",
     "\n",
-    "\n",
+    "\"\"\"---设置是否需要解答题的空格---\"\"\"\n",
+    "spaceflag = False\n",
+    "\"\"\"---设置空格结束---\"\"\"\n",
     "\n",
     "#读取系统日期\n",
     "current_time = time.localtime()\n",
@@ -126,7 +128,7 @@
     "            else:\n",
     "                objects_string += \"\\\\textcolor{blue}{\" + obj + \"|\" + obj_dict[obj][\"content\"] + \"}\\n\\n\"\n",
     "        objects = objects_string\n",
-    "    space = (\"\" if problemset[\"space\"] == \"\" else \"\\n\"+r\"\\vspace*{\"+problemset[\"space\"]+\"}\\n\")\n",
+    "    space = (\"\" if problemset[\"space\"] == \"\" or spaceflag == False else \"\\n\"+r\"\\vspace*{\"+problemset[\"space\"]+\"}\\n\")\n",
     "    tags = (\"|\".join(problemset[\"tags\"]) if len(problemset[\"origin\"])>0 else \"暂无标签\")\n",
     "    raw_string = \"\\\\item \" + \"{\\\\tiny (\"+id+\")} \"+problem\n",
     "    teachers_string = raw_string.replace(\"\\\\tiny \",\"\")+\"\\n\\n关联目标:\\n\\n\"+ objects + \"\\n\\n标签: \" + tags + \"\\n\\n答案: \"+answer + \"\\n\\n\" + \"解答或提示: \" + solution + \"\\n\\n使用记录:\\n\\n\"+ usage + \"\\n\" + \"\\n\\n备注: \" + remarks + \"\\n\\n出处: \"+origin + \"\\n\"\n",
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 082ba988..ba9995e0 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -110575,7 +110575,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220331\t2022届高三01班\t1.000"
+            "20220331\t2022届高三01班\t1.000",
+            "20230304\t2023届高三11班\t0.789",
+            "20230304\t2023届高三12班\t0.875",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.781",
+            "20230304\t2023届高三03班\t0.839",
+            "20230304\t2023届高三04班\t1.000",
+            "20230304\t2023届高三05班\t0.950",
+            "20230304\t2023届高三06班\t0.974",
+            "20230304\t2023届高三07班\t0.939",
+            "20230304\t2023届高三08班\t0.875",
+            "20230304\t2023届高三09班\t0.879"
         ],
         "origin": "2022届高三下学期测验卷04第7题",
         "edit": [
@@ -110601,7 +110612,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220331\t2022届高三01班\t0.953"
+            "20220331\t2022届高三01班\t0.953",
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t0.875",
+            "20230304\t2023届高三01班\t0.969",
+            "20230304\t2023届高三02班\t0.906",
+            "20230304\t2023届高三03班\t0.935",
+            "20230304\t2023届高三04班\t0.900",
+            "20230304\t2023届高三05班\t0.875",
+            "20230304\t2023届高三06班\t0.872",
+            "20230304\t2023届高三07班\t0.939",
+            "20230304\t2023届高三08班\t0.875",
+            "20230304\t2023届高三09班\t0.970"
         ],
         "origin": "2022届高三下学期测验卷04第8题",
         "edit": [
@@ -110628,7 +110650,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220331\t2022届高三01班\t0.953"
+            "20220331\t2022届高三01班\t0.953",
+            "20230304\t2023届高三11班\t0.737",
+            "20230304\t2023届高三12班\t0.917",
+            "20230304\t2023届高三01班\t0.969",
+            "20230304\t2023届高三02班\t0.969",
+            "20230304\t2023届高三03班\t0.903",
+            "20230304\t2023届高三04班\t0.900",
+            "20230304\t2023届高三05班\t0.900",
+            "20230304\t2023届高三06班\t0.974",
+            "20230304\t2023届高三07班\t0.909",
+            "20230304\t2023届高三08班\t0.844",
+            "20230304\t2023届高三09班\t0.939"
         ],
         "origin": "2022届高三下学期测验卷04第9题",
         "edit": [
@@ -110972,7 +111005,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220407\t2022届高三01班\t0.977"
+            "20220407\t2022届高三01班\t0.977",
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t0.958",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.969",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t1.000",
+            "20230304\t2023届高三05班\t1.000",
+            "20230304\t2023届高三06班\t0.949",
+            "20230304\t2023届高三07班\t1.000",
+            "20230304\t2023届高三08班\t0.969",
+            "20230304\t2023届高三09班\t1.000"
         ],
         "origin": "2022届高三下学期测验卷05第1题",
         "edit": [
@@ -111710,7 +111754,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220421\t2022届高三01班\t0.953"
+            "20220421\t2022届高三01班\t0.953",
+            "20230304\t2023届高三11班\t0.789",
+            "20230304\t2023届高三12班\t0.750",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.906",
+            "20230304\t2023届高三03班\t0.839",
+            "20230304\t2023届高三04班\t0.833",
+            "20230304\t2023届高三05班\t0.900",
+            "20230304\t2023届高三06班\t0.974",
+            "20230304\t2023届高三07班\t0.909",
+            "20230304\t2023届高三08班\t0.812",
+            "20230304\t2023届高三09班\t0.788"
         ],
         "origin": "2022届高三下学期测验卷06第6题",
         "edit": [
@@ -111839,7 +111894,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220421\t2022届高三01班\t0.977"
+            "20220421\t2022届高三01班\t0.977",
+            "20230304\t2023届高三11班\t0.368",
+            "20230304\t2023届高三12班\t0.417",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.844",
+            "20230304\t2023届高三03班\t0.871",
+            "20230304\t2023届高三04班\t0.867",
+            "20230304\t2023届高三05班\t0.650",
+            "20230304\t2023届高三06班\t0.718",
+            "20230304\t2023届高三07班\t0.697",
+            "20230304\t2023届高三08班\t0.625",
+            "20230304\t2023届高三09班\t0.545"
         ],
         "origin": "2022届高三下学期测验卷06第11题",
         "edit": [
@@ -112234,7 +112300,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220428\t2022届高三01班\t1.000"
+            "20220428\t2022届高三01班\t1.000",
+            "20230304\t2023届高三11班\t0.684",
+            "20230304\t2023届高三12班\t0.583",
+            "20230304\t2023届高三01班\t0.875",
+            "20230304\t2023届高三02班\t0.906",
+            "20230304\t2023届高三03班\t0.677",
+            "20230304\t2023届高三04班\t0.900",
+            "20230304\t2023届高三05班\t0.650",
+            "20230304\t2023届高三06班\t0.872",
+            "20230304\t2023届高三07班\t0.697",
+            "20230304\t2023届高三08班\t0.812",
+            "20230304\t2023届高三09班\t0.636"
         ],
         "origin": "2022届高三下学期测验卷07第5题",
         "edit": [
@@ -112257,7 +112334,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220428\t2022届高三01班\t0.977"
+            "20220428\t2022届高三01班\t0.977",
+            "20230304\t2023届高三11班\t0.947",
+            "20230304\t2023届高三12班\t0.708",
+            "20230304\t2023届高三01班\t0.781",
+            "20230304\t2023届高三02班\t0.875",
+            "20230304\t2023届高三03班\t0.774",
+            "20230304\t2023届高三04班\t0.933",
+            "20230304\t2023届高三05班\t0.750",
+            "20230304\t2023届高三06班\t0.795",
+            "20230304\t2023届高三07班\t0.818",
+            "20230304\t2023届高三08班\t0.844",
+            "20230304\t2023届高三09班\t0.606"
         ],
         "origin": "2022届高三下学期测验卷07第6题",
         "edit": [
@@ -113370,7 +113458,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220512\t2022届高三01班\t0.977"
+            "20220512\t2022届高三01班\t0.977",
+            "20230304\t2023届高三11班\t0.316",
+            "20230304\t2023届高三12班\t0.375",
+            "20230304\t2023届高三01班\t0.938",
+            "20230304\t2023届高三02班\t0.781",
+            "20230304\t2023届高三03班\t0.839",
+            "20230304\t2023届高三04班\t0.967",
+            "20230304\t2023届高三05班\t0.825",
+            "20230304\t2023届高三06班\t0.744",
+            "20230304\t2023届高三07班\t0.667",
+            "20230304\t2023届高三08班\t0.688",
+            "20230304\t2023届高三09班\t0.364"
         ],
         "origin": "2022届高三下学期测验卷09第7题",
         "edit": [
@@ -114957,7 +115056,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20220607\t2022届高三01班\t0.953"
+            "20220607\t2022届高三01班\t0.953",
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t0.917",
+            "20230304\t2023届高三01班\t0.969",
+            "20230304\t2023届高三02班\t0.938",
+            "20230304\t2023届高三03班\t0.903",
+            "20230304\t2023届高三04班\t1.000",
+            "20230304\t2023届高三05班\t0.975",
+            "20230304\t2023届高三06班\t1.000",
+            "20230304\t2023届高三07班\t0.939",
+            "20230304\t2023届高三08班\t0.938",
+            "20230304\t2023届高三09班\t0.970"
         ],
         "origin": "2022届高三下学期测验卷12第3题",
         "edit": [
@@ -121129,7 +121239,18 @@
         "solution": "",
         "duration": -1,
         "usages": [
-            "20211123\t2022届高三01班\t1.000\t0.968\t0.484"
+            "20211123\t2022届高三01班\t1.000\t0.968\t0.484",
+            "20230304\t2023届高三11班\t0.895\t0.632\t0.125",
+            "20230304\t2023届高三12班\t0.958\t0.750\t0.135",
+            "20230304\t2023届高三01班\t1.000\t0.953\t0.547",
+            "20230304\t2023届高三02班\t0.875\t0.818\t0.285",
+            "20230304\t2023届高三03班\t0.935\t0.839\t0.153",
+            "20230304\t2023届高三04班\t1.000\t0.900\t0.362",
+            "20230304\t2023届高三05班\t0.975\t0.933\t0.134",
+            "20230304\t2023届高三06班\t1.000\t0.940\t0.324",
+            "20230304\t2023届高三07班\t1.000\t0.818\t0.171",
+            "20230304\t2023届高三08班\t0.938\t0.792\t0.270",
+            "20230304\t2023届高三09班\t0.909\t0.798\t0.235"
         ],
         "origin": "2022届高三上学期测验卷08第20题",
         "edit": [
@@ -125138,7 +125259,18 @@
         "duration": -1,
         "usages": [
             "20211209\t2022届高三\t0.893\t0.867",
-            "20211209\t2022届高三01班\t0.977\t0.977"
+            "20211209\t2022届高三01班\t0.977\t0.977",
+            "20230304\t2023届高三11班\t0.912\t0.895",
+            "20230304\t2023届高三12班\t0.875\t0.875",
+            "20230304\t2023届高三01班\t1.000\t0.969",
+            "20230304\t2023届高三02班\t0.958\t0.938",
+            "20230304\t2023届高三03班\t0.979\t0.944",
+            "20230304\t2023届高三04班\t0.989\t0.958",
+            "20230304\t2023届高三05班\t0.946\t0.838",
+            "20230304\t2023届高三06班\t0.979\t0.968",
+            "20230304\t2023届高三07班\t0.965\t0.936",
+            "20230304\t2023届高三08班\t0.969\t0.859",
+            "20230304\t2023届高三09班\t0.929\t0.932"
         ],
         "origin": "2022届高三上月考卷02第18题",
         "edit": [
@@ -280286,7 +280418,19 @@
         "ans": "(1) 有效去污时间可达$8$分钟; (2) 最小值约为$1.4$($24-16\\sqrt{2}\\approx 1.4$)",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.912\t0.210",
+            "20230304\t2023届高三12班\t0.979\t0.302",
+            "20230304\t2023届高三01班\t0.984\t0.926",
+            "20230304\t2023届高三02班\t1.000\t0.680",
+            "20230304\t2023届高三03班\t0.957\t0.637",
+            "20230304\t2023届高三04班\t0.933\t0.679",
+            "20230304\t2023届高三05班\t1.000\t0.494",
+            "20230304\t2023届高三06班\t0.987\t0.814",
+            "20230304\t2023届高三07班\t0.980\t0.492",
+            "20230304\t2023届高三08班\t0.875\t0.594",
+            "20230304\t2023届高三09班\t0.970\t0.330"
+        ],
         "origin": "2022届高三上学期国庆卷3试题19",
         "edit": [
             "20220817\t王伟叶"
@@ -284076,7 +284220,19 @@
         "ans": "(1) $\\{a_n\\}$不是指数数列, $\\{b_n\\}$是指数数列; (2) 证明略; (3) 证明略",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.908\t0.307\t0.007",
+            "20230304\t2023届高三12班\t0.885\t0.590\t0.031",
+            "20230304\t2023届高三01班\t1.000\t0.943\t0.309",
+            "20230304\t2023届高三02班\t0.930\t0.755\t0.062",
+            "20230304\t2023届高三03班\t0.806\t0.688\t0.097",
+            "20230304\t2023届高三04班\t1.000\t0.678\t0.283",
+            "20230304\t2023届高三05班\t0.975\t0.742\t0.106",
+            "20230304\t2023届高三06班\t1.000\t0.778\t0.157",
+            "20230304\t2023届高三07班\t1.000\t0.399\t0.023",
+            "20230304\t2023届高三08班\t0.969\t0.771\t0.125",
+            "20230304\t2023届高三09班\t0.939\t0.540\t0.008"
+        ],
         "origin": "2022届高三下学期周末卷7试题21",
         "edit": [
             "20220818\t王伟叶"
@@ -298177,7 +298333,18 @@
             "20221106\t2023届高三05班\t0.853",
             "20221106\t2023届高三08班\t0.867",
             "20221106\t2023届高三09班\t0.839",
-            "20221109\t2023届高三03班\t0.964"
+            "20221109\t2023届高三03班\t0.964",
+            "20230304\t2023届高三11班\t0.842",
+            "20230304\t2023届高三12班\t0.917",
+            "20230304\t2023届高三01班\t0.969",
+            "20230304\t2023届高三02班\t0.906",
+            "20230304\t2023届高三03班\t0.935",
+            "20230304\t2023届高三04班\t0.800",
+            "20230304\t2023届高三05班\t0.850",
+            "20230304\t2023届高三06班\t1.000",
+            "20230304\t2023届高三07班\t0.879",
+            "20230304\t2023届高三08班\t0.781",
+            "20230304\t2023届高三09班\t0.788"
         ],
         "origin": "2022届杨浦高三基础考试题13",
         "edit": [
@@ -306803,7 +306970,19 @@
         "ans": "C",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.421",
+            "20230304\t2023届高三12班\t0.583",
+            "20230304\t2023届高三01班\t0.938",
+            "20230304\t2023届高三02班\t0.812",
+            "20230304\t2023届高三03班\t0.710",
+            "20230304\t2023届高三04班\t0.600",
+            "20230304\t2023届高三05班\t0.700",
+            "20230304\t2023届高三06班\t0.795",
+            "20230304\t2023届高三07班\t0.424",
+            "20230304\t2023届高三08班\t0.594",
+            "20230304\t2023届高三09班\t0.424"
+        ],
         "origin": "2012届春季高考试题18",
         "edit": [
             "20221212\t王伟叶"
@@ -308718,7 +308897,19 @@
         "ans": "A",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.947",
+            "20230304\t2023届高三12班\t0.875",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.906",
+            "20230304\t2023届高三03班\t0.935",
+            "20230304\t2023届高三04班\t0.900",
+            "20230304\t2023届高三05班\t0.950",
+            "20230304\t2023届高三06班\t0.949",
+            "20230304\t2023届高三07班\t0.939",
+            "20230304\t2023届高三08班\t0.906",
+            "20230304\t2023届高三09班\t0.909"
+        ],
         "origin": "2015届春季高考正卷试题23",
         "edit": [
             "20221212\t王伟叶"
@@ -310656,7 +310847,17 @@
         "ans": "$\\{2,3,4\\}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t1.000",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t1.000",
+            "20230304\t2023届高三05班\t1.000",
+            "20230304\t2023届高三07班\t1.000",
+            "20230304\t2023届高三08班\t1.000",
+            "20230304\t2023届高三09班\t1.000"
+        ],
         "origin": "2023届青浦区一模试题1",
         "edit": [
             "20221214\t王伟叶"
@@ -310677,7 +310878,17 @@
         "ans": "$-1$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t1.000",
+            "20230304\t2023届高三02班\t0.969",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t1.000",
+            "20230304\t2023届高三05班\t1.000",
+            "20230304\t2023届高三07班\t1.000",
+            "20230304\t2023届高三08班\t0.963",
+            "20230304\t2023届高三09班\t0.952"
+        ],
         "origin": "2023届青浦区一模试题2",
         "edit": [
             "20221214\t王伟叶"
@@ -310698,7 +310909,17 @@
         "ans": "$23$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.789",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三02班\t0.906",
+            "20230304\t2023届高三03班\t0.920",
+            "20230304\t2023届高三04班\t0.917",
+            "20230304\t2023届高三05班\t0.975",
+            "20230304\t2023届高三07班\t0.897",
+            "20230304\t2023届高三08班\t0.889",
+            "20230304\t2023届高三09班\t0.905"
+        ],
         "origin": "2023届青浦区一模试题3",
         "edit": [
             "20221214\t王伟叶"
@@ -310719,7 +310940,17 @@
         "ans": "$(-3,2)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t0.952",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t0.958",
+            "20230304\t2023届高三05班\t1.000",
+            "20230304\t2023届高三07班\t0.862",
+            "20230304\t2023届高三08班\t1.000",
+            "20230304\t2023届高三09班\t0.952"
+        ],
         "origin": "2023届青浦区一模试题4",
         "edit": [
             "20221214\t王伟叶"
@@ -310740,7 +310971,17 @@
         "ans": "$\\dfrac 65$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.684",
+            "20230304\t2023届高三12班\t0.952",
+            "20230304\t2023届高三02班\t0.875",
+            "20230304\t2023届高三03班\t0.920",
+            "20230304\t2023届高三04班\t0.875",
+            "20230304\t2023届高三05班\t0.875",
+            "20230304\t2023届高三07班\t0.862",
+            "20230304\t2023届高三08班\t0.963",
+            "20230304\t2023届高三09班\t0.952"
+        ],
         "origin": "2023届青浦区一模试题5",
         "edit": [
             "20221214\t王伟叶"
@@ -310761,7 +311002,17 @@
         "ans": "$\\dfrac\\pi 4$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.947",
+            "20230304\t2023届高三12班\t0.952",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t0.960",
+            "20230304\t2023届高三04班\t0.958",
+            "20230304\t2023届高三05班\t0.975",
+            "20230304\t2023届高三07班\t1.000",
+            "20230304\t2023届高三08班\t0.926",
+            "20230304\t2023届高三09班\t1.000"
+        ],
         "origin": "2023届青浦区一模试题6",
         "edit": [
             "20221214\t王伟叶"
@@ -310782,7 +311033,17 @@
         "ans": "$3$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.895",
+            "20230304\t2023届高三12班\t0.905",
+            "20230304\t2023届高三02班\t0.969",
+            "20230304\t2023届高三03班\t0.960",
+            "20230304\t2023届高三04班\t0.958",
+            "20230304\t2023届高三05班\t0.975",
+            "20230304\t2023届高三07班\t0.931",
+            "20230304\t2023届高三08班\t0.926",
+            "20230304\t2023届高三09班\t0.952"
+        ],
         "origin": "2023届青浦区一模试题7",
         "edit": [
             "20221214\t王伟叶"
@@ -310803,7 +311064,17 @@
         "ans": "$\\dfrac 23$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.684",
+            "20230304\t2023届高三12班\t0.571",
+            "20230304\t2023届高三02班\t0.469",
+            "20230304\t2023届高三03班\t0.600",
+            "20230304\t2023届高三04班\t0.750",
+            "20230304\t2023届高三05班\t0.500",
+            "20230304\t2023届高三07班\t0.586",
+            "20230304\t2023届高三08班\t0.593",
+            "20230304\t2023届高三09班\t0.762"
+        ],
         "origin": "2023届青浦区一模试题8",
         "edit": [
             "20221214\t王伟叶"
@@ -310824,7 +311095,17 @@
         "ans": "$2\\sqrt{30}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.789",
+            "20230304\t2023届高三12班\t0.905",
+            "20230304\t2023届高三02班\t0.812",
+            "20230304\t2023届高三03班\t0.760",
+            "20230304\t2023届高三04班\t0.875",
+            "20230304\t2023届高三05班\t0.650",
+            "20230304\t2023届高三07班\t0.793",
+            "20230304\t2023届高三08班\t0.889",
+            "20230304\t2023届高三09班\t0.809"
+        ],
         "origin": "2023届青浦区一模试题9",
         "edit": [
             "20221214\t王伟叶"
@@ -310845,7 +311126,17 @@
         "ans": "$-\\dfrac 35$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.474",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三02班\t0.719",
+            "20230304\t2023届高三03班\t0.840",
+            "20230304\t2023届高三04班\t0.917",
+            "20230304\t2023届高三05班\t0.700",
+            "20230304\t2023届高三07班\t0.724",
+            "20230304\t2023届高三08班\t0.667",
+            "20230304\t2023届高三09班\t0.762"
+        ],
         "origin": "2023届青浦区一模试题10",
         "edit": [
             "20221214\t王伟叶"
@@ -310866,7 +311157,17 @@
         "ans": "$\\dfrac{125\\pi}{48}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.684",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三02班\t0.750",
+            "20230304\t2023届高三03班\t0.920",
+            "20230304\t2023届高三04班\t0.750",
+            "20230304\t2023届高三05班\t0.725",
+            "20230304\t2023届高三07班\t0.655",
+            "20230304\t2023届高三08班\t0.815",
+            "20230304\t2023届高三09班\t0.714"
+        ],
         "origin": "2023届青浦区一模试题11",
         "edit": [
             "20221214\t王伟叶"
@@ -310887,7 +311188,17 @@
         "ans": "$(\\dfrac{13}{15},\\dfrac 76)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.000",
+            "20230304\t2023届高三12班\t0.143",
+            "20230304\t2023届高三02班\t0.344",
+            "20230304\t2023届高三03班\t0.320",
+            "20230304\t2023届高三04班\t0.500",
+            "20230304\t2023届高三05班\t0.175",
+            "20230304\t2023届高三07班\t0.103",
+            "20230304\t2023届高三08班\t0.074",
+            "20230304\t2023届高三09班\t0.000"
+        ],
         "origin": "2023届青浦区一模试题12",
         "edit": [
             "20221214\t王伟叶"
@@ -310908,7 +311219,17 @@
         "ans": "D",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.947",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三02班\t0.969",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t0.917",
+            "20230304\t2023届高三05班\t0.925",
+            "20230304\t2023届高三07班\t0.966",
+            "20230304\t2023届高三08班\t0.889",
+            "20230304\t2023届高三09班\t0.857"
+        ],
         "origin": "2023届青浦区一模试题13",
         "edit": [
             "20221214\t王伟叶"
@@ -310929,7 +311250,17 @@
         "ans": "A",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.895",
+            "20230304\t2023届高三12班\t1.000",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t0.960",
+            "20230304\t2023届高三04班\t0.875",
+            "20230304\t2023届高三05班\t0.925",
+            "20230304\t2023届高三07班\t0.966",
+            "20230304\t2023届高三08班\t0.963",
+            "20230304\t2023届高三09班\t0.905"
+        ],
         "origin": "2023届青浦区一模试题14",
         "edit": [
             "20221214\t王伟叶"
@@ -310950,7 +311281,17 @@
         "ans": "B",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.368",
+            "20230304\t2023届高三12班\t0.381",
+            "20230304\t2023届高三02班\t0.625",
+            "20230304\t2023届高三03班\t0.480",
+            "20230304\t2023届高三04班\t0.292",
+            "20230304\t2023届高三05班\t0.375",
+            "20230304\t2023届高三07班\t0.483",
+            "20230304\t2023届高三08班\t0.444",
+            "20230304\t2023届高三09班\t0.333"
+        ],
         "origin": "2023届青浦区一模试题15",
         "edit": [
             "20221214\t王伟叶"
@@ -310971,7 +311312,17 @@
         "ans": "D",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.053",
+            "20230304\t2023届高三12班\t0.095",
+            "20230304\t2023届高三02班\t0.156",
+            "20230304\t2023届高三03班\t0.120",
+            "20230304\t2023届高三04班\t0.000",
+            "20230304\t2023届高三05班\t0.250",
+            "20230304\t2023届高三07班\t0.069",
+            "20230304\t2023届高三08班\t0.074",
+            "20230304\t2023届高三09班\t0.191"
+        ],
         "origin": "2023届青浦区一模试题16",
         "edit": [
             "20221214\t王伟叶"
@@ -310992,7 +311343,17 @@
         "ans": "(1) $[k\\pi-\\dfrac\\pi 6,k\\pi+\\dfrac\\pi 3]$, $k\\in \\mathbf{Z}$; (2) 最大值为$\\dfrac{\\sqrt{3}-1}2$, 最小值为$-\\dfrac 32$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t1.000\t0.474",
+            "20230304\t2023届高三12班\t0.857\t0.333",
+            "20230304\t2023届高三02班\t0.906\t0.750",
+            "20230304\t2023届高三03班\t0.800\t0.840",
+            "20230304\t2023届高三04班\t0.792\t0.625",
+            "20230304\t2023届高三05班\t0.700\t0.775",
+            "20230304\t2023届高三07班\t0.759\t0.759",
+            "20230304\t2023届高三08班\t0.667\t0.593",
+            "20230304\t2023届高三09班\t0.952\t0.286"
+        ],
         "origin": "2023届青浦区一模试题17",
         "edit": [
             "20221214\t王伟叶"
@@ -311013,7 +311374,17 @@
         "ans": "(1) 证明略; (2) 证明略",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t1.000\t0.842",
+            "20230304\t2023届高三12班\t1.000\t0.571",
+            "20230304\t2023届高三02班\t0.844\t0.906",
+            "20230304\t2023届高三03班\t1.000\t1.000",
+            "20230304\t2023届高三04班\t0.500\t0.750",
+            "20230304\t2023届高三05班\t0.850\t0.950",
+            "20230304\t2023届高三07班\t0.724\t0.862",
+            "20230304\t2023届高三08班\t0.926\t0.963",
+            "20230304\t2023届高三09班\t1.000\t0.524"
+        ],
         "origin": "2023届青浦区一模试题18",
         "edit": [
             "20221214\t王伟叶"
@@ -311034,7 +311405,17 @@
         "ans": "(1) $2480$人; (2) $11$月$11$日新感染者人数最多, 为$630$人",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.895\t0.526",
+            "20230304\t2023届高三12班\t0.857\t0.809",
+            "20230304\t2023届高三02班\t0.844\t0.781",
+            "20230304\t2023届高三03班\t0.680\t0.800",
+            "20230304\t2023届高三04班\t0.833\t0.833",
+            "20230304\t2023届高三05班\t0.775\t0.800",
+            "20230304\t2023届高三07班\t0.793\t0.759",
+            "20230304\t2023届高三08班\t0.704\t0.815",
+            "20230304\t2023届高三09班\t0.809\t0.571"
+        ],
         "origin": "2023届青浦区一模试题19",
         "edit": [
             "20221214\t王伟叶"
@@ -311055,7 +311436,17 @@
         "ans": "(1) $\\dfrac{\\sqrt{2}}2$; (2) 过定点$(\\dfrac 23,0)$; (3) $\\dfrac 19$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.895\t0.263\t0.210",
+            "20230304\t2023届高三12班\t1.000\t0.667\t0.238",
+            "20230304\t2023届高三02班\t0.938\t0.688\t0.312",
+            "20230304\t2023届高三03班\t1.000\t0.960\t0.760",
+            "20230304\t2023届高三04班\t0.917\t0.375\t0.542",
+            "20230304\t2023届高三05班\t0.975\t0.800\t0.375",
+            "20230304\t2023届高三07班\t0.931\t0.414\t0.138",
+            "20230304\t2023届高三08班\t0.963\t0.704\t0.185",
+            "20230304\t2023届高三09班\t0.952\t0.524\t0.143"
+        ],
         "origin": "2023届青浦区一模试题20",
         "edit": [
             "20221214\t王伟叶"
@@ -311076,7 +311467,17 @@
         "ans": "(1) $5$; (2) 在定直线$y=2x$上; (3) 当且仅当$a=-\\dfrac 2{\\mathrm{e}}$时存在, $k=3$, $x_0=2$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.632\t0.263\t0.000",
+            "20230304\t2023届高三12班\t0.762\t0.286\t0.000",
+            "20230304\t2023届高三02班\t0.875\t0.750\t0.219",
+            "20230304\t2023届高三03班\t1.000\t0.800\t0.320",
+            "20230304\t2023届高三04班\t0.917\t0.625\t0.167",
+            "20230304\t2023届高三05班\t0.925\t0.600\t0.200",
+            "20230304\t2023届高三07班\t0.897\t0.414\t0.035",
+            "20230304\t2023届高三08班\t0.852\t0.593\t0.185",
+            "20230304\t2023届高三09班\t0.714\t0.143\t0.000"
+        ],
         "origin": "2023届青浦区一模试题21",
         "edit": [
             "20221214\t王伟叶"
@@ -322282,7 +322683,20 @@
         "ans": "$[-\\dfrac {7\\pi}{12}+k\\pi,-\\dfrac{\\pi}{12}+k\\pi]$, $k\\in \\mathbf{Z}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.432",
+            "20230304\t2023届高三11班\t0.762",
+            "20230304\t2023届高三12班\t0.762",
+            "20230304\t2023届高三01班\t0.926",
+            "20230304\t2023届高三02班\t0.742",
+            "20230304\t2023届高三03班\t0.480",
+            "20230304\t2023届高三04班\t0.536",
+            "20230304\t2023届高三05班\t0.605",
+            "20230304\t2023届高三06班\t0.475",
+            "20230304\t2023届高三07班\t0.625",
+            "20230304\t2023届高三08班\t0.484",
+            "20230304\t2023届高三09班\t0.484"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -322366,7 +322780,20 @@
         "ans": "$\\{x|x=\\dfrac\\pi 3+2k\\pi\\text{或}\\dfrac{5\\pi}3+2k\\pi, \\ k\\in \\mathbf{Z}\\}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.540",
+            "20230304\t2023届高三11班\t0.619",
+            "20230304\t2023届高三12班\t0.524",
+            "20230304\t2023届高三01班\t0.704",
+            "20230304\t2023届高三02班\t0.645",
+            "20230304\t2023届高三03班\t0.760",
+            "20230304\t2023届高三04班\t0.714",
+            "20230304\t2023届高三05班\t0.684",
+            "20230304\t2023届高三06班\t0.525",
+            "20230304\t2023届高三07班\t0.406",
+            "20230304\t2023届高三08班\t0.548",
+            "20230304\t2023届高三09班\t0.484"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -322387,7 +322814,20 @@
         "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.027",
+            "20230304\t2023届高三11班\t0.333",
+            "20230304\t2023届高三12班\t0.000",
+            "20230304\t2023届高三01班\t0.111",
+            "20230304\t2023届高三02班\t0.065",
+            "20230304\t2023届高三03班\t0.640",
+            "20230304\t2023届高三04班\t0.000",
+            "20230304\t2023届高三05班\t0.605",
+            "20230304\t2023届高三06班\t0.050",
+            "20230304\t2023届高三07班\t0.125",
+            "20230304\t2023届高三08班\t0.419",
+            "20230304\t2023届高三09班\t0.000"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -322555,7 +322995,20 @@
         "ans": "$2$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t1.000",
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t0.952",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.968",
+            "20230304\t2023届高三03班\t0.960",
+            "20230304\t2023届高三04班\t1.000",
+            "20230304\t2023届高三05班\t0.974",
+            "20230304\t2023届高三06班\t0.925",
+            "20230304\t2023届高三07班\t0.969",
+            "20230304\t2023届高三08班\t1.000",
+            "20230304\t2023届高三09班\t0.968"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -322576,7 +323029,19 @@
         "ans": "$\\dfrac{4\\pi}{3}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.694",
+            "20230304\t2023届高三11班\t0.850",
+            "20230304\t2023届高三12班\t0.809",
+            "20230304\t2023届高三01班\t0.600",
+            "20230304\t2023届高三02班\t0.719",
+            "20230304\t2023届高三03班\t0.733",
+            "20230304\t2023届高三04班\t0.679",
+            "20230304\t2023届高三05班\t0.795",
+            "20230304\t2023届高三07班\t0.625",
+            "20230304\t2023届高三08班\t0.655",
+            "20230304\t2023届高三09班\t0.862"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -322597,7 +323062,19 @@
         "ans": "$1$或$-2$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.833",
+            "20230304\t2023届高三11班\t0.800",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三01班\t0.800",
+            "20230304\t2023届高三02班\t0.781",
+            "20230304\t2023届高三03班\t0.833",
+            "20230304\t2023届高三04班\t0.750",
+            "20230304\t2023届高三05班\t0.821",
+            "20230304\t2023届高三07班\t0.875",
+            "20230304\t2023届高三08班\t0.793",
+            "20230304\t2023届高三09班\t0.690"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -322618,7 +323095,19 @@
         "ans": "\\textcircled{2}\\textcircled{4}",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.667",
+            "20230304\t2023届高三11班\t0.600",
+            "20230304\t2023届高三12班\t0.714",
+            "20230304\t2023届高三01班\t0.800",
+            "20230304\t2023届高三02班\t0.719",
+            "20230304\t2023届高三03班\t0.667",
+            "20230304\t2023届高三04班\t0.571",
+            "20230304\t2023届高三05班\t0.846",
+            "20230304\t2023届高三07班\t0.844",
+            "20230304\t2023届高三08班\t0.724",
+            "20230304\t2023届高三09班\t0.724"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -322673,7 +323162,19 @@
         "ans": "(1) $[1-\\sqrt{3},1+\\sqrt{3}]$; (2) $\\dfrac 16$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.917\t0.750",
+            "20230304\t2023届高三11班\t0.900\t0.700",
+            "20230304\t2023届高三12班\t1.000\t0.857",
+            "20230304\t2023届高三01班\t0.960\t0.960",
+            "20230304\t2023届高三02班\t0.969\t0.688",
+            "20230304\t2023届高三03班\t0.833\t0.600",
+            "20230304\t2023届高三04班\t0.929\t0.714",
+            "20230304\t2023届高三05班\t0.974\t0.821",
+            "20230304\t2023届高三07班\t0.938\t0.656",
+            "20230304\t2023届高三08班\t0.897\t0.793",
+            "20230304\t2023届高三09班\t0.931\t0.621"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324674,7 +325175,19 @@
         "ans": "$\\sqrt{19}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.947",
+            "20230304\t2023届高三12班\t0.571",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.875",
+            "20230304\t2023届高三03班\t0.769",
+            "20230304\t2023届高三04班\t0.852",
+            "20230304\t2023届高三05班\t0.947",
+            "20230304\t2023届高三06班\t0.947",
+            "20230304\t2023届高三07班\t0.862",
+            "20230304\t2023届高三08班\t0.939",
+            "20230304\t2023届高三09班\t0.778"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324695,7 +325208,19 @@
         "ans": "$\\dfrac{2\\pi}3$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.632",
+            "20230304\t2023届高三12班\t1.000",
+            "20230304\t2023届高三01班\t0.935",
+            "20230304\t2023届高三02班\t0.781",
+            "20230304\t2023届高三03班\t0.692",
+            "20230304\t2023届高三04班\t0.630",
+            "20230304\t2023届高三05班\t0.711",
+            "20230304\t2023届高三06班\t0.763",
+            "20230304\t2023届高三07班\t0.759",
+            "20230304\t2023届高三08班\t0.636",
+            "20230304\t2023届高三09班\t0.889"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324716,7 +325241,19 @@
         "ans": "$-\\dfrac 12\\overrightarrow{a}+\\dfrac 34\\overrightarrow{b}+\\dfrac 14\\overrightarrow{c}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.737",
+            "20230304\t2023届高三12班\t0.762",
+            "20230304\t2023届高三01班\t0.774",
+            "20230304\t2023届高三02班\t0.750",
+            "20230304\t2023届高三03班\t0.846",
+            "20230304\t2023届高三04班\t0.518",
+            "20230304\t2023届高三05班\t0.711",
+            "20230304\t2023届高三06班\t0.842",
+            "20230304\t2023届高三07班\t0.690",
+            "20230304\t2023届高三08班\t0.909",
+            "20230304\t2023届高三09班\t0.556"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324927,7 +325464,19 @@
         "ans": "$4$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.947",
+            "20230304\t2023届高三12班\t1.000",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t1.000",
+            "20230304\t2023届高三05班\t1.000",
+            "20230304\t2023届高三06班\t0.974",
+            "20230304\t2023届高三07班\t0.897",
+            "20230304\t2023届高三08班\t0.970",
+            "20230304\t2023届高三09班\t0.963"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324969,7 +325518,19 @@
         "ans": "$\\dfrac{10\\sqrt{13}}{13}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.947",
+            "20230304\t2023届高三12班\t0.762",
+            "20230304\t2023届高三01班\t1.000",
+            "20230304\t2023届高三02班\t0.875",
+            "20230304\t2023届高三03班\t0.923",
+            "20230304\t2023届高三04班\t0.926",
+            "20230304\t2023届高三05班\t0.947",
+            "20230304\t2023届高三06班\t0.763",
+            "20230304\t2023届高三07班\t0.897",
+            "20230304\t2023届高三08班\t0.970",
+            "20230304\t2023届高三09班\t0.778"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -326087,7 +326648,19 @@
         "ans": "(1) $\\begin{cases}x'=x+\\sqrt{3}y,\\\\y'=\\sqrt{3}x-y;\\end{cases}$ (2) $P(\\dfrac{3\\sqrt{3}}4,\\dfrac 14)$; (3) $\\dfrac{\\sqrt{3}}3$或$-\\sqrt{3}$.",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.684\t0.737\t0.421",
+            "20230304\t2023届高三12班\t0.857\t0.714\t0.714",
+            "20230304\t2023届高三01班\t1.000\t0.968\t0.935",
+            "20230304\t2023届高三02班\t0.812\t0.812\t0.500",
+            "20230304\t2023届高三03班\t0.808\t0.731\t0.692",
+            "20230304\t2023届高三04班\t1.000\t0.926\t0.778",
+            "20230304\t2023届高三05班\t0.816\t0.842\t0.763",
+            "20230304\t2023届高三06班\t0.921\t0.868\t0.868",
+            "20230304\t2023届高三07班\t1.000\t0.897\t0.690",
+            "20230304\t2023届高三08班\t0.849\t0.758\t0.697",
+            "20230304\t2023届高三09班\t0.815\t0.667\t0.407"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -339971,7 +340544,19 @@
         "ans": "$1-\\sqrt{2}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.806",
+            "20230304\t2023届高三11班\t1.000",
+            "20230304\t2023届高三12班\t0.809",
+            "20230304\t2023届高三01班\t0.880",
+            "20230304\t2023届高三02班\t0.844",
+            "20230304\t2023届高三03班\t0.667",
+            "20230304\t2023届高三04班\t0.821",
+            "20230304\t2023届高三05班\t0.949",
+            "20230304\t2023届高三07班\t0.875",
+            "20230304\t2023届高三08班\t0.793",
+            "20230304\t2023届高三09班\t0.897"
+        ],
         "origin": "2020年空中课堂高三复习课11",
         "edit": [
             "20230128\t王伟叶"
@@ -340013,7 +340598,19 @@
         "ans": "(1) 当$a=0$时, $g(x)$是偶函数; 当$a\\ne 0$时, $g(x)$既不是奇函数也不是偶函数; (2) $10$或$11$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.583\t0.611",
+            "20230304\t2023届高三11班\t0.200\t0.350",
+            "20230304\t2023届高三12班\t0.714\t0.619",
+            "20230304\t2023届高三01班\t0.880\t0.960",
+            "20230304\t2023届高三02班\t0.688\t0.812",
+            "20230304\t2023届高三03班\t0.633\t0.767",
+            "20230304\t2023届高三04班\t0.429\t0.893",
+            "20230304\t2023届高三05班\t0.436\t0.718",
+            "20230304\t2023届高三07班\t0.406\t0.594",
+            "20230304\t2023届高三08班\t0.655\t0.897",
+            "20230304\t2023届高三09班\t0.448\t0.621"
+        ],
         "origin": "2020年空中课堂高三复习课11",
         "edit": [
             "20230128\t王伟叶"
@@ -340034,7 +340631,19 @@
         "ans": "$\\dfrac{25\\pi}3$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.778",
+            "20230304\t2023届高三11班\t0.650",
+            "20230304\t2023届高三12班\t0.524",
+            "20230304\t2023届高三01班\t0.680",
+            "20230304\t2023届高三02班\t0.750",
+            "20230304\t2023届高三03班\t0.767",
+            "20230304\t2023届高三04班\t0.714",
+            "20230304\t2023届高三05班\t0.821",
+            "20230304\t2023届高三07班\t0.656",
+            "20230304\t2023届高三08班\t0.759",
+            "20230304\t2023届高三09班\t0.621"
+        ],
         "origin": "2020年空中课堂高三复习课11",
         "edit": [
             "20230128\t王伟叶"
@@ -340118,7 +340727,19 @@
         "ans": "(如)$\\dfrac\\pi 4$(所有可能的解为$\\dfrac\\pi 4+\\dfrac{k\\pi}2$, $k\\in \\mathbf{Z}$)",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.861",
+            "20230304\t2023届高三11班\t0.950",
+            "20230304\t2023届高三12班\t0.809",
+            "20230304\t2023届高三01班\t0.920",
+            "20230304\t2023届高三02班\t0.844",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t0.750",
+            "20230304\t2023届高三05班\t0.974",
+            "20230304\t2023届高三07班\t0.875",
+            "20230304\t2023届高三08班\t0.828",
+            "20230304\t2023届高三09班\t1.000"
+        ],
         "origin": "2020年空中课堂高三复习课11",
         "edit": [
             "20230128\t王伟叶"
@@ -340139,7 +340760,20 @@
         "ans": "$(3,+\\infty)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.595",
+            "20230304\t2023届高三11班\t0.667",
+            "20230304\t2023届高三12班\t0.619",
+            "20230304\t2023届高三01班\t0.815",
+            "20230304\t2023届高三02班\t0.452",
+            "20230304\t2023届高三03班\t0.560",
+            "20230304\t2023届高三04班\t0.500",
+            "20230304\t2023届高三05班\t0.658",
+            "20230304\t2023届高三06班\t0.675",
+            "20230304\t2023届高三07班\t0.469",
+            "20230304\t2023届高三08班\t0.419",
+            "20230304\t2023届高三09班\t0.710"
+        ],
         "origin": "2020年空中课堂高三复习课11",
         "edit": [
             "20230128\t王伟叶"
@@ -340181,7 +340815,20 @@
         "ans": "$\\dfrac 32$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.865",
+            "20230304\t2023届高三11班\t0.905",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三01班\t0.963",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t0.960",
+            "20230304\t2023届高三04班\t0.964",
+            "20230304\t2023届高三05班\t0.921",
+            "20230304\t2023届高三06班\t0.900",
+            "20230304\t2023届高三07班\t0.875",
+            "20230304\t2023届高三08班\t1.000",
+            "20230304\t2023届高三09班\t0.903"
+        ],
         "origin": "2020年空中课堂高三复习课11",
         "edit": [
             "20230128\t王伟叶"
@@ -340623,7 +341270,19 @@
         "ans": "$3$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.579",
+            "20230304\t2023届高三12班\t0.667",
+            "20230304\t2023届高三01班\t0.806",
+            "20230304\t2023届高三02班\t0.719",
+            "20230304\t2023届高三03班\t0.846",
+            "20230304\t2023届高三04班\t0.704",
+            "20230304\t2023届高三05班\t0.737",
+            "20230304\t2023届高三06班\t0.737",
+            "20230304\t2023届高三07班\t0.655",
+            "20230304\t2023届高三08班\t0.667",
+            "20230304\t2023届高三09班\t0.704"
+        ],
         "origin": "2020年空中课堂高三复习课13",
         "edit": [
             "20230128\t王伟叶"
@@ -340812,7 +341471,19 @@
         "ans": "(1) 证明略; (2) 最小值为$\\sqrt{3}$, 取到最小值时$t=1$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.789\t0.474",
+            "20230304\t2023届高三12班\t1.000\t0.952",
+            "20230304\t2023届高三01班\t1.000\t0.903",
+            "20230304\t2023届高三02班\t0.906\t0.812",
+            "20230304\t2023届高三03班\t0.846\t0.923",
+            "20230304\t2023届高三04班\t0.963\t0.778",
+            "20230304\t2023届高三05班\t0.763\t0.763",
+            "20230304\t2023届高三06班\t0.974\t0.737",
+            "20230304\t2023届高三07班\t0.793\t0.862",
+            "20230304\t2023届高三08班\t0.879\t0.818",
+            "20230304\t2023届高三09班\t1.000\t0.667"
+        ],
         "origin": "2020年空中课堂高三复习课14",
         "edit": [
             "20230128\t王伟叶"
@@ -340897,7 +341568,19 @@
         "ans": "$\\sqrt{3}+\\sqrt{2}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.210",
+            "20230304\t2023届高三12班\t0.381",
+            "20230304\t2023届高三01班\t0.677",
+            "20230304\t2023届高三02班\t0.562",
+            "20230304\t2023届高三03班\t0.500",
+            "20230304\t2023届高三04班\t0.556",
+            "20230304\t2023届高三05班\t0.632",
+            "20230304\t2023届高三06班\t0.658",
+            "20230304\t2023届高三07班\t0.276",
+            "20230304\t2023届高三08班\t0.485",
+            "20230304\t2023届高三09班\t0.407"
+        ],
         "origin": "2020年空中课堂高三复习课14",
         "edit": [
             "20230128\t王伟叶"
@@ -344776,7 +345459,19 @@
         "ans": "C",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.737",
+            "20230304\t2023届高三12班\t0.750",
+            "20230304\t2023届高三01班\t0.875",
+            "20230304\t2023届高三02班\t0.750",
+            "20230304\t2023届高三03班\t0.742",
+            "20230304\t2023届高三04班\t0.833",
+            "20230304\t2023届高三05班\t0.675",
+            "20230304\t2023届高三06班\t0.846",
+            "20230304\t2023届高三07班\t0.515",
+            "20230304\t2023届高三08班\t0.750",
+            "20230304\t2023届高三09班\t0.667"
+        ],
         "origin": "2020年空中课堂高三复习课30",
         "edit": [
             "20230128\t王伟叶"
@@ -348377,7 +349072,19 @@
         "ans": "$6$或$-6$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.417",
+            "20230304\t2023届高三11班\t0.550",
+            "20230304\t2023届高三12班\t0.333",
+            "20230304\t2023届高三01班\t0.640",
+            "20230304\t2023届高三02班\t0.844",
+            "20230304\t2023届高三03班\t0.567",
+            "20230304\t2023届高三04班\t0.536",
+            "20230304\t2023届高三05班\t0.564",
+            "20230304\t2023届高三07班\t0.594",
+            "20230304\t2023届高三08班\t0.586",
+            "20230304\t2023届高三09班\t0.207"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348396,7 +349103,19 @@
         "ans": "$[-\\sqrt{3},1]$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.778",
+            "20230304\t2023届高三11班\t0.900",
+            "20230304\t2023届高三12班\t0.714",
+            "20230304\t2023届高三01班\t0.920",
+            "20230304\t2023届高三02班\t0.906",
+            "20230304\t2023届高三03班\t0.800",
+            "20230304\t2023届高三04班\t0.929",
+            "20230304\t2023届高三05班\t0.897",
+            "20230304\t2023届高三07班\t0.844",
+            "20230304\t2023届高三08班\t0.862",
+            "20230304\t2023届高三09班\t0.828"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348453,7 +349172,20 @@
         "ans": "(1) $[\\dfrac\\pi{12}+k\\pi,\\dfrac{7\\pi}{12}+k\\pi]$, $k\\in \\mathbf{Z}$; (2) 最大值为$2$, 最小值为$1$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.649\t0.703",
+            "20230304\t2023届高三11班\t0.809\t0.524",
+            "20230304\t2023届高三12班\t0.762\t0.524",
+            "20230304\t2023届高三01班\t0.852\t0.704",
+            "20230304\t2023届高三02班\t0.903\t0.935",
+            "20230304\t2023届高三03班\t0.840\t0.840",
+            "20230304\t2023届高三04班\t0.571\t0.679",
+            "20230304\t2023届高三05班\t0.579\t0.500",
+            "20230304\t2023届高三06班\t0.800\t0.625",
+            "20230304\t2023届高三07班\t0.750\t0.781",
+            "20230304\t2023届高三08班\t0.677\t0.839",
+            "20230304\t2023届高三09班\t0.677\t0.581"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348567,7 +349299,20 @@
         "ans": "$\\dfrac\\pi 6$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.838",
+            "20230304\t2023届高三11班\t0.905",
+            "20230304\t2023届高三12班\t0.905",
+            "20230304\t2023届高三01班\t0.963",
+            "20230304\t2023届高三02班\t0.871",
+            "20230304\t2023届高三03班\t0.920",
+            "20230304\t2023届高三04班\t0.821",
+            "20230304\t2023届高三05班\t0.763",
+            "20230304\t2023届高三06班\t0.950",
+            "20230304\t2023届高三07班\t0.969",
+            "20230304\t2023届高三08班\t0.806",
+            "20230304\t2023届高三09班\t0.871"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348643,7 +349388,20 @@
         "ans": "$\\dfrac \\pi 2$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t1.000",
+            "20230304\t2023届高三11班\t0.714",
+            "20230304\t2023届高三12班\t0.905",
+            "20230304\t2023届高三01班\t0.963",
+            "20230304\t2023届高三02班\t0.968",
+            "20230304\t2023届高三03班\t0.880",
+            "20230304\t2023届高三04班\t0.893",
+            "20230304\t2023届高三05班\t0.947",
+            "20230304\t2023届高三06班\t0.950",
+            "20230304\t2023届高三07班\t0.969",
+            "20230304\t2023届高三08班\t1.000",
+            "20230304\t2023届高三09班\t0.968"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348662,7 +349420,19 @@
         "ans": "$0$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t1.000",
+            "20230304\t2023届高三11班\t0.950",
+            "20230304\t2023届高三12班\t0.905",
+            "20230304\t2023届高三01班\t0.920",
+            "20230304\t2023届高三02班\t0.969",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t0.929",
+            "20230304\t2023届高三05班\t0.923",
+            "20230304\t2023届高三07班\t0.906",
+            "20230304\t2023届高三08班\t0.966",
+            "20230304\t2023届高三09班\t0.931"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348700,7 +349470,20 @@
         "ans": "C",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.757",
+            "20230304\t2023届高三11班\t0.905",
+            "20230304\t2023届高三12班\t0.762",
+            "20230304\t2023届高三01班\t0.852",
+            "20230304\t2023届高三02班\t0.839",
+            "20230304\t2023届高三03班\t0.920",
+            "20230304\t2023届高三04班\t0.786",
+            "20230304\t2023届高三05班\t0.816",
+            "20230304\t2023届高三06班\t0.750",
+            "20230304\t2023届高三07班\t0.781",
+            "20230304\t2023届高三08班\t0.645",
+            "20230304\t2023届高三09班\t0.677"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348719,7 +349502,19 @@
         "ans": "$2$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.861",
+            "20230304\t2023届高三11班\t0.950",
+            "20230304\t2023届高三12班\t0.952",
+            "20230304\t2023届高三01班\t0.960",
+            "20230304\t2023届高三02班\t0.969",
+            "20230304\t2023届高三03班\t0.933",
+            "20230304\t2023届高三04班\t0.964",
+            "20230304\t2023届高三05班\t0.974",
+            "20230304\t2023届高三07班\t0.906",
+            "20230304\t2023届高三08班\t0.862",
+            "20230304\t2023届高三09班\t0.897"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348757,7 +349552,19 @@
         "ans": "$8$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.278",
+            "20230304\t2023届高三11班\t0.300",
+            "20230304\t2023届高三12班\t0.286",
+            "20230304\t2023届高三01班\t0.840",
+            "20230304\t2023届高三02班\t0.656",
+            "20230304\t2023届高三03班\t0.633",
+            "20230304\t2023届高三04班\t0.750",
+            "20230304\t2023届高三05班\t0.718",
+            "20230304\t2023届高三07班\t0.250",
+            "20230304\t2023届高三08班\t0.655",
+            "20230304\t2023届高三09班\t0.345"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348776,7 +349583,19 @@
         "ans": "(1) $f(x)=\\cos 2x$; (2) $\\lambda=1$, $n=1349$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.972\t0.000",
+            "20230304\t2023届高三11班\t0.950\t0.000",
+            "20230304\t2023届高三12班\t1.000\t0.048",
+            "20230304\t2023届高三01班\t1.000\t0.400",
+            "20230304\t2023届高三02班\t0.875\t0.312",
+            "20230304\t2023届高三03班\t0.900\t0.300",
+            "20230304\t2023届高三04班\t0.964\t0.321",
+            "20230304\t2023届高三05班\t0.949\t0.333",
+            "20230304\t2023届高三07班\t0.969\t0.062",
+            "20230304\t2023届高三08班\t0.931\t0.241",
+            "20230304\t2023届高三09班\t0.966\t0.035"
+        ],
         "origin": "2023年空中课堂高三复习课10",
         "edit": [
             "20230131\t王伟叶"
@@ -348833,7 +349652,20 @@
         "ans": "$\\{x|x=\\pm \\dfrac\\pi 3+2k\\pi, \\ k\\in \\mathbf{Z}\\}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.486",
+            "20230304\t2023届高三11班\t0.667",
+            "20230304\t2023届高三12班\t0.762",
+            "20230304\t2023届高三01班\t0.778",
+            "20230304\t2023届高三02班\t0.677",
+            "20230304\t2023届高三03班\t0.800",
+            "20230304\t2023届高三04班\t0.679",
+            "20230304\t2023届高三05班\t0.711",
+            "20230304\t2023届高三06班\t0.500",
+            "20230304\t2023届高三07班\t0.688",
+            "20230304\t2023届高三08班\t0.452",
+            "20230304\t2023届高三09班\t0.548"
+        ],
         "origin": "2023年空中课堂高三复习课11",
         "edit": [
             "20230131\t王伟叶"
@@ -348852,7 +349684,20 @@
         "ans": "A",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.973",
+            "20230304\t2023届高三11班\t0.952",
+            "20230304\t2023届高三12班\t1.000",
+            "20230304\t2023届高三01班\t0.963",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t1.000",
+            "20230304\t2023届高三04班\t0.821",
+            "20230304\t2023届高三05班\t1.000",
+            "20230304\t2023届高三06班\t0.950",
+            "20230304\t2023届高三07班\t0.875",
+            "20230304\t2023届高三08班\t0.871",
+            "20230304\t2023届高三09班\t1.000"
+        ],
         "origin": "2023年空中课堂高三复习课11",
         "edit": [
             "20230131\t王伟叶"
@@ -348909,7 +349754,20 @@
         "ans": "(1) $[-1,4]$; (2) 图像如下:\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (-0.5,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:{pi/2}] plot (\\x,{2*(sin(\\x/pi*180)+sin(\\x/pi*180+60))});\n\\draw [dashed] (0,{2*sqrt(3)}) node [left] {$2\\sqrt{3}$} -- ({pi/3},{2*sqrt(3)}) --({pi/3},0) node [below] {$\\dfrac\\pi 3$};\n\\draw [dashed] (0,3) node [left] {$3$} -- ({pi/2},3) --({pi/2},0) node [below] {$\\dfrac\\pi 2$};\n\\draw (0,{sqrt(3)}) node [left] {$\\sqrt{3}$};\n\\end{tikzpicture}\n\\end{center}\n满足条件的锐角的集合为$\\{\\arcsin\\dfrac{\\sqrt{30}}6-\\dfrac\\pi 6,\\dfrac{5\\pi}6-\\arcsin\\dfrac{\\sqrt{30}}6\\}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.757\t0.324",
+            "20230304\t2023届高三11班\t0.809\t0.286",
+            "20230304\t2023届高三12班\t0.905\t0.191",
+            "20230304\t2023届高三01班\t0.815\t0.630",
+            "20230304\t2023届高三02班\t0.645\t0.194",
+            "20230304\t2023届高三03班\t0.880\t0.680",
+            "20230304\t2023届高三04班\t0.893\t0.500",
+            "20230304\t2023届高三05班\t0.684\t0.395",
+            "20230304\t2023届高三06班\t0.750\t0.450",
+            "20230304\t2023届高三07班\t0.812\t0.312",
+            "20230304\t2023届高三08班\t0.645\t0.452",
+            "20230304\t2023届高三09班\t0.806\t0.194"
+        ],
         "origin": "2023年空中课堂高三复习课11",
         "edit": [
             "20230131\t王伟叶"
@@ -349099,7 +349957,20 @@
         "ans": "$[1,2)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.649",
+            "20230304\t2023届高三11班\t0.619",
+            "20230304\t2023届高三12班\t0.762",
+            "20230304\t2023届高三01班\t0.852",
+            "20230304\t2023届高三02班\t0.742",
+            "20230304\t2023届高三03班\t0.640",
+            "20230304\t2023届高三04班\t0.643",
+            "20230304\t2023届高三05班\t0.658",
+            "20230304\t2023届高三06班\t0.775",
+            "20230304\t2023届高三07班\t0.812",
+            "20230304\t2023届高三08班\t0.806",
+            "20230304\t2023届高三09班\t0.613"
+        ],
         "origin": "2023年空中课堂高三复习课11",
         "edit": [
             "20230131\t王伟叶"
@@ -349137,7 +350008,20 @@
         "ans": "(1) $y=10+\\dfrac{20}{\\cos\\theta}-10\\tan\\theta$, $\\theta\\in [0,\\dfrac\\pi 4)$; (2) 应使$|OP|=10-\\dfrac{10\\sqrt{3}}3\\text{km}$, 此时总长度的最小值为$10\\sqrt{3}+10\\text{km}$.",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.811\t0.297",
+            "20230304\t2023届高三11班\t0.429\t0.143",
+            "20230304\t2023届高三12班\t0.905\t0.524",
+            "20230304\t2023届高三01班\t0.963\t0.593",
+            "20230304\t2023届高三02班\t0.871\t0.419",
+            "20230304\t2023届高三03班\t1.000\t0.720",
+            "20230304\t2023届高三04班\t0.893\t0.464",
+            "20230304\t2023届高三05班\t0.895\t0.526",
+            "20230304\t2023届高三06班\t0.900\t0.675",
+            "20230304\t2023届高三07班\t0.938\t0.500",
+            "20230304\t2023届高三08班\t0.839\t0.355",
+            "20230304\t2023届高三09班\t0.839\t0.355"
+        ],
         "origin": "2023年空中课堂高三复习课11",
         "edit": [
             "20230131\t王伟叶"
@@ -349156,7 +350040,19 @@
         "ans": "$[\\dfrac{5\\pi}{18},\\dfrac{\\pi}2]$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三10班\t0.500",
+            "20230304\t2023届高三11班\t0.550",
+            "20230304\t2023届高三12班\t0.619",
+            "20230304\t2023届高三01班\t0.920",
+            "20230304\t2023届高三02班\t0.625",
+            "20230304\t2023届高三03班\t0.800",
+            "20230304\t2023届高三04班\t0.714",
+            "20230304\t2023届高三05班\t0.872",
+            "20230304\t2023届高三07班\t0.562",
+            "20230304\t2023届高三08班\t0.759",
+            "20230304\t2023届高三09班\t0.655"
+        ],
         "origin": "2023年空中课堂高三复习课11",
         "edit": [
             "20230131\t王伟叶"
@@ -350189,7 +351085,19 @@
         "ans": "$(-\\dfrac 12,2)\\cup (2,+\\infty)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.632",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三01班\t0.806",
+            "20230304\t2023届高三02班\t0.594",
+            "20230304\t2023届高三03班\t0.654",
+            "20230304\t2023届高三04班\t0.667",
+            "20230304\t2023届高三05班\t0.658",
+            "20230304\t2023届高三06班\t0.579",
+            "20230304\t2023届高三07班\t0.759",
+            "20230304\t2023届高三08班\t0.788",
+            "20230304\t2023届高三09班\t0.704"
+        ],
         "origin": "2023年空中课堂高三复习课12",
         "edit": [
             "20230202\t王伟叶"
@@ -350970,7 +351878,19 @@
         "ans": "(1) $2$或$-2$; (2) $1$; (3) $-2$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.895\t1.000\t1.000",
+            "20230304\t2023届高三12班\t0.714\t0.905\t0.857",
+            "20230304\t2023届高三01班\t0.903\t1.000\t1.000",
+            "20230304\t2023届高三02班\t1.000\t0.969\t1.000",
+            "20230304\t2023届高三03班\t0.962\t0.962\t0.962",
+            "20230304\t2023届高三04班\t1.000\t1.000\t1.000",
+            "20230304\t2023届高三05班\t0.921\t1.000\t0.974",
+            "20230304\t2023届高三06班\t1.000\t1.000\t1.000",
+            "20230304\t2023届高三07班\t0.862\t1.000\t1.000",
+            "20230304\t2023届高三08班\t0.909\t1.000\t1.000",
+            "20230304\t2023届高三09班\t0.778\t0.926\t0.963"
+        ],
         "origin": "2023年空中课堂高三复习课13",
         "edit": [
             "20230203\t王伟叶"
@@ -350989,7 +351909,19 @@
         "ans": "$2-2\\mathrm{i}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.895",
+            "20230304\t2023届高三12班\t0.905",
+            "20230304\t2023届高三01班\t0.968",
+            "20230304\t2023届高三02班\t0.938",
+            "20230304\t2023届高三03班\t0.923",
+            "20230304\t2023届高三04班\t0.926",
+            "20230304\t2023届高三05班\t0.842",
+            "20230304\t2023届高三06班\t0.947",
+            "20230304\t2023届高三07班\t0.897",
+            "20230304\t2023届高三08班\t0.849",
+            "20230304\t2023届高三09班\t0.815"
+        ],
         "origin": "2023年空中课堂高三复习课13",
         "edit": [
             "20230203\t王伟叶"
@@ -351008,7 +351940,19 @@
         "ans": "$\\sqrt{5}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.895",
+            "20230304\t2023届高三12班\t0.952",
+            "20230304\t2023届高三01班\t0.968",
+            "20230304\t2023届高三02班\t1.000",
+            "20230304\t2023届高三03班\t0.923",
+            "20230304\t2023届高三04班\t0.889",
+            "20230304\t2023届高三05班\t1.000",
+            "20230304\t2023届高三06班\t0.974",
+            "20230304\t2023届高三07班\t0.862",
+            "20230304\t2023届高三08班\t0.970",
+            "20230304\t2023届高三09班\t0.926"
+        ],
         "origin": "2023年空中课堂高三复习课13",
         "edit": [
             "20230203\t王伟叶"
@@ -351027,7 +351971,19 @@
         "ans": "$16$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.842",
+            "20230304\t2023届高三12班\t0.857",
+            "20230304\t2023届高三01班\t0.871",
+            "20230304\t2023届高三02班\t0.875",
+            "20230304\t2023届高三03班\t0.846",
+            "20230304\t2023届高三04班\t0.926",
+            "20230304\t2023届高三05班\t0.921",
+            "20230304\t2023届高三06班\t0.974",
+            "20230304\t2023届高三07班\t0.966",
+            "20230304\t2023届高三08班\t0.879",
+            "20230304\t2023届高三09班\t0.778"
+        ],
         "origin": "2023年空中课堂高三复习课13",
         "edit": [
             "20230203\t王伟叶"
@@ -351084,7 +352040,19 @@
         "ans": "(1) 轨迹方程为$(x-1)^2+(y-1)^2=1$, $|z|$的最大值为$1+\\sqrt{2}$; (2) 轨迹方程为$\\dfrac{y^2}{25}+\\dfrac{x^2}{16}=1$, $|z|$的最大值为$5$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.579\t0.526",
+            "20230304\t2023届高三12班\t0.476\t0.524",
+            "20230304\t2023届高三01班\t1.000\t0.968",
+            "20230304\t2023届高三02班\t0.812\t0.688",
+            "20230304\t2023届高三03班\t0.923\t0.885",
+            "20230304\t2023届高三04班\t0.741\t0.778",
+            "20230304\t2023届高三05班\t0.789\t0.816",
+            "20230304\t2023届高三06班\t0.868\t0.842",
+            "20230304\t2023届高三07班\t0.621\t0.621",
+            "20230304\t2023届高三08班\t0.667\t0.788",
+            "20230304\t2023届高三09班\t0.556\t0.518"
+        ],
         "origin": "2023年空中课堂高三复习课13",
         "edit": [
             "20230203\t王伟叶"
@@ -378312,7 +379280,18 @@
             "20220926\t2024届高二06班\t0.863\t0.825",
             "20220926\t2024届高二07班\t0.608\t0.703",
             "20220926\t2024届高二08班\t0.804\t0.848",
-            "20220926\t2024届高二09班\t0.708\t0.625"
+            "20220926\t2024届高二09班\t0.708\t0.625",
+            "20230304\t2023届高三11班\t0.772\t0.868",
+            "20230304\t2023届高三12班\t0.750\t0.792",
+            "20230304\t2023届高三01班\t0.938\t0.941",
+            "20230304\t2023届高三02班\t0.833\t0.848",
+            "20230304\t2023届高三03班\t0.806\t0.903",
+            "20230304\t2023届高三04班\t0.878\t0.833",
+            "20230304\t2023届高三05班\t0.733\t0.750",
+            "20230304\t2023届高三06班\t0.885\t0.888",
+            "20230304\t2023届高三07班\t0.798\t0.849",
+            "20230304\t2023届高三08班\t0.792\t0.805",
+            "20230304\t2023届高三09班\t0.818\t0.849"
         ],
         "origin": "2024届高二校本作业必修第十章",
         "edit": [
@@ -433136,7 +434115,19 @@
         "ans": "$[\\dfrac 72,+\\infty)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.842",
+            "20230304\t2023届高三12班\t0.708",
+            "20230304\t2023届高三01班\t0.906",
+            "20230304\t2023届高三02班\t0.781",
+            "20230304\t2023届高三03班\t0.742",
+            "20230304\t2023届高三04班\t0.933",
+            "20230304\t2023届高三05班\t0.750",
+            "20230304\t2023届高三06班\t0.846",
+            "20230304\t2023届高三07班\t0.849",
+            "20230304\t2023届高三08班\t0.844",
+            "20230304\t2023届高三09班\t0.727"
+        ],
         "origin": "2022届高三第二轮复习讲义-20230222修改",
         "edit": [
             "20230118\t王伟叶",
@@ -433160,7 +434151,19 @@
         "ans": "$[1,2)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230304\t2023届高三11班\t0.474",
+            "20230304\t2023届高三12班\t0.542",
+            "20230304\t2023届高三01班\t0.812",
+            "20230304\t2023届高三02班\t0.875",
+            "20230304\t2023届高三03班\t0.516",
+            "20230304\t2023届高三04班\t0.700",
+            "20230304\t2023届高三05班\t0.575",
+            "20230304\t2023届高三06班\t0.744",
+            "20230304\t2023届高三07班\t0.636",
+            "20230304\t2023届高三08班\t0.688",
+            "20230304\t2023届高三09班\t0.636"
+        ],
         "origin": "2022届高三第二轮复习讲义-20230222修改",
         "edit": [
             "20230118\t王伟叶",
@@ -433636,6 +434639,1051 @@
         "remark": "",
         "space": ""
     },
+    "031267": {
+        "id": "031267",
+        "content": "半径为$1$的球的表面积是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二上学期期末考试试题1",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031268": {
+        "id": "031268",
+        "content": "双曲线$x^2-y^2=1$的两条渐近线的夹角大小为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.929",
+            "20230302\t2024届高二11班\t0.969",
+            "20230302\t2024届高二12班\t0.966",
+            "20230302\t2024届高二01班\t0.974",
+            "20230302\t2024届高二02班\t1.000",
+            "20230302\t2024届高二03班\t1.000",
+            "20230302\t2024届高二04班\t0.971",
+            "20230302\t2024届高二05班\t0.968",
+            "20230302\t2024届高二06班\t0.952",
+            "20230302\t2024届高二07班\t0.954",
+            "20230302\t2024届高二08班\t0.917",
+            "20230302\t2024届高二09班\t0.955"
+        ],
+        "origin": "2024届高二上学期期末考试试题2",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031269": {
+        "id": "031269",
+        "content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, 直线$BD_1$与平面$ABCD$所成角的大小为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{1.5}\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 [dashed] (B)--(D1);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.821",
+            "20230302\t2024届高二11班\t0.812",
+            "20230302\t2024届高二12班\t0.897",
+            "20230302\t2024届高二01班\t0.974",
+            "20230302\t2024届高二02班\t0.925",
+            "20230302\t2024届高二03班\t0.853",
+            "20230302\t2024届高二04班\t0.765",
+            "20230302\t2024届高二05班\t0.968",
+            "20230302\t2024届高二06班\t0.881",
+            "20230302\t2024届高二07班\t0.930",
+            "20230302\t2024届高二08班\t0.833",
+            "20230302\t2024届高二09班\t0.864"
+        ],
+        "origin": "2024届高二上学期期末考试试题3",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031270": {
+        "id": "031270",
+        "content": "从$1,2,3,4,5,6,7,8,9$这$9$个数中任取$3$个不同的数, 则中位数为$5$的取法有\\blank{50}种.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.714",
+            "20230302\t2024届高二11班\t0.906",
+            "20230302\t2024届高二12班\t0.724",
+            "20230302\t2024届高二01班\t0.921",
+            "20230302\t2024届高二02班\t0.875",
+            "20230302\t2024届高二03班\t0.735",
+            "20230302\t2024届高二04班\t0.824",
+            "20230302\t2024届高二05班\t0.839",
+            "20230302\t2024届高二06班\t0.809",
+            "20230302\t2024届高二07班\t0.791",
+            "20230302\t2024届高二08班\t0.583",
+            "20230302\t2024届高二09班\t0.864"
+        ],
+        "origin": "2024届高二上学期期末考试试题4",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031271": {
+        "id": "031271",
+        "content": "已知圆锥的底面半径为$1$, 侧面积为$4 \\pi$, 则该圆锥的体积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.750",
+            "20230302\t2024届高二11班\t0.594",
+            "20230302\t2024届高二12班\t0.793",
+            "20230302\t2024届高二01班\t0.895",
+            "20230302\t2024届高二02班\t0.950",
+            "20230302\t2024届高二03班\t0.676",
+            "20230302\t2024届高二04班\t0.706",
+            "20230302\t2024届高二05班\t0.774",
+            "20230302\t2024届高二06班\t0.691",
+            "20230302\t2024届高二07班\t0.721",
+            "20230302\t2024届高二08班\t0.625",
+            "20230302\t2024届高二09班\t0.773"
+        ],
+        "origin": "2024届高二上学期期末考试试题5",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031272": {
+        "id": "031272",
+        "content": "两个实习生每人加工一个零件, 加工成一等品的概率分别为$\\dfrac{4}{5}$和$\\dfrac{9}{10}$, 两个零件是否加工成一等品相互独立, 则这两个零件中恰有一个一等品的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.714",
+            "20230302\t2024届高二11班\t0.875",
+            "20230302\t2024届高二12班\t0.966",
+            "20230302\t2024届高二01班\t0.974",
+            "20230302\t2024届高二02班\t0.900",
+            "20230302\t2024届高二03班\t0.971",
+            "20230302\t2024届高二04班\t0.941",
+            "20230302\t2024届高二05班\t1.000",
+            "20230302\t2024届高二06班\t0.857",
+            "20230302\t2024届高二07班\t0.977",
+            "20230302\t2024届高二08班\t0.917",
+            "20230302\t2024届高二09班\t0.909"
+        ],
+        "origin": "2024届高二上学期期末考试试题6",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031273": {
+        "id": "031273",
+        "content": "已知双曲线方程为$\\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$, 点$P$是该双曲线上的点, $F_1$、$F_2$分别是它的左、右焦点, 若$|PF_1| \\cdot|PF_2|=40$, 则$\\angle F_1PF_2$的大小为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.607",
+            "20230302\t2024届高二11班\t0.688",
+            "20230302\t2024届高二12班\t0.586",
+            "20230302\t2024届高二01班\t0.947",
+            "20230302\t2024届高二02班\t0.875",
+            "20230302\t2024届高二03班\t0.765",
+            "20230302\t2024届高二04班\t0.706",
+            "20230302\t2024届高二05班\t0.677",
+            "20230302\t2024届高二06班\t0.738",
+            "20230302\t2024届高二07班\t0.698",
+            "20230302\t2024届高二08班\t0.583",
+            "20230302\t2024届高二09班\t0.545"
+        ],
+        "origin": "2024届高二上学期期末考试试题7",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031274": {
+        "id": "031274",
+        "content": "设直线$a x-y+3=0$与圆$(x+1)^2+(y+2)^2=4$相交于$A$、$B$两点, 且弦$AB$长为$2 \\sqrt{3}$, 则实数$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.500",
+            "20230302\t2024届高二11班\t0.625",
+            "20230302\t2024届高二12班\t0.724",
+            "20230302\t2024届高二01班\t0.921",
+            "20230302\t2024届高二02班\t0.925",
+            "20230302\t2024届高二03班\t0.765",
+            "20230302\t2024届高二04班\t0.735",
+            "20230302\t2024届高二05班\t0.839",
+            "20230302\t2024届高二06班\t0.714",
+            "20230302\t2024届高二07班\t0.791",
+            "20230302\t2024届高二08班\t0.750",
+            "20230302\t2024届高二09班\t0.818"
+        ],
+        "origin": "2024届高二上学期期末考试试题8",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031275": {
+        "id": "031275",
+        "content": "已知样本容量为$5$的样本的平均数为$3$, 方差为$\\dfrac{18}{5}$, 现把一个新数据$15$加入原样本从而得到一个样本容量为$6$的新样本, 则该新样本的方差为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.464",
+            "20230302\t2024届高二11班\t0.688",
+            "20230302\t2024届高二12班\t0.552",
+            "20230302\t2024届高二01班\t0.789",
+            "20230302\t2024届高二02班\t0.800",
+            "20230302\t2024届高二03班\t0.676",
+            "20230302\t2024届高二04班\t0.559",
+            "20230302\t2024届高二05班\t0.806",
+            "20230302\t2024届高二06班\t0.524",
+            "20230302\t2024届高二07班\t0.605",
+            "20230302\t2024届高二08班\t0.458",
+            "20230302\t2024届高二09班\t0.455"
+        ],
+        "origin": "2024届高二上学期期末考试试题9",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031276": {
+        "id": "031276",
+        "content": "若方程$a x^2+b y^2=c$的系数$a, b, c$是从$-1,2,3,5,7,11,13$这$7$个数中任取$3$个不同的数而得到, 则这样的方程表示焦点在$x$轴上的椭圆的概率是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.857",
+            "20230302\t2024届高二11班\t0.844",
+            "20230302\t2024届高二12班\t0.931",
+            "20230302\t2024届高二01班\t0.921",
+            "20230302\t2024届高二02班\t0.975",
+            "20230302\t2024届高二03班\t0.971",
+            "20230302\t2024届高二04班\t0.794",
+            "20230302\t2024届高二05班\t0.935",
+            "20230302\t2024届高二06班\t0.881",
+            "20230302\t2024届高二07班\t0.907",
+            "20230302\t2024届高二08班\t0.927",
+            "20230302\t2024届高二09班\t0.864"
+        ],
+        "origin": "2024届高二上学期期末考试试题10",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031277": {
+        "id": "031277",
+        "content": "已知三棱锥$P-ABC$中, $PA$、$PB$、$PC$两两垂直, 且$|PA|=|PB|=|PC|$, 若$P$、$A$、$B$、$C$这四点都落在某个半径为$\\sqrt{3}$的球的球面上, 则该球的球心到平面$ABC$的距离为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.179",
+            "20230302\t2024届高二11班\t0.281",
+            "20230302\t2024届高二12班\t0.621",
+            "20230302\t2024届高二01班\t0.737",
+            "20230302\t2024届高二02班\t0.575",
+            "20230302\t2024届高二03班\t0.471",
+            "20230302\t2024届高二04班\t0.412",
+            "20230302\t2024届高二05班\t0.387",
+            "20230302\t2024届高二06班\t0.381",
+            "20230302\t2024届高二07班\t0.372",
+            "20230302\t2024届高二08班\t0.375",
+            "20230302\t2024届高二09班\t0.091"
+        ],
+        "origin": "2024届高二上学期期末考试试题11",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031278": {
+        "id": "031278",
+        "content": "点$P(m, n)$是椭圆$4 x^2+y^2=1$上的动点且点$P$不在坐标轴上, 动点$Q(\\dfrac{1}{m}, \\dfrac{1}{n})$构成的轨迹为曲线$\\Gamma$. 若圆$x^2+y^2=r^2(r>0)$与曲线$\\Gamma$无公共点, 则实数$r$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.000",
+            "20230302\t2024届高二11班\t0.000",
+            "20230302\t2024届高二12班\t0.035",
+            "20230302\t2024届高二01班\t0.105",
+            "20230302\t2024届高二02班\t0.175",
+            "20230302\t2024届高二03班\t0.059",
+            "20230302\t2024届高二04班\t0.059",
+            "20230302\t2024届高二05班\t0.000",
+            "20230302\t2024届高二06班\t0.048",
+            "20230302\t2024届高二07班\t0.116",
+            "20230302\t2024届高二08班\t0.000",
+            "20230302\t2024届高二09班\t0.000"
+        ],
+        "origin": "2024届高二上学期期末考试试题12",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031279": {
+        "id": "031279",
+        "content": "已知直线$l$是平面$\\alpha$的一条斜线, 则\\bracket{20}.\n\\onech{在平面$\\alpha$上存在唯一的一条直线$m$, 使得$l \\perp m$}{在平面$\\alpha$上存在唯一的一条直线$m$, 使得$l\\parallel m$}{在平面$\\alpha$上存在无数多条直线$m$, 使得$l \\perp m$}{在平面$\\alpha$上存在无数多条直线$m$, 使得$l\\parallel m$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.500",
+            "20230302\t2024届高二11班\t0.781",
+            "20230302\t2024届高二12班\t0.690",
+            "20230302\t2024届高二01班\t0.816",
+            "20230302\t2024届高二02班\t0.825",
+            "20230302\t2024届高二03班\t0.559",
+            "20230302\t2024届高二04班\t0.794",
+            "20230302\t2024届高二05班\t0.742",
+            "20230302\t2024届高二06班\t0.809",
+            "20230302\t2024届高二07班\t0.721",
+            "20230302\t2024届高二08班\t0.708",
+            "20230302\t2024届高二09班\t0.955"
+        ],
+        "origin": "2024届高二上学期期末考试试题13",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031280": {
+        "id": "031280",
+        "content": "从$6$名男医生、$4$名女医生中选$3$名医生组成一个医疗小分队, 要求其中男、女医生都有, 则不同的组队方案共有\\bracket{20}.\n\\fourch{$192$种}{$96$种}{$576$种}{$384$种}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.786",
+            "20230302\t2024届高二11班\t0.969",
+            "20230302\t2024届高二12班\t0.931",
+            "20230302\t2024届高二01班\t1.000",
+            "20230302\t2024届高二02班\t0.925",
+            "20230302\t2024届高二03班\t0.971",
+            "20230302\t2024届高二04班\t0.912",
+            "20230302\t2024届高二05班\t0.935",
+            "20230302\t2024届高二06班\t0.976",
+            "20230302\t2024届高二07班\t0.977",
+            "20230302\t2024届高二08班\t1.000",
+            "20230302\t2024届高二09班\t0.909"
+        ],
+        "origin": "2024届高二上学期期末考试试题14",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031281": {
+        "id": "031281",
+        "content": "在梯形$ABCD$中, $\\angle ABC=\\dfrac{\\pi}{2}$, $AD\\parallel BC$, $AB=2$, $BC=4$, $AD=2$. 将梯形$ABCD$绕直线$AD$旋转一周而形成的曲面所围成的几何体的体积为\\bracket{20}.\n\\fourch{$16 \\pi$}{$\\dfrac{40}{3} \\pi$}{$\\dfrac{32}{3} \\pi$}{$\\dfrac{16}{3} \\pi$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.786",
+            "20230302\t2024届高二11班\t0.719",
+            "20230302\t2024届高二12班\t0.862",
+            "20230302\t2024届高二01班\t0.974",
+            "20230302\t2024届高二02班\t0.900",
+            "20230302\t2024届高二03班\t0.853",
+            "20230302\t2024届高二04班\t0.853",
+            "20230302\t2024届高二05班\t0.968",
+            "20230302\t2024届高二06班\t0.929",
+            "20230302\t2024届高二07班\t0.930",
+            "20230302\t2024届高二08班\t0.917",
+            "20230302\t2024届高二09班\t0.818"
+        ],
+        "origin": "2024届高二上学期期末考试试题15",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031282": {
+        "id": "031282",
+        "content": "设$a, b$均为非零实数, 则直线$y=a x+b$和曲线$a y^2-b x^2=a b$在同一坐标系下的图形可能是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) ellipse ({sqrt(1.3)} and {sqrt(0.6)});\n\\draw (-0.6,{-1.3*(-0.6)+0.6}) -- (1.2,{-1.3*1.2+0.6});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -0.9:0.9] plot ({sqrt(0.5*(1+\\x*\\x/0.3))},\\x) plot ({-sqrt(0.5*(1+\\x*\\x/0.3))},\\x);\n\\draw (-1.5,{0.3*(-1.5)-0.3}) -- (1.5,{0.3*1.5-0.3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) ellipse ({sqrt(0.6)} and {sqrt(1.3)});\n\\draw (-1,{-1.5*(-1)-0.3}) -- (0.7,{-1.5*0.7-0.3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1.5:1.5] plot (\\x,{sqrt(0.4*(1+\\x*\\x/0.8))}) plot (\\x,{-sqrt(0.4*(1+\\x*\\x/0.8))});\n\\draw (-0.2,{2*(-0.2)-1.1}) -- (1.3,{2*1.3-1.1});\n\\end{tikzpicture}}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.786",
+            "20230302\t2024届高二11班\t0.812",
+            "20230302\t2024届高二12班\t0.897",
+            "20230302\t2024届高二01班\t0.974",
+            "20230302\t2024届高二02班\t0.950",
+            "20230302\t2024届高二03班\t0.971",
+            "20230302\t2024届高二04班\t0.912",
+            "20230302\t2024届高二05班\t0.903",
+            "20230302\t2024届高二06班\t0.905",
+            "20230302\t2024届高二07班\t0.930",
+            "20230302\t2024届高二08班\t0.667",
+            "20230302\t2024届高二09班\t0.955"
+        ],
+        "origin": "2024届高二上学期期末考试试题16",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031283": {
+        "id": "031283",
+        "content": "某电子商务公司对$20000$名网络购物者$2022$年度的消费情况进行统计, 发现所有购物者的消费金额(单位: 万元)都在区间$[0.3,0.9]$内, 其频率分布直方图如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 7]\n\\draw [->] (0,0) -- (1.1,0) node [below] {金额/万元};\n\\draw [->] (0,0) -- (0,3.5) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j/\\k in {0.3/1.5/1.5,0.4/2.5/2.5,0.5/3/a,0.6/2/2,0.7/0.8/0.8,0.8/0.2/0.2}\n{\\draw (\\i,0) node [below] {$\\i$};\n\\draw (\\i,0) -- (\\i,\\j) --++ (0.1,0) --++ (0,-\\j);\n\\draw [dashed] (0,\\j) node [left] {$\\k$} -- (\\i,\\j);\n};\n\\draw (0.9,0) node [below] {$0.9$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求频率分布直方图中$a$的值, 并求在这些购物者中, 消费金额在区间$[0.6,0.9]$内的购物者的人数;\\\\\n(2) 对消费金额在区间$[0.6,0.7)$、$[0.7,0.8)$、$[0.8,0.9]$内的三组购物者中用分层随机抽样的方法共抽取$90$名购物者, 则消费金额在区间$[0.7,0.8)$内的购物者应抽取多少名?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.964",
+            "20230302\t2024届高二11班\t0.893",
+            "20230302\t2024届高二12班\t0.929",
+            "20230302\t2024届高二01班\t0.993",
+            "20230302\t2024届高二02班\t0.968",
+            "20230302\t2024届高二03班\t0.937",
+            "20230302\t2024届高二04班\t0.933",
+            "20230302\t2024届高二05班\t0.963",
+            "20230302\t2024届高二06班\t0.959",
+            "20230302\t2024届高二07班\t0.930",
+            "20230302\t2024届高二08班\t0.917",
+            "20230302\t2024届高二09班\t0.942"
+        ],
+        "origin": "2024届高二上学期期末考试试题17",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031284": {
+        "id": "031284",
+        "content": "如图, 在Rt$\\triangle AOB$中, $\\angle AOB$为直角, $AO=4$, $BO=2$. Rt$\\triangle AOC$可以通过Rt$\\triangle AOB$以直线$AO$为轴旋转得到, 且二面角$B-AO-C$是直二面角. 动点$D$在线段$AB$上.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (0,0,0) node [above right] {$O$} coordinate (O);\n\\draw (2,0,0) node [right] {$B$} coordinate (B);\n\\draw (0,0,2) node [below left] {$C$} coordinate (C);\n\\draw (0,4,0) node [above] {$A$} coordinate (A);\n\\draw ($(A)!0.4!(B)$) node [right] {$D$} coordinate (D);\n\\draw (A)--(B)--(C)--cycle(C)--(D);\n\\draw [dashed] (A)--(O)--(B)(O)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 当$D$为$AB$的中点时, 求异面直线$AO$与$CD$所成角的大小;\\\\\n(2) 求$CD$与平面$AOB$所成角的最大值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.686",
+            "20230302\t2024届高二11班\t0.799",
+            "20230302\t2024届高二12班\t0.820",
+            "20230302\t2024届高二01班\t0.917",
+            "20230302\t2024届高二02班\t0.863",
+            "20230302\t2024届高二03班\t0.813",
+            "20230302\t2024届高二04班\t0.847",
+            "20230302\t2024届高二05班\t0.862",
+            "20230302\t2024届高二06班\t0.804",
+            "20230302\t2024届高二07班\t0.865",
+            "20230302\t2024届高二08班\t0.655",
+            "20230302\t2024届高二09班\t0.828"
+        ],
+        "origin": "2024届高二上学期期末考试试题18",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031285": {
+        "id": "031285",
+        "content": "已知椭圆$C$的方程为$\\dfrac{x^2}{2}+y^2=1$, $F_1$、$F_2$分别是它的左、右焦点.\\\\\n(1) 求椭圆$C$的长轴长以及离心率;\\\\\n(2) 过点$F_2$的直线$l$与椭圆$C$相交于$P$、$Q$两点, $O$为坐标原点, 若直线$l$的斜率为$k$且$\\overrightarrow{OP} \\perp \\overrightarrow{OQ}$, 求直线$l$的方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.699",
+            "20230302\t2024届高二11班\t0.790",
+            "20230302\t2024届高二12班\t0.690",
+            "20230302\t2024届高二01班\t0.885",
+            "20230302\t2024届高二02班\t0.905",
+            "20230302\t2024届高二03班\t0.805",
+            "20230302\t2024届高二04班\t0.681",
+            "20230302\t2024届高二05班\t0.827",
+            "20230302\t2024届高二06班\t0.835",
+            "20230302\t2024届高二07班\t0.829",
+            "20230302\t2024届高二08班\t0.688",
+            "20230302\t2024届高二09班\t0.867"
+        ],
+        "origin": "2024届高二上学期期末考试试题19",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031286": {
+        "id": "031286",
+        "content": "我国古代数学名著《九章算术》中记载: ``刍甍者, 下有袤有广, 而上有袤无广. 刍, 草也. 甍, 屋盖也. ''翻译为``底面有长有宽为矩形, 顶部只有长没有宽为一条棱. 刍甍的字面意思为茅草屋顶. ''\n现有一个``刍甍''如图所示, 四边形$ABCD$为正方形, 四边形$ABFE$、$CDEF$为两个全等的等腰梯形, $EF\\parallel AB$, $AB=4$, $EF=2$, $EA=ED=FB=FC=\\sqrt{10}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw (-2,0,2) node [left] {$A$} coordinate (A);\n\\draw (2,0,2) node [right] {$B$} coordinate (B);\n\\draw (2,0,-2) node [right] {$C$} coordinate (C);\n\\draw (-2,0,-2) node [below] {$D$} coordinate (D);\n\\draw (-1,{sqrt(5)},0) node [above] {$E$} coordinate (E);\n\\draw (1,{sqrt(5)},0) node [above] {$F$} coordinate (F);\n\\draw (E)--(A)--(B)--(C)--(F)--cycle(B)--(F);\n\\draw [dashed] (E)--(D)--(A)(D)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 设过点$F$且与直线$EF$垂直的平面为平面$\\alpha$, 且平面$\\alpha$与直线$AB$、$CD$分别交于$P$、$Q$两点, 求$\\triangle FPQ$的周长;\\\\\n(2) 求四面体$ABDE$的体积;\\\\\n(3) 点$N$在线段$AD$上且满足$\\dfrac{AN}{AD}=\\dfrac{1}{3}$. 试问: 在线段$CF$上是否存在点$M$, 使$NF\\parallel$平面$BDM$? 若存在, 求出$\\dfrac{CM}{CF}$的值; 若不存在, 请说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二上学期期末考试试题20",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031287": {
+        "id": "031287",
+        "content": "已知椭圆$\\Gamma$的方程为$\\dfrac{x^2}{a^2}+\\dfrac{y^2}{9}=1$(常数$a>3$), 点$A$、$B$分别为椭圆短轴的上端点、 下端点, 点$P$是椭圆$\\Gamma$上异于点$A$的一个动点. 若动点$P$到定点$A$的距离的最大值仅在点$P$运动到点$B$时取到, 则称此椭圆为``圆椭圆''.\\\\\n(1) 若$a=5$, 判断椭圆$\\Gamma$是否为``圆椭圆'';\\\\\n(2) 若椭圆$\\Gamma$是``圆椭圆'', 求$a$的取值范围;\\\\\n(3) 已知椭圆$\\Gamma$是``圆椭圆'', 且$a$取最大值. 点$P$关于原点$O$的对称点为点$Q$(点$Q$也异于点$A$), 且直线$AP$、$AQ$分别与$x$轴交于$M$、$N$两点. 试问以线段$MN$为直径的圆是否过定点? 证明你的结论.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [
+            "20230302\t2024届高二10班\t0.155",
+            "20230302\t2024届高二11班\t0.309",
+            "20230302\t2024届高二12班\t0.330",
+            "20230302\t2024届高二01班\t0.547",
+            "20230302\t2024届高二02班\t0.597",
+            "20230302\t2024届高二03班\t0.328",
+            "20230302\t2024届高二04班\t0.284",
+            "20230302\t2024届高二05班\t0.272",
+            "20230302\t2024届高二06班\t0.352",
+            "20230302\t2024届高二07班\t0.397",
+            "20230302\t2024届高二08班\t0.208",
+            "20230302\t2024届高二09班\t0.197"
+        ],
+        "origin": "2024届高二上学期期末考试试题21",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031288": {
+        "id": "031288",
+        "content": "已知全集$U=\\{x | 2<x \\leq 10\\}$, $A=\\{x | 2<x<7\\}$, 则$\\overline {A}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题1",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031289": {
+        "id": "031289",
+        "content": "函数$f(x)=\\dfrac{\\sqrt{3-x}}{2+x}$的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题2",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031290": {
+        "id": "031290",
+        "content": "已知幂函数$f(x)=(m^2+m-5) \\cdot x^{m^2-3 m-2}$的图像不经过原点, 则实数$m=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题3",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031291": {
+        "id": "031291",
+        "content": "数列$\\{a_n\\}$中, 若$a_1=3$, 且$a_{n+1}=a_n+\\dfrac{1}{2}$, 则$a_9=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题4",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031292": {
+        "id": "031292",
+        "content": "``函数$f(x)=x^2-2 a x-1$在区间$[1,3]$上为严格减函数''的充要条件是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题5",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031293": {
+        "id": "031293",
+        "content": "设函数$f(x)=\\begin{cases}-x,& x \\leq 0, \\\\ x^2, & x>0\\end{cases}$ 若$f(a)=9$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题6",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031294": {
+        "id": "031294",
+        "content": "若数列$\\{a_n\\}$满足$a_{n+1}=-\\dfrac{1}{3} a_n$, 前$5$项和为$\\dfrac{61}{27}$, 则$a_5=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题7",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031295": {
+        "id": "031295",
+        "content": "若定义在$\\mathbf{R}$上的奇函数$f(x)$在$[0,+\\infty)$上的图像如图所示, 则不等式$x \\cdot f(x) \\geq 0$的解集是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [->] (-5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3.8] plot (\\x,{\\x*(3-\\x)/2.25*3});\n\\draw [dashed] (0,3) -- (1.5,3);\n\\draw (0,3) node [left] {$3$} (3,0) node [below] {$3$};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题8",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031296": {
+        "id": "031296",
+        "content": "已知$a_n=\\dfrac{n-\\sqrt{2022}}{n-\\sqrt{2023}}$($n$为正整数), 且数列$\\{a_n\\}$共有$100$项, 则此数列中最大项为第\\blank{50}项.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题9",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031297": {
+        "id": "031297",
+        "content": "已知函数$f(x)=\\begin{cases}\\log _a x, &  0<x \\leq 1, \\\\ (3-a) \\cdot x-a, & x>1\\end{cases}$在$(0,+\\infty)$上严格单调增, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题10",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031298": {
+        "id": "031298",
+        "content": "已知函数$f(x)=a^2 \\cdot x+3 a$, $x \\in[-\\dfrac{1}{2}, 1]$, 与函数$g(x)=(\\dfrac{1}{5})^x-1$, $x \\in[-1,0]$. 对任意的$x_1 \\in[-\\dfrac{1}{2}, 1]$, 总存在$x_2 \\in[-1,0]$, 使得$f(x_1)=g(x_2)$成立, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题11",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031299": {
+        "id": "031299",
+        "content": "已知函数$f(x)=x^3+\\lg \\dfrac{5+x}{5-x}+2$, 若实数$a$、$b$满足$f(3 a^2)+f(b^2-1)=4$, 则$a \\sqrt{1+2 b^2}$的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题12",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031300": {
+        "id": "031300",
+        "content": "已知$a, b \\in \\mathbf{R}$, 则$a b(a-b)<0$成立的一个充要条件是\\bracket{20}.\n\\fourch{$\\dfrac{1}{a}>\\dfrac{1}{b}>0$}{$\\dfrac{1}{a}<\\dfrac{1}{b}$}{$0<\\dfrac{1}{a}<\\dfrac{1}{b}$}{$\\dfrac{1}{a}>\\dfrac{1}{b}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题13",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031301": {
+        "id": "031301",
+        "content": "若函数$y=\\log _2(k x^2+4 k x+3)$的定义域为$\\mathbf{R}$, 则$k$的取值范围是\\bracket{20}.\n\\fourch{$(0, \\dfrac{3}{4})$}{$[0, \\dfrac{3}{4})$}{$[0, \\dfrac{3}{4}]$}{$(-\\infty, 0] \\cup(\\dfrac{3}{4},+\\infty)$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题14",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031302": {
+        "id": "031302",
+        "content": "等差数列$\\{a_n\\}$中, 首项为$a_1$公差$d$不为零, 前$n$项和为$S_n$. 若$S_8$是$S_4$的 3倍, 则$a_1$与$d$的比为\\bracket{20}.\n\\fourch{$5: 2$}{$2: 5$}{$5: 1$}{$1: 5$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题15",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031303": {
+        "id": "031303",
+        "content": "已知非空集合$A, B$满足: $A \\cup B=\\mathbf{R}$, $A \\cap B=\\varnothing$. 已知函数$f(x)=\\begin{cases}-x^2, & x \\in A, \\\\ -2 x+1, & x \\in B,\\end{cases}$ 对于下列两个命题: \\textcircled{1} 存在无穷多非空集合对$(A, B)$, 使得方程$f(x)=-2$无解; \\textcircled{2} 存在唯一的非空集合对$(A, B)$, 使得$f(x)$为偶函数. 下面判断正确的是\\bracket{20}.\n\\fourch{\\textcircled{1}正确, \\textcircled{2}错误}{\\textcircled{1}错误, \\textcircled{2}正确}{\\textcircled{1}、\\textcircled{2}都正确}{\\textcircled{1}、 \\textcircled{2}都错误}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题16",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "031304": {
+        "id": "031304",
+        "content": "已知等差数列$\\{a_n\\}$中, 首项$a_1=16$, 公差$d \\neq 0$, 且$a_1, a_5, a_6$是等比数列$\\{b_n\\}$的前三项.\\\\\n(1) 求数列$\\{a_n\\}$与$\\{b_n\\}$的通项公式;\\\\\n(2) 设数列$\\{a_n\\}$的前$n$项和为$S_n$, 且记$T_n=\\log _4 b_n^n$, 试比较$S_n$与$T_n$的大小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题17",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031305": {
+        "id": "031305",
+        "content": "已知函数$f(x)=|2 x-a|+a$.\\\\\n(1) 当$a=2$时, 求不等式$f(x) \\leq 6$的解集;\\\\\n(2) 设$g(x)=|2 x-1|$, 若不等式$f(x)+g(x) \\geq 3$对任意$x \\in \\mathbf{R}$恒成立, 求实数$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题18",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031306": {
+        "id": "031306",
+        "content": "新冠肺炎疫情发生以来, 口罩供不应求, 某口罩厂日夜加班生产, 为抗击疫情做贡献. 生产口罩的固定成本为$400$万元, 然后每生产$x$万箱($x \\in \\mathbf{N}$, $x>0$), 需另外投入生产成本$p(x)$万元: 当产量不足$60$万箱时, $p(x)=\\dfrac{1}{2} x^2+50 x$; 当产量不小于$60$万箱时, $p(x)=101 x+\\dfrac{6400}{x}-1860$. 若每箱口罩售价$100$元, 通过市场分析, 该口罩厂生产的口罩可以全部销售完.\\\\\n(1) 求口罩销售利润$y$(万元)关于产量$x$(万箱)的函数关系式;(定义: 销售利润$=$销售总价固定成本$-$生产成本)\\\\\n(2) 当产量为多少万箱时, 该口罩生产厂所获得利润最大, 最大利润值是多少(万元)?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题19",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031307": {
+        "id": "031307",
+        "content": "已知数列$\\{a_n\\}$的前$n$项和$S_n$满足: $S_n=\\dfrac{m}{m-1}(a_n-1)$($m$为常数, 且$m \\neq 0$, $m \\neq 1$).\\\\\n(1) 求$\\{a_n\\}$的通项公式 (结果用含$m$的式子表示); \\\\\n(2) 设$b_n=\\dfrac{2S_n}{a_n}+1$, 若数列$\\{b_n\\}$为等比数列, 求$m$的值;\\\\\n(3) 若数列$\\{b_n\\}$是 (2) 中的等比数列, 记数列$\\{c_n\\}$的第$n$项$c_n=(n-1) b_n$, 求数列$\\{c_n\\}$的前$n$项和$T_n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题20",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "031308": {
+        "id": "031308",
+        "content": "已知函数$f(x)=2^x$($x \\in \\mathbf{R}$), 记$g(x)=f(x)-f(-x)$, $h(x)=f(x)+f(-x)$.\\\\\n(1) 求不等式的解集: $f(2 x)-2 f(x) \\leq 8$;\\\\\n(2) 设$t$为实数, 若存在实数$x_0 \\in[1,2]$, 使得$h(2 x_0)=t \\cdot g(x_0)-1$成立, 求$t$的取值范围;\\\\\n(3) 记$H(x)=8 \\cdot f(2 x)+2 a \\cdot f(x)+2 b$(其中$a$、$b$均为实数), 若对于任意的$x \\in[0,1]$, 均有$|H(x)| \\leq 1$, 求$a$、$b$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一上学期期末考试试题21",
+        "edit": [
+            "20230303\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
     "040001": {
         "id": "040001",
         "content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",
@@ -435327,7 +437375,7 @@
         "content": "化简: $\\sin (\\alpha-30^{\\circ}) \\cdot \\sin \\alpha+\\cos (\\alpha-30^{\\circ}) \\cdot \\cos \\alpha=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435346,7 +437394,7 @@
         "content": "化简: $\\cos x+\\cos (120^{\\circ}-x)+\\cos (120^{\\circ}+x)=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435365,7 +437413,7 @@
         "content": "方程$\\cos x=1$, $x \\in[-2 \\pi, 0]$的解集是\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435384,7 +437432,7 @@
         "content": "已知$\\tan x=-\\dfrac{\\sqrt{3}}{3}$, $x \\in[-\\pi, \\pi)$, 则$x=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435403,7 +437451,7 @@
         "content": "化简: $\\dfrac{\\cos (\\alpha+\\beta)+\\cos (\\alpha-\\beta)}{\\sin (\\alpha+\\beta)+\\sin (\\alpha-\\beta)}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435422,7 +437470,7 @@
         "content": "若$\\tan \\alpha=2$, 则$\\dfrac{\\sin (\\alpha+\\dfrac{\\pi}{3})}{\\sin (\\alpha-\\dfrac{\\pi}{3})}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435441,7 +437489,7 @@
         "content": "若$\\sin (\\alpha-\\dfrac{\\pi}{4})=\\dfrac{\\sqrt{6}-\\sqrt{2}}{4}$, 则$\\cos (\\alpha+\\dfrac{\\pi}{4})=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435460,7 +437508,7 @@
         "content": "若$\\alpha$是锐角, 且$\\sin (\\alpha-\\dfrac{\\pi}{6})=\\dfrac{1}{6}$, 则$\\sin \\alpha=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435479,7 +437527,7 @@
         "content": "已知$\\cos \\alpha=\\dfrac{1}{7}$, $\\cos (\\alpha+\\beta)=-\\dfrac{11}{14}$, 且$\\alpha$、$\\beta$均为锐角, 则$\\cos \\beta$的值为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435498,7 +437546,7 @@
         "content": "若$\\dfrac{\\sin (A-B)}{\\sin (A+B)}=\\dfrac{2}{3}$, 则$\\dfrac{\\tan A}{\\tan B}$的值为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435517,7 +437565,7 @@
         "content": "若$\\cos A+\\cos B+\\cos C=0$, $\\sin A+\\sin B+\\sin C=0$, 则$\\cos (A-B)=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435536,7 +437584,7 @@
         "content": "满足方程$\\sin (2 x+\\dfrac{\\pi}{4})=\\cos (\\dfrac{\\pi}{6}-x)$的最小的正角是\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435555,7 +437603,7 @@
         "content": "方程$2 \\sin ^2 x-5 \\cos x-4=0$的解集是\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435574,7 +437622,7 @@
         "content": "若$x=\\dfrac{\\pi}{3}$是方程$2 \\cos (x+\\theta)=1$的解, 其中$\\theta \\in(0,2 \\pi)$, 则$\\theta=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435593,7 +437641,7 @@
         "content": "若$\\alpha$、$\\beta \\in(0, \\dfrac{\\pi}{2})$, 则下列各式中成立的序号为\\blank{50}.\\\\\n\\textcircled{1} $\\cos (\\alpha+\\beta)>0$; \\textcircled{2} $\\cos (\\alpha+\\beta)<0$; \\textcircled{3} $\\cos (\\alpha-\\beta)<\\cos (\\alpha+\\beta)$; \\textcircled{4} $\\cos (\\alpha-\\beta)>\\cos (\\alpha+\\beta)$.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435612,7 +437660,7 @@
         "content": "若$S_n=\\sin \\dfrac{\\pi}{7}+\\sin \\dfrac{2 \\pi}{7}+\\sin \\dfrac{3 \\pi}{7}+\\ldots+\\sin \\dfrac{n \\pi}{7}$($n \\geq 1$, $n \\in \\mathbf{N}$), 则在$S_1, S_2, S_3, \\ldots, S_{100}$中, 正数的个数是\\bracket{20}.\n\\fourch{$16$}{$72$}{$86$}{$100$}",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "选择题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435631,7 +437679,7 @@
         "content": "若$\\sin \\alpha=\\dfrac{1}{3}$, $\\cos \\beta=-\\dfrac{1}{2}$, 且$\\alpha \\in(0, \\dfrac{\\pi}{2})$, $\\beta \\in(\\dfrac{\\pi}{2}, \\pi)$, 求$\\cos (\\alpha+\\beta)$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435643,14 +437691,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040100": {
         "id": "040100",
         "content": "已知$\\cos (\\alpha+\\beta)=\\dfrac{4}{5}$, $\\cos (\\alpha-\\beta)=-\\dfrac{4}{5}$, $\\alpha+\\beta \\in(\\dfrac{7 \\pi}{4}, 2 \\pi)$, $\\alpha-\\beta \\in(\\dfrac{3 \\pi}{4}, \\pi)$, 求$\\cos 2 \\alpha$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435662,14 +437710,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040101": {
         "id": "040101",
         "content": "已知锐角$\\alpha, \\beta, \\gamma$满足$\\sin \\alpha+\\sin \\gamma=\\sin \\beta$, $\\cos \\alpha-\\cos \\gamma=\\cos \\beta$, 求$\\alpha-\\beta$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435681,14 +437729,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040102": {
         "id": "040102",
         "content": "在直角坐标系$x O y$中, 线段$OM$绕着原点$O$逆时针旋转大小为$\\dfrac{\\pi}{2}$的角至$OM'$. 设点$M$的坐标为$(\\dfrac{5}{13}, \\dfrac{12}{13})$, 求点$M'$的坐标.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435700,14 +437748,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040103": {
         "id": "040103",
         "content": "在直角坐标系$x O y$中, 线段$OM$绕着原点$O$顺时针旋转大小为$\\dfrac{\\pi}{3}$的角至$OM'$. 设点$M$的坐标为$(5,12)$, 求点$M'$的坐标.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435719,14 +437767,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040104": {
         "id": "040104",
         "content": "已知$\\sin A=4 \\sin (A+B)$, 求证: $\\tan (A+B)=\\dfrac{\\sin B}{\\cos B-4}$.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435738,14 +437786,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040105": {
         "id": "040105",
         "content": "若$\\sin \\alpha=\\dfrac{8}{17}$, $\\cos \\beta=-\\dfrac{5}{13}$, $\\alpha, \\beta \\in(\\dfrac{\\pi}{2}, \\pi)$, 则$\\cos (\\alpha-\\beta)=\\cos (\\alpha+\\beta)=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435764,7 +437812,7 @@
         "content": "方程$\\cos x=-1$, $x \\in[-2 \\pi, 0]$的解集是\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435783,7 +437831,7 @@
         "content": "已知$\\alpha \\in(0, \\dfrac{\\pi}{2})$, $\\beta \\in(0, \\dfrac{\\pi}{2})$.如果$\\cos \\beta=\\dfrac{2 \\sqrt{2}}{3}$, $\\cos (\\alpha+\\beta)=\\dfrac{3}{5}$, 则$\\sin \\alpha=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435802,7 +437850,7 @@
         "content": "化简$\\dfrac{\\sin (\\theta-5 \\pi)}{\\tan (3 \\pi-\\theta)} \\cdot \\dfrac{\\cot (\\dfrac{\\pi}{2}-\\theta)}{\\tan (\\theta-\\dfrac{3 \\pi}{2})} \\cdot \\dfrac{\\cos (8 \\pi-\\theta)}{\\sin (-\\theta-4 \\pi)}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435821,7 +437869,7 @@
         "content": "已知$\\alpha, \\beta \\in(\\dfrac{3 \\pi}{4}, \\pi)$, $\\sin (\\alpha+\\beta)=-\\dfrac{3}{5}$, $\\sin (\\beta-\\dfrac{\\pi}{4})=\\dfrac{12}{13}$, 则$\\cos (\\alpha+\\dfrac{\\pi}{4})=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435840,7 +437888,7 @@
         "content": "已知$\\sin \\alpha=\\dfrac{\\sqrt{5}}{5}$, $\\sin \\beta=\\dfrac{\\sqrt{10}}{10}$, $\\alpha$、$\\beta$都是锐角, 求$\\alpha+\\beta$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435852,14 +437900,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040111": {
         "id": "040111",
         "content": "求证: $\\dfrac{1-2 \\sin \\alpha \\cos \\alpha}{\\tan \\alpha-1}=\\dfrac{1}{\\tan \\alpha+\\cot \\alpha}-\\cos ^2 \\alpha$.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435871,14 +437919,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040112": {
         "id": "040112",
         "content": "已知$\\dfrac{\\cos ^4 \\alpha}{\\cos ^2 \\beta}+\\dfrac{\\sin ^4 \\alpha}{\\sin ^2 \\beta}=1$. 求证: $\\dfrac{\\sin ^4 \\beta}{\\cos ^2 \\alpha}+\\dfrac{\\sin ^4 \\beta}{\\sin ^2 \\alpha}=1$.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435890,14 +437938,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040113": {
         "id": "040113",
         "content": "已知$\\sin x=\\dfrac{3}{5}$, $\\cos y=\\dfrac{4}{5}$, 其中$x, y$是第一象限角, 则$\\cos (x+y)=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435916,7 +437964,7 @@
         "content": "已知$\\sin x=\\dfrac{3}{5}$, 则$\\cos 2 x=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435935,7 +437983,7 @@
         "content": "已知$\\cos (\\alpha+\\dfrac{\\pi}{6})=\\dfrac{3}{5}$, $\\alpha \\in[0, \\pi)$, 则$\\sin \\alpha=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435954,7 +438002,7 @@
         "content": "已知$\\tan \\alpha=-\\dfrac{1}{7}$, $\\tan (2 \\alpha-\\beta)=2$, 则$\\tan (\\alpha-\\beta)=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435973,7 +438021,7 @@
         "content": "化简: $(\\cos ^4 \\theta-\\sin ^4 \\theta) \\dfrac{\\tan \\theta}{1-\\tan ^2 \\theta}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -435992,7 +438040,7 @@
         "content": "$\\cos 12^{\\circ} \\cos 24^{\\circ} \\cos 48^{\\circ} \\cos 96^{\\circ}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436011,7 +438059,7 @@
         "content": "$\\cos ^2 \\alpha+\\cos ^2(\\dfrac{\\pi}{3}+\\alpha)+\\cos ^2(\\dfrac{\\pi}{3}-\\alpha)=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436030,7 +438078,7 @@
         "content": "$\\sin \\dfrac{\\alpha}{2} \\cos \\dfrac{\\alpha}{2}=\\dfrac{1}{6}$, 则$\\sin \\alpha=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436049,7 +438097,7 @@
         "content": "若$\\cos (\\dfrac{\\pi}{4}-\\theta) \\cdot \\cos (\\dfrac{\\pi}{4}+\\theta)=\\dfrac{1}{3}$, 则$\\sin ^4 \\theta+\\cos ^4 \\theta=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436068,7 +438116,7 @@
         "content": "已知$\\dfrac{3 \\pi}{2}<\\alpha<2 \\pi$, 化简: $\\sqrt{\\dfrac{1}{2}-\\dfrac{1}{2} \\sqrt{\\dfrac{1}{2}+\\dfrac{1}{2} \\cos 2 \\alpha}}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436087,7 +438135,7 @@
         "content": "若$x$为锐角, 则$\\sqrt{1+\\sin x}+\\sqrt{1-\\sin x}-\\sqrt{2+2 \\cos x}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436106,7 +438154,7 @@
         "content": "已知$\\dfrac{\\pi}{2}<\\alpha<\\pi$, $-\\pi<\\beta<0$, $\\tan \\alpha=-\\dfrac{1}{3}$, $\\tan \\beta=-\\dfrac{1}{7}$, 则$2 \\alpha+\\beta$的大小为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436125,7 +438173,7 @@
         "content": "已知$x, y \\in(0, \\dfrac{\\pi}{2})$, $\\sin x=\\dfrac{\\sqrt{2}}{10}$, $\\sin y=\\dfrac{\\sqrt{10}}{10}$, 则$2 x+4 y$的值为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436144,7 +438192,7 @@
         "content": "已知$\\dfrac{\\pi}{2}<\\alpha<\\pi$, 且$\\sin \\alpha=\\dfrac{3}{5}$, $\\tan (\\alpha-\\beta)=-1$, 则$2 \\cos ^2 \\beta-\\dfrac{4}{5} \\tan \\dfrac{\\alpha}{2}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436163,7 +438211,7 @@
         "content": "设$\\alpha, \\beta \\in(-\\dfrac{\\pi}{2}, \\dfrac{\\pi}{2})$, $\\tan \\alpha$、$\\tan \\beta$是一元二次方程$x^2+3 \\sqrt{3} x-8=0$的两个根, 求$\\alpha+\\beta$.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436175,14 +438223,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040128": {
         "id": "040128",
         "content": "化简$\\sin ^2 \\alpha \\cdot \\sin ^2 \\beta+\\cos ^2 \\alpha \\cdot \\cos ^2 \\beta-\\dfrac{1}{2} \\cdot \\cos 2 \\alpha \\cdot \\cos 2 \\beta$.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436194,14 +438242,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040129": {
         "id": "040129",
         "content": "已知$\\dfrac{\\pi}{4}<\\alpha<\\dfrac{\\pi}{2}$, 且$\\dfrac{2 \\sin ^2 \\alpha+\\sin 2 \\alpha}{1+\\tan \\alpha}=k$, 试用$k$表示$\\sin \\alpha-\\cos \\alpha$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436213,14 +438261,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040130": {
         "id": "040130",
         "content": "已知: $\\cos (\\alpha-\\dfrac{\\beta}{2})=-\\dfrac{1}{9}$, $\\sin (\\dfrac{\\alpha}{2}-\\beta)=\\dfrac{2}{3}$, 且$\\dfrac{\\pi}{2}<\\alpha<\\pi,  0<\\beta<\\dfrac{\\pi}{2}$. 求$\\cos (\\alpha+\\beta)$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436232,14 +438280,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040131": {
         "id": "040131",
         "content": "若$\\cos \\alpha=\\dfrac{4}{5}$, 且$\\alpha$是第四象限角, 则$\\tan \\alpha+\\cot \\alpha=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436258,7 +438306,7 @@
         "content": "若$\\sin 2 \\alpha=\\dfrac{4}{5}$, 则$\\tan \\alpha+\\cot \\alpha=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436277,7 +438325,7 @@
         "content": "若$\\sin \\alpha=\\dfrac{\\sqrt{5}}{5}, \\alpha \\in(0, \\dfrac{\\pi}{2}), \\cos \\beta=\\dfrac{\\sqrt{10}}{10}, \\beta \\in(0, \\dfrac{\\pi}{2})$, 则$\\alpha-\\beta=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436296,7 +438344,7 @@
         "content": "计算: $\\cos 76^{\\circ} \\cos 44^{\\circ}+\\cos 166^{\\circ} \\cos 46^{\\circ}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436315,7 +438363,7 @@
         "content": "若$\\tan \\alpha=3$, 则$\\dfrac{\\sin ^2 \\alpha-\\sin \\alpha \\cos \\alpha}{\\sin ^2 \\alpha+1}=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436334,7 +438382,7 @@
         "content": "若$\\cos (\\dfrac{\\pi}{6}-\\alpha)=\\dfrac{\\sqrt{3}}{3}$, 则$\\cos (\\dfrac{5 \\pi}{6}+\\alpha)=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436353,7 +438401,7 @@
         "content": "若$\\tan (\\alpha+\\beta)=\\dfrac{2}{5}, \\tan (\\alpha-\\dfrac{\\pi}{4})=\\dfrac{1}{4}$, 则$\\tan (\\beta+\\dfrac{\\pi}{4})=$\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436372,7 +438420,7 @@
         "content": "已知$\\sin (\\alpha+\\beta)=\\dfrac{2}{3}, \\sin (\\alpha-\\beta)=\\dfrac{2}{5}$, 求$\\dfrac{\\tan \\alpha}{\\tan \\beta}$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436384,14 +438432,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040139": {
         "id": "040139",
         "content": "已知$\\dfrac{\\pi}{2}<\\beta<\\alpha<\\dfrac{3 \\pi}{4}, \\cos (\\alpha-\\beta)=\\dfrac{12}{13}, \\sin (\\alpha+\\beta)=-\\dfrac{3}{5}$, 求$\\cos 2 \\beta$的值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436403,14 +438451,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040140": {
         "id": "040140",
         "content": "直线$y=2 x+b$被圆$x^2+y^2=4$所截得的弦长为$2 \\sqrt{2}$, 则实数$b$的值为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436429,7 +438477,7 @@
         "content": "过$P(4,3)$的直线$l$与抛物线$y^2=4 x$相交于$A$、$B$两点, 且$P$为线段$AB$的中点, 则直线$l$的方程为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436448,7 +438496,7 @@
         "content": "若过点$(0,2)$且斜率为$k$的直线$l$与双曲线$x^2-y^2=1$的右支有两个不同的公共点, 则$k$的取值范围为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436467,7 +438515,7 @@
         "content": "设直线$l$过点$A(0,2)$且与抛物线$y^2=4 x$只有一个公共点, 则直线$l$的方程为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436486,7 +438534,7 @@
         "content": "椭圆$x^2+\\dfrac{y^2}{4}=1$上的点$P(x, y)$到定点$(0,1)$的最远距离为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436505,7 +438553,7 @@
         "content": "已知动圆$P$过点$A(3,0)$, 且与圆$(x+3)^2+y^2=4$相外切, 则动圆圆心$P$的轨迹方程为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436524,7 +438572,7 @@
         "content": "已知$A(3,1), F$是抛物线$y^2=4 x$的焦点, $P$是抛物线上的一个动点, 则$\\triangle APF$周长的最小值为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436543,7 +438591,7 @@
         "content": "设两条不同的直线$l_1: a_1 x+b_1 y+1=0$和$l_2: a_2 x+b_2 y+1=0$交于点$(2,3)$, 则过点$P(a_1, b_1)$和$Q(a_2, b_2)$的直线方程为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436562,7 +438610,7 @@
         "content": "设双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0, b>0)$的左、右焦点分别为$F_1$、$F_2$, 其渐近线方程为$y=\\pm \\dfrac{4}{3} x$. 若双曲线$C$的实轴长为$6$, 点$P$为$C$的右支上一点, 且$|PF_2|=|F_1F_2|$, 则$\\triangle PF_1F_2$的面积为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436581,7 +438629,7 @@
         "content": "若$a, b, c$成等差数列, 则直线$a x+b y+c=0$被椭圆$\\dfrac{x^2}{2}+\\dfrac{y^2}{8}=1$截得线段的中点的轨迹方程为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436600,7 +438648,7 @@
         "content": "巳知圆$C$和圆$\\begin{cases}x=4+4 \\cos \\theta, \\\\ y=5+4 \\sin \\theta\\end{cases}$($\\theta$为参数)关于直线$\\begin{cases}x=\\dfrac{1}{\\sqrt{10}} t,\\\\ y=3-\\dfrac{1}{\\sqrt{10}} t\\end{cases}$($t$为参数)对称, 则圆$C$的普通方程是\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436619,7 +438667,7 @@
         "content": "已知双曲线方程$\\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$, 点$P$是双曲线上的点, $F_1$、$F_2$是它的左、右焦点, 且$|PF_1| \\cdot|PF_2|=32$, 则$\\overrightarrow{PF_1} \\cdot \\overrightarrow{PF_2}$的值为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436638,7 +438686,7 @@
         "content": "$P$是椭圆$\\dfrac{x^2}{9}+\\dfrac{y^2}{4}=1$上的点, $F_1, F_2$是两个焦点, 则$|PF_1| \\cdot|PF_2|$的最大值与最小值之差是\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436657,7 +438705,7 @@
         "content": "已知双曲线$x^2-\\dfrac{y^2}{3}=1$的右焦点为$F$, $P$是双曲线坐支上的一点, $M(0,2)$, 则$\\triangle PFM$周长的最小值为\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436676,7 +438724,7 @@
         "content": "已知斜率为$\\dfrac{1}{2}$的直线$l$与抛物线$y^2=2 p x$($p>0$)交于$x$轴上方的不同两点$A, B$, 记直线$OA, OB$的斜率分别为$k_1, k_2$, 则$k_1+k_2$的取值范围是\\blank{50}.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "填空题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436695,7 +438743,7 @@
         "content": "过抛物线$y^2=16 x$的焦点作一条直线与抛物线相交于$A$、$B$两点, 它们的横坐标之和等于$15$, 则这样的直线\\bracket{20}.\n\\fourch{有且仅有一条}{有且仅有两条}{有无穷多条}{不存在}",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "选择题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436714,7 +438762,7 @@
         "content": "方程$\\dfrac{x^2}{2 \\cos \\theta+3}+\\dfrac{y^2}{\\sin \\theta-2}=1$表示的曲线是\\bracket{20}.\n\\twoch{焦点在$x$轴上的椭圆}{焦点在$y$轴上的椭圆}{焦点在$x$轴上的双曲线}{焦点在$y$轴上的双曲线}",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "选择题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436733,7 +438781,7 @@
         "content": "过点$A(1,3)$的直线$l$与$x$轴、$y$轴分别交于$P, Q$两点, 求使$|AP| \\cdot|AQ|$最小的直线$l$的方程.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436745,14 +438793,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040158": {
         "id": "040158",
         "content": "设$k \\in \\mathbf{R}$, 直线$l: a x-y+1=0$, 双曲线$C: 3 x^2-y^2=1$, 若直线$l$与双曲线$C$有两个公共点$A$、$B$.\\\\\n(1) 若以线段$AB$为直径的圆过坐标原点, 求$k$的值;\\\\\n(2) 若$\\angle AOB$为钝角(其中$O$为坐标原点), 求$k$的取值范围;\\\\\n(3) 是否存在这样的实数$k$, 使得$A$、$B$关于直线$y=2 x$对称? 若存在, 求出$k$的值; 若不存在, 说明理由.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436764,14 +438812,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040159": {
         "id": "040159",
         "content": "椭圆$\\dfrac{x^2}{m^2}+\\dfrac{y^2}{144}=1$($m>0$)与双曲线$\\dfrac{x^2}{n^2}-\\dfrac{y^2}{9}=1$($n>0$)有公共的焦点$F_1$和$F_2, P$为它们的一个交点, 试求$\\angle F_1PF_2$及$\\triangle F_1PF_2$的面积.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436783,14 +438831,14 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     },
     "040160": {
         "id": "040160",
         "content": "在平面直角坐标系$x O y$中, 已知椭圆$\\Gamma: \\dfrac{x^2}{m^2+1}+\\dfrac{y^2}{m^2}=1$($m>0$)的左、右焦点分别为$F_1$、$F_2$, $Q$是椭圆上任意一点, 且$\\triangle F_1QF_2$的周长为$2+2 \\sqrt{2}$. 过$F_2$作两条互相垂直的弦$AB$、$CD$, 设$AB$、$CD$中点分别为$M$、$N$.\\\\\n(1) 求椭圆$\\Gamma$的标准方程;\\\\\n(2) 证明: 直线$MN$必过定点, 并求出此定点坐标;\\\\\n(3) 若弦$AB$、$CD$的斜率均存在, 求$\\triangle FMN$面积的最大值.",
         "objs": [],
         "tags": [],
-        "genre": "",
+        "genre": "解答题",
         "ans": "",
         "solution": "",
         "duration": -1,
@@ -436802,6 +438850,6 @@
         "same": [],
         "related": [],
         "remark": "",
-        "space": ""
+        "space": "12ex"
     }
 }
\ No newline at end of file