From 5d3adababf82d520f686089df5ed642698c3d2ee Mon Sep 17 00:00:00 2001
From: "weiye.wang" <kj_wangweiye@126.com>
Date: Sat, 18 Mar 2023 23:33:55 +0800
Subject: [PATCH] 20230318 night

---
 工具/修改题目数据库.ipynb                     |    6 +-
 .../小闲平台作业测验数据导入_2023届.ipynb     |    2 +-
 工具/寻找tex文件中未赋答案的题目.ipynb        |  179 +++
 工具/寻找阶段末尾空闲题号.ipynb               |    2 +-
 工具/批量添加题库字段数据.ipynb               |  434 +++---
 工具/批量题号选题pdf生成.ipynb                |   12 +-
 工具/文本文件/metadata.txt                    |  936 +++++-------
 工具/添加题目到数据库.ipynb                   |   73 +-
 工具/识别题库中尚未标注的题目类型.ipynb       |  243 +---
 工具/题号选题pdf生成.ipynb                    |   10 +-
 题库0.3/Problems.json                         | 1290 ++++++++++++++++-
 11 files changed, 2087 insertions(+), 1100 deletions(-)

diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb
index 90719ef1..3306201b 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": 1,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -11,7 +11,7 @@
        "0"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 4,
      "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 = \"31329\"\n",
+    "problems = \"13079\"\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/小闲平台作业测验数据导入_2023届.ipynb b/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb
index 6a64ef18..d387ddf3 100644
--- a/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb
+++ b/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb
index cb0a71d6..ca876bfd 100644
--- a/工具/寻找tex文件中未赋答案的题目.ipynb
+++ b/工具/寻找tex文件中未赋答案的题目.ipynb
@@ -103,6 +103,9 @@
       "赋能19.tex\n",
       "赋能20.tex\n",
       "赋能21.tex\n",
+      "031243\n",
+      "\n",
+      "\n",
       "2017届上海春季高考.tex\n",
       "2018届上海春季高考.tex\n",
       "2019届上海春季高考.tex\n",
@@ -398,6 +401,182 @@
       "012938\n",
       "\n",
       "\n",
+      "17_计数原理与二项式定理.tex\n",
+      "013222\n",
+      "\n",
+      "\n",
+      "013228\n",
+      "\n",
+      "\n",
+      "013232\n",
+      "\n",
+      "\n",
+      "013236\n",
+      "\n",
+      "\n",
+      "014074\n",
+      "\n",
+      "\n",
+      "014570\n",
+      "\n",
+      "\n",
+      "014583\n",
+      "\n",
+      "\n",
+      "013223\n",
+      "\n",
+      "\n",
+      "014579\n",
+      "\n",
+      "\n",
+      "014096\n",
+      "\n",
+      "\n",
+      "014589\n",
+      "\n",
+      "\n",
+      "014075\n",
+      "\n",
+      "\n",
+      "014588\n",
+      "\n",
+      "\n",
+      "014578\n",
+      "\n",
+      "\n",
+      "014079\n",
+      "\n",
+      "\n",
+      "013221\n",
+      "\n",
+      "\n",
+      "013229\n",
+      "\n",
+      "\n",
+      "014574\n",
+      "\n",
+      "\n",
+      "014575\n",
+      "\n",
+      "\n",
+      "014581\n",
+      "\n",
+      "\n",
+      "014582\n",
+      "\n",
+      "\n",
+      "014584\n",
+      "\n",
+      "\n",
+      "014586\n",
+      "\n",
+      "\n",
+      "013224\n",
+      "\n",
+      "\n",
+      "014587\n",
+      "\n",
+      "\n",
+      "014076\n",
+      "\n",
+      "\n",
+      "014070\n",
+      "\n",
+      "\n",
+      "014071\n",
+      "\n",
+      "\n",
+      "014080\n",
+      "\n",
+      "\n",
+      "18_概率与统计.tex\n",
+      "013217\n",
+      "\n",
+      "\n",
+      "014083\n",
+      "\n",
+      "\n",
+      "014090\n",
+      "\n",
+      "\n",
+      "014577\n",
+      "\n",
+      "\n",
+      "014585\n",
+      "\n",
+      "\n",
+      "014591\n",
+      "\n",
+      "\n",
+      "014593\n",
+      "\n",
+      "\n",
+      "014601\n",
+      "\n",
+      "\n",
+      "014599\n",
+      "\n",
+      "\n",
+      "014603\n",
+      "\n",
+      "\n",
+      "014598\n",
+      "\n",
+      "\n",
+      "014594\n",
+      "\n",
+      "\n",
+      "014094\n",
+      "\n",
+      "\n",
+      "014597\n",
+      "\n",
+      "\n",
+      "014608\n",
+      "\n",
+      "\n",
+      "014081\n",
+      "\n",
+      "\n",
+      "014086\n",
+      "\n",
+      "\n",
+      "014091\n",
+      "\n",
+      "\n",
+      "014580\n",
+      "\n",
+      "\n",
+      "013234\n",
+      "\n",
+      "\n",
+      "014592\n",
+      "\n",
+      "\n",
+      "014602\n",
+      "\n",
+      "\n",
+      "014605\n",
+      "\n",
+      "\n",
+      "014606\n",
+      "\n",
+      "\n",
+      "014604\n",
+      "\n",
+      "\n",
+      "014607\n",
+      "\n",
+      "\n",
+      "014595\n",
+      "\n",
+      "\n",
+      "014596\n",
+      "\n",
+      "\n",
+      "014600\n",
+      "\n",
+      "\n",
       "高三下学期月考01.tex\n",
       "高三下学期测验01.tex\n",
       "高三下学期测验02.tex\n",
diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb
index 69f27270..77e1c347 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
@@ -11,7 +11,7 @@
      "text": [
       "首个空闲id: 14764 , 直至 020000\n",
       "首个空闲id: 22048 , 直至 030000\n",
-      "首个空闲id: 31332 , 直至 040000\n",
+      "首个空闲id: 31353 , 直至 040000\n",
       "首个空闲id: 40202 , 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 0d03aab8..2dca31a1 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
@@ -2,265 +2,193 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n",
-      "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n",
-      "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n",
-      "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.882\n",
-      "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n",
-      "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.853\n",
-      "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n",
-      "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.912\n",
-      "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.853\n",
-      "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.765\n",
-      "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.794\n",
-      "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.676\n",
-      "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.971\n",
-      "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.941\n",
-      "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.882\n",
-      "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.206\n",
-      "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\t0.941\n",
-      "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\t0.941\n",
-      "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.824\t0.588\n",
-      "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\t0.853\t0.088\n",
-      "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.912\t0.559\t0.118\n",
-      "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.895\n",
-      "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.895\n",
-      "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.947\n",
-      "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.895\n",
-      "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.737\n",
-      "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.842\n",
-      "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.632\n",
-      "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n",
-      "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.105\n",
-      "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.632\t1.000\n",
-      "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\t0.895\n",
-      "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.737\t0.789\n",
-      "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.947\t0.789\t0.053\n",
-      "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.842\t0.316\t0.000\n",
-      "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\n",
-      "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\n",
-      "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\n",
-      "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.857\n",
-      "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.952\n",
-      "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.952\n",
-      "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\n",
-      "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.952\n",
-      "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.809\n",
-      "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.857\n",
-      "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.857\n",
-      "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.809\n",
-      "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\n",
-      "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.905\n",
-      "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.905\n",
-      "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.000\n",
-      "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.952\t0.952\n",
-      "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\t0.952\n",
-      "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t0.952\t0.714\n",
-      "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\t0.857\t0.048\n",
-      "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三12班\t1.000\t0.857\t0.143\n",
-      "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.964\n",
-      "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.893\n",
-      "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.929\n",
-      "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.964\n",
-      "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.964\n",
-      "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.964\n",
-      "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\n",
-      "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.321\n",
-      "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t0.964\t0.929\n",
-      "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\t0.964\n",
-      "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\t0.929\n",
-      "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\t0.929\t0.714\n",
-      "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三01班\t1.000\t0.964\t0.714\n",
-      "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三02班\t0.933\n",
-      "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三02班\t1.000\n",
-      "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三02班\t1.000\n",
-      "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三02班\t0.967\n",
-      "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三02班\t0.967\n",
-      "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三02班\t0.933\n",
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+      "题号: 014366 , 字段: usages 中已添加数据: 20230318\t2023届高三07班\t0.483\t0.759\t0.448\n",
+      "题号: 013970 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.815\n",
+      "题号: 013070 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.963\n",
+      "题号: 013071 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t1.000\n",
+      "题号: 014369 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.815\n",
+      "题号: 014373 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.889\n",
+      "题号: 013104 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.963\n",
+      "题号: 013069 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.333\n",
+      "题号: 013105 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.963\n",
+      "题号: 013063 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.704\n",
+      "题号: 031228 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.741\n",
+      "题号: 013076 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.815\n",
+      "题号: 031229 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.370\n",
+      "题号: 013077 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.963\t0.815\n",
+      "题号: 013101 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.963\t0.556\n",
+      "题号: 014366 , 字段: usages 中已添加数据: 20230318\t2023届高三08班\t0.741\t0.704\t0.741\n",
+      "题号: 013970 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.821\n",
+      "题号: 013070 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.893\n",
+      "题号: 013071 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.964\n",
+      "题号: 014369 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.643\n",
+      "题号: 014373 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.821\n",
+      "题号: 013104 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.929\n",
+      "题号: 013069 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.464\n",
+      "题号: 013105 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.964\n",
+      "题号: 013063 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.393\n",
+      "题号: 031228 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.500\n",
+      "题号: 013076 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.750\n",
+      "题号: 031229 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.286\n",
+      "题号: 013077 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.786\t0.679\n",
+      "题号: 013101 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.964\t0.393\n",
+      "题号: 014366 , 字段: usages 中已添加数据: 20230318\t2023届高三09班\t0.786\t0.536\t0.714\n"
      ]
     }
    ],
diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb
index 59af1651..5e12783f 100644
--- a/工具/批量题号选题pdf生成.ipynb
+++ b/工具/批量题号选题pdf生成.ipynb
@@ -2,16 +2,16 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "开始编译教师版本pdf文件:  临时文件/本学期高一高二年级新试卷_教师用_20230308.tex\n",
+      "开始编译教师版本pdf文件:  临时文件/本学期高一高二年级新试卷_教师用_20230318.tex\n",
       "0\n",
-      "开始编译学生版本pdf文件:  临时文件/本学期高一高二年级新试卷_学生用_20230308.tex\n",
+      "开始编译学生版本pdf文件:  临时文件/本学期高一高二年级新试卷_学生用_20230318.tex\n",
       "0\n"
      ]
     }
@@ -38,7 +38,9 @@
     "\"2024届高二上学期期末考试\":\"31267:31287\",\n",
     "\"2025届高一上学期期末考试\":\"31288:31308\",\n",
     "\"2024届高二下学期周末卷04\":\"40161:40180\",\n",
-    "\"2025届高一下学期周末卷04\":\"40181:40201\"\n",
+    "\"2025届高一下学期周末卷04\":\"40181:40201\",\n",
+    "\"2024届高二下学期周末卷05\":\"40202:40225\",\n",
+    "\"2025届高一下学期周末卷05\":\"40226:40245\"\n",
     "\n",
     "}\n",
     "\n",
@@ -152,7 +154,7 @@
     "            objects = objects_string\n",
     "        space = (\"\" if problemset[\"space\"] == \"\" else 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",
+    "        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出处: \"+origin + \"\\n\\n\"\n",
     "        students_string = raw_string + space + \"\\n\\n\"\n",
     "        data_teachers += teachers_string\n",
diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt
index 98fa6a36..ebfcf040 100644
--- a/工具/文本文件/metadata.txt
+++ b/工具/文本文件/metadata.txt
@@ -1,758 +1,542 @@
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-20230316	2023届高三02班	1.000	0.800	0.500
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-20230316	2023届高三03班	1.000
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+20230318	2023届高三05班	0.838	0.730	0.486
 
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-20230316	2023届高三03班	0.960	0.920
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+20230318	2023届高三06班	0.972	0.583
 
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+20230318	2023届高三06班	0.833	0.250	0.778
 
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-20230316	2023届高三04班	0.920	0.960
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-20230316	2023届高三04班	0.960	0.880	0.400
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-20230316	2023届高三04班	0.920	0.400	0.120
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+20230318	2023届高三07班	0.966	0.586
 
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-20230316	2023届高三05班	1.000
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+20230318	2023届高三07班	1.000	0.690
 
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-20230316	2023届高三05班	1.000
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+20230318	2023届高三07班	0.483	0.759	0.448
 
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-20230316	2023届高三06班	1.000
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+20230318	2023届高三09班	0.964	0.393
 
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-
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-
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-
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-
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-
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-20230316	2023届高三07班	0.833
-
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-20230316	2023届高三07班	1.000
-
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-20230316	2023届高三07班	0.967
-
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-
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-20230316	2023届高三07班	0.800
-
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-20230316	2023届高三07班	0.967
-
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-
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-20230316	2023届高三07班	0.967
-
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-
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-20230316	2023届高三07班	0.067
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-20230316	2023届高三07班	1.000	0.867
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-
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-20230316	2023届高三09班	1.000
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-
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-
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-
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+20230318	2023届高三09班	0.786	0.536	0.714
 
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 5679be01..6375c6df 100644
--- a/工具/添加题目到数据库.ipynb
+++ b/工具/添加题目到数据库.ipynb
@@ -7,11 +7,11 @@
    "outputs": [],
    "source": [
     "#修改起始id,出处,文件名\n",
-    "starting_id = 31332\n",
+    "starting_id = 40202\n",
     "raworigin = \"\"\n",
-    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目9.tex\"\n",
-    "editor = \"20230316\\t王伟叶\"\n",
-    "indexed = True\n"
+    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目10.tex\"\n",
+    "editor = \"20230318\\t王伟叶\"\n",
+    "indexed = False\n"
    ]
   },
   {
@@ -23,27 +23,50 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "添加题号031332, 来源: 上海市高三数学学科素养测试试题1\n",
-      "添加题号031333, 来源: 上海市高三数学学科素养测试试题2\n",
-      "添加题号031334, 来源: 上海市高三数学学科素养测试试题3\n",
-      "添加题号031335, 来源: 上海市高三数学学科素养测试试题4\n",
-      "添加题号031336, 来源: 上海市高三数学学科素养测试试题5\n",
-      "添加题号031337, 来源: 上海市高三数学学科素养测试试题6\n",
-      "添加题号031338, 来源: 上海市高三数学学科素养测试试题7\n",
-      "添加题号031339, 来源: 上海市高三数学学科素养测试试题8\n",
-      "添加题号031340, 来源: 上海市高三数学学科素养测试试题9\n",
-      "添加题号031341, 来源: 上海市高三数学学科素养测试试题10\n",
-      "添加题号031342, 来源: 上海市高三数学学科素养测试试题11\n",
-      "添加题号031343, 来源: 上海市高三数学学科素养测试试题12\n",
-      "添加题号031344, 来源: 上海市高三数学学科素养测试试题13\n",
-      "添加题号031345, 来源: 上海市高三数学学科素养测试试题14\n",
-      "添加题号031346, 来源: 上海市高三数学学科素养测试试题15\n",
-      "添加题号031347, 来源: 上海市高三数学学科素养测试试题16\n",
-      "添加题号031348, 来源: 上海市高三数学学科素养测试试题17\n",
-      "添加题号031349, 来源: 上海市高三数学学科素养测试试题18\n",
-      "添加题号031350, 来源: 上海市高三数学学科素养测试试题19\n",
-      "添加题号031351, 来源: 上海市高三数学学科素养测试试题20\n",
-      "添加题号031352, 来源: 上海市高三数学学科素养测试试题21\n"
+      "添加题号040202, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040203, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040204, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040205, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040206, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040207, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040208, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040209, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040210, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040211, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040212, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040213, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040214, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040215, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040216, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040217, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040218, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040219, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040220, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040221, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040222, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040223, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040224, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040225, 来源: 2024届高二下学期周末卷05\n",
+      "添加题号040226, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040227, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040228, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040229, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040230, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040231, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040232, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040233, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040234, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040235, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040236, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040237, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040238, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040239, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040240, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040241, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040242, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040243, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040244, 来源: 2025届高一下学期周末卷05\n",
+      "添加题号040245, 来源: 2025届高一下学期周末卷05\n"
      ]
     }
    ],
diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb
index 8a5c0fb8..ec0c0ea1 100644
--- a/工具/识别题库中尚未标注的题目类型.ipynb
+++ b/工具/识别题库中尚未标注的题目类型.ipynb
@@ -9,205 +9,50 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "014628 选择题\n",
-      "014629 填空题\n",
-      "014630 填空题\n",
-      "014631 选择题\n",
-      "014632 填空题\n",
-      "014633 解答题\n",
-      "014634 解答题\n",
-      "014635 填空题\n",
-      "014636 选择题\n",
-      "014637 解答题\n",
-      "014638 解答题\n",
-      "014639 填空题\n",
-      "014640 填空题\n",
-      "014641 填空题\n",
-      "014642 填空题\n",
-      "014643 填空题\n",
-      "014644 解答题\n",
-      "014645 解答题\n",
-      "014646 解答题\n",
-      "014647 填空题\n",
-      "014648 填空题\n",
-      "014649 填空题\n",
-      "014650 选择题\n",
-      "014651 选择题\n",
-      "014652 填空题\n",
-      "014653 填空题\n",
-      "014654 填空题\n",
-      "014655 填空题\n",
-      "014656 填空题\n",
-      "014657 填空题\n",
-      "014658 填空题\n",
-      "014659 填空题\n",
-      "014660 解答题\n",
-      "014661 解答题\n",
-      "014662 选择题\n",
-      "014663 选择题\n",
-      "014664 解答题\n",
-      "014665 选择题\n",
-      "014666 填空题\n",
-      "014667 选择题\n",
-      "014668 选择题\n",
-      "014669 选择题\n",
-      "014670 填空题\n",
-      "014671 选择题\n",
-      "014672 解答题\n",
-      "014673 填空题\n",
-      "014674 填空题\n",
-      "014675 填空题\n",
-      "014676 填空题\n",
-      "014677 填空题\n",
-      "014678 填空题\n",
-      "014679 解答题\n",
-      "014680 填空题\n",
-      "014681 填空题\n",
-      "014682 解答题\n",
-      "014683 填空题\n",
-      "014684 选择题\n",
-      "014685 填空题\n",
-      "014686 填空题\n",
-      "014687 填空题\n",
-      "014688 选择题\n",
-      "014689 选择题\n",
-      "014690 选择题\n",
-      "014691 选择题\n",
-      "014692 填空题\n",
-      "014693 填空题\n",
-      "014694 填空题\n",
-      "014695 填空题\n",
-      "014696 解答题\n",
-      "014697 填空题\n",
-      "014698 填空题\n",
-      "014699 填空题\n",
-      "014700 选择题\n",
-      "014701 填空题\n",
-      "014702 填空题\n",
-      "014703 填空题\n",
-      "014704 填空题\n",
-      "014705 解答题\n",
-      "014706 填空题\n",
-      "014707 填空题\n",
-      "014708 选择题\n",
-      "014709 填空题\n",
-      "014710 填空题\n",
-      "014711 填空题\n",
-      "014712 填空题\n",
-      "014713 填空题\n",
-      "014714 填空题\n",
-      "014715 填空题\n",
-      "014716 填空题\n",
-      "014717 填空题\n",
-      "014718 填空题\n",
-      "014719 填空题\n",
-      "014720 填空题\n",
-      "014721 填空题\n",
-      "014722 解答题\n",
-      "014723 解答题\n",
-      "014724 填空题\n",
-      "014725 填空题\n",
-      "014726 解答题\n",
-      "014727 解答题\n",
-      "014728 解答题\n",
-      "014729 解答题\n",
-      "014730 解答题\n",
-      "014731 解答题\n",
-      "014732 填空题\n",
-      "014733 解答题\n",
-      "014734 解答题\n",
-      "014735 填空题\n",
-      "014736 填空题\n",
-      "014737 解答题\n",
-      "014738 解答题\n",
-      "014739 解答题\n",
-      "014740 解答题\n",
-      "014741 解答题\n",
-      "014742 解答题\n",
-      "014743 填空题\n",
-      "014744 填空题\n",
-      "014745 填空题\n",
-      "014746 填空题\n",
-      "014747 填空题\n",
-      "014748 填空题\n",
-      "014749 填空题\n",
-      "014750 填空题\n",
-      "014751 填空题\n",
-      "014752 填空题\n",
-      "014753 填空题\n",
-      "014754 填空题\n",
-      "014755 选择题\n",
-      "014756 选择题\n",
-      "014757 选择题\n",
-      "014758 选择题\n",
-      "014759 解答题\n",
-      "014760 解答题\n",
-      "014761 解答题\n",
-      "014762 解答题\n",
-      "014763 解答题\n",
-      "031311 填空题\n",
-      "031312 填空题\n",
-      "031313 填空题\n",
-      "031314 填空题\n",
-      "031315 填空题\n",
-      "031316 填空题\n",
-      "031317 填空题\n",
-      "031318 填空题\n",
-      "031319 填空题\n",
-      "031320 填空题\n",
-      "031321 填空题\n",
-      "031322 填空题\n",
-      "031323 选择题\n",
-      "031324 选择题\n",
-      "031325 选择题\n",
-      "031326 选择题\n",
-      "031327 解答题\n",
-      "031328 解答题\n",
-      "031329 解答题\n",
-      "031330 解答题\n",
-      "031331 解答题\n",
-      "031332 填空题\n",
-      "031333 填空题\n",
-      "031334 填空题\n",
-      "031335 填空题\n",
-      "031336 填空题\n",
-      "031337 填空题\n",
-      "031338 填空题\n",
-      "031339 填空题\n",
-      "031340 填空题\n",
-      "031341 填空题\n",
-      "031342 填空题\n",
-      "031343 填空题\n",
-      "031344 选择题\n",
-      "031345 选择题\n",
-      "031346 选择题\n",
-      "031347 选择题\n",
-      "031348 解答题\n",
-      "031349 解答题\n",
-      "031350 解答题\n",
-      "031351 解答题\n",
-      "031352 解答题\n",
-      "040181 填空题\n",
-      "040182 填空题\n",
-      "040183 填空题\n",
-      "040184 填空题\n",
-      "040185 填空题\n",
-      "040186 填空题\n",
-      "040187 填空题\n",
-      "040188 填空题\n",
-      "040189 填空题\n",
-      "040190 填空题\n",
-      "040191 填空题\n",
-      "040192 填空题\n",
-      "040193 选择题\n",
-      "040194 选择题\n",
-      "040195 选择题\n",
-      "040196 选择题\n",
-      "040197 解答题\n",
-      "040198 解答题\n",
-      "040199 解答题\n",
-      "040200 解答题\n",
-      "040201 解答题\n"
+      "040202 填空题\n",
+      "040203 填空题\n",
+      "040204 填空题\n",
+      "040205 填空题\n",
+      "040206 填空题\n",
+      "040207 填空题\n",
+      "040208 填空题\n",
+      "040209 填空题\n",
+      "040210 填空题\n",
+      "040211 填空题\n",
+      "040212 填空题\n",
+      "040213 填空题\n",
+      "040214 填空题\n",
+      "040215 填空题\n",
+      "040216 填空题\n",
+      "040217 填空题\n",
+      "040218 填空题\n",
+      "040219 填空题\n",
+      "040220 填空题\n",
+      "040221 解答题\n",
+      "040222 选择题\n",
+      "040223 选择题\n",
+      "040224 解答题\n",
+      "040225 解答题\n",
+      "040226 填空题\n",
+      "040227 填空题\n",
+      "040228 填空题\n",
+      "040229 填空题\n",
+      "040230 填空题\n",
+      "040231 填空题\n",
+      "040232 填空题\n",
+      "040233 填空题\n",
+      "040234 填空题\n",
+      "040235 填空题\n",
+      "040236 填空题\n",
+      "040237 填空题\n",
+      "040238 填空题\n",
+      "040239 填空题\n",
+      "040240 填空题\n",
+      "040241 填空题\n",
+      "040242 解答题\n",
+      "040243 解答题\n",
+      "040244 解答题\n",
+      "040245 解答题\n"
      ]
     }
    ],
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 6bb5f7e8..1ac76ac4 100644
--- a/工具/题号选题pdf生成.ipynb
+++ b/工具/题号选题pdf生成.ipynb
@@ -2,16 +2,16 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "开始编译教师版本pdf文件:  临时文件/8_概率统计备选_教师用_20230312.tex\n",
+      "开始编译教师版本pdf文件:  临时文件/题库_教师用_20230318.tex\n",
       "0\n",
-      "开始编译学生版本pdf文件:  临时文件/8_概率统计备选_学生用_20230312.tex\n",
+      "开始编译学生版本pdf文件:  临时文件/题库_学生用_20230318.tex\n",
       "0\n"
      ]
     }
@@ -26,13 +26,13 @@
     "\"\"\"---设置题目列表---\"\"\"\n",
     "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
     "problems = r\"\"\"\n",
-    "13217:13239,14070:14080,14081:14094,14095:14102,14570:14590,14591:14608,14628:14646\n",
+    "\n",
     "\"\"\"\n",
     "\"\"\"---设置题目列表结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置文件名---\"\"\"\n",
     "#目录和文件的分隔务必用/\n",
-    "filename = \"临时文件/8_概率统计备选\"\n",
+    "filename = \"临时文件/题库\"\n",
     "\"\"\"---设置文件名结束---\"\"\"\n",
     "\n",
     "\"\"\"---设置是否需要解答题的空格---\"\"\"\n",
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index d21a9f25..8e3ea943 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -324493,7 +324493,20 @@
         "ans": "$4-\\sqrt{2}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.676",
+            "20230318\t2023届高三11班\t0.250",
+            "20230318\t2023届高三12班\t0.579",
+            "20230318\t2023届高三01班\t0.821",
+            "20230318\t2023届高三02班\t0.452",
+            "20230318\t2023届高三03班\t0.652",
+            "20230318\t2023届高三04班\t0.565",
+            "20230318\t2023届高三05班\t0.568",
+            "20230318\t2023届高三06班\t0.556",
+            "20230318\t2023届高三07班\t0.448",
+            "20230318\t2023届高三08班\t0.704",
+            "20230318\t2023届高三09班\t0.393"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324632,7 +324645,20 @@
         "ans": "$\\{-3,2,-1\\}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.588",
+            "20230318\t2023届高三11班\t0.300",
+            "20230318\t2023届高三12班\t0.684",
+            "20230318\t2023届高三01班\t0.750",
+            "20230318\t2023届高三02班\t0.484",
+            "20230318\t2023届高三03班\t0.609",
+            "20230318\t2023届高三04班\t0.391",
+            "20230318\t2023届高三05班\t0.676",
+            "20230318\t2023届高三06班\t0.611",
+            "20230318\t2023届高三07班\t0.517",
+            "20230318\t2023届高三08班\t0.333",
+            "20230318\t2023届高三09班\t0.464"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324653,7 +324679,20 @@
         "ans": "$(2,-4)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.765",
+            "20230318\t2023届高三11班\t0.750",
+            "20230318\t2023届高三12班\t0.842",
+            "20230318\t2023届高三01班\t0.893",
+            "20230318\t2023届高三02班\t1.000",
+            "20230318\t2023届高三03班\t1.000",
+            "20230318\t2023届高三04班\t0.870",
+            "20230318\t2023届高三05班\t1.000",
+            "20230318\t2023届高三06班\t0.917",
+            "20230318\t2023届高三07班\t0.828",
+            "20230318\t2023届高三08班\t0.963",
+            "20230318\t2023届高三09班\t0.893"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324674,7 +324713,20 @@
         "ans": "$\\dfrac 43$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t1.000",
+            "20230318\t2023届高三11班\t1.000",
+            "20230318\t2023届高三12班\t1.000",
+            "20230318\t2023届高三01班\t0.929",
+            "20230318\t2023届高三02班\t0.968",
+            "20230318\t2023届高三03班\t0.957",
+            "20230318\t2023届高三04班\t0.957",
+            "20230318\t2023届高三05班\t0.865",
+            "20230318\t2023届高三06班\t0.972",
+            "20230318\t2023届高三07班\t0.966",
+            "20230318\t2023届高三08班\t1.000",
+            "20230318\t2023届高三09班\t0.964"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324805,7 +324857,20 @@
         "ans": "C",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.676",
+            "20230318\t2023届高三11班\t0.750",
+            "20230318\t2023届高三12班\t0.895",
+            "20230318\t2023届高三01班\t0.857",
+            "20230318\t2023届高三02班\t0.839",
+            "20230318\t2023届高三03班\t0.957",
+            "20230318\t2023届高三04班\t0.696",
+            "20230318\t2023届高三05班\t0.838",
+            "20230318\t2023届高三06班\t0.917",
+            "20230318\t2023届高三07班\t0.552",
+            "20230318\t2023届高三08班\t0.815",
+            "20230318\t2023届高三09班\t0.750"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324826,7 +324891,20 @@
         "ans": "(1) $45^\\circ$; (2) $3x+7y-13=0$或$7x-3y-11=0$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.941\t0.824",
+            "20230318\t2023届高三11班\t1.000\t0.250",
+            "20230318\t2023届高三12班\t0.947\t0.895",
+            "20230318\t2023届高三01班\t0.964\t0.857",
+            "20230318\t2023届高三02班\t0.871\t0.581",
+            "20230318\t2023届高三03班\t0.957\t0.870",
+            "20230318\t2023届高三04班\t0.870\t0.435",
+            "20230318\t2023届高三05班\t0.973\t0.784",
+            "20230318\t2023届高三06班\t0.972\t0.583",
+            "20230318\t2023届高三07班\t0.966\t0.586",
+            "20230318\t2023届高三08班\t0.963\t0.815",
+            "20230318\t2023届高三09班\t0.786\t0.679"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324868,7 +324946,20 @@
         "ans": "$\\pm 4$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.788",
+            "20230318\t2023届高三11班\t0.444",
+            "20230318\t2023届高三12班\t0.600",
+            "20230318\t2023届高三01班\t0.967",
+            "20230318\t2023届高三02班\t0.812",
+            "20230318\t2023届高三03班\t1.000",
+            "20230318\t2023届高三04班\t0.654",
+            "20230318\t2023届高三05班\t0.553",
+            "20230318\t2023届高三06班\t0.946",
+            "20230318\t2023届高三07班\t0.774",
+            "20230318\t2023届高三08班\t0.786",
+            "20230318\t2023届高三09班\t0.630"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324910,7 +325001,20 @@
         "ans": "$\\dfrac{x^2}2-\\dfrac{y^2}6=1$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.909",
+            "20230318\t2023届高三11班\t0.722",
+            "20230318\t2023届高三12班\t0.550",
+            "20230318\t2023届高三01班\t1.000",
+            "20230318\t2023届高三02班\t0.750",
+            "20230318\t2023届高三03班\t0.920",
+            "20230318\t2023届高三04班\t0.731",
+            "20230318\t2023届高三05班\t0.842",
+            "20230318\t2023届高三06班\t0.946",
+            "20230318\t2023届高三07班\t0.903",
+            "20230318\t2023届高三08班\t0.893",
+            "20230318\t2023届高三09班\t0.815"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -324973,7 +325077,20 @@
         "ans": "$(2x-1)^2+(4y-1)^2=1$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.909",
+            "20230318\t2023届高三11班\t0.611",
+            "20230318\t2023届高三12班\t0.700",
+            "20230318\t2023届高三01班\t1.000",
+            "20230318\t2023届高三02班\t0.812",
+            "20230318\t2023届高三03班\t0.920",
+            "20230318\t2023届高三04班\t0.808",
+            "20230318\t2023届高三05班\t0.763",
+            "20230318\t2023届高三06班\t0.946",
+            "20230318\t2023届高三07班\t0.774",
+            "20230318\t2023届高三08班\t0.714",
+            "20230318\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"
@@ -324994,7 +325111,20 @@
         "ans": "$\\dfrac{h_1}{\\tan\\theta_1}+\\dfrac{h_2}{\\tan\\theta_2}\\le 2a$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.849",
+            "20230318\t2023届高三11班\t0.722",
+            "20230318\t2023届高三12班\t0.850",
+            "20230318\t2023届高三01班\t0.867",
+            "20230318\t2023届高三02班\t0.875",
+            "20230318\t2023届高三03班\t0.920",
+            "20230318\t2023届高三04班\t0.731",
+            "20230318\t2023届高三05班\t0.868",
+            "20230318\t2023届高三06班\t0.676",
+            "20230318\t2023届高三07班\t0.806",
+            "20230318\t2023届高三08班\t0.821",
+            "20230318\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"
@@ -325101,7 +325231,20 @@
         "ans": "$y=-\\dfrac 1{32}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.727",
+            "20230318\t2023届高三11班\t0.722",
+            "20230318\t2023届高三12班\t0.650",
+            "20230318\t2023届高三01班\t0.767",
+            "20230318\t2023届高三02班\t0.625",
+            "20230318\t2023届高三03班\t0.800",
+            "20230318\t2023届高三04班\t0.615",
+            "20230318\t2023届高三05班\t0.579",
+            "20230318\t2023届高三06班\t0.838",
+            "20230318\t2023届高三07班\t0.742",
+            "20230318\t2023届高三08班\t0.786",
+            "20230318\t2023届高三09班\t0.667"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -325227,7 +325370,20 @@
         "ans": "$\\dfrac{x^2}{9/4}-\\dfrac{y^2}{187/4}=1$($x>0$)",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.121",
+            "20230318\t2023届高三11班\t0.111",
+            "20230318\t2023届高三12班\t0.300",
+            "20230318\t2023届高三01班\t0.400",
+            "20230318\t2023届高三02班\t0.438",
+            "20230318\t2023届高三03班\t0.400",
+            "20230318\t2023届高三04班\t0.269",
+            "20230318\t2023届高三05班\t0.210",
+            "20230318\t2023届高三06班\t0.351",
+            "20230318\t2023届高三07班\t0.161",
+            "20230318\t2023届高三08班\t0.357",
+            "20230318\t2023届高三09班\t0.074"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -325248,7 +325404,20 @@
         "ans": "$(\\dfrac\\pi 4,\\pi)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.364",
+            "20230318\t2023届高三11班\t0.444",
+            "20230318\t2023届高三12班\t0.300",
+            "20230318\t2023届高三01班\t0.800",
+            "20230318\t2023届高三02班\t0.750",
+            "20230318\t2023届高三03班\t0.520",
+            "20230318\t2023届高三04班\t0.615",
+            "20230318\t2023届高三05班\t0.368",
+            "20230318\t2023届高三06班\t0.676",
+            "20230318\t2023届高三07班\t0.387",
+            "20230318\t2023届高三08班\t0.786",
+            "20230318\t2023届高三09班\t0.444"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -325290,7 +325459,20 @@
         "ans": "$2\\sqrt{2}$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.515",
+            "20230318\t2023届高三11班\t0.389",
+            "20230318\t2023届高三12班\t0.550",
+            "20230318\t2023届高三01班\t0.967",
+            "20230318\t2023届高三02班\t0.750",
+            "20230318\t2023届高三03班\t0.960",
+            "20230318\t2023届高三04班\t0.808",
+            "20230318\t2023届高三05班\t0.737",
+            "20230318\t2023届高三06班\t0.865",
+            "20230318\t2023届高三07班\t0.419",
+            "20230318\t2023届高三08班\t0.679",
+            "20230318\t2023届高三09班\t0.259"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -325334,7 +325516,20 @@
         "ans": "(1) $2$; (2) 恒等于$4$, 是定值",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.971\t0.559",
+            "20230318\t2023届高三11班\t1.000\t0.500",
+            "20230318\t2023届高三12班\t1.000\t0.737",
+            "20230318\t2023届高三01班\t1.000\t0.964",
+            "20230318\t2023届高三02班\t1.000\t0.774",
+            "20230318\t2023届高三03班\t0.913\t0.826",
+            "20230318\t2023届高三04班\t0.957\t0.826",
+            "20230318\t2023届高三05班\t0.946\t0.540",
+            "20230318\t2023届高三06班\t1.000\t0.750",
+            "20230318\t2023届高三07班\t1.000\t0.690",
+            "20230318\t2023届高三08班\t0.963\t0.556",
+            "20230318\t2023届高三09班\t0.964\t0.393"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -325397,7 +325592,20 @@
         "ans": "$x^2+y^2=25$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.941",
+            "20230318\t2023届高三11班\t0.950",
+            "20230318\t2023届高三12班\t1.000",
+            "20230318\t2023届高三01班\t0.964",
+            "20230318\t2023届高三02班\t0.968",
+            "20230318\t2023届高三03班\t0.913",
+            "20230318\t2023届高三04班\t1.000",
+            "20230318\t2023届高三05班\t1.000",
+            "20230318\t2023届高三06班\t0.944",
+            "20230318\t2023届高三07班\t0.966",
+            "20230318\t2023届高三08班\t0.963",
+            "20230318\t2023届高三09班\t0.929"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -325418,7 +325626,20 @@
         "ans": "$(2,3)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.941",
+            "20230318\t2023届高三11班\t0.900",
+            "20230318\t2023届高三12班\t1.000",
+            "20230318\t2023届高三01班\t0.929",
+            "20230318\t2023届高三02班\t0.839",
+            "20230318\t2023届高三03班\t0.957",
+            "20230318\t2023届高三04班\t0.783",
+            "20230318\t2023届高三05班\t0.973",
+            "20230318\t2023届高三06班\t0.972",
+            "20230318\t2023届高三07班\t0.862",
+            "20230318\t2023届高三08班\t0.963",
+            "20230318\t2023届高三09班\t0.964"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -325733,7 +325954,20 @@
         "ans": "$4$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.939",
+            "20230318\t2023届高三11班\t1.000",
+            "20230318\t2023届高三12班\t0.900",
+            "20230318\t2023届高三01班\t0.967",
+            "20230318\t2023届高三02班\t0.938",
+            "20230318\t2023届高三03班\t0.920",
+            "20230318\t2023届高三04班\t0.962",
+            "20230318\t2023届高三05班\t0.921",
+            "20230318\t2023届高三06班\t0.892",
+            "20230318\t2023届高三07班\t0.968",
+            "20230318\t2023届高三08班\t0.929",
+            "20230318\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"
@@ -325943,7 +326177,20 @@
         "ans": "$\\dfrac{x^2}4+y^2=1$或$x^2+\\dfrac{y^2}{4}=1$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.455",
+            "20230318\t2023届高三11班\t0.278",
+            "20230318\t2023届高三12班\t0.400",
+            "20230318\t2023届高三01班\t0.767",
+            "20230318\t2023届高三02班\t0.594",
+            "20230318\t2023届高三03班\t0.600",
+            "20230318\t2023届高三04班\t0.346",
+            "20230318\t2023届高三05班\t0.447",
+            "20230318\t2023届高三06班\t0.460",
+            "20230318\t2023届高三07班\t0.355",
+            "20230318\t2023届高三08班\t0.500",
+            "20230318\t2023届高三09班\t0.370"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -326027,7 +326274,20 @@
         "ans": "(1) $(\\pm \\sqrt{3},0)$; (2) 最大值为$5$, 最小值为$\\dfrac{\\sqrt{2}}2$; (3) $(1,1+\\sqrt{2}]$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t1.000\t0.727\t0.273",
+            "20230318\t2023届高三11班\t0.944\t0.778\t0.167",
+            "20230318\t2023届高三12班\t1.000\t0.800\t0.600",
+            "20230318\t2023届高三01班\t0.967\t0.833\t0.867",
+            "20230318\t2023届高三02班\t0.969\t0.812\t0.688",
+            "20230318\t2023届高三03班\t0.960\t0.760\t0.600",
+            "20230318\t2023届高三04班\t0.923\t0.923\t0.538",
+            "20230318\t2023届高三05班\t0.895\t0.763\t0.579",
+            "20230318\t2023届高三06班\t0.919\t0.892\t0.460",
+            "20230318\t2023届高三07班\t0.903\t0.613\t0.452",
+            "20230318\t2023届高三08班\t0.964\t0.821\t0.357",
+            "20230318\t2023届高三09班\t0.963\t0.630\t0.407"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -326090,7 +326350,20 @@
         "ans": "$\\dfrac{x^2}{16}-\\dfrac{y^2}{9}=1$($x>0$)",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.273",
+            "20230318\t2023届高三11班\t0.500",
+            "20230318\t2023届高三12班\t0.550",
+            "20230318\t2023届高三01班\t0.567",
+            "20230318\t2023届高三02班\t0.125",
+            "20230318\t2023届高三03班\t0.200",
+            "20230318\t2023届高三04班\t0.115",
+            "20230318\t2023届高三05班\t0.158",
+            "20230318\t2023届高三06班\t0.189",
+            "20230318\t2023届高三07班\t0.226",
+            "20230318\t2023届高三08班\t0.179",
+            "20230318\t2023届高三09班\t0.815"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -326281,7 +326554,20 @@
         "ans": "(1) $x^2-\\dfrac{y^2}3=1$; (2) $\\lambda$存在, $\\lambda=2$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.970\t0.333",
+            "20230318\t2023届高三11班\t1.000\t0.167",
+            "20230318\t2023届高三12班\t0.850\t0.250",
+            "20230318\t2023届高三01班\t1.000\t0.733",
+            "20230318\t2023届高三02班\t1.000\t0.250",
+            "20230318\t2023届高三03班\t1.000\t0.480",
+            "20230318\t2023届高三04班\t1.000\t0.154",
+            "20230318\t2023届高三05班\t0.974\t0.553",
+            "20230318\t2023届高三06班\t1.000\t0.540",
+            "20230318\t2023届高三07班\t1.000\t0.161",
+            "20230318\t2023届高三08班\t0.893\t0.214",
+            "20230318\t2023届高三09班\t1.000\t0.074"
+        ],
         "origin": "2022届高三第二轮复习讲义",
         "edit": [
             "20230118\t王伟叶"
@@ -344384,7 +344670,20 @@
         "ans": "$5$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.971",
+            "20230318\t2023届高三11班\t0.800",
+            "20230318\t2023届高三12班\t1.000",
+            "20230318\t2023届高三01班\t0.929",
+            "20230318\t2023届高三02班\t0.774",
+            "20230318\t2023届高三03班\t0.870",
+            "20230318\t2023届高三04班\t0.783",
+            "20230318\t2023届高三05班\t1.000",
+            "20230318\t2023届高三06班\t0.917",
+            "20230318\t2023届高三07班\t0.724",
+            "20230318\t2023届高三08班\t0.815",
+            "20230318\t2023届高三09班\t0.821"
+        ],
         "origin": "2020年空中课堂高三复习课20",
         "edit": [
             "20230128\t王伟叶"
@@ -344656,7 +344955,20 @@
         "ans": "$(0,1]$(单位: $\\text{cm}$)",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.697",
+            "20230318\t2023届高三11班\t0.111",
+            "20230318\t2023届高三12班\t0.950",
+            "20230318\t2023届高三01班\t0.867",
+            "20230318\t2023届高三02班\t0.438",
+            "20230318\t2023届高三03班\t0.720",
+            "20230318\t2023届高三04班\t0.231",
+            "20230318\t2023届高三05班\t0.684",
+            "20230318\t2023届高三06班\t0.676",
+            "20230318\t2023届高三07班\t0.097",
+            "20230318\t2023届高三08班\t0.821",
+            "20230318\t2023届高三09班\t0.556"
+        ],
         "origin": "2020年空中课堂高三复习课21",
         "edit": [
             "20230128\t王伟叶"
@@ -353468,7 +353780,20 @@
         "ans": "(1) $x-y-1=0$或$7x+2y-23=0$; (2) 弦$PQ$最短时, 所在直线的方程为$x+y-3=0$; 弦$PQ$最长时, 所在直线的方程为$x-y+3=0$; (3) 当$a=2$时, 两圆内切; 当$a\\in (2-2\\sqrt{2},2)\\cup (2,2+2\\sqrt{2})$时, 两圆相交; 当$a=2\\pm 2\\sqrt{2}$时, 两圆外切; 当$a\\in (-\\infty,2-2\\sqrt{2})\\cup (2+2\\sqrt{2},+\\infty)$时, 两圆外离",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.647\t0.529\t0.735",
+            "20230318\t2023届高三11班\t0.750\t0.500\t0.250",
+            "20230318\t2023届高三12班\t0.684\t0.474\t0.842",
+            "20230318\t2023届高三01班\t0.893\t0.393\t0.929",
+            "20230318\t2023届高三02班\t0.516\t0.323\t0.742",
+            "20230318\t2023届高三03班\t0.870\t0.913\t0.739",
+            "20230318\t2023届高三04班\t0.478\t0.739\t0.478",
+            "20230318\t2023届高三05班\t0.838\t0.730\t0.486",
+            "20230318\t2023届高三06班\t0.833\t0.250\t0.778",
+            "20230318\t2023届高三07班\t0.483\t0.759\t0.448",
+            "20230318\t2023届高三08班\t0.741\t0.704\t0.741",
+            "20230318\t2023届高三09班\t0.786\t0.536\t0.714"
+        ],
         "origin": "2023年空中课堂高三复习课18",
         "edit": [
             "20230202\t王伟叶"
@@ -353538,7 +353863,20 @@
         "ans": "$[0,\\dfrac\\pi 4]\\cup (\\dfrac {3\\pi}4,\\pi)$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.735",
+            "20230318\t2023届高三11班\t0.550",
+            "20230318\t2023届高三12班\t0.632",
+            "20230318\t2023届高三01班\t0.714",
+            "20230318\t2023届高三02班\t0.871",
+            "20230318\t2023届高三03班\t0.870",
+            "20230318\t2023届高三04班\t0.565",
+            "20230318\t2023届高三05班\t0.838",
+            "20230318\t2023届高三06班\t0.722",
+            "20230318\t2023届高三07班\t0.724",
+            "20230318\t2023届高三08班\t0.815",
+            "20230318\t2023届高三09班\t0.643"
+        ],
         "origin": "2023年空中课堂高三复习课18",
         "edit": [
             "20230202\t王伟叶"
@@ -353614,7 +353952,20 @@
         "ans": "$-1$或$-11$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.676",
+            "20230318\t2023届高三11班\t0.850",
+            "20230318\t2023届高三12班\t0.789",
+            "20230318\t2023届高三01班\t0.929",
+            "20230318\t2023届高三02班\t0.871",
+            "20230318\t2023届高三03班\t0.957",
+            "20230318\t2023届高三04班\t0.826",
+            "20230318\t2023届高三05班\t0.811",
+            "20230318\t2023届高三06班\t0.639",
+            "20230318\t2023届高三07班\t0.690",
+            "20230318\t2023届高三08班\t0.889",
+            "20230318\t2023届高三09班\t0.821"
+        ],
         "origin": "2023年空中课堂高三复习课18",
         "edit": [
             "20230202\t王伟叶"
@@ -438715,7 +439066,20 @@
         "ans": "$2x+3y-8=0$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.471",
+            "20230318\t2023届高三11班\t0.500",
+            "20230318\t2023届高三12班\t0.842",
+            "20230318\t2023届高三01班\t0.893",
+            "20230318\t2023届高三02班\t0.548",
+            "20230318\t2023届高三03班\t0.783",
+            "20230318\t2023届高三04班\t0.652",
+            "20230318\t2023届高三05班\t0.568",
+            "20230318\t2023届高三06班\t0.806",
+            "20230318\t2023届高三07班\t0.586",
+            "20230318\t2023届高三08班\t0.741",
+            "20230318\t2023届高三09班\t0.500"
+        ],
         "origin": "2020年空中课堂高三复习课20-20230214修改",
         "edit": [
             "20230128\t王伟叶",
@@ -438739,7 +439103,20 @@
         "ans": "$[-5\\sqrt{2},1]$",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.412",
+            "20230318\t2023届高三11班\t0.350",
+            "20230318\t2023届高三12班\t0.421",
+            "20230318\t2023届高三01班\t0.857",
+            "20230318\t2023届高三02班\t0.452",
+            "20230318\t2023届高三03班\t0.652",
+            "20230318\t2023届高三04班\t0.391",
+            "20230318\t2023届高三05班\t0.649",
+            "20230318\t2023届高三06班\t0.444",
+            "20230318\t2023届高三07班\t0.448",
+            "20230318\t2023届高三08班\t0.370",
+            "20230318\t2023届高三09班\t0.286"
+        ],
         "origin": "2020年空中课堂高三复习课20-20230214修改",
         "edit": [
             "20230128\t王伟叶",
@@ -438763,7 +439140,20 @@
         "ans": "$y^2=16x$($x\\ne 0$)",
         "solution": "",
         "duration": -1,
-        "usages": [],
+        "usages": [
+            "20230318\t2023届高三10班\t0.818",
+            "20230318\t2023届高三11班\t0.722",
+            "20230318\t2023届高三12班\t0.950",
+            "20230318\t2023届高三01班\t0.100",
+            "20230318\t2023届高三02班\t0.188",
+            "20230318\t2023届高三03班\t0.160",
+            "20230318\t2023届高三04班\t0.154",
+            "20230318\t2023届高三05班\t0.789",
+            "20230318\t2023届高三06班\t0.162",
+            "20230318\t2023届高三07班\t0.129",
+            "20230318\t2023届高三08班\t0.143",
+            "20230318\t2023届高三09班\t0.889"
+        ],
         "origin": "2022届高三第二轮复习讲义-20230214修改",
         "edit": [
             "20230118\t王伟叶",
@@ -439186,13 +439576,13 @@
         "id": "031243",
         "content": "若数列$\\{a_n\\}$的前$n$项和$S_n=-3n^2+2n+1$($n\\in \\mathbf{N}$, $n\\ge 1$), 则$\\{a_n\\}$的通项公式为$a_n=$\\blank{50}.",
         "objs": [
-            "KNONE"
+            ""
         ],
         "tags": [
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "$$",
+        "ans": "$\\begin{cases}    0, & n=1,\\\\    5-6n, & n \\ge 2\\end{cases}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -445823,5 +446213,841 @@
         "related": [],
         "remark": "",
         "space": "12ex"
+    },
+    "040202": {
+        "id": "040202",
+        "content": "设函数$y=f_i(x)$($i=1,2,3$)的导数分别为$y'=f_i'(x)$($i=1,2,3$).\\\\\n(1) 若$f_1(x)=\\sqrt{x}$, $f_2(x)=\\sqrt[3]{x}$, $f_3(x)=\\dfrac{1}{\\sqrt{x}}$, 则\\\\$f_1'(x)=$\\blank{50}; $f_2'(x)=$\\blank{50}; $f_3'(x)=$\\blank{50}.\\\\\n(2) 若$f_1(x)=x^2-\\mathrm{e}^x$, $f_2(x)=\\ln x+\\cos x$, $f_3(x)=\\sqrt{x}+\\sin x$, 则\\\\$f_1'(x)=$\\blank{50}; $f_2'(x)=$\\blank{50}; $f_3'(x)=$\\blank{50}.\\\\\n(3) 若$f_1(x)=x^3 \\cdot \\mathrm{e}^x$, $f_2(x)=x \\ln x$, $f_3(x)=\\dfrac{x}{\\sin x}$, 则\\\\$f_1'(x)=$\\blank{50}; $f_2'(x)=$\\blank{50}; $f_3'(x)=$\\blank{50}.\\\\\n(4) 若$f_1(x)=\\mathrm{e}^{2 x-1}$, $f_2(x)=2^x$, $f_3(x)=(\\dfrac{1}{3})^{x+1}$, 则\\\\$f_1'(x)=$\\blank{50}; $f_2'(x)=$\\blank{50}; $f_3'(x)=$\\blank{50}.\\\\\n(5) 若$f_1(x)=\\lg x$, $f_2(x)=\\ln (2 x-1)$, $f_3(x)=\\log _3(3-2 x)$, 则\\\\$f_1'(x)=$\\blank{50}; $f_2'(x)=$\\blank{50}; $f_3'(x)=$\\blank{50}.\\\\\n(6) 若$f_1(x)=\\sin (x-\\dfrac{\\pi}{3})$, $f_2(x)=\\cos (\\dfrac{x}{3}+\\dfrac{\\pi}{4})$, $f_3(x)=\\tan (2 x)$, 则\\\\$f_1'(x)=$\\blank{50}; $f_2'(x)=$\\blank{50}; $f_3'(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040203": {
+        "id": "040203",
+        "content": "对于函数$y=f(x)$, 先求导数$y'=f'(x)$, 再写$y=f(x)$的单调区间.\\\\\n(1) 若$f(x)=x^3-x^2-x$, 导数$f'(x)=$\\blank{100};\\\\$y=f(x)$的递增区间为\\blank{100}; 递减区间为\\blank{100}.\\\\\n(2) 若$f(x)=x-\\ln x$, 导数$f'(x)=$\\blank{100};\\\\$y=f(x)$的递增区间为\\blank{100}; 递减区间为\\blank{100}.\\\\\n(3) 若$f(x)=\\sin (\\dfrac{\\pi}{3}-2 x)$, 导数$f'(x)=$\\blank{100};\\\\$y=f(x)$的递增区间为\\blank{100}; 递减区间为\\blank{100}.\\\\\n(4) 若$f(x)=x \\cdot 2^x$, 导数$f'(x)=$\\blank{100};\\\\$y=f(x)$的递增区间为\\blank{100}; 递减区间为\\blank{100}.\\\\\n(5) 若$f(x)=2 x^2-\\sqrt{x}$, 导数$f'(x)=$\\blank{100};\\\\$y=f(x)$的递增区间为\\blank{100}; 递减区间为\\blank{100}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040204": {
+        "id": "040204",
+        "content": "设$f(x)=\\cos x$. \\\\\n(1) 函数$y=f(x)$的驻点的集合为\\blank{50};\\\\\n(2) 函数$y=x+2 f(x)$的驻点的集合为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040205": {
+        "id": "040205",
+        "content": "设函数$y=f(x)$的导数为$y'=f'(x)$. 若$f'(1)=-3$.\\\\\n(1) $\\displaystyle\\lim _{h \\to 0} \\dfrac{f(1+3 h)-f(1)}{h}=$\\blank{50};\\\\\n(2) $\\displaystyle\\lim _{h \\to 0} \\dfrac{f(1+h)-f(1-h)}{h}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040206": {
+        "id": "040206",
+        "content": "若直线$l$是曲线$f(x)=x^3+x^2$在$x=1$处的切线.\\\\\n(1) $f(1)=$\\blank{50};\n(2) 直线$l$的方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040207": {
+        "id": "040207",
+        "content": "设$a \\in \\mathbf{R}$, 函数$f(x)=a x^3+3 x^2+2$的导数为$y=f'(x)$.\\\\\n(1) 若$a=-1$, 则$f'(x)=$\\blank{50};\\\\\n(2) 若$f'(-1)=6$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040208": {
+        "id": "040208",
+        "content": "设$a, b, k \\in \\mathbf{R}$, 已知直线$y=k x+1$与曲线$y=x^3+a x+b$相切于点$(1,3)$.\\\\ \n(1) $k=$\\blank{50};\\\\\n(2) 数对$(a, b)$为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040209": {
+        "id": "040209",
+        "content": "曲线$y=f(x)$在$x=1$处的切线为直线$y=x-2$.\\\\\n(1) $f(1)=$\\blank{50};\\\\ \n(2) $f'(1)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040210": {
+        "id": "040210",
+        "content": "点$P$在曲线$y=x^3-3 x^2$上移动, 设$P$处的该曲线的切线的斜率为$k$, 倾斜角为$\\alpha$.\\\\\n(1) $k$的取值范围是\\blank{50};\\\\\n(2) $\\alpha$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040211": {
+        "id": "040211",
+        "content": "设$a, b, c \\in \\mathbf{R}$, $a \\neq 0$, 函数$f(x)=a x^2+b x+c$的导数为$y=f'(x)$.\\\\\n(1) 设$\\lambda, \\mu \\in \\mathbf{R}$, 且$a: b: c=1: \\lambda: \\mu$, $f'(x)=b x+c$, 则$\\lambda+2 \\mu=$\\blank{50};\\\\\n(2) 若关于$x$的的不等式$f'(x)>0$的解集为$(-\\infty, 1)$, 则关于$x$的的不等式$f(x)>c$的解集为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040212": {
+        "id": "040212",
+        "content": "设$m \\in \\mathbf{R}$, 若点$P$为曲线$y=x^3(x>0)$上一动点, 过$P$作直线$b$平行于直线$a: y=3 x+m$.\\\\\n(1) 若直线$b$是该曲线的切线, 则$P$的坐标为\\blank{50};\\\\\n(2) 若点$P$总不在直线$a$上, 则$m$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040213": {
+        "id": "040213",
+        "content": "设$n \\in \\mathbf{R}$, 若点$Q$为曲线$y=\\ln x$上一动点, 过$P$作直线$d$平行于直线$c: y=3 x+n$.\\\\\n(1) 若直线$d$是该曲线的切线, 则$Q$的坐标为\\blank{50};\\\\\n(2) 若点$Q$总不在直线$c$上, 则$n$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040214": {
+        "id": "040214",
+        "content": "某种动物的体温$T$(单位: 摄氏度) 与太阳落山后的时间$t$(单位: 分钟) 满足函数关系$T(t)=\\dfrac{120}{t+5}+15$. 若在$t=t_0$时刻该动物体温的瞬时变化率是$-2$摄氏度/分钟, 则$t_0=$\\blank{50}分钟.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040215": {
+        "id": "040215",
+        "content": "吹一个球形气球时, 气球半径将随着空气容量$V$的增加而变化. 当$V=8$时, 气球的瞬时膨胀率(即气球半径关于气球内空气容量的瞬时变化率)为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040216": {
+        "id": "040216",
+        "content": "设函数$y=f(x)$的导数为$y'=f'(x)$. 若$f(x)=x^2+2 x \\cdot f'(1)$, 则$f'(1)+f'(0)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040217": {
+        "id": "040217",
+        "content": "设函数$f(x)=\\dfrac{\\mathrm{e}^x-\\mathrm{e}^{-x}}{\\mathrm{e}^{2 x}}$的导数$f'(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040218": {
+        "id": "040218",
+        "content": "设函数$f(x)=x^2 \\cos 3 x+\\lg (-x)$的导数$f'(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040219": {
+        "id": "040219",
+        "content": "设函数$f(x)=\\sqrt{x} \\tan x$的导数$f'(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040220": {
+        "id": "040220",
+        "content": "设函数$f(x)=x \\cdot \\mathrm{e}^x \\cdot \\ln x$的导数$f'(x)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040221": {
+        "id": "040221",
+        "content": "完成``求函数$y=f(x)$的导数$y'=f'(x)$''的过程与结论.\\\\\n(1) $y=\\dfrac{1-\\sin x}{1+\\cos x}$;\\\\\n(2) $y=\\dfrac{x^5+\\sqrt{x}+\\sin x}{x^2}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040222": {
+        "id": "040222",
+        "content": "已知函数$y=f(x)$的导数$y=f'(x)$的图像如下图所示, 则$y=f(x)$的图像可能是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:3] plot (\\x,{\\x*(\\x-2)});\n\\draw (2,0.2) -- (2,0) node [below] {$2$};\n\\draw (1,0.2) -- (1,0) node [below] {$1$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{\\begin{tikzpicture}[>=latex, scale = 0.8]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -0.4:2.2] plot (\\x,{-\\x*(\\x-1)*(\\x-2)});\n\\draw [dashed] ({(3-sqrt(3))/3},{-2/3/sqrt(3)}) -- ({(3-sqrt(3))/3},0) node [above] {$1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.8]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -0.2:2.4] plot (\\x,{1.1*\\x*(\\x-1)*(\\x-2)});\n\\draw (2,0.2) -- (2,0) node [below] {$2$};\n\\draw (1,0.2) -- (1,0) node [below] {$1$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.8]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [domain = -1:2.85] plot (\\x,{\\x*\\x-\\x*\\x*\\x/3-0.5});\n\\draw [dashed] (2,{4-8/3-0.5}) -- (2,0) node [below] {$2$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.8]\n\\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:2.85] plot (\\x,{-\\x*\\x+\\x*\\x*\\x/3+1});\n\\draw [dashed] (2,{-4+8/3+1}) -- (2,0) node [above] {$2$};\n\\end{tikzpicture}}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040223": {
+        "id": "040223",
+        "content": "已知函数$y=f(x)$的图像如下图所示, 则导数$y=f'(x)$的图像可能是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:3, samples = 100] plot (\\x,{(2*pow(pow(\\x,2)-5,2)/25-2)*0.75});\n\\draw [dashed] (-3,{-18*0.75/25}) -- (-3,0) node [above] {$-3$};\n\\draw [dashed] (3,{-18*0.75/25}) -- (3,0) node [above] {$3$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{\\begin{tikzpicture}[>=latex, scale = 0.4]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (-3,3) -- (3,-3);\n\\draw [dashed] (-3,3) -- (-3,0) node [below] {$-3$};\n\\draw [dashed] (3,-3) -- (3,0) node [above] {$3$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.4]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:3] plot (\\x,{pow(\\x,2)/1.5-3});\n\\draw [dashed] (-3,3) -- (-3,0) node [below] {$-3$};\n\\draw [dashed] (3,3) -- (3,0) node [below] {$3$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.4]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:3] plot (\\x,{-pow(\\x,2)/1.5+3});\n\\draw [dashed] (-3,-3) -- (-3,0) node [above] {$-3$};\n\\draw [dashed] (3,-3) -- (3,0) node [above] {$3$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.4]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-4) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3:3] plot (\\x,{(pow(\\x,2)-5)*\\x*8/25*0.75});\n\\draw [dashed] (-3,-3) -- (-3,0) node [above] {$-3$};\n\\draw [dashed] (3,3) -- (3,0) node [below] {$3$};\n\\end{tikzpicture}}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040224": {
+        "id": "040224",
+        "content": "已知函数$y=f(x)$的图像如下图所示, 则下列数值排序正确的是($)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-1,0) -- (6,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,6) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 1:5.5] plot ({pow(\\x,3)/pow(5.5,3)*6+0.2},\\x);\n\\foreach \\i in {1,2,...,5}\n{\\draw (\\i,0.2) -- (\\i,0) node [below] {$\\i$};\n\\draw (0,\\i) -- (-0.2,\\i) node [left] {$\\i$};};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$0<f(3)-f(2)<f'(2)<f'(3)$}{$0<f'(3)<f(3)-f(2)<f'(2)$}{$0<f'(3)<f'(2)<f(3)-f(2)$}{$0<f'(2)<f'(3)<f(3)-f(2)$}",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040225": {
+        "id": "040225",
+        "content": "设曲线$C_1: y=x^2$、$C_2: y=-(x-2)^2$, 直线$l$与$C_1$、$C_2$均相切, 求$l$的方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2024届高二下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040226": {
+        "id": "040226",
+        "content": "$\\sin \\dfrac{\\alpha}{4} \\cos \\dfrac{\\alpha}{4}=\\dfrac{1}{6}$, $\\alpha \\in(0, \\dfrac{\\pi}{2})$, 则$\\sin \\alpha=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040227": {
+        "id": "040227",
+        "content": "化简: $(\\cos ^4 \\theta-\\sin ^4 \\theta) \\dfrac{\\tan \\theta}{1-\\tan ^2 \\theta}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040228": {
+        "id": "040228",
+        "content": "化简: $\\cos 12^{\\circ} \\cos 24^{\\circ} \\cos 48^{\\circ} \\cos 96^{\\circ}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040229": {
+        "id": "040229",
+        "content": "化简: $\\cos ^2 \\alpha+\\cos ^2(\\dfrac{\\pi}{3}+\\alpha)+\\cos ^2(\\dfrac{\\pi}{3}-\\alpha)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040230": {
+        "id": "040230",
+        "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": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040231": {
+        "id": "040231",
+        "content": "已知$\\sin \\alpha-\\cos \\alpha=\\dfrac{1}{2}$, 且$\\pi<\\alpha<2 \\pi$, 则$\\tan \\dfrac{\\alpha}{2}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040232": {
+        "id": "040232",
+        "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": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040233": {
+        "id": "040233",
+        "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": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040234": {
+        "id": "040234",
+        "content": "在$\\triangle ABC$中, $\\cos (\\dfrac{\\pi}{4}+A)=\\dfrac{5}{13}$, 则$\\cos 2A=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040235": {
+        "id": "040235",
+        "content": "在$\\triangle ABC$中, $a=7$, $b=8$, $A=60^{\\circ}$, 则$c=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040236": {
+        "id": "040236",
+        "content": "在$A$为顶角的等腰$\\triangle ABC$中, $\\sin B=\\dfrac{3}{5}$, 则$A=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040237": {
+        "id": "040237",
+        "content": "在$A$为顶角的等腰$\\triangle ABC$中, $\\sin A=\\dfrac{3}{5}$, 则$B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040238": {
+        "id": "040238",
+        "content": "在$\\triangle ABC$中, 角$A, B, C$所对的边分别是$a, b, c$. 若$a=2 \\sqrt{3}$, $B=45^{\\circ}$, $b=2 \\sqrt{2}$, 则$A=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040239": {
+        "id": "040239",
+        "content": "在$\\triangle ABC$中, $\\sin ^2A+\\sin ^2B+\\sin A \\sin B=\\sin ^2C$, 则角$C=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040240": {
+        "id": "040240",
+        "content": "若$f(\\alpha)=2 \\tan \\alpha-\\dfrac{2 \\sin ^2 \\dfrac{\\alpha}{2}-1}{\\sin \\dfrac{\\alpha}{2} \\cos \\dfrac{\\alpha}{2}}$, 则$f(\\dfrac{\\pi}{12})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040241": {
+        "id": "040241",
+        "content": "按下列条件解三角形$ABC$时, 其中有唯一解的那一组的序号为\\blank{50}.\n\\textcircled{1} $a=20, b=28, A=45^{\\circ}$; \\textcircled{2} $a=18, b=20, A=105^{\\circ}$; \n\\textcircled{3} $b=20, c=34, B=45^{\\circ}$; \\textcircled{4} $b=60, c=50, B=45^{\\circ}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040242": {
+        "id": "040242",
+        "content": "已知$\\triangle ABC$为等腰三角形, $\\sin A=\\dfrac{3}{5}$, 求$\\sin B$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040243": {
+        "id": "040243",
+        "content": "在$\\triangle ABC$中, 角$A, B, C$所对的边分别是$a, b, c$. 分别根据条件解三角形:\\\\\n(1) $b=2 \\sqrt{2}$, $c=2 \\sqrt{3}$, $\\angle C=60^{\\circ}$;\\\\\n(2) $a=2 \\sqrt{6}$, $b=6$, $\\angle A=45^{\\circ}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040244": {
+        "id": "040244",
+        "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": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040245": {
+        "id": "040245",
+        "content": "已知$\\sin 2 \\alpha+\\sin 2 \\beta=\\sin 2 \\alpha \\sin 2 \\beta$, $\\tan \\dfrac{\\alpha-\\beta}{2}=\\dfrac{1}{3}$. 求: $\\sin ^2 \\dfrac{\\alpha+\\beta}{2}$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷05",
+        "edit": [
+            "20230318\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
     }
 }
\ No newline at end of file