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20230308 evening

This commit is contained in:
weiye.wang 2023-03-08 22:34:03 +08:00
parent 0027d54161
commit 371c02529e
10 changed files with 1730 additions and 150 deletions
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8
工具/修改题目数据库.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 3,
"metadata": {},
"outputs": [
{
@ -11,7 +11,7 @@
"0"
]
},
"execution_count": 1,
"execution_count": 3,
"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 = \"003683,003698,011567,013880\"\n",
"problems = \"31303\"\n",
"\n",
"def generate_number_set(string,dict):\n",
" string = re.sub(r\"[\\n\\s]\",\"\",string)\n",
@ -51,7 +51,7 @@
},
{
"cell_type": "code",
"execution_count": 71,
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [

20
工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb
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@ -2,23 +2,9 @@
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 1,
"metadata": {},
"outputs": [
{
"ename": "KeyboardInterrupt",
"evalue": "Interrupted by user",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[2], line 31\u001b[0m\n\u001b[0;32m 29\u001b[0m problems_indexes \u001b[39m=\u001b[39m \u001b[39mlist\u001b[39m(df[df\u001b[39m.\u001b[39mcolumns[\u001b[39m0\u001b[39m]][\u001b[39m2\u001b[39m:])\n\u001b[0;32m 30\u001b[0m \u001b[39mfor\u001b[39;00m p \u001b[39min\u001b[39;00m problems_indexes:\n\u001b[1;32m---> 31\u001b[0m t \u001b[39m=\u001b[39m \u001b[39minput\u001b[39;49m(\u001b[39m\"\u001b[39;49m\u001b[39m答题纸区域\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39m+\u001b[39;49mp\u001b[39m+\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39m的题号为(1-\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39m+\u001b[39;49m\u001b[39mstr\u001b[39;49m(\u001b[39mlen\u001b[39;49m(problems_list))\u001b[39m+\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39m, a为自动对应点前的题号):\u001b[39;49m\u001b[39m\"\u001b[39;49m)\n\u001b[0;32m 32\u001b[0m \u001b[39mif\u001b[39;00m t\u001b[39m.\u001b[39mupper() \u001b[39m==\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mA\u001b[39m\u001b[39m\"\u001b[39m:\n\u001b[0;32m 33\u001b[0m correspondence_dict[p] \u001b[39m=\u001b[39m problems_list[\u001b[39mint\u001b[39m(re\u001b[39m.\u001b[39mfindall(\u001b[39mr\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m([\u001b[39m\u001b[39m\\\u001b[39m\u001b[39md]+?)\u001b[39m\u001b[39m\\\u001b[39m\u001b[39m.\u001b[39m\u001b[39m\"\u001b[39m,p)[\u001b[39m0\u001b[39m])\u001b[39m-\u001b[39m\u001b[39m1\u001b[39m]\n",
"File \u001b[1;32mc:\\Users\\weiye\\.conda\\envs\\mathdept\\lib\\site-packages\\ipykernel\\kernelbase.py:1175\u001b[0m, in \u001b[0;36mKernel.raw_input\u001b[1;34m(self, prompt)\u001b[0m\n\u001b[0;32m 1171\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_allow_stdin:\n\u001b[0;32m 1172\u001b[0m \u001b[39mraise\u001b[39;00m StdinNotImplementedError(\n\u001b[0;32m 1173\u001b[0m \u001b[39m\"\u001b[39m\u001b[39mraw_input was called, but this frontend does not support input requests.\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[0;32m 1174\u001b[0m )\n\u001b[1;32m-> 1175\u001b[0m \u001b[39mreturn\u001b[39;00m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_input_request(\n\u001b[0;32m 1176\u001b[0m \u001b[39mstr\u001b[39;49m(prompt),\n\u001b[0;32m 1177\u001b[0m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_parent_ident[\u001b[39m\"\u001b[39;49m\u001b[39mshell\u001b[39;49m\u001b[39m\"\u001b[39;49m],\n\u001b[0;32m 1178\u001b[0m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49mget_parent(\u001b[39m\"\u001b[39;49m\u001b[39mshell\u001b[39;49m\u001b[39m\"\u001b[39;49m),\n\u001b[0;32m 1179\u001b[0m password\u001b[39m=\u001b[39;49m\u001b[39mFalse\u001b[39;49;00m,\n\u001b[0;32m 1180\u001b[0m )\n",
"File \u001b[1;32mc:\\Users\\weiye\\.conda\\envs\\mathdept\\lib\\site-packages\\ipykernel\\kernelbase.py:1217\u001b[0m, in \u001b[0;36mKernel._input_request\u001b[1;34m(self, prompt, ident, parent, password)\u001b[0m\n\u001b[0;32m 1214\u001b[0m \u001b[39mbreak\u001b[39;00m\n\u001b[0;32m 1215\u001b[0m \u001b[39mexcept\u001b[39;00m \u001b[39mKeyboardInterrupt\u001b[39;00m:\n\u001b[0;32m 1216\u001b[0m \u001b[39m# re-raise KeyboardInterrupt, to truncate traceback\u001b[39;00m\n\u001b[1;32m-> 1217\u001b[0m \u001b[39mraise\u001b[39;00m \u001b[39mKeyboardInterrupt\u001b[39;00m(\u001b[39m\"\u001b[39m\u001b[39mInterrupted by user\u001b[39m\u001b[39m\"\u001b[39m) \u001b[39mfrom\u001b[39;00m \u001b[39mNone\u001b[39m\n\u001b[0;32m 1218\u001b[0m \u001b[39mexcept\u001b[39;00m \u001b[39mException\u001b[39;00m:\n\u001b[0;32m 1219\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mlog\u001b[39m.\u001b[39mwarning(\u001b[39m\"\u001b[39m\u001b[39mInvalid Message:\u001b[39m\u001b[39m\"\u001b[39m, exc_info\u001b[39m=\u001b[39m\u001b[39mTrue\u001b[39;00m)\n",
"\u001b[1;31mKeyboardInterrupt\u001b[0m: Interrupted by user"
]
}
],
"outputs": [],
"source": [
"import zipfile,os,re,time\n",
"import pandas as pd\n",
@ -113,7 +99,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.15"
"version": "3.9.15"
},
"orig_nbformat": 4,
"vscode": {

2
工具/寻找阶段末尾空闲题号.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 1,
"metadata": {},
"outputs": [
{

276
工具/批量添加题库字段数据.ipynb
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@ -2,35 +2,265 @@
"cells": [
{
"cell_type": "code",
"execution_count": 13,
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"题号: 010168 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.977\t0.954\t1.000\t0.767\n",
"题号: 010169 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.977\n",
"题号: 010170 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.884\t1.000\t0.861\n",
"题号: 010171 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.302\t0.791\n",
"题号: 010172 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t1.000\t0.721\t0.861\n",
"题号: 010173 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.791\n",
"题号: 010176 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t1.000\t0.861\t0.977\t0.977\n",
"题号: 010182 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t1.000\n",
"题号: 010184 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.954\n",
"题号: 010183 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.977\t0.961\n",
"题号: 010185 , 字段: usages 中已添加数据: 20230200\t2025届高一11班\t0.954\t1.000\t0.930\t0.977\t0.791\t0.907\n",
"题号: 010168 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t0.972\t0.917\t0.972\t0.722\n",
"题号: 010169 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t0.944\n",
"题号: 010170 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t0.861\t0.917\t0.861\n",
"题号: 010171 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t0.472\t0.722\n",
"题号: 010172 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t1.000\t0.972\t1.000\n",
"题号: 010173 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t0.889\n",
"题号: 010176 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t1.000\t0.917\t0.972\t1.000\n",
"题号: 010182 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t1.000\n",
"题号: 010184 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t0.972\n",
"题号: 010183 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t0.972\t0.806\n",
"题号: 010185 , 字段: usages 中已添加数据: 20230200\t2025届高一12班\t1.000\t1.000\t0.972\t1.000\t1.000\t1.000\n"
"题号: 003675 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.921\n",
"题号: 012165 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t1.000\n",
"题号: 004252 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.842\n",
"题号: 031239 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.895\n",
"题号: 031238 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.421\n",
"题号: 031266 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.842\n",
"题号: 031240 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.947\n",
"题号: 031237 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.605\n",
"题号: 004256 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.026\n",
"题号: 004499 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.342\n",
"题号: 004132 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.263\n",
"题号: 004217 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.132\n",
"题号: 008972 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.947\n",
"题号: 009082 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.632\n",
"题号: 012445 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.684\n",
"题号: 030691 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.368\n",
"题号: 010000 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.874\n",
"题号: 011301 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.913\n",
"题号: 003691 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.660\n",
"题号: 011450 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.281\n",
"题号: 031236 , 字段: usages 中已添加数据: 20230308\t2023届高三10班\t0.248\n",
"题号: 003675 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.917\n",
"题号: 012165 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.958\n",
"题号: 004252 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.958\n",
"题号: 031239 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.833\n",
"题号: 031238 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.250\n",
"题号: 031266 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.833\n",
"题号: 031240 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.917\n",
"题号: 031237 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.583\n",
"题号: 004256 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.042\n",
"题号: 004499 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.542\n",
"题号: 004132 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.333\n",
"题号: 004217 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.042\n",
"题号: 008972 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t1.000\n",
"题号: 009082 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.500\n",
"题号: 012445 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.625\n",
"题号: 030691 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.208\n",
"题号: 010000 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.845\n",
"题号: 011301 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.839\n",
"题号: 003691 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.667\n",
"题号: 011450 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.227\n",
"题号: 031236 , 字段: usages 中已添加数据: 20230308\t2023届高三11班\t0.225\n",
"题号: 003675 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t1.000\n",
"题号: 012165 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t1.000\n",
"题号: 004252 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.957\n",
"题号: 031239 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.913\n",
"题号: 031238 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.261\n",
"题号: 031266 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.783\n",
"题号: 031240 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.957\n",
"题号: 031237 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.522\n",
"题号: 004256 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.087\n",
"题号: 004499 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.478\n",
"题号: 004132 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.304\n",
"题号: 004217 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.130\n",
"题号: 008972 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.957\n",
"题号: 009082 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.609\n",
"题号: 012445 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.652\n",
"题号: 030691 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.522\n",
"题号: 010000 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.761\n",
"题号: 011301 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.820\n",
"题号: 003691 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.537\n",
"题号: 011450 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.208\n",
"题号: 031236 , 字段: usages 中已添加数据: 20230308\t2023届高三12班\t0.220\n",
"题号: 003675 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t1.000\n",
"题号: 012165 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t1.000\n",
"题号: 004252 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t1.000\n",
"题号: 031239 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t1.000\n",
"题号: 031238 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t0.710\n",
"题号: 031266 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t0.839\n",
"题号: 031240 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t0.935\n",
"题号: 031237 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t0.839\n",
"题号: 004256 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t0.323\n",
"题号: 004499 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t0.839\n",
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"题号: 004217 , 字段: usages 中已添加数据: 20230308\t2023届高三01班\t0.839\n",
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"题号: 004499 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.455\n",
"题号: 004132 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.303\n",
"题号: 004217 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.182\n",
"题号: 008972 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.970\n",
"题号: 009082 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.697\n",
"题号: 012445 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.849\n",
"题号: 030691 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.303\n",
"题号: 010000 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.916\n",
"题号: 011301 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.896\n",
"题号: 003691 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.682\n",
"题号: 011450 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.280\n",
"题号: 031236 , 字段: usages 中已添加数据: 20230308\t2023届高三09班\t0.251\n"
]
}
],

31
工具/批量题号选题pdf生成.ipynb
View File

@ -2,16 +2,16 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 3,
"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_20230307.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_20230308.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_20230307.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_20230308.tex\n",
"0\n"
]
}
@ -26,18 +26,19 @@
"\"\"\"---设置题目列表---\"\"\"\n",
"#字典字段为文件名, 之后为内容的题号\n",
"problems_dict = {\n",
" \"2024届高二下学期周末卷01\":\"40001:40017\",\n",
" \"2025届高一下学期周末卷01\":\"40018:40036\",\n",
" \"2024届高二下学期周末卷02\":\"40037:40056\",\n",
" \"2025届高一下学期周末卷02\":\"40057:40082\",\n",
" \"2025届高一下学期周末卷03\":\"40083:40104\",\n",
" \"2025届高一下学期周末卷03小测\":\"40105:40112\",\n",
" \"2025届高一下学期周末卷04旧版\":\"40113:40130\",\n",
" \"2025届高一下学期周末卷04小测\":\"40131:40139\",\n",
" \"2024届高二下学期周末卷03\":\"40140:40160\",\n",
" \"2024届高二上学期期末考试\":\"31267:31287\",\n",
" \"2025届高一上学期期末考试\":\"31288:31308\",\n",
" \"2024届高二上学期周末卷04\":\"40161:40180\"\n",
"\"2024届高二下学期周末卷01\":\"40001:40017\",\n",
"\"2025届高一下学期周末卷01\":\"40018:40036\",\n",
"\"2024届高二下学期周末卷02\":\"40037:40056\",\n",
"\"2025届高一下学期周末卷02\":\"40057:40082\",\n",
"\"2025届高一下学期周末卷03\":\"40083:40104\",\n",
"\"2025届高一下学期周末卷03小测\":\"40105:40112\",\n",
"\"2025届高一下学期周末卷04旧版\":\"40113:40130\",\n",
"\"2025届高一下学期周末卷04小测\":\"40131:40139\",\n",
"\"2024届高二下学期周末卷03\":\"40140:40160\",\n",
"\"2024届高二上学期期末考试\":\"31267:31287\",\n",
"\"2025届高一上学期期末考试\":\"31288:31308\",\n",
"\"2024届高二下学期周末卷04\":\"40161:40180\",\n",
"\"2025届高一下学期周末卷04\":\"40181:40201\"\n",
"\n",
"}\n",
"\n",

778
工具/文本文件/metadata.txt
View File

@ -1,68 +1,758 @@
usages
010168
20230200 2025届高一11班 0.977 0.954 1.000 0.767
003675
20230308 2023届高三10班 0.921
010169
20230200 2025届高一11班 0.977
012165
20230308 2023届高三10班 1.000
010170
20230200 2025届高一11班 0.884 1.000 0.861
004252
20230308 2023届高三10班 0.842
010171
20230200 2025届高一11班 0.302 0.791
031239
20230308 2023届高三10班 0.895
010172
20230200 2025届高一11班 1.000 0.721 0.861
031238
20230308 2023届高三10班 0.421
010173
20230200 2025届高一11班 0.791
031266
20230308 2023届高三10班 0.842
010176
20230200 2025届高一11班 1.000 0.861 0.977 0.977
031240
20230308 2023届高三10班 0.947
010182
20230200 2025届高一11班 1.000
031237
20230308 2023届高三10班 0.605
010184
20230200 2025届高一11班 0.954
004256
20230308 2023届高三10班 0.026
010183
20230200 2025届高一11班 0.977 0.961
004499
20230308 2023届高三10班 0.342
010185
20230200 2025届高一11班 0.954 1.000 0.930 0.977 0.791 0.907
004132
20230308 2023届高三10班 0.263
010168
20230200 2025届高一12班 0.972 0.917 0.972 0.722
004217
20230308 2023届高三10班 0.132
010169
20230200 2025届高一12班 0.944
008972
20230308 2023届高三10班 0.947
010170
20230200 2025届高一12班 0.861 0.917 0.861
009082
20230308 2023届高三10班 0.632
010171
20230200 2025届高一12班 0.472 0.722
012445
20230308 2023届高三10班 0.684
010172
20230200 2025届高一12班 1.000 0.972 1.000
030691
20230308 2023届高三10班 0.368
010173
20230200 2025届高一12班 0.889
010000
20230308 2023届高三10班 0.874
010176
20230200 2025届高一12班 1.000 0.917 0.972 1.000
011301
20230308 2023届高三10班 0.913
010182
20230200 2025届高一12班 1.000
003691
20230308 2023届高三10班 0.660
010184
20230200 2025届高一12班 0.972
011450
20230308 2023届高三10班 0.281
010183
20230200 2025届高一12班 0.972 0.806
031236
20230308 2023届高三10班 0.248
010185
20230200 2025届高一12班 1.000 1.000 0.972 1.000 1.000 1.000
003675
20230308 2023届高三11班 0.917
012165
20230308 2023届高三11班 0.958
004252
20230308 2023届高三11班 0.958
031239
20230308 2023届高三11班 0.833
031238
20230308 2023届高三11班 0.250
031266
20230308 2023届高三11班 0.833
031240
20230308 2023届高三11班 0.917
031237
20230308 2023届高三11班 0.583
004256
20230308 2023届高三11班 0.042
004499
20230308 2023届高三11班 0.542
004132
20230308 2023届高三11班 0.333
004217
20230308 2023届高三11班 0.042
008972
20230308 2023届高三11班 1.000
009082
20230308 2023届高三11班 0.500
012445
20230308 2023届高三11班 0.625
030691
20230308 2023届高三11班 0.208
010000
20230308 2023届高三11班 0.845
011301
20230308 2023届高三11班 0.839
003691
20230308 2023届高三11班 0.667
011450
20230308 2023届高三11班 0.227
031236
20230308 2023届高三11班 0.225
003675
20230308 2023届高三12班 1.000
012165
20230308 2023届高三12班 1.000
004252
20230308 2023届高三12班 0.957
031239
20230308 2023届高三12班 0.913
031238
20230308 2023届高三12班 0.261
031266
20230308 2023届高三12班 0.783
031240
20230308 2023届高三12班 0.957
031237
20230308 2023届高三12班 0.522
004256
20230308 2023届高三12班 0.087
004499
20230308 2023届高三12班 0.478
004132
20230308 2023届高三12班 0.304
004217
20230308 2023届高三12班 0.130
008972
20230308 2023届高三12班 0.957
009082
20230308 2023届高三12班 0.609
012445
20230308 2023届高三12班 0.652
030691
20230308 2023届高三12班 0.522
010000
20230308 2023届高三12班 0.761
011301
20230308 2023届高三12班 0.820
003691
20230308 2023届高三12班 0.537
011450
20230308 2023届高三12班 0.208
031236
20230308 2023届高三12班 0.220
003675
20230308 2023届高三01班 1.000
012165
20230308 2023届高三01班 1.000
004252
20230308 2023届高三01班 1.000
031239
20230308 2023届高三01班 1.000
031238
20230308 2023届高三01班 0.710
031266
20230308 2023届高三01班 0.839
031240
20230308 2023届高三01班 0.935
031237
20230308 2023届高三01班 0.839
004256
20230308 2023届高三01班 0.323
004499
20230308 2023届高三01班 0.839
004132
20230308 2023届高三01班 0.871
004217
20230308 2023届高三01班 0.839
008972
20230308 2023届高三01班 1.000
009082
20230308 2023届高三01班 1.000
012445
20230308 2023届高三01班 0.903
030691
20230308 2023届高三01班 0.645
010000
20230308 2023届高三01班 0.949
011301
20230308 2023届高三01班 0.945
003691
20230308 2023届高三01班 0.894
011450
20230308 2023届高三01班 0.475
031236
20230308 2023届高三01班 0.477
003675
20230308 2023届高三02班 0.879
012165
20230308 2023届高三02班 0.970
004252
20230308 2023届高三02班 0.909
031239
20230308 2023届高三02班 0.939
031238
20230308 2023届高三02班 0.606
031266
20230308 2023届高三02班 0.849
031240
20230308 2023届高三02班 0.909
031237
20230308 2023届高三02班 0.636
004256
20230308 2023届高三02班 0.394
004499
20230308 2023届高三02班 0.788
004132
20230308 2023届高三02班 0.636
004217
20230308 2023届高三02班 0.636
008972
20230308 2023届高三02班 1.000
009082
20230308 2023届高三02班 0.849
012445
20230308 2023届高三02班 0.758
030691
20230308 2023届高三02班 0.545
010000
20230308 2023届高三02班 0.946
011301
20230308 2023届高三02班 0.913
003691
20230308 2023届高三02班 0.825
011450
20230308 2023届高三02班 0.431
031236
20230308 2023届高三02班 0.460
003675
20230308 2023届高三03班 1.000
012165
20230308 2023届高三03班 1.000
004252
20230308 2023届高三03班 0.935
031239
20230308 2023届高三03班 0.903
031238
20230308 2023届高三03班 0.548
031266
20230308 2023届高三03班 0.871
031240
20230308 2023届高三03班 0.903
031237
20230308 2023届高三03班 0.839
004256
20230308 2023届高三03班 0.258
004499
20230308 2023届高三03班 0.806
004132
20230308 2023届高三03班 0.516
004217
20230308 2023届高三03班 0.355
008972
20230308 2023届高三03班 0.935
009082
20230308 2023届高三03班 0.935
012445
20230308 2023届高三03班 1.000
030691
20230308 2023届高三03班 0.581
010000
20230308 2023届高三03班 0.919
011301
20230308 2023届高三03班 0.894
003691
20230308 2023届高三03班 0.774
011450
20230308 2023届高三03班 0.409
031236
20230308 2023届高三03班 0.441
003675
20230308 2023届高三04班 1.000
012165
20230308 2023届高三04班 1.000
004252
20230308 2023届高三04班 0.833
031239
20230308 2023届高三04班 0.933
031238
20230308 2023届高三04班 0.467
031266
20230308 2023届高三04班 0.867
031240
20230308 2023届高三04班 0.967
031237
20230308 2023届高三04班 0.700
004256
20230308 2023届高三04班 0.333
004499
20230308 2023届高三04班 0.733
004132
20230308 2023届高三04班 0.767
004217
20230308 2023届高三04班 0.533
008972
20230308 2023届高三04班 0.933
009082
20230308 2023届高三04班 0.900
012445
20230308 2023届高三04班 0.733
030691
20230308 2023届高三04班 0.733
010000
20230308 2023届高三04班 0.895
011301
20230308 2023届高三04班 0.919
003691
20230308 2023届高三04班 0.769
011450
20230308 2023届高三04班 0.404
031236
20230308 2023届高三04班 0.398
003675
20230308 2023届高三05班 1.000
012165
20230308 2023届高三05班 0.974
004252
20230308 2023届高三05班 0.974
031239
20230308 2023届高三05班 0.789
031238
20230308 2023届高三05班 0.605
031266
20230308 2023届高三05班 0.816
031240
20230308 2023届高三05班 0.921
031237
20230308 2023届高三05班 0.684
004256
20230308 2023届高三05班 0.263
004499
20230308 2023届高三05班 0.579
004132
20230308 2023届高三05班 0.553
004217
20230308 2023届高三05班 0.474
008972
20230308 2023届高三05班 0.974
009082
20230308 2023届高三05班 0.763
012445
20230308 2023届高三05班 0.789
030691
20230308 2023届高三05班 0.395
010000
20230308 2023届高三05班 0.880
011301
20230308 2023届高三05班 0.835
003691
20230308 2023届高三05班 0.844
011450
20230308 2023届高三05班 0.311
031236
20230308 2023届高三05班 0.342
003675
20230308 2023届高三06班 0.976
012165
20230308 2023届高三06班 1.000
004252
20230308 2023届高三06班 0.951
031239
20230308 2023届高三06班 0.902
031238
20230308 2023届高三06班 0.488
031266
20230308 2023届高三06班 0.854
031240
20230308 2023届高三06班 0.902
031237
20230308 2023届高三06班 0.707
004256
20230308 2023届高三06班 0.220
004499
20230308 2023届高三06班 0.634
004132
20230308 2023届高三06班 0.634
004217
20230308 2023届高三06班 0.488
008972
20230308 2023届高三06班 0.927
009082
20230308 2023届高三06班 0.902
012445
20230308 2023届高三06班 0.658
030691
20230308 2023届高三06班 0.439
010000
20230308 2023届高三06班 0.875
011301
20230308 2023届高三06班 0.822
003691
20230308 2023届高三06班 0.836
011450
20230308 2023届高三06班 0.289
031236
20230308 2023届高三06班 0.339
003675
20230308 2023届高三07班 0.943
012165
20230308 2023届高三07班 0.971
004252
20230308 2023届高三07班 1.000
031239
20230308 2023届高三07班 0.771
031238
20230308 2023届高三07班 0.400
031266
20230308 2023届高三07班 0.771
031240
20230308 2023届高三07班 0.829
031237
20230308 2023届高三07班 0.629
004256
20230308 2023届高三07班 0.057
004499
20230308 2023届高三07班 0.514
004132
20230308 2023届高三07班 0.314
004217
20230308 2023届高三07班 0.257
008972
20230308 2023届高三07班 0.914
009082
20230308 2023届高三07班 0.657
012445
20230308 2023届高三07班 0.600
030691
20230308 2023届高三07班 0.229
010000
20230308 2023届高三07班 0.888
011301
20230308 2023届高三07班 0.886
003691
20230308 2023届高三07班 0.763
011450
20230308 2023届高三07班 0.243
031236
20230308 2023届高三07班 0.316
003675
20230308 2023届高三08班 1.000
012165
20230308 2023届高三08班 1.000
004252
20230308 2023届高三08班 0.933
031239
20230308 2023届高三08班 0.867
031238
20230308 2023届高三08班 0.600
031266
20230308 2023届高三08班 0.833
031240
20230308 2023届高三08班 0.933
031237
20230308 2023届高三08班 0.700
004256
20230308 2023届高三08班 0.133
004499
20230308 2023届高三08班 0.600
004132
20230308 2023届高三08班 0.533
004217
20230308 2023届高三08班 0.333
008972
20230308 2023届高三08班 0.967
009082
20230308 2023届高三08班 0.833
012445
20230308 2023届高三08班 0.800
030691
20230308 2023届高三08班 0.500
010000
20230308 2023届高三08班 0.919
011301
20230308 2023届高三08班 0.857
003691
20230308 2023届高三08班 0.757
011450
20230308 2023届高三08班 0.339
031236
20230308 2023届高三08班 0.348
003675
20230308 2023届高三09班 1.000
012165
20230308 2023届高三09班 1.000
004252
20230308 2023届高三09班 0.970
031239
20230308 2023届高三09班 0.939
031238
20230308 2023届高三09班 0.333
031266
20230308 2023届高三09班 0.727
031240
20230308 2023届高三09班 0.879
031237
20230308 2023届高三09班 0.697
004256
20230308 2023届高三09班 0.182
004499
20230308 2023届高三09班 0.455
004132
20230308 2023届高三09班 0.303
004217
20230308 2023届高三09班 0.182
008972
20230308 2023届高三09班 0.970
009082
20230308 2023届高三09班 0.697
012445
20230308 2023届高三09班 0.849
030691
20230308 2023届高三09班 0.303
010000
20230308 2023届高三09班 0.916
011301
20230308 2023届高三09班 0.896
003691
20230308 2023届高三09班 0.682
011450
20230308 2023届高三09班 0.280
031236
20230308 2023届高三09班 0.251

5
工具/模板文件/题目清单.txt
View File

@ -9,6 +9,7 @@
\usepackage{makecell}
\usepackage{longtable}
\usepackage{diagbox}
\usepackage{hyperref}
\usetikzlibrary{arrows,calc,intersections,patterns,decorations.pathreplacing,3d,angles,quotes,positioning,shapes.geometric}
\usepackage[top=1in, bottom=1in,left=0.8in,right=0.8in]{geometry}
\renewcommand{\baselinestretch}{1.65}
@ -44,6 +45,10 @@ A.~#1 &B.~#2& C.~#3& D.~#4
\end{tabular}}
\begin{document}
\tableofcontents
\newpage
\begin{enumerate}[1.]
编译模板

47
工具/添加题目到数据库.ipynb
View File

@ -7,10 +7,10 @@
"outputs": [],
"source": [
"#修改起始id,出处,文件名\n",
"starting_id = 40161\n",
"starting_id = 40181\n",
"raworigin = \"\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n",
"editor = \"20230307\\t王伟叶\"\n",
"editor = \"20230308\\t王伟叶\"\n",
"indexed = False\n"
]
},
@ -23,26 +23,27 @@
"name": "stdout",
"output_type": "stream",
"text": [
"添加题号040161, 来源: 2024届高二下学期周末卷04\n",
"添加题号040162, 来源: 2024届高二下学期周末卷04\n",
"添加题号040163, 来源: 2024届高二下学期周末卷04\n",
"添加题号040164, 来源: 2024届高二下学期周末卷04\n",
"添加题号040165, 来源: 2024届高二下学期周末卷04\n",
"添加题号040166, 来源: 2024届高二下学期周末卷04\n",
"添加题号040167, 来源: 2024届高二下学期周末卷04\n",
"添加题号040168, 来源: 2024届高二下学期周末卷04\n",
"添加题号040169, 来源: 2024届高二下学期周末卷04\n",
"添加题号040170, 来源: 2024届高二下学期周末卷04\n",
"添加题号040171, 来源: 2024届高二下学期周末卷04\n",
"添加题号040172, 来源: 2024届高二下学期周末卷04\n",
"添加题号040173, 来源: 2024届高二下学期周末卷04\n",
"添加题号040174, 来源: 2024届高二下学期周末卷04\n",
"添加题号040175, 来源: 2024届高二下学期周末卷04\n",
"添加题号040176, 来源: 2024届高二下学期周末卷04\n",
"添加题号040177, 来源: 2024届高二下学期周末卷04\n",
"添加题号040178, 来源: 2024届高二下学期周末卷04\n",
"添加题号040179, 来源: 2024届高二下学期周末卷04\n",
"添加题号040180, 来源: 2024届高二下学期周末卷04\n"
"添加题号040181, 来源: 2025届高一下学期周末卷04\n",
"添加题号040182, 来源: 2025届高一下学期周末卷04\n",
"添加题号040183, 来源: 2025届高一下学期周末卷04\n",
"添加题号040184, 来源: 2025届高一下学期周末卷04\n",
"添加题号040185, 来源: 2025届高一下学期周末卷04\n",
"添加题号040186, 来源: 2025届高一下学期周末卷04\n",
"添加题号040187, 来源: 2025届高一下学期周末卷04\n",
"添加题号040188, 来源: 2025届高一下学期周末卷04\n",
"添加题号040189, 来源: 2025届高一下学期周末卷04\n",
"添加题号040190, 来源: 2025届高一下学期周末卷04\n",
"添加题号040191, 来源: 2025届高一下学期周末卷04\n",
"添加题号040192, 来源: 2025届高一下学期周末卷04\n",
"添加题号040193, 来源: 2025届高一下学期周末卷04\n",
"添加题号040194, 来源: 2025届高一下学期周末卷04\n",
"添加题号040195, 来源: 2025届高一下学期周末卷04\n",
"添加题号040196, 来源: 2025届高一下学期周末卷04\n",
"添加题号040197, 来源: 2025届高一下学期周末卷04\n",
"添加题号040198, 来源: 2025届高一下学期周末卷04\n",
"添加题号040199, 来源: 2025届高一下学期周末卷04\n",
"添加题号040200, 来源: 2025届高一下学期周末卷04\n",
"添加题号040201, 来源: 2025届高一下学期周末卷04\n"
]
}
],
@ -161,7 +162,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.15"
"version": "3.9.15"
},
"orig_nbformat": 4,
"vscode": {

4
文本处理工具/剪贴板文本整理_mathpix.ipynb
View File

@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
@ -207,7 +207,9 @@
"\n",
"#替换题号\n",
"data = re.sub(\"(^[例]*[0-9]+[\\s]*\\.[\\s]+)\",\"\\\\n\\\\\\\\item \",data)\n",
"data = re.sub(\"(^[例]*[0-9]+[\\s]*、[\\s]*)\",\"\\\\n\\\\\\\\item \",data)\n",
"data = re.sub(\"(\\\\n[例]*[0-9]+[\\s]*\\.[\\s]+)\",\"\\\\n\\\\\\\\item \",data)\n",
"data = re.sub(\"(\\\\n[例]*[0-9]+[\\s]*、[\\s]*)\",\"\\\\n\\\\\\\\item \",data)\n",
"\n",
"#公式标志换成$符号\n",
"data = re.sub(\"\\\\\\\\\\[\",r\"$\",data)\n",

709
题库0.3/Problems.json
View File

@ -99394,7 +99394,20 @@
"ans": "$(-\\infty,0)$",
"solution": "即$\\dfrac 1x<0$",
"duration": -1,
"usages": [],
"usages": [
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"origin": "上海2017年秋季高考试题3",
"edit": [
"20220701\t王伟叶"
@ -99820,7 +99833,20 @@
"ans": "(1) $935$辆; (2) 因$8782>8736$, 故第$42$个月底单车保有量超过了容纳量",
"solution": "(1) 前$4$个月的累计投放量为$a_1+a_2+a_3+a_4=20+95+420+430=965$. 前$4$个月的累计损失量为$b_1+b_2+b_3+b_4=6+7+8+9=30$, 因此该地区第$4$个月底的共享单车的保有量为$965-30=935$.\\\\\n(2) 考察不等式$a_n \\geq b_n$在整数范围内的解集. 当$n \\leq 3$时, $5 n^4+15 \\geq n+5$确实成立, 当$n \\geq 4$时, 由$-10 n+470 \\geq n+5$, 解得$n \\leq \\dfrac{465}{11}\\approx 42.27$, 因此第$42$个月底, 保有量达到最大. 当$n \\geq 4$时, $\\{a_n\\}$是公差为$-10$的等差数列, 而$\\{b_n\\}$是公差为$1$的等差数列, 于是到第$42$个月底, 单车保有量为$\\dfrac{38(a_5+a_{42})}{2}+965-\\dfrac{42(b_1+b_{42})}{2}=\\dfrac{38(420+50)}{2}+965-\\dfrac{42(6+47)}{2}=8782$. 而$S_{42}=-4\\times 16+8800=8736<8782$. 因此该月底单车保有量超过了容纳量.",
"duration": -1,
"usages": [],
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"origin": "上海2017年秋季高考试题19",
"edit": [
"20220701\t王伟叶"
@ -110713,7 +110739,19 @@
"solution": "设$MN$的中点为$T$, 则$|OT|=1$且$T$能取遍单位圆上的每一个点. 而$\\overrightarrow{AM}\\cdot \\overrightarrow{AN}=(\\overrightarrow{AT}+\\overrightarrow{TM})\\cdot (\\overrightarrow{AT}-\\overrightarrow{TM})=\\overrightarrow{AT}^2-3$, 而$|AT|$的范围为$[0,2]$, 所以$\\overrightarrow{AM}\\cdot \\overrightarrow{AN}$的取值范围为$[-3,1]$",
"duration": -1,
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"origin": "2022届高三下学期测验卷04第11题",
"edit": [
@ -113028,7 +113066,19 @@
"solution": "$f(2020)=f(2^{10}\\cdot \\dfrac{2020}{1024})=2^{10}(2-\\dfrac{2020}{1024})=28$. 而当$x\\in (2^i,2^{i+1}]$($i\\in \\mathbf{Z}$)时, $f(x)$的取值范围为$[0,2^i)$. 所以$x>32$, 设$x\\in (32,64]$, 则$f(x)=32f(\\dfrac{x}{32})=32\\cdot (2-\\dfrac{x}{32})=64-x$, 解$64-x=28$得$x=36$",
"duration": -1,
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"origin": "2022届高三下学期测验卷08第12题",
"edit": [
@ -114015,7 +114065,19 @@
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"origin": "2022届高三下学期测验卷10第5题",
"edit": [
@ -114115,7 +114177,19 @@
"solution": "该函数在$x>0$时的取值范围为$(b,1+b)$, 所以该函数存在反函数的一个充要条件为$(-b-1,-b)$, $\\{0\\}$, $(b,b+1)$两两的交集为$\\varnothing$, 解得$b\\le -1$或$b\\ge 0$",
"duration": -1,
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"origin": "2022届高三下学期测验卷10第9题",
"edit": [
@ -121007,7 +121081,19 @@
"solution": "最大数为$1$的集合有$2^0$个, 最大数为$2$的集合有$2^1$个, 以此类推. 所以$S_{10}=\\displaystyle\\sum_{i=1}^{10}(i\\cdot 2^{i-1})=9217$",
"duration": -1,
"usages": [
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],
"origin": "2022届高三上学期测验卷08第11题",
"edit": [
@ -226861,7 +226947,20 @@
"ans": "B",
"solution": "根据复数相等的定义, $z_1=z_2$时必有$a=c$, 反之如$z_1=1$, $z_2=1+\\mathrm{i}$, 则有$a=c$且$z_1\\ne z_2$",
"duration": -1,
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"origin": "二期课改练习册高二第二学期",
"edit": [
"20220726\t王伟叶"
@ -229269,7 +229368,20 @@
"ans": "D",
"solution": "如图, 点$(x,y)$的轨迹为图中的圆, 圆上动点与原点连线斜率的最大值是如图切线的斜率\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (2,0) circle ({sqrt(3)});\n\\draw (0,0) --++ (60:2);\n\\filldraw (2,0) node [below] {$C$} coordinate (C) circle (0.03);\n\\end{tikzpicture}\n\\end{center}",
"duration": -1,
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"edit": [
"20220726\t王伟叶"
@ -250681,7 +250793,19 @@
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"origin": "上海2022年秋季高考试题17",
"edit": [
@ -282309,7 +282433,20 @@
"ans": "(1) $c=8$; (2) $6\\sqrt{6}$",
"solution": "(1) 由$a^2+c^2-2ac\\cos B=b^2$, 即$c^2-5c-24=0$解得$c=8$或$-3$(负数舍去). 故$c=8$.\\\\\n(2) 延长$CM$至$N$, 使得$CM=MN$, 则四边形$ACBN$是平行四边形, 故$S_{\\triangle ABC}=S_{\\triangle ACN}$. $\\triangle ACN$的三边长分别为$5,6,7$, 故$\\cos \\angle CAN=\\dfrac{5^2+7^2-6^2}{2\\times 5\\times 7}=\\dfrac{19}{35}$, 所以$\\sin \\angle CAN=\\dfrac{12\\sqrt{6}}{35}$. 由此, $S_{\\triangle ACN}=\\dfrac 12\\cdot AC\\cdot AN\\cdot \\sin \\angle CAN=6\\sqrt{6}$. 综上, 三角形$ABC$的面积为$6\\sqrt{6}$.",
"duration": -1,
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"origin": "2022届高三下学期周末卷3试题18",
"edit": [
"20220818\t王伟叶"
@ -285654,7 +285791,20 @@
"ans": "(1) $x=\\dfrac{\\sqrt{2}}2$或$x=-\\dfrac{\\sqrt{2}}2$; (2) $x_1^2+x_2^2=1$, $y_1^2+y_2^2=2$; (3) 不存在, 证明略.",
"solution": "(1) 设直线$l$的方程为$x=m$, 由$S_{\\triangle OPQ}=\\dfrac 12\\cdot |m|\\cdot |PQ|=\\dfrac{\\sqrt{2}}{2}$得$|PQ|=\\dfrac{\\sqrt{2}}{|m|}$, 于是点$(m,\\dfrac{\\sqrt{2}}{2|m|})$在椭圆上. 代入椭圆$C$的方程, 得$m^2+\\dfrac{2}{8m^2}=1$, 解得$m^2=\\dfrac 12$. 故直线$l$的方程为$x=\\dfrac{\\sqrt{2}}2$或$x=-\\dfrac{\\sqrt{2}}2$.\\\\\n(2) 当直线$l$的斜率不存在时, 点$P,Q$关于$x$轴对称, 设$P(x_1,y_1)$, $Q(x_1,-y_1)$, 由$x_1^2+\\dfrac{y_1^2}{2}=1$及$|x_1y_1|=\\dfrac{\\sqrt{2}}{2}$解得$|x_1|=\\dfrac{\\sqrt{2}}2$, $|y_1|=1$, 故此时$x_1^2+x_2^2=1$, $y_1^2+y_2^2=2$.\\\\\n当直线$l$的斜率存在时, 设直线$l$的方程为$y=kx+m$, 与椭圆$C$的方程联立, 整理得$(2+k^2)x^2+2kmx+m^2-2=0$, 由$\\dfrac 12|x_1y_2-x_2y_1|=\\dfrac 12|x_1(kx_2+m)-x_2(kx_1+m)|=\\dfrac 12|m||x_1-x_2|=\\dfrac{\\sqrt{2}}{2}$得$\\sqrt{2}(2+k^2)=|m|\\sqrt{2+k^2-m^2}$. 于是$2m^2=2+k^2$, $x_1^2+x_2^2=(x_1+x_2)^2-2x_1x_2=(\\dfrac{-2km}{2+k^2})^2-\\dfrac{2m^2-4}{2+k^2}=1$, $y_1^2+y_2^2=2(1-x_1^2+1-x_2^2)=2$.\\\\\n(3) 假设这样的三角形存在, 则三点$D(x_1,y_1)$, $E(x_2,y_2)$, $G(x_3,y_3)$应满足$x_1^2+x_2^2=x_2^2+x_3^2=x_3^2+x_1^2=1$, 从而$x_1^2=x_2^2=x_3^2=\\dfrac 12$, 但椭圆$C$上任取横坐标为$\\pm \\dfrac{\\sqrt{2}}{2}$的三点, 总有两个点与原点共线, 此时三角形不存在, 矛盾. 因此假设不成立, 满足条件的三角形不存在.",
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"edit": [
"20220818\t王伟叶"
@ -302285,13 +302435,25 @@
"第一单元"
],
"genre": "填空题",
"ans": "$4$",
"ans": "$6$",
"solution": "解$1\\cdot a-2\\cdot 3=0$得$a=6$, 此时方程组确实无解",
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@ -309108,7 +309270,20 @@
"ans": "B",
"solution": "要求$a^2-(k+2)ab+b^2\\ge 0$恒成立, 即要求$(k+2)^2b^2-4b^2\\le 0$对一切$b\\in \\mathbf{R}$恒成立, 即要求$(k^2+4k)\\le 0$, 解得$k$的范围为$[-4,0]$",
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@ -422157,7 +422332,20 @@
"ans": "B",
"solution": "注意到$1^2=2\\cdot 1-1$, 因此$A=\\{x|x\\in \\mathbf{R},\\ x\\ne 1\\}$与$B=\\{1\\}$时$f(x)$是偶函数, 而$A=\\{x|x\\in \\mathbf{R},\\ x\\ne 1, \\ x\\ne 0\\}$与$B=\\{0,1\\}$时$f(x)$也是偶函数, 故\\textcircled{1}错误.\\\\\n任何一组满足$\\dfrac 32\\in A$, $\\pm \\sqrt{2}\\in B$的满足要求的集合都能使得$f(x)=2$无解, 注意到$3,4,5,6,\\cdot$都可以随意放置在$A$或$B$之一内, 因此这样的集合确实有无穷多对, \\textcircled{2}正确.",
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"origin": "2022届杨浦一模试题16",
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"20230107\t王伟叶"
@ -434124,7 +434312,20 @@
"ans": "(1) $y=x$; (2) $g'(x)=\\mathrm{e}^x(\\ln (x+1)+\\dfrac 1{x+1}+\\dfrac{x}{(x+1)^2})$, 故$g(x)$在$[1,+\\infty)$上是严格增函数; (3) 证明略.",
"solution": "(1) $f'(0)=\\mathrm{e}^0(\\dfrac{1}{1+0}+\\ln (1+0))=1$, 又$f(0)=0$, 故所求切线的方程为$y=x$.\\\\\n(2) $g(x)=f'(x)=\\mathrm{e}^x(\\dfrac{1}{1+x}+\\ln (1+x))$. $g'(x)=\\mathrm{e}^x(\\ln (1+x)+\\dfrac{2}{1+x}-\\dfrac{1}{(1+x)^2})$, 当$x>0$时, $\\mathrm{e}^x>1>0$, $\\ln(1+x)>0$, 且$\\dfrac{2}{1+x}-\\dfrac{1}{(1+x)^2}=\\dfrac{2x+1}{(1+x)^2}>0$, 所以$g'(x)$在$(0,+\\infty)$上恒正. 因此$g(x)$在$[0,+\\infty)$上是严格增函数.\\\\\n(3) 对于固定的常数$t$, 令$h(x)=f(x+t)-f(x)-f(t)$, 则$h(t)=0$, 而$h'(x)=f'(x+t)-f'(x)=g(x+t)-g(x)$. 由(2)可知$g(x+t)>g(x)$, 故$h'(x)$在$(0,+\\infty)$上恒正, 于是有$h(s)>h(0)=0$, 即$f(s+t)>f(s)+f(t)$.",
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"20230220\t王伟叶"
@ -434149,7 +434350,20 @@
"ans": "$\\dfrac 35$",
"solution": "所有取法共有$\\mathrm{C}_6^3=20$种, 其中恰有两个小球编号相邻的取法有$124$, $125$, $126$, $235$, $236$, $134$, $346$, $145$, $245$, $156$, $256$, $356$共$12$种, 所以所求概率为$\\dfrac{12}{20}=\\dfrac 35$",
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"20220624\t王伟叶, 余利成",
@ -434176,7 +434390,20 @@
"ans": "$17$",
"solution": "考虑$(x^{\\frac 12}+x^{-\\frac 13})^{100}$展开式的通项$T_{r+1}=\\mathrm{C}_{100}^rx^{\\frac{100-r}2}\\cdot (x^{-\\frac 13})^r=\\mathrm{C}_{100}^rx^{50-\\dfrac{3r}6}$.\n令$r=6k$($k\\in \\mathbf{Z}$), 则$0\\le 6k\\le 100$, 即$r=0,6,12,\\cdots ,96$.\n因此共有$17$个有理项.",
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"edit": [
"20220720\t王伟叶",
@ -434200,7 +434427,20 @@
"ans": "$\\dfrac 23$",
"solution": "$\\dfrac{1}{\\sin^2\\alpha+2\\sin\\alpha\\cos\\alpha}=\\dfrac{\\sin^2\\alpha+\\cos^2\\alpha}{\\sin^2\\alpha+2\\sin\\alpha\\cos\\alpha}=\\dfrac{\\tan^2\\alpha+1}{\\tan^2\\alpha+2\\tan\\alpha}=\\dfrac 2 3$",
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"20220726\t王伟叶",
@ -434225,7 +434465,20 @@
"ans": "$\\dfrac{2\\pi}3$",
"solution": "因$\\overrightarrow{b}\\cdot \\overrightarrow{b}=36$, 故$\\overrightarrow{a}\\cdot \\overrightarrow{b}=-15$, 进而$\\cos\\langle \\overrightarrow a,\\overrightarrow b\\rangle=\\dfrac{-15}{30}=-\\dfrac 12$",
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"20220730\t王伟叶",
@ -434763,7 +435016,20 @@
"ans": "$6$",
"solution": "从小到大排列后, 第$9$和第$10$个数的算术平均数为$5$. $18\\cdot 0.75=13.5$, 故第$14$个数也为$5$, 从而第$10$个数小于等于$5$, 因此它等于$5$, 第九个数也必须等于$5$, 这样, 第$9,10,11,12,13,14$这六个数都等于$5$. 另一方面, $8$个$4$, $6$个$5$, $4$个$6$的数据满足要求.",
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@ -439664,5 +439930,404 @@
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"space": "12ex"
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"040181": {
"id": "040181",
"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}.",
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"content": "若角$\\alpha$满足$\\dfrac{1}{2} \\cos \\alpha-\\dfrac{\\sqrt{3}}{2} \\sin \\alpha=1$, 则$\\alpha=$\\blank{50}.",
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"040183": {
"id": "040183",
"content": "已知$\\cos (\\alpha+\\dfrac{\\pi}{6})=\\dfrac{3}{5}$, $\\alpha \\in[0, \\pi)$, 则$\\sin \\alpha=$\\blank{50}.",
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"040184": {
"id": "040184",
"content": "若$3 \\sin \\alpha=4 \\cos \\alpha$, 则$\\tan (\\alpha-\\dfrac{\\pi}{4})=$\\blank{50}.",
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"040185": {
"id": "040185",
"content": "将$4 \\sin \\alpha-4 \\cos \\alpha$化成$A \\sin (\\alpha+\\varphi)$(其中$A>0$, $\\varphi \\in[0,2 \\pi)$)的形式为\\blank{50}.",
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"040186": {
"id": "040186",
"content": "已知$\\tan \\alpha=-\\dfrac{1}{7}$, $\\tan (2 \\alpha-\\beta)=2$, 则$\\tan (\\alpha-\\beta)=$\\blank{50}.",
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"040187": {
"id": "040187",
"content": "化简: $\\cos ^2 \\alpha+\\cos ^2(\\dfrac{\\pi}{3}+\\alpha)+\\cos ^2(\\dfrac{\\pi}{3}-\\alpha)=$\\blank{50}.",
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"040188": {
"id": "040188",
"content": "求值: $\\tan 36^{\\circ}+\\sqrt{3} \\tan 24^{\\circ} \\tan 36^{\\circ}+\\tan 24^{\\circ}=$\\blank{50}.",
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"040189": {
"id": "040189",
"content": "若$A+B=-\\dfrac{\\pi}{4}$, 则$(\\tan A-1)(\\tan B-1)=$\\blank{50}.",
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"040190": {
"id": "040190",
"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": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040191": {
"id": "040191",
"content": "已知$\\dfrac{\\pi}{2}<\\boldsymbol{\\alpha}<\\pi$, $-\\pi<\\beta<0$, $\\tan \\alpha=-\\dfrac{1}{3}$, $\\tan \\beta=-\\dfrac{1}{7}$, 则$2 \\alpha+\\beta$的大小为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040192": {
"id": "040192",
"content": "已知$\\dfrac{\\pi}{2}<\\alpha<\\pi$, 且$\\sin \\alpha=\\dfrac{3}{5}$, $\\tan (\\alpha-\\beta)=-1$, 则$2 \\cos ^2 \\beta-\\dfrac{4}{5} \\tan \\alpha=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040193": {
"id": "040193",
"content": "若$\\alpha$、$\\beta$均为锐角, 且$\\sin \\alpha=\\dfrac{m}{\\sqrt{1+m^2}}, \\tan \\beta=\\dfrac{1}{m}$, 则$\\alpha+\\beta$的值为\\bracket{20}.\n\\fourch{$150^{\\circ}$}{$120^{\\circ}$}{$90^{\\circ}$}{$60^{\\circ}$}",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040194": {
"id": "040194",
"content": "若$\\sin 2 x \\sin 3 x=\\cos 2 x \\cos 3 x$, 则$x$的一个值是\\bracket{20}.\n\\fourch{$18^{\\circ}$}{$36^{\\circ}$}{$30^{\\circ}$}{$45^{\\circ}$}",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040195": {
"id": "040195",
"content": "下列关系中, 角$\\alpha$存在的是\\bracket{20}.\n\\twoch{$\\sin \\alpha+\\cos \\alpha=\\dfrac{3}{2}$}{$\\sin \\alpha+\\cos \\alpha=\\dfrac{4}{3}$}{$\\sin \\alpha=\\dfrac{1}{3}$且$\\cos \\alpha=\\dfrac{2}{3}$}{$\\cos \\alpha-\\sin \\alpha=-\\sqrt{3}$}",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040196": {
"id": "040196",
"content": "若$f(x)=2^{\\sin x}, g(x)=2^{\\cos x}, x \\in R$, 则积函数$f(x) \\cdot g(x)$必有\\bracket{20}.\n\\fourch{最大值$4$}{最小值$4$}{最大值$2^{\\sqrt{2}}$}{最小值$2^{\\sqrt{2}}$}",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040197": {
"id": "040197",
"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": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040198": {
"id": "040198",
"content": "已知$\\alpha$是$\\triangle ABC$的一个内角, 且满足$\\sin \\alpha-\\sqrt{3} \\cos \\alpha=\\sqrt{3}$, 求$\\alpha$的值.",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040199": {
"id": "040199",
"content": "已知$5 \\sin \\beta=\\sin (2 \\alpha+\\beta)$, 求$\\tan (\\alpha+\\beta) \\cot \\alpha$的值.",
"objs": [],
"tags": [],
"genre": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040200": {
"id": "040200",
"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": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040201": {
"id": "040201",
"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": "",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下学期周末卷04",
"edit": [
"20230308\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
}
}