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weiye.wang 2023-02-20 19:15:21 +08:00
parent beb289de7a 8447f36324
commit 3711c36f53
12 changed files with 1042 additions and 159 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": 7,
"execution_count": 3,
"metadata": {},
"outputs": [
{
@ -11,7 +11,7 @@
"0"
]
},
"execution_count": 7,
"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 = \"14039\"\n",
"problems = \"4256\"\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": 6,
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [

6
工具/关键字筛选题号.ipynb
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"cells": [
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 2,
"metadata": {},
"outputs": [
{
@ -11,7 +11,7 @@
"0"
]
},
"execution_count": 9,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -21,7 +21,7 @@
"\n",
"\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n",
"keywords_dict_table = [\n",
" {\"tags\":[\"第九单元\"],\"origin\":[\"高考\"]}\n",
" {\"tags\":[\"第二单元\"],\"genre\":[\"选择题\"]}\n",
"]\n",
"\"\"\"---关键字设置完毕---\"\"\"\n",
"# 示例： keywords_dict_table = [\n",

158
工具/寻找tex文件中未赋答案的题目.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"execution_count": 1,
"metadata": {},
"outputs": [
{
@ -648,6 +648,158 @@
"013205\n",
"\n",
"\n",
"09_立体几何综合.tex\n",
"013175\n",
"\n",
"\n",
"013178\n",
"\n",
"\n",
"031234\n",
"\n",
"\n",
"014028\n",
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"014042\n",
"\n",
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"\n",
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"\n",
"014352\n",
"\n",
"\n",
"014053\n",
"\n",
"\n",
"014037\n",
"\n",
"\n",
"10_空间向量与应用.tex\n",
"014040\n",
"\n",
"\n",
"014039\n",
"\n",
"\n",
"014448\n",
"\n",
"\n",
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"\n",
"\n",
"014437\n",
"\n",
"\n",
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"\n",
"\n",
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"\n",
"\n",
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"\n",
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"\n",
"\n",
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"\n",
"\n",
"11_直线与圆.tex\n",
"014367\n",
"\n",
@ -922,6 +1074,10 @@
"\n",
"\n",
"高三下学期测验01.tex\n",
"高三下学期周末卷01.tex\n",
"高三下学期周末卷02.tex\n",
"高三下学期周末卷03.tex\n",
"高三下学期周末卷04.tex\n",
"中档题.tex\n",
"容易题.tex\n",
"寒假作业反馈练习.tex\n",

9
工具/寻找阶段末尾空闲题号.ipynb
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@ -9,9 +9,10 @@
"name": "stdout",
"output_type": "stream",
"text": [
"首个空闲id: 14511 , 直至 020000\n",
"首个空闲id: 14532 , 直至 020000\n",
"首个空闲id: 22048 , 直至 030000\n",
"首个空闲id: 31236 , 直至 999999\n"
"首个空闲id: 31236 , 直至 040000\n",
"首个空闲id: 40037 , 直至 999999\n"
]
}
],
@ -45,7 +46,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "mathdept",
"display_name": "pythontest",
"language": "python",
"name": "python3"
},
@ -64,7 +65,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
}
}
},

165
工具/批量添加题库字段数据.ipynb
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@ -9,27 +9,146 @@
"name": "stdout",
"output_type": "stream",
"text": [
"题号: 014511 , 字段: ans 中已修改数据: $(-\\infty,2)$\n",
"题号: 014512 , 字段: ans 中已修改数据: $(-3,5)$\n",
"题号: 014513 , 字段: ans 中已修改数据: $80$\n",
"题号: 014514 , 字段: ans 中已修改数据: $-2$\n",
"题号: 014515 , 字段: ans 中已修改数据: $\\sqrt{10}$\n",
"题号: 014516 , 字段: ans 中已修改数据: $10.8$\n",
"题号: 014517 , 字段: ans 中已修改数据: $\\dfrac{7}{25}$\n",
"题号: 014518 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{3}}3\\pi$\n",
"题号: 014519 , 字段: ans 中已修改数据: $\\dfrac{2\\sqrt{6}}5$\n",
"题号: 014520 , 字段: ans 中已修改数据: $\\dfrac{3}{10}$\n",
"题号: 014521 , 字段: ans 中已修改数据: $10$\n",
"题号: 014522 , 字段: ans 中已修改数据: $\\dfrac{3\\pi}{8}$\n",
"题号: 014523 , 字段: ans 中已修改数据: C\n",
"题号: 014524 , 字段: ans 中已修改数据: D\n",
"题号: 014525 , 字段: ans 中已修改数据: B\n",
"题号: 014526 , 字段: ans 中已修改数据: A\n",
"题号: 014527 , 字段: ans 中已修改数据: (1) $2n-1$; (2) $4n^2+\\dfrac{9^n}{4}-\\dfrac 14$\n",
"题号: 014528 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\dfrac{2\\sqrt{3}}3$\n",
"题号: 014529 , 字段: ans 中已修改数据: (1) 如设$AE=x$百米, 则$y=4x+8-2\\sqrt{x^2-9}$($3<x<5$); 如设$\\angle MAE=x$, 则$y=\\dfrac{12}{\\cos x}+8-6\\tan x$($0<x<\\arctan\\dfrac 43$)等; (2) 约$18.39$百米\n",
"题号: 014530 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}8+\\dfrac{y^2}4=1$; (2) 证明略; (3) 斜率的最小值为$\\dfrac{\\sqrt{6}}2$, 此时直线$l_1$的方程为$y=\\dfrac{\\sqrt{6}}6x+\\dfrac{2\\sqrt{7}}7$\n",
"题号: 014531 , 字段: ans 中已修改数据: (1) $f(x)=2^x$是关于$(0,+\\infty)$的同变函数, 不是关于$(0,1)$的同变函数; (2) $f(x)=\\sqrt{2(x-2k)}+2k$, 当$x=2k+\\dfrac 12$($k\\in\\mathbf{Z}$)时, $f(x)=x+\\dfrac 12$, 当$x\\ne 2k+\\dfrac 12$($k\\in\\mathbf{Z}$)时, $f(x)<x+\\dfrac 12$; (3) 证明略\n"
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.974\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.921\t0.868\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.895\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.895\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.868\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.895\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.474\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.974\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.184\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.684\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.921\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.789\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.895\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三10班\t0.342\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.727\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.773\t0.727\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.909\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.545\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.682\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t1.000\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.636\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.727\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.136\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.545\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.864\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.545\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.455\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三11班\t0.091\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.792\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.833\t0.875\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.958\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.917\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.792\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.958\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.542\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.958\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.125\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.667\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t1.000\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.792\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.917\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三12班\t0.375\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.938\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.938\t0.906\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.969\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.938\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.906\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.969\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.562\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.875\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.344\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.750\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.906\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.719\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t1.000\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三02班\t0.031\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.897\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.793\t0.862\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.897\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.966\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.793\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.759\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.724\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.828\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.414\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.690\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.931\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.724\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.931\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三03班\t0.103\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.862\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.828\t0.862\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.655\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.931\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.828\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.862\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.621\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t1.000\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.207\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.517\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.828\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.552\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.931\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三04班\t0.103\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.800\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.825\t0.875\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.850\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.800\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.800\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.825\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.550\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.950\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.225\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.625\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.900\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.800\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.825\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三05班\t0.675\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.727\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.818\t0.818\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.788\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.879\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.818\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.879\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.576\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.879\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.333\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.515\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.818\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.636\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.849\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三07班\t0.091\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.727\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.909\t0.939\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.879\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.849\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.758\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.818\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.727\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.909\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.333\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.636\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.939\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.727\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.909\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三08班\t0.182\n",
"题号: 014133 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.765\n",
"题号: 013724 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.912\t0.941\n",
"题号: 012816 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.824\n",
"题号: 013736 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.765\n",
"题号: 014164 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.794\n",
"题号: 013742 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.882\n",
"题号: 013727 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.588\n",
"题号: 013746 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.853\n",
"题号: 013747 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.176\n",
"题号: 013720 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.529\n",
"题号: 014157 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.882\n",
"题号: 031224 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.588\n",
"题号: 013752 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.853\n",
"题号: 013738 , 字段: usages 中已添加数据: 20230220\t2023届高三09班\t0.118\n"
]
}
],
@ -127,7 +246,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "mathdept",
"display_name": "pythontest",
"language": "python",
"name": "python3"
},
@ -146,7 +265,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
}
}
},

444
工具/文本文件/metadata.txt
View File

@ -1,64 +1,422 @@
ans
usages
14511
$(-\infty,2)$
014133
20230220 2023届高三10班 0.974
14512
$(-3,5)$
013724
20230220 2023届高三10班 0.921 0.868
14513
$80$
012816
20230220 2023届高三10班 0.895
14514
$-2$
013736
20230220 2023届高三10班 0.895
14515
$\sqrt{10}$
014164
20230220 2023届高三10班 0.868
14516
$10.8$
013742
20230220 2023届高三10班 0.895
14517
$\dfrac{7}{25}$
013727
20230220 2023届高三10班 0.474
14518
$\dfrac{\sqrt{3}}3\pi$
013746
20230220 2023届高三10班 0.974
14519
$\dfrac{2\sqrt{6}}5$
013747
20230220 2023届高三10班 0.184
14520
$\dfrac{3}{10}$
013720
20230220 2023届高三10班 0.684
14521
$10$
014157
20230220 2023届高三10班 0.921
14522
$\dfrac{3\pi}{8}$
031224
20230220 2023届高三10班 0.789
14523
C
013752
20230220 2023届高三10班 0.895
14524
D
013738
20230220 2023届高三10班 0.342
14525
B
014133
20230220 2023届高三11班 0.727
14526
A
013724
20230220 2023届高三11班 0.773 0.727
14527
(1) $2n-1$; (2) $4n^2+\dfrac{9^n}{4}-\dfrac 14$
012816
20230220 2023届高三11班 0.909
14528
(1) 证明略; (2) $\dfrac{2\sqrt{3}}3$
013736
20230220 2023届高三11班 0.545
14529
(1) 如设$AE=x$百米, 则$y=4x+8-2\sqrt{x^2-9}$($3<x<5$); 如设$\angle MAE=x$, 则$y=\dfrac{12}{\cos x}+8-6\tan x$($0<x<\arctan\dfrac 43$)等; (2) 约$18.39$百米
014164
20230220 2023届高三11班 0.682
14530
(1) $\dfrac{x^2}8+\dfrac{y^2}4=1$; (2) 证明略; (3) 斜率的最小值为$\dfrac{\sqrt{6}}2$, 此时直线$l_1$的方程为$y=\dfrac{\sqrt{6}}6x+\dfrac{2\sqrt{7}}7$
013742
20230220 2023届高三11班 1.000
013727
20230220 2023届高三11班 0.636
013746
20230220 2023届高三11班 0.727
013747
20230220 2023届高三11班 0.136
013720
20230220 2023届高三11班 0.545
014157
20230220 2023届高三11班 0.864
031224
20230220 2023届高三11班 0.545
013752
20230220 2023届高三11班 0.455
013738
20230220 2023届高三11班 0.091
014133
20230220 2023届高三12班 0.792
013724
20230220 2023届高三12班 0.833 0.875
012816
20230220 2023届高三12班 0.958
013736
20230220 2023届高三12班 0.917
014164
20230220 2023届高三12班 0.792
013742
20230220 2023届高三12班 0.958
013727
20230220 2023届高三12班 0.542
013746
20230220 2023届高三12班 0.958
013747
20230220 2023届高三12班 0.125
013720
20230220 2023届高三12班 0.667
014157
20230220 2023届高三12班 1.000
031224
20230220 2023届高三12班 0.792
013752
20230220 2023届高三12班 0.917
013738
20230220 2023届高三12班 0.375
014133
20230220 2023届高三02班 0.938
013724
20230220 2023届高三02班 0.938 0.906
012816
20230220 2023届高三02班 0.969
013736
20230220 2023届高三02班 0.938
014164
20230220 2023届高三02班 0.906
013742
20230220 2023届高三02班 0.969
013727
20230220 2023届高三02班 0.562
013746
20230220 2023届高三02班 0.875
013747
20230220 2023届高三02班 0.344
013720
20230220 2023届高三02班 0.750
014157
20230220 2023届高三02班 0.906
031224
20230220 2023届高三02班 0.719
013752
20230220 2023届高三02班 1.000
013738
20230220 2023届高三02班 0.031
014133
20230220 2023届高三03班 0.897
013724
20230220 2023届高三03班 0.793 0.862
012816
20230220 2023届高三03班 0.897
013736
20230220 2023届高三03班 0.966
014164
20230220 2023届高三03班 0.793
013742
20230220 2023届高三03班 0.759
013727
20230220 2023届高三03班 0.724
013746
20230220 2023届高三03班 0.828
013747
20230220 2023届高三03班 0.414
013720
20230220 2023届高三03班 0.690
014157
20230220 2023届高三03班 0.931
031224
20230220 2023届高三03班 0.724
013752
20230220 2023届高三03班 0.931
013738
20230220 2023届高三03班 0.103
014133
20230220 2023届高三04班 0.862
013724
20230220 2023届高三04班 0.828 0.862
012816
20230220 2023届高三04班 0.655
013736
20230220 2023届高三04班 0.931
014164
20230220 2023届高三04班 0.828
013742
20230220 2023届高三04班 0.862
013727
20230220 2023届高三04班 0.621
013746
20230220 2023届高三04班 1.000
013747
20230220 2023届高三04班 0.207
013720
20230220 2023届高三04班 0.517
014157
20230220 2023届高三04班 0.828
031224
20230220 2023届高三04班 0.552
013752
20230220 2023届高三04班 0.931
013738
20230220 2023届高三04班 0.103
014133
20230220 2023届高三05班 0.800
013724
20230220 2023届高三05班 0.825 0.875
012816
20230220 2023届高三05班 0.850
013736
20230220 2023届高三05班 0.800
014164
20230220 2023届高三05班 0.800
013742
20230220 2023届高三05班 0.825
013727
20230220 2023届高三05班 0.550
013746
20230220 2023届高三05班 0.950
013747
20230220 2023届高三05班 0.225
013720
20230220 2023届高三05班 0.625
014157
20230220 2023届高三05班 0.900
031224
20230220 2023届高三05班 0.800
013752
20230220 2023届高三05班 0.825
013738
20230220 2023届高三05班 0.675
014133
20230220 2023届高三07班 0.727
013724
20230220 2023届高三07班 0.818 0.818
012816
20230220 2023届高三07班 0.788
013736
20230220 2023届高三07班 0.879
014164
20230220 2023届高三07班 0.818
013742
20230220 2023届高三07班 0.879
013727
20230220 2023届高三07班 0.576
013746
20230220 2023届高三07班 0.879
013747
20230220 2023届高三07班 0.333
013720
20230220 2023届高三07班 0.515
014157
20230220 2023届高三07班 0.818
031224
20230220 2023届高三07班 0.636
013752
20230220 2023届高三07班 0.849
013738
20230220 2023届高三07班 0.091
014133
20230220 2023届高三08班 0.727
013724
20230220 2023届高三08班 0.909 0.939
012816
20230220 2023届高三08班 0.879
013736
20230220 2023届高三08班 0.849
014164
20230220 2023届高三08班 0.758
013742
20230220 2023届高三08班 0.818
013727
20230220 2023届高三08班 0.727
013746
20230220 2023届高三08班 0.909
013747
20230220 2023届高三08班 0.333
013720
20230220 2023届高三08班 0.636
014157
20230220 2023届高三08班 0.939
031224
20230220 2023届高三08班 0.727
013752
20230220 2023届高三08班 0.909
013738
20230220 2023届高三08班 0.182
014133
20230220 2023届高三09班 0.765
013724
20230220 2023届高三09班 0.912 0.941
012816
20230220 2023届高三09班 0.824
013736
20230220 2023届高三09班 0.765
014164
20230220 2023届高三09班 0.794
013742
20230220 2023届高三09班 0.882
013727
20230220 2023届高三09班 0.588
013746
20230220 2023届高三09班 0.853
013747
20230220 2023届高三09班 0.176
013720
20230220 2023届高三09班 0.529
014157
20230220 2023届高三09班 0.882
031224
20230220 2023届高三09班 0.588
013752
20230220 2023届高三09班 0.853
013738
20230220 2023届高三09班 0.118
14531
(1) $f(x)=2^x$是关于$(0,+\infty)$的同变函数, 不是关于$(0,1)$的同变函数; (2) $f(x)=\sqrt{2(x-2k)}+2k$, 当$x=2k+\dfrac 12$($k\in\mathbf{Z}$)时, $f(x)=x+\dfrac 12$, 当$x\ne 2k+\dfrac 12$($k\in\mathbf{Z}$)时, $f(x)<x+\dfrac 12$; (3) 证明略

2
工具/文本文件/题号筛选.txt
View File

@ -1 +1 @@
003617,011704,011719,012385,012745,012752
000049,000055,000062,000070,001152,001210,001287,002838,002853,002854,002863,002864,002865,002874,002875,002880,002902,002909,002913,002924,002925,002938,002954,002965,002987,003022,003601,003625,003667,003718,003730,003757,003770,003772,003801,003815,003862,003892,003907,003921,003936,003966,003980,003981,004074,004094,004116,004155,004157,004220,004284,004305,004347,004366,004368,004385,004401,004403,004422,004439,004440,004523,004525,004544,004546,004563,004631,004697,004739,004757,004760,004902,004907,005008,005016,005103,005104,005105,005193,005194,005195,005196,005197,005198,005283,005284,005285,005286,005287,005288,005296,005298,005299,005300,005301,005302,005303,005329,005330,005331,005332,005333,005362,005368,005369,005370,005371,005372,005373,005374,005375,005376,005377,005378,005379,005380,005381,005382,005383,005384,005385,005386,005424,005445,005446,005447,005448,005449,005450,005472,005473,005474,005475,005476,005477,005491,005492,005493,005494,005495,005496,005501,005502,005503,005504,005505,005506,005507,005508,005523,005524,005525,005526,005527,005528,005529,005530,005541,005542,005543,005563,005564,005565,005566,005567,005568,005569,005570,005571,005572,005573,005574,005612,005613,005614,005615,005616,005617,005618,005619,005620,005621,005653,005654,005655,005656,005657,005658,005659,005660,005687,005688,005689,005690,005691,005692,005693,005694,005695,005696,005713,005714,005718,005719,005720,005721,005722,005723,005724,005758,005759,005760,005761,005762,005763,005764,005782,005783,005784,005785,005786,007861,007892,007958,007959,007966,007984,008036,008037,008081,008082,008094,008095,008371,008372,008387,008388,008389,009476,009508,009537,010137,010149,010150,010173,010938,010977,010999,011041,011042,011043,011126,011145,011147,011148,011196,011212,011215,011233,011236,011256,011320,011404,011446,011529,011548,011594,011616,011687,011733,011911,011915,011927,011929,011947,011985,012001,012003,012022,012023,012090,012130,012132,012153,012173,012194,012215,012257,012259,012278,012300,012301,012302,012320,012344,012365,012367,012371,012374,012399,012401,012428,012430,012466,012471,012502,012543,012564,012605,012626,012628,012709,012733,012751,012783,012792,012836,012843,012849,012850,012860,012861,012863,012884,012885,012890,012895,012904,012905,012906,012907,012913,013297,013314,013342,013388,013418,013433,013447,013449,013477,013479,013508,013523,013539,013553,013554,013583,013600,013621,013768,013798,013799,013801,013829,013841,020358,020359,020365,020366,020377,020378,020379,020386,020387,020406,020407,020408,020417,020418,020419,020439,020440,020441,020442,020451,020465,020476,020477,020478,020487,020498,020499,020504,020524,020525,020526,020529,020554,020555,020561,020562,020566,020678,020679,020680,020681,021369,021388,030300,030307,030372,030379,030393,030400,030442,030667,030668,030671,030672,030673,030674,030675,030689,030690,030691,030692,030701,030722,030723,030728,030729,030755,030756

6
工具/添加关联题目.ipynb
View File

@ -2,15 +2,15 @@
"cells": [
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import os,re,json,time\n",
"\n",
"\"\"\"---设置原题目id与新题目id列表, 新id的数目不能小于旧id的数目---\"\"\"\n",
"old_ids = \"13193,13179\"\n",
"new_ids = \"31234,31235\"\n",
"old_ids = \"221,7528,8380,9626\"\n",
"new_ids = \"31237:31240\"\n",
"\"\"\"---设置完毕---\"\"\"\n",
"\"\"\"---完成编辑后记得运行第二个单元格---\"\"\"\n",
"\n",

53
工具/添加题目到数据库.ipynb
View File

@ -2,63 +2,28 @@
"cells": [
{
"cell_type": "code",
"execution_count": 49,
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#修改起始id,出处,文件名\n",
"starting_id = 40001\n",
"raworigin = \"\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n",
"editor = \"20230218\\t王伟叶\"\n",
"starting_id = 31236\n",
"raworigin = \"2022年北京高考\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目8.tex\"\n",
"editor = \"20230220\\t王伟叶\"\n",
"indexed = False\n"
]
},
{
"cell_type": "code",
"execution_count": 50,
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"添加题号040001, 来源: 2024届高二下学期周末卷01\n",
"添加题号040002, 来源: 2024届高二下学期周末卷01\n",
"添加题号040003, 来源: 2024届高二下学期周末卷01\n",
"添加题号040004, 来源: 2024届高二下学期周末卷01\n",
"添加题号040005, 来源: 2024届高二下学期周末卷01\n",
"添加题号040006, 来源: 2024届高二下学期周末卷01\n",
"添加题号040007, 来源: 2024届高二下学期周末卷01\n",
"添加题号040008, 来源: 2024届高二下学期周末卷01\n",
"添加题号040009, 来源: 2024届高二下学期周末卷01\n",
"添加题号040010, 来源: 2024届高二下学期周末卷01\n",
"添加题号040011, 来源: 2024届高二下学期周末卷01\n",
"添加题号040012, 来源: 2024届高二下学期周末卷01\n",
"添加题号040013, 来源: 2024届高二下学期周末卷01\n",
"添加题号040014, 来源: 2024届高二下学期周末卷01\n",
"添加题号040015, 来源: 2024届高二下学期周末卷01\n",
"添加题号040016, 来源: 2024届高二下学期周末卷01\n",
"添加题号040017, 来源: 2024届高二下学期周末卷01\n",
"添加题号040018, 来源: 2025届高一下学期周末卷01\n",
"添加题号040019, 来源: 2025届高一下学期周末卷01\n",
"添加题号040020, 来源: 2025届高一下学期周末卷01\n",
"添加题号040021, 来源: 2025届高一下学期周末卷01\n",
"添加题号040022, 来源: 2025届高一下学期周末卷01\n",
"添加题号040023, 来源: 2025届高一下学期周末卷01\n",
"添加题号040024, 来源: 2025届高一下学期周末卷01\n",
"添加题号040025, 来源: 2025届高一下学期周末卷01\n",
"添加题号040026, 来源: 2025届高一下学期周末卷01\n",
"添加题号040027, 来源: 2025届高一下学期周末卷01\n",
"添加题号040028, 来源: 2025届高一下学期周末卷01\n",
"添加题号040029, 来源: 2025届高一下学期周末卷01\n",
"添加题号040030, 来源: 2025届高一下学期周末卷01\n",
"添加题号040031, 来源: 2025届高一下学期周末卷01\n",
"添加题号040032, 来源: 2025届高一下学期周末卷01\n",
"添加题号040033, 来源: 2025届高一下学期周末卷01\n",
"添加题号040034, 来源: 2025届高一下学期周末卷01\n",
"添加题号040035, 来源: 2025届高一下学期周末卷01\n",
"添加题号040036, 来源: 2025届高一下学期周末卷01\n"
"添加题号031236, 来源: 2022年北京高考\n"
]
}
],
@ -163,7 +128,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "mathdept",
"display_name": "pythontest",
"language": "python",
"name": "python3"
},
@ -182,7 +147,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
}
}
},

14
工具/讲义生成.ipynb
View File

@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 3,
"metadata": {},
"outputs": [
{
@ -15,9 +15,9 @@
"题块 2 处理完毕.\n",
"正在处理题块 3 .\n",
"题块 3 处理完毕.\n",
"开始编译教师版本pdf文件: 临时文件/高三下学期周末卷04_教师_20230217.tex\n",
"开始编译教师版本pdf文件: 临时文件/高三下月考01预选_教师_20230220.tex\n",
"0\n",
"开始编译学生版本pdf文件: 临时文件/高三下学期周末卷04_学生_20230217.tex\n",
"开始编译学生版本pdf文件: 临时文件/高三下月考01预选_学生_20230220.tex\n",
"0\n"
]
}
@ -35,7 +35,7 @@
"\"\"\"---设置题块编号---\"\"\"\n",
"\n",
"problems = [\n",
"\"14511:14522\",\"14523:14526\",\"14527:14531\"\n",
"\"3675,12165,31237,31238,31239,4252,4256,31240,4499,4132,4217,4235\",\"8972,9082,12445,30691\",\"11301,10000,3691,11450,31236\"\n",
"]\n",
"\n",
"\"\"\"---设置结束---\"\"\"\n",
@ -49,7 +49,7 @@
"elif paper_type == 2:\n",
" enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n",
" template_file = \"模板文件/测验周末卷模板.txt\" #设置模板文件名\n",
" exec_list = [(\"标题替换\",\"高三下学期周末卷04\")] #设置讲义标题\n",
" exec_list = [(\"标题替换\",\"高三下月考01预选\")] #设置讲义标题\n",
" destination_file = \"临时文件/\"+exec_list[0][1] # 设置输出文件名\n",
"elif paper_type == 3:\n",
" enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n",
@ -204,7 +204,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "mathdept",
"display_name": "pythontest",
"language": "python",
"name": "python3"
},
@ -223,7 +223,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
}
}
},

6
工具/题号选题pdf生成.ipynb
View File

@ -9,9 +9,9 @@
"name": "stdout",
"output_type": "stream",
"text": [
"开始编译教师版本pdf文件: 临时文件/题库_教师用_20230219.tex\n",
"开始编译教师版本pdf文件: 临时文件/选题_教师用_20230220.tex\n",
"0\n",
"开始编译学生版本pdf文件: 临时文件/题库_学生用_20230219.tex\n",
"开始编译学生版本pdf文件: 临时文件/选题_学生用_20230220.tex\n",
"0\n"
]
}
@ -33,7 +33,7 @@
"\n",
"\"\"\"---设置文件名---\"\"\"\n",
"#目录和文件的分隔务必用/\n",
"filename = \"临时文件/题库\"\n",
"filename = \"临时文件/选题\"\n",
"\"\"\"---设置文件名结束---\"\"\"\n",
"\n",
"\n",

330
题库0.3/Problems.json
View File

@ -5765,7 +5765,9 @@
"20220624\t王伟叶, 余利成"
],
"same": [],
"related": [],
"related": [
"031237"
],
"remark": "",
"space": "12ex"
},
@ -113891,7 +113893,7 @@
},
"004256": {
"id": "004256",
"content": "设$f(x)$是定义在$\\mathbf{R}$上的奇函数, 当$x>0$时, $f(x)=a^x+b$($0<a<1$, $b\\in \\mathbf{R}$), 若$f(x)$存在反函数, 则b的取值范围是\\blank{50}.",
"content": "设$f(x)$是定义在$\\mathbf{R}$上的奇函数, 当$x>0$时, $f(x)=a^x+b$($0<a<1$, $b\\in \\mathbf{R}$), 若$f(x)$存在反函数, 则$b$的取值范围是\\blank{50}.",
"objs": [
"K0218001B",
"K0225002B"
@ -191798,7 +191800,9 @@
"20220720\t王伟叶"
],
"same": [],
"related": [],
"related": [
"031238"
],
"remark": "",
"space": "12ex"
},
@ -212282,7 +212286,8 @@
"000100"
],
"related": [
"009553"
"009553",
"031239"
],
"remark": "",
"space": "12ex"
@ -226521,7 +226526,7 @@
},
"008972": {
"id": "008972",
"content": "已知复数$z_1=a+b\\mathrm{i}(ab\\in \\mathbf{R})$和复数$z_2=c+d\\mathrm{i}(cd\\in \\mathbf{R})$. ``$a=c$''是``$z_1=z_2$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}",
"content": "已知复数$z_1=a+b\\mathrm{i}$($a,b\\in \\mathbf{R}$)和复数$z_2=c+d\\mathrm{i}$($c,d\\in \\mathbf{R}$). ``$a=c$''是``$z_1=z_2$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}",
"objs": [],
"tags": [
"第五单元"
@ -241430,7 +241435,9 @@
"20220730\t王伟叶"
],
"same": [],
"related": [],
"related": [
"031240"
],
"remark": "",
"space": ""
},
@ -307935,7 +307942,7 @@
},
"012411": {
"id": "012411",
"content": "已知数列$\\{a_n\\}$满足$a_n>0$, 双曲线$C_n: \\dfrac{x^2}{a_n}-\\dfrac{y^2}{a_{n+1}}=1$($n \\in \\mathbf{N}$, $n\\ge 1$).\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\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 = {sqrt(2)}:4,samples = 100] plot (\\x,{sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (-\\x,{sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (\\x,{-sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (-\\x,{-sqrt(\\x*\\x-2)});\n\\draw (-4,-4) -- (4,4) (-4,4) -- (4,-4);\n\\draw (2,2) node [left] {$Q_n$} coordinate (Q_n);\n\\draw ({sqrt(6)},2) node [right] {$P_n$} coordinate (P_n);\n\\filldraw [pattern = north west lines] (O) -- (P_n) -- (Q_n);\n\\end{tikzpicture}\n\\end{center}\n(1) 若$a_1=1$, $a_2=2$, 双曲线$C_n$的焦距为$2 c_n$, $c_n=\\sqrt {4 n-1}$, 求$\\{a_n\\}$的通项公式;\\\\\n(2) 如图, 在双曲线$C_n$的右支上取点$P_n(x_{P_n}, n)$, 过$P_n$作$y$轴的垂线, 在第一象限内交$C_n$的渐近线于点$Q_n$, 联结$O P_n$, 记$\\triangle OP_nQ_n$的面积为$S_n$, 若$\\displaystyle\\lim_{n \\to \\infty} a_n=2$, 求$\\displaystyle \\lim_{n \\to \\infty} S_n$.(关于数列极限的运算, 还可参考如下性质: 若$\\displaystyle \\lim_{n \\to \\infty} u_n=A(u_n \\geq 0)$, 则$\\displaystyle \\lim_{n \\to \\infty} \\sqrt {u_n}=\\sqrt A$)",
"content": "已知数列$\\{a_n\\}$满足$a_n>0$, 双曲线$C_n: \\dfrac{x^2}{a_n}-\\dfrac{y^2}{a_{n+1}}=1$($n \\in \\mathbf{N}$, $n\\ge 1$).\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\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] {$O$} coordinate (O);\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (\\x,{sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (-\\x,{sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (\\x,{-sqrt(\\x*\\x-2)});\n\\draw [domain = {sqrt(2)}:4,samples = 100] plot (-\\x,{-sqrt(\\x*\\x-2)});\n\\draw (-4,-4) -- (4,4) (-4,4) -- (4,-4);\n\\draw (2,2) node [left] {$Q_n$} coordinate (Q_n);\n\\draw ({sqrt(6)},2) node [right] {$P_n$} coordinate (P_n);\n\\filldraw [pattern = north west lines] (O) -- (P_n) -- (Q_n);\n\\end{tikzpicture}\n\\end{center}\n(1) 若$a_1=1$, $a_2=2$, 双曲线$C_n$的焦距为$2 c_n$, $c_n=\\sqrt {4 n-1}$, 求$\\{a_n\\}$的通项公式;\\\\\n(2) 如图, 在双曲线$C_n$的右支上取点$P_n(x_{P_n}, n)$, 过$P_n$作$y$轴的垂线, 在第一象限内交$C_n$的渐近线于点$Q_n$, 联结$O P_n$, 记$\\triangle OP_nQ_n$的面积为$S_n$, 若$\\displaystyle\\lim_{n \\to \\infty} a_n=2$, 求$\\displaystyle \\lim_{n \\to \\infty} S_n$.(关于数列极限的运算, 还可参考如下性质: 若$\\displaystyle \\lim_{n \\to \\infty} u_n=A(u_n \\geq 0)$, 则$\\displaystyle \\lim_{n \\to \\infty} \\sqrt {u_n}=\\sqrt A$)",
"objs": [],
"tags": [
"第七单元",
@ -316567,7 +316574,18 @@
"ans": "C",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20230220\t2023届高三11班\t0.909",
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"20230220\t2023届高三02班\t0.969",
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],
"origin": "2022届高三第二轮复习讲义",
"edit": [
"20230118\t王伟叶"
@ -316742,7 +316760,7 @@
},
"012824": {
"id": "012824",
"content": "函数$d(x)=\\begin{cases}0, & x \\in \\mathbf{Q}, \\\\ 1, & x \\notin \\mathrm{Q},\\end{cases}$ 则$d(d(x))=$\\blank{50}.",
"content": "函数$d(x)=\\begin{cases}0, & x \\in \\mathbf{Q}, \\\\ 1, & x \\notin \\mathbf{Q},\\end{cases}$ 则$d(d(x))=$\\blank{50}.",
"objs": [],
"tags": [
"第二单元"
@ -335649,7 +335667,18 @@
"ans": "$(0,16]$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
"20230220\t2023届高三10班\t0.684",
"20230220\t2023届高三11班\t0.545",
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"origin": "2020年空中课堂高三复习课02",
"edit": [
"20230128\t王伟叶"
@ -335739,7 +335768,18 @@
"ans": "\\textcircled{4}",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20230220\t2023届高三02班\t0.938\t0.906",
"20230220\t2023届高三03班\t0.793\t0.862",
"20230220\t2023届高三04班\t0.828\t0.862",
"20230220\t2023届高三05班\t0.825\t0.875",
"20230220\t2023届高三07班\t0.818\t0.818",
"20230220\t2023届高三08班\t0.909\t0.939",
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"origin": "2020年空中课堂高三复习课02",
"edit": [
"20230128\t王伟叶"
@ -335802,7 +335842,18 @@
"ans": "$1$",
"solution": "",
"duration": -1,
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"origin": "2020年空中课堂高三复习课02",
"edit": [
"20230128\t王伟叶"
@ -335991,7 +336042,18 @@
"ans": "$[-1,-\\dfrac 13]$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20230220\t2023届高三03班\t0.966",
"20230220\t2023届高三04班\t0.931",
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"20230220\t2023届高三08班\t0.849",
"20230220\t2023届高三09班\t0.765"
],
"origin": "2020年空中课堂高三复习课03",
"edit": [
"20230128\t王伟叶"
@ -336035,7 +336097,18 @@
"ans": "$[\\dfrac 14,\\dfrac 34)$",
"solution": "",
"duration": -1,
"usages": [],
"usages": [
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"20230220\t2023届高三03班\t0.103",
"20230220\t2023届高三04班\t0.103",
"20230220\t2023届高三05班\t0.675",
"20230220\t2023届高三07班\t0.091",
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"20230220\t2023届高三09班\t0.118"
],
"origin": "2020年空中课堂高三复习课03",
"edit": [
"20230128\t王伟叶"
@ -336126,7 +336199,18 @@
"ans": "$(1,2)\\cup (\\sqrt{10},+\\infty)$",
"solution": "",
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"content": "设$b>0$. 如图, 在平面直角坐标系$xOy$中, $A(x_A, y_A)$是双曲线$\\Gamma_1: \\dfrac{x^2}{4}-\\dfrac{y^2}{b^2}=1$和圆$\\Gamma_2: x^2+y^2=4+b^2$在第一象限内的交点, 曲线$\\Gamma$由$\\Gamma_1$中满足$|x|>x_A$的部分和$\\Gamma_2$中满足$|x|>x_A$的部分构成.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\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 [dashed] (0,0) circle ({2*sqrt(2)});\n\\draw [domain = -4:4,dashed] plot ({sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = -4:4,dashed] plot ({-sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({-sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({-sqrt(\\x*\\x+4)},-\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({sqrt(\\x*\\x+4)},-\\x);\n\\draw [thick] ({sqrt(6)},{sqrt(2)}) coordinate (A1) arc (30:-30:{2*sqrt(2)}) coordinate (A2);\n\\draw [thick] ({-sqrt(6)},{-sqrt(2)}) coordinate (A3) arc (210:150:{2*sqrt(2)}) coordinate (A4);\n\\foreach \\i in {1,2,3,4}\n{\\filldraw [fill = white] (A\\i) circle (0.1);};\n\\end{tikzpicture}\n\\end{center}\n(1) 若$x_A=\\sqrt{6}$, 求$b$的值;\\\\\n(2) 设$b=\\sqrt{5}$, $F_1$、$F_2$分别为$\\Gamma$与$x$轴的左、右两个交点. 第一象限内的点$P$也在$\\Gamma$上, 且$|PF_1|=8$, 求$\\angle F_1PF_2$的大小;\n(3) 若与$\\Gamma_1$的一条渐近线平行的直线$l$与$\\Gamma$在第一象限内恰有两个不同的公共点, 求$b^2$的取值范围.",
"content": "设$b>0$. 如图, 在平面直角坐标系$xOy$中, $A(x_A, y_A)$是双曲线$\\Gamma_1: \\dfrac{x^2}{4}-\\dfrac{y^2}{b^2}=1$和圆$\\Gamma_2: x^2+y^2=4+b^2$在第一象限内的交点, 曲线$\\Gamma$由$\\Gamma_1$中满足$|x|>x_A$的部分和$\\Gamma_2$中满足$|x|>x_A$的部分构成.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\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 [dashed] (0,0) circle ({2*sqrt(2)});\n\\draw [domain = -4:4,dashed] plot ({sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = -4:4,dashed] plot ({-sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({-sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({sqrt(\\x*\\x+4)},\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({-sqrt(\\x*\\x+4)},-\\x);\n\\draw [domain = {sqrt(2)}:4, thick] plot ({sqrt(\\x*\\x+4)},-\\x);\n\\draw [thick] ({sqrt(6)},{sqrt(2)}) coordinate (A1) arc (30:-30:{2*sqrt(2)}) coordinate (A2);\n\\draw [thick] ({-sqrt(6)},{-sqrt(2)}) coordinate (A3) arc (210:150:{2*sqrt(2)}) coordinate (A4);\n\\foreach \\i in {1,2,3,4}\n{\\filldraw [fill = white] (A\\i) circle (0.1);};\n\\end{tikzpicture}\n\\end{center}\n(1) 若$x_A=\\sqrt{6}$, 求$b$的值;\\\\\n(2) 设$b=\\sqrt{5}$, $F_1$、$F_2$分别为$\\Gamma$与$x$轴的左、右两个交点. 第一象限内的点$P$也在$\\Gamma$上, 且$|PF_1|=8$, 求$\\angle F_1PF_2$的大小.",
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@ -427988,7 +428138,18 @@
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"031236": {
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"content": "已知函数 $f(x)=\\mathrm{e}^x \\ln (1+x)$.\\\\\n(1) 求曲线$y=f(x)$在点$(0, f(0))$处的切线方程;\\\\\n(2) 设$g(x)=f'(x)$, 讨论函数$g(x)$在$[0,+\\infty)$上的单调性;\\\\\n(3) 证明: 对任意$s,t\\in (0,+\\infty)$, 均成立$f(s+t)>f(s)+f(t)$.",
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"040001": {
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"content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",
@ -428946,5 +429126,109 @@
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"031237": {
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"content": "从编号分别为$1$、$2$、$3$、$4$、$5$、$6$的$6$个大小与质地相同的小球中随机取出$3$个, 则恰有$2$个小球编号相邻的概率为\\blank{50}.",
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"031238": {
"id": "031238",
"content": "在$(\\sqrt x+\\dfrac 1{\\sqrt[3]x})^{100}$的展开式中, 有理项有\\blank{50}项.",
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"ans": "有$17$项是有理项",
"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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"content": "已知$\\tan \\alpha =3$, 则$\\dfrac 1{\\sin ^2\\alpha +2\\sin \\alpha \\cos \\alpha}$的值为\\blank{50}.",
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"content": "设向量$\\overrightarrow a$、$\\overrightarrow b$满足$|\\overrightarrow a|=5$, $|\\overrightarrow b|=6$, $(\\overrightarrow a+\\overrightarrow b)\\cdot \\overrightarrow b=21$, 则$\\langle \\overrightarrow a, \\overrightarrow b\\rangle =$\\blank{50}.",
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