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20221220 night

This commit is contained in:
weiye.wang 2022-12-21 06:45:11 +08:00
parent 67651b8d4d
commit 8a04fe7a48
9 changed files with 452 additions and 53 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": 11,
"execution_count": 13,
"metadata": {},
"outputs": [
{
@ -11,7 +11,7 @@
"0"
]
},
"execution_count": 11,
"execution_count": 13,
"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 = \"12263\"\n",
"problems = \"12527\"\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": 8,
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [

10
工具/关键字筛选题号.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 4,
"metadata": {},
"outputs": [
{
@ -11,7 +11,7 @@
"0"
]
},
"execution_count": 2,
"execution_count": 4,
"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",
" {\"origin\":[\"2023\"],\"origin2\":[\"松江\"]}\n",
" {\"origin\":[\"2023\"],\"origin2\":[\"虹口\"]}\n",
"]\n",
"\"\"\"---关键字设置完毕---\"\"\"\n",
"# 示例： keywords_dict_table = [\n",
@ -89,7 +89,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.15 ('pythontest')",
"display_name": "mathdept",
"language": "python",
"name": "python3"
},
@ -108,7 +108,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
}
}
},

2
工具/寻找阶段末尾空闲题号.ipynb
View File

@ -9,7 +9,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"首个空闲id: 12655 , 直至 020000\n",
"首个空闲id: 12676 , 直至 020000\n",
"首个空闲id: 20227 , 直至 030000\n",
"首个空闲id: 30503 , 直至 999999\n"
]

2
工具/文本文件/题号筛选.txt
View File

@ -1 +1 @@
012287,012288,012289,012290,012291,012292,012293,012294,012295,012296,012297,012298,012299,012300,012301,012302,012303,012304,012305,012306,012307
012508,012509,012510,012511,012512,012513,012514,012515,012516,012517,012518,012519,012520,012521,012522,012523,012524,012525,012526,012527,012528

8
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 = 12655\n",
"origin = \"2023届宝山区一模\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目3.tex\"\n",
"editor = \"20221217\\t王伟叶\""
"starting_id = 12676\n",
"origin = \"2023届浦东新区一模\"\n",
"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\temp.tex\"\n",
"editor = \"20221220\\t王伟叶\""
]
},
{

12
工具/讲义生成.ipynb
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@ -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/2023届青浦区一模_教师_20221219.tex\n",
"开始编译教师版本pdf文件: 临时文件/2023届虹口区一模_教师_20221220.tex\n",
"0\n",
"开始编译学生版本pdf文件: 临时文件/2023届青浦区一模_学生_20221219.tex\n",
"开始编译学生版本pdf文件: 临时文件/2023届虹口区一模_学生_20221220.tex\n",
"0\n"
]
}
@ -51,13 +51,13 @@
"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
"\n",
"\"\"\"---设置目标文件名---\"\"\"\n",
"destination_file = \"临时文件/2023届青浦区一模\"\n",
"destination_file = \"临时文件/2023届虹口区一模\"\n",
"\"\"\"---设置目标文件名结束---\"\"\"\n",
"\n",
"\n",
"\"\"\"---设置题号数据---\"\"\"\n",
"problems = [\n",
"\"012529,012530,012531,012532,012533,012534,012535,012536,012537,012538,012539,012540\",\"012541,012542,012543,012544\",\"012545,012546,012547,012548,012549\"\n",
"\"012508,012509,012510,012511,012512,012513,012514,012515,012516,012517,012518,012519\",\"012520,012521,012522,012523\",\"012524,012525,012526,012527,012528\"\n",
"\n",
"\n",
"]\n",
@ -210,7 +210,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.15 ('pythontest')",
"display_name": "mathdept",
"language": "python",
"name": "python3"
},
@ -229,7 +229,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
}
}
},

48
工具/识别题库中尚未标注的题目类型.ipynb
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@ -2,34 +2,34 @@
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"012655 填空题\n",
"012656 填空题\n",
"012657 填空题\n",
"012658 填空题\n",
"012659 填空题\n",
"012660 填空题\n",
"012661 填空题\n",
"012662 填空题\n",
"012663 填空题\n",
"012664 填空题\n",
"012665 填空题\n",
"012666 填空题\n",
"012667 选择题\n",
"012668 选择题\n",
"012669 选择题\n",
"012670 选择题\n",
"012671 解答题\n",
"012672 解答题\n",
"012673 解答题\n",
"012674 解答题\n",
"012675 解答题\n"
"012676 填空题\n",
"012677 填空题\n",
"012678 填空题\n",
"012679 填空题\n",
"012680 填空题\n",
"012681 填空题\n",
"012682 填空题\n",
"012683 填空题\n",
"012684 填空题\n",
"012685 填空题\n",
"012686 填空题\n",
"012687 填空题\n",
"012688 选择题\n",
"012689 选择题\n",
"012690 选择题\n",
"012691 选择题\n",
"012692 解答题\n",
"012693 解答题\n",
"012694 解答题\n",
"012695 解答题\n",
"012696 解答题\n"
]
}
],
@ -71,7 +71,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.9.15 ('pythontest')",
"display_name": "mathdept",
"language": "python",
"name": "python3"
},
@ -90,7 +90,7 @@
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
}
}
},

14
工具/题号选题pdf生成.ipynb
View File

@ -2,16 +2,16 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"开始编译教师版本pdf文件: 临时文件/松江_教师用_20221220.tex\n",
"开始编译教师版本pdf文件: 临时文件/虹口一模待校对_教师用_20221220.tex\n",
"0\n",
"开始编译学生版本pdf文件: 临时文件/松江_学生用_20221220.tex\n",
"开始编译学生版本pdf文件: 临时文件/虹口一模待校对_学生用_20221220.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/松江\"\n",
"filename = \"临时文件/虹口一模待校对\"\n",
"\"\"\"---设置文件名结束---\"\"\"\n",
"\n",
"\n",
@ -174,7 +174,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.8.15 ('mathdept')",
"display_name": "mathdept",
"language": "python",
"name": "python3"
},
@ -188,12 +188,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.15"
"version": "3.9.15"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2"
"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
}
}
},

401
题库0.3/Problems.json
View File

@ -309280,7 +309280,7 @@
},
"012527": {
"id": "012527",
"content": "本市某区对全区高中生的身高(单位: 厘米)进行统计, 得到如下的频率分布直方图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.6, yscale = 100]\n\\draw [->] (-0,0) -- (0.1,0) -- (0.2,0.0008) -- (0.4,-0.0008) -- (0.5,0) -- (10,0) node [below] {身高/厘米};\n\\draw [->] (0,-0) -- (0,0.035) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {150/0.022,160/0.027,170/0.025,180/0.015,190/0.01,200/0.001} \n{\\draw ({(\\i-130)/10},0) node [below] {\\small $\\i$} --++ (0,\\j) --++ (1,0) --++ (0,{-\\j});\n\\draw [dashed] (0,\\j) node [left] {\\small $\\j$} -- ({(\\i-130)/10},\\j);};\n\\draw (8,0) node [below] {\\small $210$};\n\\end{tikzpicture}\n\\end{center}\n(1) 若数据分布均匀, 记随机变量$X$为各区间中点所代表的身高, 写出$X$的分布及期望;\\\\\n(2) 已知本市身高在区间$[180,210]$的市民人数约占全市总人数的$10 \\%$, 且全市高中生约占全市总人数的$1.2 \\%$. 现在要以该区本次统计数据估算全市高中生身高情况, 从本市市民中任取$1$人, 若此人的身高位于区间$[180,210]$, 试估计此人是高中生的概率;\\\\\n(3) 现从身高在区间$[170,190)$的高中生中分层抽样抽取一个$80$人的样本. 若身高在区间$[170,180)$中样本的均值为$176$厘米, 方差为$10$; 身高在区间$[180,190)$中样本的均值为$184$厘米, 方差为$16$, 试求这$80$人的方差.",
"content": "本市某区对全区高中生的身高(单位: 厘米)进行统计, 得到如下的频率分布直方图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.6, yscale = 100]\n\\draw [->] (-0,0) -- (0.1,0) -- (0.2,0.0008) -- (0.4,-0.0008) -- (0.5,0) -- (10,0) node [below] {身高/厘米};\n\\draw [->] (0,-0) -- (0,0.035) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j/\\k in {150/0.022/0.022,160/0.027/0.027,170/0.025/0.025,180/0.015/x,190/0.01/0.01,200/0.001/0.001} \n{\\draw ({(\\i-130)/10},0) node [below] {\\small $\\i$} --++ (0,\\j) --++ (1,0) --++ (0,{-\\j});\n\\draw [dashed] (0,\\j) node [left] {\\small $\\k$} -- ({(\\i-130)/10},\\j);};\n\\draw (8,0) node [below] {\\small $210$};\n\\end{tikzpicture}\n\\end{center}\n(1) 若数据分布均匀, 记随机变量$X$为各区间中点所代表的身高, 写出$X$的分布及期望;\\\\\n(2) 已知本市身高在区间$[180,210]$的市民人数约占全市总人数的$10 \\%$, 且全市高中生约占全市总人数的$1.2 \\%$. 现在要以该区本次统计数据估算全市高中生身高情况, 从本市市民中任取$1$人, 若此人的身高位于区间$[180,210]$, 试估计此人是高中生的概率;\\\\\n(3) 现从身高在区间$[170,190)$的高中生中分层抽样抽取一个$80$人的样本. 若身高在区间$[170,180)$中样本的均值为$176$厘米, 方差为$10$; 身高在区间$[180,190)$中样本的均值为$184$厘米, 方差为$16$, 试求这$80$人的方差.",
"objs": [],
"tags": [
"第八单元",
@ -312161,6 +312161,405 @@
"remark": "",
"space": "12ex"
},
"012676": {
"id": "012676",
"content": "设集合$A=(-2,2)$, $B=(-3,1)$, 则$A \\cap B=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题1",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012677": {
"id": "012677",
"content": "若幂函数$y=x^a$的图像经过点$(\\sqrt[4]3, 3)$, 则实数$a=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题2",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012678": {
"id": "012678",
"content": "函数$y=\\log_2(2-x)$的定义域为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题3",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012679": {
"id": "012679",
"content": "$(x+2)^5$的二项展开式中$x^2$的系数为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题4",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012680": {
"id": "012680",
"content": "若圆锥的轴截面是边长为$1$的正三角形, 则圆锥的侧面积是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题5",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012681": {
"id": "012681",
"content": "已知$\\alpha$为锐角, 若$\\sin (\\alpha+\\dfrac{\\pi}2)=\\dfrac 35$, 则$\\tan (\\alpha+\\dfrac{\\pi}4)=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题6",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012682": {
"id": "012682",
"content": "已知某射击爱好者的打靶成绩(单位: 环)的茎叶图如图所示, 其中整数部分为 ``茎'', 小数部分为``叶'', 则这组数据的方差为\\blank{50}(精确到0.01).\n\\begin{center}\n\\begin{tabular}{r|l}\n5 & 6 \\ 8\\\\\n6 & 2 \\ 3 \\ 6 \\ 6\\\\\n7 & 3 \\ 4\n\\end{tabular}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题7",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012683": {
"id": "012683",
"content": "已知拋物线$C: y^2=16 x$的焦点为$F$, 在$C$上有一点$P$满足$|PF|=13$, 则点$P$到$x$轴的距离为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题8",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012684": {
"id": "012684",
"content": "某医院需要从$4$名男医生和$3$名女医生中选出$3$名医生去担任``中国进博会''三个不同区域的核酸检测服务工作, 则选出的$3$名医生中, 恰有$1$名女医生的概率是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023届浦东新区一模试题9",
"edit": [
"20221220\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"012685": {
"id": "012685",
"content": "如图, 在$\\triangle ABC$中, 点$D$、$E$是线段$BC$上两个动点, 且$\\overrightarrow{AD}+\\overrightarrow{AE}=x \\overrightarrow{AB}+y \\overrightarrow{AC}$, 则$\\dfrac 1x+\\dfrac 9y$的最小值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$A$} coordinate (A);\n\\draw (-1,-2) node [left] {$B$} coordinate (B);\n\\draw (2,-2) node [right] {$C$} coordinate (C);\n\\draw ($(B)!0.3!(C)$) node [below] {$D$} coordinate (D);\n\\draw ($(B)!0.55!(C)$) node [below] {$E$} coordinate (E);\n\\draw [->] (A) -- (B);\n\\draw [->] (A) -- (C);\n\\draw [->] (A) -- (D);\n\\draw [->] (A) -- (E);\n\\draw (B) -- (C);\n\\end{tikzpicture}\n\\end{center}",
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"012686": {
"id": "012686",
"content": "已知定义在$(-\\pi, \\pi)$上的函数$f(x)=x \\cos (x+\\varphi)-\\cos x$($0<\\varphi<\\pi$)为偶函数, 则$f(x)$的严格递减区间为\\blank{50}.",
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"012687": {
"id": "012687",
"content": "已知项数为$m$的有限数列$\\{a_n\\}$($m \\in \\mathbf{N}$, $m \\geq 2$)是$1,2,3, \\ldots, m$的一个排列. 若$|a_1-a_2|\\leq|a_2-a_3|\\leq \\ldots \\leq|a_{m-1}-a_m|$, 且$\\displaystyle\\sum_{k=1}^{m-1}|a_k-a_{k+1}|=m+2$, 则所有可能的$m$值之和为\\blank{50}.",
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"012688": {
"id": "012688",
"content": "已知实数$a$、$b$, 那么``$|a+b|=|a|+|b|$''是``$a b>0$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}",
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"012689": {
"id": "012689",
"content": "虚数的平方一定是\\bracket{20}.\n\\fourch{正实数}{负实数}{虚数}{虚数或负实数}",
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"012690": {
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"content": "已知直线$l$与平面$\\alpha$相交, 则下列命题中, 正确的个数为\\bracket{20}.\\\\\n\\textcircled{1} 平面$\\alpha$内的所有直线均与直线$l$异面;\\\\\n\\textcircled{2} 平面$\\alpha$内存在与直线$l$垂直的直线;\\\\\n\\textcircled{3} 平面$\\alpha$内不存在直线与直线$l$平行;\\\\\n\\textcircled{4} 平面$\\alpha$内所有直线均与直线$l$相交.\n\\fourch{1}{2}{3}{4}",
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"012691": {
"id": "012691",
"content": "已知平面直角坐标系中的直线$l_1: y=3 x$、$l_2: y=-3 x$. 设到$l_1$、$l_2$距离之和为$2 p_1$的点的轨迹是曲线$C_1$, 到$l_1$、$l_2$距离平方和为$2 p_2$的点的轨迹是曲线$C_2$, 其中$p_1$、$p_2>0$. 则$C_1$、$C_2$公共点的个数不可能为\\bracket{20}.\n\\fourch{$0$个}{$4$个}{$8$个}{$12$个}",
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"012692": {
"id": "012692",
"content": "已知数列$\\{a_n\\}$是公差不为$0$的等差数列, $a_1=4$, 且$a_1$、$a_3$、$a_4$成等比数列.\\\\\n(1) 求数列$\\{a_n\\}$的通项公式;\\\\\n(2) 求当$n$为何值时, 数列$\\{a_n\\}$的前$n$项和$S_n$取得最大值.",
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"space": "12ex"
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"012693": {
"id": "012693",
"content": "如图, 三棱锥$P-ABC$中, 侧面$PAB$垂直于底面$ABC$, $PA=PB$, 底面$ABC$是斜边为$AB$的直角三角形, 且$\\angle ABC=30^{\\circ}$, 记$O$为$AB$的中点, $E$为$OC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [above] {$O$} coordinate (O);\n\\draw (-1,0,0) node [left] {$B$} coordinate (B);\n\\draw (1,0,0) node [right] {$A$} coordinate (A);\n\\draw (0.5,0,{sqrt(3)/2}) node [below] {$C$} coordinate (C);\n\\draw ($(O)!0.5!(C)$) node [left] {$E$} coordinate (E);\n\\draw (0,{sqrt(3)},0) node [above] {$P$} coordinate (P);\n\\draw (B) -- (C) -- (A) -- (P) -- cycle (P) -- (C);\n\\draw [dashed] (A) -- (B) (O) -- (C) (A) -- (E);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $PC \\perp AE$;\\\\\n(2) 若$AB=2$, 直线$PC$与底面$ABC$所成角的大小为$60^{\\circ}$, 求四面体$PAOC$的体积.",
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"012694": {
"id": "012694",
"content": "在临港滴水湖畔拟建造一个四边形的露营基地, 如图$ABCD$所示. 为考虑露营客人娱乐休闲的需求, 在四边形$ABCD$区域中, 将$\\triangle ABD$区域设立成花卉观赏区, $\\triangle BCD$区域设立成烧烤区, 边$AB$、$BC$、$CD$、$DA$修建成观赏步道, 边$BD$修建隔离防护栏. 其中$CD=100$米, $BC=200$米, $\\angle A=\\dfrac{\\pi}3$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.7]\n\\draw (0,0) node [right] {$C$} coordinate (C);\n\\draw (-1,0) node [left] {$D$} coordinate (D);\n\\draw (-80:2) node [right] {$B$} coordinate (B);\n\\draw ($(B)!{1/sqrt(3)}!30:(D)$) coordinate (O);\n\\draw ($(O)!1!100:(D)$) node [left] {$A$} coordinate (A);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (D) -- (B);\n\\draw (barycentric cs:A=1,B=1,D=1) node {花卉观赏区};\n\\draw (barycentric cs:B=1,C=1,D=1) node {烧烤区};\n\\end{tikzpicture}\n\\end{center}\n(1) 如果烧烤区是一个占地面积为$9600$平方米的钝角三角形, 那么需要修建多长的隔离防护栏(精确到$0.1$米)?\\\\\n(2) 考虑到烧烤区的安全性, 在规划四边形$ABCD$区域时, 首先保证烧烤区的占地面积最大时, 再使得花卉观赏区的面积尽可能大, 则应如何设计观赏步道?",
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"012695": {
"id": "012695",
"content": "已知$F_1$、$F_2$分别为椭圆$C_1: \\dfrac{x^2}4+y^2=1$的左、右焦点, 直线$l_1$交椭圆$C_1$于$A$、$B$两点.\\\\\n(1) 求焦点$F_1$、$F_2$的坐标与椭圆$C_1$的离心率$e_1$的值;\\\\\n(2) 若直线$l_1$过点$F_2$且与圆$x^2+y^2=1$相切, 求弦长$|AB|$的值;\\\\\n(3) 若双曲线$C_2$与椭圆共焦点, 离心率为$e_2$, 满足$e_2=2 e_1$, 过点$F_2$作斜率为$k$($k \\neq 0$)的直线$l_2$交$C_2$的渐近线于$C$、$D$两点, 过$C$、$D$的中点$M$分别作两条渐近线的平行线交$C_2$于$P$、$Q$两点, 证明: 直线$PQ$平行于$l_2$.",
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"space": "12ex"
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"012696": {
"id": "012696",
"content": "已知定义域为$\\mathbf{R}$的函数$y=f(x)$. 当$a \\in \\mathbf{R}$时, 若$g(x)=\\dfrac{f(x)-f(a)}{x-a}$($x>a$)是严格增函数, 则称$f(x)$是一个``$T(a)$函数''.\\\\\n(1) 分别判断函数$f_1(x)=5 x+3$、$f_2(x)=2 x^2+x+2$是否为$T(1)$函数;\\\\\n(2) 是否存在实数$b$, 使得函数$h(x)=\\begin{cases}\\mathrm{e}^x,& x<0, \\\\b x+1,& x \\geq 0\\end{cases}$是$T(-1)$函数? 若存在, 求实数$b$的取值范围; 否则, 证明你的结论;\\\\\n(3) 已知$J(x)=\\mathrm{e}^x(q x^2+1)$, 其中$q \\in \\mathbf{R}$. 证明: 若$J'(x)$是$\\mathbf{R}$上的严格增函数, 则对任意$n \\in \\mathbf{Z}, J(x)$都是$T(n)$函数.",
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"space": "12ex"
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"020001": {
"id": "020001",
"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",