From 96441d55c60ab85c5c631ad7b22815e825f60ddc Mon Sep 17 00:00:00 2001 From: Wang Weiye Date: Mon, 19 Sep 2022 18:55:40 +0800 Subject: [PATCH] 20220919 evening --- .../讲义题目分类按顺序梳理_制答题卡用.ipynb | 52 ++++---- 工具/添加关联题目.ipynb | 10 +- 工具/讲义生成.ipynb | 33 +++-- 题库0.3/Problems.json | 115 +++++++++++++++--- 4 files changed, 139 insertions(+), 71 deletions(-) diff --git a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb index d272385f..4d4b1b68 100644 --- a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb +++ b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb @@ -2,53 +2,47 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1 填空题 1\n", - "2 填空题 1\n", - "3 填空题 1\n", - "4 填空题 1\n", - "5 填空题 1\n", - "6 填空题 1\n", + "1 填空题 8\n", + "2 解答题 1\n", + "3 解答题 2\n", + "4 选择题 1\n", + "5 解答题 1\n", + "6 选择题 1\n", "7 填空题 1\n", "8 填空题 1\n", "9 解答题 1\n", - "10 解答题 1\n", - "11 解答题 2\n", - "12 解答题 1\n", - "13 解答题 1\n", - "14 解答题 1\n", - "15 填空题 1\n", - "16 选择题 1\n", - "1 填空题 1\n", - "2 填空题 1\n", - "3 填空题 1\n", - "4 填空题 1\n", - "5 填空题 1\n", - "6 选择题 1\n", - "7 选择题 1\n", + "10 填空题 1\n", + "1 填空题 8\n", + "2 解答题 1\n", + "3 解答题 3\n", + "4 解答题 1\n", + "5 解答题 2\n", + "6 解答题 1\n", + "7 填空题 1\n", "8 解答题 1\n", - "9 解答题 1\n", - "10 解答题 1\n", - "11 解答题 1\n", - "12 选择题 1\n" + "9 选择题 1\n", + "10 选择题 1\n", + "11 解答题 4\n" ] } ], "source": [ "import os,re\n", "#修改文件名\n", - "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\12_和差倍角公式.tex\"\n", + "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\15_周期性与其他三角函数.tex\"\n", "outputfile = \"临时文件/题目状态.txt\"\n", "\n", "outputstr = \"\"\n", "with open(filename,\"r\",encoding = \"utf8\") as f:\n", " data = f.read()\n", + "data = re.sub(r\"\\\\begin\\{center\\}[\\s\\S]*?\\\\end\\{center\\}\",\"\",data)\n", "sections = re.findall(r\"\\\\begin\\{enumerate\\}([\\s\\S]*?\\\\end\\{enumerate\\})\",data)\n", "for sec in sections:\n", " sec = sec.replace(\"\\\\item\",\"\\\\enditem\\\\item\").replace(\"\\\\end{enumerate}\",\"\\\\enditem\")\n", @@ -84,7 +78,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -98,12 +92,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb index d1fd20f6..c840365b 100644 --- a/工具/添加关联题目.ipynb +++ b/工具/添加关联题目.ipynb @@ -9,8 +9,8 @@ "import os,re,json,time\n", "\n", "\"\"\"---设置原题目id与新题目id---\"\"\"\n", - "old_id = \"333\"\n", - "new_id = \"30022\"\n", + "old_id = \"1166\"\n", + "new_id = \"30025\"\n", "\"\"\"---设置完毕---\"\"\"\n", "\n", "old_id = old_id.zfill(6)\n", @@ -50,7 +50,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -64,12 +64,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index f71b3384..122980fd 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -13,11 +13,9 @@ "题块 1 处理完毕.\n", "正在处理题块 2 .\n", "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/九月月考_教师_20220918.tex\n", + "开始编译教师版本pdf文件: 临时文件/15_周期性与其他三角函数_教师_20220919.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/九月月考_学生_20220918.tex\n", + "开始编译学生版本pdf文件: 临时文件/15_周期性与其他三角函数_学生_20220919.tex\n", "0\n" ] } @@ -30,30 +28,29 @@ "\"\"\"---设置模式结束---\"\"\"\n", "\n", "\"\"\"---设置模板文件名---\"\"\"\n", - "# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n", - "template_file = \"模板文件/测验周末卷模板.tex\"\n", + "template_file = \"模板文件/第一轮复习讲义模板.tex\"\n", + "# template_file = \"模板文件/测验周末卷模板.tex\"\n", "\"\"\"---设置模板文件名结束---\"\"\"\n", "\n", "\"\"\"---设置其他预处理替换命令---\"\"\"\n", "#2023届第一轮讲义更换标题\n", - "# exec_list = [(\"标题数字待处理\",\"12\"),(\"标题文字待处理\",\"和差倍角公式\")] \n", - "# enumi_mode = 0\n", + "exec_list = [(\"标题数字待处理\",\"15\"),(\"标题文字待处理\",\"周期性与其他三角函数\")] \n", + "enumi_mode = 0\n", "\n", "#2023届测验卷与周末卷\n", - "exec_list = [(\"标题替换\",\"九月月考\")]\n", - "enumi_mode = 1\n", + "# exec_list = [(\"标题替换\",\"周末卷03\")]\n", + "# enumi_mode = 1\n", "\"\"\"---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/九月月考\"\n", + "destination_file = \"临时文件/15_周期性与其他三角函数\"\n", "\"\"\"---设置目标文件名结束---\"\"\"\n", "\n", "\n", "\"\"\"---设置题号数据---\"\"\"\n", "problems = [\n", - "\"4080,4122,4312,4451,4557,4276,30019,4356,4320,4359,30020,4091\",\n", - "\"4400,8101,4157,4440\",\n", - "\"4370,4224,4328,4444,4184\"\n", + "\"1496,1497,136,3154,6096,3179,1535,3172,9612,3152,10109\",\n", + "\"1492,1498,1513,9597,1495,1538,3177,1537,6225,6062,6097\"\n", "]\n", "\"\"\"---设置题号数据结束---\"\"\"\n", "\n", @@ -197,7 +194,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -211,12 +208,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f2050531..57da641b 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -29290,7 +29290,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030025" + ], "remark": "", "space": "12ex" }, @@ -34945,7 +34947,7 @@ }, "001378": { "id": "001378", - "content": "[选做]\n在三角形$ABC$中, 已知三条边上的高$h_a,h_b,h_c$分别为$1/3,1/4,1/5$, 解这个三角形.", + "content": "在三角形$ABC$中, 已知三条边$a,b,c$上的高$h_a,h_b,h_c$分别为$1/3,1/4,1/5$, 求$A$.", "objs": [ "K0315003B" ], @@ -68075,7 +68077,7 @@ }, "002745": { "id": "002745", - "content": "使不等式$2x^2-5x-3\\ge 0$成立的一个充分不必要条件是\\bracket{20}. \n\\fourch{$x<0$}{$x\\ge 0$}{$x\\in \\{-1,3,5\\}$}{$x\\le \\dfrac12$或x$\\ge 3$}", + "content": "使不等式$2x^2-5x-3\\ge 0$成立的一个充分不必要条件是\\bracket{20}. \n\\fourch{$x<0$}{$x\\ge 0$}{$x\\in \\{-1,3,5\\}$}{$x\\le \\dfrac12$或$x\\ge 3$}", "objs": [ "K0106001B" ], @@ -77258,7 +77260,7 @@ }, "003128": { "id": "003128", - "content": "在三角形$ABC$中,\n(1) 用三个角$A,B,C$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(2) 用三条边$a,b,c$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(3) 用内切圆半径$r$, 周长$2p$表示三角形面积$S$, 得$S=$\\blank{50}.", + "content": "在三角形$ABC$中,\\\\\n(1) 用三个角$A,B,C$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(2) 用三条边$a,b,c$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(3) 用内切圆半径$r$, 周长$2p$表示三角形面积$S$, 得$S=$\\blank{50}.", "objs": [ "K0314004B", "K0314006B" @@ -77553,7 +77555,7 @@ }, "003141": { "id": "003141", - "content": "在三角形$ABC$中, $(a+b)^2-c^2=4$, $C=\\dfrac{\\pi}3$, 则面积$S=$\\blank{50}.", + "content": "在三角形$ABC$中, 若$(a+b)^2-c^2=4$, $C=\\dfrac{\\pi}3$, 则面积$S=$\\blank{50}.", "objs": [ "K0314001B", "K0315003B" @@ -77644,7 +77646,7 @@ }, "003145": { "id": "003145", - "content": "已知$D,C,B$三点在地面同一直线上, $DC=a$, 从$C,D$两点测得$A$点的仰角分别为$\\alpha,\\beta$($\\alpha>\\beta$), 则点$A$离地面的高$AB=$\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw (0,0) node [below left] {$D$} -- (4,0) node [below] {$C$} -- (7,0) node [below right] {$B$} -- (7,3) node [above right] {$A$};\n \\draw (4,0) -- (7,3);\n \\draw (0,0) -- (7,3);\n \\draw (4.5,0) arc (0:atan(1):0.5);\n \\draw (5,0) node [above] {$\\alpha$};\n \\draw (0.5,0) arc(0:atan(3/7):0.5);\n \\draw (1.5,0) node [above] {$\\beta$};\n \\end{tikzpicture}\n\\end{center}", + "content": "已知$D,C,B$三点在地面同一直线上, $DC=a$, 从$C,D$两点测得$A$点的仰角分别为$\\alpha,\\beta$($\\alpha>\\beta$), 则点$A$离地面的高$AB=$\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex,scale = 0.6]\n \\draw (0,0) node [below left] {$D$} -- (4,0) node [below] {$C$} -- (7,0) node [below right] {$B$} -- (7,3) node [above right] {$A$};\n \\draw (4,0) -- (7,3);\n \\draw (0,0) -- (7,3);\n \\draw (4.5,0) arc (0:atan(1):0.5);\n \\draw (5,0) node [above] {$\\alpha$};\n \\draw (0.5,0) arc(0:atan(3/7):0.5);\n \\draw (1.5,-0.2) node [above] {$\\beta$};\n \\end{tikzpicture}\n\\end{center}", "objs": [ "K0317002B" ], @@ -77667,7 +77669,7 @@ }, "003146": { "id": "003146", - "content": "在一个特定时段内, 以点$E$为中心的$7$海里以内海域被设为警戒水域. 点$E$正北$55$海里处有一个雷达观测站$A$. 某时刻测得一艘匀速直线行驶的船只位于点$A$北偏东$45^\\circ$且与点$A$相距$40\\sqrt 2$海里的位置$B$, 经过$40$分钟又测得该船已行驶到点$A$北偏东$45^\\circ+\\arcsin\\dfrac{\\sqrt{26}}{26}$且与点$A$相距$10\\sqrt{13}$海里的位置$C$.\n(1) 求该船的行驶速度(单位: 海里$/$小时);\n(2) 若该船不改变航行方向继续行驶, 判断它是否会进入警戒水域, 并说明理由.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.5]\n \\draw (0,0) -- (0,5.5) node [left] {$A$} coordinate (A);\n \\draw (0,5.5) -- ++ (45:{4*sqrt(2)}) coordinate (B) node [right] {$B$};\n \\draw (A) ++ ({45-asin(1/sqrt(26))}:{sqrt(13)}) coordinate (C) node [right] {$C$} -- (B);\n \\draw (C) -- (A);\n \\end{tikzpicture}\n\\end{center}", + "content": "在一个特定时段内, 以点$E$为中心的$7$海里以内海域被设为警戒水域. 如图, 点$E$正北$55$海里处有一个雷达观测站$A$. 某时刻测得一艘匀速直线行驶的船只位于点$A$北偏东$45^\\circ$且与点$A$相距$40\\sqrt 2$海里的位置$B$, 经过$40$分钟又测得该船已行驶到点$A$北偏东$45^\\circ+\\arcsin\\dfrac{\\sqrt{26}}{26}$且与点$A$相距$10\\sqrt{13}$海里的位置$C$.\\\\\n(1) 求该船的行驶速度(单位: 海里$/$小时);\\\\\n(2) 若该船不改变航行方向继续行驶, 判断它是否会进入警戒水域, 并说明理由.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.5]\n \\draw (0,0) node [below] {$E$} -- (0,5.5) node [left] {$A$} coordinate (A);\n \\draw (0,5.5) -- ++ (45:{4*sqrt(2)}) coordinate (B) node [right] {$B$};\n \\draw (A) ++ ({45-asin(1/sqrt(26))}:{sqrt(13)}) coordinate (C) node [right] {$C$} -- (B);\n \\draw (C) -- (A);\n \\end{tikzpicture}\n\\end{center}", "objs": [ "K0317002B" ], @@ -78090,7 +78092,7 @@ }, "003164": { "id": "003164", - "content": "*设函数$f(x)=\\dfrac{2\\sin x\\cos x+\\dfrac 52}{\\sin x+\\cos x}, 0\\le x\\le \\dfrac{\\pi}2$, 求$f(x)$的最大值与最小值.", + "content": "设函数$f(x)=\\dfrac{2\\sin x\\cos x+\\dfrac 52}{\\sin x+\\cos x}, 0\\le x\\le \\dfrac{\\pi}2$, 求$f(x)$的最大值与最小值.", "objs": [ "K0320002B" ], @@ -78159,7 +78161,7 @@ }, "003167": { "id": "003167", - "content": "设$A>0$, $\\omega>0$, $0\\le \\varphi<2\\pi$. 如图为定义在$\\mathbf{R}$上的函数$f(x)=A\\sin (\\omega x+\\varphi)$的图像的一部分, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.8]\n \\draw [->] (-1,0) -- (7,0) node [below] {$x$};\n \\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -pi/6:25*pi/12, samples = 1000] plot (\\x, {2*sin(2*\\x/3/pi*180+20)});\n \\draw [dashed] (7*pi/12,2) -- (0,2) node [left] {$2$};\n \\draw [dashed] (25*pi/12,0) node [above] {$\\dfrac{25\\pi}{12}$} --++ (0,-2) -- (0,-2) node [left] {$-2$};\n \\draw (-pi/6,0) node [below] {$-\\dfrac{\\pi}{6}$};\n \\end{tikzpicture}\n\\end{center}", + "content": "设$A>0$, $\\omega>0$, $0\\le \\varphi<2\\pi$. 如图为定义在$\\mathbf{R}$上的函数$f(x)=A\\sin (\\omega x+\\varphi)$的图像的一部分, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.5]\n \\draw [->] (-1,0) -- (7,0) node [below] {$x$};\n \\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -pi/6:25*pi/12, samples = 1000] plot (\\x, {2*sin(2*\\x/3/pi*180+20)});\n \\draw [dashed] (7*pi/12,2) -- (0,2) node [left] {$2$};\n \\draw [dashed] (25*pi/12,0) node [above] {$\\dfrac{25\\pi}{12}$} --++ (0,-2) -- (0,-2) node [left] {$-2$};\n \\draw (-pi/6,0) node [below] {$-\\dfrac{\\pi}{6}$};\n \\end{tikzpicture}\n\\end{center}", "objs": [ "K0323003B" ], @@ -78341,7 +78343,7 @@ }, "003175": { "id": "003175", - "content": "已知函数$f(x)=(2\\sin(x+\\dfrac{\\pi}3)+\\sin x)\\cos x-\\sqrt 3\\sin^2 x$.\\\\\n(1) 求函数$f(x)$的值域与周期;\\\\\n(2) 若$x\\in [0,\\dfrac{\\pi}2]$, 求$f(x)$的单调递减区间;\\\\\n(3) *设常数$a>0$, 若函数$y=f(x)$的图像关于直线$x=a$对称, 求$a$的最小值;\\\\\n(4) 设常数$m\\in \\mathbf{R}$, 若存在$x_0\\in [0,\\dfrac{5\\pi}{12}]$, 使得$mf(x_0)-2=0$成立, 求$m$的取值范围.", + "content": "已知函数$f(x)=(2\\sin(x+\\dfrac{\\pi}3)+\\sin x)\\cos x-\\sqrt 3\\sin^2 x$.\\\\\n(1) 求函数$f(x)$的值域与周期;\\\\\n(2) 若$x\\in [0,\\dfrac{\\pi}2]$, 求$f(x)$的单调递减区间;\\\\\n(3) 设常数$a>0$, 若函数$y=f(x)$的图像关于直线$x=a$对称, 求$a$的最小值;\\\\\n(4) 设常数$m\\in \\mathbf{R}$, 若存在$x_0\\in [0,\\dfrac{5\\pi}{12}]$, 使得$mf(x_0)-2=0$成立, 求$m$的取值范围.", "objs": [ "K0319005B", "K0320002B", @@ -78367,7 +78369,7 @@ }, "003176": { "id": "003176", - "content": "设$A\\ne 0$, $\\omega>0$, $-\\dfrac{\\pi}2<\\varphi<\\dfrac{\\pi}2$, 函数$f(x)=A\\sin(\\omega x+\\varphi)$的部分图像如右图所示, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.4]\n \\draw [->] (-4,0) -- (11,0) node [below] {$x$};\n \\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -2:11, samples = 1000] plot (\\x, {-4*sin(180*\\x/8+45)});\n \\draw [dashed] (2,-4) -- (0,-4) node [left] {$-4$} (10,4) -- (0,4) node [left] {$4$};\n \\draw (-2,0) node [above] {$-2$};\n \\draw (6,0) node [below] {$6$};\n \\end{tikzpicture}\n\\end{center}", + "content": "设$A\\ne 0$, $\\omega>0$, $-\\dfrac{\\pi}2<\\varphi<\\dfrac{\\pi}2$, 函数$f(x)=A\\sin(\\omega x+\\varphi)$的部分图像如图所示, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.3]\n \\draw [->] (-4,0) -- (11,0) node [below] {$x$};\n \\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -2:11, samples = 1000] plot (\\x, {-4*sin(180*\\x/8+45)});\n \\draw [dashed] (2,-4) -- (0,-4) node [left] {$-4$} (10,4) -- (0,4) node [left] {$4$};\n \\draw (-2,0) node [above] {$-2$};\n \\draw (6,0) node [below] {$6$};\n \\end{tikzpicture}\n\\end{center}", "objs": [ "K0321004B" ], @@ -78484,7 +78486,7 @@ }, "003181": { "id": "003181", - "content": "*设常数$a\\in \\mathbf{R}$. 若函数$y=\\sin 2x+a\\cos 2x$的图像关于直线$x=-\\dfrac{\\pi}6$对称, 则$a=$\\blank{50}.", + "content": "设常数$a\\in \\mathbf{R}$. 若函数$y=\\sin 2x+a\\cos 2x$的图像关于直线$x=-\\dfrac{\\pi}6$对称, 则$a=$\\blank{50}.", "objs": [ "K0321001B" ], @@ -99291,7 +99293,7 @@ }, "004119": { "id": "004119", - "content": "如图, $A,B,C$三地在以$O$为圆心的圆形区域边界上, $AB=30$公里, $AC=10$公里, $\\angle BAC=60^\\circ$, $D$是圆形区域外一景点, $\\angle DBC=90^\\circ$, $\\angle DCB=60^\\circ$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [left] {$A$} -- (3,0) node [right] {$B$} -- (60:1) node [above] {$C$} coordinate (C) -- (0,0);\n \\draw (1.5,-0.288675) node [below] {$O$} circle (1.52752523);\n \\filldraw (1.5,-0.288675) circle (0.03);\n \\draw (43.90:6.245) node [above] {$D$} coordinate (D) -- (C) (D) -- (3,0) (D) -- (0,0);\n \\end{tikzpicture}\n\\end{center}\n(1) $O$、$A$相距多少公里(精确到小数点后两位)?\n(2) 若一汽车从$A$处出发, 以每小时$50$公里的速度沿公路$AD$行驶到$D$处, 需要多少小时(精确到小数点后两位)?", + "content": "如图, $A,B,C$三地在以$O$为圆心的圆形区域边界上, $AB=30$公里, $AC=10$公里, $\\angle BAC=60^\\circ$, $D$是圆形区域外一景点, $\\angle DBC=90^\\circ$, $\\angle DCB=60^\\circ$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [left] {$A$} -- (3,0) node [right] {$B$} -- (60:1) node [above] {$C$} coordinate (C) -- (0,0);\n \\draw (1.5,-0.288675) node [below] {$O$} circle (1.52752523);\n \\filldraw (1.5,-0.288675) circle (0.03);\n \\draw (43.90:6.245) node [above] {$D$} coordinate (D) -- (C) (D) -- (3,0) (D) -- (0,0);\n \\end{tikzpicture}\n\\end{center}\n(1) $O$、$A$相距多少公里(精确到小数点后两位)?\\\\\n(2) 若一汽车从$A$处出发, 以每小时$50$公里的速度沿公路$AD$行驶到$D$处, 需要多少小时(精确到小数点后两位)?", "objs": [ "K0317002B" ], @@ -104415,7 +104417,7 @@ }, "004328": { "id": "004328", - "content": "经济订货批量模型, 是目前大多数工厂、企业等最常采用的订货方式, 即某种物资在单位时间的需求量为某常数, 经过某段时间后, 存储量消耗下降到零, 此时开始订货并随即到货, 然后开始下一个存储周期. 该模型适用于整批间隔进货、不允许缺货的存储问题. 具体如下:\\\\\n年存储成本费$T$(元)关于每次订货$x$(单位: 吨)的函数关系为$T(x)=\\dfrac{Bx}2+\\dfrac{AC}x$, 其中$A$为年需求量, $B$为每单位物资的年存储费, $C$为每次订货费.\\\\\n某化工厂需用甲醇作为原料, 年需求量为$6000$吨, 每吨存储费为$120$元/年, 每次订货费为$2500$元.\n(1) 若该化工厂每次订购$300$吨甲醇, 求年存储成本费;\\\\\n(2) 每次需订购多少吨甲醇, 可使该化工厂年存储成本费最少? 最少费用为多少?", + "content": "经济订货批量模型, 是目前大多数工厂、企业等最常采用的订货方式, 即某种物资在单位时间的需求量为某常数, 经过某段时间后, 存储量消耗下降到零, 此时开始订货并随即到货, 然后开始下一个存储周期. 该模型适用于整批间隔进货、不允许缺货的存储问题. 具体如下:\\\\\n年存储成本费$T$(元)关于每次订货$x$(单位: 吨)的函数关系为$T(x)=\\dfrac{Bx}2+\\dfrac{AC}x$, 其中$A$为年需求量, $B$为每单位物资的年存储费, $C$为每次订货费.\\\\\n某化工厂需用甲醇作为原料, 年需求量为$6000$吨, 每吨存储费为$120$元/年, 每次订货费为$2500$元.\\\\\n(1) 若该化工厂每次订购$300$吨甲醇, 求年存储成本费;\\\\\n(2) 每次需订购多少吨甲醇, 可使该化工厂年存储成本费最少? 最少费用为多少?", "objs": [ "K0222002B" ], @@ -113044,7 +113046,7 @@ }, "004672": { "id": "004672", - "content": "在$\\triangle ABC$中, $b=2,c=1$, $\\angle B-\\angle C=\\dfrac{\\pi}2$, 则$\\triangle ABC$的周长为\\blank{50}.", + "content": "在$\\triangle ABC$中, $b=2,c=1$, $B-C=\\dfrac{\\pi}2$, 则$\\triangle ABC$的周长为\\blank{50}.", "objs": [ "K0315003B" ], @@ -234717,7 +234719,6 @@ "id": "010109", "content": "求下列各式中$x$的值(其中$x>0$):\n(1) $x^3=27$;\\\\\n(2) $x^4=121$;\\\\\n(3) $x^\\frac 32=1000$;\\\\\n(4) $x^{-\\frac 43}=\\dfrac{16}{625}$.", "objs": [ - "K0324006B", "K0203002B", "K0201004B" ], @@ -253602,7 +253603,7 @@ }, "010965": { "id": "010965", - "content": "已知全集$U=\\mathbf{R}$, 集合$A=\\{x||x-1|>1\\}$, $B=\\{x|\\dfrac{x-3}{x+1}<0\\}$, 则$\\complement _UA\\cap B=$\\blank{50}.", + "content": "已知全集$U=\\mathbf{R}$, 集合$A=\\{x||x-1|>1\\}$, $B=\\{x|\\dfrac{x-3}{x+1}<0\\}$, 则$\\overline{A}\\cap B=$\\blank{50}.", "objs": [], "tags": [ "" @@ -253665,7 +253666,9 @@ "same": [ "000499" ], - "related": [], + "related": [ + "030023" + ], "remark": "", "space": "" }, @@ -253801,7 +253804,9 @@ "20220817\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030024" + ], "remark": "", "space": "" }, @@ -281706,5 +281711,77 @@ ], "remark": "", "space": "" + }, + "030023": { + "id": "030023", + "content": "若$S_n$是等差数列$\\{a_n\\}$($n\\in \\mathbf{N}$且$n\\ge 1$): $-1,2,5,8,\\cdots$的前$n$项和, 则$S_n=$\\blank{50}.", + "objs": [], + "tags": [ + "第四单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三上学期周末卷3试题3-20220919修改", + "edit": [ + "20220817\t王伟叶", + "20220919\t徐慧" + ], + "same": [], + "related": [ + "010967" + ], + "remark": "", + "space": "" + }, + "030024": { + "id": "030024", + "content": "已知数列$\\{a_n\\}$($n\\in \\mathbf{N}^*$), 若$a_1=1$, $a_{n+1}+a_n=(\\dfrac 12)^n$, 则$a_{2n}=$\\blank{50}.", + "objs": [], + "tags": [ + "第四单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届高三上学期周末卷3试题9-20220919修改", + "edit": [ + "20220817\t王伟叶", + "20220919\t徐慧" + ], + "same": [], + "related": [ + "010973" + ], + "remark": "", + "space": "" + }, + "030025": { + "id": "030025", + "content": "若函数$f(x)=\\sqrt{kx^2+4kx+3}$的定义域为$\\mathbf{R}$, 则实数$k$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2016届创新班作业\t1131-函数与函数的三要素-20220919修改", + "edit": [ + "20220625\t王伟叶", + "20220919\t徐慧" + ], + "same": [], + "related": [ + "001166" + ], + "remark": "", + "space": "" } } \ No newline at end of file