From a6e37c5f80cea7f7df53101d1a7c0f321d7adebb Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sat, 3 Dec 2022 23:32:14 +0800 Subject: [PATCH] 20221203 night --- 工具/寻找tex文件中未赋答案的题目.ipynb | 79 +++++++- 工具/批量添加题库字段数据.ipynb | 39 ++-- 工具/文本文件/metadata.txt | 63 +++--- 题库0.3/Problems.json | 254 ++++++++++++------------- 4 files changed, 251 insertions(+), 184 deletions(-) diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb index a35aea5f..0dec26f1 100644 --- a/工具/寻找tex文件中未赋答案的题目.ipynb +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -2,14 +2,77 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "33_立体几何中的定量计算.tex\n" + "测验09.tex\n", + "012075\n", + "\n", + "\n", + "012076\n", + "\n", + "\n", + "012077\n", + "\n", + "\n", + "012078\n", + "\n", + "\n", + "012079\n", + "\n", + "\n", + "012080\n", + "\n", + "\n", + "012081\n", + "\n", + "\n", + "012082\n", + "\n", + "\n", + "012083\n", + "\n", + "\n", + "012084\n", + "\n", + "\n", + "012085\n", + "\n", + "\n", + "012086\n", + "\n", + "\n", + "012087\n", + "\n", + "\n", + "012088\n", + "\n", + "\n", + "012089\n", + "\n", + "\n", + "012090\n", + "\n", + "\n", + "012091\n", + "\n", + "\n", + "012092\n", + "\n", + "\n", + "012093\n", + "\n", + "\n", + "012094\n", + "\n", + "\n", + "012095\n", + "\n", + "\n" ] } ], @@ -17,9 +80,9 @@ "import os,json,re\n", "\n", "#这里需要修改, 设定路径与选择文件\n", - "fileind = 33\n", - "# path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", - "path = r\"C:\\Users\\wang weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", + "fileind = 12\n", + "path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\上学期测验卷\"\n", + "# path = r\"C:\\Users\\wang weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", "\n", "fileind = fileind - 1\n", "with open(\"../题库0.3/Problems.json\",\"r\",encoding = \"utf8\") as f:\n", @@ -47,7 +110,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -61,12 +124,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb index 4945268c..efdbb4cc 100644 --- a/工具/批量添加题库字段数据.ipynb +++ b/工具/批量添加题库字段数据.ipynb @@ -2,28 +2,29 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 000293 , 字段: ans 中已修改数据: (1) $(\\dfrac 73,\\dfrac 76,\\dfrac 76)$, $(0,0,0)$, $(\\dfrac 72,0,\\dfrac 72)$; (2) $\\dfrac{5\\sqrt{3}}3$\n", - "题号: 000304 , 字段: ans 中已修改数据: (1) 证明略; (2) $1$; (3) $(\\dfrac 13,1)$\n", - "题号: 010721 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\dfrac{\\sqrt{51}}{17}$; (3) $\\dfrac{\\sqrt{41}}8$\n", - "题号: 000294 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arcsin \\dfrac{\\sqrt{10}}5$\n", - "题号: 030462 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\dfrac{\\sqrt{2}}3$\n", - "题号: 000305 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\dfrac\\pi 3$与$\\dfrac{2\\pi}3$\n", - "题号: 000299 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arccos \\dfrac 23$\n", - "题号: 004096 , 字段: ans 中已修改数据: (1) $\\arcsin \\dfrac{\\sqrt{15}}5$; (2) $\\arccos \\dfrac{\\sqrt{10}}5$\n", - "题号: 010730 , 字段: ans 中已修改数据: $\\arccos \\dfrac{3\\sqrt{10}}{10}$\n", - "题号: 004348 , 字段: ans 中已修改数据: (1) $\\arccos\\dfrac{\\sqrt{10}}{10}$; (2) $\\dfrac{2\\sqrt{33}}{11}$\n", - "题号: 004698 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arcsin \\dfrac{4\\sqrt{5}}{25}$\n", - "题号: 030472 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\dfrac{\\sqrt{15}}{5}$; (3) 存在, $\\dfrac{PM}{PC}=\\dfrac 13$\n", - "题号: 004243 , 字段: ans 中已修改数据: (1) $\\dfrac{\\sqrt{21}}7$; (2) $\\sqrt{2}$\n", - "题号: 000296 , 字段: ans 中已修改数据: (1) 证明略; (2) $2$\n", - "题号: 030468 , 字段: ans 中已修改数据: B\n" + "题号: 011070 , 字段: ans 中已修改数据: $(-\\infty,0)\\cup (0,+\\infty)$\n", + "题号: 011072 , 字段: ans 中已修改数据: $2$\n", + "题号: 011073 , 字段: ans 中已修改数据: $1$\n", + "题号: 011074 , 字段: ans 中已修改数据: $2$\n", + "题号: 011075 , 字段: ans 中已修改数据: $\\dfrac 35$\n", + "题号: 011076 , 字段: ans 中已修改数据: $\\dfrac 72$\n", + "题号: 011078 , 字段: ans 中已修改数据: $[2-\\sqrt{10},2+\\sqrt{10}]$\n", + "题号: 011079 , 字段: ans 中已修改数据: $-2$\n", + "题号: 011081 , 字段: ans 中已修改数据: $\\sqrt{3}$\n", + "题号: 011082 , 字段: ans 中已修改数据: C\n", + "题号: 011083 , 字段: ans 中已修改数据: D\n", + "题号: 011084 , 字段: ans 中已修改数据: C\n", + "题号: 011086 , 字段: ans 中已修改数据: (1) $\\sqrt{3}$; (2) $\\dfrac{\\sqrt{3}}6$\n", + "题号: 011087 , 字段: ans 中已修改数据: (1) $\\{1,\\log_2 3\\}$; (2) $[0,4]$\n", + "题号: 011088 , 字段: ans 中已修改数据: (1) $n=400$; (2) $|x-y|=4$; (3) $\\dfrac{7}{10}$\n", + "题号: 011090 , 字段: ans 中已修改数据: (1) 具有性质$P$, 理由略; (2) 证明略; (3) $[-4043,-4041]$\n" ] } ], @@ -121,7 +122,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -135,12 +136,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index b7e2c010..3a50f1c0 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,46 +1,49 @@ ans -000293 -(1) $(\dfrac 73,\dfrac 76,\dfrac 76)$, $(0,0,0)$, $(\dfrac 72,0,\dfrac 72)$; (2) $\dfrac{5\sqrt{3}}3$ +011070 +$(-\infty,0)\cup (0,+\infty)$ -000304 -(1) 证明略; (2) $1$; (3) $(\dfrac 13,1)$ +011072 +$2$ -010721 -(1) 证明略; (2) $\dfrac{\sqrt{51}}{17}$; (3) $\dfrac{\sqrt{41}}8$ +011073 +$1$ -000294 -(1) 证明略; (2) $\arcsin \dfrac{\sqrt{10}}5$ +011074 +$2$ -030462 -(1) 证明略; (2) $\dfrac{\sqrt{2}}3$ +011075 +$\dfrac 35$ -000305 -(1) 证明略; (2) $\dfrac\pi 3$与$\dfrac{2\pi}3$ +011076 +$\dfrac 72$ -000299 -(1) 证明略; (2) $\arccos \dfrac 23$ +011078 +$[2-\sqrt{10},2+\sqrt{10}]$ -004096 -(1) $\arcsin \dfrac{\sqrt{15}}5$; (2) $\arccos \dfrac{\sqrt{10}}5$ +011079 +$-2$ -010730 -$\arccos \dfrac{3\sqrt{10}}{10}$ +011081 +$\sqrt{3}$ -004348 -(1) $\arccos\dfrac{\sqrt{10}}{10}$; (2) $\dfrac{2\sqrt{33}}{11}$ +011082 +C -004698 -(1) 证明略; (2) $\arcsin \dfrac{4\sqrt{5}}{25}$ +011083 +D -030472 -(1) 证明略; (2) $\dfrac{\sqrt{15}}{5}$; (3) 存在, $\dfrac{PM}{PC}=\dfrac 13$ +011084 +C -004243 -(1) $\dfrac{\sqrt{21}}7$; (2) $\sqrt{2}$ +011086 +(1) $\sqrt{3}$; (2) $\dfrac{\sqrt{3}}6$ -000296 -(1) 证明略; (2) $2$ +011087 +(1) $\{1,\log_2 3\}$; (2) $[0,4]$ -030468 -B +011088 +(1) $n=400$; (2) $|x-y|=4$; (3) $\dfrac{7}{10}$ + +011090 +(1) 具有性质$P$, 理由略; (2) 证明略; (3) $[-4043,-4041]$ \ No newline at end of file diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 224be0b4..904a7400 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -6477,7 +6477,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y=-\\dfrac 23 x$或$y=-x+1$", "solution": "", "duration": -1, "usages": [ @@ -6740,7 +6740,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\dfrac 23 x$", "solution": "", "duration": -1, "usages": [ @@ -6877,7 +6877,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "图形略, 面积为$2$", "solution": "", "duration": -1, "usages": [ @@ -6987,7 +6987,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 不正确, 如$(1,-1)$; (2) 正确, 理由略; (3) 不正确, 如$(1,0)$", "solution": "", "duration": -1, "usages": [ @@ -7193,7 +7193,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$x^2+9y^2=4$", "solution": "", "duration": -1, "usages": [ @@ -7532,7 +7532,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "$y^2=k(x^2-36)$($y\\ne 0$且$k\\ne \\pm 6$)", "solution": "", "duration": -1, "usages": [ @@ -58600,7 +58600,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$3(x-2)+4(y+3)=0$", "solution": "", "duration": -1, "usages": [ @@ -58760,7 +58760,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$3$或$\\dfrac 32$", "solution": "", "duration": -1, "usages": [ @@ -59349,7 +59349,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$[0,\\dfrac\\pi 3]\\cup (\\dfrac \\pi 2,\\pi)$", "solution": "", "duration": -1, "usages": [ @@ -59531,7 +59531,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$[0,\\dfrac\\pi 4]\\cup [\\dfrac {3\\pi}4,\\pi)$", "solution": "", "duration": -1, "usages": [ @@ -59599,7 +59599,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{24}{7}$", "solution": "", "duration": -1, "usages": [ @@ -59837,7 +59837,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$y=-2x+4$", "solution": "", "duration": -1, "usages": [ @@ -59983,7 +59983,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$3\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -60106,7 +60106,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$-4$", "solution": "", "duration": -1, "usages": [ @@ -60419,7 +60419,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$-3$或$1$", "solution": "", "duration": -1, "usages": [ @@ -60592,7 +60592,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 13$", "solution": "", "duration": -1, "usages": [ @@ -60855,7 +60855,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$(-2,2)$", "solution": "", "duration": -1, "usages": [ @@ -61479,7 +61479,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "过$(10,-15)$", "solution": "", "duration": -1, "usages": [ @@ -61593,7 +61593,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "(1) $a^2+b^2=r^2$; (2) $b=0$; (3) $b=r$或$b=-r$; (4) $a^2=b^2=r^2$", "solution": "", "duration": -1, "usages": [ @@ -61715,7 +61715,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$D=E$", "solution": "", "duration": -1, "usages": [ @@ -61780,7 +61780,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$x-y-3=0$, $x+y-3=0$", "solution": "", "duration": -1, "usages": [ @@ -61919,7 +61919,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [ @@ -61960,7 +61960,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1)\\cup (4,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -61999,7 +61999,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -62062,7 +62062,7 @@ "圆" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -62290,7 +62290,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -62356,7 +62356,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$x^2+y^2-2x+8y+9=0$", "solution": "", "duration": -1, "usages": [ @@ -62479,7 +62479,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "最大值为$8$, $l$的方程为$y=2\\sqrt{2}(x-3)$或$y=-2\\sqrt{2}(x-3)$", "solution": "", "duration": -1, "usages": [ @@ -62546,7 +62546,7 @@ "圆" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -62645,7 +62645,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -62795,7 +62795,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tabular}{c|c|c|c|c|c}\n$m$ & $(-\\dfrac{\\sqrt{2}}2,\\dfrac{\\sqrt{2}}2)$ & $\\pm \\dfrac{\\sqrt{2}}2$ & $(-\\dfrac{3\\sqrt{2}}2,-\\dfrac{\\sqrt{2}}2)\\cup (\\dfrac{\\sqrt{2}}2,\\dfrac{3\\sqrt{2}}2)$ & $\\pm \\dfrac{3\\sqrt{2}}2$ & $(-\\infty,-\\dfrac{3\\sqrt{2}}2)\\cup (\\dfrac{3\\sqrt{2}}2,+\\infty)$\\\\\\hline\n位置关系 & 内含 & 内切 & 相交 & 外切 & 相离\n\\end{tabular}", "solution": "", "duration": -1, "usages": [ @@ -62861,7 +62861,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$4x+3y-10=0$, $10$", "solution": "", "duration": -1, "usages": [ @@ -90554,7 +90554,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$\\pi-\\arctan \\dfrac ba$", "solution": "", "duration": -1, "usages": [ @@ -91121,7 +91121,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -91377,7 +91377,7 @@ "圆" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -103559,7 +103559,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=x$或$y=7x$; (2) $y=2x+\\dfrac{5\\sqrt{3}}2$或$y=2x-\\dfrac{5\\sqrt{3}}2$", "solution": "", "duration": -1, "usages": [ @@ -111705,7 +111705,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{34}}{85}$", "solution": "", "duration": -1, "usages": [ @@ -120688,7 +120688,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$2x-y-3=0$", "solution": "", "duration": -1, "usages": [ @@ -123632,7 +123632,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 43$", "solution": "", "duration": -1, "usages": [ @@ -140610,7 +140610,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "$x$的范围为$[0,2]$, $x^2+y^2$的范围为$[0,4]$", "solution": "", "duration": -1, "usages": [ @@ -219547,7 +219547,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$l_{BC}:2x+y-5=0$, $l_{AC}:4x-5y+13=0$", "solution": "", "duration": -1, "usages": [ @@ -219634,7 +219634,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\dfrac 12 x+\\dfrac 52$或$y=\\dfrac 23 x+2$", "solution": "", "duration": -1, "usages": [ @@ -219674,7 +219674,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$a=7$", "solution": "", "duration": -1, "usages": [ @@ -220774,7 +220774,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y=-\\dfrac 56 x$或$y=-\\dfrac{11}2 x$", "solution": "", "duration": -1, "usages": [ @@ -220937,7 +220937,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$19x-4y-22=0$", "solution": "", "duration": -1, "usages": [ @@ -221425,7 +221425,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$[0,\\dfrac\\pi 4]\\cup [\\dfrac{3\\pi}4,\\pi)$", "solution": "", "duration": -1, "usages": [ @@ -221462,7 +221462,7 @@ "直线" ], "genre": "填空题", - "ans": "", + "ans": "$x+2y+2=0$", "solution": "", "duration": -1, "usages": [ @@ -221499,7 +221499,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$3x+y-13=0$", "solution": "", "duration": -1, "usages": [ @@ -222002,7 +222002,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(x+\\dfrac 32)^2+(y-3)^2=3$; (2) $(x-\\sqrt{2})^2+(y-1)^2=6$; (3) $(x-3)^2+(y-1)^2=5$或$(x-3)^2+(y+1)^2=5$", "solution": "", "duration": -1, "usages": [ @@ -222067,7 +222067,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$4x-3y-35=0$", "solution": "", "duration": -1, "usages": [ @@ -222257,7 +222257,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$x^2+(y-\\dfrac 12)^2=\\dfrac 14$且$x\\ne 0$", "solution": "", "duration": -1, "usages": [ @@ -222320,7 +222320,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$3x+4y+20=0$或$3x+4y-10=0$", "solution": "", "duration": -1, "usages": [ @@ -222357,7 +222357,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$(x-\\dfrac {24}5)^2+(y+\\dfrac{18}5)^2=1$", "solution": "", "duration": -1, "usages": [ @@ -224220,7 +224220,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(x-3)^2+(y+3)^2=10$; (2) $(x-1)^2+(y+2)^2=2$", "solution": "", "duration": -1, "usages": [ @@ -224258,7 +224258,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=x+\\sqrt{2}$或$y=x-\\sqrt{2}$; (2) $y=x+\\sqrt{2}$或$y=-x+\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -227259,7 +227259,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$(0,-1)$", "solution": "", "duration": -1, "usages": [ @@ -243464,7 +243464,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y=-\\dfrac{\\sqrt 3}{3}(x+1)$", "solution": "", "duration": -1, "usages": [ @@ -243648,7 +243648,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "总经过定点$(-1,0)$, 证明略", "solution": "", "duration": -1, "usages": [ @@ -243733,7 +243733,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac 94$", "solution": "", "duration": -1, "usages": [ @@ -243919,7 +243919,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\arccos\\dfrac{\\sqrt{170}}{170}$; (2) $\\arccos \\dfrac{7\\sqrt{65}}{65}$", "solution": "", "duration": -1, "usages": [ @@ -243981,7 +243981,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y+3=(2+\\sqrt{3})(x-4)$或$y+3=(2-\\sqrt{3})(x-4)$", "solution": "", "duration": -1, "usages": [ @@ -244115,7 +244115,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$(x-5)^2+(y-4)^2=25$", "solution": "", "duration": -1, "usages": [ @@ -244151,7 +244151,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$x^2+y^2-5x-y+4=0$", "solution": "", "duration": -1, "usages": [ @@ -262547,7 +262547,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$a=-\\dfrac 57$, 斜率为$-\\dfrac 16$", "solution": "", "duration": -1, "usages": [ @@ -262610,7 +262610,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$\\begin{cases}\\dfrac\\pi 2-\\theta, & 0\\le \\theta\\le \\dfrac \\pi 2, \\\\ \\dfrac{3\\pi}2-\\theta, & \\dfrac\\pi 2<\\theta<\\pi.\\end{cases}$", "solution": "", "duration": -1, "usages": [ @@ -262723,7 +262723,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y=\\dfrac 34x+4$或$y=-\\dfrac 34 x+4$", "solution": "", "duration": -1, "usages": [ @@ -262786,7 +262786,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\pi-\\arctan 5$; (2) $\\dfrac 25$", "solution": "", "duration": -1, "usages": [ @@ -262824,7 +262824,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$y-1=\\dfrac{5+\\sqrt{33}}4(x+2)$或$y-1=\\dfrac{5-\\sqrt{33}}4(x+2)$", "solution": "", "duration": -1, "usages": [ @@ -263298,7 +263298,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,-5)\\cup (-5,8)\\cup (8,+\\infty)$; (2) $\\{-5\\}$; (3) $\\{8\\}$", "solution": "", "duration": -1, "usages": [ @@ -263505,7 +263505,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [ @@ -263543,7 +263543,7 @@ "直线" ], "genre": "解答题", - "ans": "", + "ans": "$x+3y-6=0$或$3x-y+6=0$", "solution": "", "duration": -1, "usages": [ @@ -264019,7 +264019,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$x-y+1=0$", "solution": "", "duration": -1, "usages": [ @@ -264130,7 +264130,7 @@ "圆" ], "genre": "解答题", - "ans": "", + "ans": "$(x-\\dfrac{12}5)^2+(y+\\dfrac{16}5)^2=1$", "solution": "", "duration": -1, "usages": [ @@ -273830,7 +273830,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-4,-3)$", "solution": "", "duration": -1, "usages": [ @@ -273891,7 +273891,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1-\\mathrm{i}$", "solution": "", "duration": -1, "usages": [ @@ -273926,7 +273926,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [ @@ -273962,7 +273962,7 @@ "概率" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 16$", "solution": "", "duration": -1, "usages": [ @@ -273998,7 +273998,7 @@ "二项式定理" ], "genre": "填空题", - "ans": "", + "ans": "$160$", "solution": "", "duration": -1, "usages": [ @@ -274070,7 +274070,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pi$", "solution": "", "duration": -1, "usages": [ @@ -274105,7 +274105,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{5}}5$", "solution": "", "duration": -1, "usages": [ @@ -274161,7 +274161,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{9\\}$", "solution": "", "duration": -1, "usages": [ @@ -274196,7 +274196,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(0,0)$或$(1,0)$", "solution": "", "duration": -1, "usages": [ @@ -274252,7 +274252,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -274285,7 +274285,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -274320,7 +274320,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -274355,7 +274355,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\arccos\\dfrac{\\sqrt{5}}{10}$; (2) $3$", "solution": "", "duration": -1, "usages": [ @@ -274390,7 +274390,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 最小正周期为$\\pi$, 对称中心为$(\\dfrac{k\\pi}2-\\dfrac\\pi{12},-\\dfrac 12)$($k\\in \\mathbf{Z}$); (2) $a$的取值范围为$[0,\\dfrac 12)$, $x_1+x_2=\\dfrac\\pi 3$", "solution": "", "duration": -1, "usages": [ @@ -274423,7 +274423,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 完成三种部件依次需要$\\dfrac{1000}{x}$天, $\\dfrac{2000}{kx}$天, $\\dfrac{1500}{200-(k+1)x}$天; (2) $k=2$时能使完成订单任务的时间最短, 具体人数分组方案为甲$44$人, 乙$88$人, 丙$68$人", "solution": "", "duration": -1, "usages": [ @@ -274498,7 +274498,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,0)\\cup (0,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -274557,7 +274557,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -274588,7 +274588,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -274621,7 +274621,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -274654,7 +274654,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 35$", "solution": "", "duration": -1, "usages": [ @@ -274685,7 +274685,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 72$", "solution": "", "duration": -1, "usages": [ @@ -274737,7 +274737,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$[2-\\sqrt{10},2+\\sqrt{10}]$", "solution": "", "duration": -1, "usages": [ @@ -274768,7 +274768,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2$", "solution": "", "duration": -1, "usages": [ @@ -274820,7 +274820,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -274851,7 +274851,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -274882,7 +274882,7 @@ "第九单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -274913,7 +274913,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -274965,7 +274965,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\sqrt{3}$; (2) $\\dfrac{\\sqrt{3}}6$", "solution": "", "duration": -1, "usages": [ @@ -274996,7 +274996,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{1,\\log_2 3\\}$; (2) $[0,4]$", "solution": "", "duration": -1, "usages": [ @@ -275028,7 +275028,7 @@ "第八单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $n=400$; (2) $|x-y|=4$; (3) $\\dfrac{7}{10}$", "solution": "", "duration": -1, "usages": [ @@ -275080,7 +275080,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 具有性质$P$, 理由略; (2) 证明略; (3) $[-4043,-4041]$", "solution": "", "duration": -1, "usages": [ @@ -276062,7 +276062,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -276097,7 +276097,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{4\\}$", "solution": "", "duration": -1, "usages": [ @@ -276134,7 +276134,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pi$", "solution": "", "duration": -1, "usages": [ @@ -276170,7 +276170,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$9\\pi$", "solution": "", "duration": -1, "usages": [ @@ -276207,7 +276207,7 @@ "二项式定理" ], "genre": "填空题", - "ans": "", + "ans": "$-20$", "solution": "", "duration": -1, "usages": [ @@ -276241,7 +276241,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$12\\pi$", "solution": "", "duration": -1, "usages": [ @@ -276272,7 +276272,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[2,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -276303,7 +276303,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 3$", "solution": "", "duration": -1, "usages": [ @@ -276335,7 +276335,7 @@ "概率" ], "genre": "填空题", - "ans": "", + "ans": "$0.30$", "solution": "", "duration": -1, "usages": [ @@ -276366,7 +276366,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 92$", "solution": "", "duration": -1, "usages": [ @@ -276397,7 +276397,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -276428,7 +276428,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -276459,7 +276459,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -276490,7 +276490,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -276521,7 +276521,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -276553,7 +276553,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -276584,7 +276584,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\sqrt{2}$; (2) $16$", "solution": "", "duration": -1, "usages": [ @@ -276615,7 +276615,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $a=b=2$; (2) 直角三角形($A$为直角顶点)或等腰三角形($C$为顶角)", "solution": "", "duration": -1, "usages": [ @@ -276646,7 +276646,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 约$1.12$米; (2) $[3,4]$(单位: 米)", "solution": "", "duration": -1, "usages": [ @@ -276677,7 +276677,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 奇函数, 理由略; (2) $f(x)=3^{x-2k-1}$; (3) 存在, $k=0$", "solution": "", "duration": -1, "usages": [ @@ -276708,7 +276708,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(0,+\\infty)$; (2) $a=-\\dfrac 14$或$0$; (3) $[\\dfrac 23,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -317471,7 +317471,7 @@ "暂无对应" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{5\\pi}{6}$", "solution": "", "duration": -1, "usages": [ @@ -317520,7 +317520,7 @@ "圆" ], "genre": "填空题", - "ans": "", + "ans": "$[0,\\sqrt{3}]$", "solution": "", "duration": -1, "usages": [