From dff321e589b62f98c441b1ffd65b238bc5e547c7 Mon Sep 17 00:00:00 2001 From: Wang Weiye Date: Wed, 19 Oct 2022 16:51:06 +0800 Subject: [PATCH] 20221019 afternoon --- 工具/寻找阶段末尾空闲题号.ipynb | 2 +- 工具/批量题号选题pdf生成.ipynb | 83 +- 工具/根据目标列表批量生成对应题目的字典.ipynb | 63 +- 工具/添加题目到数据库.ipynb | 8 +- 工具/识别题库中尚未标注的题目类型.ipynb | 8 +- 文本处理工具/剪贴板文本整理_word文件.ipynb | 6 +- 文本处理工具/表格整理.ipynb | 6 +- 题库0.3/Problems.json | 1047 ++++++++++++++++- 8 files changed, 1073 insertions(+), 150 deletions(-) diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index 094796ad..1fee40e3 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -11,7 +11,7 @@ "text": [ "首个空闲id: 11988 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30169 , 直至 999999\n" + "首个空闲id: 30170 , 直至 999999\n" ] } ], diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb index 17390e02..b2d25c4a 100644 --- a/工具/批量题号选题pdf生成.ipynb +++ b/工具/批量题号选题pdf生成.ipynb @@ -9,65 +9,33 @@ "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0616003B_教师用_20221012.tex\n", + "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0807002B_教师用_20221019.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0616003B_学生用_20221012.tex\n", + "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0807002B_学生用_20221019.tex\n", "0\n", - "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0616004B_教师用_20221012.tex\n", + "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0807003B_教师用_20221019.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0616004B_学生用_20221012.tex\n", + "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0807003B_学生用_20221019.tex\n", "0\n", - "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0617002B_教师用_20221012.tex\n", + "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0808002B_教师用_20221019.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0617002B_学生用_20221012.tex\n", + "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0808002B_学生用_20221019.tex\n", "0\n", - "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0617004B_教师用_20221012.tex\n", + "开始编译教师版本pdf文件: 临时文件/批量生成题目/K0808003B_教师用_20221019.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/批量生成题目/K0617004B_学生用_20221012.tex\n", + "开始编译学生版本pdf文件: 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"\"\"\"---设置题目列表---\"\"\"\n", "#字典字段为文件名, 之后为内容的题号\n", "problems_dict = {\n", - "\"K0616003B\":\"000204,004061,009211,009212,010496,010498,010505\",\n", - "\"K0616004B\":\"009710,009711\",\n", - "\"K0617002B\":\"000210,000690,004084\",\n", - "\"K0617004B\":\"010499,010500\",\n", - "\"K0617006B\":\"003475,004994,009209,009210,009988,010497\",\n", - "\"K0617007B\":\"009712,010521,010522\",\n", - "\"K0619003B\":\"000199,000202,000211,000212,000216,000364,000411,005136,009214,009218,009400,010507,010514,010519,010524\",\n", - "\"K0619004B\":\"009868,010515,010520\",\n", - "\"K0619005B\":\"009720\",\n", - "\"K0620002B\":\"000352,004669,004995,010513\",\n", - "\"K0620004B\":\"000217,000372,000402,009207,010511,010516,010518\",\n", - "\"K0620005B\":\"010517\",\n", - "\"K0623001B\":\"004196\",\n", - "\"K0623002B\":\"000215,000394,009242,009731,010814,011332\",\n", - "\"K0623004B\":\"000200,000201,000205,000213,000419,009399,009417,009732,010532\"\n", - "\n", + "\"K0807002B\":\"009356\",\n", + "\"K0807003B\":\"000224,000230,003734,009357,009747,009748,009749,010552,010553,010554\",\n", + "\"K0808002B\":\"000226,000611,000624,000685,000695,000704,000812,004087,004150,004324,004750,009750,010555,010559,010560\",\n", + "\"K0808003B\":\"009751,010557,010558\",\n", + "\"K0809001B\":\"009752\",\n", + "\"K0809002B\":\"009753\",\n", + "\"K0809003B\":\"009754\",\n", "}\n", "\n", "\"\"\"---设置题目列表结束---\"\"\"\n", diff --git a/工具/根据目标列表批量生成对应题目的字典.ipynb b/工具/根据目标列表批量生成对应题目的字典.ipynb index f11b0119..485dcbb0 100644 --- a/工具/根据目标列表批量生成对应题目的字典.ipynb +++ b/工具/根据目标列表批量生成对应题目的字典.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -14,63 +14,40 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# 输入目标列表\n", - "t = \"\"\"K0616001B\n", - "K0616002B\n", - "K0616003B\n", - "K0616004B\n", - "K0617001B\n", - "K0617002B\n", - "K0617003B\n", - "K0617004B\n", - "K0617005B\n", - "K0617006B\n", - "K0617007B\n", - "K0619001B\n", - "K0619002B\n", - "K0619003B\n", - "K0619004B\n", - "K0619005B\n", - "K0620001B\n", - "K0620002B\n", - "K0620003B\n", - "K0620004B\n", - "K0620005B\n", - "K0623001B\n", - "K0623002B\n", - "K0623003B\n", - "K0623004B\n", + "t = \"\"\"K0807001B\n", + "K0807002B\n", + "K0807003B\n", + "K0808001B\n", + "K0808002B\n", + "K0808003B\n", + "K0808004B\n", + "K0809001B\n", + "K0809002B\n", + "K0809003B\n", "\"\"\"" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "\"K0616003B\":\"000204,004061,009211,009212,010496,010498,010505\",\n", - "\"K0616004B\":\"009710,009711\",\n", - "\"K0617002B\":\"000210,000690,004084\",\n", - "\"K0617004B\":\"010499,010500\",\n", - "\"K0617006B\":\"003475,004994,009209,009210,009988,010497\",\n", - "\"K0617007B\":\"009712,010521,010522\",\n", - "\"K0619003B\":\"000199,000202,000211,000212,000216,000364,000411,005136,009214,009218,009400,010507,010514,010519,010524\",\n", - "\"K0619004B\":\"009868,010515,010520\",\n", - "\"K0619005B\":\"009720\",\n", - "\"K0620002B\":\"000352,004669,004995,010513\",\n", - "\"K0620004B\":\"000217,000372,000402,009207,010511,010516,010518\",\n", - "\"K0620005B\":\"010517\",\n", - "\"K0623001B\":\"004196\",\n", - "\"K0623002B\":\"000215,000394,009242,009731,010814,011332\",\n", - "\"K0623004B\":\"000200,000201,000205,000213,000419,009399,009417,009732,010532\",\n" + "\"K0807002B\":\"009356\",\n", + "\"K0807003B\":\"000224,000230,003734,009357,009747,009748,009749,010552,010553,010554\",\n", + "\"K0808002B\":\"000226,000611,000624,000685,000695,000704,000812,004087,004150,004324,004750,009750,010555,010559,010560\",\n", + "\"K0808003B\":\"009751,010557,010558\",\n", + "\"K0809001B\":\"009752\",\n", + "\"K0809002B\":\"009753\",\n", + "\"K0809003B\":\"009754\",\n" ] } ], diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 7a35222d..5e7d91a2 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -7,10 +7,10 @@ "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 30113\n", - "origin = \"人教B版教材例题与习题\"\n", - "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目1.tex\"\n", - "editor = \"20221010\\t王伟叶\"" + "starting_id = 30170\n", + "origin = \"高中数学教与学例题与习题\"\n", + "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目2.tex\"\n", + "editor = \"20221019\\t王伟叶\"" ] }, { diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb index 2a054eec..a4972478 100644 --- a/工具/识别题库中尚未标注的题目类型.ipynb +++ b/工具/识别题库中尚未标注的题目类型.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -39,7 +39,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -53,12 +53,12 @@ "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/文本处理工具/剪贴板文本整理_word文件.ipynb b/文本处理工具/剪贴板文本整理_word文件.ipynb index 2e059c87..0d137649 100644 --- a/文本处理工具/剪贴板文本整理_word文件.ipynb +++ b/文本处理工具/剪贴板文本整理_word文件.ipynb @@ -480,7 +480,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -494,12 +494,12 @@ "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/文本处理工具/表格整理.ipynb b/文本处理工具/表格整理.ipynb index d5b51bdb..946124a8 100644 --- a/文本处理工具/表格整理.ipynb +++ b/文本处理工具/表格整理.ipynb @@ -68,7 +68,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -82,12 +82,12 @@ "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 230af540..92c59f96 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -291371,7 +291371,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -291393,7 +291393,7 @@ "K0621001B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291415,7 +291415,7 @@ "K0615005B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291436,7 +291436,7 @@ "K0621002B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291459,7 +291459,7 @@ "K0618002B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291481,7 +291481,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -291502,7 +291502,7 @@ "K0615002B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291524,7 +291524,7 @@ "K0615004B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291545,7 +291545,7 @@ "K0618001B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291566,7 +291566,7 @@ "K0618002B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291587,7 +291587,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291608,7 +291608,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291629,7 +291629,7 @@ "K0615007B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291651,7 +291651,7 @@ "K0622006B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291672,7 +291672,7 @@ "K0615008B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291693,7 +291693,7 @@ "K0618005B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291714,7 +291714,7 @@ "K0622004B" ], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -291736,7 +291736,7 @@ "K0622003B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291758,7 +291758,7 @@ "K0622003B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291779,7 +291779,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291800,7 +291800,7 @@ "K0615004B" ], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -291822,7 +291822,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291844,7 +291844,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291865,7 +291865,7 @@ "K0618006B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291887,7 +291887,7 @@ "K0622006B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291908,7 +291908,7 @@ "K0622005B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291931,7 +291931,7 @@ "K0618007B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291952,7 +291952,7 @@ "K0618004B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291974,7 +291974,7 @@ "K0622002B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -291995,7 +291995,7 @@ "K0621002B" ], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -292687,5 +292687,992 @@ ], "remark": "", "space": "" + }, + "030170": { + "id": "030170", + "content": "2019年, 我国施行个人所得税专项附加扣除办法, 涉及子女教育、继续教育、大病医疗、住房贷款利息、住房租金、赡养老人等六项专项附加扣除, 某单位老、中、青员工分别有$72, 108, 120$人, 现采用分层抽样的方法, 从该单位上述员工中抽取$25$人调查专项附加扣除的享受情况.\\\\\n(1) 应从老、中、青员工中分别抽取多少人?\\\\\n(2) 抽取的$25$人中, 享受至少两项专项附加扣除的员工有$6$人, 分别记为$A, B, C, D, E, F$. 享受情况见下表, 其中``\\checkmark''表示享受, ``$\\times$''表示不享受, 现从这$6$人中随机抽取$2$人接受采访.\\\\\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n项目 & 员工$A$ & 员工$B$ & 员工$C$ & 员工$D$ & 员工$E$ & 员工$F$ \\\\ \\hline\n子女教育 & \\checkmark & \\checkmark & $\\times$ & \\checkmark & $\\times$ & \\checkmark \\\\ \\hline\n继续教育 & $\\times$ & $\\times$ & \\checkmark & $\\times$ & \\checkmark & \\checkmark \\\\ \\hline\n大病医疗 & $\\times$ & $\\times$ & $\\times$ & \\checkmark & $\\times$ & $\\times$ \\\\ \\hline\n住房贷款利息 & \\checkmark & \\checkmark & $\\times$ & $\\times$ & \\checkmark & \\checkmark \\\\ \\hline\n住房租金 & $\\times$ & $\\times$ & \\checkmark & $\\times$ & $\\times$ & $\\times$ \\\\ \\hline\n赡养老人 & \\checkmark & \\checkmark & $\\times$ & $\\times$ & $\\times$ & \\checkmark \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(i) 试用所给字母列举出所有可能的抽取结果;\\\\\n(ii) 设$M$为事件``抽取的$2$人享受的专项附加扣除至少有一项相同'', 求事件$M$发生的概率.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030171": { + "id": "030171", + "content": "有红、黄、蓝三种颜色的旗帜各$3$面, 在每种颜色的$3$面旗帜上分别标上号码$1$, $2$和$3$. 现任取$3$面, 它们的颜色与号码均不相同的概率是\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030172": { + "id": "030172", + "content": "若某群体中的成员只用现金支付的概率为$0.45$. 既用现金支付也用非现金支付的概率为$0.15$, 则不用现金支付的概率为\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030173": { + "id": "030173", + "content": "连续掷两次骰子, 出现点数之和等于$4$的概率是\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030174": { + "id": "030174", + "content": "甲、乙、丙三人同在某公司上班, 若该公司规定, 每位职工可以在每周七天中任选两天休息(如选定周一、周三), 以后不再改动, 则他们远定的两个休息日相同的概率是\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030175": { + "id": "030175", + "content": "围棋盒子中有多粒黑子和白子, 已知从中任意取出$2$粒, 都是黑子的概率为$\\dfrac 17$, 都是白子的概率为$\\dfrac{12}{35}$, 则从中任意取出$2$粒, 恰好是同一色的概率是\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030176": { + "id": "030176", + "content": "任意投掷两枚骰子, 则``出现的点数之和为奇数''的概率是\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030177": { + "id": "030177", + "content": "已知$5$件产品中有$2$件次品, 其余为合格品, 现从这$5$件产品中任取$2$件, 恰有一件次品的概率为\\bracket{20}.\n\\fourch{$0.2$}{$0.4$}{$0.6$}{$0.8$}", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030178": { + "id": "030178", + "content": "投掷两颗做子, 得到其向上的点数分别为$m$和$n$, 则复数$(m+n\\mathrm{i})(n-m\\mathrm{i})$为实数的概率为\\bracket{20}.\n\\fourch{$\\dfrac 13$}{$\\dfrac 14$}{$\\dfrac 16$}{$\\dfrac 1{12}$}", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030179": { + "id": "030179", + "content": "把$5$个不同的球任意放入$6$个不同的盒子中, 每个球进人每个盒子中的可能性相同, 求: \\\\\n(1) 指定的$5$个盒中各有一球(事件$A$)的概率;\\\\ \n(2) 没有两个球在同一盒中(事件$B$)的概率.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030180": { + "id": "030180", + "content": "$6$个房间安排$4$个旅游者, 每人可进住任一房间, 且进住房间是等可能的(每个房间可入住多人)求:\\\\ \n(1) 指定的某四个房间各住$1$人的概率;\\\\ \n(2) 恰有四个房间各住$1$人的概率;\\\\\n(3) 指定的某房间有$2$人的概率;\\\\\n(4) 指定的两个房间各有$2$人的概率.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030181": { + "id": "030181", + "content": "设$O$为正方形$ABCD$的中心, 在$O, A, B, C, D$中任取$3$点, 则取到的$3$点共线的概率为\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030182": { + "id": "030182", + "content": "从男生和女生共$36$人的班级中随机选出$2$人去完成某项任务, 如果选出的$2$人性别相同的概率是\n$\\dfrac 12$, 那么这个班级中的男生, 女生各有多少人?", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030183": { + "id": "030183", + "content": "随机抽取一个年份, 对上海市该年$11$月的天气情况进行统计, 结果如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n日期 & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ & $11$ & $12$ & $13$ & $14$ & $15$ \\\\ \\hline\n天气 & 雨 & 雨 & 云 & 云 & 云 & 晴 & 晴 & 晴 & 云 & 晴 & 晴 & 云 & 晴 & 晴 & 云 \\\\ \\hline\n日期 & $16$ & $17$ & $18$ & $19$ & $20$ & $21$ & $22$ & $23$ & $24$ & $25$ & $26$ & $27$ & $28$ & $29$ & $30$ \\\\ \\hline\n天气 & 雨 & 云 & 云 & 阴 & 云 & 雨 & 雨 & 阴 & 雨 & 雨 & 雨 & 雨 & 阴 & 云 & 阴 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n注: 雨表示下雨, 云表示多云.\\\\\n(1) 在$11$月份任取一天, 估计上海市在该天不下雨的概率;\\\\\n(2) 上海市某学校拟从$11$月份的一个晴天或多云的日子开始举行连续$2$天的运动会, 估计运动会期间不下雨的概率.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030184": { + "id": "030184", + "content": "用$K$, $A_1$, $A_2$三类不同的元件连接成一个系统, 当且仅当$K$正常工作且$A_1,A_2$至少有一个正常工作时, 系统正常工作, 已知$K$, $A_1$, $A_2$正常工作的概率分别是$0.9, 0.8, 0.8$, 且是否正常工作互相独立, 则系统正常工作的概率为\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030185": { + "id": "030185", + "content": "某中学举办电脑知识竞赛, 满分为$100$分, $80$分以上(含$80$分)为优秀, 现将参赛学生的成续进行整理后分成五组: 第一组$[50, 60)$, 第二组$[60, 70)$, 第三组$[70, 80)$, 第四组$[80, 90)$, 第五组$[90, 100]$. 其中第一、三、四、五小组的频率分别为$0.30, 0.15, 0.10, 0.05$. 而第二小组的频数是$40$, 则参赛的人数为\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030186": { + "id": "030186", + "content": "两个实习生每人加工一个零件, 加工为一等品的概率分别为$\\dfrac 56$和$\\dfrac 34$, 两个零件是否加工为一等品相互独立, 则这两个零件中恰有一个一等品的概率为\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030187": { + "id": "030187", + "content": "出租车司机从饭店到火车站途中经过六个交通岗, 假设他在各交通岗遇到红灯这一事件是相互独立的, 并且概率都是$\\dfrac 13$, 则这位司机首次遇到红灯前恰好通过了三个交通岗的概率为\\blank{50}.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030188": { + "id": "030188", + "content": "某杀毒软件的病毒查杀比赛规则为每个软件进行四轮考核, 每轮考核中能够准确对病毒进行查杀的进入下一轮考核, 否则被淘汰, 已知某个软件在四轮考核中能够准确杀毒的概率依次是$\\dfrac 56,\\dfrac 35,\\dfrac 34,\\dfrac 13$, 凡各轮考核能否通过互不影响, 则下列结论中, 正确的是\\blank{50}(写出所有正确结论的序号).\\\\\n\\textcircled{1} 该软件通过考核的概率为$\\dfrac 18$; \\textcircled{2} 该软件在第三轮考核被淘汰的概率为$\\dfrac 18$; \\textcircled{3} 该软件至少能够通过两轮考核的概率为$\\dfrac 23$; \\textcircled{4} 在此次比赛中该软件平均考核了$\\dfrac{65}{24}$轮.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030189": { + "id": "030189", + "content": "有$6$个相同的球, 分别标有数字$1, 2, 3, 4,5,6$, 从中有放回地随机取两次, 每次取$1$个球, 甲表示事件``第一次取出的球的数字是$1$'', 乙表示事件``第二次取出的球的数字是$2$'', 丙表示事件``两次取出的球的数字之和是$8$'', 丁表示事件``两次取出的球的数字之和是$7$'', 则\\bracket{20}.\n\\fourch{甲与丙相互独立}{甲与丁相互独立}{乙与丙相互独立}{丙与丁相互独立}", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030190": { + "id": "030190", + "content": "投掷一枚均匀硬币和一枚均匀骰子各一次, 记``硬币正面向上''为事件$A$, ``骰子向上的点数是$3$''为事件$B$, 则事件$A, B$中至少有一件发生的概率是\\bracket{20}.\n\\fourch{$\\dfrac 5{12}$}{$\\dfrac 12$}{$\\dfrac 7{12}$}{$\\dfrac 34$}", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030191": { + "id": "030191", + "content": "甲、乙、丙三名学生进行羽毛球比赛, 约定赛制如下: 累计负两场者被淘汰; 比赛前抽签决定首先比赛的两人, 另一人轮空; 每场比赛的胜者与轮空者进行下一场比赛, 负者下一场轮空, 直至有一人被淘汰; 当一人被淘汰后, 剩余的两人继续比赛, 直至其中一人被淘汰, 另一人最终获胜, 比赛结束, 经抽签, 甲、乙首先比赛, 丙轮空, 设每场比赛双方获胜的概率都为$\\dfrac 12$.\\\\\n(1) 求甲连胜四场的概率;\\\\\n(2) 求需要进行第五场比赛的概率;\\\\ \n(3) 求丙最终获胜的概率.", + "objs": [], + "tags": [ + "第八单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030192": { + "id": "030192", + "content": "某厂接受了一项加工业务, 加工出来的产品(单位: 件)按标准分为$A, B, C, D$四个等级, 加工业务约定: 对于$A$级品、$B$级品、$C$级品, 厂家每件分别收取加工费$90$元, $50$元, $20$元; 对于$D$级品, 厂家每件要赔偿原料损失费$50$元, 该厂有甲、乙两个分厂可承接加工业务, 甲分厂加工成本费为$25$元/件, 乙分厂加工成本费为$20$元/件, 厂家为决定由哪个分厂承接加工业务, 在两个分厂各试加工了$100$件这种产品, 并统计了这些产品的等级, 整理如下: \n\\begin{center}\n\\begin{tabular}{cc}\n甲分厂产品等级的频数分布表 & 乙分厂产品等级的频数分布表\\\\\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n等级 & $A$ & $B$ & $C$ & $D$ \\\\ \\hline\n频数 & $40$ & $20$ & $20$ & $20$ \\\\ \\hline\n\\end{tabular} \n &\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n等级 & $A$ & $B$ & $C$ & $D$ \\\\ \\hline\n频数 & $28$ & $17$ & $34$ & $21$ \\\\ \\hline\n\\end{tabular}\n\\end{tabular}\n\\end{center} \n(1) 分别估计甲、乙两分厂加工出来的一件产品为$A$级品的概率;\\\\ \n(2) 分别求甲、乙两分厂加工出来的$100$件产品的平均利润, 以平均利润为依据, 厂家应选哪个分厂承接加工业务?", + 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班主任欲了解全班同学的成绩情况, 已知班级中共$38$名同学, 期中考试考了语文、数学、英语、物理、化学、历史、政治、生物、地理共$9$门学科, 在这个调查中, 总体的容量是\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030198": { + "id": "030198", + "content": "教育部调查某地区学生的午餐情况, 在该地区的$30$个学校中每校抽取了$20$名同学做问卷调查, 此次调查的样本容量为\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030199": { + "id": "030199", + "content": "在新冠肺炎疫情中, 某校出现了一例新冠确诊病例, 需通过核酸检测调查该校园疫情传播的情况, 采用的数据获取手段应当是\\blank{50}(填写``普查''或``抽样调查'')", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": 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"same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030204": { + "id": "030204", + "content": "为了解某工厂开展群众体育活动的情况, 拟采用分展抽样的方法从$A, B, C$三个区中抽取$7$个工厂进行调查, 已知$A, B, C$区中分别有$18, 27, 18$个工厂.\\\\\n(1) 求从$A, B, C$区中分别抽域的工厂个数;\\\\\n(2) 若从抽取的$7$个工厂中随机抽取$2$个进行调查结果的对比, 计算这$2$个工厂中至少有$1$个来自$A$区的概率.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030205": { + "id": "030205", + "content": "把总体的每一个个体编上号, 按某种相等的间隔抽取样本的方法, 称之为系统抽样. 某学校采用系统抽样的方法从$1500$名同学(编号$1$到$1500$)中抽取$100$名同学进行行为规范调查, 如果抽取的学生中有一名编号为$29$, 则抽取的学生编号中最接近$1000$的是\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030206": { + "id": "030206", + "content": "在体育课体测$1000$米时, 大多学生跑得气喘吁吁且成绩不理想, 体育老师说: ``看来, 我们班的同学体能方面问题比较大, 需要加强训练.''请你从统计的角度来讨论下面的问题:\\\\\n(1) 在这个情境中, 总体和样本分别是什么?\\\\\n(2) 你同意体育老师的说法吗? 请说明理由.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030207": { + "id": "030207", + "content": "根据如图所示的频率分布直方图, 如果样本容量为$100$, 则在区间$[6,10)$上的数据的频数为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.15,yscale =25]\n\\draw [->] (0,0) -- (30,0) node [below] {样本数据};\n\\draw [->] (0,0) -- (0,0.11) node [left] {频率/组距};\n\\draw (0,0) node [below left] {$O$};\n\\draw (2,0) -- (2,0.02) -- (6,0.02) (6,0) -- (6,0.08) -- (10,0.08) (10,0) -- (10,0.09) -- (14,0.09) -- (14,0) (14,0.03) -- (18,0.03) -- (18,0) (18,0.03) -- (22,0.03) -- (22,0);\n\\foreach \\i in {2,6,...,22} {\\draw (\\i,0) node [below] {$\\i$};};\n\\draw (0,0.02) node [left] {$0.02$} (0,0.03) node [left] {$0.03$} (0,0.08) node [left] {$x$} (0,0.09) node [left] {$0.09$};\n\\draw [dashed] (0,0.02) -- (2,0.02) (0,0.03) -- (14,0.03) (0,0.08) -- (6,0.08) (0,0.09) -- (10,0.09);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030208": { + "id": "030208", + "content": "一个班的语文成绩的茎叶图如图所示, 则优秀率(80及以上)为\\blank{50}, 最高分是\\blank{50}, 最低分是\\blank{50}, 中位数是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{c|ccccccccc}\n$6$ & $0$ & $3$ & $4$ & $4$ & $6$ & $7$ & $8$ & $8$ & $9$ \\\\ \n$7$ & $2$ & $3$ & $5$ & $5$ & $5$ & $6$ & $7$ & $9$ & \\\\\n$8$ & $0$ & $2$ & $3$ & $3$ & $5$ & $7$ & $9$ & & \\\\ \n$9$ & $1$ & & & & & & & & \n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030209": { + "id": "030209", + "content": "某厂研制了一种生产高精产品的设备, 为检验新设备生产产品的某项指标有无提高, 用一台旧设备和一台新设各各生产了$10$件产品, 得到各件产品该项指标数据如下: \n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n旧设备 & $9.8$ & $10.3$ & $10.0$ & $10.2$ & $9.9$ & $9.8$ & $10.0$ & $10.1$ & $10.2$ & $9.7$ \\\\ \\hline\n新设备 & $10.1$ & $10.4$ & $10.1$ & $10.0$ & $10.1$ & $10.3$ & $10.6$ & $10.5$ & $10.4$ & $10.5$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n旧设备和新设备生产产品的该项指标的样本平均数分别记为$\\overline{x}$和$\\overline{y}$, 样本方差分别记为$S_1^2$和$S_2^2$.\\\\\n(1) 求$\\overline{x}$, $\\overline{y}$, $S_1^2$, $S_2^2$;\\\\\n(2) 判断新设备生产产品的该项指标的均值较旧设备是否有显著提高(如果$\\overline{y}-\\overline{x}\\ge 2\\sqrt{\\dfrac{S_1^2+S_2^2}2}$, 则认为新设备生产产品的该项指标的均值较旧设备有显著提高, 否则不认为有显著提高).", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030210": { + "id": "030210", + "content": "一个社会调查机构就某地居民的月收人调查了$10000$人, 并根据所得数据画了样本的频率分布直方图, 则月收入不足$3500$的人占全部居民的百分比为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 1.5,yscale = 6000]\n\\draw [->] (0,0) -- (6,0) node [below] {月收入/元};\n\\draw [->] (0,0) -- (0,0.0006) node [left] {频率/组距};\n\\draw (2,0) -- (2,0.0002) -- (2.5,0.0002) (2.5,0) -- (2.5,0.0004) -- (3,0.0004) (3,0) -- (3,0.0005) -- (3.5,0.0005) (3.5,0) -- (3.5,0.0005) -- (4,0.0005) -- (4,0) (4,0.0003) -- (4.5,0.0003) -- (4.5,0) (4.5,0.0001) -- (5,0.0001) -- (5,0);\n\\foreach \\i in {2000,2500,...,5000} {\\draw ({\\i/1000},0) node [below] {$\\i$};};\n\\foreach \\i/\\j in {0.0001/4.5,0.0002/2,0.0003/4,0.0004/2.5,0.0005/3} {\\draw (0,\\i) node [left] {$\\i$}; \\draw [dashed] (0,\\i) -- (\\j,\\i);};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030211": { + "id": "030211", + "content": "如图所示的茎叶图记录了甲、乙两组各$5$名工人某日的产量数据(单位: 件). 若这两组数据的中位数相等, 且平均值也相等, 则$x$和$y$的值分别为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{r|c|l}\n甲组 & & 乙组 \\\\ \\hline\n$6$ & $5$ & $9$ \\\\ \n$2\\ 5$ & $6$ & $1\\ 7\\ y$ \\\\ \n$x\\ 4$ & $7$ & $8$ \n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030212": { + "id": "030212", + "content": "下图是根据某校某次期中考试统计语文和英语学科的得分绘制的散点图, 根据散点图可知学生的语文成绩与英语成绩\\blank{50}明显关系. (填写``存在''或``不存在'')\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw [->] (0,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\filldraw (1.47,1.53) circle (0.01);\n\\filldraw (0.82,0.89) circle (0.01);\n\\filldraw (1.17,1.19) circle (0.01);\n\\filldraw (1.06,1.06) circle (0.01);\n\\filldraw (0.59,0.72) circle (0.01);\n\\filldraw (1.4,1.53) circle (0.01);\n\\filldraw (0.85,0.91) circle (0.01);\n\\filldraw (1.05,1.16) circle (0.01);\n\\filldraw (0.91,0.92) circle (0.01);\n\\filldraw (0.64,0.68) circle (0.01);\n\\filldraw (0.9,0.95) circle (0.01);\n\\filldraw (0.55,0.59) circle (0.01);\n\\filldraw (1.45,1.5) circle (0.01);\n\\filldraw (0.72,0.74) circle (0.01);\n\\filldraw (0.83,0.86) circle (0.01);\n\\filldraw (0.52,0.71) circle (0.01);\n\\filldraw (1.31,1.4) circle (0.01);\n\\filldraw (0.86,1.06) circle (0.01);\n\\filldraw (1.29,1.42) circle (0.01);\n\\filldraw (0.88,0.99) circle (0.01);\n\\filldraw (0.5,0.57) circle (0.01);\n\\filldraw (1.24,1.41) circle (0.01);\n\\filldraw (0.8,0.96) circle (0.01);\n\\filldraw (0.74,0.92) circle (0.01);\n\\filldraw (1.11,1.2) circle (0.01);\n\\filldraw (1.43,1.6) circle (0.01);\n\\filldraw (0.55,0.61) circle (0.01);\n\\filldraw (0.65,0.68) circle (0.01);\n\\filldraw (1.05,1.12) circle (0.01);\n\\filldraw (0.79,0.88) circle (0.01);\n\\filldraw (0.68,0.79) circle (0.01);\n\\filldraw (0.51,0.56) circle (0.01);\n\\filldraw (1.43,1.45) circle (0.01);\n\\filldraw (1.15,1.25) circle (0.01);\n\\filldraw (0.64,0.77) circle (0.01);\n\\filldraw (1.2,1.33) circle (0.01);\n\\filldraw (0.78,0.87) circle (0.01);\n\\filldraw (1.16,1.27) circle (0.01);\n\\filldraw (0.87,0.99) circle (0.01);\n\\filldraw (0.75,0.76) circle (0.01);\n\\filldraw (1.38,1.42) circle (0.01);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030213": { + "id": "030213", + "content": "从一批零件中抽取$80$个, 测量其直径(单位: $\\text{mm}$), 将所得数据分为$9$组: $[5.31, 5.33)$, $[5.33, 5.35)$, $\\cdots$, $[5.45, 5.47)$, $[5.47, 5.49]$, 并整理得到如图的频率分布直方图, 则在被抽取的零件中, 直径落在区间$[5.43, 5.47)$内的个数为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, yscale = 0.3, xscale = 40]\n\\draw [->] (5.3,0) -- (5.53,0) node [below] {直径/$\\text{mm}$};\n\\draw [->] (5.3,0) -- (5.3,12) node [left] {频率/组距}; \n\\draw (5.3,0) node [left] {$0$};\n\\foreach \\i/\\j in {5.31/1.25,5.33/3.75,5.35/2.5,5.37/7.5,5.39/10,5.41/8.75,5.43/6.25,5.45/5,5.47/5}\n{\\draw (\\i,0) node [below] {\\small $\\i$}; \\draw (\\i,0) -- (\\i,\\j) --++ (0.02,0) --++ (0,{-\\j});};\n\\draw (5.49,0) node [below] {\\small $5.49$};\n\\foreach \\i/\\j in {5.31/1.25,5.33/3.75,5.35/2.5,5.37/7.5,5.39/10,5.41/8.75,5.43/6.25,5.45/5}\n{\\draw (5.3,\\j) node [left] {\\small $\\j$}; \\draw [dashed] (5.3,\\j) -- (\\i,\\j);};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030214": { + "id": "030214", + "content": "演讲比赛共有$9$位评委分别给出某选手的原始评分, 评定该选手的成绩时, 从$9$个原始评分中去掉$1$个最高分、$1$个最低分, 得到$7$个有效评分. $7$个有效评分与$9$个原始评分相比, 不变的数字特征是\\bracket{20}.\n\\fourch{中位数}{平均数}{方差}{极差}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030215": { + "id": "030215", + "content": "已知$100$个数据的第$25$百分位数是$9.3$, 则下列说法正确的是\\bracket{20}.\n\\onech{这$100$个数据中一定有$25$个数小于或等于$9.3$}{把这$100$个数据从小到大排列后, $9.3$是第$25$个数据}{把这$100$个数据从小到大排列后, $9.3$是第$25$个数据和第$26$个数据的平均数}{把这$100$个数据从小到大排列后, $9.3$是第$25$个数据和第$24$个数据的平均数}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030216": { + "id": "030216", + "content": "某校为举办甲、乙两项不同活动, 分别设计了相应的活动方案: 方案一、方案二. 为了解该校学生对活动方案是否支持, 对学生进行简单随机抽样, 获得数据见下表: \n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\n & 男生, 支持 & 男生, 不支持 & 女生, 支持 & 女生, 不支持 \\\\ \\hline\n方案一 & $200$人 & $400$人 & $300$人 & $100$人 \\\\ \\hline\n方案二 & $350$人 & $250$人 & $150$人 & $250$人 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n假设所有学生对活动方案是否支持相互独立.\\\\\n(1) 分别估计该校男生支持方案一的概率和该校女生支持方案一的概率;\\\\\n(2) 从该校全体男生中随机抽取$2$人, 全体女生中随机抽取$1$人, 估计这$3$人中恰有$2$人支持方案一的概率;\\\\\n(3) 将该校学生支持方案二的概率估计值记为$p_0$, 假设该校一年级有$500$名男生和$300$名女生, 除一年级外其他年级学生支持方案二的概率估计值记为$p_1$, 试比较$p_0$与$p_1$的大小(结论不要求证明).", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "高中数学教与学例题与习题", + "edit": [ + "20221019\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" } } \ No newline at end of file