20221011 evening
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 2,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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"name": "stdout",
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"name": "stdout",
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"output_type": "stream",
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"output_type": "stream",
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"text": [
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"text": [
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"1 解答题 1\n",
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"1 选择题 1\n",
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"2 解答题 1\n",
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"2 解答题 1\n",
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"3 解答题 1\n",
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"3 解答题 1\n",
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"4 解答题 1\n",
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"4 解答题 1\n",
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"5 填空题 2\n",
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"5 解答题 1\n",
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"6 解答题 2\n",
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"6 解答题 4\n",
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"7 填空题 10\n",
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"7 填空题 4\n",
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"8 解答题 1\n",
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"8 填空题 1\n",
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"9 解答题 1\n",
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"9 填空题 1\n",
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"10 解答题 1\n",
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"10 解答题 2\n",
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"11 解答题 1\n",
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"11 解答题 1\n",
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"12 解答题 1\n",
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"12 解答题 1\n",
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"13 填空题 6\n",
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"13 解答题 1\n",
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"14 解答题 1\n",
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"14 解答题 1\n",
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"15 填空题 1\n",
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"15 解答题 4\n",
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"16 解答题 1\n",
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"1 解答题 5\n",
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"17 填空题 3\n",
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"2 选择题 1\n",
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"18 填空题 1\n",
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"3 解答题 1\n",
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"19 填空题 1\n",
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"4 解答题 1\n",
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"1 解答题 2\n",
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"5 解答题 2\n",
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"2 解答题 1\n",
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"6 解答题 1\n",
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"3 填空题 6\n",
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"7 填空题 1\n"
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"4 填空题 1\n",
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"5 选择题 1\n",
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"6 选择题 1\n",
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"7 填空题 2\n",
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"8 解答题 1\n",
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"9 解答题 1\n",
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"10 解答题 1\n",
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"11 解答题 1\n",
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"12 解答题 2\n",
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"13 解答题 1\n"
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]
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]
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}
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}
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],
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],
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"source": [
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"source": [
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"import os,re\n",
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"import os,re\n",
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"#修改文件名\n",
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"#修改文件名\n",
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"filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\20_描述空间位置关系的公理.tex\"\n",
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"filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\22_空间平面与平面的位置关系.tex\"\n",
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"# filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\上学期周末卷\\国庆卷.tex\"\n",
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"# filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\上学期周末卷\\国庆卷.tex\"\n",
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"outputfile = \"临时文件/题目状态.txt\"\n",
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"outputfile = \"临时文件/题目状态.txt\"\n",
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"\n",
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"\n",
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@ -2,15 +2,15 @@
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 8,
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"import os,re,json,time\n",
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"import os,re,json,time\n",
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"\n",
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"\n",
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"\"\"\"---设置原题目id与新题目id---\"\"\"\n",
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"\"\"\"---设置原题目id与新题目id---\"\"\"\n",
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"old_id = \"1598\"\n",
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"old_id = \"9697\"\n",
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"new_id = \"30112\"\n",
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"new_id = \"30151\"\n",
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"\"\"\"---设置完毕---\"\"\"\n",
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"\"\"\"---设置完毕---\"\"\"\n",
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"\n",
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"\n",
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"old_id = old_id.zfill(6)\n",
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"old_id = old_id.zfill(6)\n",
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@ -2,7 +2,7 @@
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 4,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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@ -13,11 +13,9 @@
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"题块 1 处理完毕.\n",
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"题块 1 处理完毕.\n",
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"正在处理题块 2 .\n",
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"正在处理题块 2 .\n",
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"题块 2 处理完毕.\n",
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"题块 2 处理完毕.\n",
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"正在处理题块 3 .\n",
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"开始编译教师版本pdf文件: 临时文件/22_空间平面与平面的位置关系_教师_20221011.tex\n",
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"题块 3 处理完毕.\n",
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"开始编译教师版本pdf文件: 临时文件/周末卷04_教师_20221010.tex\n",
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"0\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/周末卷04_学生_20221010.tex\n",
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"开始编译学生版本pdf文件: 临时文件/22_空间平面与平面的位置关系_学生_20221011.tex\n",
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"0\n"
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"0\n"
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]
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]
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}
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}
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@ -30,19 +28,19 @@
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"\"\"\"---设置模式结束---\"\"\"\n",
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"\"\"\"---设置模式结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置模板文件名---\"\"\"\n",
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"\"\"\"---设置模板文件名---\"\"\"\n",
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"# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
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"template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
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"template_file = \"模板文件/测验周末卷模板.tex\"\n",
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"# template_file = \"模板文件/测验周末卷模板.tex\"\n",
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"# template_file = \"模板文件/日常选题讲义模板.tex\"\n",
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"# template_file = \"模板文件/日常选题讲义模板.tex\"\n",
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"\"\"\"---设置模板文件名结束---\"\"\"\n",
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"\"\"\"---设置模板文件名结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置其他预处理替换命令---\"\"\"\n",
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"\"\"\"---设置其他预处理替换命令---\"\"\"\n",
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"#2023届第一轮讲义更换标题\n",
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"#2023届第一轮讲义更换标题\n",
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"# exec_list = [(\"标题数字待处理\",\"20\"),(\"标题文字待处理\",\"描述空间位置关系的公理\")] \n",
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"exec_list = [(\"标题数字待处理\",\"21\"),(\"标题文字待处理\",\"空间平面与平面的位置关系\")] \n",
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"# enumi_mode = 0\n",
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"enumi_mode = 0\n",
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"\n",
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"\n",
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"#2023届测验卷与周末卷\n",
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"#2023届测验卷与周末卷\n",
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"exec_list = [(\"标题替换\",\"周末卷04\")]\n",
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"# exec_list = [(\"标题替换\",\"周末卷04\")]\n",
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"enumi_mode = 1\n",
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"# enumi_mode = 1\n",
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"\n",
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"\n",
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"#日常选题讲义\n",
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"#日常选题讲义\n",
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"# exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n",
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"# exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n",
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@ -51,15 +49,14 @@
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"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
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"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置目标文件名---\"\"\"\n",
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"\"\"\"---设置目标文件名---\"\"\"\n",
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"destination_file = \"临时文件/周末卷04\"\n",
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"destination_file = \"临时文件/22_空间平面与平面的位置关系\"\n",
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"\"\"\"---设置目标文件名结束---\"\"\"\n",
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"\"\"\"---设置目标文件名结束---\"\"\"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\"\"\"---设置题号数据---\"\"\"\n",
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"\"\"\"---设置题号数据---\"\"\"\n",
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"problems = [\n",
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"problems = [\n",
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"\"1853,30108,3355,655,724,1860,2038,30106,30107,3621\",\n",
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"'1649,30095,30144,30096,30100,9698,3499,1665,1659,303,30097,30145,188,9700',\n",
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"\"1846,2013,3703\",\n",
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"\"9697,9158,1645,189,9154,1704,1670,294\"\n",
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"\"1557,4702\"\n",
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"]\n",
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"]\n",
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"\"\"\"---设置题号数据结束---\"\"\"\n",
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"\"\"\"---设置题号数据结束---\"\"\"\n",
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"\n",
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"\n",
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 4,
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"execution_count": 5,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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"name": "stdout",
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"name": "stdout",
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"output_type": "stream",
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"output_type": "stream",
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"text": [
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"text": [
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"开始编译教师版本pdf文件: 临时文件/多面体与旋转体选题_教师用_20221010.tex\n",
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"开始编译教师版本pdf文件: 临时文件/多面体与旋转体选题_教师用_20221011.tex\n",
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"0\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/多面体与旋转体选题_学生用_20221010.tex\n",
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"开始编译学生版本pdf文件: 临时文件/多面体与旋转体选题_学生用_20221011.tex\n",
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"0\n"
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"0\n"
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]
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]
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}
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}
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"\"\"\"---设置题目列表---\"\"\"\n",
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"\"\"\"---设置题目列表---\"\"\"\n",
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"#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
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"#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
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"problems = r\"\"\"\n",
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"problems = r\"\"\"\n",
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"a\n",
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"30146:30151\n",
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"\n",
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"\n",
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"\"\"\"\n",
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"\"\"\"\n",
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"\"\"\"---设置题目列表结束---\"\"\"\n",
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"\"\"\"---设置题目列表结束---\"\"\"\n",
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"K0617006B": {
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"K0617006B": {
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"id": "K0617006B",
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"id": "K0617006B",
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"unit_obj": "D06006B",
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"unit_obj": "D06006B",
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"content": "能用直圆柱的侧面积公式和表面积公式计算数学情境或现实情境中的直棱柱的侧面积与表面积."
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"content": "能用圆柱的侧面积公式和表面积公式计算数学情境或现实情境中的圆柱的侧面积与表面积."
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},
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},
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"K0617007B": {
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"K0617007B": {
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"id": "K0617007B",
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"id": "K0617007B",
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"K0620004B": {
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"K0620004B": {
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"id": "K0620004B",
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"id": "K0620004B",
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"unit_obj": "D06006B",
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"unit_obj": "D06006B",
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"content": "会在简单的具体情境中计算锥体的表面积."
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"content": "会在简单的具体情境中计算锥体的侧面积与表面积."
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},
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},
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"K0620005B": {
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"K0620005B": {
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"id": "K0620005B",
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"id": "K0620005B",
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"20220624\t王伟叶, 余利成"
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"20220624\t王伟叶, 余利成"
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],
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],
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"same": [],
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"same": [],
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"related": [],
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"related": [
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"030148"
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],
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"remark": "",
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"remark": "",
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"space": "12ex"
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"space": "12ex"
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},
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},
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},
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},
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"001620": {
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"001620": {
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"id": "001620",
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"id": "001620",
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"content": "正方体$ABCD-A'B'C'D'$中, 求证:\\\\ \n(1) $D'B\\perp AC$;\\\\ \n(2) $D'B\\perp$平面$AB'C$. \n\\begin{center}\n\\begin{tikzpicture}\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{3/2}) node [right] {$C$} coordinate (C)\n --++ (0,3) node [above right] {$C'$} coordinate (C1)\n --++ (-3,0) node [above left] {$D'$} coordinate (D1) --++ (225:{3/2}) node [left] {$A'$} coordinate (A1) -- cycle;\n \\draw (A) ++ (3,3) node [right] {$B'$} coordinate (B1) -- (B) (B1) --++ (45:{3/2}) (B1) --++ (-3,0);\n \\draw [dashed] (A) --++ (45:{3/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,3);\n \\draw (A) -- (B1) -- (C);\n \\draw [dashed] (A) -- (C) (B) -- (D1);\n\\end{tikzpicture}\n\\end{center}",
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"content": "正方体$ABCD-A'B'C'D'$中, 求证:\\\\ \n(1) $D'B\\perp AC$;\\\\ \n(2) $D'B\\perp$平面$AB'C$. \n\\begin{center}\n\\begin{tikzpicture}[scale = 0.5]\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{3/2}) node [right] {$C$} coordinate (C)\n --++ (0,3) node [above right] {$C'$} coordinate (C1)\n --++ (-3,0) node [above left] {$D'$} coordinate (D1) --++ (225:{3/2}) node [left] {$A'$} coordinate (A1) -- cycle;\n \\draw (A) ++ (3,3) node [right] {$B'$} coordinate (B1) -- (B) (B1) --++ (45:{3/2}) (B1) --++ (-3,0);\n \\draw [dashed] (A) --++ (45:{3/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,3);\n \\draw (A) -- (B1) -- (C);\n \\draw [dashed] (A) -- (C) (B) -- (D1);\n\\end{tikzpicture}\n\\end{center}",
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"objs": [
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"objs": [
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"K0611002B"
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"K0611002B"
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],
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],
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},
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},
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"001641": {
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"001641": {
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"id": "001641",
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"id": "001641",
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"content": "已知$PA\\perp$三角形$ABC$所在平面, 且$AB=AC=13$, $BC=10$, $PA=12$, $D$是$BC$中点.\\\\ \n(1) 求直线$PD$与平面$ABC$所成角的大小;\\\\ \n(2) 求直线$PC$与平面$PAD$所成角的正切;\\\\ \n(3) 求直线$PC$与平面$PAB$所成角的正切.",
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"content": "已知$PA\\perp$三角形$ABC$所在平面, 且$AB=AC=13$, $BC=10$, $PA=12$, $D$是$BC$中点.\\\\ \n(1) 求直线$PD$与平面$ABC$所成角的大小;\\\\ \n(2) 求直线$PC$与平面$PAD$所成角的正切值;\\\\ \n(3) 求直线$PC$与平面$PAB$所成角的正切值.",
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"objs": [
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"objs": [
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"K0610004B"
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"K0610004B"
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],
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],
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},
|
},
|
||||||
"001649": {
|
"001649": {
|
||||||
"id": "001649",
|
"id": "001649",
|
||||||
"content": "下列命题中不正确的是\\bracket{20}.\\\\ \n\\onech{垂直于同一条直线的两个平面平行}{垂直于同一个平面的两条直线相互平行}{若一个平面内有无数条直线都平行于另一个平面, 则这两个平面互相平行}{若两个平行平面分别和第三个平面相交, 则它们的交线互相平行}",
|
"content": "下列命题中不正确的是\\bracket{20}.\n\\onech{垂直于同一条直线的两个平面平行}{垂直于同一个平面的两条直线相互平行}{若一个平面内有无数条直线都平行于另一个平面, 则这两个平面互相平行}{若两个平行平面分别和第三个平面相交, 则它们的交线互相平行}",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0612001B"
|
"K0612001B"
|
||||||
],
|
],
|
||||||
|
|
@ -42863,7 +42865,9 @@
|
||||||
"20220625\t王伟叶"
|
"20220625\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030146"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": ""
|
"space": ""
|
||||||
},
|
},
|
||||||
|
|
@ -105871,7 +105875,7 @@
|
||||||
},
|
},
|
||||||
"004283": {
|
"004283": {
|
||||||
"id": "004283",
|
"id": "004283",
|
||||||
"content": "在正方体$ABCD-A_1B_1C_1D_1$中, $P$、$Q$两点分别从点$B$和点$A_1$出发, 以相同的速度在棱$BA$和$A_1D_1$上运动至点$A$和点$D_1$, 在运动过程中, 直线$PQ$与平面$ABCD$所成角$\\theta$的变化范围为\\bracket{20}.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-2,0);\n \\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n \\draw [dashed] ($(A1)!0.3!(D1)$) node [above left] {$Q$} -- ($(B)!0.3!(A)$) node [below] {$P$};\n \\end{tikzpicture}\n\\end{center}\n\\twoch{$[\\dfrac\\pi4,\\dfrac\\pi3]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\arctan\\sqrt 2]$}{$[\\dfrac\\pi4,\\arctan\\sqrt 2]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\dfrac\\pi2]$}",
|
"content": "在正方体$ABCD-A_1B_1C_1D_1$中, $P$、$Q$两点分别从点$B$和点$A_1$出发, 以相同的速度在棱$BA$和$A_1D_1$上运动至点$A$和点$D_1$, 在运动过程中, 直线$PQ$与平面$ABCD$所成角$\\theta$的变化范围为\\bracket{20}.\n\\begin{center}\n \\begin{tikzpicture}[scale = 0.7]\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-2,0);\n \\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n \\draw [dashed] ($(A1)!0.3!(D1)$) node [above left] {$Q$} -- ($(B)!0.3!(A)$) node [below] {$P$};\n \\end{tikzpicture}\n\\end{center}\n\\twoch{$[\\dfrac\\pi4,\\dfrac\\pi3]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\arctan\\sqrt 2]$}{$[\\dfrac\\pi4,\\arctan\\sqrt 2]$}{$[\\arctan\\dfrac{\\sqrt{2}}2,\\dfrac\\pi2]$}",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0610004B"
|
"K0610004B"
|
||||||
],
|
],
|
||||||
|
|
@ -105879,7 +105883,7 @@
|
||||||
"第六单元"
|
"第六单元"
|
||||||
],
|
],
|
||||||
"genre": "选择题",
|
"genre": "选择题",
|
||||||
"ans": "",
|
"ans": "C",
|
||||||
"solution": "",
|
"solution": "",
|
||||||
"duration": -1,
|
"duration": -1,
|
||||||
"usages": [
|
"usages": [
|
||||||
|
|
@ -116412,7 +116416,7 @@
|
||||||
},
|
},
|
||||||
"004696": {
|
"004696": {
|
||||||
"id": "004696",
|
"id": "004696",
|
||||||
"content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, 点$MN$分别在棱$AA_1CC_1$上, 则``直线$MN\\perp\\text{直线}C_1B$''是``直线$MN\\perp\\text{平面}C_1BD$''的\\bracket{20}.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (40:{2/2}) node [right] {$C$} coordinate (C)\n --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (220:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (40:{2/2}) (B1) --++ (-2,0);\n \\draw [dashed] (A) --++ (40:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n \\draw ($(A)!0.8!(A1)$) node [left] {$M$} coordinate (M);\n \\draw ($(C1)!0.8!(C)$) node [right] {$N$} coordinate (N);\n \\draw [dashed] (M) -- (N) (C1) -- (D) -- (B);\n \\draw (B) -- (C1);\n \\end{tikzpicture}\n\\end{center}\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既不充分又不必要条件}",
|
"content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, 点$MN$分别在棱$AA_1CC_1$上, 则``直线$MN\\perp\\text{直线}C_1B$''是``直线$MN\\perp\\text{平面}C_1BD$''的\\bracket{20}.\n\\begin{center}\n \\begin{tikzpicture}[scale = 0.6]\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (40:{2/2}) node [right] {$C$} coordinate (C)\n --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (220:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (40:{2/2}) (B1) --++ (-2,0);\n \\draw [dashed] (A) --++ (40:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n \\draw ($(A)!0.8!(A1)$) node [left] {$M$} coordinate (M);\n \\draw ($(C1)!0.8!(C)$) node [right] {$N$} coordinate (N);\n \\draw [dashed] (M) -- (N) (C1) -- (D) -- (B);\n \\draw (B) -- (C1);\n \\end{tikzpicture}\n\\end{center}\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既不充分又不必要条件}",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0609003B",
|
"K0609003B",
|
||||||
"K0611002B"
|
"K0611002B"
|
||||||
|
|
@ -116421,7 +116425,7 @@
|
||||||
"第六单元"
|
"第六单元"
|
||||||
],
|
],
|
||||||
"genre": "选择题",
|
"genre": "选择题",
|
||||||
"ans": "",
|
"ans": "C",
|
||||||
"solution": "",
|
"solution": "",
|
||||||
"duration": -1,
|
"duration": -1,
|
||||||
"usages": [
|
"usages": [
|
||||||
|
|
@ -217016,7 +217020,7 @@
|
||||||
},
|
},
|
||||||
"009144": {
|
"009144": {
|
||||||
"id": "009144",
|
"id": "009144",
|
||||||
"content": "如图, $EF$分别是空间四边形$ABCD$的边$BCAD$的中点, 过$EF$且平行于$AB$的平面与$AC$交于点$G$, 求证: $G$是$AC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (3,0) node [right] {$D$} coordinate (D);\n\\draw (2,-1) node [below] {$C$} coordinate (C);\n\\draw (1.5,2) node [above] {$A$} coordinate (A);\n\\draw ($(B)!0.5!(C)$) node [below left] {$E$} coordinate (E);\n\\draw ($(A)!0.5!(D)$) node [above right] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(C)$) node [above left] {$G$} coordinate (G);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (A) -- (C) (E) -- (G) -- (F);\n\\draw [dashed] (E) -- (F) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
|
"content": "如图, $E$、$F$分别是空间四边形$ABCD$的边$BC$、$AD$的中点, 过$EF$且平行于$AB$的平面与$AC$交于点$G$, 求证: $G$是$AC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (3,0) node [right] {$D$} coordinate (D);\n\\draw (2,-1) node [below] {$C$} coordinate (C);\n\\draw (1.5,2) node [above] {$A$} coordinate (A);\n\\draw ($(B)!0.5!(C)$) node [below left] {$E$} coordinate (E);\n\\draw ($(A)!0.5!(D)$) node [above right] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(C)$) node [above left] {$G$} coordinate (G);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (A) -- (C) (E) -- (G) -- (F);\n\\draw [dashed] (E) -- (F) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0608004B"
|
"K0608004B"
|
||||||
],
|
],
|
||||||
|
|
@ -217039,7 +217043,7 @@
|
||||||
},
|
},
|
||||||
"009145": {
|
"009145": {
|
||||||
"id": "009145",
|
"id": "009145",
|
||||||
"content": "在长方体$ABCD-A_1B_1C_1D_1$中, 矩形$AA_1D_1D$和$D_1C_1CD$的中心分别为$MN$, 求证: $MN\\parallel$平面$ABCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n--++ (0,2\n) node [above right] {$C_1$} coordinate (C1)\n--++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (3,2\n) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-3,0);\n\\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,2\n);\n\\draw [dashed] ($(A)!0.5!(D1)$) node [above] {$M$} -- ($(C)!0.5!(D1)$) node [right] {$N$}; \n\\end{tikzpicture}\n\\end{center}",
|
"content": "在长方体$ABCD-A_1B_1C_1D_1$中, 矩形$AA_1D_1D$和$D_1C_1CD$的中心分别为$M$、$N$, 求证: $MN\\parallel$平面$ABCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{2/2}) node [right] {$C$} coordinate (C)\n--++ (0,2\n) node [above right] {$C_1$} coordinate (C1)\n--++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (3,2\n) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{2/2}) (B1) --++ (-3,0);\n\\draw [dashed] (A) --++ (45:{2/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,2\n);\n\\draw [dashed] ($(A)!0.5!(D1)$) node [above] {$M$} -- ($(C)!0.5!(D1)$) node [right] {$N$}; \n\\end{tikzpicture}\n\\end{center}",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0608004B"
|
"K0608004B"
|
||||||
],
|
],
|
||||||
|
|
@ -217320,7 +217324,7 @@
|
||||||
},
|
},
|
||||||
"009158": {
|
"009158": {
|
||||||
"id": "009158",
|
"id": "009158",
|
||||||
"content": "选择题:\n(1) $\\alpha,\\beta$是两个不重合的平面, $a,b$是两条不同的直线, 在下列条件中可判定$\\alpha \\parallel\\beta$的是\\bracket{20}.\n\\onech{平面$\\alpha,\\beta$都平行于直线$a,b$}{平面内有三个不共线的点到平面$\\beta$的距离相等}{$a,b$是平面$\\alpha$内的两条直线, 且$\\alpha \\parallel\\beta$, $b\\parallel\\beta$}{$a,b$是两条异面直线, 且$a\\parallel\\alpha$, $b\\parallel\\alpha$, $\\alpha \\parallel\\beta$, $b\\parallel\\beta$}",
|
"content": "$\\alpha,\\beta$是两个不重合的平面, $a,b$是两条不同的直线, 在下列条件中可判定$\\alpha \\parallel\\beta$的是\\bracket{20}.\n\\onech{平面$\\alpha,\\beta$都平行于直线$a,b$}{平面$\\alpha$内有三个不共线的点到平面$\\beta$的距离相等}{$a,b$是平面$\\alpha$内的两条直线, 且$a \\parallel\\beta$, $b\\parallel\\beta$}{$a,b$是两条异面直线, 且$a\\parallel\\alpha$, $b\\parallel\\alpha$, $a \\parallel\\beta$, $b\\parallel\\beta$}",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0612002B"
|
"K0612002B"
|
||||||
],
|
],
|
||||||
|
|
@ -217467,7 +217471,9 @@
|
||||||
"20220726\t王伟叶"
|
"20220726\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030144"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -228930,7 +228936,9 @@
|
||||||
"20220730\t王伟叶"
|
"20220730\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030149"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -229023,7 +229031,7 @@
|
||||||
},
|
},
|
||||||
"009690": {
|
"009690": {
|
||||||
"id": "009690",
|
"id": "009690",
|
||||||
"content": "如图, 已知$PA$垂直于平面$\\alpha$, $PB$垂直于平面$\\beta$, $A$、$B$为相应的垂足, 且$l$为平面$\\alpha$与平面$\\beta$的交线. 求证: $l\\perp$平面$PAB$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\draw (0,0,0) coordinate (O) (2,0,0) coordinate (R) (-1,1,0) coordinate (L);\n\\draw (O) ++ (0,0,2) coordinate (O1) (R) ++ (0,0,2) coordinate (R1) (L) ++ (0,0,2) coordinate (L1);\n\\draw (L) -- (L1) -- (O1) -- (R1) -- (R);\n\\path [name path = OR] (O) -- (R);\n\\path [name path = OL] (O) -- (L);\n\\draw [name path = AP] (1.5,0,1) node [right] {$A$} coordinate (A) --++ (0,2,0) node [right] {$P$} coordinate (P);\n\\draw [name path = BP] (A) --++ (-1.5,0,0) coordinate (O2) --++ (-0.7,0.7,0) node[above] {$B$} coordinate (B) -- (P);\n\\draw [name intersections = {of = AP and OR, by = T}];\n\\draw [name intersections = {of = BP and OL, by = S}];\n\\draw (O2) -- (O1) (T) -- (R) (S) -- (L);\n\\draw [dashed] (O) -- (O1) (T) -- (O) -- (S);\n\\draw (1.9,0,2) node [above] {$\\alpha$} (L1) ++ (0.2,-0.2,0) node [above] {$\\beta$} (O1) node [above] {$l$};\n\\end{tikzpicture}\n\\end{center}",
|
"content": "如图, 已知$PA$垂直于平面$\\alpha$, $PB$垂直于平面$\\beta$, $A$、$B$为相应的垂足, 且$l$为平面$\\alpha$与平面$\\beta$的交线. 求证: $l\\perp$平面$PAB$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.8]\n\\draw (0,0,0) coordinate (O) (2,0,0) coordinate (R) (-1,1,0) coordinate (L);\n\\draw (O) ++ (0,0,2) coordinate (O1) (R) ++ (0,0,2) coordinate (R1) (L) ++ (0,0,2) coordinate (L1);\n\\draw (L) -- (L1) -- (O1) -- (R1) -- (R);\n\\path [name path = OR] (O) -- (R);\n\\path [name path = OL] (O) -- (L);\n\\draw [name path = AP] (1.5,0,1) node [right] {$A$} coordinate (A) --++ (0,2,0) node [right] {$P$} coordinate (P);\n\\draw [name path = BP] (A) --++ (-1.5,0,0) coordinate (O2) --++ (-0.7,0.7,0) node[above] {$B$} coordinate (B) -- (P);\n\\draw [name intersections = {of = AP and OR, by = T}];\n\\draw [name intersections = {of = BP and OL, by = S}];\n\\draw (O2) -- (O1) (T) -- (R) (S) -- (L);\n\\draw [dashed] (O) -- (O1) (T) -- (O) -- (S);\n\\draw (1.9,0,2) node [above] {$\\alpha$} (L1) ++ (0.2,-0.2,0) node [above] {$\\beta$} (O1) node [above] {$l$};\n\\end{tikzpicture}\n\\end{center}",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0609003B"
|
"K0609003B"
|
||||||
],
|
],
|
||||||
|
|
@ -229107,7 +229115,9 @@
|
||||||
"20220730\t王伟叶"
|
"20220730\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030143"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -229183,7 +229193,7 @@
|
||||||
},
|
},
|
||||||
"009697": {
|
"009697": {
|
||||||
"id": "009697",
|
"id": "009697",
|
||||||
"content": "判断下列命题的真假, 并说明理由:\\\\\n(1) 若一个平面内的两条直线均平行于另一个平面, 则这两个平面平行;\n(2) 若一个平面内两条不平行的直线都平行于另一个平面, 则这两个平面平行;\n(3) 若两个平面平行, 则其中一个平面中的任何直线都平行于另一个平面;\n(4) 平行于同一个平面的两个平面平行;\n(5) 若一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.",
|
"content": "判断下列命题的真假, 并说明理由:\\\\\n(1) 若一个平面内的两条直线均平行于另一个平面, 则这两个平面平行;\\\\\n(2) 若一个平面内两条不平行的直线都平行于另一个平面, 则这两个平面平行;\\\\\n(3) 若两个平面平行, 则其中一个平面中的任何直线都平行于另一个平面;\\\\\n(4) 平行于同一个平面的两个平面平行;\\\\\n(5) 若一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0612002B",
|
"K0612002B",
|
||||||
"K0612004B"
|
"K0612004B"
|
||||||
|
|
@ -229201,7 +229211,9 @@
|
||||||
"20220730\t王伟叶"
|
"20220730\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030151"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -229270,7 +229282,9 @@
|
||||||
"20220730\t王伟叶"
|
"20220730\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030150"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -229293,7 +229307,9 @@
|
||||||
"20220730\t王伟叶"
|
"20220730\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030145"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -288079,7 +288095,7 @@
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": ""
|
"space": "18ex"
|
||||||
},
|
},
|
||||||
"030093": {
|
"030093": {
|
||||||
"id": "030093",
|
"id": "030093",
|
||||||
|
|
@ -288121,7 +288137,7 @@
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": ""
|
"space": "18ex"
|
||||||
},
|
},
|
||||||
"030095": {
|
"030095": {
|
||||||
"id": "030095",
|
"id": "030095",
|
||||||
|
|
@ -288164,7 +288180,7 @@
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": ""
|
"space": "18ex"
|
||||||
},
|
},
|
||||||
"030097": {
|
"030097": {
|
||||||
"id": "030097",
|
"id": "030097",
|
||||||
|
|
@ -288204,7 +288220,7 @@
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": ""
|
"space": "18ex"
|
||||||
},
|
},
|
||||||
"030099": {
|
"030099": {
|
||||||
"id": "030099",
|
"id": "030099",
|
||||||
|
|
@ -288228,7 +288244,8 @@
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [
|
"related": [
|
||||||
"009169"
|
"009169",
|
||||||
|
"030147"
|
||||||
],
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "24ex"
|
"space": "24ex"
|
||||||
|
|
@ -289114,5 +289131,223 @@
|
||||||
"related": [],
|
"related": [],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": ""
|
"space": ""
|
||||||
|
},
|
||||||
|
"030143": {
|
||||||
|
"id": "030143",
|
||||||
|
"content": "如图, 平面$\\alpha$上的斜线$l$与平面$\\alpha$所成的角为$\\theta$, $l'$是$l$在平面$\\alpha$上的投影, $O$是$l$与平面$\\alpha$的交点, 点$B$是$l$上一点$A$在$\\alpha$上的投影, $OC$是$\\alpha$上的任意一条直线.\\\\\n(1) 如果$\\theta =45^\\circ$, $\\angle BOC=45^\\circ$, 求$\\angle AOC$;\\\\\n(2) 试证明: $\\angle AOC>\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0,0) -- (3,0,0) node [right] {$l'$} (2,2,0) node [above] {$A$} coordinate (A) -- (2,0,0) coordinate (B) node [below] {$B$} (2.5,2.5,0) node [right] {$l$} -- (0,0,0) coordinate (O) node [below] {$O$};\n\\draw (1,0,1) node [below] {$C$} coordinate (C);\n\\draw ($(O)!-0.5!(C)$) -- ($(O)!1.8!(C)$);\n\\draw [name path = edge] (-1.5,0,-2.5) coordinate (L) -- (-1.5,0,2.5) --++ (5,0,0) --++ (0,0,-5) coordinate (R);\n\\path [name path = LR] (L) -- (R);\n\\path [name path = OA] (O) -- (A);\n\\path [name path = AB] (A) -- (B);\n\\path [name intersections = {of = OA and LR, by = A1}];\n\\path [name intersections = {of = AB and LR, by = B1}];\n\\draw (L) -- (A1) (B1) -- (R);\n\\draw [dashed] (A1) -- (B1);\n\\path [name path = down] ($(O)!-0.6!(A)$) -- (O);\n\\path [name intersections = {of = down and edge, by = T}];\n\\draw (T) -- ($(O)!-0.6!(A)$);\n\\draw [dashed] (T) -- (O);\n\\draw (O) pic [\"$\\theta$\",draw,angle eccentricity = 1.5] {angle = B--O--A};\n\\draw (O) pic [scale = 1.1,draw,angle eccentricity = 1.7]{angle = C--O--B};\n\\end{tikzpicture}\n\\end{center}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "新教材必修第三册课堂练习-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220730\t王伟叶",
|
||||||
|
"20221011\t余利成"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"009693"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"030144": {
|
||||||
|
"id": "030144",
|
||||||
|
"content": "已知不共面的三条射线$a,b,c$均以点$P$为端点, 平面$\\alpha,\\beta$与直线$a,b,c$分别相交于$A,B,C$和$A_1,B_1,C_1$, 且$\\dfrac{PA}{PA_1}=\\dfrac{PB}{PB_1}=\\dfrac{PC}{PC_1}$, 求证: $\\alpha \\parallel\\beta$.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "二期课改练习册高三-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220726\t王伟叶",
|
||||||
|
"20221011\t徐慧"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"009164"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"030145": {
|
||||||
|
"id": "030145",
|
||||||
|
"content": "如图, 已知$AB\\perp$平面$BCD$, $BC\\perp CD$, 有哪些平面互相垂直? 选择其中一对互相垂直的平面给出证明. \n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$B$} coordinate (B) -- (2.4,0,1.6) node [below] {$C$} coordinate (C) -- (3.6,0,0) node [right] {$D$} coordinate (D) -- (0,2,0) node [above] {$A$} coordinate (A);\n\\draw (A) -- (B) (A) -- (C);\n\\draw [dashed] (B) -- (D); \n\\end{tikzpicture}\n\\end{center}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "新教材必修第三册课堂练习-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220730\t王伟叶",
|
||||||
|
"20221011\t徐慧"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"009701"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"030146": {
|
||||||
|
"id": "030146",
|
||||||
|
"content": "过$60^\\circ$的二面角$\\alpha-l-\\beta$的棱上一点$A$, 分别在$\\alpha,\\beta$内引两条射线, 使得它们与$l$都成$45^\\circ$角, 则这两条射线夹角的余弦值为\\blank{60}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2016届创新班作业\t2214-二面角[2]-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220625\t王伟叶",
|
||||||
|
"20221011\t徐慧"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"001665"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"030147": {
|
||||||
|
"id": "030147",
|
||||||
|
"content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 垂直于同一直线的两个平面平行;\\\\\n(2) 平行于同一平面的两条直线平行;\\\\\n(3) 垂直于同一平面的两条直线平行.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "二期课改练习册高三-20221002修改-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220726\t王伟叶",
|
||||||
|
"20221002\t王伟叶",
|
||||||
|
"20221011\t吴惠群, 余利成"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"009169",
|
||||||
|
"030099"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "24ex"
|
||||||
|
},
|
||||||
|
"030148": {
|
||||||
|
"id": "030148",
|
||||||
|
"content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 若直线$l$与平面$M$斜交, 则$M$内不存在与$l$垂直的直线;\\\\\n(2) 若直线$l\\perp\\text{平面}M$, 则$M$内不存在与$l$不垂直的直线;\\\\\n(3) 若直线$l$与平面$M$斜交, 则$M$内不存在与$l$平行的直线;\\\\\n(4) 若直线$l\\parallel\\text{平面}M$, 则$M$内不存在与$l$不平行的直线.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "教材复习题-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220624\t王伟叶, 余利成",
|
||||||
|
"20221011\t吴惠群, 余利成"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"000178"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"030149": {
|
||||||
|
"id": "030149",
|
||||||
|
"content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 若两直线$a$、$b$互相平行, 则$a$平行于经过$b$的任何平面;\\\\\n(2) 若直线$a$与平面$\\alpha$平行, 则$a$平行于$\\alpha$内的任何直线;\\\\\n(3) 若两直线$a$、$b$都与平面$\\alpha$平行, 则$a\\parallel b$;\\\\\n(4) 若直线$a$平行于平面$\\alpha$, 直线$b$在平面$\\alpha$上, 则$a\\parallel b$或者$a$与$b$为异面直线.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "新教材必修第三册课堂练习-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220730\t王伟叶",
|
||||||
|
"20221011\t吴惠群, 余利成"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"009685"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"030150": {
|
||||||
|
"id": "030150",
|
||||||
|
"content": "已知平面$\\alpha\\perp$平面$\\beta$, 下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\ \n(1) 平面$\\alpha$上的任意一条直线都垂直于平面$\\beta$上的任意一条直线;\\\\\n(2) 平面$\\alpha$上的任意一条直线都垂直于平面$\\beta$上的无数条直线;\\\\\n(3) 平面$\\alpha$上的任意一条直线都垂直于平面$\\beta$;\\\\\n(4) 过平面$\\alpha$上任意一点作平面$\\alpha$与$\\beta$交线的垂线$l$, 则$l\\perp \\beta$.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "新教材必修第三册课堂练习-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220730\t王伟叶",
|
||||||
|
"20221011\t吴惠群, 徐慧"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"009700"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"030151": {
|
||||||
|
"id": "030151",
|
||||||
|
"content": "下列命题是否为真命题? 如果是, 请回答``真''; 如果不是, 请说明理由:\\\\\n(1) 若一个平面内的两条直线均平行于另一个平面, 则这两个平面平行;\\\\\n(2) 若一个平面内两条不平行的直线都平行于另一个平面, 则这两个平面平行;\\\\\n(3) 若两个平面平行, 则其中一个平面中的任何直线都平行于另一个平面;\\\\\n(4) 平行于同一个平面的两个平面平行;\\\\\n(5) 若一个平面内的任何一条直线都平行于另一个平面, 则这两个平面平行.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "新教材必修第三册课堂练习-20221011修改",
|
||||||
|
"edit": [
|
||||||
|
"20220730\t王伟叶",
|
||||||
|
"20221011\t吴惠群, 徐慧"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"009697"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
Reference in New Issue