20221010evening
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commit
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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@ -11,7 +11,7 @@
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"0"
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]
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},
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"execution_count": 1,
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -21,7 +21,8 @@
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"\n",
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"\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n",
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"keywords_dict_table = [\n",
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" {\"tags\":[\"第五单元\"]}\n",
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" {\"content\":[\"棱柱\",\"圆柱\",\"棱锥\",\"圆锥\",\"棱台\",\"圆台\",\"球\",\"多面体\",\"旋转体\"], \"content_not\":[\"体积\",\"表面积\",\"侧面积\"], \"tags\":[\"第五单元\"]},\n",
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" {\"objs\":[\"K0615\",\"K0618\",\"K0621\",\"K0622\"]}\n",
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"]\n",
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"\"\"\"---关键字设置完毕---\"\"\"\n",
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"# 示例： keywords_dict_table = [\n",
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@ -2,50 +2,52 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1 填空题 1\n",
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"2 解答题 5\n",
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"3 解答题 2\n",
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"4 填空题 1\n",
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"5 填空题 1\n",
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"6 填空题 1\n",
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"7 解答题 4\n",
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"1 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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"4 解答题 1\n",
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"5 填空题 2\n",
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"6 解答题 2\n",
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"7 填空题 10\n",
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"8 解答题 1\n",
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"9 选择题 2\n",
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"10 填空题 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 1\n",
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"13 填空题 1\n",
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"13 填空题 6\n",
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"14 解答题 1\n",
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"15 解答题 2\n",
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"15 填空题 1\n",
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"16 解答题 1\n",
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"1 填空题 1\n",
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"2 填空题 1\n",
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"3 填空题 1\n",
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"17 填空题 3\n",
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"18 填空题 1\n",
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"19 填空题 1\n",
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"1 解答题 2\n",
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"2 解答题 1\n",
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"3 填空题 6\n",
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"4 填空题 1\n",
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"5 填空题 1\n",
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"6 填空题 1\n",
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"7 填空题 1\n",
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"8 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 填空题 1\n",
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"11 填空题 1\n",
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"12 选择题 1\n",
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"13 解答题 1\n",
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"14 解答题 3\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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"source": [
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"import os,re\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\\18_复数的代数运算与性质.tex\"\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\\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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"\n",
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@ -33,24 +33,24 @@ number=\chinese{section},
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\newtheorem{prop}{性质~}
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\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
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\newcommand{\bracket}[1]{(\hbox to #1pt{})}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\linewidth}}
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A.~#1\\
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B.~#2\\
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C.~#3\\
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D.~#4
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\end{tabular}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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A.~#1& B.~#2\\
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C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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(1)~#1& (2)~#2\\
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(3)~#3& (4)~#4
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\end{tabular}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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A.~#1 &B.~#2& C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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(1)~#1 &(2)~#2& (3)~#3& (4)~#4
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\end{tabular}}
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@ -33,24 +33,24 @@ number=\chinese{section},
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\newtheorem{prop}{性质~}
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\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
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\newcommand{\bracket}[1]{(\hbox to #1pt{})}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\linewidth}}
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A.~#1\\
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B.~#2\\
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C.~#3\\
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D.~#4
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\end{tabular}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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A.~#1& B.~#2\\
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C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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(1)~#1& (2)~#2\\
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(3)~#3& (4)~#4
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\end{tabular}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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A.~#1 &B.~#2& C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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(1)~#1 &(2)~#2& (3)~#3& (4)~#4
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\end{tabular}}
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@ -33,24 +33,24 @@ number=\chinese{section},
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\newtheorem{prop}{性质~}
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\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
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\newcommand{\bracket}[1]{(\hbox to #1pt{})}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\linewidth}}
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A.~#1\\
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B.~#2\\
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C.~#3\\
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D.~#4
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\end{tabular}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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A.~#1& B.~#2\\
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C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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(1)~#1& (2)~#2\\
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(3)~#3& (4)~#4
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\end{tabular}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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A.~#1 &B.~#2& C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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(1)~#1 &(2)~#2& (3)~#3& (4)~#4
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\end{tabular}}
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@ -21,24 +21,24 @@
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\newtheorem{prop}{性质~}
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\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
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\newcommand{\bracket}[1]{(\hbox to #1pt{})}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\linewidth}}
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A.~#1\\
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B.~#2\\
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C.~#3\\
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D.~#4
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\end{tabular}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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A.~#1& B.~#2\\
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C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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(1)~#1& (2)~#2\\
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(3)~#3& (4)~#4
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\end{tabular}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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A.~#1 &B.~#2& C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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(1)~#1 &(2)~#2& (3)~#3& (4)~#4
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\end{tabular}}
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\begin{document}
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\renewcommand{\baselinestretch}{2}
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\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
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\newcommand{\bracket}[1]{(\hbox to #1pt{})}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\linewidth}}
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A.~#1\\
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B.~#2\\
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C.~#3\\
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D.~#4
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\end{tabular}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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A.~#1& B.~#2\\
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C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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(1)~#1& (2)~#2\\
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(3)~#3& (4)~#4
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\end{tabular}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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A.~#1 &B.~#2& C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
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(1)~#1 &(2)~#2& (3)~#3& (4)~#4
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\end{tabular}}
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\begin{document}
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\begin{longtable}{|p{.15\textwidth}|p{.15\textwidth}|p{.65\textwidth}|}
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\begin{longtable}{|p{.15\linewidth}|p{.15\linewidth}|p{.65\linewidth}|}
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\hline
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课时目标 & 对应单元目标 & 目标内容 \\ \hline
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课时目标待替换
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\newpage
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\begin{longtable}{|p{.15\textwidth}|p{.75\textwidth}|}
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\begin{longtable}{|p{.15\linewidth}|p{.75\linewidth}|}
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\hline
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单元目标 & 目标内容 \\ \hline
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单元目标待替换
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\newtheorem{prop}{性质~}
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\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
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\newcommand{\bracket}[1]{(\hbox to #1pt{})}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
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A.~#1\\
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B.~#2\\
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C.~#3\\
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D.~#4
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\end{tabular}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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A.~#1& B.~#2\\
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C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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(1)~#1& (2)~#2\\
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(3)~#3& (4)~#4
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\end{tabular}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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A.~#1 &B.~#2& C.~#3& D.~#4
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\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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\begin{document}
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\newtheorem{prop}{性质~}
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\newcommand{\blank}[1]{\underline{\hbox to #1pt{}}}
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\newcommand{\bracket}[1]{(\hbox to #1pt{})}
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\newcommand{\onech}[4]{\par\begin{tabular}{p{.9\textwidth}}
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A.~#1\\
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D.~#4
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\end{tabular}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\twoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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A.~#1& B.~#2\\
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C.~#3& D.~#4
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\end{tabular}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\textwidth}p{.46\textwidth}}
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\newcommand{\vartwoch}[4]{\par\begin{tabular}{p{.46\linewidth}p{.46\linewidth}}
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(1)~#1& (2)~#2\\
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(3)~#3& (4)~#4
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\end{tabular}}
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\newcommand{\fourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
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A.~#1 &B.~#2& C.~#3& D.~#4
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\end{tabular}}
|
||||
\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}p{.23\textwidth}}
|
||||
\newcommand{\varfourch}[4]{\par\begin{tabular}{p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}p{.23\linewidth}}
|
||||
(1)~#1 &(2)~#2& (3)~#3& (4)~#4
|
||||
\end{tabular}}
|
||||
\begin{document}
|
||||
|
|
|
|||
|
|
@ -9,8 +9,8 @@
|
|||
"import os,re,json,time\n",
|
||||
"\n",
|
||||
"\"\"\"---设置原题目id与新题目id---\"\"\"\n",
|
||||
"old_id = \"3541\"\n",
|
||||
"new_id = \"30110\"\n",
|
||||
"old_id = \"1598\"\n",
|
||||
"new_id = \"30112\"\n",
|
||||
"\"\"\"---设置完毕---\"\"\"\n",
|
||||
"\n",
|
||||
"old_id = old_id.zfill(6)\n",
|
||||
|
|
|
|||
|
|
@ -2,7 +2,7 @@
|
|||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -13,9 +13,11 @@
|
|||
"题块 1 处理完毕.\n",
|
||||
"正在处理题块 2 .\n",
|
||||
"题块 2 处理完毕.\n",
|
||||
"开始编译教师版本pdf文件: 临时文件/22_空间两平面的位置关系_预选_教师_20221009.tex\n",
|
||||
"正在处理题块 3 .\n",
|
||||
"题块 3 处理完毕.\n",
|
||||
"开始编译教师版本pdf文件: 临时文件/周末卷04_教师_20221010.tex\n",
|
||||
"0\n",
|
||||
"开始编译学生版本pdf文件: 临时文件/22_空间两平面的位置关系_预选_学生_20221009.tex\n",
|
||||
"开始编译学生版本pdf文件: 临时文件/周末卷04_学生_20221010.tex\n",
|
||||
"0\n"
|
||||
]
|
||||
}
|
||||
|
|
@ -28,19 +30,19 @@
|
|||
"\"\"\"---设置模式结束---\"\"\"\n",
|
||||
"\n",
|
||||
"\"\"\"---设置模板文件名---\"\"\"\n",
|
||||
"template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
|
||||
"# template_file = \"模板文件/测验周末卷模板.tex\"\n",
|
||||
"# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
|
||||
"template_file = \"模板文件/测验周末卷模板.tex\"\n",
|
||||
"# template_file = \"模板文件/日常选题讲义模板.tex\"\n",
|
||||
"\"\"\"---设置模板文件名结束---\"\"\"\n",
|
||||
"\n",
|
||||
"\"\"\"---设置其他预处理替换命令---\"\"\"\n",
|
||||
"#2023届第一轮讲义更换标题\n",
|
||||
"exec_list = [(\"标题数字待处理\",\"22\"),(\"标题文字待处理\",\"空间两平面的位置关系\")] \n",
|
||||
"enumi_mode = 0\n",
|
||||
"# 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",
|
||||
"# enumi_mode = 0\n",
|
||||
"\n",
|
||||
"#2023届测验卷与周末卷\n",
|
||||
"# exec_list = [(\"标题替换\",\"测验03\")]\n",
|
||||
"# enumi_mode = 1\n",
|
||||
"exec_list = [(\"标题替换\",\"周末卷04\")]\n",
|
||||
"enumi_mode = 1\n",
|
||||
"\n",
|
||||
"#日常选题讲义\n",
|
||||
"# exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n",
|
||||
|
|
@ -49,14 +51,15 @@
|
|||
"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
|
||||
"\n",
|
||||
"\"\"\"---设置目标文件名---\"\"\"\n",
|
||||
"destination_file = \"临时文件/22_空间两平面的位置关系_预选\"\n",
|
||||
"destination_file = \"临时文件/周末卷04\"\n",
|
||||
"\"\"\"---设置目标文件名结束---\"\"\"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\"\"\"---设置题号数据---\"\"\"\n",
|
||||
"problems = [\n",
|
||||
"\"30095,1649,9163,9164,30096,30100,9698,3499,1665,303,1659,1677,30096,9701,188,30097,9702\",\n",
|
||||
"\"9156,1645,1646,9158,9697,9697,1670,1704,9154,294,9700,189\"\n",
|
||||
"\"1853,30108,3355,655,724,1860,2038,30106,30107,3621\",\n",
|
||||
"\"1846,2013,3703\",\n",
|
||||
"\"1557,4702\"\n",
|
||||
"]\n",
|
||||
"\"\"\"---设置题号数据结束---\"\"\"\n",
|
||||
"\n",
|
||||
|
|
|
|||
|
|
@ -2,16 +2,16 @@
|
|||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"开始编译教师版本pdf文件: 临时文件/测试_教师用_20221009.tex\n",
|
||||
"开始编译教师版本pdf文件: 临时文件/多面体选题_教师用_20221010.tex\n",
|
||||
"0\n",
|
||||
"开始编译学生版本pdf文件: 临时文件/测试_学生用_20221009.tex\n",
|
||||
"开始编译学生版本pdf文件: 临时文件/多面体选题_学生用_20221010.tex\n",
|
||||
"0\n"
|
||||
]
|
||||
}
|
||||
|
|
@ -26,14 +26,14 @@
|
|||
"\"\"\"---设置题目列表---\"\"\"\n",
|
||||
"#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",
|
||||
"problems = r\"\"\"\n",
|
||||
"2026\n",
|
||||
"a\n",
|
||||
"\n",
|
||||
"\"\"\"\n",
|
||||
"\"\"\"---设置题目列表结束---\"\"\"\n",
|
||||
"\n",
|
||||
"\"\"\"---设置文件名---\"\"\"\n",
|
||||
"#目录和文件的分隔务必用/\n",
|
||||
"filename = \"临时文件/测试\"\n",
|
||||
"filename = \"临时文件/多面体选题\"\n",
|
||||
"\"\"\"---设置文件名结束---\"\"\"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
|
|
@ -90,6 +90,7 @@
|
|||
"elif problems.strip()[0] == \"a\":\n",
|
||||
" with open(\"临时文件/题号筛选.txt\",\"r\",encoding = \"utf8\") as f:\n",
|
||||
" problems = f.read()\n",
|
||||
" problem_list = [id for id in generate_number_set(problems.strip(),pro_dict) if id in pro_dict]\n",
|
||||
"else:\n",
|
||||
" problem_list = [id for id in generate_number_set(problems.strip(),pro_dict) if id in pro_dict]\n",
|
||||
"\n",
|
||||
|
|
|
|||
|
|
@ -41117,7 +41117,9 @@
|
|||
"20220625\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"related": [
|
||||
"030111"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
|
|
@ -41151,7 +41153,7 @@
|
|||
},
|
||||
"001597": {
|
||||
"id": "001597",
|
||||
"content": "指出图中正方体各线段所在直线的位置关系(相交, 平行或异面):\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 [dashed] (D1) -- (B) (A1) -- (C);\n \\draw (C) -- (B1) (A1) -- (C1);\n\\end{tikzpicture}\n\\end{center}\n\\begin{enumerate}[\\blank{50}(1)]\n\\item $AB$和$CC'$;\\\\ \n\\item $A'C$和$BD'$;\\\\ \n\\item $AA'$和$CB'$;\\\\ \n\\item $A'C'$和$CB'$;\\\\ \n\\item $A'B'$和$DC$;\\\\ \n\\item $BD'$和$DC$.\\\\ \n\\end{enumerate}",
|
||||
"content": "指出图中正方体各线段所在直线的位置关系(相交, 平行或异面):\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 [dashed] (D1) -- (B) (A1) -- (C);\n \\draw (C) -- (B1) (A1) -- (C1);\n\\end{tikzpicture}\n\\end{center}\n(1) $AB$和$CC'$\\blank{20};\n(2) $A'C$和$BD'$\\blank{20};\n(3) $AA'$和$CB'$\\blank{20};\n(4) $A'C'$和$CB'$\\blank{20};\n(5) $A'B'$和$DC$\\blank{20};\n(6) $BD'$和$DC$\\blank{20}.",
|
||||
"objs": [
|
||||
"K0606001B"
|
||||
],
|
||||
|
|
@ -41199,7 +41201,9 @@
|
|||
"20220625\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"related": [
|
||||
"030112"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
|
|
@ -41305,7 +41309,7 @@
|
|||
},
|
||||
"001603": {
|
||||
"id": "001603",
|
||||
"content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, $E,F$分别是棱$A_1B_1$和棱$B_1C_1$的中点.\\\\ \n(1) 求异面直线$A_1D$和$BC_1$所成角的大小;\\\\ \n(2) 求异面直线$BE$和$CF$所成角的余弦值.\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] {$C_1$} coordinate (C1)\n --++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{3/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (3,3) node [right] {$B_1$} 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 [dashed] (A1) -- (D);\n \\draw (C1) -- (B) -- ($(A1)!0.5!(B1)$) node [above] {$E$};\n \\draw (C) -- ($(C1)!0.5!(B1)$) node [above left] {$F$};\n\\end{tikzpicture}\n\\end{center}",
|
||||
"content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, $E,F$分别是棱$A_1B_1$和棱$B_1C_1$的中点.\\\\ \n(1) 求异面直线$A_1D$和$BC_1$所成角的大小;\\\\ \n(2) 求异面直线$BE$和$CF$所成角的余弦值.\n\\begin{center}\n\\begin{tikzpicture}[scale = 0.6]\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] {$C_1$} coordinate (C1)\n --++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{3/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (3,3) node [right] {$B_1$} 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 [dashed] (A1) -- (D);\n \\draw (C1) -- (B) -- ($(A1)!0.5!(B1)$) node [above] {$E$};\n \\draw (C) -- ($(C1)!0.5!(B1)$) node [above left] {$F$};\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [
|
||||
"K0607004B"
|
||||
],
|
||||
|
|
@ -49108,7 +49112,7 @@
|
|||
},
|
||||
"001910": {
|
||||
"id": "001910",
|
||||
"content": "已知$\\overrightarrow{a}=(1,-2),\\overrightarrow{b}=(2,3),\\overrightarrow{c}=(1,1)$, 将$\\overrightarrow{a}$表示为$\\overrightarrow{b_1}+\\overrightarrow{c_1}$的形式,\n其中$\\overrightarrow{b_1},\\overrightarrow{c_1}$分别为$\\overrightarrow{b},\\overrightarrow{c}$的单位向量, 结果为$\\overrightarrow{a}=$\\blank{30}$\\overrightarrow{b_1}+$\\blank{30}$\\overrightarrow{c_1}$.",
|
||||
"content": "已知$\\overrightarrow{a}=(1,-2),\\overrightarrow{b}=(2,3),\\overrightarrow{c}=(1,1)$, 将$\\overrightarrow{a}$表示为$\\overrightarrow{b_1},\\overrightarrow{c_1}$的线性组合, 其中$\\overrightarrow{b_1},\\overrightarrow{c_1}$分别为$\\overrightarrow{b},\\overrightarrow{c}$的单位向量, 结果为$\\overrightarrow{a}=$\\blank{30}$\\overrightarrow{b_1}+$\\blank{30}$\\overrightarrow{c_1}$.",
|
||||
"objs": [
|
||||
"K0506003B"
|
||||
],
|
||||
|
|
@ -86798,7 +86802,7 @@
|
|||
},
|
||||
"003466": {
|
||||
"id": "003466",
|
||||
"content": "对于分别与两条异面直线都相交的两条直线, 下列结论中, 真命题有\\blank{50}(填入序号).\\\\\n(1) 一定是异面直线; (2) 不可能是平行直线; (3) 不可能是相交直线.",
|
||||
"content": "对于分别与两条异面直线都相交的两条直线, 下列结论中, 真命题有\\blank{50}(填入序号).\\\\\n\\textcircled{1} 一定是异面直线; \\textcircled{2} 不可能是平行直线; \\textcircled{3} 不可能是相交直线.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第六单元"
|
||||
|
|
@ -90341,7 +90345,7 @@
|
|||
},
|
||||
"003621": {
|
||||
"id": "003621",
|
||||
"content": "已知$\\overrightarrow{a_1}, \\overrightarrow{a_2}, \\overrightarrow{b_1}, \\overrightarrow{b_2},\\cdots,\\overrightarrow{b_k}\\ (k\\in \\mathbf{N}^*)$是平面内两两互不相等的向量, 满足$|\\overrightarrow{a_1}-\\overrightarrow{a_2}|=1$, 且$|\\overrightarrow{a_i}-\\overrightarrow{b_j}|\\in \\{1,2\\}$(其中$i=1,2$, $j=1,2,\\cdots,k$), 则$k$的最大值为\\blank{50}.",
|
||||
"content": "已知$\\overrightarrow{a_1}, \\overrightarrow{a_2}, \\overrightarrow{b_1}, \\overrightarrow{b_2},\\cdots,\\overrightarrow{b_k}$($k\\in \\mathbf{N}$, $k\\ge 1$)是平面内两两互不相等的向量, 满足$|\\overrightarrow{a_1}-\\overrightarrow{a_2}|=1$, 且$|\\overrightarrow{a_i}-\\overrightarrow{b_j}|\\in \\{1,2\\}$(其中$i=1,2$, $j=1,2,\\cdots,k$), 则$k$的最大值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第五单元"
|
||||
|
|
@ -92258,7 +92262,7 @@
|
|||
},
|
||||
"003703": {
|
||||
"id": "003703",
|
||||
"content": "如图, 在平面内, $l_1,l_2$是两条平行直线, 它们之间的距离为$2$, 点$P$位于$l_1,l_2$的下方, 它到$l_1$的距离为$1$, 动点$N,M$分别在$l_1,l_2$上, 满足$|\\overrightarrow{PM}+\\overrightarrow{PN}|=6$, 则$\\overrightarrow{PM}\\cdot \\overrightarrow{PN}$的最大值为\\bracket{20}.\n\\fourch{$6$}{$8$}{$12$}{$15$}\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw (0,0) -- (5,0) node [right] {$l_1$} (0,2) -- (5,2) node [right] {$l_2$};\n \\draw [->] (4.5,-1) node [below right] {$P$} -- (2,0) node [below] {$N$};\n \\draw [->] (4.5,-1) -- (2.5,2) node [below] {$M$};\n \\end{tikzpicture}\n\\end{center}",
|
||||
"content": "如图, 在平面内, $l_1,l_2$是两条平行直线, 它们之间的距离为$2$, 点$P$位于$l_1,l_2$的下方, 动点$N,M$分别在$l_1,l_2$上, 满足$|\\overrightarrow{PM}+\\overrightarrow{PN}|=6$, 则$\\overrightarrow{PM}\\cdot \\overrightarrow{PN}$的最大值为\\bracket{20}.\n\\fourch{$6$}{$8$}{$12$}{$15$}\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw (0,0) -- (5,0) node [right] {$l_1$} (0,2) -- (5,2) node [right] {$l_2$};\n \\draw [->] (4.5,-1) node [below right] {$P$} -- (2,0) node [below] {$N$};\n \\draw [->] (4.5,-1) -- (2.5,2) node [below] {$M$};\n \\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第五单元"
|
||||
|
|
@ -112418,7 +112422,7 @@
|
|||
},
|
||||
"004539": {
|
||||
"id": "004539",
|
||||
"content": "如图是正四面体的平面展开图, $M,N,G$分别为$DE,BE,FE$的中点, 则在这个四面体中, 异面直线$MN$与$CG$所成的角的大小为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[scale = 1.5]\n \\draw (0,0) node [below] {$E$} coordinate (E);\n \\draw (1,0) node [below right] {$C$} coordinate (C);\n \\draw (-1,0) node [below left] {$B$} coordinate (B);\n \\draw (0,{sqrt(3)}) node [above] {$A$} coordinate (A);\n \\draw ($(A)!0.5!(B)$) node [left] {$D$} coordinate (D);\n \\draw ($(A)!0.5!(C)$) node [right] {$F$} coordinate (F);\n \\draw ($(E)!0.5!(F)$) node [above] {$G$} coordinate (G);\n \\draw ($(D)!0.5!(E)$) node [above] {$M$} coordinate (M);\n \\draw ($(B)!0.5!(E)$) node [below] {$N$} coordinate (N);\n \\draw (A) -- (B) -- (C) -- cycle (D) -- (E) -- (F) -- cycle;\n \\draw (M) -- (N) (C) -- (G);\n \\end{tikzpicture}\n\\end{center}",
|
||||
"content": "如图是正四面体的平面展开图, $M,N,G$分别为$DE,BE,FE$的中点, 则在这个四面体中, 异面直线$MN$与$CG$所成的角的大小为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[scale = 1]\n \\draw (0,0) node [below] {$E$} coordinate (E);\n \\draw (1,0) node [below right] {$C$} coordinate (C);\n \\draw (-1,0) node [below left] {$B$} coordinate (B);\n \\draw (0,{sqrt(3)}) node [above] {$A$} coordinate (A);\n \\draw ($(A)!0.5!(B)$) node [left] {$D$} coordinate (D);\n \\draw ($(A)!0.5!(C)$) node [right] {$F$} coordinate (F);\n \\draw ($(E)!0.5!(F)$) node [above] {$G$} coordinate (G);\n \\draw ($(D)!0.5!(E)$) node [above] {$M$} coordinate (M);\n \\draw ($(B)!0.5!(E)$) node [below] {$N$} coordinate (N);\n \\draw (A) -- (B) -- (C) -- cycle (D) -- (E) -- (F) -- cycle;\n \\draw (M) -- (N) (C) -- (G);\n \\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [
|
||||
"K0607004B"
|
||||
],
|
||||
|
|
@ -228608,7 +228612,7 @@
|
|||
},
|
||||
"009671": {
|
||||
"id": "009671",
|
||||
"content": "如图, 在长方体$ABCD-A_1B_1C_1D_1$中,\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:{3/2}) node [right] {$C$} coordinate (C)\n--++ (0,2) node [above right] {$C_1$} coordinate (C1)\n--++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{3/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (3,2) node [right] {$B_1$} 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) --++ (0,2);\n\\end{tikzpicture}\n\\end{center}\n(1) 设$AC$与$BD$的交点为$O$, $O$必为平面\\blank{50}与平面\\blank{50}的公共点(答案不唯一);\\\\\n(2) 画出平面$A_1BCD_1$与平面$B_1BDD_1$的交线.",
|
||||
"content": "如图, 在长方体$ABCD-A_1B_1C_1D_1$中,\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\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--++ (0,2) node [above right] {$C_1$} coordinate (C1)\n--++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{3/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (3,2) node [right] {$B_1$} 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) --++ (0,2);\n\\end{tikzpicture}\n\\end{center}\n(1) 设$AC$与$BD$的交点为$O$, $O$必为平面\\blank{50}与平面\\blank{50}的公共点(答案不唯一);\\\\\n(2) 画出平面$A_1BCD_1$与平面$B_1BDD_1$的交线.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第六单元"
|
||||
|
|
@ -228669,7 +228673,7 @@
|
|||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "12ex"
|
||||
"space": "0ex"
|
||||
},
|
||||
"009674": {
|
||||
"id": "009674",
|
||||
|
|
@ -246192,7 +246196,7 @@
|
|||
},
|
||||
"010454": {
|
||||
"id": "010454",
|
||||
"content": "如图, 在四面体$ABCD$中, $AC=8$, $BD=6$, $M$、$N$分别为$AB$、$CD$的中点, 并且异面直线$AC$与$BD$所成的角为$90^\\circ$. 求$MN$的长.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$D$} coordinate (D);\n\\draw (3,0) node [right] {$B$} coordinate (B);\n\\draw (1.4,2.3) node [above] {$A$} coordinate (A);\n\\draw (2,-0.8) node [below] {$C$} coordinate (C);\n\\draw ($(B)!0.5!(C)$) node [below right] {$N$} coordinate (N);\n\\draw ($(A)!0.5!(D)$) node [above left] {$M$} coordinate (M);\n\\draw (A) -- (C) (B) -- (C) -- (D) (D) -- (A) -- (B);\n\\draw [dashed] (M) -- (N) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"content": "如图, 在四面体$ABCD$中, $AC=8$, $BD=6$, $M$、$N$分别为$AB$、$CD$的中点, 并且异面直线$AC$与$BD$所成的角为$90^\\circ$. 求$MN$的长.\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 (1.4,2.3) node [above] {$A$} coordinate (A);\n\\draw (2,-0.8) node [below] {$C$} coordinate (C);\n\\draw ($(D)!0.5!(C)$) node [below right] {$N$} coordinate (N);\n\\draw ($(A)!0.5!(B)$) node [above left] {$M$} coordinate (M);\n\\draw (A) -- (C) (B) -- (C) -- (D) (D) -- (A) -- (B);\n\\draw [dashed] (M) -- (N) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [
|
||||
"K0607001B"
|
||||
],
|
||||
|
|
@ -287811,7 +287815,7 @@
|
|||
},
|
||||
"030080": {
|
||||
"id": "030080",
|
||||
"content": "已知三条直线$l_1$, $l_2$和$l_3$两两相交, 且不交于同一个点. 求证: 直线$l_1l_2$和$l_3$在同一个平面上.",
|
||||
"content": "已知三条直线$l_1$, $l_2$和$l_3$两两相交, 且不交于同一个点. 求证: 直线$l_1$, $l_2$和$l_3$在同一个平面上.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
|
|
@ -287826,11 +287830,11 @@
|
|||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
"space": "12ex"
|
||||
},
|
||||
"030081": {
|
||||
"id": "030081",
|
||||
"content": "已知$E$、$F$分别是正方体$ABCD-A_1B_1C_1D_1$的棱$A_1B_1$、$B_1C_1$的中点. 画出由$D$、$E$、$F$确定的平面与正方体表面的交线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{3}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A1)!0.5!(B1)$) node [above] {$E$} coordinate (E);\n\\draw ($(B1)!0.5!(C1)$) node [above] {$F$} coordinate (F);\n\\filldraw (D) circle (0.03) (E) circle (0.03) (F) circle (0.03);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"content": "已知$E$、$F$分别是正方体$ABCD-A_1B_1C_1D_1$的棱$A_1B_1$、$B_1C_1$的中点. 画出由$D$、$E$、$F$确定的平面与正方体表面的交线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A1)!0.5!(B1)$) node [above] {$E$} coordinate (E);\n\\draw ($(B1)!0.5!(C1)$) node [above] {$F$} coordinate (F);\n\\filldraw (D) circle (0.03) (E) circle (0.03) (F) circle (0.03);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [
|
||||
"K0603003B",
|
||||
"K0603005B"
|
||||
|
|
@ -287852,7 +287856,7 @@
|
|||
},
|
||||
"030082": {
|
||||
"id": "030082",
|
||||
"content": "如图, 已知$E$、$F$分别是正方体$ABCD-A_1B_1C_1D_1$的棱$A_1A$、$C_1C$的中点. 求证: 四边形$BED_1F$是平行四边形.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A)!0.5!(A1)$) node [left] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(C1)$) node [right] {$F$} coordinate (F);\n\\draw (E) -- (B) -- (F);\n\\draw [dashed] (E) -- (D1) -- (F);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"content": "如图, 已知$E$、$F$分别是正方体$ABCD-A_1B_1C_1D_1$的棱$A_1A$、$C_1C$的中点. 求证: 四边形$BED_1F$是平行四边形.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{1.5}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A)!0.5!(A1)$) node [left] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(C1)$) node [right] {$F$} coordinate (F);\n\\draw (E) -- (B) -- (F);\n\\draw [dashed] (E) -- (D1) -- (F);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
|
|
@ -287894,7 +287898,7 @@
|
|||
},
|
||||
"030084": {
|
||||
"id": "030084",
|
||||
"content": "如图, 在四面体$A-BCD$中, $E,F,G$分别为$AB,AC,AD$上的点. 若$EF\\parallel BC$, $FG\\parallel CD$, 则$\\triangle EFG$和$\\triangle BCD$有什么关系? 为什么?\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$A$} coordinate (A);\n\\draw (-0.5,-1) node [left] {$E$} coordinate (E);\n\\draw (0.5,-1) node [right] {$G$} coordinate (G);\n\\draw (0.2,-1.4) node [below left] {$F$} coordinate (F);\n\\draw ($(A)!2!(E)$) node [left] {$B$} coordinate (B);\n\\draw ($(A)!2!(F)$) node [below] {$C$} coordinate (C);\n\\draw ($(A)!2!(G)$) node [right] {$D$} coordinate (D);\n\\draw (A) -- (B) (A) -- (C) (A) -- (D) (B) -- (C) -- (D) (E) -- (F) -- (G);\n\\draw [dashed] (E) -- (G) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"content": "如图, 在四面体$A-BCD$中, $E,F,G$分别为$AB,AC,AD$上的点. 若$EF\\parallel BC$, $FG\\parallel CD$, 则$\\triangle EFG$和$\\triangle BCD$有什么关系? 为什么?\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw (0,0) node [above] {$A$} coordinate (A);\n\\draw (-0.5,-1) node [left] {$E$} coordinate (E);\n\\draw (0.5,-1) node [right] {$G$} coordinate (G);\n\\draw (0.2,-1.4) node [below left] {$F$} coordinate (F);\n\\draw ($(A)!2!(E)$) node [left] {$B$} coordinate (B);\n\\draw ($(A)!2!(F)$) node [below] {$C$} coordinate (C);\n\\draw ($(A)!2!(G)$) node [right] {$D$} coordinate (D);\n\\draw (A) -- (B) (A) -- (C) (A) -- (D) (B) -- (C) -- (D) (E) -- (F) -- (G);\n\\draw [dashed] (E) -- (G) (B) -- (D);\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
|
|
@ -287930,7 +287934,7 @@
|
|||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
"space": "18ex"
|
||||
},
|
||||
"030086": {
|
||||
"id": "030086",
|
||||
|
|
@ -288490,5 +288494,55 @@
|
|||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"030111": {
|
||||
"id": "030111",
|
||||
"content": "判断下列命题的真假, 在横线上用``T''或``F''表示.\\\\\n\\blank{20}(1) 空间任意三点确定一个平面;\\\\ \n\\blank{20}(2) 空间任意两条直线确定一个平面;\\\\ \n\\blank{20}(3) 空间两条平行直线确定一个平面;\\\\ \n\\blank{20}(4) 空间一条直线和不在该直线上的一个点确定一个平面;\\\\ \n\\blank{20}(5) 空间两条没有交点的直线必平行;\\\\ \n\\blank{20}(6) 若空间四边形$ABCD$若满足$AB=BC=CD=DA$, 则它一定是菱形;\\\\ \n\\blank{20}(7) 若空间的一条直线如果和一对平行直线之一相交, 则一定与另一条也相交;\\\\ \n\\blank{20}(8) 若空间三点$A,B,C$若满足$AB^2+BC^2=CA^2$, 则$\\triangle ABC$是以$B$为直角顶点的直角三角形;\\\\ \n\\blank{20}(9) 若空间三条直线两两相交, 则通过它们中至少两条的平面有且仅有$1$个;\\\\ \n\\blank{20}(10) 若空间三条直线两两相交, 则通过它们中至少两条的平面有且仅有$3$个.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第一单元",
|
||||
"第六单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2016届创新班作业\t2201-点线面与立体几何三公理-20221010修改",
|
||||
"edit": [
|
||||
"20220625\t王伟叶",
|
||||
"20221010\t谈荣"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"001595"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"030112": {
|
||||
"id": "030112",
|
||||
"content": "判断下列命题的真假, 在横线上用``T''或``F''表示.\\\\\n\\blank{20}(1) 已知$\\alpha$, $\\beta$是两个平面, $l,m$是两条直线, 若$l\\subset \\alpha$, $m\\subset \\beta$, 则$l,m$异面;\\\\ \n\\blank{20}(2) 已知平面$\\alpha,\\beta$相交于直线$l$. 若直线$m\\subset \\alpha$, $l \\parallel m$, 直线$n\\subset \\beta$, $l$与$n$相交, 则$m$与$n$异面;\\\\ \n\\blank{20}(3) 已知$l,m$是异面直线, 若直线$n\\parallel l$, 则$m,n$异面;\\\\ \n\\blank{20}(4) 已知$l,m$是异面直线, 若直线$n$和$l$异面, 则$m,n$异面;\\\\ \n\\blank{20}(5) 已知$l,m$是异面直线, 若直线$n$和$l$异面, 则$m,n$共面;\\\\ \n\\blank{20}(6) 正方体的任意两条对角线(对角线指连接不在同一表面上的两顶点的线段)相交.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第一单元",
|
||||
"第六单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2016届创新班作业\t2202-平行相交与异面-20221010修改",
|
||||
"edit": [
|
||||
"20220625\t王伟叶",
|
||||
"20221010\t谈荣"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"001598"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
}
|
||||
}
|
||||
Reference in New Issue