diff --git a/工具/关键字筛选题号.ipynb b/工具/关键字筛选题号.ipynb index 100497a0..c08597ed 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 4, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -21,14 +21,14 @@ "\n", "\"\"\"---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", "keywords_dict_table = [\n", - " {\"tags\":[\"第六单元\"],\"content\":[\"perp\"]}\n", + " {\"tags\":[\"第三单元\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", "# {\"tags\": [\"第三单元\"], \"content1\": [r\"[\\d]\\alpha\",\"2x\"], \"content2\": [\"sin\"], \"content3\": [\"cos\"],\"content4\": [\"cot\"], \"content5\": [\"tan\"]},\n", "# ]\n", "\"\"\"---设置输出文件名---\"\"\"\n", - "filename = \"临时文件/K0602.txt\"\n", + "filename = \"临时文件/题号筛选.txt\"\n", "\"\"\"---文件名设置完毕---\"\"\"\n", "\n", "\n", @@ -85,7 +85,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -99,12 +99,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb index 2fc5ea68..efd000a3 100644 --- a/工具/批量添加题库字段数据.ipynb +++ b/工具/批量添加题库字段数据.ipynb @@ -2,133 +2,46 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.895\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.868\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.842\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.737\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.842\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.579\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.342\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.763\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.553\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三10班\t0.421\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.696\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.913\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.870\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.391\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.826\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.522\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.304\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.652\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.348\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三11班\t0.174\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.905\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.905\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.762\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.524\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.905\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.905\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.429\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.905\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.762\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三12班\t0.191\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.839\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.871\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.871\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.710\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.839\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.677\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.484\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.774\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.419\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三02班\t0.710\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.897\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.966\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.966\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.724\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.966\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.931\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.621\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.759\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.724\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三01班\t0.897\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.929\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.929\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.893\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.643\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.964\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.750\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.500\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.857\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.643\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三03班\t0.857\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.871\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.839\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.839\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.516\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.774\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.677\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.484\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.613\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.323\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三04班\t0.581\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.947\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.921\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.921\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.579\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.842\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.711\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.500\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.737\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.368\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三05班\t0.395\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.889\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.889\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.861\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.611\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.917\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.694\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.444\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.722\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.639\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三06班\t0.694\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.844\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.906\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.844\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.500\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.875\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.688\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.531\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.844\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.219\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三07班\t0.250\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.606\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.909\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.727\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.545\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.818\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.606\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.424\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.849\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.636\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三08班\t0.515\n", - "题号: 003115 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.800\n", - "题号: 006264 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.800\n", - "题号: 003096 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.967\n", - "题号: 001472 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.667\n", - "题号: 006604 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.800\n", - "题号: 030027 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.567\n", - "题号: 030028 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.367\n", - "题号: 006305 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.767\n", - "题号: 006460 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.667\n", - "题号: 006463 , 字段: usages 中已添加数据: 20220929\t2023届高三09班\t0.200\n" + "题号: 030077 , 字段: objs 中已添加数据: K0601002B\n", + "题号: 001596 , 字段: objs 中已添加数据: K0601003B\n", + "题号: 001596 , 字段: objs 中已添加数据: K0601005B\n", + "题号: 001596 , 字段: objs 中已添加数据: K0601006B\n", + "题号: 000179 , 字段: objs 中已添加数据: K0601004B\n", + "题号: 030087 , 字段: objs 中已添加数据: K0601005B\n", + "题号: 001595 , 字段: objs 中已添加数据: K0602001B\n", + "题号: 001595 , 字段: objs 中已添加数据: K0602002B\n", + "题号: 009666 , 字段: objs 中已添加数据: K0602003B\n", + "题号: 030089 , 字段: objs 中已添加数据: K0603001B\n", + "题号: 030081 , 字段: objs 中已添加数据: K0603003B\n", + "题号: 030081 , 字段: objs 中已添加数据: K0603005B\n", + "题号: 010435 , 字段: objs 中已添加数据: K0603004B\n", + "题号: 009195 , 字段: objs 中已添加数据: K0604001B\n", + "题号: 009195 , 字段: objs 中已添加数据: K0604003B\n", + "题号: 009673 , 字段: objs 中已添加数据: K0604002B\n", + "题号: 030090 , 字段: objs 中已添加数据: K0605001B\n", + "题号: 009674 , 字段: objs 中已添加数据: K0605002B\n", + "题号: 009674 , 字段: objs 中已添加数据: K0605003B\n", + "题号: 030083 , 字段: objs 中已添加数据: K0605002B\n", + "题号: 030083 , 字段: objs 中已添加数据: K0605004B\n", + "题号: 030083 , 字段: objs 中已添加数据: K0605005B\n", + "题号: 001597 , 字段: objs 中已添加数据: K0606001B\n", + "题号: 003454 , 字段: objs 中已添加数据: K0606001B\n", + "题号: 003454 , 字段: objs 中已添加数据: K0606003B\n", + "题号: 001600 , 字段: objs 中已添加数据: K0606002B\n", + "题号: 010453 , 字段: objs 中已添加数据: K0606002B\n", + "题号: 030085 , 字段: objs 中已添加数据: K0606005B\n", + "题号: 010454 , 字段: objs 中已添加数据: K0607001B\n", + "题号: 030086 , 字段: objs 中已添加数据: K0607002B\n", + "题号: 001603 , 字段: objs 中已添加数据: K0607004B\n", + "题号: 003875 , 字段: objs 中已添加数据: K0607004B\n", + "题号: 004539 , 字段: objs 中已添加数据: K0607004B\n" ] } ], diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb index 84563b7c..3f34ccf6 100644 --- a/工具/添加关联题目.ipynb +++ b/工具/添加关联题目.ipynb @@ -2,15 +2,15 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import os,re,json,time\n", "\n", "\"\"\"---设置原题目id与新题目id---\"\"\"\n", - "old_id = \"30035\"\n", - "new_id = \"30076\"\n", + "old_id = \"9169\"\n", + "new_id = \"30099\"\n", "\"\"\"---设置完毕---\"\"\"\n", "\n", "old_id = old_id.zfill(6)\n", @@ -50,7 +50,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -64,12 +64,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 35d4d3d9..db2d4fdc 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -7,14 +7,15 @@ "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 30016\n", - "origin = \"\"\n", - "filename = \"临时文件/增加题目.tex\"" + "starting_id = 30100\n", + "origin = \"自拟题目\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目.tex\"\n", + "editor = \"20220930\\t王伟叶\"" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -46,11 +47,12 @@ " return NewProblem\n", "\n", "# 创建新题目\n", - "def CreateNewProblem(id,content,origin,dict):\n", + "def CreateNewProblem(id,content,origin,dict,editor):\n", " NewProblem = CreateEmptyProblem(dict[\"000001\"])\n", " NewProblem[\"id\"] = str(id).zfill(6)\n", " NewProblem[\"content\"] = content\n", " NewProblem[\"origin\"] = origin\n", + " NewProblem[\"edit\"] = [editor]\n", " return NewProblem\n", "\n", "\n", @@ -65,7 +67,7 @@ "id = starting_id\n", "for p in problems:\n", " pid = str(id).zfill(6)\n", - " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin, dict = pro_dict)\n", + " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin, dict = pro_dict,editor = editor)\n", " pro_dict[pid] = NewProblem\n", " id += 1\n", "\n", diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb index 9f96948a..fe8634dc 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/垂直_教师用_20220930.tex\n", + "开始编译教师版本pdf文件: 临时文件/第三单元_教师用_20221002.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/垂直_学生用_20220930.tex\n", + "开始编译学生版本pdf文件: 临时文件/第三单元_学生用_20221002.tex\n", "0\n" ] } @@ -26,18 +26,21 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库\n", "problems = r\"\"\"\n", - "000178,000181,000182,000184,000187,000189,000191,000192,000212,000294,000297,000298,000299,000304,000305,000615,001605,001606,001619,001620,001621,001624,001628,001629,001630,001633,001636,001637,001641,001656,001658,001659,001662,001670,001676,001679,001680,001701,001710,001950,001968,001973,001984,003454,003458,003460,003462,003468,003478,003480,003486,003489,003494,003495,003500,003816,003830,003846,003879,003891,003950,003968,003999,004075,004117,004133,004136,004159,004180,004223,004243,004306,004367,004398,004437,004460,004479,004505,004656,004696,004719,004761,009133,009146,009153,009162,009177,009184,009416,009690,009694,009695,009696,009700,009701,009867,009869,009870,009871,010000,010449,010461,010465,010467,010468,010470,010474,010479,010480,010483,010508,010531,010709,010710,010713,010718,010720,010721,010729,010733,010734,010735,010736,010737,010739\n", - "\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/垂直\"\n", + "filename = \"临时文件/第三单元\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", + "if 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", + "\n", "#读取系统日期\n", "current_time = time.localtime()\n", "time_string = \"_\"+str(current_time.tm_year).zfill(4)+str(current_time.tm_mon).zfill(2)+str(current_time.tm_mday).zfill(2)\n", @@ -164,7 +167,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -178,12 +181,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 4ca9b32b..f3aab400 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -4451,7 +4451,8 @@ "objs": [ "K0610001B", "K0608001B", - "K0609007B" + "K0609007B", + "K0601004B" ], "tags": [ "第六单元" @@ -40851,7 +40852,9 @@ "content": "判断下列命题的真假, 在横线上用``T''或``F''表示.\n\\begin{enumerate}[\\blank{30}(1)]\n\\item 空间任意三点确定一个平面;\\\\ \n\\item 空间任意两条直线确定一个平面;\\\\ \n\\item 空间两条平行直线确定一个平面;\\\\ \n\\item 空间一条直线和不在该直线上的一个点确定一个平面;\\\\ \n\\item 空间一个点和不通过该点的一条直线确定一个平面;\\\\ \n\\item 空间两条没有交点的直线必平行;\\\\ \n\\item 若空间四边形$ABCD$若满足$AB=BC=CD=DA$, 则它一定是菱形;\\\\ \n\\item 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\\item 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\\item 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\\item 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.\\\\ \n\\end{enumerate}", "objs": [ "K0602003B", - "K0606003B" + "K0606003B", + "K0602001B", + "K0602002B" ], "tags": [ "第一单元", @@ -40877,7 +40880,11 @@ "001596": { "id": "001596", "content": "已知不共线的三点$A,B,C$均在平面$\\alpha$上. 证明以下命题(每一步均需说明根据):\\\\ \n(1) 直线$AB$上的每一点都在平面$\\alpha$上;\\\\ \n(2) 三角形$ABC$的重心$G$在平面$\\alpha$上.", - "objs": [], + "objs": [ + "K0601003B", + "K0601005B", + "K0601006B" + ], "tags": [ "第六单元" ], @@ -40901,7 +40908,9 @@ "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}", - "objs": [], + "objs": [ + "K0606001B" + ], "tags": [ "第六单元" ], @@ -40977,7 +40986,9 @@ "001600": { "id": "001600", "content": "已知$m,n$是异面直线, 直线$s$分别与$m,n$相交于点$A,B$, 直线$t$分别与$m,n$相交于点$C,D$, $A,B,C,D$两两不同. 求证: $s,t$也是异面直线.", - "objs": [], + "objs": [ + "K0606002B" + ], "tags": [ "第六单元" ], @@ -41051,7 +41062,9 @@ "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}", - "objs": [], + "objs": [ + "K0607004B" + ], "tags": [ "第六单元" ], @@ -85782,7 +85795,10 @@ "003454": { "id": "003454", "content": "对于空间三条直线$a,b,c$, 若$a\\perp b$, $b\\perp c$, 则$a$与$c$\\bracket{20}.\n\\twoch{一定相交}{一定平行}{一定异面}{平行、相交、异面都有可能}", - "objs": [], + "objs": [ + "K0606001B", + "K0606003B" + ], "tags": [ "第六单元" ], @@ -95312,7 +95328,9 @@ "003875": { "id": "003875", "content": "在长方体$ABCD-A_1B_1C_1D_1$中, $B_1C$和$C_1D$与底面所成的角分别为$60^\\circ$和$45^\\circ$, 则异面直线$B_1C$和$C_1D$所成的角的余弦值为\\bracket{20}.\n\\fourch{$\\dfrac{\\sqrt{3}}6$}{$\\dfrac{\\sqrt{2}}{6}$}{$\\dfrac{\\sqrt{6}}{3}$}{$\\dfrac{\\sqrt{6}}{4}$}", - "objs": [], + "objs": [ + "K0607004B" + ], "tags": [ "第六单元" ], @@ -111646,7 +111664,9 @@ "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}", - "objs": [], + "objs": [ + "K0607004B" + ], "tags": [ "第六单元" ], @@ -146638,14 +146658,14 @@ }, "005993": { "id": "005993", - "content": "在同一个坐标系内, 为了得到$y=3\\sin (2x+\\dfrac{\\pi}4)$的图像, 只需将$y=3\\cos 2x$的图像\\bracket{20}.\n\\fourch{向左平移$\\dfrac{\\pi}4$}{向右平移$\\dfrac{\\pi}4$}{向左平移$\\dfrac{\\pi}8$}{向右平移$\\dfrac{\\pi}8$}\n解答在这里 令$f(x)=3\\cos 2x$, 则\n\\begin{align*}f(x-m)&=3\\cos 2(x-m)=3\\cos (2x-2m)=3\\cos (2m-2x)=3\\sin [\\dfrac{\\pi}2-(2m-2x)] \\\\ &=3\\sin (2x+\\dfrac{\\pi}2-2m).\n\\end{align*}\n按题意应有$3\\sin (2x+\\dfrac{\\pi}2-2m)=3\\sin (2x+\\dfrac{\\pi}4)$.\n令$\\dfrac{\\pi}2-2m=\\dfrac{\\pi}4$, 得$m=\\dfrac{\\pi}8$, 故选D.\\\\\n也可以这样解:\n因为$f(x)=3\\sin (2x+\\dfrac{\\pi}4)=3\\cos [(2x+\\dfrac{\\pi}4)-\\dfrac{\\pi}2]=3\\cos (2x-\\dfrac{\\pi}4)=3\\cos [2(x-\\dfrac{\\pi}8)]=f(x-\\dfrac{\\pi}8)$,\n所以选D.", + "content": "在同一个坐标系内, 为了得到$y=3\\sin (2x+\\dfrac{\\pi}4)$的图像, 只需将$y=3\\cos 2x$的图像\\bracket{20}.\n\\fourch{向左平移$\\dfrac{\\pi}4$}{向右平移$\\dfrac{\\pi}4$}{向左平移$\\dfrac{\\pi}8$}{向右平移$\\dfrac{\\pi}8$}", "objs": [], "tags": [ "第三单元" ], "genre": "选择题", - "ans": "", - "solution": "", + "ans": "D", + "solution": "令$f(x)=3\\cos 2x$, 则\n\\begin{align*}f(x-m)&=3\\cos 2(x-m)=3\\cos (2x-2m)=3\\cos (2m-2x)=3\\sin [\\dfrac{\\pi}2-(2m-2x)] \\\\ &=3\\sin (2x+\\dfrac{\\pi}2-2m).\n\\end{align*}\n按题意应有$3\\sin (2x+\\dfrac{\\pi}2-2m)=3\\sin (2x+\\dfrac{\\pi}4)$.\n令$\\dfrac{\\pi}2-2m=\\dfrac{\\pi}4$, 得$m=\\dfrac{\\pi}8$, 故选D.\\\\\n也可以这样解:\n因为$f(x)=3\\sin (2x+\\dfrac{\\pi}4)=3\\cos [(2x+\\dfrac{\\pi}4)-\\dfrac{\\pi}2]=3\\cos (2x-\\dfrac{\\pi}4)=3\\cos [2(x-\\dfrac{\\pi}8)]=f(x-\\dfrac{\\pi}8)$,\n所以选D.", "duration": -1, "usages": [], "origin": "代数精编第四章三角函数", @@ -216699,7 +216719,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030099" + ], "remark": "", "space": "12ex" }, @@ -217231,7 +217253,10 @@ "009195": { "id": "009195", "content": "画一个底面边长是$3\\text{cm}$、高是$4.5\\text{cm}$的正三棱柱的直观图.", - "objs": [], + "objs": [ + "K0604001B", + "K0604003B" + ], "tags": [ "第六单元" ], @@ -227593,7 +227618,9 @@ "009666": { "id": "009666", "content": "已知$a$、$b$、$c$是空间的三条直线, $a\\parallel b$, 且$c$与$a$、$b$\n都相交. 求证: 直线$a$、$b$、$c$在同一平面上.", - "objs": [], + "objs": [ + "K0602003B" + ], "tags": [ "第六单元" ], @@ -227740,7 +227767,9 @@ "009673": { "id": "009673", "content": "画出如图水平放置的直角梯形$OABC$的直观图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw [->] (-1.5,0) -- (5.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {-1,1,2,3,4,5} {\\draw (\\i,0.2) -- (\\i,0);};\n\\foreach \\i in {-1,1,2,3} {\\draw (0.2,\\i) -- (0,\\i);};\n\\draw (4,0) node [below] {$C$} -- (2,2) node [above] {$B$} -- (0,2) node [left] {$A$};\n\\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0604002B" + ], "tags": [ "第六单元" ], @@ -227761,7 +227790,10 @@ "009674": { "id": "009674", "content": "如图, 在长方体$ABCD-A_1B_1C_1D_1$中, 直线$A_1C$与$BD_1$相交吗? 为什么?\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\\draw [dashed] (B) -- (D1) (C) -- (A1);\n\\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0605002B", + "K0605003B" + ], "tags": [ "第六单元" ], @@ -244839,7 +244871,9 @@ "010435": { "id": "010435", "content": "如图, 已知直线$l$与平面$\\alpha$相交于点$O$, $A$、$B \\in l$, $C$、$D\\in \\alpha$, 且$AC\\parallel BD$. 求证: $O$、$C$、$D$三点共线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [name path = plane] (0,0) -- (3,0) -- (4.5,1.5) -- (1.5,1.5) -- (0,0) ++ (0.5,0) node [above] {$\\alpha$};\n\\filldraw (1.5,0.5) circle (0.03) node [left] {$O$} coordinate (O);\n\\filldraw (2.7,0.8) circle (0.03) node [below] {$C$} coordinate (C);\n\\filldraw ($(O)!0.5!(C)$) circle (0.03) node [below] {$D$} coordinate (D);\n\\filldraw (2.4,1.6) circle (0.03) node [above left] {$A$} coordinate (A);\n\\filldraw ($(O)!0.5!(A)$) circle (0.03) node [above left] {$B$} coordinate (B);\n\\draw (O) -- ($(O)!1.4!(A)$) node [right] {$l$};\n\\draw (B) -- (D) (A) -- (C);\n\\path [name path = AO] ($(O)!1.4!(A)$) -- ($(O)!-1!(A)$);\n\\path [name intersections = {of = AO and plane, by = T}];\n\\draw [dashed] (O) -- (T);\n\\draw (T) -- ($(O)!-1!(A)$);\n\\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0603004B" + ], "tags": [ "第六单元" ], @@ -245217,7 +245251,9 @@ "010453": { "id": "010453", "content": "如图, 已知不在同一平面上的三条直线$a$、$b$、$c$相交于点$O$, $M$、$P$是直线$a$上的两点, $N$、$Q$分别是直线$b$、$c$上与点$O$不重合的点. 求证: $MN$和$PQ$是异面直线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0.3,0.6) --++ (3.1,0) --++ (1.1,1.1) --++ (-3.1,0) -- (0.3,0.6) ++ (0.5,0) node [above] {$\\alpha$};\n\\draw (1.3,1.2) node [below left] {$O$} coordinate (O);\n\\draw (2.7,2.5) node [above] {$P$} coordinate (P);\n\\draw ($(O)!0.7!(P)$) node [above] {$M$} coordinate (M);\n\\draw (O) -- ($(O)!1.5!(P)$) node [right] {$a$} coordinate (a);\n\\draw (2.2,1) node [below] {$N$} coordinate (N);\n\\draw (2.9,1.5) node [below] {$Q$} coordinate (Q);\n\\draw (O) -- ($(O)!1.8!(N)$) node [right] {$b$} coordinate (b);\n\\draw (O) -- ($(O)!1.2!(Q)$) node [right] {$c$} coordinate (c);\n\\draw (M) -- (N) (P) -- (Q);\n\\end{tikzpicture}\n\\end{center}", - "objs": [], + "objs": [ + "K0606002B" + ], "tags": [ "第六单元" ], @@ -245238,7 +245274,9 @@ "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}", - "objs": [], + "objs": [ + "K0607001B" + ], "tags": [ "第六单元" ], @@ -286270,5 +286308,485 @@ "related": [], "remark": "", "space": "" + }, + "030077": { + "id": "030077", + "content": "用集合符号表述下列语句:\\\\\n(1) 点$A$在平面$\\alpha$上, 并且平面$\\alpha$经过直线$AB$:\\blank{50};\\\\ \n(2) 点$C$不在平面$\\beta$上, 并且直线$CD$平行于平面$\\beta$:\\blank{50}.", + "objs": [ + "K0601002B" + ], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030078": { + "id": "030078", + "content": "画出下列符号语言表示的点、直线、平面的位置关系的示意图.\\\\ \n(1) $a\\subset \\alpha$, $b\\subset \\alpha$, $a\\cap b=A$;\\\\\n(2) $a\\subset \\alpha$, $b\\cap \\alpha =A$, $A\\notin a$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册例题与习题", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030079": { + "id": "030079", + "content": "直线$l$经过平面$\\alpha$内一点$A$和平面$\\alpha$外一点$B$, 则直线$l$与平面$\\alpha$有几个公共点? 为什么?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册例题与习题", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "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.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册例题与习题", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "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}", + "objs": [ + "K0603003B", + "K0603005B" + ], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册例题与习题", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "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}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂必修第三册例题与习题", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030083": { + "id": "030083", + "content": "如图, $AA'$, $BB'$, $CC'$不共面, 且$AA'$, $BB'$, $CC'$三条线段平行且相等. 求证: $\\triangle ABC\\cong \\triangle A'B'C'$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$A$} coordinate (A);\n\\draw (-1,-1) node [left] {$B$} coordinate (B);\n\\draw (1,-1.5) node [below] {$C$} coordinate (C);\n\\draw (A) ++ (3,0.3) node [above] {$A'$} coordinate (A1);\n\\draw (B) ++ (3,0.3) node [above left] {$B'$} coordinate (B1);\n\\draw (C) ++ (3,0.3) node [right] {$C'$} coordinate (C1);\n\\draw (B) -- (C) -- (C1) -- (A1) -- (A) -- cycle (A) -- (C);\n\\draw [dashed] (B) -- (B1) -- (C1) (B1) -- (A1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [ + "K0605002B", + "K0605004B", + "K0605005B" + ], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版例题与习题", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "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}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "人教A版例题与习题", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030085": { + "id": "030085", + "content": "复述并证明异面直线判定定理.", + "objs": [ + "K0606005B" + ], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030086": { + "id": "030086", + "content": "两异面直线所成的角的范围为\\blank{50}.", + "objs": [ + "K0607002B" + ], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030087": { + "id": "030087", + "content": "复述``空间直线与平面''一章中的公理1.", + "objs": [ + "K0601005B" + ], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030088": { + "id": "030088", + "content": "复述``空间直线与平面''一章中的公理2.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030089": { + "id": "030089", + "content": "复述``空间直线与平面''一章中的公理3.", + "objs": [ + "K0603001B" + ], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030090": { + "id": "030090", + "content": "复述``空间直线与平面''一章中的公理4.", + "objs": [ + "K0605001B" + ], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20220930\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030091": { + "id": "030091", + "content": "叙述直线与平面平行的判定定理.", + "objs": [], + 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