From 9480231c6f24734b08efad1cc5730578d5deffd5 Mon Sep 17 00:00:00 2001 From: Wang Weiye Date: Fri, 14 Oct 2022 15:14:59 +0800 Subject: [PATCH] 20221014 afternoon --- .../讲义题目分类按顺序梳理_制答题卡用.ipynb | 50 +- 工具/寻找tex文件中未赋答案的题目.ipynb | 74 +- 工具/批量添加题库字段数据.ipynb | 208 +---- 工具/文本文件/metadata.txt | 715 ++---------------- 工具/讲义生成.ipynb | 14 +- 题库0.3/Problems.json | 352 ++++----- 6 files changed, 312 insertions(+), 1101 deletions(-) diff --git a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb index e3e101f4..3ececd13 100644 --- a/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb +++ b/工具/分年级专用工具/讲义题目分类按顺序梳理_制答题卡用.ipynb @@ -2,42 +2,52 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1 选择题 1\n", - "2 解答题 1\n", - "3 解答题 1\n", - "4 解答题 1\n", - "5 解答题 1\n", - "6 解答题 4\n", - "7 填空题 4\n", - "8 填空题 1\n", - "9 填空题 1\n", - "10 解答题 2\n", + "1 填空题 2\n", + "2 填空题 1\n", + "3 填空题 4\n", + "4 填空题 1\n", + "5 填空题 8\n", + "6 填空题 2\n", + "7 填空题 1\n", + "8 解答题 1\n", + "9 解答题 1\n", + "10 填空题 4\n", "11 解答题 1\n", "12 解答题 1\n", "13 解答题 1\n", + "14 填空题 1\n", + "15 选择题 1\n", + "16 填空题 1\n", + "17 选择题 1\n", + "1 填空题 1\n", + "2 解答题 1\n", + "3 填空题 1\n", + "4 填空题 1\n", + "5 填空题 1\n", + "6 填空题 3\n", + "7 填空题 1\n", + "8 解答题 3\n", + "9 选择题 1\n", + "10 选择题 1\n", + "11 解答题 1\n", + "12 解答题 1\n", + "13 解答题 2\n", "14 解答题 1\n", - "15 解答题 4\n", - "1 解答题 5\n", - "2 选择题 1\n", - "3 解答题 1\n", - "4 解答题 1\n", - "5 解答题 2\n", - "6 解答题 1\n", - "7 填空题 1\n" + "15 填空题 1\n" ] } ], "source": [ "import os,re\n", "#修改文件名\n", - "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", + "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\23_多面体及旋转体的概念与性质.tex\"\n", "# filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\上学期周末卷\\国庆卷.tex\"\n", "outputfile = \"临时文件/题目状态.txt\"\n", "\n", diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb index 5a02ea25..c9029477 100644 --- a/工具/寻找tex文件中未赋答案的题目.ipynb +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -2,74 +2,14 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "国庆卷.tex\n", - "030033\n", - "\n", - "\n", - "030030\n", - "\n", - "\n", - "030076\n", - "\n", - "\n", - "030038\n", - "\n", - "\n", - "030042\n", - "\n", - "\n", - "030048\n", - "\n", - "\n", - "030046\n", - "\n", - "\n", - "030051\n", - "\n", - "\n", - "030043\n", - "\n", - "\n", - "030050\n", - "\n", - "\n", - "030058\n", - "\n", - "\n", - "030056\n", - "\n", - "\n", - "030057\n", - "\n", - "\n", - "030060\n", - "\n", - "\n", - "030063\n", - "\n", - "\n", - "030062\n", - "\n", - "\n", - "030065\n", - "\n", - "\n", - "030067\n", - "\n", - "\n", - "030066\n", - "\n", - "\n", - "030064\n", - "\n", - "\n" + "19_复数的几何意义与实系数二次方程.tex\n" ] } ], @@ -77,9 +17,9 @@ "import os,json,re\n", "\n", "#这里需要修改, 设定路径与选择文件\n", - "fileind = 5\n", + "fileind = 19\n", "# path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", - "path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\上学期周末卷\"\n", + "path = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n", "\n", "fileind = fileind - 1\n", "with open(\"../题库0.3/Problems.json\",\"r\",encoding = \"utf8\") as f:\n", @@ -107,7 +47,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -121,12 +61,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/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 ec6ac499..0c290b33 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 @@ -2,184 +2,42 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 009733 , 字段: objs 中已添加数据: K0801001B\n", - "题号: 009734 , 字段: objs 中已添加数据: K0801001B\n", - "题号: 009735 , 字段: objs 中已添加数据: K0802002B\n", - "题号: 009736 , 字段: objs 中已添加数据: K0802003B\n", - "题号: 009737 , 字段: objs 中已添加数据: K0802003B\n", - "题号: 010539 , 字段: objs 中已添加数据: K0802003B\n", - "题号: 010540 , 字段: objs 中已添加数据: K0802003B\n", - "题号: 009736 , 字段: objs 中已添加数据: K0802004B\n", - "题号: 009737 , 字段: objs 中已添加数据: K0802004B\n", - "题号: 010539 , 字段: objs 中已添加数据: K0802004B\n", - "题号: 010540 , 字段: objs 中已添加数据: K0802004B\n", - "题号: 010534 , 字段: objs 中已添加数据: K0802005B\n", - "题号: 010535 , 字段: objs 中已添加数据: K0802005B\n", - "题号: 010537 , 字段: objs 中已添加数据: K0802005B\n", - "题号: 010538 , 字段: objs 中已添加数据: K0802005B\n", - "题号: 000223 , 字段: objs 中已添加数据: K0802006B\n", - "题号: 009735 , 字段: objs 中已添加数据: K0802006B\n", - "题号: 010536 , 字段: objs 中已添加数据: K0802006B\n", - "题号: 009409 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009410 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009738 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009739 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009740 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009741 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 010541 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 010542 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 010547 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 010548 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 010549 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 010554 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 010556 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003887 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003914 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003993 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004031 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004110 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009349 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009354 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009364 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004193 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004297 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004341 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004535 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004612 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004647 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 004731 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009346 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 009347 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 002645 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 002650 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 002651 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 002662 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 002663 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 002664 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003585 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003598 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003660 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003727 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003787 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 003872 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000512 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000564 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000581 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000601 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000654 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000659 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000744 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000773 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000779 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000829 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000844 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000969 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 002640 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000218 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000219 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000220 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000221 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000222 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000223 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000227 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000228 , 字段: objs 中已有该数据: K0803002B\n", - "题号: 000332 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000384 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000391 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000401 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000420 , 字段: objs 中已添加数据: K0803002B\n", - "题号: 000714 , 字段: objs 中已添加数据: K0805002B\n", - "题号: 009743 , 字段: objs 中已添加数据: K0805002B\n", - "题号: 010543 , 字段: objs 中已添加数据: K0805002B\n", - "题号: 010546 , 字段: objs 中已添加数据: K0805002B\n", - "题号: 010544 , 字段: objs 中已添加数据: K0805003B\n", - "题号: 010550 , 字段: objs 中已添加数据: K0805003B\n", - "题号: 000231 , 字段: objs 中已添加数据: K0805006B\n", - "题号: 000624 , 字段: objs 中已添加数据: K0806002B\n", - "题号: 009751 , 字段: objs 中已添加数据: K0806002B\n", - "题号: 004324 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 004750 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 009366 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 009739 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 009741 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 009745 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 009746 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010545 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010546 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010550 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010551 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010557 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010558 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010559 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 010560 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000225 , 字段: objs 中已有该数据: K0806004B\n", - "题号: 000227 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000229 , 字段: objs 中已有该数据: K0806004B\n", - "题号: 000231 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000384 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000512 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000564 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000672 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000685 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000695 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000704 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000714 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 000812 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 002645 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 003598 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 004039 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 004087 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 004150 , 字段: objs 中已添加数据: K0806004B\n", - "题号: 009744 , 字段: objs 中已添加数据: K0806005B\n", - "题号: 010553 , 字段: objs 中已添加数据: K0807001B\n", - "题号: 009356 , 字段: objs 中已添加数据: K0807002B\n", - "题号: 000224 , 字段: objs 中已有该数据: K0807003B\n", - "题号: 000230 , 字段: objs 中已有该数据: K0807003B\n", - "题号: 003734 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 009357 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 009747 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 009748 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 009749 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 010552 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 010553 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 010554 , 字段: objs 中已添加数据: K0807003B\n", - "题号: 000226 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 000231 , 字段: objs 中已有该数据: K0808002B\n", - "题号: 000611 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 000624 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 000685 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 000695 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 000704 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 000812 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 004039 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 004087 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 004150 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 004324 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 004750 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 009750 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 009751 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 009753 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 009754 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 010555 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 010558 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 010557 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 010559 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 010560 , 字段: objs 中已添加数据: K0808002B\n", - "题号: 009751 , 字段: objs 中已添加数据: K0808003B\n", - "题号: 009753 , 字段: objs 中已添加数据: K0808003B\n", - "题号: 010557 , 字段: objs 中已添加数据: K0808003B\n", - "题号: 010558 , 字段: objs 中已添加数据: K0808003B\n", - "题号: 009754 , 字段: objs 中已添加数据: K0808004B\n", - "题号: 009752 , 字段: objs 中已添加数据: K0809001B\n", - "题号: 009753 , 字段: objs 中已添加数据: K0809002B\n", - "题号: 009754 , 字段: objs 中已添加数据: K0809003B\n" + "题号: 002010 , 字段: ans 中已修改数据: $6$或$-2+12\\mathrm{i}$或$2-8\\mathrm{i}$\n", + "题号: 002020 , 字段: ans 中已修改数据: $1+\\dfrac{14}5\\mathrm{i}$\n", + "题号: 003521 , 字段: ans 中已修改数据: $\\dfrac\\pi 2$\n", + "题号: 002018 , 字段: ans 中已修改数据: $4$\n", + "题号: 003524 , 字段: ans 中已修改数据: (1) 直线$y=0$; (2) 圆$(x+1)^2+y^2=1$; (3) 椭圆$\\dfrac{x^2}{36}+\\dfrac{y^2}{11}=1$; (4) 线段$y=0 \\ (x\\in [-1,1])$; (5) 双曲线的一支: $y^2-\\dfrac{x^2}{3}=1 \\ (y<0)$\n", + "题号: 003534 , 字段: ans 中已修改数据: (1) $[4\\sqrt{2}-2,4\\sqrt{2}+2]$; (2) $(3+\\sqrt{2})-(4+\\sqrt{2})\\mathrm{i}$\n", + "题号: 003535 , 字段: ans 中已修改数据: 以$(1,0)$为圆心, $\\dfrac 12$为半径的圆\n", + "题号: 002057 , 字段: ans 中已修改数据: $2+\\mathrm{i}$与$-2-\\mathrm{i}$\n", + "题号: 003542 , 字段: ans 中已修改数据: \\textcircled{2}\\textcircled{5}\n", + "题号: 000168 , 字段: ans 中已修改数据: (1) 解为$2+\\mathrm{i}$与$2-\\mathrm{i}$; (2) 解为$\\dfrac{-1+\\sqrt{10}}3$与$\\dfrac{-1-\\sqrt{10}}3$\n", + "题号: 030110 , 字段: ans 中已修改数据: (1) $-1\\pm \\dfrac{\\sqrt{2}}2\\mathrm{i}$; (2) $2(x+1+\\dfrac{\\sqrt{2}}2\\mathrm{i})(x+1-\\dfrac{\\sqrt{2}}2\\mathrm{i})$\n", + "题号: 003544 , 字段: ans 中已修改数据: $p=12$, $q=26$\n", + "题号: 002085 , 字段: ans 中已修改数据: 证明略\n", + "题号: 002086 , 字段: ans 中已修改数据: $\\dfrac 52$或$-2$\n", + "题号: 000163 , 字段: ans 中已修改数据: (1) $11$, $-60$, $61$, $11+60\\mathrm{i}$; (2) \\textcircled{3}\n", + "题号: 003519 , 字段: ans 中已修改数据: B\n", + "题号: 003520 , 字段: ans 中已修改数据: A\n", + "题号: 003523 , 字段: ans 中已修改数据: $a+b\\mathrm{i}$\n", + "题号: 003522 , 字段: ans 中已修改数据: $-2+\\mathrm{i}$\n", + "题号: 002012 , 字段: ans 中已修改数据: 二\n", + "题号: 002016 , 字段: ans 中已修改数据: $\\{-2,0\\}$\n", + "题号: 002017 , 字段: ans 中已修改数据: $40$\n", + "题号: 003528 , 字段: ans 中已修改数据: 以$(-3,7)$为圆心, $12$为半径的圆\n", + "题号: 007313 , 字段: ans 中已修改数据: $3+2\\mathrm{i}$与$-3-2\\mathrm{i}$\n", + "题号: 007314 , 字段: ans 中已修改数据: 解为$\\dfrac{\\sqrt{2}}2+\\dfrac{\\sqrt{2}}2\\mathrm{i}$与$-\\dfrac{\\sqrt{2}}2-\\dfrac{\\sqrt{2}}2\\mathrm{i}$\n", + "题号: 003758 , 字段: ans 中已修改数据: 不存在推出关系, 因为$P$成立当且仅当$a\\in (-2\\sqrt{2},2\\sqrt{2})$, $Q$成立当且仅当$a\\in [-3,-1]\\cup [1,3]$, $a=0$时$P$成立但$Q$不成立, $a=3$时$Q$成立但$P$不成立\n", + "题号: 004167 , 字段: ans 中已修改数据: $2\\sqrt{3}$\n", + "题号: 009032 , 字段: ans 中已修改数据: (1) $(x+\\sqrt{5}\\mathrm{i}y)(x-\\sqrt{5}\\mathrm{i}y)$; (2) $2(x-\\dfrac{3+\\mathrm{i}}2)(x-\\dfrac{3-\\mathrm{i}}2)$\n", + "题号: 003551 , 字段: ans 中已修改数据: (1) $-\\dfrac 14$或$\\dfrac{17}{4}$; (2) $-\\dfrac 14$或$\\dfrac 94$\n" ] } ], @@ -277,7 +135,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -291,12 +149,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index bac1983e..b3cb1435 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,686 +1,89 @@ -objs -9733 -K0801001B +ans +02010 +$6$或$-2+12\mathrm{i}$或$2-8\mathrm{i}$ -9734 -K0801001B +002020 +$1+\dfrac{14}5\mathrm{i}$ +003521 +$\dfrac\pi 2$ -9735 -K0802002B +002018 +$4$ +003524 +(1) 直线$y=0$; (2) 圆$(x+1)^2+y^2=1$; (3) 椭圆$\dfrac{x^2}{36}+\dfrac{y^2}{11}=1$; (4) 线段$y=0 \ (x\in [-1,1])$; (5) 双曲线的一支: $y^2-\dfrac{x^2}{3}=1 \ (y<0)$ -9736 -K0802003B +003534 +(1) $[4\sqrt{2}-2,4\sqrt{2}+2]$; (2) $(3+\sqrt{2})-(4+\sqrt{2})\mathrm{i}$ +003535 +以$(1,0)$为圆心, $\dfrac 12$为半径的圆 -9737 -K0802003B +002057 +$2+\mathrm{i}$与$-2-\mathrm{i}$ +003542 +\textcircled{2}\textcircled{5} -10539 -K0802003B +000168 +(1) 解为$2+\mathrm{i}$与$2-\mathrm{i}$; (2) 解为$\dfrac{-1+\sqrt{10}}3$与$\dfrac{-1-\sqrt{10}}3$ +030110 +(1) $-1\pm \dfrac{\sqrt{2}}2\mathrm{i}$; (2) $2(x+1+\dfrac{\sqrt{2}}2\mathrm{i})(x+1-\dfrac{\sqrt{2}}2\mathrm{i})$ -10540 -K0802003B +003544 +$p=12$, $q=26$ +002085 +证明略 -9736 -K0802004B +002086 +$\dfrac 52$或$-2$ +000163 +(1) $11$, $-60$, $61$, $11+60\mathrm{i}$; (2) \textcircled{3} -9737 -K0802004B +003519 +B +003520 +A -10539 -K0802004B +003523 +$a+b\mathrm{i}$ +003522 +$-2+\mathrm{i}$ -10540 -K0802004B +002012 +二 +002016 +$\{-2,0\}$ -10534 -K0802005B +002017 +$40$ +003528 +以$(-3,7)$为圆心, $12$为半径的圆 -10535 -K0802005B +007313 +$3+2\mathrm{i}$与$-3-2\mathrm{i}$ +007314 +解为$\dfrac{\sqrt{2}}2+\dfrac{\sqrt{2}}2\mathrm{i}$与$-\dfrac{\sqrt{2}}2-\dfrac{\sqrt{2}}2\mathrm{i}$ -10537 -K0802005B +003758 +不存在推出关系, 因为$P$成立当且仅当$a\in (-2\sqrt{2},2\sqrt{2})$, $Q$成立当且仅当$a\in [-3,-1]\cup [1,3]$, $a=0$时$P$成立但$Q$不成立, $a=3$时$Q$成立但$P$不成立 +004167 +$2\sqrt{3}$ -10538 -K0802005B - - -223 -K0802006B - - -9735 -K0802006B - - -10536 -K0802006B - - -9409 -K0803002B - - -9410 -K0803002B - - -9738 -K0803002B - - -9739 -K0803002B - - -9740 -K0803002B - - -9741 -K0803002B - - -10541 -K0803002B - - -10542 -K0803002B - - -10547 -K0803002B - - -10548 -K0803002B - - -10549 -K0803002B - - -10554 -K0803002B - - -10556 -K0803002B - - -3887 -K0803002B - - -3914 -K0803002B - - -3993 -K0803002B - - -4031 -K0803002B - - -4110 -K0803002B - - -9349 -K0803002B - - -9354 -K0803002B - - -9364 -K0803002B - - -4193 -K0803002B - - -4297 -K0803002B - - -4341 -K0803002B - - -4535 -K0803002B - - -4612 -K0803002B - - -4647 -K0803002B - - -4731 -K0803002B - - -9346 -K0803002B - - -9347 -K0803002B - - -2645 -K0803002B - - -2650 -K0803002B - - -2651 -K0803002B - - -2662 -K0803002B - - -2663 -K0803002B - - -2664 -K0803002B - - -3585 -K0803002B - - -3598 -K0803002B - - -3660 -K0803002B - - -3727 -K0803002B - - -3787 -K0803002B - - -3872 -K0803002B - - -512 -K0803002B - - -564 -K0803002B - - -581 -K0803002B - - -601 -K0803002B - - -654 -K0803002B - - -659 -K0803002B - - -744 -K0803002B - - -773 -K0803002B - - -779 -K0803002B - - -829 -K0803002B - - -844 -K0803002B - - -969 -K0803002B - - -2640 -K0803002B - - -218 -K0803002B - - -219 -K0803002B - - -220 -K0803002B - - -221 -K0803002B - - -222 -K0803002B - - -223 -K0803002B - - -227 -K0803002B - - -228 -K0803002B - - -332 -K0803002B - - -384 -K0803002B - - -391 -K0803002B - - -401 -K0803002B - - -420 -K0803002B - - -714 -K0805002B - - -9743 -K0805002B - - -10543 -K0805002B - - -10546 -K0805002B - - -10544 -K0805003B - - -10550 -K0805003B - - -231 -K0805006B - - -624 -K0806002B - - -9751 -K0806002B - - -4324 -K0806004B - - -4750 -K0806004B - - -9366 -K0806004B - - -9739 -K0806004B - - -9741 -K0806004B - - -9745 -K0806004B - - -9746 -K0806004B - - -10545 -K0806004B - - -10546 -K0806004B - - -10550 -K0806004B - - -10551 -K0806004B - - -10557 -K0806004B - - -10558 -K0806004B - - -10559 -K0806004B - - -10560 -K0806004B - - -225 -K0806004B - - -227 -K0806004B - - -229 -K0806004B - - -231 -K0806004B - - -384 -K0806004B - - -512 -K0806004B - - -564 -K0806004B - - -672 -K0806004B - - -685 -K0806004B - - -695 -K0806004B - - -704 -K0806004B - - -714 -K0806004B - - -812 -K0806004B - - -2645 -K0806004B - - -3598 -K0806004B - - -4039 -K0806004B - - -4087 -K0806004B - - -4150 -K0806004B - - -9744 -K0806005B - - -10553 -K0807001B - - -9356 -K0807002B - - -224 -K0807003B - - -230 -K0807003B - - -3734 -K0807003B - - -9357 -K0807003B - - -9747 -K0807003B - - -9748 -K0807003B - - -9749 -K0807003B - - -10552 -K0807003B - - -10553 -K0807003B - - -10554 -K0807003B - - -226 -K0808002B - - -231 -K0808002B - - -611 -K0808002B - - -624 -K0808002B - - -685 -K0808002B - - -695 -K0808002B - - -704 -K0808002B - - -812 -K0808002B - - -4039 -K0808002B - - -4087 -K0808002B - - -4150 -K0808002B - - -4324 -K0808002B - - -4750 -K0808002B - - -9750 -K0808002B - - -9751 -K0808002B - - -9753 -K0808002B - - -9754 -K0808002B - - -10555 -K0808002B - - -10558 -K0808002B - - -10557 -K0808002B - - -10559 -K0808002B - - -10560 -K0808002B - - -9751 -K0808003B - - -9753 -K0808003B - - -10557 -K0808003B - - -10558 -K0808003B - - -9754 -K0808004B - - -9752 -K0809001B - - -9753 -K0809002B - - -9754 -K0809003B - +009032 +(1) $(x+\sqrt{5}\mathrm{i}y)(x-\sqrt{5}\mathrm{i}y)$; (2) $2(x-\dfrac{3+\mathrm{i}}2)(x-\dfrac{3-\mathrm{i}}2)$ +003551 +(1) $-\dfrac 14$或$\dfrac{17}{4}$; (2) $-\dfrac 14$或$\dfrac 94$ diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index c33cf5e0..6ac01e80 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -13,9 +13,9 @@ "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/24_体积及表面积的计算_预选_教师_20221013.tex\n", + "开始编译教师版本pdf文件: 临时文件/23_多面体及旋转体的概念与性质_教师_20221014.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/24_体积及表面积的计算_预选_学生_20221013.tex\n", + "开始编译学生版本pdf文件: 临时文件/23_多面体及旋转体的概念与性质_学生_20221014.tex\n", "0\n" ] } @@ -35,7 +35,7 @@ "\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\",\"24\"),(\"标题文字待处理\",\"体积及表面积的计算 预选\")] \n", + "exec_list = [(\"标题数字待处理\",\"23\"),(\"标题文字待处理\",\"多面体及旋转体的概念与性质\")] \n", "enumi_mode = 0\n", "\n", "#2023届测验卷与周末卷\n", @@ -49,14 +49,14 @@ "\"\"\"---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/24_体积及表面积的计算_预选\"\n", + "destination_file = \"临时文件/23_多面体及旋转体的概念与性质\"\n", "\"\"\"---设置目标文件名结束---\"\"\"\n", "\n", "\n", "\"\"\"---设置题号数据---\"\"\"\n", "problems = [\n", - "\"204,9211,9212,210,10500,3475,4994,9210,9712,199,202,9400,10524,9868,9720,9207,10517,4196,9731,9399\",\n", - "\"10498,4061,9710,4084,10499,9209,10521,10522,212,411,10519,10515,10516,215,11332,201\"\n", + "\"30116,30119,30120,10523,1695,30122,1700,207,10510,30125,9202,203,214,1712,3996,30126,3982\",\n", + "\"30128,197,30137,1697,30124,30139,30142,9191,9227,7379,9200,1704,9716,10531,10529\"\n", "]\n", "\"\"\"---设置题号数据结束---\"\"\"\n", "\n", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 1b340893..181a60a2 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -3274,7 +3274,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y=50\\sin(\\dfrac \\pi {15}t-\\dfrac\\pi 2)+60$, $t\\in [0,+\\infty)$; (2) $10$分钟.", "solution": "", "duration": -1, "usages": [ @@ -3404,7 +3404,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $f(x)=6-x$; (2) $k=\\dfrac 17$或$-\\dfrac 17$", "solution": "", "duration": -1, "usages": [ @@ -3494,7 +3494,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\overrightarrow{a}$与$\\overrightarrow{b}$同向", "solution": "", "duration": -1, "usages": [ @@ -3531,7 +3531,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -3568,7 +3568,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$[1,4]$", "solution": "", "duration": -1, "usages": [ @@ -3605,7 +3605,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-7,-\\dfrac{\\sqrt{14}}2)\\cup (-\\dfrac{\\sqrt{14}}2,-\\dfrac 12)$", "solution": "", "duration": -1, "usages": [ @@ -3817,7 +3817,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -3909,7 +3909,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -4069,7 +4069,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "大小为$1000\\sqrt{13-6\\sqrt{3}}\\text{N}$(约$1614.84\\text{N}$), 方向如图, 与$\\overrightarrow{f}$的夹角为$\\arctan \\dfrac 1{3-\\sqrt{3}}$(约$38.26^\\circ$).", "solution": "", "duration": -1, "usages": [ @@ -4182,7 +4182,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $11$, $-60$, $61$, $11+60\\mathrm{i}$; (2) \\textcircled{3}", "solution": "", "duration": -1, "usages": [], @@ -4231,7 +4231,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -4269,7 +4269,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $10+11\\mathrm{i}$; (2) $25$; (3) $11+7\\mathrm{i}$; (4) $-\\dfrac 85$; (5) $4\\sqrt{3}+4\\mathrm{i}$", "solution": "", "duration": -1, "usages": [ @@ -4329,7 +4329,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解为$2+\\mathrm{i}$与$2-\\mathrm{i}$; (2) 解为$\\dfrac{-1+\\sqrt{10}}3$与$\\dfrac{-1-\\sqrt{10}}3$", "solution": "", "duration": -1, "usages": [], @@ -4358,7 +4358,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "(1) B; (2) C", "solution": "", "duration": -1, "usages": [ @@ -4396,7 +4396,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -4504,7 +4504,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$-21+\\mathrm{i}$", "solution": "", "duration": -1, "usages": [ @@ -38880,7 +38880,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $2\\pi^2$; (2) $\\dfrac{2\\pi}{\\omega}$; (3) 不存在; (4) 不存在; (5) $1$; (6) $30\\pi$; (7) 不存在; (8) 不存在", "solution": "", "duration": -1, "usages": [ @@ -38968,7 +38968,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 如$f(x)=\\cos x$, $g(x)=\\sin x$等; (2) 如$f(x)=\\cos x$, $g(x)=-\\cos x$等", "solution": "", "duration": -1, "usages": [ @@ -39006,7 +39006,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $2\\pi$; (2) $\\pi$; (3) $\\pi$; (4) $\\pi$; (5) $\\dfrac\\pi 2$; (6) $2\\pi$; (7) $2\\pi$; (8) $1$", "solution": "", "duration": -1, "usages": [ @@ -39044,7 +39044,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "最小正周期为$2\\pi$, 证明略", "solution": "", "duration": -1, "usages": [ @@ -39084,7 +39084,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "最小正周期为$\\dfrac\\pi 2$, 证明略", "solution": "", "duration": -1, "usages": [ @@ -39470,7 +39470,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 值域为$[0,1]$, 单调增区间为$[-1+2k,2k] \\ (k\\in \\mathbf{Z})$; (2) $\\{x|x=\\pm \\dfrac{\\sqrt{2}}2+2k, \\ k\\in \\mathbf{Z}\\}$; (3) $f(x)=-x^2+200x-9999$", "solution": "", "duration": -1, "usages": [ @@ -40030,7 +40030,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pi$", "solution": "", "duration": -1, "usages": [ @@ -40094,7 +40094,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "在$(-\\dfrac \\pi 3+2k\\pi,\\dfrac{5\\pi}3+2k\\pi) \\ (k\\in \\mathbf{Z})$上是严格减函数", "solution": "", "duration": -1, "usages": [ @@ -40135,7 +40135,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "定义域为$\\{x|x\\ne \\dfrac{k\\pi}2, \\ k\\in \\mathbf{Z}\\}$; 值域为$(-\\infty,-2]\\cup [2,+\\infty)$; 最小正周期为$\\pi$; 在$(k\\pi,k\\pi+\\dfrac{\\pi}4] \\ (k\\in \\mathbf{Z})$与$[k\\pi+\\dfrac{3\\pi}4,k\\pi+\\pi) \\ (k\\in \\mathbf{Z})$上是严格减函数, 在$[k\\pi+\\dfrac{\\pi}4,k\\pi+\\dfrac\\pi 2) \\ (k\\in \\mathbf{Z})$与$(k\\pi+\\dfrac\\pi 2,k\\pi+\\dfrac{3\\pi}4] \\ (k\\in \\mathbf{Z})$上是严格增函数.", "solution": "", "duration": -1, "usages": [ @@ -44060,7 +44060,7 @@ }, "001695": { "id": "001695", - "content": "判断下列命题的真假, 真命题用``{\\textrm T}'', 假命题用``{\\textrm F}''表示.\\\\ \n\\begin{enumerate}[\\blank{30}(1)]\n\\item 有一个面是多边形，其余各面都是三角形的多面体是棱锥.\\\\ \n\\item 侧面都是全等等腰三角形的棱锥是正棱锥.\\\\ \n\\item 相邻两条侧棱间的夹角都相等的棱锥是正棱锥.\\\\ \n\\item 各条侧棱与底面的所成角都相等的棱锥是正棱锥.\\\\ \n\\item 各侧棱在底面内的射影都相等的棱锥是正棱锥.\\\\ \n\\item 各侧棱都相等且底面多边形的各边也都相等的棱锥是正棱锥.\\\\ \n\\item 底面三角形的各边分别与相对的侧棱垂直的三棱锥是正三棱锥.\\\\ \n\\item 一个三棱锥的底面是直角三角形，则它的三个侧面至多有两个直角三角形.\n\\end{enumerate}", + "content": "判断下列命题的真假, 真命题用``{\\textrm T}'', 假命题用``{\\textrm F}''表示.\\\\ \n\\blank{20}(1) 有一个面是多边形，其余各面都是三角形的多面体是棱锥.\\\\ \n\\blank{20}(2) 侧面都是全等等腰三角形的棱锥是正棱锥.\\\\ \n\\blank{20}(3) 相邻两条侧棱间的夹角都相等的棱锥是正棱锥.\\\\ \n\\blank{20}(4) 各条侧棱与底面的所成角都相等的棱锥是正棱锥.\\\\ \n\\blank{20}(5) 各侧棱在底面内的射影都相等的棱锥是正棱锥.\\\\ \n\\blank{20}(6) 各侧棱都相等且底面多边形的各边也都相等的棱锥是正棱锥.\\\\ \n\\blank{20}(7) 底面三角形的各边分别与相对的侧棱垂直的三棱锥是正三棱锥.\\\\ \n\\blank{20}(8) 一个三棱锥的底面是直角三角形，则它的三个侧面至多有两个直角三角形.", "objs": [ "K0618001B", "K0618002B" @@ -48041,7 +48041,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -48080,7 +48080,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -48144,7 +48144,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -48211,7 +48211,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\overrightarrow{AC}$", "solution": "", "duration": -1, "usages": [ @@ -48330,7 +48330,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) F; (2) T; (3) F; (4) F; (5) T; (6) T; (7) T; (8) T", "solution": "", "duration": -1, "usages": [ @@ -48370,7 +48370,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -48407,7 +48407,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 13$", "solution": "", "duration": -1, "usages": [ @@ -48548,7 +48548,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -48585,7 +48585,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -48728,7 +48728,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -48766,7 +48766,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac 23,\\dfrac 13)$", "solution": "", "duration": -1, "usages": [ @@ -48804,7 +48804,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-6$", "solution": "", "duration": -1, "usages": [ @@ -48971,7 +48971,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -49115,7 +49115,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -49235,7 +49235,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -49303,7 +49303,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\dfrac 35,\\dfrac 45)$", "solution": "", "duration": -1, "usages": [ @@ -49346,7 +49346,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac 45,\\dfrac 35)$或$(-\\dfrac 45,-\\dfrac 35)$", "solution": "", "duration": -1, "usages": [ @@ -49437,7 +49437,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-1,\\dfrac 23)\\cup (\\dfrac 23, +\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -49501,7 +49501,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-4$", "solution": "", "duration": -1, "usages": [ @@ -49539,7 +49539,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(6,5)$或$(0,3)$", "solution": "", "duration": -1, "usages": [ @@ -49576,7 +49576,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -49642,7 +49642,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$(11,6)$", "solution": "", "duration": -1, "usages": [ @@ -49761,7 +49761,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{5\\sqrt{3}}2$", "solution": "", "duration": -1, "usages": [ @@ -49851,7 +49851,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{\\pi}{4}$或$\\dfrac{3\\pi}{4}$", "solution": "", "duration": -1, "usages": [ @@ -49889,7 +49889,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$9$", "solution": "", "duration": -1, "usages": [ @@ -49926,7 +49926,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -50016,7 +50016,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-3\\sqrt{13}$, $7\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -50055,7 +50055,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{15}2$", "solution": "", "duration": -1, "usages": [ @@ -50092,7 +50092,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac{243}{25},\\dfrac{324}{25})$", "solution": "", "duration": -1, "usages": [ @@ -50131,7 +50131,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1-\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -50168,7 +50168,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{2}-3$", "solution": "", "duration": -1, "usages": [ @@ -50234,7 +50234,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 12$; (2) $-\\dfrac 34$或$\\dfrac 74$或$\\dfrac{1\\pm \\sqrt{5}}2$", "solution": "", "duration": -1, "usages": [ @@ -52128,7 +52128,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\mathbf{N}\\subset \\mathbf{Z}\\subset \\mathbf{Q}\\subset \\mathbf{R}\\subset \\mathbf{C}$", "solution": "", "duration": -1, "usages": [ @@ -52322,7 +52322,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [ @@ -52348,7 +52348,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $m=2$或$3$; (2) $m$的取值范围为$\\{m|m\\in \\mathbf{R}, m\\not\\in \\{-5,2,3,5\\}\\}$; (3) 不存在; (4) $m=3$", "solution": "", "duration": -1, "usages": [ @@ -52389,7 +52389,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 15+\\dfrac{37}{5}\\mathrm{i}$; (2) $\\dfrac 15-\\dfrac{37}5\\mathrm{i}$", "solution": "", "duration": -1, "usages": [ @@ -52486,7 +52486,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -52565,7 +52565,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$k=-6$", "solution": "", "duration": -1, "usages": [ @@ -52595,7 +52595,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-1,1)$; (2) 证明略", "solution": "", "duration": -1, "usages": [ @@ -52658,7 +52658,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$或$-2+12\\mathrm{i}$或$2-8\\mathrm{i}$", "solution": "", "duration": -1, "usages": [ @@ -52710,7 +52710,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "二", "solution": "", "duration": -1, "usages": [ @@ -52815,7 +52815,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{-2,0\\}$", "solution": "", "duration": -1, "usages": [ @@ -52841,7 +52841,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$40$", "solution": "", "duration": -1, "usages": [ @@ -52870,7 +52870,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -52923,7 +52923,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1+\\dfrac{14}5\\mathrm{i}$", "solution": "", "duration": -1, "usages": [ @@ -53061,7 +53061,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -53090,7 +53090,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -53260,7 +53260,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -53899,7 +53899,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$2+\\mathrm{i}$与$-2-\\mathrm{i}$", "solution": "", "duration": -1, "usages": [ @@ -54606,7 +54606,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -54633,7 +54633,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 52$或$-2$", "solution": "", "duration": -1, "usages": [ @@ -54684,7 +54684,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [ @@ -80608,7 +80608,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-5$", "solution": "", "duration": -1, "usages": [ @@ -80644,7 +80644,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -80680,7 +80680,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -80877,7 +80877,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-4,4]$", "solution": "", "duration": -1, "usages": [ @@ -81011,7 +81011,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "最大值为$\\dfrac 52$, 最小值为$\\sqrt{6}$", "solution": "", "duration": -1, "usages": [ @@ -81068,7 +81068,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 3$", "solution": "", "duration": -1, "usages": [ @@ -81106,7 +81106,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$f(x)=2\\sin(\\dfrac 23 x+\\dfrac \\pi 9)$", "solution": "", "duration": -1, "usages": [ @@ -81142,7 +81142,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -81238,7 +81238,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$k\\pi \\ (k\\in \\mathbf{Z})$", "solution": "", "duration": -1, "usages": [ @@ -81275,7 +81275,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-1,0]$", "solution": "", "duration": -1, "usages": [ @@ -81430,7 +81430,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac{k\\pi}4,0) \\ (k\\in \\mathbf{Z})$", "solution": "", "duration": -1, "usages": [ @@ -81503,7 +81503,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -81601,7 +81601,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "$a$的取值范围为$(-5,4)\\cup (4,5)$. 当$a\\in (-5,4)$时, $\\alpha+\\beta=\\pi-2\\arccos \\dfrac 35$; 当$a\\in (-5,4)$时, $\\alpha+\\beta=3\\pi-\\arccos \\dfrac 35$", "solution": "", "duration": -1, "usages": [ @@ -81639,7 +81639,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "最小正周期为$\\pi$, 值域为$[-2,2]$, 递增区间为$[0,\\dfrac\\pi 3]$和$[\\dfrac{5\\pi}6,\\pi]$", "solution": "", "duration": -1, "usages": [ @@ -84991,7 +84991,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -85028,7 +85028,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -85087,7 +85087,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{\\sqrt{19}}{19}\\overrightarrow{a}+\\dfrac{\\sqrt{19}}{19}\\overrightarrow{b}$, $\\sqrt{7}$", "solution": "", "duration": -1, "usages": [ @@ -85123,7 +85123,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$[1,17]$", "solution": "", "duration": -1, "usages": [ @@ -85158,7 +85158,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -85287,7 +85287,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 23 \\overrightarrow{a}+\\dfrac 13\\overrightarrow{b}$", "solution": "", "duration": -1, "usages": [ @@ -85392,7 +85392,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac\\pi 6$; (2) $4$", "solution": "", "duration": -1, "usages": [ @@ -85453,7 +85453,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac{\\sqrt{2}}2,\\dfrac{\\sqrt{2}}2)$", "solution": "", "duration": -1, "usages": [ @@ -85512,7 +85512,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -85548,7 +85548,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$或$-1$", "solution": "", "duration": -1, "usages": [ @@ -85586,7 +85586,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac 65,\\dfrac{12}5)$", "solution": "", "duration": -1, "usages": [ @@ -85811,7 +85811,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$[0,1+\\sqrt{2}]$", "solution": "", "duration": -1, "usages": [ @@ -85943,7 +85943,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -88978,7 +88978,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1-4\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -89051,7 +89051,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -89125,7 +89125,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) 真; (2) 假, $z=0$; (3) 真; (4) 假, $1+\\sqrt{3}\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -89174,7 +89174,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\sqrt{10}$", "solution": "", "duration": -1, "usages": [ @@ -89288,7 +89288,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2$", "solution": "", "duration": -1, "usages": [], @@ -89363,7 +89363,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $|z|=2$; (2) $(-4,4)$; (3) $2\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -89408,7 +89408,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -89431,7 +89431,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -89456,7 +89456,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 2$", "solution": "", "duration": -1, "usages": [], @@ -89479,7 +89479,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2+\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -89494,7 +89494,7 @@ }, "003523": { "id": "003523", - "content": "设$z=a+b\\mathrm{i}$($a,b\\in\\mathbf{R}$), 则$\\mathrm{i}\\cdot \\overline{z}$所表示的点、关于直线$y=x$对称的点的复数表示为\\blank{50}.", + "content": "设$z=a+b\\mathrm{i}$($a,b\\in\\mathbf{R}$), 则$\\mathrm{i}\\cdot \\overline{z}$所表示的点关于直线$y=x$对称的点的复数表示为\\blank{50}.", "objs": [ "K0511005B", "K0512005B", @@ -89504,7 +89504,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$a+b\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -89527,7 +89527,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) 直线$y=0$; (2) 圆$(x+1)^2+y^2=1$; (3) 椭圆$\\dfrac{x^2}{36}+\\dfrac{y^2}{11}=1$; (4) 线段$y=0 \\ (x\\in [-1,1])$; (5) 双曲线的一支: $y^2-\\dfrac{x^2}{3}=1 \\ (y<0)$", "solution": "", "duration": -1, "usages": [], @@ -89618,7 +89618,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "以$(-3,7)$为圆心, $12$为半径的圆", "solution": "", "duration": -1, "usages": [], @@ -89758,7 +89758,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[4\\sqrt{2}-2,4\\sqrt{2}+2]$; (2) $(3+\\sqrt{2})-(4+\\sqrt{2})\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -89782,7 +89782,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "以$(1,0)$为圆心, $\\dfrac 12$为半径的圆", "solution": "", "duration": -1, "usages": [], @@ -89854,7 +89854,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -89968,7 +89968,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{5}", "solution": "", "duration": -1, "usages": [], @@ -90014,7 +90014,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$p=12$, $q=26$", "solution": "", "duration": -1, "usages": [], @@ -90158,7 +90158,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [], @@ -90185,7 +90185,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-\\dfrac 14$或$\\dfrac{17}{4}$; (2) $-\\dfrac 14$或$\\dfrac 94$", "solution": "", "duration": -1, "usages": [], @@ -91940,7 +91940,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\omega = \\dfrac 12$; (2) $[-\\dfrac 12,0]$", "solution": "", "duration": -1, "usages": [ @@ -94999,7 +94999,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "不存在推出关系, 因为$P$成立当且仅当$a\\in (-2\\sqrt{2},2\\sqrt{2})$, $Q$成立当且仅当$a\\in [-3,-1]\\cup [1,3]$, $a=0$时$P$成立但$Q$不成立, $a=3$时$Q$成立但$P$不成立", "solution": "", "duration": -1, "usages": [], @@ -102287,7 +102287,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{2,3,4\\}$", "solution": "", "duration": -1, "usages": [ @@ -102594,7 +102594,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{2\\}$", "solution": "", "duration": -1, "usages": [ @@ -103380,7 +103380,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 14$", "solution": "", "duration": -1, "usages": [ @@ -104292,7 +104292,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -104562,7 +104562,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -105940,7 +105940,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $0$; (2) $(-\\infty,-\\dfrac 12]\\cup [\\dfrac 72,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -106515,7 +106515,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[-2,+\\infty)$; (2) 具有性质$P$; (3) 证明略", "solution": "", "duration": -1, "usages": [ @@ -106550,7 +106550,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 43$", "solution": "", "duration": -1, "usages": [ @@ -107256,7 +107256,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -108168,7 +108168,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,0)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -108391,7 +108391,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[0,1]$", "solution": "", "duration": -1, "usages": [ @@ -108449,7 +108449,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{7\\pi}{11}$", "solution": "", "duration": -1, "usages": [ @@ -108606,7 +108606,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 年存储成本费为$68000$元; (2) 每次订购$500$吨甲醇, 可使化工厂年存储成本费最少, 最少费用为$60000$元", "solution": "", "duration": -1, "usages": [ @@ -109294,7 +109294,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1)\\cup (1,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -109383,7 +109383,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\dfrac 12,4)$", "solution": "", "duration": -1, "usages": [ @@ -109679,7 +109679,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(0,1]$; (2) $(0,81]$", "solution": "", "duration": -1, "usages": [ @@ -110468,7 +110468,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -111491,7 +111491,7 @@ "第二单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -111599,7 +111599,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $7$; (2) $\\dfrac{2\\sqrt{3}}3$; (3) $(0,\\dfrac 2{27}]$", "solution": "", "duration": -1, "usages": [ @@ -111798,7 +111798,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 18$", "solution": "", "duration": -1, "usages": [ @@ -114495,7 +114495,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$-2$", "solution": "", "duration": -1, "usages": [ @@ -146678,7 +146678,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{27}2$", "solution": "", "duration": -1, "usages": [ @@ -147942,7 +147942,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\pm \\dfrac{\\sqrt{2}}2$", "solution": "", "duration": -1, "usages": [ @@ -150533,7 +150533,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -150569,7 +150569,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -151302,7 +151302,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [ @@ -151338,7 +151338,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 证明略; (3) $a$是一个周期, 证明略", "solution": "", "duration": -1, "usages": [ @@ -154281,7 +154281,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -156916,7 +156916,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -178061,7 +178061,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "$3+2\\mathrm{i}$与$-3-2\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -178084,7 +178084,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "解为$\\dfrac{\\sqrt{2}}2+\\dfrac{\\sqrt{2}}2\\mathrm{i}$与$-\\dfrac{\\sqrt{2}}2-\\dfrac{\\sqrt{2}}2\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -196150,7 +196150,7 @@ "第三单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -201571,7 +201571,7 @@ }, "008337": { "id": "008337", - "content": "作出$y=2\\sin (x-\\dfrac{\\pi}4)+1$在区间$[-\\pi ,\\pi]$上的图像, 并写出它的振幅、周期、频率、初相、单调区间及值域.", + "content": "作出$y=2\\sin (x-\\dfrac{\\pi}4)+1$, $x\\in [-\\pi ,\\pi]$的图像, 并写出它的振幅、周期、频率、初相、单调区间及值域.", "objs": [ "K0323003B" ], @@ -201579,7 +201579,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -pi:pi,samples = 200] plot (\\x,{2*sin(\\x/pi*180-45)+1});\n\\draw [dashed] (0,-1) -- (-pi/4,-1) -- (-pi/4,0) (-pi,0) -- (-pi,{1+sqrt(2)}) (3*pi/4,0) -- (3*pi/4,3) -- (0,3) (pi,0) -- (pi,{1+sqrt(2)});\n\\draw (0,-1) node [right] {$-1$} (-pi/4,0) node [above] {$-\\dfrac \\pi 4$} (-pi,0) node [below] {$-\\pi$} (pi,0) node [below] {$\\pi$} (3*pi/4,0) node [below] {$\\dfrac {3\\pi}4$} (0,3) node [left] {$3$};\n\\end{tikzpicture}\n振幅: $2$; 周期: $2\\pi$; 频率: $\\dfrac 1{2\\pi}$; 初相: $-\\dfrac\\pi 4$; 单调区间: $[-\\dfrac \\pi 4,\\dfrac{3\\pi}{4}]$(严格增), $[-\\pi,-\\dfrac \\pi 4]$(严格减), $[\\dfrac{3\\pi}4,\\pi]$(严格减); 值域: $[-1,3]$", "solution": "", "duration": -1, "usages": [ @@ -216919,7 +216919,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(x+\\sqrt{5}\\mathrm{i}y)(x-\\sqrt{5}\\mathrm{i}y)$; (2) $2(x-\\dfrac{3+\\mathrm{i}}2)(x-\\dfrac{3-\\mathrm{i}}2)$", "solution": "", "duration": -1, "usages": [], @@ -221114,7 +221114,7 @@ }, "009227": { "id": "009227", - "content": "选择题:\n如果一个三棱锥的底面是直角三角形, 那么这个三棱锥的三个侧面\\bracket{20}\n\\twoch{都不是直角三角形}{至多只能有一个是直角三角形}{至多只能有两个是直角三角形}{可能都是直角三角形}", + "content": "如果一个三棱锥的底面是直角三角形, 那么这个三棱锥的三个侧面\\bracket{20}\n\\twoch{都不是直角三角形}{至多只能有一个是直角三角形}{至多只能有两个是直角三角形}{可能都是直角三角形}", "objs": [ "K0618004B" ], @@ -229405,7 +229405,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "如$760\\text{ms}$等", "solution": "", "duration": -1, "usages": [ @@ -229735,7 +229735,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "定义域为$\\{x|x\\ne \\dfrac \\pi{12}+\\dfrac{k\\pi}3, \\ k\\in \\mathbf{Z}\\}$; 单调区间为$(\\dfrac\\pi{12}+\\dfrac{k\\pi}3,\\dfrac{5\\pi}{12}+\\dfrac{k\\pi}3) \\ (k\\in \\mathbf{Z})$, 在这些区间上是严格增函数", "solution": "", "duration": -1, "usages": [ @@ -288442,7 +288442,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\arccos \\dfrac 5{13}$", "solution": "", "duration": -1, "usages": [ @@ -288480,7 +288480,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{\\sqrt{3}}2$", "solution": "", "duration": -1, "usages": [ @@ -290991,7 +290991,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{9\\sqrt{10}}{50}$", "solution": "", "duration": -1, "usages": [ @@ -291028,7 +291028,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$y=2\\cos(\\dfrac x2+\\dfrac{5\\pi}3)$", "solution": "", "duration": -1, "usages": [ @@ -291063,7 +291063,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $h(x)=\\begin{cases}\\dfrac{x^2}{x-1}, & x\\ne 1,\\\\ 1, & x=1;\\end{cases}$ (2) $(-\\infty,0]\\cup \\{1\\}\\cup [4,+\\infty)$; (3) 答案不唯一, 如$f(x)=\\cos 2x+\\sin 2x$, $\\alpha=\\dfrac\\pi 4$等", "solution": "", "duration": -1, "usages": [ @@ -291100,7 +291100,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\cos\\alpha$", "solution": "", "duration": -1, "usages": [ @@ -291233,7 +291233,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$8\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -291260,7 +291260,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $-1\\pm \\dfrac{\\sqrt{2}}2\\mathrm{i}$; (2) $2(x+1+\\dfrac{\\sqrt{2}}2\\mathrm{i})(x+1-\\dfrac{\\sqrt{2}}2\\mathrm{i})$", "solution": "", "duration": -1, "usages": [], @@ -291482,7 +291482,7 @@ }, "030120": { "id": "030120", - "content": "判断下列命题是否正确, 正确的在横线上画``$\\checkmark$'', 错误的画``$\\times$''.\\\\\n\\blank{30}(1) 侧棱垂直于底面的棱柱一定是直棱柱;\\\\\n\\blank{30}(2) 底面是正多边形的棱柱一定是正棱柱;\\\\\n\\blank{30}(3) 棱柱的侧面都是平行四边形;\\\\\n\\blank{30}(4) 斜柱的侧面都不可能是矩形.", + "content": "判断下列命题是否正确, 正确的在横线上画``$\\checkmark$'', 错误的画``$\\times$''.\\\\\n\\blank{30}(1) 侧棱垂直于底面的棱柱一定是直棱柱;\\\\\n\\blank{30}(2) 底面是正多边形的棱柱一定是正棱柱;\\\\\n\\blank{30}(3) 棱柱的侧面都是平行四边形;\\\\\n\\blank{30}(4) 斜棱柱的侧面都不可能是矩形.", "objs": [ "K0615002B", "K0615004B" @@ -291716,7 +291716,7 @@ }, "030131": { "id": "030131", - "content": "判断下列命题是否正确, 正确的在横线上画``$\\checkmark$'', 错误的画``$\\times$''.\\\\\n\\blank{30}(1) 球面上任意一点与球心的连线都是球的半径;\\\\\n\\blank{30}(2) 球面上任意两点连成的线段都是球的直径;\\\\\n\\blank{30}(3) 用一个球面截一个球, 得到的截面是一个圆面.", + "content": "判断下列命题是否正确, 正确的在横线上画``$\\checkmark$'', 错误的画``$\\times$''.\\\\\n\\blank{30}(1) 球面上任意一点与球心的连线都是球的半径;\\\\\n\\blank{30}(2) 球面上任意两点连成的线段都是球的直径;\\\\\n\\blank{30}(3) 用一个平面截一个球, 得到的截面是一个圆面.", "objs": [ "K0622001B", "K0622003B"