From c09336e727490bd031dcf1ee8f4dc22a3109531f Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sat, 7 Jan 2023 23:29:26 +0800 Subject: [PATCH] 20230107 evening --- 工具/修改题目数据库.ipynb | 6 +- 工具/关键字筛选题号.ipynb | 6 +- 工具/寻找阶段末尾空闲题号.ipynb | 4 +- 工具/批量添加题库字段数据.ipynb | 146 +- 工具/批量题号选题pdf生成.ipynb | 8 +- 工具/文本文件/metadata.txt | 311 +- 工具/文本文件/题号筛选.txt | 2 +- 工具/添加题目到数据库.ipynb | 12 +- 工具/题号选题pdf生成.ipynb | 10 +- 文本处理工具/剪贴板文本整理_word文件.ipynb | 4 + 题库0.3/LessonObj.json | 2 +- 题库0.3/Problems.json | 5043 +++++++++++++++++++- 12 files changed, 5313 insertions(+), 241 deletions(-) diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb index c667fe72..46ae1d54 100644 --- a/工具/修改题目数据库.ipynb +++ b/工具/修改题目数据库.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 5, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" } @@ -19,7 +19,7 @@ "source": [ "import os,re,json\n", "\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n", - "problems = \"12266:12280\"\n", + "problems = \"30524\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", 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 3a2c11c1..e0b3726a 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": 1, + "execution_count": 27, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 1, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -21,7 +21,7 @@ "\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", - " {\"origin\":[\"普陀\"],\"origin2\":[\"2023\"]}\n", + " {\"usages\":[r\"2023届高三02班\"],\"usages2\":[r\"202209\",r\"20221[012]\"],\"usages3\":[r\"0\\.[678][\\d]{2}\"],\"usages_not\":[r\"2023届高三02班[^\\n]*0\\.[0-59][\\d]{2}\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index cb56a220..f0dce079 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "text": [ "首个空闲id: 12739 , 直至 020000\n", "首个空闲id: 21441 , 直至 030000\n", - "首个空闲id: 30553 , 直至 999999\n" + "首个空闲id: 30757 , 直至 999999\n" ] } ], 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 a0a045c4..543c7f62 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 @@ -2,76 +2,94 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 030534 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030535 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030536 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030537 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030538 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030539 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030540 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030541 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030542 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030543 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030544 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030545 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030546 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030547 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030548 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030549 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030550 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030551 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030552 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 030553 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030554 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030555 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030556 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030557 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030558 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030559 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030560 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030561 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030562 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030563 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030564 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030565 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030566 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030567 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030568 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030569 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030570 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030571 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030572 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030573 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030574 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030575 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030576 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030577 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030578 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030579 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030580 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030581 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030582 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030583 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030584 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030585 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030586 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030587 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030588 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030589 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030590 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030591 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030592 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030593 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030594 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030595 , 字段: tags 中已添加数据: 第九单元\n", - "题号: 030596 , 字段: tags 中已添加数据: 第九单元\n" + "题号: 030757 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030758 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030759 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030760 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030761 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030762 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030763 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030764 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030765 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030766 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030767 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030768 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030769 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030770 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030771 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030772 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030773 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030774 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030775 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030776 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030777 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030778 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030779 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030780 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030781 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030782 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030783 , 字段: tags 中已添加数据: a\n", + "题号: 030783 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030784 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030785 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030786 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030787 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030788 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030789 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030790 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030791 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030792 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030793 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030794 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030795 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030796 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030797 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030798 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030799 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030800 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030801 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030802 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030803 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030804 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030805 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030806 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030807 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030808 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030809 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030810 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030811 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030812 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030813 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030814 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030815 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030816 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030817 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030818 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030819 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030820 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030821 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030822 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030823 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030824 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030825 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030826 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030827 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030828 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030829 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030830 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030831 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030832 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030833 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030834 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030835 , 字段: tags 中已添加数据: 第三单元\n", + "题号: 030836 , 字段: tags 中已添加数据: 第三单元\n" ] } ], diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb index 76929772..081c397a 100644 --- a/工具/批量题号选题pdf生成.ipynb +++ b/工具/批量题号选题pdf生成.ipynb @@ -27,11 +27,11 @@ "#字典字段为文件名, 之后为内容的题号\n", "problems_dict = {\n", "\"7.3.3-正态分布-done\":\"30515,30516,10903,30519,30534,30517,30518,30520,30535,30538,30540,30552\",\n", - "\"8.1.1-成对数据间的关系\":\"30521,30522,30523,30524,30554,30555\",\n", - "\"8.1.2-相关系数\":\"10905,10906,10908,30525,30526,30558,30559,30560,30561,30562,30591\",\n", - "\"8.2.1-一元线性回归分析的基本思想\":\"10911,10912,10914,30527,30528,30567,30568,30573\",\n", + "\"8.1.1-成对数据间的关系-done\":\"030554,030521,030522,030523,030524\",\n", + "\"8.1.2-相关系数-done\":\"10905,10906,10908,30525,30526,30591\",\n", + "\"8.2.1-一元线性回归分析的基本思想-done\":\"30527,30528,30567,10911,10912,30573\",\n", "\"8.2.2-一元线性回归分析的应用举例\":\"10913,10915,10916,10917,10918,30529,30570\",\n", - "\"8.3.1-2乘2列联表独立性检验\":\"10920,10922,30530,30531,30532,30578,30579,30580,30593\",\n", + "\"8.3.1-2乘2列联表独立性检验-done\":\"10920,10922,30530,30531,30532,30578,30579,30580,30593\",\n", "\"8.3.2-独立性检验的具体应用\":\"10919,10921,30533,30582,30583,30588,30596\"\n", "\n", "}\n", diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 3e396190..9a99b1df 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,317 +1,326 @@ tags -30534 -第八单元 -30535 -第八单元 +30757 +第三单元 -30536 -第八单元 +30758 +第三单元 +30759 +第三单元 -30537 -第八单元 +30760 +第三单元 -30538 -第八单元 +30761 +第三单元 +30762 +第三单元 -30539 -第八单元 +30763 +第三单元 -30540 -第八单元 +30764 +第三单元 +30765 +第三单元 -30541 -第八单元 +30766 +第三单元 -30542 -第八单元 +30767 +第三单元 +30768 +第三单元 -30543 -第八单元 +30769 +第三单元 -30544 -第八单元 +30770 +第三单元 +30771 +第三单元 -30545 -第八单元 +30772 +第三单元 -30546 -第八单元 +30773 +第三单元 +30774 +第三单元 -30547 -第八单元 +30775 +第三单元 -30548 -第八单元 +30776 +第三单元 +30777 +第三单元 -30549 -第八单元 +30778 +第三单元 -30550 -第八单元 +30779 +第三单元 +30780 +第三单元 -30551 -第八单元 +30781 +第三单元 -30552 -第八单元 +30782 +第三单元 +30783a +第三单元 -30553 -第九单元 +30784 +第三单元 -30554 -第九单元 +30785 +第三单元 +30786 +第三单元 -30555 -第九单元 +30787 +第三单元 -30556 -第九单元 +30788 +第三单元 +30789 +第三单元 -30557 -第九单元 +30790 +第三单元 -30558 -第九单元 +30791 +第三单元 +30792 +第三单元 -30559 -第九单元 +30793 +第三单元 -30560 -第九单元 +30794 +第三单元 +30795 +第三单元 -30561 -第九单元 +30796 +第三单元 -30562 -第九单元 +30797 +第三单元 +30798 +第三单元 -30563 -第九单元 +30799 +第三单元 -30564 -第九单元 +30800 +第三单元 +30801 +第三单元 -30565 -第九单元 +30802 +第三单元 -30566 -第九单元 +30803 +第三单元 +30804 +第三单元 -30567 -第九单元 +30805 +第三单元 -30568 -第九单元 +30806 +第三单元 +30807 +第三单元 -30569 -第九单元 +30808 +第三单元 -30570 -第九单元 +30809 +第三单元 +30810 +第三单元 -30571 -第九单元 +30811 +第三单元 -30572 -第九单元 +30812 +第三单元 +30813 +第三单元 -30573 -第九单元 +30814 +第三单元 -30574 -第九单元 +30815 +第三单元 +30816 +第三单元 -30575 -第九单元 +30817 +第三单元 -30576 -第九单元 +30818 +第三单元 +30819 +第三单元 -30577 -第九单元 +30820 +第三单元 -30578 -第九单元 +30821 +第三单元 +30822 +第三单元 -30579 -第九单元 +30823 +第三单元 -30580 -第九单元 +30824 +第三单元 +30825 +第三单元 -30581 -第九单元 +30826 +第三单元 -30582 -第九单元 +30827 +第三单元 +30828 +第三单元 -30583 -第九单元 +30829 +第三单元 -30584 -第九单元 +30830 +第三单元 +30831 +第三单元 -30585 -第九单元 +30832 +第三单元 -30586 -第九单元 +30833 +第三单元 +30834 +第三单元 -30587 -第九单元 +30835 +第三单元 -30588 -第九单元 - - - -30589 -第九单元 - - - -30590 -第九单元 - - - -30591 -第九单元 - - - -30592 -第九单元 - - - -30593 -第九单元 - - - -30594 -第九单元 - - - -30595 -第九单元 - - - -30596 -第九单元 - +30836 +第三单元 diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index 97a5b55a..1b338e02 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1 +1 @@ -012592,012593,012594,012595,012596,012597,012598,012599,012600,012601,012602,012603,012604,012605,012606,012607,012608,012609,012610,012611,012612 \ No newline at end of file +000023,000035,000060,000069,000087,000092,000141,000182,000230,000233,000312,000322,000360,000413,000474,000540,000655,000704,000749,000778,000795,000863,000884,000908,000939,001049,001050,001069,001072,001074,001231,001239,001242,001244,001262,001308,001309,001316,001324,001325,001328,001340,001351,001352,001353,001631,001643,001667,001668,001677,001726,001803,001853,001894,002004,002010,002017,002088,002273,002369,002372,002417,002424,002429,002434,002662,002750,002773,002775,002778,002785,002790,002791,002794,002838,002863,002871,002878,002884,002888,002893,002894,002895,002898,002905,002911,002914,002918,002966,002994,003138,003253,003281,003309,003312,003322,003337,003400,003421,003431,003567,003585,003648,003747,003777,003781,003828,003884,003959,003985,004008,004243,004409,004448,004463,004636,005016,005236,005239,005463,005508,005569,005621,005650,005720,005851,006468,006968,007911,007939,007941,007950,008392,008811,008912,008956,009200,009333,009349,009488,009490,009511,009517,009744,009858,009860,009887,009912,010060,010114,010178,010196,010453,010470,010523,010540,010631,010721,010947,011057,011078,011100,011993,012004,012015,030030,030096,030160,030202,030215,030253,030262,030280,030291,030322,030337,030398,030427,030438,030441,030462,030468,030478 \ No newline at end of file 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 ee3eab6f..a036c0b8 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 @@ -2,20 +2,20 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 30553\n", - "origin = \"人教A版成对数据的统计分析习题\"\n", - "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目.tex\"\n", - "editor = \"20230104\\t王伟叶\"" + "starting_id = 30757\n", + "origin = \"\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", + "editor = \"20230107\\t王伟叶\"" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ 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 31184f02..cdc7e21c 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": 1, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/新_教师用_20230104.tex\n", + "开始编译教师版本pdf文件: 临时文件/中档题_ver2_教师用_20230107.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/新_学生用_20230104.tex\n", + "开始编译学生版本pdf文件: 临时文件/中档题_ver2_学生用_20230107.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", - "30534:40000\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/新\"\n", + "filename = \"临时文件/中档题_ver2\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", diff --git a/文本处理工具/剪贴板文本整理_word文件.ipynb b/文本处理工具/剪贴板文本整理_word文件.ipynb index 33e085ac..819743fc 100644 --- a/文本处理工具/剪贴板文本整理_word文件.ipynb +++ b/文本处理工具/剪贴板文本整理_word文件.ipynb @@ -495,6 +495,10 @@ "modified_data = re.sub(r\"_\\{\\\\dfrac\",r\"^{_{\\\\frac\",modified_data)\n", "modified_data = re.sub(r\"_\\{-\\\\dfrac\",r\"^{_{-\\\\frac\",modified_data)\n", "\n", + "\n", + "modified_data = re.sub(r\"\\\\begin\\{array\\}[rcl]*\",r\"\\\\begin{cases}\",modified_data)\n", + "modified_data = re.sub(r\"\\\\end{array}\",r\"\\\\end{cases}\",modified_data)\n", + "\n", "setCopy(modified_data)\n", "\n", "with open(\"临时文件/outputfile.txt\",\"w\",encoding = \"utf8\") as f:\n", diff --git a/题库0.3/LessonObj.json b/题库0.3/LessonObj.json index 50edab38..2f89aca4 100644 --- a/题库0.3/LessonObj.json +++ b/题库0.3/LessonObj.json @@ -4412,7 +4412,7 @@ "K0909002X": { "id": "K0909002X", "unit_obj": "D09006X", - "content": "了解拟合误差的概念和公式, 能够根据所给数据计算离差, 知道拟合误差是描述数据与函数贴合程度的指标." + "content": "了解拟合误差的概念和公式, 能够根据所给数据计算拟合误差, 知道拟合误差是描述数据与函数贴合程度的指标." }, "K0909003X": { "id": "K0909003X", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 3f5ee56e..225515bf 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -359917,7 +359917,7 @@ }, "030524": { "id": "030524", - "content": "某地区的环境条件适合天鹅栖息繁衍. 有人发现了一个有趣的现象, 该地区有 5 个村庄, 其中 3 个村庄附近栖息的天鹅较多, 婴儿出生率也较高; 2 个村庄附近栖息的天鹅较少, 婴儿出生率也较低. 有人认为婴儿出生率和天㧴数之间存在相关关系, 并得出一个结论: 天鹅能够带来孩子. 你同意这个结论吗?", + "content": "某地区的环境条件适合天鹅栖息繁衍. 有人发现了一个有趣的现象, 该地区有 5 个村庄, 其中 3 个村庄附近栖息的天鹅较多, 婴儿出生率也较高; 2 个村庄附近栖息的天鹅较少, 婴儿出生率也较低. 有人认为婴儿出生率和天鹅数之间存在相关关系, 并得出一个结论: 天鹅能够带来孩子. 你同意这个结论吗?", "objs": [], "tags": [ "第九单元" @@ -361447,5 +361447,5046 @@ "related": [], "remark": "", "space": "12ex" + }, + "030597": { + "id": "030597", + "content": "已知集合$A=\\{-1,3,0\\}$, $B=\\{3, m^2\\}$, 若$B \\subseteq A$, 则实数$m$的值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山二模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030598": { + "id": "030598", + "content": "已知集合$A=\\{1,2,3\\}$, $B=\\{3,4,5\\}$, 则$A \\cup B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤二模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030599": { + "id": "030599", + "content": "若全集$U=\\{1,2,3\\}$, 集合$A=\\{2,3\\}$, 则$\\overline A=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦二模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030600": { + "id": "030600", + "content": "设全集$U=\\{x | x^3-x=0\\}$, 集合$A=\\{0,1\\}$, 则$\\overline A=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行二模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030601": { + "id": "030601", + "content": "已知集合$A=\\{1,2\\}$, $B=\\{a, 3\\}$, 若$A \\cap B=\\{1\\}$, 则$A \\cup B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明一模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030602": { + "id": "030602", + "content": "若全集$U=\\{1,2,3,4,5,6\\}$, $M=\\{1,3,4\\}$, $N=\\{2,3,4\\}$, 则集合\n$\\overline{M \\cap N}=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030603": { + "id": "030603", + "content": "已知集合$A=\\{x | x \\leq 2\\}$, $B=\\{1,3,5,7\\}$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁一模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030604": { + "id": "030604", + "content": "已知集合$A=\\{-1,0,1,2\\}$, $B=\\{x | 02\\}$, $B=\\{x | x<3\\}$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山一模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030618": { + "id": "030618", + "content": "已知集合$A=[-2,2]$, $B=[0,4]$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安二模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030619": { + "id": "030619", + "content": "已知集合$A=(1,3)$, $B=(2,+\\infty)$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030620": { + "id": "030620", + "content": "已知集合$A=(-1,2)$, $B=[1,+\\infty)$, 则集合$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦二模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030621": { + "id": "030621", + "content": "设集合$A=\\{x | 2 x-3 \\leq 0\\}$, $B=[0,3]$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁二模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030622": { + "id": "030622", + "content": "已知集合$A=\\{x |-10\\}$, $N=\\{x \\|x | \\leq 1\\}$, 则$M \\cup N=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇一模试题01", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030624": { + "id": "030624", + "content": "已知集合$A=\\{m | 1b>0, c>d>0$, 则$\\dfrac{a+c}d>\\dfrac{b+d}c$; \\textcircled{2} 若$a>b>0, c>d>0$, 则$a^c>b^d$. 关于上述命题描述正确的是\\bracket{20}.\n\\twoch{\\textcircled{1}和\\textcircled{2}均为真命题}{\\textcircled{1}和\\textcircled{2}均为假命题}{\\textcircled{1}为真命题, \\textcircled{2}为假命题}{\\textcircled{1}为假命题, \\textcircled{2}为真命题}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤一模试题15", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030626": { + "id": "030626", + "content": "已知$a$、$b \\in \\mathbf{R}$且$a \\cdot b \\neq 0$, 则 ``$a\\dfrac 1b$'' 的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇一模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030627": { + "id": "030627", + "content": "已知$a$、$b \\in \\mathbf{R}$, 则 ``$\\dfrac ba>1$'' 是 ``$b>a$'' 的 \\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山一模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030628": { + "id": "030628", + "content": "``$x>y>0$'' 是 ``$x-\\dfrac 1x>y-\\dfrac 1y$'' 的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀二模试题14", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030629": { + "id": "030629", + "content": "已知$x \\in \\mathbf{R}$, 则 ``$|x|>1$'' 是 ``$x>1$'' 的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定一模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030630": { + "id": "030630", + "content": "``$\\dfrac 1x<1$'' 是 ``$x>1$'' 的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁一模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030631": { + "id": "030631", + "content": "设$\\alpha$: 实数$x$满足$\\dfrac{x-3}{x+1}<0$, $\\beta$: 实数$x$满足$|x-1|<2$, 那么$\\alpha$是$\\beta$的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口一模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030632": { + "id": "030632", + "content": "如果$a<0$, $b>0$, 那么下列不等式中正确的是\\bracket{20}.\n\\twoch{$a^2|b|$}{$\\dfrac 1a<\\dfrac 1b$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明二模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030633": { + "id": "030633", + "content": "下列不等式恒成立的是\\bracket{20}.\n\\twoch{$|x+y|\\geq|x-y|$}{$\\sqrt {x^2+1}+x>0$}{$x+\\dfrac 1x \\geq 2$}{$|x+y|+|x-y|\\leq|x|+|y|$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦二模试题14", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030634": { + "id": "030634", + "content": "下列不等式中, 与不等式$\\dfrac{x+8}{x^2+2 x+3}<2$解集相同的是\\bracket{20}.\n\\twoch{$(x+8)(x^2+2 x+3)<2$}{$x+8<2(x^2+2 x+3)$}{$\\dfrac 1{x^2+2 x+3}<\\dfrac 2{x+8}$}{$\\dfrac{x^2+2 x+3}{x+8}>\\dfrac 12$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦一模试题15", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030635": { + "id": "030635", + "content": "若命题: ``存在整数$x$使不等式$(k x-k^2-1)(x-2)<0$成立'' 是假命题, 则实数$k$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦二模试题10", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030636": { + "id": "030636", + "content": "设集合$P_1=\\{x | x^2+a x+1>0\\}$, $P_2=\\{x | x^2+a x+2>0\\}$, $Q_1=\\{x | x^2+x+b>0\\}$, $Q_2=\\{x | x^2+2 x+b>0\\}$, 其中$a$、$b \\in \\mathbf{R}$, 给出下列两个命题: 命题$q_1$: 对任意的$a, P_1$是$P_2$的子集; 命题$q_2$: 对任意的$b, Q_1$不是$Q_2$的子集. 下列说法正确的是\\bracket{20}.\n\\twoch{命题$q_1$是真命题, 命题$q_2$是假命题}{命题$q_1$是假命题, 命题$q_2$是真命题}{命题$q_1$、$q_2$都是真命题}{命题$q_1$、$q_2$都是假命题}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明二模试题16", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030637": { + "id": "030637", + "content": "不等式$\\dfrac{x-1}{x+2}<0$的解为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030638": { + "id": "030638", + "content": "不等式$\\dfrac 1{x-1}<1$的解集是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030639": { + "id": "030639", + "content": "不等式$\\dfrac 1{x+1}>1$的解集为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀一模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030640": { + "id": "030640", + "content": "不等式$\\dfrac{2-3 x}{x-1}>0$的解集为\\bracket{20}.\n\\fourch{$(-\\infty, \\dfrac 34)$}{$(-\\infty, \\dfrac 23)$}{$(-\\infty, \\dfrac 23) \\cup(1,+\\infty)$}{$(\\dfrac 23, 1)$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明一模试题14", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030641": { + "id": "030641", + "content": "已知函数$f(x)$满足:$f(x)=\\begin{cases}\\dfrac x{x+1}, & x \\geq 0 \\\\-f(-x), & x<0,\\end{cases}$ 则不等式$f(x)+\\dfrac 12 \\geq 0$的解集为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁二模试题10", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030642": { + "id": "030642", + "content": "不等式$|x-1|<1$的解集为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦一模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030643": { + "id": "030643", + "content": "不等式$2^x-5<0$的解集为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行二模试题02", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030644": { + "id": "030644", + "content": "``$\\log_2 a>\\log_2 b$'' 是 ``$a>b$'' 的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东二模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030645": { + "id": "030645", + "content": "``$\\log_2(x+1)<0$'' 成立的一个必要而不充分条件是\\bracket{20}.\n\\fourch{$-10$}{$-10, y>0$, 且$\\dfrac 4x+\\dfrac 1y=1$, 则$4 x+y$的最小值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山一模试题08", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030648": { + "id": "030648", + "content": "已知正实数$a$、$b$满足$a+b+4=2 a b$, 则$a+b$的最小值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江二模试题09", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030649": { + "id": "030649", + "content": "设$x$、$y \\in \\mathbf{R}$, $a>0$, $b>0$, 若$a^x=b^y=3$, $a+2 b=2 \\sqrt 6$, 则$\\dfrac 1x+\\dfrac 1y$的最大值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁一模试题09", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030650": { + "id": "030650", + "content": "已知$a>0, b>0$, 且$\\dfrac 1{a+2}+\\dfrac 2b=\\dfrac 23$, 则$2 a+b$的最小值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江一模试题10", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030651": { + "id": "030651", + "content": "若$a$、$b$均为非零实数, 则不等式$\\dfrac ba+\\dfrac ab \\geq 2$成立的一个充要条件为\\bracket{20}.\n\\fourch{$a b>0$}{$a b \\geq 0$}{$a b<0$}{$a b \\leq 0$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦二模试题13", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030652": { + "id": "030652", + "content": "若$a>0, b>0$, 且$\\dfrac 4a+\\dfrac 1b=1$, 则$a b$的最小值为\\bracket{20}.\n\\fourch{$16$}{$4$}{$\\dfrac 1{16}$}{$\\dfrac 14$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题14", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030653": { + "id": "030653", + "content": "已知实数$x_1$、$y_1$、$x_2$、$y_2$、$x_3$、$y_3$满足$x_1^2+y_1^2=x_2^2+y_2^2=x_3^2+y_3^2=2$, 则$x_1 y_2$、$x_2 y_3$、$x_3 y_1$三个数中, 大于$1$的个数最多是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{$3$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行一模试题15", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030654": { + "id": "030654", + "content": "设$m$、$n \\in \\mathbf{R}$, 定义运算 ``$\\blacktriangle$'' 和 ``$\\blacktriangledown$'' 如下:$m \\blacktriangle n=\\begin{cases}m, & m \\leq n,\\\\n, & m>n,\\end{cases}$ $m \\blacktriangledown n=\\begin{cases}n, & m \\leq n, \\\\m, & m>n.\\end{cases}$ 若正数$m$、$n$、$p$、$q$满足$m n \\geq 4$, $p+q \\leq 4$, 则\\bracket{20}.\n\\twoch{$m \\blacktriangle n \\geq 2$, $p \\blacktriangle q \\leq 2$}{$m \\blacktriangledown n \\geq 2$, $p \\blacktriangledown q \\geq 2$}{$m \\blacktriangle n \\geq 2$, $p \\blacktriangledown q \\geq 2$}{$m \\blacktriangledown n \\geq 2$, $p \\blacktriangle q \\leq 2$}", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山一模试题16", + "edit": [ + "20230106\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030655": { + "id": "030655", + "content": "函数$y=\\log_2(x-1)$的定义域是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山一模试题02", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030656": { + "id": "030656", + "content": "函数$y=\\log_2(1-x^2)$的定义域为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行一模试题01", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030657": { + "id": "030657", + "content": "函数$f(x)=\\ln \\dfrac{2^x-4}{2^x+1}$的定义域是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山一模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030658": { + "id": "030658", + "content": "函数$y=\\lg \\dfrac{3-2^x}{3+2^x}$的定义域是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤一模试题07", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030659": { + "id": "030659", + "content": "函数$f(x)=x+\\dfrac 9x(x>0)$的值域为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口二模试题02", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030660": { + "id": "030660", + "content": "设集合$A=\\{y | y=(\\dfrac 12)^x, \\ x \\in \\mathbf{R}\\}$, 集合$B=\\{y | y=x^{\\frac 12}, \\ x \\geq 0\\}$, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安一模试题02", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030661": { + "id": "030661", + "content": "已知函数$f(x)=x^2+2 x+3+m$, 若$f(x) \\geq 0$对任意的$x \\in[1,2]$恒成立, 则实数$m$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东一模试题09", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030662": { + "id": "030662", + "content": "若函数$f(x)=x(\\sqrt {a^2-x^2}+\\sqrt {1-x^2})$的最大值为 2 , 则由满足条件的实数$a$的值组成的集合是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东二模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030663": { + "id": "030663", + "content": "若函数$f(x)=a \\cdot 3^x+\\dfrac 1{3^x}$为偶函数, 则实数$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇一模试题05", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030664": { + "id": "030664", + "content": "函数$y=x^3+a \\cos x$是奇函数, 则实数$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤一模试题05", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030665": { + "id": "030665", + "content": "若$y=a x^2+x \\ln (\\mathrm{e}^x+1)$是奇函数, 则$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山二模试题07", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030666": { + "id": "030666", + "content": "已知函数$f(x)=\\log_4(4^x+m)-\\dfrac 12 x$的定义域为$\\mathbf{R}$, 且对任意实数$a$, 都满足$f(a) \\geq f(-a)$, 则实数$m=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行二模试题10", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030667": { + "id": "030667", + "content": "函数$y=x^2+|\\lg (x+\\sqrt {x^2+1})|+1$的图像关于\\bracket{20}对称.\n\\fourch{原点}{$x$轴}{$y$轴}{直线$y=x$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安一模试题15", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030668": { + "id": "030668", + "content": "函数$y=f(x)$是定义域为$\\mathbf{R}$的奇函数, 且对于任意的$x_1 \\neq x_2$, 都有$\\dfrac{f(x_1)-f(x_2)}{x_1-x_2}<1$成立. 如果$f(m)>m$, 则实数$m$的取值集合是\\bracket{20}.\n\\fourch{$\\{0\\}$}{$\\{m | m>0\\}$}{$\\{m | m<0\\}$}{$\\mathbf{R}$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口二模试题15", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030669": { + "id": "030669", + "content": "设$a$为常数, 函数$f(x)=\\log_2 \\dfrac{x+1}{x+a}$.\\\\\n(1) 若$a=0$, 求函数$y=f(x)$的反函数$y=f^{-1}(x)$;\\\\\n(2) 若$a \\leq 0$, 根据$a$的不同取值, 讨论函数$y=f(x)$的奇偶性, 并说明理由.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030670": { + "id": "030670", + "content": "已知函数$f(x)=-x^2+2 a x+3$在区间$(-\\infty, 4)$上是增函数, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山一模试题05", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030671": { + "id": "030671", + "content": "下列函数中, 在区间$(0,+\\infty)$上为增函数的是\\bracket{20}.\n\\fourch{$y=(\\dfrac 13)^x$}{$y=\\log_3 x$}{$y=\\dfrac 1x$}{$y=(x-1)^2$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明一模试题13", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030672": { + "id": "030672", + "content": "下列函数中为奇函数且在$\\mathbf{R}$上为增函数的是\\bracket{20}.\n\\fourch{$y=2^x$}{$y=|x|$}{$y=\\sin x$}{$y=x^3$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤一模试题13", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030673": { + "id": "030673", + "content": "下列函数中, 既是偶函数, 又在区间$(0,+\\infty)$上单调递减的函数为\\bracket{20}.\n\\fourch{$y=x^{-2}$}{$y=x^{-1}$}{$y=x^2$}{$y=x^{\\frac 13}$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦一模试题13", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030674": { + "id": "030674", + "content": "下列函数中, 与函数$y=x^3$的奇偶性和单调性都一致的函数是\\bracket{20}.\n\\fourch{$y=x^2$}{$y=x+\\sin x$}{$y=2^{|x|}$}{$y=\\tan x$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江二模试题13", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030675": { + "id": "030675", + "content": "已知函数$f(x)=2^x-(\\dfrac 12)^x$, 则$f(x)$\\bracket{20}.\n\\twoch{是奇函数, 且在$(0,+\\infty)$上是增函数}{是偶函数, 且在$\\mathbf{R}$上是增函数}{是奇函数, 且在$(0,+\\infty)$上是减函数}{是偶函数, 且在$\\mathbf{R}$上是减函数}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山一模试题14", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030676": { + "id": "030676", + "content": "已知函数$f(x)=x^2+a x+1$, $a \\in \\mathbf{R}$.\\\\\n(1) 判断函数$f(x)$的奇偶性, 并说明理由;\\\\\n(2) 若函数$g(x)=\\dfrac{f(x)}x$($x>0$), 写出函数$g(x)$的单调递增区间并用定义证明.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030677": { + "id": "030677", + "content": "已知函数$f(x)=3^x$.\\\\\n(1) 设$y=f^{-1}(x)$是$y=f(x)$的反函数, 若$f^{-1}(x_1 x_2)=1$, 求$f^{-1}(x_1^3)+f^{-1}(x_2^3)$的值;\\\\\n(2) 是否存在常数$m \\in \\mathbf{R}$, 使得函数$g(x)=1+\\dfrac m{f(x)+1}$为奇函数, 若存在, 求$m$的值, 并证明此时$g(x)$在$(-\\infty,+\\infty)$上单调递增, 若不存在, 请说明理由.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030678": { + "id": "030678", + "content": "已知$f(x)$是定义域为$\\mathbf{R}$的奇函数, 且对任意的$x$满足$f(x+2)=f(x)$, 若$0=latex,scale = 0.6]\n\\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2.5:2.5] plot (\\x,{-(2/(1+exp(\\x))-1)*sin(\\x/pi*180)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2.5:2.5] plot (\\x,{(2/(1+exp(\\x))-1)*cos(\\x/pi*180)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2.5:2.5] plot (\\x,{(2/(1+exp(\\x))-1)*sin(\\x/pi*180)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2.5:2.5] plot (\\x,{-(2/(1+exp(\\x))-1)*cos(\\x/pi*180)});\n\\end{tikzpicture}}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇二模试题14", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030690": { + "id": "030690", + "content": "设函数$f(x)=\\begin{cases}-x|x+2 a|, & x<-1,\\\\0.5+\\log_a(x+2), &x \\geq-1\\end{cases}$($a>0$且$a \\neq 1$)在区间$(-\\infty,+\\infty)$上是单调函数, 若函数$g(x)=|f(x)|-|a x-\\dfrac 12|$有三个不同的零点, 则实数$a$的取值范围是\\bracket{20}.\n\\fourch{$(0, \\dfrac 12]$}{$(\\dfrac 18, \\dfrac 14]$}{$(\\dfrac 16, \\dfrac 12]$}{$(\\dfrac 16, \\dfrac 14]$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀一模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030691": { + "id": "030691", + "content": "已知非空集合$A$、$B$满足$A \\cup B=\\mathbf{R}$, $A \\cap B=\\varnothing$, 函数$f(x)=\\begin{cases}x^2,& x \\in A, \\\\2 x-1, & x \\in B,\\end{cases}$ 对于下列两个命题: \\textcircled{1} 存在唯一的非空集合对$(A, B)$, 使得$f(x)$为偶函数; \\textcircled{2} 存在无穷多非空集合对$(A, B)$, 使得方程$f(x)=2$无解. 下面判断正确的是\\bracket{20}.\n\\fourch{\\textcircled{1}正确, \\textcircled{2}错误}{\\textcircled{1}错误, \\textcircled{2}正确}{\\textcircled{1}\\textcircled{2}都正确}{\\textcircled{1}\\textcircled{2}都错误}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦一模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030692": { + "id": "030692", + "content": "已知定义在$\\mathbf{R}$上的偶函数$f(x)$, 满足$[f(x)]^3-[f(x)]^2-x^2 f(x)+x^2=0$对任意的实数$x$都成立, 且值域为$[0,1]$. 设函数$g(x)=|x-m|-|x-1|$($m<1$), 若对任意的$x_1 \\in(-2, \\dfrac 12)$, 存在$x_2>x_1$, 使得$g(x_2)=f(x_1)$成立, 则实数$m$的取值范围为\\bracket{20}.\n\\fourch{$[-6,1)$}{$[-\\dfrac 52,-\\dfrac 12]$}{$[0,1)$}{$[-\\dfrac 12, 0]$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀二模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030693": { + "id": "030693", + "content": "已知$\\alpha \\in\\{-2,-1,-\\dfrac 12, \\dfrac 12, 1,2,3\\}$, 若幂函数$f(x)=x^\\alpha$为奇函数, 且在$(0,+\\infty)$上单调递减, 则$\\alpha=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口一模试题03", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030694": { + "id": "030694", + "content": "已知$\\alpha \\in\\{-2,-1,-\\dfrac 12, \\dfrac 12, 1,2,3\\}$, 若幂函数$f(x)=x^\\alpha$在区间$(-\\infty, 0)$上单调递增, 且其图像不过坐标原点, 则$\\alpha=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦二模试题07", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030695": { + "id": "030695", + "content": "已知$\\alpha \\in\\{-2,-1,-\\dfrac 12, \\dfrac 12, 1,2,3\\}$, 若幂函数$f(x)=x^\\alpha$为奇函数, 且在$(0,+\\infty)$上递减, 则$f(x)$的反函数$f^{-1}(x)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤二模试题08", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030696": { + "id": "030696", + "content": "已知集合$A=\\{-2,-1,-\\dfrac 12, \\dfrac 13, \\dfrac 12, 1,2,3\\}$, 从集合$A$中任取一个元素$a$, 使函数$y=x^a$是奇函数且在$(0,+\\infty)$上递增的概率为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦二模试题08", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030697": { + "id": "030697", + "content": "已知指数函数$y=a^x$(其中$a>1$) 在闭区间$[1,2]$上的最大值比最小值大$\\dfrac a3$, 则实数$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安一模试题03", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030698": { + "id": "030698", + "content": "指数方程$2^{x+3}=3^{x^2-9}$的解为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安二模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030699": { + "id": "030699", + "content": "方程$\\log_2(x+1)+\\log_2(x-1)=1$的解为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东一模试题08", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030700": { + "id": "030700", + "content": "方程$\\log_3(x^2-1)=2+\\log_3(x-1)$的解为$x=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦一模试题08", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030701": { + "id": "030701", + "content": "方程$3^{\\log_2 x}=\\dfrac 19$的解是\\bracket{20}.\n\\fourch{$x=\\dfrac 14$}{$x=\\dfrac{\\sqrt 2}2$}{$x=\\sqrt 2$}{$x=4$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安一模试题13", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030702": { + "id": "030702", + "content": "预测$A$省未来$50$年新能源汽车的保有量, 采用阻滞型模型$x(t)=\\dfrac M{1+(\\dfrac M{x_0}-1) \\mathrm{e}^{-r t}}$, 其中, $t$年后的汽车拥有量为$x(t)$, $r$为年增长率, $M$为饱和量, $x_0$为初始值(单位: 万辆). 已知: $A$省 $2020$年底的新能源汽车拥有量为$16.8$万辆, 以此为初始值, 若以后每年的增长率为$0.115$, 饱和量为$1400$, 那么, $2040$年底, 该省新能源汽车的保有量为\\blank{50}.(精确到$1$万辆)", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山二模试题09", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030703": { + "id": "030703", + "content": "由于疫情防控需要, 某地铁站每天都对站内进行消毒工作, 设在药物释放过程中, 站内空气中的含药量$y$(毫克/每立方米)与时间$x$($0=latex,scale = 1.3]\n\\draw [->] (0,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) -- ({1/3},1);\n\\draw [domain = {1/3}:2] plot (\\x,{pow(9,1/3-\\x)});\n\\draw [dashed] (1/3,0) -- (1/3,1) -- (0,1);\n\\draw ({1/3},0) node [below] {$\\frac 13$};\n\\draw (0,1) node [left] {$1$};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀一模试题10", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030704": { + "id": "030704", + "content": "某地政府决定向当地纳税额在$4$万元至$8$万元(包括$4$万元和$8$万元)的小微企业发放补助款, 发放方案规定: 补助款随企业纳税额的增加而增加, 且补助款不低于纳税额的$50 \\%$. 设企业纳税额为$x$(单位: 万元), 补助款为$f(x)=\\dfrac 14 x^2-b x+b+\\dfrac 12$(单位: 万元), 其中$b$为常数.\\\\\n(1) 分别判断$b=0$, $b=1$时, $f(x)$是否符合发放方案规定, 并说明理由;\\\\\n(2) 若函数$f(x)$符合发放方案规定, 求$b$的取值范围.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030705": { + "id": "030705", + "content": "考虑到高速公路行车安全需要, 一般要求高速公路的车速$v$(公里/小时)控制在$[60,120]$范围内. 已知汽车以$v$公里/小时的速度在高速公路上匀速行驶时, 每小时的油耗(所需要的汽油量)为$\\dfrac 15(v-k+\\dfrac{4500}v)$升, 其中$k$为常数, 不同型号汽车$k$值不同, 且满足$60 \\leq k \\leq 120$.\\\\\n(1) 若某型号汽车以$120$公里/小时的速度行驶时, 每小时的油耗为$11.5$升, 欲使这种型号的汽车每小时的油耗不超过$9$升, 求车速$v$的取值范围;\\\\\n(2) 求不同型号汽车行驶$100$千米的油耗的最小值.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030706": { + "id": "030706", + "content": "某公司经过测算, 计划投资$A$、$B$两个项目. 若投入$A$项目资金$x$(万元), 则一年创造的利润为$\\dfrac x2$(万元); 若投入$B$项目资金$x$(万元), 则一年创造的利润为$f(x)=\\begin{cases}\\dfrac{10 x}{30-x}, & 0 \\leq x \\leq 20, \\\\20, & x>20\\end{cases}$(万元).\\\\\n(1) 当投入$A$、$B$两个项目的资金相同且$B$项目比$A$项目创造的利润高, 求投入$A$项目的资金$x$(万元)的取值范围;\\\\\n(2) 若该公司共有资金$30$万元, 全部用于投资$A$、$B$两个项目, 则该公司一年分别投入$A$、$B$两个项目多少万元, 创造的利润最大.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030707": { + "id": "030707", + "content": "如图所示, 边长为$2$(百米)的正方形$ABCD$区域是某绿地公园的\n一个局部, 环线$AEFCDA$是修建的健身步道(不计宽度), 其中弯道段$EF$是抛物线的一段, 该抛物线的对称轴与$AD$平行, 端点$E$是该抛物线的顶点且为$AB$的中点, 端点$F$在$BC$上, 且$FB$长为$0.5$(百米), 建立适当的平面直角坐标系, 解决下列问题.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A) -- (1,0) node [below] {$E$} coordinate (E) (2,0.5) node [right] {$F$} coordinate (F) -- (2,2) node [right] {$C$} coordinate (C) -- (0,2) node [left] {$D$} coordinate (D) -- (0,0);\n\\draw [dashed] (E) -- (2,0) node [right] {$B$} coordinate (B) -- (F);\n\\draw [domain = 1:2] plot (\\x,{pow(\\x-1,2)/2});\n\\draw (1.4,0.08) node [above = 0.2] {$P$} coordinate (P);\n\\draw (C) -- (P) -- (D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求弯道段$EF$所确定的函数$y=f(x)$的表达式;\\\\\n(2) 绿地管理部门欲在弯道段$EF$上选取一点$P$安装监控设备, 使得点$P$处监测$CD$段的张角($\\angle CPD$)最大, 求点$P$的坐标.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030708": { + "id": "030708", + "content": "如图, 某飞行器研究基地$E$在指挥中心$F$的正北方向$4$千米处; 小镇$A$在$E$的正西方向$8$千米处, 小镇$B$在$F$的正南方向$8$千米处. 已知一新型飞行器在试飞过程中到点$F$和到直线$AE$的距离始终相等, 该飞行器产生一定的噪音污染, 距离该飞行器$1$千米以内(含边界)为$10$级噪音, 每远离飞行器$1$千米, 噪音污染就会减弱$1$级, 直至$0$级为无噪音污染(飞行器的大小及高度均忽略不计).\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.2]\n\\filldraw (0,0) circle (0.15) node [above] {$E$} coordinate (E);\n\\filldraw (0,-2) circle (0.15) node [left] {$O$} coordinate (O);\n\\filldraw (0,-4) circle (0.15) node [right] {$F$} coordinate (F);\n\\filldraw (0,-12) circle (0.15) node [left] {$B$} coordinate (B);\n\\filldraw (-8,0) circle (0.15) node [left] {$A$} coordinate (A);\n\\draw (A) -- ($(E)!{-1}!(A)$) (E) -- (B);\n\\end{tikzpicture}\n\\end{center}\n(1) 判断该飞行器是否经过线段$EF$的中点$O$, 并判断小镇$A$是否会受到该飞行器的噪音污染?\\\\\n(2) 小镇$B$受该飞行器噪音污染的最强等级为多少级?", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030709": { + "id": "030709", + "content": "某会展中心, 由展览场馆、通道等组成, 可以假设抽象成下图, 图中的大正方形$AA_1A_2A_3$是由四个相等的小正方形(如$ABCD$)和宽度相等的矩形通道组成. 展览馆可以根据实际需要进行重新布局成展览区域和休闲区域, 展览区域由四部分组成, 每部分是八边形, 且它们互相全等. 图中的八边形$EFTSHQMG$是小正方形$ABCD$中的展览区域, 小正方形$ABCD$中的四个全等的直角三角形是休闲区域, 四个八边形是整个的展览区域, $16$个全等的直角三角形是整个的休闲区域. 设$ABCD$的边长为$300$米, $\\triangle AEF$的周长为$180$米.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw (0,0) node [above left] {$A$} coordinate (A);\n\\draw (A) --++ (7,0) node [above right] {$A_1$} coordinate (A_1);\n\\draw (A_1) --++ (0,-7) node [below right] {$A_2$} coordinate (A_2);\n\\draw (A_2) --++ (-7,0) node [below left] {$A_3$} coordinate (A_3) -- (A);\n\\draw ($(A)!{3/7}!(A_1)$) node [above] {$B$} coordinate (B);\n\\draw ($(A)!{4/7}!(A_1)$) node [above] {$U$} coordinate (U);\n\\draw (B) --++ (0,-7) (U) --++ (0,-7) ($(B)!0.5!(U)$) --++ (0,-7);\n\\draw ($(A)!{3/7}!(A_3)$) node [left] {$D$} coordinate (D);\n\\draw ($(A)!{4/7}!(A_3)$) coordinate (D_1);\n\\draw (D) --++ (7,0) (D_1) --++ (7,0) ($(D)!0.5!(D_1)$) --++ (7,0);\n\\draw (A) ++ (0.45,0) node [above] {$E$} coordinate (E) (A) ++ (0,-0.6) node [left] {$F$} coordinate (F) (E) -- (F);\n\\draw (B) ++ (-0.45,0) node [above] {$G$} coordinate (G) (B) ++ (0,-0.6) node [right] {$M$} coordinate (M) (G) -- (M);\n\\draw (B) ++ (0,-3) node [below right] {$C$} coordinate (C) (C) ++ (-0.45,0) node [below] {$H$} coordinate (H) (C) ++ (0,0.6) node [right] {$Q$} coordinate (Q) (Q) -- (H);\n\\draw (A) ++ (0,-3) node [left] {$D$} coordinate (D) coordinate (D) (D) ++ (0.45,0) node [below] {$S$} coordinate (S) (D) ++ (0,0.6) node [left] {$T$} coordinate (T) (S) -- (T);\n\\draw (M) --++ (1,0) --++ (0.45,0.6) ++ (2.1,0) --++ (0.45,-0.6) ++ (0,-1.8) --++ (-0.45,-0.6) ++ (-2.1,0) --++ (-0.45,0.6) --++ (-1,0);\n\\draw (S) --++ (0,-1) --++ (-0.45,-0.6) ++ (0,-1.8) --++ (0.45,-0.6) ++ (2.1,0) --++ (0.45,0.6) ++ (0,1.8) --++ (-0.45,0.6) --++ (0,1);\n\\draw (A_2) ++ (-0.45,4) --++ (0,-1) --++ (0.45,-0.6) ++ (0,-1.8) --++ (-0.45,-0.6) ++ (-2.1,0) --++ (-0.45,0.6) ++ (0,1.8) --++ (0.45,0.6) --++ (0,1);\n\\draw (C) ++ (0,-1.6) --++ (1,0) ++ (0,-1.8) --++ (-1,0);\n\\end{tikzpicture}\n\\end{center}\n(1) 设$AE=x$, 求$\\triangle AEF$的面积$y$关于$x$的函数关系式;\\\\\n(2) 问$AE$取多少时, 使得整个的休闲区域面积最大.(长度精确到$1$米, 面积精确到$1$平方米)", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030710": { + "id": "030710", + "content": "某学校对面有一块空地要围建成一个面积为$360 \\text{m}^2$的矩形场地, 要求矩形场地的一面利用旧墙(旧墙需要整修), 其它三面围墙要新建, 在旧墙对面的新墙上要留一个宽度为$2 \\text{m}$的进出口, 如图所示. 已知旧墙的整修费用为$45$元$/ \\text{m}$, 新建墙的造价为$180$元$/ \\text{m}$, 建$2 \\text{m}$宽的进出口需$2360$元的单独费用, 设利用的旧墙的长度为$x$(单位:$\\text{m}$), 设修建此矩形场地围墙的总费用(含建进出口的费用)为$y$(单位: 元).\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.15]\n\\fill [pattern = north east lines] (-18,2) rectangle (18,0);\n\\draw (-18,0) -- (18,0);\n\\draw (-15,0) --++ (0,-12) --++ (14,0) ++ (2,0) --++ (14,0) --++ (0,12);\n\\draw [<->] (-15,-4) -- (15,-4) node [midway, fill = white] {$x$};\n\\end{tikzpicture}\n\\end{center}\n(1) 将$y$表示为$x$的函数;\\\\\n(2) 试确定$x$, 使修建此矩形场地围墙的总费用(含建进出口的费用)最少, 并求出最少总费用.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030711": { + "id": "030711", + "content": "某油库的设计容量为$30$万吨, 年初储量为$10$万吨, 从年初起计划每月先购进石油$m$万吨, 以满足区域内和区域外的需求, 若区域内每月用石油$1$万吨, 区域外前$x$个月的需求量$y$(万吨)与$x$的函数关系为$y=\\sqrt {2 p x}$($p>0$, $1 \\leq x \\leq 16$, $x \\in \\mathbf{N}$), 并且前$4$个月, 区域外的需求量为$20$万吨.\\\\\n(1) 试写出第$x$个月石油调出后, 油库内储油量$M$(万吨)与$x$的函数关系式;\\\\\n(2) 要使$16$个月内每月按计划购进石油之后, 油库总能满足区域内和区域外的需求, 且每月石油调出后, 油库的石油剩余量不超过油库的容量, 求$m$的取值范围.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030712": { + "id": "030712", + "content": "某便民超市经销一种小袋装地方特色桃酥食品, 每袋桃酥的成本为$6$元, 预计当一袋桃酥的售价为$x$元($9 \\leq x \\leq 11$)时, 一年的销售量为$\\dfrac{48}{x-5}$万袋, 并且全年该桃酥食品共需支付$3 x$万元的管理费. 一年的利润$=$一年的销售量$\\times$售价$-$(一年销售桃酥的成本$+$一年的管理费).(单位: 万元)\\\\\n(1) 求该超市一年的利润$L$(万元)与每袋桃酥食品的售价$x$的函数关系式;\\\\\n(2) 当每袋桃酥的售价为多少元时, 该超市一年的利润$L$最大, 并求出$L$的最大值.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030713": { + "id": "030713", + "content": "某研究所开发了一种抗病毒新药, 用小白鼠进行抗病毒实验. 已知小白鼠服用$1$粒药后, 每毫升血液含药量$y$(微克)随着时间$x$(小时)变化的函数关系式近似为$y=\\begin{cases}\\dfrac{2 x}{8-x}, & 0 \\leq x \\leq 6, \\\\12-x, & 60$且$a \\neq 1$). 分析表格中的数据, 请说明哪类函数模型更合适, 并求出该函数解析式;\\\\\n(2) 若这$30$天内该公司此商品的日销售利润始终不能超过$4$万元, 则考虑转型. 请判断该公司是否需要转型? 并说明理由.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030715": { + "id": "030715", + "content": "环保生活, 低碳出行, 电动汽车正成为人们购车的热门选择. 某型号的电动汽车在国道上进行测试, 国道限速$80 \\text{km} / \\text{h}$. 经多次测试得到该汽车每小时耗电量$M$(单位:$\\text{Wh}$)与速度$v$(单位:$\\text{km} / \\text{h}$) 的数据如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$v$& 0 & 10 & 40 & 60 \\\\\n\\hline$M$& 0 & 1325 & 4400 & 7200 \\\\\n\\hline\n\\end{tabular} \n\\end{center}\n为了描述国道上该汽车每小时耗电量$M$与速度$v$的关系, 现有以下三种函数模型供选择: \\textcircled{1} $M_1(v)=\\dfrac 1{40} v^3+b v^2+c v$; \\textcircled{2} $M_2(v)=1000 \\cdot(\\dfrac 23)^v+a$; \\textcircled{3} $M_3(v)=300 \\log_a v+b$.\\\\\n(1) 当$0 \\leq v \\leq 80$时, 请选出你认为最符合表格中所列数据的函数模型 (需说明理由), 并求出相应的函数解析式;\\\\\n(2) 现有一辆同型号电动汽车从$A$地行驶到$B$地, 其中高速上行驶$200 \\text{km}$, 国道上行驶$30 \\text{km}$, 若高速路上该汽车每小时耗电量$N$(单位:$\\text{Wh}$) 与速度$v$(单位:$\\text{km} / \\text{h}$) 的关系满足$N(v)=2 v^2-10 v+200$($80 \\leq v \\leq 120$), 则如何行驶才能使得总耗电量最少, 最少为多少?", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030716": { + "id": "030716", + "content": "已知函数$y=f(x)$是定义域为$\\mathbf{R}$的奇函数, 且当$x<0$时, $f(x)=x+\\dfrac ax+1$. 若函数$y=f(x)$在$[3,+\\infty)$上的最小值为$3$, 则实数$a$的值为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题10", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030717": { + "id": "030717", + "content": "设二次函数$f(x)=m x^2-2 x+n$($m, n \\in \\mathbf{R}$), 若函数$f(x)$的值域为$[0,+\\infty)$, 且$f(1) \\leq 2$, 则$\\dfrac{m^2}{n^2+1}+\\dfrac{n^2}{m^2+1}$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀一模试题11", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030718": { + "id": "030718", + "content": "已知函数$f(x)=\\begin{cases}x^2-x+3, & x \\leq 1, \\\\x+\\dfrac 2x, &x>1.\\end{cases}$ 设$a \\in \\mathbf{R}$, 若关于$x$的不等式$f(x) \\geq|\\dfrac x2+a|$在$\\mathbf{R}$上恒成立, 则$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题11", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030719": { + "id": "030719", + "content": "已知函数$f(x)=\\begin{cases}\\log_2 x,& x>0, \\\\|2 x+1|,& x \\leq 0.\\end{cases}$ 设集合$A=\\{(a, b)|a \\leq-1$且$n \\leq b \\leq m\\}$, $m, n \\in \\mathbf{R}\\}$, 若对任意的$(a, b) \\in A$, 总有$a \\cdot f(b)-b-3 a \\geq 0$成立, 则$m-n$的最大值为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇一模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030720": { + "id": "030720", + "content": "已知函数$f(x)=\\begin{cases}x-\\dfrac 8x, & x<0 \\\\|x-a|, & x \\geq 0,\\end{cases}$ 若对任意的$x_1 \\in[2,+\\infty)$, 都存在$x_2 \\in[-2,-1]$, 使得$f(x_1) \\cdot f(x_2) \\geq a$, 则实数$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江一模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030721": { + "id": "030721", + "content": "已知函数$f(x)=\\begin{cases}\\log_2 x,& x>0, \\\\|2 x+1|,& x \\leq 0,\\end{cases}$ 若对任意$a \\leq-1$, 当$-10$)时, 都有$|2 x-1|+|x^2-a|\\leq 4$, 则实数$m$的最大值为\\bracket{20}.\n\\fourch{$1$}{$\\dfrac 32$}{$2$}{$\\dfrac 52$}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定一模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030724": { + "id": "030724", + "content": "设常数$a \\in \\mathbf{R}$, 函数$f(x)=2^{x+1}+\\dfrac a{2^x}$.\\\\\n(1) 若函数$y=f(x)$是偶函数, 求实数$a$的值;\\\\\n(2) 若对任意$x \\in[1,+\\infty)$, $f(x)>3$, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030725": { + "id": "030725", + "content": "已知$k>0$, 函数$f(x)=\\begin{cases}\\dfrac kx,& x>1, \\\\2^x, & x \\leq 1,\\end{cases}$ $F(x)=f(x)+4 x$.\\\\\n(1) 当$k=1$时, 解不等式$F(x) \\geq 6$;\\\\\n(2) 若$F(x)$在$\\mathbf{R}$上是增函数, 求$k$的取值范围.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030726": { + "id": "030726", + "content": "已知函数$f(x)=\\dfrac{3^x+b}{3^x+1}$是定义域为$\\mathbf{R}$的奇函数.\\\\\n(1) 求实数$b$的值, 并证明$f(x)$在$\\mathbf{R}$上单调递增;\\\\\n(2) 已知$a>0$且$a \\neq 1$, 若对于任意的$x_1$、$x_2 \\in[1,3]$, 都有$f(x_1)+\\dfrac 32 \\geq a^{x_2-2}$恒成立, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030727": { + "id": "030727", + "content": "已知函数$f(x)=\\dfrac 1{2^x+1}$($x \\in \\mathbf{R}$).\\\\\n(1) 求证: 函数$f(x)$是$\\mathbf{R}$上的减函数;\\\\\n(2) 已知函数$f(x)$的图像存在对称中心$(a, b)$的充要条件是$g(x)=f(x+a)-b$的图像关于原点中心对称, 判断函数$f(x)$的图像是否存在对称中心, 若存在, 求出该对称中心的坐标; 若不存在, 说明理由;\\\\\n(3) 若对任意$x_1 \\in[1, n]$, 都存在$x_2 \\in[1, \\dfrac 32]$及实数$m$, 使得$f(1-m x_1)+f(x_1 x_2)=1$, 求实数$n$的最大值.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁一模试题20", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030728": { + "id": "030728", + "content": "对于定义在$D$上的函数$y=f(x)$, 若同时满足: \\textcircled{1} 对任意的$x \\in D$, 均有$f(-x)+f(x)=0$; \\textcircled{2} 对任意的$x_1 \\in D$, 存在$x_2 \\in D$, 且$x_2 \\neq-x_1$, 使得$f(x_1)-x_1=x_2-f(x_2)$成立, 则称函数$y=f(x)$为 ``等均'' 函数. 下列函数: \\textcircled{1} $f(x)=x$; \\textcircled{2} $f(x)=|\\dfrac{x-1}{x+1}|$; \\textcircled{3} $f(x)=\\dfrac 2x$; \\textcircled{4} $f(x)=\\sin x$之中, ``等均'' 函数的个数是\\bracket{20}.\n\\fourch{1}{2}{3}{4}", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山二模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030729": { + "id": "030729", + "content": "记函数$y_1=f_1(x)$, $x \\in D$, 函数$y_2=f_2(x)$, $x \\in D$, 若对任意的$x \\in D$, 总有$|f_2(x)|\\leq|f_1(x)|$成立, 则称函数$f_1(x)$包裹函数$f_2(x)$. 判断如下两个命题真假:\\\\\n\\textcircled{1} 函数$f_1(x)=k x$包表函数$f_2(x)=x \\cos x$的充要条件是$|k|\\geq 1$;\\\\\n\\textcircled{2} 若对于任意$p>0,|f_1(x)-f_2(x)|0$, 以及关于$x$的函数$f(x)=|1-\\dfrac kx|$, 是否存在实数$a$、$b$($a0$, 均存在区间$I=(M,+\\infty)$, 使得函数$y=f(x)$与$y=g(x)$具有性质$P(I, a)$, 求证:$g(x)=0$;\\\\\n(3) 已知$I=[1, m]$, $f(x)=x^2$, 若存在一次函数$y=g(x)$与$y=f(x)$具有性质$P(I, 1)$, 求实数$m$的最大值.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦一模试题21", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030732": { + "id": "030732", + "content": "已知函数$y=f(x)$的定义域为区间$D$, 若对于给定的非零实数$m$, 存在$x_0$, 使得$f(x_0)=f(x_0+m)$, 则称函数$y=f(x)$在区间$D$上具有性质$P(m)$.\\\\\n(1) 判断函数$f(x)=x^2$在区间$[-1,1]$上是否具有性质$P(\\dfrac 12)$, 并说明理由;\\\\\n(2) 若函数$f(x)=\\sin x$在区间$(0, n)(n>0)$上具有性质$P(\\dfrac{\\pi}4)$, 求$n$的取值范围;\\\\\n(3) 已知函数$y=f(x)$的图像是连续不断的曲线, 且$f(0)=f(2)$, 求证: 函数$y=f(x)$在区间$[0,2]$上具有性质$P(\\dfrac 13)$.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定一模试题21", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030733": { + "id": "030733", + "content": "设函数$y=f(x)$定义在区间$(a, b)$上, 若对任意的$x_1$、$x_2$、$x_1'$、$x_2' \\in(a, b)$, 当$x_1+x_2=x_1'+x_2'$且$|x_1'-x_2'|<|x_1-x_2|$时, 不等式$f(x_1)+f(x_2)0)$上单调递增, 且$h(x)$的图像关于点$(p, q)$成中心对称 (其中$p$、$q$为常数), 证明: $h(x)$是 ``拟线性函数''.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江一模试题21", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030735": { + "id": "030735", + "content": "设函数$f(x)=x^2+p x+q$($p$、$q \\in \\mathbf{R}$), 定义集合$D_f=\\{x|f(f(x))=x,\\ x \\in \\mathbf{R}\\}$, 集合$E_f=\\{x|f(f(x))=0,\\ x \\in \\mathbf{R}\\}$.\\\\\n(1) 若$p=q=0$, 写出相应的集合$D_f$和$E_f$;\\\\\n(2) 若集合$D_f=\\{0\\}$, 求出所有满足条件的$p$、$q$;\\\\\n(3) 若集合$E_f$只含有一个元素, 求证:$p \\geq 0$, $q \\geq 0$.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦二模试题21", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030736": { + "id": "030736", + "content": "已知函数$f(x)$的定义域为$(0,+\\infty)$, 若存在常数$T>0$, 使得对任意$x \\in(0,+\\infty)$, 都有$f(T x)=f(x)+T$, 则称函数$f(x)$具有性质$P(T)$.\\\\\n(1) 若函数$f(x)$具有性质$P(2)$, 求$f(2)-f(\\dfrac 12)$的值;\\\\\n(2) 设$f(x)=\\log_a x$, 若$00$, 使得$f(x)$具有性质$P(T)$;\\\\\n(3) 若函数$f(x)$具有性质$P(T)$, 且$f(x)$的图像是一条连续不断的曲线, 求证: 函数$f(x)$在$(0,+\\infty)$上存在零点.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁二模试题21", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030737": { + "id": "030737", + "content": "对于定义在$\\mathbf{R}$上的函数$f(x)$, 若存在正数$m$与集合$A$, 使得对任意的$x_1$、$x_2 \\in \\mathbf{R}$, 当$x_10$且$a \\neq 1$, $b>1$, 若函数$f(x)=-a^x+\\log_{\\frac 1b} x$与$g(x)=-a^x+\\log_b x$``具有性质$M(1)$'', 求$\\dfrac 12 x_1-x_2$的取值范围.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀二模试题21", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030741": { + "id": "030741", + "content": "函数$f(x)=\\sqrt x+1$的反函数为$f^{-1}(x)$, 则$f^{-1}(3)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东一模试题02", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030742": { + "id": "030742", + "content": "已知函数$f(x)=\\dfrac{x-1}{x+2}$的反函数为$f^{-1}(x)$, 则$f^{-1}(0)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦一模试题03", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030743": { + "id": "030743", + "content": "函数$y=f(x)$的反函数为$y=\\log_2 x+1$, 则$f(3)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇二模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030744": { + "id": "030744", + "content": "已知函数$y=f(x)$的图像经过点$(2,3), y=f(x)$的反函数为$y=f^{-1}(x)$, 则函数$y=f^{-1}(x-2)$的图像必经过点\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030745": { + "id": "030745", + "content": "若函数$f(x)=\\log_2(x+m)+2$的反函数的图像经过点$(3,1)$, 则$f(3)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定一模试题05", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030746": { + "id": "030746", + "content": "若函数$f(x)=\\log_a(x+1)$($a>0$, $a \\neq 1$)的反函数图像经过点$(1,3)$, 则$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东二模试题03", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030747": { + "id": "030747", + "content": "若函数$f(x)=a^x$($a>0$, $a \\neq 1$)的反函数的图像经过点$(4,2)$, \n则$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江二模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030748": { + "id": "030748", + "content": "设$a>0$且$a \\neq 1$, 若函数$y=a^x$的反函数的图像过点$(2,-1)$, \n则$a=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦一模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030749": { + "id": "030749", + "content": "已知函数$y=f(x)$的反函数为$y=2^x$, 则$f(3)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦二模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030750": { + "id": "030750", + "content": "若函数$f(x)=x^3-3$的反函数为$y=f^{-1}(x)$, 则方程$f^{-1}(x)=0$的根为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行一模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030751": { + "id": "030751", + "content": "已知函数$f(x)=1+\\log_2 x$, 它的反函数为$y=f^{-1}(x)$, 则$f^{-1}(3)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030752": { + "id": "030752", + "content": "已知$f(x)=\\sqrt {x+a}$的反函数$y=f^{-1}(x)$的零点为$2$, 则实数$a$的值为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行二模试题04", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030753": { + "id": "030753", + "content": "函数$f(x)=1+\\lg x$的反函数是$f^{-1}(x)=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦二模试题06", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030754": { + "id": "030754", + "content": "若函数$f(x)=2+\\dfrac 2x+\\dfrac 1{x^2}(x>0)$的反函数为$f^{-1}(x)$, 则不等式$f^{-1}(x)>3$的解集是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安二模试题09", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030755": { + "id": "030755", + "content": "设函数$f(x)=x^{\\frac 12}$的反函数是$f^{-1}(x)$, 若对任意的$x \\in(0,1)$, 则$f(x)$与$f^{-1}(x)$的大小关系为\\bracket{20}.\n\\fourch{$f(x)>f^{-1}(x)$}{$f(x)=f^{-1}(x)$}{$f(x)0$), 若$f(x) \\leq f(\\dfrac{\\pi}4)$对任意的实数$x$都成立, 则$\\omega$的最小值为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江一模试题09", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030777": { + "id": "030777", + "content": "设函数$f(x)=\\cos (\\omega x+\\dfrac{\\pi}3)$($0<\\omega<2$), 若将$f(x)$图像向左平移$\\dfrac{4 \\pi}5$个单位后, 所得函数图像的对称轴与原函数图像的对称轴重合, 则$\\omega=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇一模试题09", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030778": { + "id": "030778", + "content": "设$a$、$b \\in \\mathbf{R}$, $c \\in[0,4 \\pi)$. 若对任意实数$x$都有$\\sin (2 x-\\dfrac{\\pi}3)=a \\sin (b x+c)$, 则满足条件的有序实数组$(a, b, c)$的组数为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦二模试题10", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030779": { + "id": "030779", + "content": "若$x \\in(-\\dfrac{3 \\pi}2, \\pi)$, 则等式$\\dfrac{\\cos (x+\\dfrac{\\pi}4)}{\\cos x}+\\dfrac{\\sin (x+\\dfrac{\\pi}4)}{\\sin x}=2$成立的\n一个$x$的值可以是\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀二模试题10", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030780": { + "id": "030780", + "content": "设函数$f(x)=\\sin x-m(x \\in[0, \\dfrac{5 \\pi}2])$的零点为$x_1$、$x_2$、$x_3$, 若$x_1$、$x_2$、$x_3$成等比数列, 则$m=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明一模试题10", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030781": { + "id": "030781", + "content": "已知将函数$y=\\sqrt 5 \\sin x+\\sqrt 5 \\cos x$的图像向右平移$\\theta(0<\\theta<\\dfrac{\\pi}2)$个单位得到函数$y=3 \\sin x+a \\cos x$($a<0$)的图像, 则$\\tan \\theta=$\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题10", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030782": { + "id": "030782", + "content": "已知函数$f(x)=\\sin (\\omega x+\\varphi)$, 其中$\\omega>0$,$0<\\varphi<\\pi$, $f(x) \\leq f(\\dfrac{\\pi}4)$恒成立, 且$y=f(x)$在区间$(0, \\dfrac{3 \\pi}8)$上恰有$3$个零点, 则$\\omega$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030783": { + "id": "030783", + "content": "下列函数中, 以$\\dfrac{\\pi}2$为周期且在区间$[\\dfrac{\\pi}4, \\dfrac{\\pi}2]$上单调递增的是\\bracket{20}.\n\\fourch{$f(x)=|\\cos 2 x|$}{$f(x)=|\\sin 2 x|$}{$f(x)=\\sin 4 x$}{$f(x)=\\cos 2 x$}", + "objs": [], + "tags": [ + "a", + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山一模试题14", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030784": { + "id": "030784", + "content": "设函数$f(x)=a \\sin x+b \\cos x$, 其中$a>0$, $b>0$, 若$f(x) \\leq f(\\dfrac{\\pi}4)$对任意的$x \\in \\mathbf{R}$恒成立, 则下列结论正确的是\\bracket{20}.\n\\onech{$f(\\dfrac{\\pi}2)>f(\\dfrac{\\pi}6)$}{$f(x)$的图像关于直线$x=\\dfrac{3 \\pi}4$对称}{$f(x)$在$[\\dfrac{\\pi}4, \\dfrac{5 \\pi}4]$上单调递增}{过点$(a, b)$的直线与函数$f(x)$的图像必有公共点}", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口一模试题14", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030785": { + "id": "030785", + "content": "设函数$f(x)=\\sin (\\omega x+\\dfrac{\\pi}6)$($0<\\omega<5$)图像的一条对称轴方程为$x=\\dfrac{\\pi}{12}$, 若$x_1$、$x_2$是函数$f(x)$的两个不同的零点, 则$|x_1-x_2|$的最小值为\\bracket{20}.\n\\fourch{$\\dfrac{\\pi}6$}{$\\dfrac{\\pi}4$}{$\\dfrac{\\pi}2$}{$\\pi$}", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江二模试题15", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030786": { + "id": "030786", + "content": "已知函数$f(x)=2 \\sin x(\\sin x+\\sqrt 3 \\cos x)-1$的定义域为$[m, n]$$(m0)$的值域为$[4, 5]$, 则$\\cos \\dfrac{\\omega \\pi}3$的取值范围为\\bracket{20}.\n\\fourch{$[\\dfrac 7{25}, \\dfrac 45]$}{$[\\dfrac 7{25}, \\dfrac 35]$}{$[-\\dfrac 7{25}, \\dfrac 45]$}{$[-\\dfrac 7{25}, \\dfrac 35]$}", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁一模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030790": { + "id": "030790", + "content": "函数$f(x)=\\sin x-\\dfrac 12, x \\in[t, t+40]$零点的个数不可能是 \\bracket{20}.\n\\fourch{$12$个}{$13$个}{$14$个}{$15$个}", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东一模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030791": { + "id": "030791", + "content": "设$\\omega$为正实数, 若存在$a$、$b$($\\pi \\leq a\\sin B$, $\\beta: a>b$, 则$\\alpha$是$\\beta$的\\bracket{20}条件.\n\\fourch{充分非必要}{必要非充分}{充要}{既非充分也非必要}", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤二模试题13", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030799": { + "id": "030799", + "content": "在$\\triangle ABC$中, $A$、$B$、$C$所对边$a$、$b$、$c$满足$(a+b-c)(a-b+c)=b c$.\\\\\n(1) 求$A$的值;\\\\\n(2) 若$a=\\sqrt 3, \\cos B=\\dfrac 45$, 求$\\triangle ABC$的周长.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤一模试题17", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030800": { + "id": "030800", + "content": "已知$\\triangle ABC$三个内角$A$、$B$、$C$对应边分别为$a$、$b$、$c$, $a=4$, $\\cos B=-\\dfrac 14$.\\\\\n(1) 若$\\sin A=2 \\sin C$, 求$\\triangle ABC$的面积;\\\\\n(2) 设线段$AB$的中点为$D$, 若$CD=\\sqrt {19}$, 求$\\triangle ABC$外接圆半径$R$的值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030801": { + "id": "030801", + "content": "在$\\triangle ABC$中, 内角$A$、$B$、$C$所对边的长分别为$a$、$b$、$c$, $a=5$, $b=6$.\\\\\n(1) 若$\\cos B=-\\dfrac 45$, 求$A$和$\\triangle ABC$外接圆半径$R$的值;\\\\\n(2) 若三角形的面积$S_{\\triangle}=\\dfrac{15 \\sqrt 7}4$, 求$c$.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030802": { + "id": "030802", + "content": "在$\\triangle ABC$中, 内角$A$、$B$、$C$所对边分别为$a$、$b$、$c$, 已知$c \\sin C-b \\sin B=a(\\sin A-\\sin B)$.\\\\\n(1) 求角$C$的值;\\\\\n(2) 若$c=3$, 求$\\triangle ABC$周长的最大值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030803": { + "id": "030803", + "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 已知$a=4$, $c=6$, $\\cos C=\\dfrac 18$.\\\\\n(1) 求$\\sin A$的值;\\\\\n(2) 求$b$的值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030804": { + "id": "030804", + "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 若$a \\cos C+\\sqrt 3 a \\sin C-b-c=0$.\\\\\n(1) 求角$A$的大小;\\\\\n(2) 若$a=2, \\triangle ABC$的面积为$\\sqrt 3$, 求$b$、$c$的值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030805": { + "id": "030805", + "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$.\\\\\n(1) 若$\\sin ^2A=\\sin ^2B+\\sin ^2C+\\sin B \\sin C$, 求$A$;\\\\\n(2) 若$C=60^{\\circ}$, $\\triangle ABC$的面积$S=\\sqrt 3$, 求$\\triangle ABC$外接圆半径$R$的最小值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届长宁二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030806": { + "id": "030806", + "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$所对的边分别为$a$、$b$、$c$. 已知$2 b \\sin A-\\sqrt 3 a=0$, 且$B$为锐角.\\\\\n(1) 求角$B$的大小;\\\\\n(2) 若$3 c=3 a+\\sqrt 3 b$, 证明$\\triangle ABC$是直角三角形.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030807": { + "id": "030807", + "content": "吴淞口灯塔$AE$采用世界先进的北斗卫星导航遥测遥控系统, 某校数学建模小组测量其高度$H$(单位: $\\text{m}$), 如示意图, 垂直放置的标杆$BC$的高度$h=3 \\text{m}$, 使$A$、$B$、$D$在同一直线上, 也在同一水平面上, 仰角$\\angle ABE=\\alpha$, $\\angle ADE=\\beta$.(本题的距离精确到$0.1 \\text{m}$)\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw [ultra thick] (0,0) node [above left] {$B$} coordinate (B) -- (0,1) node [above] {$C$} coordinate (C) node [midway, right] {$h$};\n\\draw (-1.1,0) node [left] {$D$} coordinate (D);\n\\draw ($(D)!2.5!(B)$) node [right] {$A$} coordinate (A);\n\\draw ($(D)!2.5!(C)$) node [right] {$E$} coordinate (E);\n\\draw [ultra thick] (A) -- (E) node [midway, right] {$H$};\n\\draw (D) -- (A);\n\\draw [dashed] (D) -- (E) (B) -- (E);\n\\draw (B) --++ (0,-0.4) coordinate (B1) (A) --++ (0,-0.4) coordinate (A1);\n\\draw [<->] ($(B)!0.5!(B1)$) -- ($(A)!0.5!(A1)$) node [midway, fill = white] {$d$};\n\\draw (D) pic [\"$\\beta$\", draw, angle eccentricity = 1.5] {angle = B--D--C};\n\\draw (B) pic [\"$\\alpha$\", draw, angle eccentricity = 1.5] {angle = A--B--E};\n\\end{tikzpicture}\n\\end{center}\n(1) 该小组测得$\\alpha$、$\\beta$的一组值为$\\alpha=51.83^{\\circ}, \\beta=47.33^{\\circ}$, 请据此计算$H$的值;\\\\\n(2) 该小组分析若干测得的数据后, 认为适当调整标杆到灯塔的距离$d$(单位: $\\text{m}$), 使$\\alpha$与$\\beta$之差较大, 可以提高测量精确度. 若灯塔的实际高度为$20.1 \\text{m}$, 试问$d$为多少时, $\\alpha-\\beta$最大?", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030808": { + "id": "030808", + "content": "某水产养殖户承包一片靠岸水域, 如图, $AO$、$OB$为直线岸线, $OA=1000$米, $OB=1500$米, $\\angle AOB=\\dfrac{\\pi}3$, 该承包水域的水面边界是某圆的一段弧$AB$, 过弧$AB$上一点$P$按线段$PA$和$PB$修建养殖网箱, 已知$\\angle APB=\\dfrac{2 \\pi}3$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (1,{sqrt(3)}) node [right] {$A$} coordinate (A);\n\\draw (-1.5,{1.5*sqrt(3)}) node [left] {$B$} coordinate (B);\n\\draw (A) arc ({atan((sqrt(3)-5/sqrt(12))/1.5)}:{180+atan((1.5*sqrt(3)-5/sqrt(12))/(-1))}:{sqrt(7/3)});\n\\draw (-0.5,{5/sqrt(12)}) ++ (85:{sqrt(7/3)}) node [above] {$P$} coordinate (P);\n\\draw (A) -- (P) -- (B) (O) -- (A) (O) -- (B);\n\\draw [dashed] (A) -- (B);\n\\end{tikzpicture}\n\\end{center}\n(1) 求岸线上点$A$与点$B$之间的直线距离;\\\\\n(2) 如果线段$PA$上的网箱每米可获得 40 元的经济收益, 线段$PB$上的网箱每米可获得 30 元的经济收益, 记$\\angle PAB=\\theta$, 则这两段网箱获得的经济总收益最高为多少?(精确到元)", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030809": { + "id": "030809", + "content": "落户上海的某休闲度假区预计于$2022$年开工建设. 如图, 拟在该度假园区入口处修建平面图呈直角三角形的迎宾区, $\\angle ACB=\\dfrac{\\pi}2$, 迎宾区的入口设置在点$A$处, 出口在点$B$处, 游客可从入口沿着观景通道$A-C-B$到达出口, 其中$AC=300$米, $BC=200$米, 也可以沿便捷通道$A-P-B$到达出口($P$为$\\triangle ABC$内一点).\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$C$} coordinate (C);\n\\draw (2,0) node [below right] {$B$} coordinate (B);\n\\draw (0,3) node [above left] {$A$} coordinate (A);\n\\draw (1,{1/sqrt(3)}) node [left] {$P$} coordinate (P);\n\\draw (A) -- (C) -- (B) -- cycle (A) -- (P) (B) -- (P) (C) -- (P);\n\\end{tikzpicture}\n\\end{center}\n(1) 若$\\triangle PBC$是以$P$为直角顶点的等腰直角三角形, 某游客的步行速度为每分钟$50$米, 则该游客从入口步行至出口, 走便捷通道比走观景通道可以快几分钟?(结果精确到$1$分钟)\\\\\n(2) 园区计划将$\\triangle PBC$区域修建成室外游乐场, 若$\\angle BPC=\\dfrac{2 \\pi}3$, 该如何设计使室外游乐场的面积最大, 请说明理由.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山一模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030810": { + "id": "030810", + "content": "如图, 某市在两条直线公路$OA$、$OB$上修建地铁站$A$和$B$, $\\angle AOB=120^{\\circ}$, 为了方便市民出行, 要求公园$O$到$AB$的距离为$1 \\text{km}$. 设$\\angle BAO=\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below right] {$O$} coordinate (O);\n\\draw (O) ++ (180:2) node [below] {$A$} coordinate (A);\n\\draw (O) ++ (60:3) node [right] {$B$} coordinate (B);\n\\draw (A) -- (B);\n\\draw (O) -- ($(O)!1.2!(A)$) (O) -- ($(O)!1.2!(B)$);\n\\draw (A) pic [\"$\\theta$\",draw, angle eccentricity = 1.5] {angle = O--A--B};\n\\end{tikzpicture}\n\\end{center}\n(1) 试求$AB$的长度$l$关于$\\theta$的函数关系式;\\\\\n(2) 问当$\\theta$取何值时, 才能使$AB$的长度最短, 并求其最短距离.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030811": { + "id": "030811", + "content": "如图, 某公园拟划出形如平行四边形$ABCD$的区域进行绿化, 在此绿化区域中, 分别以$\\angle DCB$和$\\angle DAB$为圆心角的两个扇形区域种植花卉, 且这两个扇形的圆弧均与$BD$相切.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.1]\n\\draw (0,0) node [below right] {$A$} coordinate (A);\n\\draw (A) ++ (60:{3*sqrt(37)}) node [above right] {$B$} coordinate (B);\n\\draw (A) ++ ({-4*sqrt(37)},0) node [below left] {$D$} coordinate (D);\n\\draw (B) ++ ({-4*sqrt(37)},0) node [above left] {$C$} coordinate (C);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (B) -- (D);\n\\draw (A) ++ (60:{sqrt(108)}) arc (60:180:{sqrt(108)});\n\\draw (C) ++ (240:{sqrt(108)}) arc (240:360:{sqrt(108)});\n\\end{tikzpicture}\n\\end{center}\n(1) 若$AD=4 \\sqrt {37}$, $AB=3 \\sqrt {37}, BD=37$(长度单位: 米), 求种植花卉区域的面积;\\\\\n(2) 若扇形的半径为$10$米, 圆心角为$135^{\\circ}$, 则$\\angle BDA$多大时, 平行四边形绿地$ABCD$占地面积最小?", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030812": { + "id": "030812", + "content": "某公司要在一条笔直的道路边安装路灯, 要求灯柱$AB$与地面垂直, 灯杆$BC$与灯柱$AB$所在的平面与道路走向垂直, 路灯$C$采用锥形灯罩, 射出的光线与平面$ABC$的部分截面如图中阴影部分所示. 已知$\\angle ABC=\\dfrac{2 \\pi}3$, $\\angle ACD=\\dfrac{\\pi}3$, 路宽$AD=24$米. 设$\\angle ACB=\\theta$($\\dfrac{\\pi}6 \\leq \\theta \\leq \\dfrac{\\pi}4$).\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A);\n\\draw (0,2) node [left] {$B$} coordinate (B);\n\\draw (B) ++ (30:0.4) node [above] {$C$} coordinate (C);\n\\path [name path = CD] (C) -- ($(C)!1.6!60:(A)$);\n\\path [name path = AD] (A) --++ (3.2,0);\n\\path [name intersections = {of = CD and AD, by = D}];\n\\fill [gray!20] (A) -- (C) -- (D) -- cycle;\n\\draw (A) -- (B) -- (C) -- (D) node [below right] {$D$}-- cycle (A) -- (C);\n\\end{tikzpicture}\n\\end{center}\n(1) 当$\\theta=\\dfrac{\\pi}6$时, 求$\\triangle ABC$的面积;\\\\\n(2) 求灯杆$BC$与灯柱$AB$长度之和$L$(米)关于$\\theta$的函数解析式, 并求当$\\theta$为何值时, $L$取得最小值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届嘉定二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030813": { + "id": "030813", + "content": "如图, 农户在$AB=100$米、$BC=80$米的长方形地块$ABCD$上种植向日葵, 并在$A$处安装监控摄像头及时了解向日葵的生长情况. 监控摄像头可捕捉到图像的角度范围为$\\angle PAQ=45^{\\circ}$, 其中点$P$、$Q$分别在长方形的边$BC$、$CD$上, 监控的区域为四边形$APCQ$. 记$\\angle BAP=\\theta$($0^{\\circ} \\leq \\theta \\leq 45^{\\circ}$).\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A);\n\\draw (3,0) node [below right] {$B$} coordinate (B);\n\\draw (3,2.4) node [above right] {$C$} coordinate (C);\n\\draw (0,2.4) node [above left] {$D$} coordinate (D);\n\\draw (3,{3*tan(20)}) node [right] {$P$} coordinate (P);\n\\draw ({2.4*tan(25)},2.4) node [above] {$Q$} coordinate (Q);\n\\fill [gray!20] (A) -- (P) -- (C) -- (Q) -- cycle;\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (A) -- (P) (A) -- (Q);\n\\draw (A) pic [\"$45^\\circ$\",draw, angle eccentricity = 1.7] {angle = P--A--Q};\n\\end{tikzpicture}\n\\end{center}\n(1) 当$\\theta=30^{\\circ}$时, 求$P$、$Q$两点间的距离;(结果保留整数)\\\\\n(2) 问当$\\theta$取何值时, 监控区域四边形$APCQ$的面积$S$最大? 最大值为多少?\n(结果保留整数)", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届松江二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030814": { + "id": "030814", + "content": "如图所示, 鸟类观测站需同时观测两处鸟类栖息地. $A$地在观测站正北方向, 且距离观测站$2$公里处, $B$地在观测站北偏东$\\arcsin \\dfrac 45$方向, 且距离观测站$5$公里. 观测站派出一辆观测车(记为点$M$)沿着公路向正东方向行驶进行观测, 记$\\angle AMB$为观测角.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1,0) -- (3,0) node [right] {东};\n\\draw [->] (0,-0.5) -- (0,2) node [above] {北};\n\\filldraw (0,0) circle (0.03) node [below left] {观测站};\n\\filldraw (0,1) circle (0.03) node [left] {$A$} coordinate (A);\n\\filldraw (2,1.5) circle (0.03) node [right] {$B$} coordinate (B);\n\\filldraw (0.5,0) circle (0.03) node [below] {$M$} coordinate (M);\n\\draw [dashed] (A) -- (M) -- (B);\n\\draw (M) pic [draw, scale = 0.5] {angle = B--M--A};\n\\end{tikzpicture}\n\\end{center}\n(1) 当观测车行驶至距观测站$1$公里时, 求观测角$\\angle AMB$的大小;(精确到$0.1^{\\circ}$)\\\\\n(2) 为了确保观测质量, 要求观测角$\\angle AMB$不小于$45^{\\circ}$, 求观测车行驶过程中满足要求的路程有多长.(精确到$0.1$公里)", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030815": { + "id": "030815", + "content": "某公园要建造如图所示的绿地$OABC$, $OA$、$OC$为互相垂直的墙体, 已有材料可建成的围栏$AB$与$BC$的总长度为$12$米, 且$\\angle BAO=\\angle BCO$. 设$\\angle BAO=\\alpha$($0<\\alpha<\\dfrac{\\pi}2$).\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.4]\n\\draw (0,0) node [above right] {$B$} coordinate (B);\n\\draw (B) --++ (-60:4) node [above right] {$A$} coordinate (A);\n\\draw (B) --++ (150:8) node [above right] {$C$} coordinate (C);\n\\draw (A) ++ ({-4*sqrt(3)-2},0) coordinate (O);\n\\draw ($(O)!1.2!(C)$) coordinate (C1) ($(O)!1.1!(A)$) coordinate (C4);\n\\draw ($(O)!(C1)!(A)$) ++ (-0.5,-0.5) coordinate (C2) (C4) ++ (0,-0.5) coordinate (C3);\n\\fill [pattern = north east lines] (C1) --++ (-0.5,0) -- (C2) -- (C3) -- (C4) -- (O) -- cycle;\n\\draw (O) node [below left, fill = white] {$O$};\n\\draw (C1) -- (O) -- (C4);\n\\draw pic [draw, \"$\\alpha$\", angle eccentricity = 1.5] {angle = B--A--O};\n\\draw pic [draw, \"$\\alpha$\", angle eccentricity = 1.5] {angle = O--C--B};\n\\end{tikzpicture}\n\\end{center}\n(1) 当$AB=4, \\alpha=\\dfrac{\\pi}3$时, 求$AC$的长; (结果精确到$0.1$米)\\\\\n(2) 当$AB=6$时, 求$OABC$面积$S$的最大值及此时$\\alpha$的值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届黄浦二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030816": { + "id": "030816", + "content": "某学校举办毕业联欢晩会, 舞台上方设计了三处光源. 如图, $\\triangle ABC$是边长为$6$的等边三角形, 边$BC$的中点$M$处为固定光源, $E$、$F$分别为边$AB$、$AC$上的移动光源, 且$ME$始终垂直于$MF$, 三处光源把舞台照射出五彩缤纷的若干区域.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$A$} coordinate (A);\n\\path [name path = AB] (A) --++ (240:3) node [left] {$B$} coordinate (B);\n\\path [name path = AC] (A) --++ (-60:3) node [right] {$C$} coordinate (C);\n\\draw ($(B)!0.5!(C)$) node [below] {$M$} coordinate (M);\n\\path [name path = MF] (M) --++ (70:2.5);\n\\path [name path = ME] (M) --++ (160:1.5);\n\\path [name intersections = {of = MF and AC, by = F}];\n\\path [name intersections = {of = ME and AB, by = E}];\n\\draw (A) -- (B) -- (C) -- cycle;\n\\draw (M) -- (E) node [above left] {$E$}-- (F) node [above right] {$F$}-- cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 当$F$为边$AC$的中点时, 求线段$EF$的长度;\\\\\n(2) 求$\\triangle EFM$的面积的最小值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030817": { + "id": "030817", + "content": "如图, 某地有三家工厂, 分别位于矩形$ABCD$的两个顶点$A$、$B$及$CD$的中点$P$处. $AB=20 \\text{km}, BC=10 \\text{km}$. 为了处理这三家工厂的污水, 现要在该矩形区域内 (含边界) 且与$A$、$B$等距的二点$O$处, 建造一个污水处理厂, 并铺设三条排污管道$AO, BO, PO$. 记铺设管道的总长度为$y \\text{km}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (3,0) node [right] {$B$} coordinate (B);\n\\draw (3,1.5) node [right] {$C$} coordinate (C);\n\\draw (0,1.5) node [left] {$D$} coordinate (D);\n\\draw (1.5,0.75) node [below] {$O$} coordinate (O);\n\\draw ($(C)!0.5!(D)$) node [above] {$P$} coordinate (P);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle (P) -- (O) (A) -- (O) -- (B);\n\\end{tikzpicture}\n\\end{center}\n(1) 设$\\angle BAO=\\theta$(弧度), 将$y$表示成$\\theta$的函数并求函数的定义域;\\\\\n(2)假设铺设的污水管道总长度是$(10+10 \\sqrt 3) \\text{km}$, 请确定污水处理厂的位置.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030818": { + "id": "030818", + "content": "如图所示, 等腰直角$\\triangle ABC$是某大型商场一楼大厅的局部, 商场管理部门拟用围栏在其中围出一个三角形区域$OEF$, 供商家开展促销活动. 已知$AB=AC=20$(米), $E$、$F$分别是$AB$、$AC$上的动点, $O$为$BC$的中点, 且$\\angle EOF=\\dfrac{2 \\pi}3$, 设$\\angle OEA=\\alpha$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A);\n\\draw (3,0) node [right] {$B$} coordinate (B);\n\\draw (0,3) node [above] {$C$} coordinate (C);\n\\draw ($(B)!0.5!(C)$) node [above right] {$O$} coordinate (O);\n\\draw ($(A)!(O)!(B)$) node [below] {$E$} coordinate (E);\n\\draw (O) ++ (-1.5,{1.5/sqrt(3)}) node [left] {$F$} coordinate (F);\n\\draw (A) -- (B) -- (C) -- cycle (O) -- (E) -- (F) -- cycle;\n\\end{tikzpicture}\n\\end{center}\n(1) 当$\\alpha=\\dfrac{\\pi}2$时, 求围栏$EF$段的长度(精确到$0.01$);\\\\\n(2) 求区域$OEF$面积的最小值(精确到$0.01$), 并指出面积达到最小值时的相应的$\\alpha$值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀二模试题19", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030819": { + "id": "030819", + "content": "函数$y=\\cos ^2 x-4 \\cos x+1, x \\in \\mathbf{R}$, 当$y$取最大值时, $x$的取值集合是\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安一模试题07", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030820": { + "id": "030820", + "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$所对的边分别为$a$、$b$、$c$, 且$\\cos ^2B+\\dfrac 12 \\sin 2B=1$, $00$, $x \\in \\mathbf{Z}$)的值域中仅有$5$个不同的值, 则$\\omega$的最小值为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦二模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030822": { + "id": "030822", + "content": "设$f(x)=|a+\\sin x|$, 若存在$x_1, x_2, \\cdots, x_n \\in[\\dfrac{\\pi}3, \\dfrac{5 \\pi}6]$, 使$f(x_1)+f(x_2)+\\cdots+f(x_{n-1})=f(x_n)$成立的最大正整数$n$为$9$, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届金山二模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030823": { + "id": "030823", + "content": "已知函数$f(x)=\\cos x$, 若对任意实数$x_1$、$x_2$, 方程$|f(x)-f(x_1)|+|f(x)-f(x_2)|=m$($m \\in \\mathbf{R}$)有解, 方程$|f(x)-f(x_1)|-|f(x)-f(x_2)|=n$($n \\in \\mathbf{R}$)也有解, 则$m+n$的值的集合为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届虹口一模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030824": { + "id": "030824", + "content": "若数列: $\\cos \\alpha$、$\\cos 2 \\alpha$、$\\cos 4 \\alpha$、$\\cdots, \\cos 2^n \\alpha$、$\\cdots$中的每一项都为负数, 则实数$\\alpha$的所有取值组成的集合为\\blank{50}.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题12", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030825": { + "id": "030825", + "content": "复数$(\\cos 2 \\theta+\\mathrm{i} \\sin 3 \\theta) \\cdot(\\cos \\theta+\\mathrm{i} \\sin \\theta)$的模为$1$, 其中$\\mathrm{i}$为虚数单位, $\\theta \\in[0,2 \\pi]$, 则这样的$\\theta$一共有\\bracket{20}个.\n\\fourch{$9$}{$10$}{$11$}{无数}", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届奉贤一模试题16", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030826": { + "id": "030826", + "content": "已知函数$f(x)=6 \\cos ^2 \\omega x+\\sqrt 3 \\sin 2 \\omega x-3$($\\omega>0$)的最小正周期为$8$.\\\\\n(1) 求$\\omega$的值及函数$f(x)$的单调减区间;\\\\\n(2) 若$f(x_0)=\\dfrac{8 \\sqrt 3}5$, 且$x_0 \\in(-\\dfrac{10}3, \\dfrac 23)$, 求$f(x_0+1)$的值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030827": { + "id": "030827", + "content": "已知$f(x)=\\sqrt 3 \\cos 2 x+2 \\sin (\\dfrac{3 \\pi}2+x) \\sin (\\pi-x)$, $x \\in \\mathbf{R}$.\\\\\n(1) 求$f(x)$的最小正周期及单调递减区间;\\\\\n(2) 已知锐角三角形$ABC$的内角$A$、$B$、$C$的对边分别为$a$、$b$、$c$且$f(A)=-\\sqrt 3$, $a=4$, 求$BC$边上的高的最大值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届青浦一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030828": { + "id": "030828", + "content": "设函数$f(x)=\\sin x$, $x \\in \\mathbf{R}$.\\\\\n(1) 若$\\theta \\in[0, \\pi)$, 函数$f(x+\\theta)$是偶函数, 求方程$f(x+\\theta)=\\dfrac 12$的解集;\\\\\n(2) 求函数$y=[f(x+\\dfrac{\\pi}{12})]^2+[f(x+\\dfrac{\\pi}4)]^2$的值域.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届宝山一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030829": { + "id": "030829", + "content": "已知向量$\\overrightarrow m=(\\dfrac 12, \\dfrac 12 \\sin 2 x+\\dfrac{\\sqrt 3}2 \\cos 2 x)$, $\\overrightarrow n=(f(x),-1)$, 且$\\overrightarrow m \\perp \\overrightarrow n$.\\\\\n(1) 求函数$f(x)$在$x \\in[0, \\pi]$上的单调递减区间;\\\\\n(2) 已知$\\triangle ABC$的三个内角分别为$A$、$B$、$C$, 其对应边分别为$a$、$b$、$c$, 若有$f(A-\\dfrac{\\pi}{12})=1$, $BC=\\sqrt 3$, 求$\\triangle ABC$面积的最大值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030830": { + "id": "030830", + "content": "设函数$f(x)=\\sqrt 2 \\sin (\\omega x+\\varphi)$($\\omega>0$,$0<\\varphi<\\pi$), 该函数图像上相邻两个最高点之间的距离为$4 \\pi$, 且$f(x)$为偶函数.\\\\\n(1) 求$\\omega$和$\\varphi$的值;\\\\\n(2) 在$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 若$(2 a-c) \\cos B=b \\cos C$, 求$f^2(A)+f^2(C)$的取值范围.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届普陀一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030831": { + "id": "030831", + "content": "已知$x \\in \\mathbf{R}$, $\\overrightarrow m=(2 \\cos x, 2 \\sqrt 3 \\sin x)$, $\\overrightarrow n=(\\cos x, \\cos x)$.\\\\\n(1) 设$f(x)=\\overrightarrow m \\cdot \\overrightarrow n$, 求函数$y=f(x)$的解析式及最大值;\\\\\n(2) 设$\\triangle ABC$的三个内角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 当$x=A$时, $\\overrightarrow m=a \\overrightarrow n$, 且$c=2 \\sqrt 3$, 求$\\triangle ABC$的面积.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届闵行一模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030832": { + "id": "030832", + "content": "已知函数$f(x)=M \\sin (\\omega x+\\varphi)$($\\omega>0,0<\\varphi<\\dfrac{\\pi}2$)的部分图像如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, yscale = 0.5]\n\\draw [->] (-0.5,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3.5] plot (\\x,{2*sin(2*\\x/pi*180+30)});\n\\draw (0,1) node [left] {$1$};\n\\filldraw ({5*pi/12},0) ellipse (0.03 and 0.06) node [below left] {$\\frac{5\\pi}{12}$};\n\\filldraw ({11*pi/12},0) ellipse (0.03 and 0.06) node [below right] {$\\frac{11\\pi}{12}$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求函数$f(x)$的解析式;\\\\\n(2) 在$\\angle A$为锐角的$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 若$f(\\dfrac A2)=\\dfrac{\\sqrt 6+\\sqrt 2}2$, $b+c=2+3 \\sqrt 2$, 且$\\triangle ABC$的面积为$3$, 求$a$的值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届徐汇二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030833": { + "id": "030833", + "content": "设函数$f(x)=\\sin (m x)$.\\\\\n(1) 若$m \\in(0,1)$, 且函数$f(x)$与$y=\\lg x$的图像有横纵坐标均为正整数的交点, 求$m$的值;\\\\\n(2) 设$m=1$, $g(x)=2 f^2(x)+f(2 x)$, 在锐角$\\triangle ABC$中, 内角$A$、$B$、$C$对应的边分别为$a$、$b$、$c$, 若$g(A)=2$, $\\overrightarrow{AB} \\cdot \\overrightarrow{AC}=2 \\sqrt 2$, 求$\\triangle ABC$的面积.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届静安二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030834": { + "id": "030834", + "content": "已知函数$f(x)=t \\sin x-\\cos x$($t \\in \\mathbf{R}$).\n(1) 若函数$f(x)$为偶函数, 求实数$t$的值;\\\\\n(2) 当$t=\\sqrt 3$时, 在$\\triangle ABC$中(角$A$、$B$、$C$所对的边分别为$a$、$b$、$c$), 若$f(2A)=2$, $c=3$, 且$\\triangle ABC$的面积为$2 \\sqrt 3$, 求$a$的值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届浦东二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030835": { + "id": "030835", + "content": "已知函数$f(x)=t \\sin x+|\\cos x|$, 其中常数$t \\in \\mathbf{R}$.\\\\\n(1) 讨论函数$f(x)$的奇偶性, 并说明理由;\\\\\n(2) $\\triangle ABC$中, 内角$A$、$B$、$C$所对的边分别为$a$、$b$、$c$, 且$a=2$, $b=\\sqrt 5$, $f(A)=2$, 求当$t=\\sqrt 3$时, $\\triangle ABC$的面积.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "030836": { + "id": "030836", + "content": "已知$f(x)=\\sqrt 3 \\sin 2 x-2 \\cos ^2 x-1$.\\\\\n(1) 求函数$y=f(x)$的单调递增区间;\\\\\n(2) 设$\\triangle ABC$的内角$A$满足$f(A)=0$, 且$\\overrightarrow{AB} \\cdot \\overrightarrow{AC}=3$, 求$BC$边长的最小值.", + "objs": [], + "tags": [ + "第三单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届崇明二模试题18", + "edit": [ + "20230107\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" } } \ No newline at end of file