From 5a25bf45c82a09188f106c09c5d40be599925ced Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 26 Mar 2023 12:45:17 +0800 Subject: [PATCH] 20230326 noon --- 工具/修改题目数据库.ipynb | 6 +- 工具/关键字筛选题号.ipynb | 8 +- 工具/寻找阶段末尾空闲题号.ipynb | 2 +- 工具/文本文件/题号筛选.txt | 2 +- 工具/添加题目到数据库.ipynb | 118 ++------ 工具/识别题库中尚未标注的题目类型.ipynb | 110 ++----- 工具/题号选题pdf生成.ipynb | 8 +- 题库0.3/Problems.json | 380 ++++++++++++++++++++++++ 8 files changed, 437 insertions(+), 197 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 5ea573ab..40c58a52 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": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 3, + "execution_count": 2, "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 = \"13543,13685\"\n", + "problems = \"14764:14783\"\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 df2cbb2b..9adae067 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": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 3, + "execution_count": 2, "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", - " {\"content\":[r\"a=13\"]}\n", + " {\"content\":[r\"双曲线\"],\"content2\":[r\"部分\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", @@ -110,7 +110,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.15" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { 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 ff1b413c..70364c1a 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 @@ -12,7 +12,7 @@ "首个空闲id: 14764 , 直至 020000\n", "首个空闲id: 22106 , 直至 030000\n", "首个空闲id: 31361 , 直至 040000\n", - "首个空闲id: 40246 , 直至 999999\n" + "首个空闲id: 40336 , 直至 999999\n" ] } ], 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 86c2f39f..94677037 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 @@ -000116,008197,008210,010266 \ No newline at end of file +004221,012238,013537,014499,014506 \ 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 f98424ea..c063af0e 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -7,10 +7,10 @@ "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 40246\n", - "raworigin = \"\"\n", - "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目10.tex\"\n", - "editor = \"20230324\\t王伟叶\"\n", + "starting_id = 14764\n", + "raworigin = \"2023年空中课堂高三复习课\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目9.tex\"\n", + "editor = \"20230326\\t王伟叶\"\n", "indexed = False\n" ] }, @@ -23,96 +23,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "添加题号040246, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040247, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040248, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040249, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040250, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040251, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040252, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040253, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040254, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040255, 来源: 2025届高一下学期周末卷05小测\n", - "添加题号040256, 来源: 2025届高一下学期周末卷06\n", - "添加题号040257, 来源: 2025届高一下学期周末卷06\n", - "添加题号040258, 来源: 2025届高一下学期周末卷06\n", - "添加题号040259, 来源: 2025届高一下学期周末卷06\n", - "添加题号040260, 来源: 2025届高一下学期周末卷06\n", - "添加题号040261, 来源: 2025届高一下学期周末卷06\n", - "添加题号040262, 来源: 2025届高一下学期周末卷06\n", - "添加题号040263, 来源: 2025届高一下学期周末卷06\n", - "添加题号040264, 来源: 2025届高一下学期周末卷06\n", - "添加题号040265, 来源: 2025届高一下学期周末卷06\n", - "添加题号040266, 来源: 2025届高一下学期周末卷06\n", - "添加题号040267, 来源: 2025届高一下学期周末卷06\n", - "添加题号040268, 来源: 2025届高一下学期周末卷06\n", - "添加题号040269, 来源: 2025届高一下学期周末卷06\n", - "添加题号040270, 来源: 2025届高一下学期周末卷06\n", - "添加题号040271, 来源: 2025届高一下学期周末卷06\n", - "添加题号040272, 来源: 2025届高一下学期周末卷06\n", - "添加题号040273, 来源: 2025届高一下学期周末卷06\n", - "添加题号040274, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040275, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040276, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040277, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040278, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040279, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040280, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040281, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040282, 来源: 2025届高一下学期周末卷06小测\n", - "添加题号040283, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040284, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040285, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040286, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040287, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040288, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040289, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040290, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040291, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040292, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040293, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040294, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040295, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040296, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040297, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040298, 来源: 2025届高一下学期期中复习一(集合逻辑不等式)\n", - "添加题号040299, 来源: 2024届高二下学期周末卷06\n", - "添加题号040300, 来源: 2024届高二下学期周末卷06\n", - "添加题号040301, 来源: 2024届高二下学期周末卷06\n", - "添加题号040302, 来源: 2024届高二下学期周末卷06\n", - "添加题号040303, 来源: 2024届高二下学期周末卷06\n", - "添加题号040304, 来源: 2024届高二下学期周末卷06\n", - "添加题号040305, 来源: 2024届高二下学期周末卷06\n", - "添加题号040306, 来源: 2024届高二下学期周末卷06\n", - "添加题号040307, 来源: 2024届高二下学期周末卷06\n", - "添加题号040308, 来源: 2024届高二下学期周末卷06\n", - "添加题号040309, 来源: 2024届高二下学期周末卷06\n", - "添加题号040310, 来源: 2024届高二下学期周末卷06\n", - "添加题号040311, 来源: 2024届高二下学期周末卷06\n", - "添加题号040312, 来源: 2024届高二下学期周末卷06\n", - "添加题号040313, 来源: 2024届高二下学期周末卷06\n", - "添加题号040314, 来源: 2024届高二下学期周末卷06\n", - "添加题号040315, 来源: 2024届高二下学期周末卷06\n", - "添加题号040316, 来源: 2024届高二下学期周末卷06\n", - "添加题号040317, 来源: 2024届高二下学期周末卷07\n", - "添加题号040318, 来源: 2024届高二下学期周末卷07\n", - "添加题号040319, 来源: 2024届高二下学期周末卷07\n", - "添加题号040320, 来源: 2024届高二下学期周末卷07\n", - "添加题号040321, 来源: 2024届高二下学期周末卷07\n", - "添加题号040322, 来源: 2024届高二下学期周末卷07\n", - "添加题号040323, 来源: 2024届高二下学期周末卷07\n", - "添加题号040324, 来源: 2024届高二下学期周末卷07\n", - "添加题号040325, 来源: 2024届高二下学期周末卷07\n", - "添加题号040326, 来源: 2024届高二下学期周末卷07\n", - "添加题号040327, 来源: 2024届高二下学期周末卷07\n", - "添加题号040328, 来源: 2024届高二下学期周末卷07\n", - "添加题号040329, 来源: 2024届高二下学期周末卷07\n", - "添加题号040330, 来源: 2024届高二下学期周末卷07\n", - "添加题号040331, 来源: 2024届高二下学期周末卷07\n", - "添加题号040332, 来源: 2024届高二下学期周末卷07\n", - "添加题号040333, 来源: 2024届高二下学期周末卷07\n", - "添加题号040334, 来源: 2024届高二下学期周末卷07\n", - "添加题号040335, 来源: 2024届高二下学期周末卷07\n" + "添加题号014764, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014765, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014766, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014767, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014768, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014769, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014770, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014771, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014772, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014773, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014774, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014775, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014776, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014777, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014778, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014779, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014780, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014781, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014782, 来源: 2023年空中课堂高三复习课24\n", + "添加题号014783, 来源: 2023年空中课堂高三复习课24\n" ] } ], diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb index f36c673d..31107fe8 100644 --- a/工具/识别题库中尚未标注的题目类型.ipynb +++ b/工具/识别题库中尚未标注的题目类型.ipynb @@ -9,96 +9,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "040246 填空题\n", - "040247 填空题\n", - "040248 填空题\n", - "040249 填空题\n", - "040250 填空题\n", - "040251 填空题\n", - "040252 填空题\n", - "040253 填空题\n", - "040254 解答题\n", - "040255 解答题\n", - "040256 填空题\n", - "040257 填空题\n", - "040258 填空题\n", - "040259 填空题\n", - "040260 填空题\n", - "040261 填空题\n", - "040262 填空题\n", - "040263 填空题\n", - "040264 解答题\n", - "040265 解答题\n", - "040266 填空题\n", - "040267 填空题\n", - "040268 填空题\n", - "040269 填空题\n", - "040270 填空题\n", - "040271 填空题\n", - "040272 填空题\n", - "040273 填空题\n", - "040274 填空题\n", - "040275 填空题\n", - "040276 填空题\n", - "040277 填空题\n", - "040278 填空题\n", - "040279 填空题\n", - "040280 填空题\n", - "040281 填空题\n", - "040282 解答题\n", - "040283 解答题\n", - "040284 解答题\n", - "040285 解答题\n", - "040286 解答题\n", - "040287 解答题\n", - "040288 解答题\n", - "040289 解答题\n", - "040290 解答题\n", - "040291 填空题\n", - "040292 填空题\n", - "040293 选择题\n", - "040294 解答题\n", - "040295 解答题\n", - "040296 解答题\n", - "040297 解答题\n", - "040298 解答题\n", - "040299 填空题\n", - "040300 填空题\n", - "040301 填空题\n", - "040302 填空题\n", - "040303 填空题\n", - "040304 填空题\n", - "040305 填空题\n", - "040306 填空题\n", - "040307 填空题\n", - "040308 填空题\n", - "040309 填空题\n", - "040310 填空题\n", - "040311 解答题\n", - "040312 解答题\n", - "040313 解答题\n", - "040314 解答题\n", - "040315 解答题\n", - "040316 解答题\n", - "040317 填空题\n", - "040318 填空题\n", - "040319 填空题\n", - "040320 填空题\n", - "040321 填空题\n", - "040322 填空题\n", - "040323 填空题\n", - "040324 填空题\n", - "040325 填空题\n", - "040326 填空题\n", - "040327 填空题\n", - "040328 填空题\n", - "040329 填空题\n", - "040330 选择题\n", - "040331 选择题\n", - "040332 解答题\n", - "040333 解答题\n", - "040334 解答题\n", - "040335 解答题\n" + "014764 填空题\n", + "014765 填空题\n", + "014766 填空题\n", + "014767 填空题\n", + "014768 选择题\n", + "014769 解答题\n", + "014770 解答题\n", + "014771 解答题\n", + "014772 填空题\n", + "014773 填空题\n", + "014774 填空题\n", + "014775 解答题\n", + "014776 填空题\n", + "014777 填空题\n", + "014778 填空题\n", + "014779 填空题\n", + "014780 填空题\n", + "014781 选择题\n", + "014782 填空题\n", + "014783 解答题\n" ] } ], diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb index 60d47b7f..db1c11d8 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -9,9 +9,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/三角_教师用_20230321.tex\n", + "开始编译教师版本pdf文件: 临时文件/轨迹_教师用_20230325.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/三角_学生用_20230321.tex\n", + "开始编译学生版本pdf文件: 临时文件/轨迹_学生用_20230325.tex\n", "0\n" ] } @@ -32,7 +32,7 @@ "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/三角\"\n", + "filename = \"临时文件/轨迹\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\"\"\"---设置是否需要解答题的空格---\"\"\"\n", @@ -191,7 +191,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.15" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 90cfaf58..d9937264 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -362298,6 +362298,386 @@ "remark": "", "space": "12ex" }, + "014764": { + "id": "014764", + "content": "某质点沿直线运动, 位移$y$(单位: $\\text{m}$) 与时间$t$(单位: $\\text{s}$) 之间的关系满足$y=f(t)$, 其中$f(t)=2 t^2+3 t$, 则该质点在$1 \\leq t \\leq 2$这段时间内的平均速度为\\blank{50}$\\text{m} / \\text{s}$, 在$t=1 \\text{s}$时的瞬时速度为\\blank{50}$\\text{m} / \\text{s}$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014765": { + "id": "014765", + "content": "已知$f(x)=x^3-2 \\ln x$, 则曲线$y=f(x)$在点$(1, f(1))$处的切线的倾斜角为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014766": { + "id": "014766", + "content": "已知$f(x)=\\mathrm{e}^x \\cos 2 x-\\mathrm{e}^2$, 则函数$y=f(x)$的导数$f'(x)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014767": { + "id": "014767", + "content": "已知函数$y=f(x)$, 其导函数$y=f'(x)$的图像如图所示, 则下列所有真命题的序号为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -0.5:4.5, samples = 100] plot (\\x,{-\\x*(\\x-2)*(\\x-4)/6});\n\\foreach \\i in {1,2,3,4}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\draw (1,1) node {$y=f'(x)$};\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} 函数$y=f(x)$在区间$(-\\infty, 1)$上严格减;\\\\\n\\textcircled{2} 函数$y=f(x)$在区间$(2,4)$上严格增;\\\\\n\\textcircled{3} 函数$y=f(x)$在$x=0$处取得极小值;\\\\\n\\textcircled{4} 函数$y=f(x)$在$x=4$处取得极大值.\\\\", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014768": { + "id": "014768", + "content": "已知函数$y=f(x)$, 其导函数$y=f'(x)$的图像如图所示. 以下四个选项中, 可能表示函数$y=f(x)$的图像是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1, samples = 100] plot (\\x,{1.5*(1-\\x*\\x)});\n\\foreach \\i in {-1,1}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\draw (1,2) node {$y=f'(x)$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1, samples = 100] plot (\\x,{pow(\\x,3)});\n\\foreach \\i in {-1,1}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\end{tikzpicture}\n}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1, samples = 100] plot (\\x,{1.5*\\x-0.5*pow(\\x,3)});\n\\foreach \\i in {-1,1}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1, samples = 100] plot (\\x,{0.5*\\x*\\x+\\x-0.5});\n\\foreach \\i in {-1,1}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1, samples = 100] plot (\\x,{-0.5*\\x*\\x+\\x+0.5});\n\\foreach \\i in {-1,1}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014769": { + "id": "014769", + "content": "现有一张半径为$2$米的圆形铁皮, 从中裁剪出一块扇形铁皮 (如图$1$中阴影部分), 并卷成一个深度为$h$米的圆锥筒 (如图$2$) 的容器. 当圆锥筒容器的深度$h$为多少米时, 其容积最大? 容积的最大值为多少立方米? (铁皮厚度忽略不计)\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) circle (2);\n\\draw (0,0) --++ (30:2) (0,0) --++ (150:2);\n\\draw (0,-2) node [below] {图$1$};\n\\draw (4,-2) --++ (1.5,3) node [midway, below right] {$2$} (4,-2) --++ (-1.5,3);\n\\draw (4,1) ellipse (1.5 and 0.5);\n\\draw (4,-2) -- (4,1) node [midway, left] {$h$} --++ (1.5,0) node [midway, above] {$r$};\n\\draw (4,-2) node [below] {图$2$};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014770": { + "id": "014770", + "content": "已知$f(x)=2 x^4-x$.\\\\\n(1) 求曲线$y=f(x)$在点$A(1,1)$处的切线$l$的方程;\\\\\n(2) 证明: 曲线$y=f(x)$上除切点$A(1,1)$外, 其余点都在该切线$l$的上方.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014771": { + "id": "014771", + "content": "已知$a \\in \\mathbf{R}$, $f(x)=a x-(2 a+1) \\ln x-\\dfrac{2}{x}$.\\\\\n(1) 若$x=1$是函数$y=f(x)$的驻点, 求$a$的值;\\\\\n(2) 当$a>0$时, 求函数$y=f(x)$的单调区间.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014772": { + "id": "014772", + "content": "设曲线$y=\\ln x+2 x$的斜率为$3$的切线为$l$, 则$l$的方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014773": { + "id": "014773", + "content": "已知$f(x)=\\dfrac{x}{x^2+1}$, 则函数$y=f(x)$的导数$f'(x)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014774": { + "id": "014774", + "content": "已知定义在区间$(-3,3)$上的奇函数$y=f(x)$的导函数是$y=f'(x)$, 当$x \\geq 0$时, $y=f(x)$的图像如图所示, 则关于$x$的不等式$\\dfrac{f'(x)}{x}>0$的解集为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-1,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:3] plot (\\x,{\\x*(2-\\x)});\n\\draw [dashed] (1,1) -- (1,0) node [below] {$1$};\n\\draw [dashed] (3,-3) -- (3,0) node [above] {$3$};\n\\draw (2,0) node [below left] {$2$};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014775": { + "id": "014775", + "content": "已知$f(x)=\\dfrac{1}{2} \\sin 2 x+\\cos x$, 求函数$y=f(x), x \\in[0,2 \\pi]$的最大值和最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "014776": { + "id": "014776", + "content": "已知$f(x)=x^2+x$, 则曲线$y=f(x)$在点$(0, f(0))$处的切线方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014777": { + "id": "014777", + "content": "函数$y=\\dfrac{\\ln x}{x}$的驻点为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014778": { + "id": "014778", + "content": "已知函数$y=f(x)$, 其导函数$y=f'(x)$的图像如图所示, 则下列所有真命题的序号为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2.5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {-2,-1,1,2,3,4}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\draw (-2,-2) .. controls ++ (0.2,0.6) and ++ (-0.1,-0.25) .. (-1,0) .. controls ++ (0.1,0.25) and ++ (-0.6,0) .. (1,2) .. controls ++ (0.6,0) and ++ (-0.1,0.4) .. (2,0) .. controls ++ (0.3,-1.2) and ++ (-0.5,0) .. (4,-2);\n\\draw [dashed] (-2,-2) -- (-2,0) (1,2) -- (1,0) (4,-2) -- (4,0);\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} $y=f(x)$在区间$[-2,-1]$上严格增;\\\\\n\\textcircled{2} $x=-1$是$y=f(x)$的极小值点;\\\\\n\\textcircled{3} $y=f(x)$在区间$[-1,2]$上严格增, 在区间$[2,4]$上严格减;\\\\\n\\textcircled{4} $x=2$是$y=f(x)$的极小值点.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014779": { + "id": "014779", + "content": "已知$0<\\varphi<\\pi$, $f(x)=x \\cos (x+\\varphi)-\\cos x$, 函数$y=f(x)$, $x \\in(-\\pi, \\pi)$是偶函数, 则$y=f(x)$的单调减区间为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014780": { + "id": "014780", + "content": "用总长$148 \\text{cm}$的钢条制作一个长方体容器的框架, 若容器底面的长比宽多$5 \\text{cm}$, 要使它的容积最大, 则容器底面的宽为\\blank{50}$\\text{cm}$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014781": { + "id": "014781", + "content": "已知函数$y=f(x)$与它的导函数$y=f'(x)$的定义域均为$\\mathbf{R}$, 现有下述两个命题:\\\\\n\\textcircled{1} ``$y=f(x)$为奇函数''是``$y=f'(x)$为偶函数''的充分非必要条件;\\\\\n\\textcircled{2} ``$y=f(x)$为严格增函数''是``$y=f'(x)$为严格增函数''的必要非充分条件. 则说法正确的选项是\\bracket{20}.\n\\twoch{命题\\textcircled{1}和\\textcircled{2}均为真命题}{命题\\textcircled{1}为真命题, 命题\\textcircled{2}为假命题}{命题\\textcircled{1}为假命题, 命题\\textcircled{2}为真命题}{命题\\textcircled{1}和\\textcircled{2}均为假命题}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014782": { + "id": "014782", + "content": "已知$a \\in \\mathbf{R}$, $f(x)=\\sin ^2 x-a \\sin x$. 若函数$y=f(x)-f(\\dfrac{\\pi}{2}-x)$在区间$[0, \\dfrac{\\pi}{2}]$上是严格增函数, 则$a$的最大值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "014783": { + "id": "014783", + "content": "设$f(x)=a x^3-(a+1) x^2+x$, $g(x)=k x+m$, 其中$a \\geq 0$, $k$、$m \\in \\mathbf{R}$. 若对任意$x \\in[0,1]$, 均有$f(x) \\leq g(x)$, 则称函数$y=g(x)$是函数$y=f(x)$的``控制函数'', 且记所有的``控制函数''$y=g(x)$在$x=x_0$($0 \\leq x_0 \\leq 1$)处的最小值为$\\overline {f}(x_0)$.\\\\\n(1) 若$a=2, g(x)=x$, 问: 函数$y=g(x)$是否为函数$y=f(x)$的``控制函数''? 请说明理由;\\\\\n(2) 若$a=0$, 且直线$y=h(x)$是曲线$y=f(x)$在点$(\\dfrac{1}{4}, f(\\dfrac{1}{4}))$处的切线, 证明: 函数$y=h(x)$是函数$y=f(x)$的``控制函数'', 并求$\\overline {f}(\\dfrac{1}{4})$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年空中课堂高三复习课24", + "edit": [ + "20230326\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",