wangweiye
/
mathdeptv2
Archived
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

20230326 noon

This commit is contained in:
weiye.wang 2023-03-26 12:45:17 +08:00
parent b6665c91ab
commit 5a25bf45c8
8 changed files with 437 additions and 197 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
工具/修改题目数据库.ipynb
View File

@ -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",

8
工具/关键字筛选题号.ipynb
View File

@ -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": {

2
工具/寻找阶段末尾空闲题号.ipynb
View File

@ -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"
]
}
],

2
工具/文本文件/题号筛选.txt
View File

@ -1 +1 @@
000116,008197,008210,010266
004221,012238,013537,014499,014506

118
工具/添加题目到数据库.ipynb
View File

@ -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"
]
}
],

110
工具/识别题库中尚未标注的题目类型.ipynb
View File

@ -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"
]
}
],

8
工具/题号选题pdf生成.ipynb
View File

@ -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": {

380
题库0.3/Problems.json
View File

@ -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.",