diff --git a/工具/分年级专用工具/赋能卷生成.ipynb b/工具/分年级专用工具/赋能卷生成.ipynb index 73f25d6b..b960e6f9 100644 --- a/工具/分年级专用工具/赋能卷生成.ipynb +++ b/工具/分年级专用工具/赋能卷生成.ipynb @@ -17,11 +17,11 @@ "#在 临时文件/赋能答题纸 目录中保留一个pdf(赋能试卷的答题纸), 不留别的pdf文件. \n", "#在 临时文件/赋能答题纸 目录中保留 赋能template.tex.\n", "\"\"\"---设置文件名---\"\"\"\n", - "filename = \"赋能04\"\n", + "filename = \"赋能05\"\n", "\n", "\"\"\"---设置题目列表---\"\"\"\n", "problems = r\"\"\"\n", - "356,357,30074,359:364,30075\n", + "366:369,30281,371:375\n", "\"\"\"\n", "#完成后将含有 filename 的文件移至其它目录\n", "\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 24fd7c2a..e7d2e0a2 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 @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "首个空闲id: 11988 , 直至 020000\n", + "首个空闲id: 12030 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30276 , 直至 999999\n" + "首个空闲id: 30282 , 直至 999999\n" ] } ], diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb index 4007b3ea..0bf35ac8 100644 --- a/工具/添加关联题目.ipynb +++ b/工具/添加关联题目.ipynb @@ -2,15 +2,15 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import os,re,json,time\n", "\n", "\"\"\"---设置原题目id与新题目id---\"\"\"\n", - "old_id = \"10518\"\n", - "new_id = \"30280\"\n", + "old_id = \"370\"\n", + "new_id = \"30281\"\n", "\"\"\"---设置完毕---\"\"\"\n", "\n", "old_id = old_id.zfill(6)\n", @@ -31,7 +31,7 @@ " pro_dict[new_id][field] = new_id\n", " pro_dict[new_id][\"related\"].append(old_id)\n", " pro_dict[new_id][\"same\"] = []\n", - " pro_dict[new_id][\"objs\"] = []\n", + " pro_dict[new_id][\"objs\"] = pro_dict[old_id][\"objs\"].copy()\n", " pro_dict[new_id][\"usages\"] = []\n", " pro_dict[new_id][\"edit\"].append(str(time.localtime().tm_year)+str(time.localtime().tm_mon).zfill(2)+str(time.localtime().tm_mday).zfill(2) + \"\\t\")\n", " pro_dict[old_id][\"related\"].append(new_id)\n", @@ -50,7 +50,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -64,12 +64,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 70501904..c2dbefe6 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": 4, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 30274\n", - "origin = \"自拟题目\"\n", - "filename = r\"C:\\Users\\wang weiye\\Documents\\wwy sync\\临时工作区\\自拟题目2.tex\"\n", - "editor = \"20221020\\t王伟叶\"" + "starting_id = 12009\n", + "origin = \"2022届杨浦高三基础考试题\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目2.tex\"\n", + "editor = \"20221027\\t王伟叶\"" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -70,7 +70,7 @@ " pid = str(id).zfill(6)\n", " if pid in pro_dict:\n", " duplicate_flag = True\n", - " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin, dict = pro_dict,editor = editor)\n", + " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + str(id - starting_id + 1), dict = pro_dict,editor = editor)\n", " pro_dict[pid] = NewProblem\n", " id += 1\n", "\n", @@ -100,7 +100,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -114,12 +114,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index 4e35799f..b0a276fd 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -15,9 +15,9 @@ "题块 2 处理完毕.\n", "正在处理题块 3 .\n", "题块 3 处理完毕.\n", - "开始编译教师版本pdf文件: 临时文件/周末卷06_教师_20221025.tex\n", + "开始编译教师版本pdf文件: 临时文件/2022届杨浦区基础考_教师_20221027.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/周末卷06_学生_20221025.tex\n", + "开始编译学生版本pdf文件: 临时文件/2022届杨浦区基础考_学生_20221027.tex\n", "0\n" ] } @@ -41,7 +41,7 @@ "# enumi_mode = 0\n", "\n", "#2023届测验卷与周末卷\n", - "exec_list = [(\"标题替换\",\"周末卷06\")]\n", + "exec_list = [(\"标题替换\",\"2021届杨浦区基础考\")]\n", "enumi_mode = 1\n", "\n", "# 日常选题讲义\n", @@ -51,15 +51,15 @@ "\"\"\"---其他预处理替换命令结束---\"\"\"\n", "\n", "\"\"\"---设置目标文件名---\"\"\"\n", - "destination_file = \"临时文件/周末卷06\"\n", + "destination_file = \"临时文件/2022届杨浦区基础考\"\n", "\"\"\"---设置目标文件名结束---\"\"\"\n", "\n", "\n", "\"\"\"---设置题号数据---\"\"\"\n", "problems = [\n", - "\"010497,010501,001726,30279,30280,001724,001668,030278,001631\",\n", - "\"001676,010487,009998,010491\",\n", - "\"010470,10533,010508,010000\"\n", + "\"12009:12020\",\n", + "\"12021:12024\",\n", + "\"12025:12029\"\n", "]\n", "\"\"\"---设置题号数据结束---\"\"\"\n", "\n", @@ -210,7 +210,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -224,12 +224,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/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 0f4aa244..721d1544 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 @@ -2,9 +2,58 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "011988 填空题\n", + "011989 填空题\n", + "011990 填空题\n", + "011991 填空题\n", + "011992 填空题\n", + "011993 填空题\n", + "011994 填空题\n", + "011995 填空题\n", + "011996 填空题\n", + "011997 填空题\n", + "011998 填空题\n", + "011999 填空题\n", + "012000 选择题\n", + "012001 选择题\n", + "012002 选择题\n", + "012003 选择题\n", + "012004 解答题\n", + "012005 解答题\n", + "012006 解答题\n", + "012007 解答题\n", + "012008 解答题\n", + "012009 填空题\n", + "012010 填空题\n", + "012011 填空题\n", + "012012 填空题\n", + "012013 填空题\n", + "012014 填空题\n", + "012015 填空题\n", + "012016 填空题\n", + "012017 填空题\n", + "012018 填空题\n", + "012019 填空题\n", + "012020 填空题\n", + "012021 选择题\n", + "012022 选择题\n", + "012023 选择题\n", + "012024 选择题\n", + "012025 解答题\n", + "012026 解答题\n", + "012027 解答题\n", + "012028 解答题\n", + "012029 解答题\n" + ] + } + ], "source": [ "import os,re,json\n", "\n", @@ -18,10 +67,13 @@ " if pro_dict[p][\"genre\"] == \"\":\n", " if \"bracket\" in pro_dict[p][\"content\"]:\n", " pro_dict[p][\"genre\"] = \"选择题\"\n", + " print(p,\"选择题\")\n", " elif \"blank\" in pro_dict[p][\"content\"]:\n", " pro_dict[p][\"genre\"] = \"填空题\"\n", + " print(p,\"填空题\")\n", " else:\n", " pro_dict[p][\"genre\"] = \"解答题\"\n", + " print(p,\"解答题\")\n", "\n", "#将修改结果写入json数据库\n", "database = json.dumps(pro_dict,indent = 4, ensure_ascii= False)\n", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 5232d927..735071ea 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -9692,7 +9692,9 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [], + "related": [ + "030281" + ], "remark": "", "space": "" }, @@ -9752,7 +9754,7 @@ }, "000373": { "id": "000373", - "content": "若$(2x^2+\\dfrac1x)^n$($n\\in \\mathbf{N}^*$)的二项展开式中的第$9$项是常数项, 则$n=$\\blank{50}.", + "content": "若$(2x^2+\\dfrac1x)^n$($n\\in \\mathbf{N}$, $n\\ge 1$)的二项展开式中的第$9$项是常数项, 则$n=$\\blank{50}.", "objs": [], "tags": [ "第八单元" @@ -284050,6 +284052,804 @@ "remark": "", "space": "" }, + "011988": { + "id": "011988", + "content": "函数$f(x)=\\sqrt {5-x}$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题1", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011989": { + "id": "011989", + "content": "已知集合$A=(-\\infty ,a]$, $B=[2,3]$且$A\\cap B$非空, 则实数$a$的取值范围\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题2", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011990": { + "id": "011990", + "content": "若函数$y=\\cos (x+\\varphi)$为奇函数, 则最小的正数$\\varphi =$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题3", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011991": { + "id": "011991", + "content": "已知长方体的长、宽、高分别为$3$、$4$、$12$, 则长方体的一条对角线长为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题4", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011992": { + "id": "011992", + "content": "幂函数$f(x)$的图像过点$(4,2)$, 其反函数为$f^{-1}(x)$, 则$f^{-1}(3)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题5", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011993": { + "id": "011993", + "content": "$(1+x)^n$的二项展开式中, 若第9项与第13项系数相等, 则第20项为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题6", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011994": { + "id": "011994", + "content": "若$f(x)$是定义在$\\mathbf{R}$上的奇函数, 当$x<0$时, $f(x)=\\log_2(2-x)$, 则$f(0)+f(2)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题7", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011995": { + "id": "011995", + "content": "用$0$、$1$、$2$、$3$、$4$这五个数可以组成\\blank{50}个没有重复数字的四位奇数(用数字作答).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题8", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011996": { + "id": "011996", + "content": "若$\\sin (\\alpha -\\dfrac{\\pi }4)=-\\dfrac 35$, 则$\\sin2\\alpha =$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题9", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011997": { + "id": "011997", + "content": "$P$是直角三角形$ABC$所在平面外一点, 已知三角形的边长$AB=3$, $BC=4$, $\\angle ABC=90^{\\circ }$, $PA=PB=PC=4$, 则直线$PB$与平面$ABC$所成角的余弦值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题10", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011998": { + "id": "011998", + "content": "函数$y=f(x)$的定义域$D$和值域$A$都是集合$\\{1,2,3\\}$的非空真子集, 如果对于$D$内任意的$x$, 总有$x+f(x)+xf(x)$的值是奇数, 则满足条件的函数$y=f(x)$的个数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题11", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "011999": { + "id": "011999", + "content": "若分段函数$\\begin{cases} 3\\sin2x, & x\\le 0,\\\\ 2^x-3, & x>0, \\end{cases}$, 将函数$y=|f(x)-f(a)|$, $x\\in [m,n]$的最大值记作\n$Z_a[m,n]$, 那么当$-2\\le m\\le 2$时, $Z_2[m,m+4]$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题12", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012000": { + "id": "012000", + "content": "设直线$a$、$b$与平面$\\alpha$所成的角相等, 则直线$a$、$b$的位置关系为\\bracket{20}.\n\\fourch{平行}{平行或异面}{平行或相交}{平行、相交或异面}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题13", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012001": { + "id": "012001", + "content": "已知$x,y\\in \\mathbf{R}$, 则``$x=y$''是``$\\ln x=\\ln y$''的\\bracket{20}\n\\fourch{充分非必要条件}{必要非充分条件}{充要条件}{非充分非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题14", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012002": { + "id": "012002", + "content": "申辉中学从$4$名有数学特长的同学A、B、C、D中挑$1$人去参加中学生数学联赛, 4名同学各自对结果的估计如下: A: ``参赛的是A''; B: ``参赛的是B''; C: ``参赛的是A或B''; D: ``参赛的既不是A也不是C''; 已知其中有且只有$2$人的估计是正确的, 则参加联赛的是\\bracket{20}.\n\\fourch{A同学}{B同学}{C同学}{D同学}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题15", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012003": { + "id": "012003", + "content": "设函数$f(x)=x\\lg x$满足$f(a)f(b)f(c)<0\\ (a=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (2,0) node [right] {$B$} coordinate (B);\n\\draw (0,2) node [above] {$S$} coordinate (S);\n\\draw ($(B)!0.5!(S)$) node [above right] {$P$} coordinate (P);\n\\draw ({2*cos(-135)},{0.5*cos(-135)}) node [below left] {$A$} coordinate (A);\n\\draw (B) arc (0:-180:2 and 0.5) (B) -- (S) -- (-2,0);\n\\draw [dashed] (B) arc (0:180:2 and 0.5) (O) -- (S) (O) -- (B) (A) -- (P) (O) -- (A);\n\\end{tikzpicture}\n\\end{center}\n(1) 求圆锥的表面积;\\\\\n(2) 求异面直线$SO$与$PA$所成角的大小(结果用反三角函数表示).", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题17", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012005": { + "id": "012005", + "content": "已知在$\\triangle ABC$中, 三边$a$、$b$、$c$分别对应三个内角$A$、$B$、$C$, 且$\\dfrac a{c+b-a}=\\dfrac{c-b+a}b$.\\\\\n(1) 求角$C$的大小;\\\\ \n(2) 当在$\\triangle ABC$外接圆半径$R=1$时, 求$\\triangle ABC$面积的最大值, 并判断此时$\\triangle ABC$的形状.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题18", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012006": { + "id": "012006", + "content": "某地区去年的水价为$4.2$元/立方米, 年用水量为$m$立方米, 今年计划将水价降到$2.8$元/立方米至$4$元/立方米之间, 而用户期望水价为$2.5$元/立方米, 经测算, 下调水价后新增的用水量与实际水价和用户期望水价的差成反比(比例系数为$0.5m$), 该地区的成本为$2$元/立方米.\\\\\n(1) 今年水价下调后, 为保证供水部门的收益不得低于去年的收益, 则实际水价$x$最低价格为多少?(保留$2$位小数)\\\\\n(2) 试问调价后, 今年供水部门收益的最小值为多少?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题19", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012007": { + "id": "012007", + "content": "设函数$f(x)$的定义域为$(0,+\\infty)$, 且同时满足以下两个条件: \n\\textcircled{1} 存在实数$a>1$, 使得$f(a)=1$; \\textcircled{2} 当$m\\in \\mathbf{R}$, $x>0$时, 有$f(x^m)-mf(x)=0$恒成立.\\\\\n(1) 函数$y=\\ln x$是否满足上述的两个条件, 并说明理由;\\\\ \n(2) 求证: 当$x,y>0$时, $f(\\dfrac xy)=f(x)-f(y)$;\\\\\n(3) 若当$t>0$时, $f(t^2+4)-f(t)\\ge 1$, 求实数$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题20", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012008": { + "id": "012008", + "content": "函数$f(x)=g(x)+h(x)$, 其中$g(x)$是定义在$\\mathbf{R}$上的周期函数, $h(x)=ax+b$, $a$、$b$为常数.\\\\\n(1) $g(x)=\\sin x$, 讨论$f(x)$的奇偶性, 并说明理由;\\\\\n(2) 求证: ``$f(x)$为奇函数''的一个必要非充分条件是``$f(x)$的图像有异于原点\n的对称中心$(m,n)$'';\\\\\n(3) $g(x)=\\sin x+\\cos x$, $f(x)$在$x\\in [0,3\\pi]$上的最大值为$M$, 求$M$的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2021届杨浦高三基础考试题21", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012009": { + "id": "012009", + "content": "函数$f(x)=x^{-\\frac 12}$的定义域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题1", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012010": { + "id": "012010", + "content": "集合$A=\\{-1, 2m-1\\}$, $B=\\{m^2\\}$, 若$B\\subseteq A$, 则实数$m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题2", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012011": { + "id": "012011", + "content": "$(1+2x)^5=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5$, 则$a_3=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题3", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012012": { + "id": "012012", + "content": "如图, 若正四棱柱$ABCD-A_1B_1C_1D_1$的底面边长为$3$, 高为$4$, 则直线$BD_1$与平面$ABCD$所成角的正切值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\def\\l{3}\n\\def\\m{3}\n\\def\\n{4}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw [dashed] (B) -- (D1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题4", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012013": { + "id": "012013", + "content": "方程$\\lg (x+2)=2\\lg x$的解为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题5", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012014": { + "id": "012014", + "content": "若$\\arccos x>\\dfrac{\\pi }3$, 则$x$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题6", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012015": { + "id": "012015", + "content": "若函数$f(x)=\\sqrt {2x+1}$的反函数为$g(x)$, 则函数$g(x)$的零点为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题7", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012016": { + "id": "012016", + "content": "已知函数$y=\\sin (\\omega x-\\dfrac{\\pi }6) \\ (\\omega >0)$图像的一条对称轴为$x=\\dfrac{\\pi }6$, 则$\\omega$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题8", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012017": { + "id": "012017", + "content": "已知圆锥的底面半径为$1$, 其侧面展开图为一个半圆, 则该圆锥的母线长为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题9", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012018": { + "id": "012018", + "content": "$7$人排成一行, 甲、乙相邻且丙不排两端的排法有\\blank{50}种(用数字作答).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题10", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012019": { + "id": "012019", + "content": "设$f(x)$是定义在$\\mathbf{R}$上的函数, 且满足$f(1)=0$.若$y=f(x)+a\\cdot 2^x$是奇函数, $y=f(x)+3^x$是偶函数, 则$a$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题11", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012020": { + "id": "012020", + "content": "在$\\triangle ABC$中, $b=2$, $c=1$, $\\angle B-\\angle C=\\dfrac{\\pi }2$, 则$\\triangle ABC$的周长为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题12", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012021": { + "id": "012021", + "content": "下列是``$a>b$''的充分不必要条件的是\\bracket{20}.\n\\fourch{$a>b+1$}{$\\dfrac ab>1$}{$a^2>b^2$}{$a^3>b^3$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题13", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012022": { + "id": "012022", + "content": "下列函数中, 既是奇函数, 又是减函数的是\\bracket{20}.\n\\fourch{$y=x^{-1}$}{$y=-\\arcsin x$}{$y=\\log_2x$}{$y=2^x$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题14", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012023": { + "id": "012023", + "content": "已知$f(x)=\\sin x$, 对任意$x_1 \\in[0, \\dfrac{\\pi}2]$, 都存在$x_2\\in [0,\\dfrac{\\pi }2]$, 使得\n$f(x_1)-2f(x_2+\\theta)=-1$成立, 则下列$\\theta$取值可能的是\\bracket{20}.\n\\fourch{$\\dfrac{3\\pi }{13}$}{$\\dfrac{5\\pi }{13}$}{$\\dfrac{7\\pi }{13}$}{$\\dfrac{9\\pi }{13}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题15", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012024": { + "id": "012024", + "content": "非空集合$A\\subseteq R$, 且满足如下性质.\\\\\n性质一: 若$a,b\\in A$, 则$a+b\\in A$; 性质二: 若$a\\in A$, 则$-a\\in A$. 则称集合$A$为一个``群''. 以下叙述\\\\\n\\textcircled{1} 若$A$为一个``群'', 则$A$必为无限集;\\\\\n\\textcircled{2} 若$A$为一个``群'', 且$a,b\\in A$, 则$a-b\\in A$;\\\\\n\\textcircled{3} 若$A,B$都是``群'', 则$A\\cap B$必定是``群'';\\\\\n\\textcircled{4} 若$A,B$都是``群'', 且$A\\cup B\\ne A,A\\cup B\\ne B,$则$A\\cup B$必定不是``群''.\\\\\n其中正确的个数为\\bracket{20}.\n\\fourch{$1$}{$2$}{$3$}{$4$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题16", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012025": { + "id": "012025", + "content": "如图, 在正三棱柱$ABC-A_1B_1C_1$中, $AA_1=2$, $AB=3$, 点$D$为$BC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (1.5,0,{1.5*sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw (3,0,0) node [right] {$C$} coordinate (C);\n\\draw (A) --++ (0,2) node [left] {$A_1$} coordinate (A1);\n\\draw (B) --++ (0,2) node [above] {$B_1$} coordinate (B1);\n\\draw (C) --++ (0,2) node [right] {$C_1$} coordinate (C1);\n\\draw ($(B)!0.5!(C)$) node [below right] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C) (A1) -- (C1) (A1) -- (B1) -- (C1);\n\\draw [dashed] (A) -- (C) (A) -- (D) (A) -- (C1);\n\\draw (A1) -- (B) (C1) -- (D) (B) -- (C1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: 直线$A_1B$与$C_1D$为异面直线;\\\\\n(2) 求三棱锥$B-AC_1D$的体积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题17", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012026": { + "id": "012026", + "content": "已知代数式$(\\dfrac 2m+\\dfrac mx)^n$($m>0$,$x>0$).\\\\\n(1) 当$m=2$, $n=6$时, 求二项展开式中二项式系数最大的项;\\\\\n(2) 若$(\\dfrac 2m+\\dfrac mx)^{10}=a_0+\\dfrac{a_1}x+\\dfrac{a_2}{x^2}+\\cdots +\\dfrac{a_{10}}{x^{10}}$, 且$a_2=180$, 求$a_i$($0\\le i \\le 10$,$i\\in \\mathbf{N}$)的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2022届杨浦高三基础考试题18", + "edit": [ + "20221027\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012027": { + "id": "012027", + "content": "为实现``碳达峰'', 减少污染, 某化工企业开发了一个废料回收项目. 经测算, 该项目日回收成本$p$(元)与日回收量$x$(吨)$(x\\in [0,50])$的函数关系可表示为$p=\\begin{cases}20x, & 0\\le x\\le 30,\\\\ x^2+16x-780, & 30