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 444ca2a0..f413cdbe 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": 4, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "首个空闲id: 12030 , 直至 020000\n", + "首个空闲id: 12033 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30474 , 直至 999999\n" + "首个空闲id: 30479 , 直至 999999\n" ] } ], @@ -45,7 +45,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -59,12 +59,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 0e7d5da8..794f9261 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 @@ -7,15 +7,15 @@ "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 12030\n", - "origin = \"2022届高三第一轮复习讲义\"\n", - "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", - "editor = \"20221105\\t王伟叶\"" + "starting_id = 12033\n", + "origin = \"2023届杨浦区高三基础考\"\n", + "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\temp.tex\"\n", + "editor = \"20221110\\t王伟叶\"" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -70,7 +70,8 @@ " 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 , dict = pro_dict,editor = editor)\n", + " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n", " pro_dict[pid] = NewProblem\n", " id += 1\n", "\n", @@ -100,7 +101,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -114,12 +115,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 473eb5e6..05fc4955 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -289008,6 +289008,405 @@ "remark": "", "space": "" }, + "012033": { + "id": "012033", + "content": "集合$A=\\{x|x\\ge 0\\}$, $B=\\{x|x\\ge a\\}$, 若$A\\subseteq B$, 则实数$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题1", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012034": { + "id": "012034", + "content": "函数$y=\\lg(2-x)$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题2", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012035": { + "id": "012035", + "content": "陈述句``$a\\ge 1$且$a\\le 3$''的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题3", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012036": { + "id": "012036", + "content": "已知$A,B$是独立事件, $P(A)=0.3$, $P(B)=0.5$, 则$P(A\\cap B)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题4", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012037": { + "id": "012037", + "content": "若圆锥的轴截面是边长为$1$的正三角形, 则圆锥的侧面积是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题5", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012038": { + "id": "012038", + "content": "若$z=\\dfrac{1-a\\mathrm{i}}{2+\\mathrm{i}}$($\\mathrm{i}$为虚数单位)为纯虚数, 则实数$a$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题6", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012039": { + "id": "012039", + "content": "已知$\\overrightarrow{a}=(2,1)$, $\\overrightarrow{b}$在$\\overrightarrow{a}$上的投影为$-2\\overrightarrow{a}$, 则$\\overrightarrow{a}\\cdot\\overrightarrow{b}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题7", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012040": { + "id": "012040", + "content": "如果幂函数$y=f(x)$的图像经过点$(2,\\dfrac 12)$, 那么$y=f(x)$的单调减区间是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题8", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012041": { + "id": "012041", + "content": "某医院对某学校高三年级的$600$名学生进行身体健康调查, 采用男女分层抽样法抽取一个容量为$50$的样本, 已知女生比男生少抽了$10$人, 则该年级的女生人数是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题9", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012042": { + "id": "012042", + "content": "偶函数$y=f(x)$在区间$[0,+\\infty)$上是严格减函数, 若$f(1)=0$, 则关于$x$的不等式$f(x)-x^2>-1$的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题10", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012043": { + "id": "012043", + "content": "已知$a,b\\in \\mathbf{R}$且$a\\ne 0$, 则$|a+b|+|\\dfrac 4a-b|$的最小值是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题11", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012044": { + "id": "012044", + "content": "已知函数$y=\\sin x+\\sin 2x$在$(-a,a)$上恰有$5$个零点, 则实数$a$的最大值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题12", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012045": { + "id": "012045", + "content": "设$x\\in \\mathbf{R}$, 则``$x<1$''是``$x^3<1$''的\\bracket{20}.\n\\twoch{充分而不必要条件}{必要而不充分条件}{充要条件}{既不充分也不必要条件}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题13", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012046": { + "id": "012046", + "content": "同时掷两枚骰子, 向上的点数之和是$6$的概率是\\bracket{20}.\n\\fourch{$\\dfrac 1{12}$}{$\\dfrac 19$}{$\\dfrac 16$}{$\\dfrac 5{36}$}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题14", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012047": { + "id": "012047", + "content": "已知某射击爱好者打靶成绩(单位:环)的茎叶图如图所示, 其中整数部分为``茎'', 小数部分为``叶'', 则这组数据的标准差为(精确到$0.01$)\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{c|cccc}\n$5$ & $7$ & $9$ \\\\\n$6$ & $1$ & $2$ & $7$ & $7$ \\\\\n$7$ & $2$ & $5$\n\\end{tabular}\n\\end{center}\n\\fourch{$0.35$}{$0.59$}{$0.40$}{$0.63$}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题15", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012048": { + "id": "012048", + "content": "如图所示, 图中多面体是由两个底面相同的正四棱锥所拼接而成, 且这六个顶点在同一个球面上. 若二面角$M-AB-C$的正切值为$1$, 则二面角$N-AB-C$的正切值为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = (-120:0.5)]\n\\draw (-1,0,1) node [left] {$A$} coordinate (A);\n\\draw (1,0,1) node [right] {$B$} coordinate (B);\n\\draw (1,0,-1) node [right] {$C$} coordinate (C);\n\\draw (-1,0,-1) node [left] {$D$} coordinate (D);\n\\draw (0,1,0) node [above] {$M$} coordinate (M);\n\\draw (0,-2,0) node [below] {$N$} coordinate (N);\n\\draw (A) -- (B) -- (C) (A) -- (N) (B) -- (N) (C) -- (N) (M) -- (D) (M) -- (A) (M) -- (B) (M) -- (C) (A) -- (D);\n\\draw [dashed] (D) -- (C) (D) -- (N);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题16", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012049": { + "id": "012049", + "content": "已知$O$为坐标原点, $\\overrightarrow{OA}=(2,3)$, $\\overrightarrow{OB}=(4,2)$, $\\overrightarrow{OC}=(x,3)$.\\\\\n(1) 若$A,B,C$三点共线, 求$x$的值;\\\\\n(2) 若$\\overrightarrow{AB}$与$\\overrightarrow{OC}$夹角为钝角, 求$x$的取值范围.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题17", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012050": { + "id": "012050", + "content": "已知函数$f(x)=ax^2+x-1$. ($a>0$)\\\\\n(1) 若关于$x$的不等式$f(x)<0$的解集为$(-1,b)$, 求实数$a$和$b$的值;\n(2) 若函数$y=f(x)$在$[-3,-1]$上的最大值为$2$, 求实数$a$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题18", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012051": { + "id": "012051", + "content": "如图, 一辆汽车在水平公路上向正西直线行驶, 到$A$处测得公路北侧远处一山顶$D$($D$在水平面上的射影为点$C$)在西偏北$30^\\circ$的方向上, 仰角为$30^\\circ$, 行驶$1\\text{km}$后到达$B$处, 测得山顶在西偏北$45^\\circ$的方向上.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = (-115:0.5)]\n\\draw (-3,0) -- (3,0);\n\\draw (1,0,0) node [below] {$B$} coordinate (B);\n\\draw (2,0,0) node [below] {$A$} coordinate (A);\n\\draw ({(sqrt(3)-1)/2},0,{1/(1-sqrt(3))}) node [left] {$C$} coordinate (C);\n\\draw [dashed] (A) -- (C) (B) -- (C);\n\\draw (C) ++ (0,{1/sin(15)*sin(45)*sin(30)}) node [above] {$D$} coordinate (D);\n\\draw [dashed] (D) -- (A) (D) -- (B) (D) -- (C);\n\\draw (D) .. controls (0.5,2) .. (-2,1);\n\\draw (D) .. controls (1,2) .. (2,1.3);\n\\end{tikzpicture}\n\\end{center}\n(1) 求此山的高度(单位: $\\text{km}$, 精确到$0.01\\text{km}$);\\\\\n(2) 求汽车行驶过程中仰望山顶$D$的仰角$\\theta$的最大值(精确到$1^\\circ$).", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题19", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012052": { + "id": "012052", + "content": "如图, 三棱柱$ABC-A_1B_1C_1$中, $\\angle CAB=90^\\circ$, $AB=AC=A_1B=A_1C=2\\sqrt{2}$, $AA_1=2$, 点$M,F$分别为$BC,A_1B_1$的中点, 点$E$为$AM$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = (-45:0.5),scale = 1.25]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,{2*sqrt(2)}) node [below] {$B$} coordinate (B);\n\\draw ({2*sqrt(2)},0,0) node [right] {$C$} coordinate (C);\n\\draw (A) ++ ({sqrt(2)/2},{sqrt(3)},{sqrt(2)/2}) node [above left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ ({sqrt(2)/2},{sqrt(3)},{sqrt(2)/2}) node [below right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ ({sqrt(2)/2},{sqrt(3)},{sqrt(2)/2}) node [above right] {$C_1$} coordinate (C_1);\n\\draw ($(B)!0.5!(C)$) node [right] {$M$} coordinate (M);\n\\draw ($(A_1)!0.5!(B_1)$) node [above] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(M)$) node [below left] {$E$} coordinate (E);\n\\draw (A) -- (B) -- (C) (A) -- (A_1) (B) -- (B_1) (C) -- (C_1) (A_1) -- (B_1) -- (C_1) (A_1) -- (C_1) (A_1) -- (B);\n\\draw [dashed] (A) -- (M) (E) -- (F) (A_1) -- (M) (A_1) -- (C) (A) -- (C);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $AA_1\\perp BC$;\\\\\n(2) 证明: $EF\\parallel$平面$BCC_1B_1$;\\\\\n(3) 求直线$EF$与平面$A_1BC$所成角的正弦值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题20", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012053": { + "id": "012053", + "content": "已知对任意正整数$n$, 都存在$n$次多项式函数$y=f_n(x)$, 使得$\\cos nx=f_n(\\cos x)$对一切$x\\in \\mathbf{R}$恒成立. 例如``$y=f_2(x)=2x^2-1$, $\\cos 2x=2\\cos^2 x-1=f_2(\\cos x)$''.\\\\\n(1) 求$f_n(0)$;\\\\\n(2) 求证: 当$n$为偶数时, 不存在函数$y=g_n(x)$使得$\\sin nx=g_n(\\sin x)$对一切$x\\in \\mathbf{R}$恒成立;\\\\\n(3) 求证: 当$n$为奇数时, 存在多项式函数$y=h_n(x)$使得$\\sin nx=h_n(\\sin x)$对一切$x\\in \\mathbf{R}$恒成立, 并求其最高次项系数.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届杨浦区高三基础考试题21", + "edit": [ + "20221110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, "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.",