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20221110 noon

This commit is contained in:
Wang Weiye 2022-11-10 13:58:50 +08:00
parent 7e7f7eb144
commit 44abe799a9
3 changed files with 415 additions and 15 deletions
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12
工具/寻找阶段末尾空闲题号.ipynb
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@ -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 @@
],
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"display_name": "Python 3.8.8 ('base')",
"display_name": "Python 3.9.7 ('base')",
"language": "python",
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@ -59,12 +59,12 @@
"name": "python",
"nbconvert_exporter": "python",
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"version": "3.9.7"
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19
工具/添加题目到数据库.ipynb
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@ -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\""
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"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",
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399
题库0.3/Problems.json
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@ -289008,6 +289008,405 @@
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"content": "函数$y=\\lg(2-x)$的定义域为\\blank{50}.",
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"content": "陈述句``$a\\ge 1$且$a\\le 3$''的定义域为\\blank{50}.",
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"012036": {
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"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}.",
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"012037": {
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"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}.",
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"012038": {
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"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}.",
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"012039": {
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"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}.",
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"012040": {
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"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}.",
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"012041": {
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"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}.",
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"duration": -1,
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"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}.",
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"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}.",
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"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": [],
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"duration": -1,
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"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": [],
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"duration": -1,
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"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{$\\dfrac 1{12}$}{$\\dfrac 19$}{$\\dfrac 16$}{$\\dfrac 5{36}$}",
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"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{$0.35$}{$0.59$}{$0.40$}{$0.63$}",
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"tags": [],
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"solution": "",
"duration": -1,
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"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}",
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"ans": "",
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"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.",
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"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.",
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"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$1^\\circ$).",
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"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.",
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"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.",
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"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.",