From 758be6558456c220b6572c8839e5259a85117143 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 11 Dec 2022 21:31:42 +0800 Subject: [PATCH] 20221211 evening --- 工具/修改题目数据库.ipynb | 12 ++++++------ 工具/题号选题pdf生成.ipynb | 2 +- 题库0.3/Problems.json | 27 ++++++++++++++++----------- 3 files changed, 23 insertions(+), 18 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 fd49b8f7..91723dbd 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": 6, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 3, + "execution_count": 6, "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 = \"12227\"\n", + "problems = \"12298,12305,12307\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", @@ -75,7 +75,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -89,12 +89,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8 (default, Apr 13 2021, 15:08:03) [MSC v.1916 64 bit (AMD64)]" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, 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 b328108b..66d1f2f1 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -189,7 +189,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15" + "version": "3.9.15 (main, Nov 24 2022, 14:39:17) [MSC v.1916 64 bit (AMD64)]" }, "orig_nbformat": 4, "vscode": { diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 385e8b24..9557feed 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -125391,7 +125391,7 @@ }, "004697": { "id": "004697", - "content": "已知非空集合$A,B$满足: $A\\cup B=R$, $A\\cap B=\\varnothing$, 函数$f(x)=\\begin{cases}\nx^2, & x\\in A, \\\\ 2x-1, & x\\in B. \\end{cases}$ 对于下列两个命题: \\textcircled{1} 存在唯一的非空集合对$(A,B)$, 使得$f(x)$为偶函数; \\textcircled{2} 存在无穷多非空集合对$(A,B)$, 使得方程$f(x)=2$无解. 下面判断正确的是\\bracket{20}.\n\\fourch{\\textcircled{1} 正确, \\textcircled{2} 错误}{\\textcircled{1} 错误, \\textcircled{2} 正确}{\\textcircled{1} 、\\textcircled{2} 都正确}{\\textcircled{1} 、\\textcircled{2} 都错误}", + "content": "已知非空集合$A,B$满足: $A\\cup B=\\mathbf{R}$, $A\\cap B=\\varnothing$, 函数$f(x)=\\begin{cases}\nx^2, & x\\in A, \\\\ 2x-1, & x\\in B. \\end{cases}$ 对于下列两个命题: \\textcircled{1} 存在唯一的非空集合对$(A,B)$, 使得$f(x)$为偶函数; \\textcircled{2} 存在无穷多非空集合对$(A,B)$, 使得方程$f(x)=2$无解. 下面判断正确的是\\bracket{20}.\n\\fourch{\\textcircled{1} 正确, \\textcircled{2} 错误}{\\textcircled{1} 错误, \\textcircled{2} 正确}{\\textcircled{1} 、\\textcircled{2} 都正确}{\\textcircled{1} 、\\textcircled{2} 都错误}", "objs": [ "K0217004B", "K0223002B" @@ -125409,7 +125409,8 @@ ], "origin": "2022届高三上一模第16题", "edit": [ - "20220711\t王伟叶" + "20220711\t王伟叶", + "20221211\t王伟叶" ], "same": [], "related": [], @@ -300008,7 +300009,7 @@ }, "012128": { "id": "012128", - "content": "已知函数$y=f(x)$在定义域$\\mathbf{R}$上是单调函数, 值域为$(-\\infty ,\\ 0)$, 满足$f(-1)=-\\dfrac 13$, 且对于任意$x,\\ y\\in \\mathbf{R}$, 都有$f(x+y)=-f(x)f(y)$. $y=f(x)$的反函数为$y=f^{-1}(x)$, 若将$y=kf(x)$(其中常数$k>0$)的反函数的图像向上平移1个单位, 将得到函数$y=f^{-1}(x)$的图像, 则实数k的值为\\blank{50}.", + "content": "已知函数$y=f(x)$在定义域$\\mathbf{R}$上是单调函数, 值域为$(-\\infty ,\\ 0)$, 满足$f(-1)=-\\dfrac 13$, 且对于任意$x,\\ y\\in \\mathbf{R}$, 都有$f(x+y)=-f(x)f(y)$. $y=f(x)$的反函数为$y=f^{-1}(x)$, 若将$y=kf(x)$(其中常数$k>0$)的反函数的图像向上平移1个单位, 将得到函数$y=f^{-1}(x)$的图像, 则实数$k$的值为\\blank{50}.", "objs": [], "tags": [], "genre": "填空题", @@ -300018,7 +300019,8 @@ "usages": [], "origin": "2021届杨浦区一模试题12", "edit": [ - "20221206\t王伟叶" + "20221206\t王伟叶", + "20221211\t王伟叶" ], "same": [], "related": [], @@ -303238,7 +303240,7 @@ }, "012298": { "id": "012298", - "content": "已知数列$\\{a_n\\}$的各项都是正数, $a_{n+1}^2-a_{n+1}=a_n$($n \\in \\mathbf{N}^*$), 若数列$\\{a_n\\}$为严格增数列, 则首项$a_1$的取值范围是\\blank{50}; 当$a_1=\\dfrac 23$时, 记$b_n=\\dfrac{(-1)^{n-1}}{a_n-1}$, 若$k=latex,scale = 0.2]\n\\draw (-8,16) node [left] {$A$} coordinate (A);\n\\draw (4,16) node [right] {$B$} coordinate (B);\n\\draw (-10,0) node [below] {$M$} coordinate (M);\n\\draw (6,0) node [below] {$N$} coordinate (N);\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (0,16) node [above] {$O'$} coordinate (O');\n\\draw (-6,16) node [above] {$C$} coordinate (C);\n\\draw (-6,9) node [left] {$D$} coordinate (D);\n\\draw (2,16) node [above] {$E$} coordinate (E);\n\\draw (2,12) node [right] {$F$} coordinate (F);\n\\draw [ultra thick] (A) -- (B) (C) -- (D) (E) -- (F);\n\\draw (M) -- (N);\n\\draw [dashed] (O) -- (O');\n\\draw [domain = -8:0] plot (\\x,{0.25*pow(\\x,2)});\n\\draw [domain = 0:4.2] plot (\\x,{16-pow(\\x-4,2)});\n\\draw [dashed] (D) --++ (0,-9) node [midway,left] {$h_1$} coordinate (h_1) (D) --++ (6,0) node [midway,above] {$a$} coordinate (a);\n\\draw [dashed] (F) --+ (0,-12) node [midway,right] {$h_2$} coordinate (h_2) (F) --++ (-2,0) node [midway,above] {$b$} coordinate (b);\n\\end{tikzpicture}\n\\end{center}\n(1) 求谷底$O$到桥面$AB$的距离和桥$AB$的长度;\\\\\n(2) 计划在谷底两侧建造平行于$OO'$的桥墩$CD$和$EF$, 且$CE$为$80$米, 其中$C$、$E$在$AB$上(不包括端点), 桥墩$EF$每米造价为$k$(万元)、桥墩$CD$每米造价为$\\dfrac 32 k$(万元)($k>0$). 问$O'E$为多少米时, 桥墩$CD$与$EF$的总造价最低?", + "content": "某地准备在山谷中建一座桥梁, 桥址位置的竖直截面图如图所示, 谷底$O$在水平线$MN$上、桥$AB$与$MN$平行, $OO'$为铅垂线($O'$在$AB$上). 经测量, 山谷左侧的轮廓曲线$AO$上任一点$D$到$MN$的距离$h_1$(米)与$D$到$OO'$的距离$a$(米) 之间满足关系式$h_1=\\dfrac 1{40} a^2$, 山谷右侧的轮廓曲线$BO$上任一点$F$到$MN$的距离$h_2$(米)与$F$到$OO'$的距离$b$(米)之间满足关系式$h_2=-\\dfrac 1{800} b^3+6 b$. 已知点$B$到$OO'$的距离为$40$米.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.2]\n\\draw (-8,16) node [left] {$A$} coordinate (A);\n\\draw (4,16) node [right] {$B$} coordinate (B);\n\\draw (-10,0) node [below] {$M$} coordinate (M);\n\\draw (6,0) node [below] {$N$} coordinate (N);\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (0,16) node [above] {$O'$} coordinate (O');\n\\draw (-6,16) node [above] {$C$} coordinate (C);\n\\draw (-6,9) node [left] {$D$} coordinate (D);\n\\draw (2,16) node [above] {$E$} coordinate (E);\n\\draw (2,12) node [right] {$F$} coordinate (F);\n\\draw [ultra thick] (A) -- (B) (C) -- (D) (E) -- (F);\n\\draw (M) -- (N);\n\\draw [dashed] (O) -- (O');\n\\draw [domain = -8:0] plot (\\x,{0.25*pow(\\x,2)});\n\\draw [domain = 0:4.2] plot (\\x,{16-pow(\\x-4,2)});\n\\draw [dashed] (D) --++ (0,-9) node [midway,left] {$h_1$} coordinate (h_1) (D) --++ (6,0) node [midway,above] {$a$} coordinate (a);\n\\draw [dashed] (F) --+ (0,-12) node [midway,right] {$h_2$} coordinate (h_2) (F) --++ (-2,0) node [midway,above] {$b$} coordinate (b);\n\\end{tikzpicture}\n\\end{center}\n(1) 求谷底$O$到桥面$AB$的距离和桥$AB$的长度;\\\\\n(2) 计划在谷底两侧建造平行于$OO'$的桥墩$CD$和$EF$, 且$CE$为$80$米, 其中$C$、$E$在$AB$上(不包括端点), 桥墩$EF$每米造价为$k$(万元)、桥墩$CD$每米造价为$\\dfrac 32 k$(万元)($k>0$). 问$O'E$为多少米时, 桥墩$CD$与$EF$的总造价最低?", "objs": [], "tags": [], "genre": "解答题", @@ -303381,7 +303384,8 @@ "usages": [], "origin": "2023届松江区一模试题19", "edit": [ - "20221210\t王伟叶" + "20221210\t王伟叶", + "20221211\t周双" ], "same": [], "related": [], @@ -303409,7 +303413,7 @@ }, "012307": { "id": "012307", - "content": "己知定义在$\\mathbf{R}$上的函数$f(x)=\\mathrm{e}^{k x+b}$($\\mathrm{e}$是自然对数的底数) 满足$f(x)=f'(x)$且$f(-1)=1$, 删除无穷数列$f(1)$、$f(2)$、$f(3)$、$\\cdots$、$f(n)$、$\\cdots$中的第$3$项、第$6$项、$\\cdots$、第$3n$项, $\\cdots$, ($n \\in \\mathbf{N}$, $n\\ge 1$), 余下的项按原来顺序组成一个新数列$\\{t_n\\}$, 记数列$\\{t_n\\}$前$n$项和为$T_n$.\\\\\n(1) 求函数$f(x)$的解析式;\\\\\n(2) 已知数列$\\{t_n\\}$的通项公式是$t_n=f(g(n))$, $n \\in \\mathbf{N}$, $n\\ge 1$, 求函数$g(n)$的解析式;\n(3) 设集合$X$是实数集$\\mathbf{R}$的非空子集, 如果正实数$a$满足: 对任意$x_1$、$x_2 \\in X$, 都有$|x_1-x_2|\\leq a$, 则称$a$为集合$X$的一个``阈度'', 记集合$H=\\{w | w=\\dfrac{T_n}{f(\\dfrac{3 n}2-\\dfrac{1+3(-1)^n}4)}, \\ n \\in \\mathbf{N}, \\ n\\ge 1\\}$, 试问集合$H$存在``阈度''吗? 若存在, 求出集合$H$``阈度''的取值范围, 若不存在, 试说明理由.", + "content": "己知定义在$\\mathbf{R}$上的函数$f(x)=\\mathrm{e}^{k x+b}$($\\mathrm{e}$是自然对数的底数) 满足$f(x)=f'(x)$且$f(-1)=1$, 删除无穷数列$f(1)$、$f(2)$、$f(3)$、$\\cdots$、$f(n)$、$\\cdots$中的第$3$项、第$6$项、$\\cdots$、第$3n$项, $\\cdots$, ($n \\in \\mathbf{N}$, $n\\ge 1$), 余下的项按原来顺序组成一个新数列$\\{t_n\\}$, 记数列$\\{t_n\\}$前$n$项和为$T_n$.\\\\\n(1) 求函数$f(x)$的解析式;\\\\\n(2) 已知数列$\\{t_n\\}$的通项公式是$t_n=f(g(n))$, $n \\in \\mathbf{N}$, $n\\ge 1$, 求函数$g(n)$的解析式;\\\\\n(3) 设集合$X$是实数集$\\mathbf{R}$的非空子集, 如果正实数$a$满足: 对任意$x_1$、$x_2 \\in X$, 都有$|x_1-x_2|\\leq a$, 则称$a$为集合$X$的一个``阈度'', 记集合$H=\\{w | w=\\dfrac{T_n}{f(\\dfrac{3 n}2-\\dfrac{1+3(-1)^n}4)}, \\ n \\in \\mathbf{N}, \\ n\\ge 1\\}$, 试问集合$H$存在``阈度''吗? 若存在, 求出集合$H$``阈度''的取值范围, 若不存在, 试说明理由.", "objs": [], "tags": [], "genre": "解答题", @@ -303419,7 +303423,8 @@ "usages": [], "origin": "2023届松江区一模试题21", "edit": [ - "20221210\t王伟叶" + "20221210\t王伟叶", + "20221211\t周双" ], "same": [], "related": [], @@ -303466,7 +303471,7 @@ }, "012310": { "id": "012310", - "content": "已知复数$z_1=2+a \\mathrm{i}$, $z_2=3+\\mathrm{i}$, 若$z_1,z_2$是纯虚数, 则实数$a=$\\blank{50}.", + "content": "已知复数$z_1=2+a \\mathrm{i}$, $z_2=3+\\mathrm{i}$, 若$z_1\\cdot z_2$是纯虚数, 则实数$a=$\\blank{50}.", "objs": [], "tags": [], "genre": "填空题",