From d6bc31c96273e2a0f0a885f6da93872ec93a41f4 Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Mon, 19 Dec 2022 20:10:14 +0800 Subject: [PATCH] 20221219 afternoon --- 工具/修改题目数据库.ipynb | 6 +- 工具/关键字筛选题号.ipynb | 10 +- 工具/寻找tex文件中未赋答案的题目.ipynb | 198 +++++++++++++++++++++- 工具/批量添加题库字段数据.ipynb | 90 +++------- 工具/文本文件/metadata.txt | 216 +++++------------------- 工具/文本文件/题号筛选.txt | 2 +- 工具/生成文件夹下的题号清单.ipynb | 2 +- 工具/讲义生成.ipynb | 18 +- 工具/识别题库中尚未标注的题目类型.ipynb | 128 +++----------- 工具/题号选题pdf生成.ipynb | 8 +- 题库0.3/Problems.json | 96 +++++------ 11 files changed, 357 insertions(+), 417 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 6c18fd6c..c19c85f0 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": 9, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 9, + "execution_count": 1, "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 = \"12576,12586\"\n", + "problems = \"12642\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", diff --git a/工具/关键字筛选题号.ipynb b/工具/关键字筛选题号.ipynb index 82e847d4..01db4efb 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 6, + "execution_count": 1, "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", - " {\"origin\":[\"2023\"],\"origin2\":[\"嘉定\"]}\n", + " {\"origin\":[\"2023\"],\"origin2\":[\"青浦\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", @@ -89,7 +89,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "Python 3.9.15 ('pythontest')", "language": "python", "name": "python3" }, @@ -108,7 +108,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb index 334f3914..41e74bd2 100644 --- a/工具/寻找tex文件中未赋答案的题目.ipynb +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -98,7 +98,199 @@ "2021届上海春季高考.tex\n", "2022届上海春季高考.tex\n", "2023届嘉定区一模.tex\n", + "2023届宝山区一模.tex\n", + "012655\n", + "\n", + "\n", + "012656\n", + "\n", + "\n", + "012657\n", + "\n", + "\n", + "012658\n", + "\n", + "\n", + "012659\n", + "\n", + "\n", + "012660\n", + "\n", + "\n", + "012661\n", + "\n", + "\n", + "012662\n", + "\n", + "\n", + "012663\n", + "\n", + "\n", + "012664\n", + "\n", + "\n", + "012665\n", + "\n", + "\n", + "012666\n", + "\n", + "\n", + "012667\n", + "\n", + "\n", + "012668\n", + "\n", + "\n", + "012669\n", + "\n", + "\n", + "012670\n", + "\n", + "\n", + "012671\n", + "\n", + "\n", + "012672\n", + "\n", + "\n", + "012673\n", + "\n", + "\n", + "012674\n", + "\n", + "\n", + "012675\n", + "\n", + "\n", "2023届崇明区一模.tex\n", + "2023届徐汇区一模.tex\n", + "012634\n", + "\n", + "\n", + "012635\n", + "\n", + "\n", + "012636\n", + "\n", + "\n", + "012637\n", + "\n", + "\n", + "012638\n", + "\n", + "\n", + "012639\n", + "\n", + "\n", + "012640\n", + "\n", + "\n", + "012641\n", + "\n", + "\n", + "012642\n", + "\n", + "\n", + "012643\n", + "\n", + "\n", + "012644\n", + "\n", + "\n", + "012645\n", + "\n", + "\n", + "012646\n", + "\n", + "\n", + "012647\n", + "\n", + "\n", + "012648\n", + "\n", + "\n", + "012649\n", + "\n", + "\n", + "012650\n", + "\n", + "\n", + "012651\n", + "\n", + "\n", + "012652\n", + "\n", + "\n", + "012653\n", + "\n", + "\n", + "012654\n", + "\n", + "\n", + "2023届普陀区一模.tex\n", + "012592\n", + "\n", + "\n", + "012593\n", + "\n", + "\n", + "012594\n", + "\n", + "\n", + "012595\n", + "\n", + "\n", + "012596\n", + "\n", + "\n", + "012597\n", + "\n", + "\n", + "012598\n", + "\n", + "\n", + "012599\n", + "\n", + "\n", + "012600\n", + "\n", + "\n", + "012601\n", + "\n", + "\n", + "012602\n", + "\n", + "\n", + "012603\n", + "\n", + "\n", + "012604\n", + "\n", + "\n", + "012605\n", + "\n", + "\n", + "012606\n", + "\n", + "\n", + "012607\n", + "\n", + "\n", + "012608\n", + "\n", + "\n", + "012609\n", + "\n", + "\n", + "012610\n", + "\n", + "\n", + "012611\n", + "\n", + "\n", + "012612\n", + "\n", + "\n", "2023届杨浦区一模.tex\n", "2023届松江区一模.tex\n", "2023届长宁区一模.tex\n", @@ -143,7 +335,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "Python 3.9.15 ('pythontest')", "language": "python", "name": "python3" }, @@ -162,7 +354,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb index c31d8eb2..b99924be 100644 --- a/工具/批量添加题库字段数据.ipynb +++ b/工具/批量添加题库字段数据.ipynb @@ -2,76 +2,34 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 012613 , 字段: ans 中已有该数据: $\\{2,4\\}$\n", - "题号: 012614 , 字段: ans 中已有该数据: $(1,2)$\n", - "题号: 012615 , 字段: ans 中已有该数据: $\\dfrac{\\sqrt{2}}2$\n", - "题号: 012616 , 字段: ans 中已有该数据: $3$\n", - "题号: 012617 , 字段: ans 中已有该数据: $3$\n", - "题号: 012618 , 字段: ans 中已有该数据: \\textcircled{1}\\textcircled{4}\n", - "题号: 012619 , 字段: ans 中已有该数据: $180$\n", - "题号: 012620 , 字段: ans 中已有该数据: $4$\n", - "题号: 012621 , 字段: ans 中已有该数据: $\\dfrac 52$\n", - "题号: 012622 , 字段: ans 中已有该数据: $\\dfrac\\pi 4$\n", - "题号: 012623 , 字段: ans 中已有该数据: $\\dfrac{8\\sqrt{2}\\pi}3$\n", - "题号: 012624 , 字段: ans 中已有该数据: $\\dfrac{8\\sqrt{3}}3$\n", - "题号: 012625 , 字段: ans 中已有该数据: A\n", - "题号: 012626 , 字段: ans 中已有该数据: C\n", - "题号: 012627 , 字段: ans 中已有该数据: D\n", - "题号: 012628 , 字段: ans 中已有该数据: C\n", - "题号: 012629 , 字段: ans 中已有该数据: (1) $b_n=3^{n-1}$; (2) $-8$\n", - "题号: 012630 , 字段: ans 中已有该数据: (1) $\\dfrac \\pi 4$; (2) $1$\n", - "题号: 012631 , 字段: ans 中已有该数据: (1) 证明略; (2) 证明略; (3) $\\dfrac\\pi 4$\n", - "题号: 012632 , 字段: ans 中已有该数据: (1) $\\sqrt{2}$; (2) $y=x+1$; (3) 过定点$(-3,0)$和$(1,0)$\n", - "题号: 012633 , 字段: ans 中已有该数据: (1) $y=x-1$; (2) 单调减区间为$(\\dfrac 12 1)$; 极小值为$-2$; (3) 证明略\n", - "题号: 012571 , 字段: ans 中已有该数据: $\\{1\\}$\n", - "题号: 012572 , 字段: ans 中已有该数据: $-1$\n", - "题号: 012573 , 字段: ans 中已有该数据: $\\dfrac\\pi 6$\n", - "题号: 012574 , 字段: ans 中已有该数据: $2$\n", - "题号: 012575 , 字段: ans 中已有该数据: $16\\pi$\n", - "题号: 012576 , 字段: ans 中已有该数据: $2800$, $31$\n", - "题号: 012577 , 字段: ans 中已有该数据: $2$\n", - "题号: 012578 , 字段: ans 中已有该数据: $(-\\infty,1)\\cup (1,3]$\n", - "题号: 012579 , 字段: ans 中已有该数据: $5$\n", - "题号: 012580 , 字段: ans 中已有该数据: $[\\dfrac 32,2]$\n", - "题号: 012581 , 字段: ans 中已有该数据: $(\\dfrac 72,0,\\dfrac 72)$\n", - "题号: 012582 , 字段: ans 中已有该数据: $\\dfrac{\\sqrt{3}}{20}v$\n", - "题号: 012583 , 字段: ans 中已有该数据: A\n", - "题号: 012584 , 字段: ans 中已有该数据: D\n", - "题号: 012585 , 字段: ans 中已有该数据: C\n", - "题号: 012586 , 字段: ans 中已有该数据: C\n", - "题号: 012587 , 字段: ans 中已有该数据: (1) 证明略; (2) $\\dfrac{3\\sqrt{22}}{11}$\n", - "题号: 012588 , 字段: ans 中已有该数据: (1) $\\dfrac 12$; (2) $a_n=\\dfrac{18}{2n+1}$\n", - "题号: 012589 , 字段: ans 中已有该数据: (1) 例如: 非通勤时段的车辆使用情况; 油价和电价的变化; 工作单位能否提供免费充电; 电动车的国家减免政策的变化; 车辆的外观、内饰与品牌效应; 车牌费用等; (2) 解答略\n", - "题号: 012590 , 字段: ans 中已有该数据: (1) $\\dfrac{x^2}4+\\dfrac{y^2}3=1$($y\\le 0$); (2) $P(-\\dfrac 32,\\dfrac{\\sqrt{3}}2)$, $Q(\\dfrac 32, \\dfrac{\\sqrt{3}}2)$; (3) $[\\sqrt{3}-1,\\sqrt{2}+1]$\n", - "题号: 012591 , 字段: ans 中已有该数据: (1) 导数为$y'=\\dfrac{1-\\ln x}{x^2}$, 单调性证明略; (2) 判断$89^{99}>99^{89}$, 证明略, 推广可以是:``对于实数$a,b$, 若$\\mathrm{e}b^a$; (3) 证明略\n", - "题号: 010965 , 字段: ans 中已修改数据: $[0,2]$\n", - "题号: 010966 , 字段: ans 中已修改数据: $(-\\infty,0)$\n", - "题号: 030023 , 字段: ans 中已修改数据: $\\dfrac{3n^2-5n}2$\n", - "题号: 010968 , 字段: ans 中已修改数据: $\\dfrac{8\\pi}3$\n", - "题号: 010969 , 字段: ans 中已修改数据: $2(x+2)-(y-1)=0$\n", - "题号: 010970 , 字段: ans 中已修改数据: $\\dfrac 32$\n", - "题号: 030025 , 字段: ans 中已修改数据: $[0,\\dfrac 34]$\n", - "题号: 010972 , 字段: ans 中已修改数据: $25$\n", - "题号: 030024 , 字段: ans 中已修改数据: $\\dfrac 23(\\dfrac 1{4^n}-1)$\n", - "题号: 010974 , 字段: ans 中已修改数据: $[1,+\\infty)$\n", - "题号: 010975 , 字段: ans 中已修改数据: $\\sqrt{3}$\n", - "题号: 010976 , 字段: ans 中已修改数据: $3-\\sqrt{3}$\n", - "题号: 010977 , 字段: ans 中已修改数据: B\n", - "题号: 002745 , 字段: ans 中已修改数据: C\n", - "题号: 010979 , 字段: ans 中已修改数据: C\n", - "题号: 010980 , 字段: ans 中已修改数据: B\n", - "题号: 010981 , 字段: ans 中已修改数据: (1) $\\dfrac 23$; (2) $\\arctan {2\\sqrt{5}}5$\n", - "题号: 010982 , 字段: ans 中已修改数据: (1) $\\log_2 3$; (2) $a=2b\\ne 0$\n", - "题号: 010983 , 字段: ans 中已修改数据: (1) $\\sqrt{7}$千米; (2) 有$\\dfrac{8-\\sqrt{15}}7$小时, 两人不能通话\n", - "题号: 010984 , 字段: ans 中已修改数据: (1) $y^2=4\\sqrt{5} x$或$y^2=-4\\sqrt{5} x$; (2) $M$的坐标为$(0,0)$或$(-\\dfrac{4\\sqrt{5}}5,0)$; (3) 证明略\n", - "题号: 010985 , 字段: ans 中已修改数据: (1) $\\{-6,-3,-2,-1,0,1,2,3,4\\}$; (2) 证明略; (3) 元素个数为$\\dfrac 12 n(n+1)$; 元素之和为$\\dfrac{n+1}2(3^{n+1}-3)$\n" + "题号: 012655 , 字段: ans 中已修改数据: $\\{2\\}$\n", + "题号: 012656 , 字段: ans 中已修改数据: $(-1,1)$\n", + "题号: 012657 , 字段: ans 中已修改数据: $\\sqrt{5}$\n", + "题号: 012658 , 字段: ans 中已修改数据: $5$\n", + "题号: 012659 , 字段: ans 中已修改数据: $3$\n", + "题号: 012660 , 字段: ans 中已修改数据: $0.3$\n", + "题号: 012661 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{3}}3\\pi$\n", + "题号: 012662 , 字段: ans 中已修改数据: $2$\n", + "题号: 012663 , 字段: ans 中已修改数据: $96$\n", + "题号: 012664 , 字段: ans 中已修改数据: $\\dfrac 53$\n", + "题号: 012665 , 字段: ans 中已修改数据: $60^\\circ$\n", + "题号: 012666 , 字段: ans 中已修改数据: $2021$\n", + "题号: 012667 , 字段: ans 中已修改数据: B\n", + "题号: 012668 , 字段: ans 中已修改数据: A\n", + "题号: 012669 , 字段: ans 中已修改数据: C\n", + "题号: 012670 , 字段: ans 中已修改数据: B\n", + "题号: 012671 , 字段: ans 中已修改数据: (1) $[k\\pi-\\dfrac{5\\pi}{12},k\\pi+\\dfrac\\pi{12}]$, $k\\in \\mathbf{Z}$; (2) $\\sqrt{13}$或$\\sqrt{61}$\n", + "题号: 012672 , 字段: ans 中已修改数据: (1) 证明略; (2) $a_n=3^n-2$; (3) $a_1+a_3+a_5+a_7+a_9=22133$\n", + "题号: 012673 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arccos \\dfrac{\\sqrt{10}}{10}$; (3) $\\dfrac 13$\n", + "题号: 012674 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{12}+\\dfrac{y^2}4=1$; (2) $3+2\\sqrt{3}$; (3) 存在, $m$的取值范围为$[-\\dfrac{\\sqrt{3}}3,0)$\n", + "题号: 012675 , 字段: ans 中已修改数据: (1) 当$a=0$时, $f(x)$是偶函数; 当$a\\ne 0$时, $f(x)$既不是奇函数又不是偶函数; (2) $(-1,\\dfrac 5{27})$; (3) $[2\\ln 2-2,1]$\n" ] } ], @@ -169,7 +127,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "Python 3.9.15 ('pythontest')", "language": "python", "name": "python3" }, @@ -188,7 +146,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 903b349c..7bb58165 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,192 +1,64 @@ ans -012613 -$\{2,4\}$ +012655 +$\{2\}$ -012614 -$(1,2)$ +012656 +$(-1,1)$ -012615 -$\dfrac{\sqrt{2}}2$ +012657 +$\sqrt{5}$ -012616 -$3$ - -012617 -$3$ - -012618 -\textcircled{1}\textcircled{4} - -012619 -$180$ - -012620 -$4$ - -012621 -$\dfrac 52$ - -012622 -$\dfrac\pi 4$ - -012623 -$\dfrac{8\sqrt{2}\pi}3$ - -012624 -$\dfrac{8\sqrt{3}}3$ - -012625 -A - -012626 -C - -012627 -D - -012628 -C - -012629 -(1) $b_n=3^{n-1}$; (2) $-8$ - -012630 -(1) $\dfrac \pi 4$; (2) $1$ - -012631 -(1) 证明略; (2) 证明略; (3) $\dfrac\pi 4$ - -012632 -(1) $\sqrt{2}$; (2) $y=x+1$; (3) 过定点$(-3,0)$和$(1,0)$ - -012633 -(1) $y=x-1$; (2) 单调减区间为$(\dfrac 12 1)$; 极小值为$-2$; (3) 证明略 - -012571 -$\{1\}$ - -012572 -$-1$ - -012573 -$\dfrac\pi 6$ - -012574 -$2$ - -012575 -$16\pi$ - -012576 -$2800$, $31$ - -012577 -$2$ - -012578 -$(-\infty,1)\cup (1,3]$ - -012579 +012658 $5$ -012580 -$[\dfrac 32,2]$ +012659 +$3$ -012581 -$(\dfrac 72,0,\dfrac 72)$ +012660 +$0.3$ -012582 -$\dfrac{\sqrt{3}}{20}v$ +012661 +$\dfrac{\sqrt{3}}3\pi$ -012583 +012662 +$2$ + +012663 +$96$ + +012664 +$\dfrac 53$ + +012665 +$60^\circ$ + +012666 +$2021$ + +012667 +B + +012668 A -012584 -D - -012585 +012669 C -012586 -C - -012587 -(1) 证明略; (2) $\dfrac{3\sqrt{22}}{11}$ - -012588 -(1) $\dfrac 12$; (2) $a_n=\dfrac{18}{2n+1}$ - -012589 -(1) 例如: 非通勤时段的车辆使用情况; 油价和电价的变化; 工作单位能否提供免费充电; 电动车的国家减免政策的变化; 车辆的外观、内饰与品牌效应; 车牌费用等; (2) 解答略 - - -012590 -(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$($y\le 0$); (2) $P(-\dfrac 32,\dfrac{\sqrt{3}}2)$, $Q(\dfrac 32, \dfrac{\sqrt{3}}2)$; (3) $[\sqrt{3}-1,\sqrt{2}+1]$ - -012591 -(1) 导数为$y'=\dfrac{1-\ln x}{x^2}$, 单调性证明略; (2) 判断$89^{99}>99^{89}$, 证明略, 推广可以是:``对于实数$a,b$, 若$\mathrm{e}b^a$; (3) 证明略 - - -010965 -$[0,2]$ - -010966 -$(-\infty,0)$ - -030023 -$\dfrac{3n^2-5n}2$ - -010968 -$\dfrac{8\pi}3$ - -010969 -$2(x+2)-(y-1)=0$ - -010970 -$\dfrac 32$ - -030025 -$[0,\dfrac 34]$ - -010972 -$25$ - -030024 -$\dfrac 23(\dfrac 1{4^n}-1)$ - -010974 -$[1,+\infty)$ - -010975 -$\sqrt{3}$ - -010976 -$3-\sqrt{3}$ - -010977 +012670 B -002745 -C +012671 +(1) $[k\pi-\dfrac{5\pi}{12},k\pi+\dfrac\pi{12}]$, $k\in \mathbf{Z}$; (2) $\sqrt{13}$或$\sqrt{61}$ -010979 -C +012672 +(1) 证明略; (2) $a_n=3^n-2$; (3) $a_1+a_3+a_5+a_7+a_9=22133$ -010980 -B +012673 +(1) 证明略; (2) $\arccos \dfrac{\sqrt{10}}{10}$; (3) $\dfrac 13$ -010981 -(1) $\dfrac 23$; (2) $\arctan {2\sqrt{5}}5$ +012674 +(1) $\dfrac{x^2}{12}+\dfrac{y^2}4=1$; (2) $3+2\sqrt{3}$; (3) 存在, $m$的取值范围为$[-\dfrac{\sqrt{3}}3,0)$ -010982 -(1) $\log_2 3$; (2) $a=2b\ne 0$ - -010983 -(1) $\sqrt{7}$千米; (2) 有$\dfrac{8-\sqrt{15}}7$小时, 两人不能通话 - -010984 -(1) $y^2=4\sqrt{5} x$或$y^2=-4\sqrt{5} x$; (2) $M$的坐标为$(0,0)$或$(-\dfrac{4\sqrt{5}}5,0)$; (3) 证明略 - -010985 -(1) $\{-6,-3,-2,-1,0,1,2,3,4\}$; (2) 证明略; (3) 元素个数为$\dfrac 12 n(n+1)$; 元素之和为$\dfrac{n+1}2(3^{n+1}-3)$ \ No newline at end of file +012675 +(1) 当$a=0$时, $f(x)$是偶函数; 当$a\ne 0$时, $f(x)$既不是奇函数又不是偶函数; (2) $(-1,\dfrac 5{27})$; (3) $[2\ln 2-2,1]$ \ No newline at end of file diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index d91dae5d..f838bfff 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1 +1 @@ -012571,012572,012573,012574,012575,012576,012577,012578,012579,012580,012581,012582,012583,012584,012585,012586,012587,012588,012589,012590,012591 \ No newline at end of file +012529,012530,012531,012532,012533,012534,012535,012536,012537,012538,012539,012540,012541,012542,012543,012544,012545,012546,012547,012548,012549 \ No newline at end of file diff --git a/工具/生成文件夹下的题号清单.ipynb b/工具/生成文件夹下的题号清单.ipynb index b4be83d0..afd918a9 100644 --- a/工具/生成文件夹下的题号清单.ipynb +++ b/工具/生成文件夹下的题号清单.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": {}, "outputs": [ { diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index 6276c98d..7e11827c 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": 3, + "execution_count": 1, "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/2023届嘉定区一模_教师_20221217.tex\n", + "开始编译教师版本pdf文件: 临时文件/2023届青浦区一模_教师_20221219.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/2023届嘉定区一模_学生_20221217.tex\n", + "开始编译学生版本pdf文件: 临时文件/2023届青浦区一模_学生_20221219.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\",\"2023届嘉定区一模\")]\n", + "exec_list = [(\"标题替换\",\"2023届青浦区一模\")]\n", "enumi_mode = 1\n", "\n", "# 日常选题讲义\n", @@ -51,13 +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/2023届嘉定区一模\"\n", + "destination_file = \"临时文件/2023届青浦区一模\"\n", "\"\"\"---设置目标文件名结束---\"\"\"\n", "\n", "\n", "\"\"\"---设置题号数据---\"\"\"\n", "problems = [\n", - "\"012571,012572,012573,012574,012575,012576,012577,012578,012579,012580,012581,012582\",\"012583,012584,012585,012586\",\"012587,012588,012589,012590,012591\"\n", + "\"012529,012530,012531,012532,012533,012534,012535,012536,012537,012538,012539,012540\",\"012541,012542,012543,012544\",\"012545,012546,012547,012548,012549\"\n", + "\n", + "\n", "]\n", "\"\"\"---设置题号数据结束---\"\"\"\n", "\n", @@ -208,7 +210,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "Python 3.9.15 ('pythontest')", "language": "python", "name": "python3" }, @@ -227,7 +229,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, 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 47c62b9a..c5966489 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 @@ -2,118 +2,34 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "012550 填空题\n", - "012551 填空题\n", - "012552 填空题\n", - "012553 填空题\n", - "012554 填空题\n", - "012555 填空题\n", - "012556 填空题\n", - "012557 填空题\n", - "012558 填空题\n", - "012559 填空题\n", - "012560 填空题\n", - "012561 填空题\n", - "012562 选择题\n", - "012563 选择题\n", - "012564 解答题\n", - "012565 选择题\n", - "012566 解答题\n", - "012567 解答题\n", - "012568 解答题\n", - "012569 解答题\n", - "012570 解答题\n", - "012571 填空题\n", - "012572 填空题\n", - "012573 填空题\n", - "012574 填空题\n", - "012575 填空题\n", - "012576 填空题\n", - "012577 填空题\n", - "012578 填空题\n", - "012579 填空题\n", - "012580 填空题\n", - "012581 填空题\n", - "012582 填空题\n", - "012583 选择题\n", - "012584 选择题\n", - "012585 选择题\n", - "012586 解答题\n", - "012587 解答题\n", - "012588 解答题\n", - "012589 解答题\n", - "012590 解答题\n", - "012591 解答题\n", - "012592 填空题\n", - "012593 填空题\n", - "012594 填空题\n", - "012595 填空题\n", - "012596 填空题\n", - "012597 填空题\n", - "012598 填空题\n", - "012599 填空题\n", - "012600 填空题\n", - "012601 填空题\n", - "012602 填空题\n", - "012603 填空题\n", - "012604 选择题\n", - "012605 选择题\n", - "012606 选择题\n", - "012607 选择题\n", - "012608 解答题\n", - "012609 解答题\n", - "012610 解答题\n", - "012611 解答题\n", - "012612 解答题\n", - "012613 填空题\n", - "012614 填空题\n", - "012615 填空题\n", - "012616 填空题\n", - "012617 填空题\n", - "012618 填空题\n", - "012619 填空题\n", - "012620 填空题\n", - "012621 填空题\n", - "012622 填空题\n", - "012623 填空题\n", - "012624 填空题\n", - "012625 选择题\n", - "012626 填空题\n", - "012627 选择题\n", - "012628 选择题\n", - "012629 解答题\n", - "012630 解答题\n", - "012631 解答题\n", - "012632 解答题\n", - "012633 解答题\n", - "012634 填空题\n", - "012635 填空题\n", - "012636 填空题\n", - "012637 填空题\n", - "012638 填空题\n", - "012639 填空题\n", - "012640 填空题\n", - "012641 填空题\n", - "012642 填空题\n", - "012643 填空题\n", - "012644 填空题\n", - "012645 填空题\n", - "012646 选择题\n", - "012647 选择题\n", - "012648 选择题\n", - "012649 选择题\n", - "012650 解答题\n", - "012651 解答题\n", - "012652 解答题\n", - "012653 解答题\n", - "012654 解答题\n" + "012655 填空题\n", + "012656 填空题\n", + "012657 填空题\n", + "012658 填空题\n", + "012659 填空题\n", + "012660 填空题\n", + "012661 填空题\n", + "012662 填空题\n", + "012663 填空题\n", + "012664 填空题\n", + "012665 填空题\n", + "012666 填空题\n", + "012667 选择题\n", + "012668 选择题\n", + "012669 选择题\n", + "012670 选择题\n", + "012671 解答题\n", + "012672 解答题\n", + "012673 解答题\n", + "012674 解答题\n", + "012675 解答题\n" ] } ], 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 5251d936..19d27c23 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/2019余_教师用_20221218.tex\n", + "开始编译教师版本pdf文件: 临时文件/2019余_教师用_20221219.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/2019余_学生用_20221218.tex\n", + "开始编译学生版本pdf文件: 临时文件/2019余_学生用_20221219.tex\n", "0\n" ] } @@ -26,7 +26,7 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n", "problems = r\"\"\"\n", - "012204,012206,012221,012222,012223\n", + "12308:12319,12320:12323,12324:12328\n", "\n", "\"\"\"\n", "\"\"\"---设置题目列表结束---\"\"\"\n", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 02a3672e..c3f5cc9b 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -311517,7 +311517,7 @@ }, "012642": { "id": "012642", - "content": "某中学从甲、乙两个班中各选出$15$名学生参加知识竞赛, 将他们的成绩(满分$100$分)进行统计分析, 绘制成如图所示的茎叶图. 设成绩在$88$分以上(含$88$分)的学生为优秀学生, 现从甲、乙两班的优秀学生中各取$1$人, 记甲班选取的学生成绩不低于乙班选取得学生成绩记为事件$A$, 则事件$A$发生的概率$P(A)=$\\blank{50}.\n\\begin{center}\n\\begin{tabular}{r|c|l}\n甲 & & 乙\\\\\n& 5 & 8\\\\\n8\\ 0& 6 & 6\\ 9\\\\\n9 \\ 8 \\ 5 & 7 & 0 \\ 5 \\ 6 \\ 6 \\ 6 \\ 8 \\ 8\\\\\n8 \\ 7 \\ 6 \\ 4 \\ 1 & 8 & 6 \\ 6 \\\\\n8 \\ 6 \\ 2 \\ 2 \\ 1 & 9 & 5 \\ 8 \\ 8\n\\end{tabular}\n\\end{center}", + "content": "某中学从甲、乙两个班中各选出$15$名学生参加知识竞赛, 将他们的成绩(满分$100$分)进行统计分析, 绘制成如图所示的茎叶图. 设成绩在$88$分以上(含$88$分)的学生为优秀学生, 现从甲、乙两班的优秀学生中各取$1$人, 记甲班选取的学生成绩不低于乙班选取得学生成绩记为事件$A$, 则事件$A$发生的概率$P(A)=$\\blank{50}.\n\\begin{center}\n\\begin{tabular}{r|c|l}\n甲 & & 乙\\\\\n& 5 & 8\\\\\n8 \\ 0& 6 & 6 \\ 9\\\\\n9 \\ 8 \\ 5 & 7 & 0 \\ 5 \\ 6 \\ 6 \\ 6 \\ 8 \\ 8\\\\\n8 \\ 7 \\ 6 \\ 4 \\ 1 & 8 & 6 \\ 6 \\\\\n8 \\ 6 \\ 2 \\ 2 \\ 1 & 9 & 5 \\ 8 \\ 8\n\\end{tabular}\n\\end{center}", "objs": [], "tags": [], "genre": "填空题", @@ -311767,8 +311767,8 @@ "content": "已知集合$A=\\{1,2\\}$, $B=\\{2,3\\}$, 则$A \\cap B=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$\\{2\\}$", "solution": "", "duration": -1, "usages": [], @@ -311786,8 +311786,8 @@ "content": "函数$y=\\log_2 \\dfrac{1+x}{1-x}$的定义域是\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$(-1,1)$", "solution": "", "duration": -1, "usages": [], @@ -311805,8 +311805,8 @@ "content": "设复数$z=\\mathrm{i}(2-\\mathrm{i})$(其中$\\mathrm{i}$为虚数单位), 则$|z|=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$\\sqrt{5}$", "solution": "", "duration": -1, "usages": [], @@ -311824,8 +311824,8 @@ "content": "设$x>1$, 则$x+\\dfrac 4{x-1}$的最小值是\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$5$", "solution": "", "duration": -1, "usages": [], @@ -311843,8 +311843,8 @@ "content": "若指数函数$y=a^x$($a>0$, $a \\neq 1$)在$[1, 2]$上的最大值与最小值之和等于$12$, 则实数$a=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -311862,8 +311862,8 @@ "content": "两个篮球运动员罚球时的命中概率分别是$0.6$和$0.5$, 两人各投一次, 则他们同时命中的概率是\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$0.3$", "solution": "", "duration": -1, "usages": [], @@ -311881,8 +311881,8 @@ "content": "将圆锥的侧面展开后得到一个半径为$2$的半圆, 则此圆锥的体积为\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$\\dfrac{\\sqrt{3}}3\\pi$", "solution": "", "duration": -1, "usages": [], @@ -311900,8 +311900,8 @@ "content": "已知平面向量$\\overrightarrow a$、$\\overrightarrow b$满足$|\\overrightarrow a|=3$, $|\\overrightarrow b|=4$, 则$2 \\overrightarrow a+\\overrightarrow b$在$\\overrightarrow a$方向上的数量投影的最小值是\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -311919,8 +311919,8 @@ "content": "从$5$名志愿者中选出$4$名分别参加测温、扫码、做核酸和信息登记的工作 (每项$1$人), 其中甲不参加测温的分配方案有\\blank{50}种. (结果用数值表示)", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$96$", "solution": "", "duration": -1, "usages": [], @@ -311938,8 +311938,8 @@ "content": "双曲线$C$的左、右焦点分别为$F_1$、$F_2$, 点$A$在$y$轴上. 双曲线$C$与线段$AF_1$交于点$P$, 与线段$AF_2$交于点$Q$, 直线$AF_1$平行于双曲线$C$的渐近线, 且$|AP|:|PQ|=5: 6$, 则双曲线$C$的离心率为\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$\\dfrac 53$", "solution": "", "duration": -1, "usages": [], @@ -311957,8 +311957,8 @@ "content": "某人去公园郊游, 在草地上搭建了如图所示的简易遮阳篷$ABC$, 遮阳篷是一个直角边长为$6$的等腰直角三角形, 斜边$AB$朝南北方向固定在地上, 正西方向射出的太阳光线与地面成$30^{\\circ}$角, 则当遮阳篷$ABC$与地面所成的角大小为\\blank{50}时, 所遮阴影面$ABC$面积达到最大.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,2) node [below] {$A$} coordinate (A);\n\\draw (0,0,-2) node [right] {$B$} coordinate (B);\n\\draw ({2*sqrt(3)},0,0) node [right] {$C'$} coordinate (C');\n\\draw (0,2,0) node [above] {$C$} coordinate (C);\n\\fill [pattern = north east lines] (A) -- (B) -- (C) -- cycle;\n\\draw (A) -- (C) -- (C') -- cycle;\n\\draw [dashed] (A) -- (B) -- (C) (B) -- (C');\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$60^\\circ$", "solution": "", "duration": -1, "usages": [], @@ -311976,8 +311976,8 @@ "content": "对于正整数$n$, 设$x_n$是关于$x$的方程$n x^3+2 x-n=0$的实数根, 记$a_n=[(n+1) x_n]$($n \\geq 2$), 其中$[x]$表示不超过$x$的最大整数, 则$\\dfrac 1{1012}(a_2+a_3+a_4+\\cdots+a_{2022})=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "填空题", + "ans": "$2021$", "solution": "", "duration": -1, "usages": [], @@ -311995,8 +311995,8 @@ "content": "已知$a , b$都是自然数, 则``$a+b$是偶数''是``$a , b$都是偶数''的\\bracket{20}条件.\n\\fourch{充分而不必要}{必要而不充分}{充要}{既不充分也不必要}", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "选择题", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -312014,8 +312014,8 @@ "content": "某高中共有学生$1200$人, 其中高一、高二、高三的学生人数比为$6: 5: 4$, 现用分层抽样的方法从该校所有学生中抽取一个容量为$60$的样本, 则高三年级应该抽取\\bracket{20}人.\n\\fourch{$16$}{$18$}{$20$}{$24$}", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "选择题", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -312033,8 +312033,8 @@ "content": "设$\\sin \\alpha+\\cos \\alpha=x$, 且$\\sin ^3 \\alpha+\\cos ^3 \\alpha=a_3 x^3+a_2 x^2+a_1 x+a_0$, 则$a_0+a_1+a_2+a_3=$\\bracket{20}.\n\\fourch{$-1$}{$\\dfrac 12$}{$1$}{$\\sqrt 2$}", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "选择题", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -312052,8 +312052,8 @@ "content": "已知$O$为坐标原点, 点$A(1,1)$在抛物线$C: x^2=2 p y$($p>0$)上, 过点$B(0,-1)$的直线交抛物线$C$于$P$、$Q$两点: \\textcircled{1} 抛物线$C$的准线为$y=-\\dfrac 12$; \\textcircled{2} 直线$AB$与抛物线$C$相切; \\textcircled{3} $|OP|\\cdot|OQ|>|OA|^2$; \\textcircled{4} $|BP|\\cdot|BQ|=|BA|^2$, 以上结论中正确的是\\bracket{20}.\n\\fourch{\\textcircled{1}\\textcircled{2}}{\\textcircled{2}\\textcircled{3}}{\\textcircled{3}\\textcircled{4}}{\\textcircled{3}\\textcircled{4}}", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "选择题", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -312071,8 +312071,8 @@ "content": "已知函数$f(x)=\\sin 2 x+\\sqrt 3 \\cos 2 x$, $x \\in \\mathbf{R}$.\\\\\n(1) 求函数$f(x)$的单调增区间;\\\\\n(2) 在锐角$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 当$f(A)=0$, $b=1$, 且三角形$ABC$的面积为$\\sqrt 3$时, 求$a$.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "解答题", + "ans": "(1) $[k\\pi-\\dfrac{5\\pi}{12},k\\pi+\\dfrac\\pi{12}]$, $k\\in \\mathbf{Z}$; (2) $\\sqrt{13}$或$\\sqrt{61}$", "solution": "", "duration": -1, "usages": [], @@ -312083,15 +312083,15 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "012672": { "id": "012672", "content": "已知数列$\\{a_n\\}$满足$a_1=1$, $a_n=3 a_{n-1}+4$($n \\geq 2$).\\\\\n(1) 求证: 数列$\\{a_n+2\\}$是等比数列;\\\\\n(2) 求数列$\\{a_n\\}$的通项公式;\\\\\n(3) 写出$\\displaystyle\\sum_{i=1}^5 a_{2 i-1}$的具体展开式, 并求其值.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "解答题", + "ans": "(1) 证明略; (2) $a_n=3^n-2$; (3) $a_1+a_3+a_5+a_7+a_9=22133$", "solution": "", "duration": -1, "usages": [], @@ -312102,15 +312102,15 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "012673": { "id": "012673", "content": "如图, 棱长为$2$的正方体$ABCD-A_1B_1C_1D_1$中, $M$、$N$、$P$分别是$C_1D_1$、$C_1C$、$A_1A$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\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,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,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\\filldraw ($(C1)!0.5!(D1)$) circle (0.03) node [above] {$M$} coordinate (M);\n\\filldraw ($(A)!0.5!(A1)$) circle (0.03) node [left] {$P$} coordinate (P);\n\\filldraw ($(C)!0.5!(C1)$) circle (0.03) node [right] {$N$} coordinate (N);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $M$、$N$、$A_1$、$B$四点共面;\\\\\n(2) 求异面直线$PD_1$与$MN$所成角的大小; (结果用反三角函数值表示)\\\\\n(3) 求三棱锥$P-MNB$的体积.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "解答题", + "ans": "(1) 证明略; (2) $\\arccos \\dfrac{\\sqrt{10}}{10}$; (3) $\\dfrac 13$", "solution": "", "duration": -1, "usages": [], @@ -312121,15 +312121,15 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "012674": { "id": "012674", "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$), $P(1,3)$, $Q(3,1)$, $M(-3,1)$, $N(0,2)$这四点中恰有三点在椭圆$C$上.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (-3.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\filldraw (1,3) circle (0.03) node [right] {$P$} coordinate (P);\n\\filldraw (3,1) circle (0.03) node [right] {$Q$} coordinate (Q);\n\\filldraw (-3,1) circle (0.03) node [right] {$M$} coordinate (M);\n\\filldraw (0,2) circle (0.03) node [right] {$N$} coordinate (N);\n\\end{tikzpicture}\n\\end{center}\n(1) 求椭圆$C$的方程;\\\\\n(2) 点$E$是椭圆$C$上的一个动点, 求$\\triangle EMN$面积的最大值;\\\\\n(3) 过$R(0,1)$的直线$l$交椭圆$C$于$A$、$B$两点, 设直线$l$的斜率$k>0$, 在$x$轴上是否存在一点$D(m, 0)$, 使得以$DA$、$DB$为邻边的平行四边形为菱形? 若存在, 求实数$m$的取值范围; 若不存在, 请说明理由.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "解答题", + "ans": "(1) $\\dfrac{x^2}{12}+\\dfrac{y^2}4=1$; (2) $3+2\\sqrt{3}$; (3) 存在, $m$的取值范围为$[-\\dfrac{\\sqrt{3}}3,0)$", "solution": "", "duration": -1, "usages": [], @@ -312140,15 +312140,15 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "012675": { "id": "012675", "content": "已知函数$f(x)=x^2-a x-a$, $a \\in \\mathbf{R}$.\\\\\n(1) 判断函数$f(x)$的奇偶性;\\\\ \n(2) 若函数$F(x)=x \\cdot f(x)$在$x=1$处有极值, 且关于$x$的方程$F(x)=m$有 $3$个不同的实根, 求实数$m$的取值范围;\\\\\n(3) 记$g(x)=-\\mathrm{e}^x$($\\mathrm{e}$是自然对数的底数). 若对任意$x_1$、$x_2 \\in[0, \\mathrm{e}]$且$x_1>x_2$时, 均有$|f(x_1)-f(x_2)|<|g(x_1)-g(x_2)|$成立, 求实数$a$的取值范围.", "objs": [], "tags": [], - "genre": "", - "ans": "", + "genre": "解答题", + "ans": "(1) 当$a=0$时, $f(x)$是偶函数; 当$a\\ne 0$时, $f(x)$既不是奇函数又不是偶函数; (2) $(-1,\\dfrac 5{27})$; (3) $[2\\ln 2-2,1]$", "solution": "", "duration": -1, "usages": [], @@ -312159,7 +312159,7 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "020001": { "id": "020001",