From d72ac71f34705ecb705d5878f0ff45e956541cb7 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sat, 1 Apr 2023 16:02:50 +0800 Subject: [PATCH] 20230401 afternoon --- 工具/修改题目数据库.ipynb | 10 +- 工具/批量收录题目.py | 12 +- 工具/批量题号选题pdf生成.ipynb | 4 +- 工具/生成文件夹下的题号清单.ipynb | 39 +- 工具/讲义生成.ipynb | 18 +- 工具/题号选题pdf生成.ipynb | 14 +- 题库0.3/Problems.json | 798 ++++++++++++++++++++++++++++++ 7 files changed, 865 insertions(+), 30 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 48999d22..51be37a1 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": 1, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 3, + "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 = \"31348:31381\"\n", + "problems = \"31158:31196\"\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": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -94,7 +94,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index d2677aee..1dcf4861 100644 --- a/工具/批量收录题目.py +++ b/工具/批量收录题目.py @@ -1,9 +1,9 @@ #修改起始id,出处,文件名 -starting_id = 40414 +starting_id = 40422 raworigin = "" -filename = r"D:\temp\test.tex" -editor = "20230330\t王伟叶" -indexed = False +filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目10.tex" +editor = "20230401\t王伟叶" +indexed = True import os,re,json @@ -64,9 +64,13 @@ problems = GenerateProblemListFromString(problems_string) id = starting_id +leading_suffix = problems[0][1] for p_and_suffix in problems: p = p_and_suffix[0] suffix = p_and_suffix[1] + if not leading_suffix == suffix: + starting_id = id + leading_suffix = suffix pid = str(id).zfill(6) if pid in pro_dict: duplicate_flag = True diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb index af517f7c..1d547a2f 100644 --- a/工具/批量题号选题pdf生成.ipynb +++ b/工具/批量题号选题pdf生成.ipynb @@ -224,7 +224,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -243,7 +243,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, 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 b7188864..c8ea7c95 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 @@ -168,7 +168,37 @@ "C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第二轮复习讲义\\16_导数及其应用.tex\n", "C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第二轮复习讲义\\17_计数原理与二项式定理.tex\n", "C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第二轮复习讲义\\18_概率与统计.tex\n", - "C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第二轮复习讲义\\19_统计.tex\n" + "C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第二轮复习讲义\\19_统计.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2022学年下学期高一高二材料_学生用_20230324.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2022学年下学期高一高二材料_学生用_20230326.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2022学年下学期高一高二材料_学生用_20230330.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2022学年下学期高一高二材料_教师用_20230324.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2022学年下学期高一高二材料_教师用_20230326.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2022学年下学期高一高二材料_教师用_20230330.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2025届1112班较难题_学生用_20230327.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2025届1112班较难题_学生用_20230328.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2025届1112班较难题_教师用_20230327.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\2025届1112班较难题_教师用_20230328.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\23届第一轮复习讲义参考答案.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\23届高三上学期周末卷参考答案.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\23届高三上学期测验卷参考答案.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\test1.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\易错题_学生用_20230328.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\易错题_教师用_20230328.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\本学期高一高二年级新试卷_学生用_20230319.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\本学期高一高二年级新试卷_教师用_20230319.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\测试_学生用_20230329.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\测试_教师用_20230329.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\立体几何综合答案.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\第二轮复习讲义参考答案.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\赋能1至30参考答案.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\赋能1至40参考答案.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\轨迹_学生用_20230325.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\轨迹_教师用_20230325.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\题库_学生用_20230401.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\题库_教师用_20230401.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\高三易错题_学生用_20230331.tex\n", + "d:\\mathdeptv2\\工具\\临时文件\\高三易错题_教师用_20230331.tex\n" ] } ], @@ -185,6 +215,7 @@ "r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\下学期测验卷\",\n", "r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\下学期周末卷\",\n", "r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第二轮复习讲义\",\n", + "r\"d:\\mathdeptv2\\工具\\临时文件\"\n", "]\n", "\"---文件夹列表输入结束---\"\n", "\n", @@ -241,7 +272,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -255,12 +286,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.15" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index b0a41103..e78b207a 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": 1, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -11,9 +11,11 @@ "text": [ "正在处理题块 1 .\n", "题块 1 处理完毕.\n", - "开始编译教师版本pdf文件: 临时文件/第四讲_教师_20230324.tex\n", + "正在处理题块 2 .\n", + "题块 2 处理完毕.\n", + "开始编译教师版本pdf文件: 临时文件/05_概率与统计_教师_20230401.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/第四讲_学生_20230324.tex\n", + "开始编译学生版本pdf文件: 临时文件/05_概率与统计_学生_20230401.tex\n", "0\n" ] } @@ -26,12 +28,12 @@ "\"\"\"2: 测验卷与周末卷(填空题, 选择题, 解答题)\"\"\"\n", "\"\"\"3: 日常选题讲义(一个section)\"\"\"\n", "\n", - "paper_type = 3 # 随后设置一下后续的讲义标题\n", + "paper_type = 1 # 随后设置一下后续的讲义标题\n", "\n", "\"\"\"---设置题块编号---\"\"\"\n", "\n", "problems = [\n", - "\"003927,013323,013422,013413,003737,013487,013453,003749,013590,013637,013639,003813,003802,013329,013602,013663,013672,013625,003834,003939,013688\"\n", + "\"332,401,654,2605,2664,3574,3640,4584,7361,7423,30227,30275,30540,31196,31320\",\"340,412,2586,3585,4575,7502,7630,10868,11993,14091,30495,30520,31158\"\n", "]\n", "\n", "\"\"\"---设置结束---\"\"\"\n", @@ -40,7 +42,7 @@ "if paper_type == 1:\n", " enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n", " template_file = \"模板文件/复习讲义模板.txt\" #设置模板文件名\n", - " exec_list = [(\"标题数字待处理\",\"16\"),(\"标题文字待处理\",\"导数及其应用\")] #设置讲义标题\n", + " exec_list = [(\"标题数字待处理\",\"05\"),(\"标题文字待处理\",\"概率与统计\")] #设置讲义标题\n", " destination_file = \"临时文件/\"+exec_list[0][1]+\"_\"+exec_list[1][1] # 设置输出文件名\n", "elif paper_type == 2:\n", " enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n", @@ -200,7 +202,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -219,7 +221,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "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 532bd2d5..f7b93a44 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": 5, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/第四单元易错题_教师用_20230328.tex\n", + "开始编译教师版本pdf文件: 临时文件/题库_教师用_20230401.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/第四单元易错题_学生用_20230328.tex\n", + "开始编译学生版本pdf文件: 临时文件/题库_学生用_20230401.tex\n", "0\n" ] } @@ -26,13 +26,13 @@ "\"\"\"---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", - "a\n", + "\n", "\"\"\"\n", "\"\"\"---设置题目列表结束---\"\"\"\n", "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/第四单元易错题\"\n", + "filename = \"临时文件/题库\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\"\"\"---设置是否需要解答题的空格---\"\"\"\n", @@ -177,7 +177,7 @@ ], "metadata": { "kernelspec": { - "display_name": "pythontest", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -196,7 +196,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 89ff70a8..09aef491 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -456212,5 +456212,803 @@ "related": [], "remark": "", "space": "" + }, + "040422": { + "id": "040422", + "content": "不等式$|x-1|<2$的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题1", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040423": { + "id": "040423", + "content": "函数$y=\\lg (-x)+\\dfrac{2}{\\sqrt{x^2-1}}$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题2", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040424": { + "id": "040424", + "content": "已知复数$z$满足$(2+\\mathrm{i}) z=3+4 \\mathrm{i}$($\\mathrm{i}$为虚数单位), 则$|z|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题3", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040425": { + "id": "040425", + "content": "对于正实数$x$, 代数式$x+\\dfrac{9}{x+1}$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题4", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040426": { + "id": "040426", + "content": "己知角$x$在第二象限, 且$\\cos (x+\\dfrac{\\pi}{2})=-\\dfrac{4}{5}$, 则$\\tan 2 x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题5", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040427": { + "id": "040427", + "content": "已知随机变量$X$服从正态分布$N(1.5, \\sigma^2)$, 且$P(1.50$, $|\\varphi|<\\dfrac{\\pi}{2}$), 若点$A(\\dfrac{1}{3}, 0)$为函数$y=f(x)$图像的对称中心, $B$、$C$是图像上相邻的最高点与最低点, 且$|BC|=4$, 则下列结论正确的是\\bracket{20}.\n\\onech{函数$y=f(x)$的对称轴方程为$x=4 k+\\dfrac{4}{3}, k \\in \\mathbf{Z}$}{函数$y=f(x-\\dfrac{\\pi}{3})$的图像关于坐标原点对称}{函数$y=f(x)$在区间$(0,2)$上是严格增函数}{若函数$y=f(x)$在区间$(0, m)$内有$5$个零点, 则它在此区间内有且有$2$个极小值点}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题16", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040438": { + "id": "040438", + "content": "已知四棱锥$P-ABCD$的底面$ABCD$为矩形, $PA \\perp$底面$ABCD$, 且$PA=AD=2AB=2$, 设$E$、$F$、$G$分别为$PC$、$BC$、$CD$的中点, $H$为$EG$的中点, 如图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$D$} coordinate (D);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw (0,0,1) node [left] {$B$} coordinate (B);\n\\draw ($(B)+(D)-(A)$) node [right] {$C$} coordinate (C);\n\\draw ($(B)!0.5!(C)$) node [below] {$F$} coordinate (F);\n\\draw ($(P)!0.5!(C)$) node [left] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(D)$) node [right] {$G$} coordinate (G);\n\\draw ($(E)!0.5!(G)$) node [above] {$H$} coordinate (H);\n\\draw (F)--(E)--(G);\n\\draw (P)--(B)--(C)--(D)--cycle(P)--(C);\n\\draw [dashed] (P)--(A)--(B)(A)--(D)(B)--(D)(F)--(G)(F)--(H);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $FH\\parallel$平面$PBD$;\\\\\n(2) 求直线$FH$与平面$PBC$所成角的正弦值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题17", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040439": { + "id": "040439", + "content": "记$S_n$为数列$\\{a_n\\}$的前$n$项和, 已知$S_n=\\dfrac{1}{2} a_n+n^2+1$($n$为正整数).\\\\\n(1) 求$a_1+a_2$的值, 并证明数列$\\{a_n+a_{n+1}\\}$是等差数列;\\\\\n(2) 求$S_n$的表达式.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题18", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040440": { + "id": "040440", + "content": "社会实践是大学生课外教育的一个重要方面, 在校大学生利用要期参加社会实践活动, 是认识社会、了解社会、提高自我能力的重要机会. 某省统计了该省其中的$4$所大学$2023$年毕业生的人数及参加过暑期社会实践活动的人数 (单位: 千人), 得到如下表格:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline 大学 &A大学 &B大学 &C大学 &D大学 \\\\\n\\hline 2023 年毕业生人数$x$(千人) & 7 & 6 & 5 & 4 \\\\\n\\hline 2023 年毕业生中参加过社会实践人数$y$(千人) & 0.5 & 0.4 & 0.3 & 0.2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 己知$y$与$x$具有较强的线性相关性, 求$y$关于$x$的线性回归方程$y=\\hat{a} x+\\hat{b}$;\\\\\n(2) 假设该省对参加过暑期社会实践活动的大学生每人发放$0.5$万元的补贴.\\\\\n(i) 若该省大学$2023$年毕业生人数为$12$万人, 估计该省要发放补贴的总金额;\\\\\n(ii) 若$2023$年毕业生中的小李、小王参加过暑期社会实践活动的概率分别为$p$、$3 p-1$, 该省对小李、小王两人补贴总金额的期望不超过$0.75$万元, 求$p$的取值范围.\\\\\n参考公式: $\\hat{a}=\\dfrac{\\displaystyle\\sum_{i=1}^n(x_i-\\overline {x})(y_i-\\overline {y})}{\\displaystyle\\sum_{i=1}^n(x_i-\\overline {x})^2}=\\dfrac{\\displaystyle\\sum_{i=1}^n(x_i y_i-n \\overline {x} \\cdot \\overline {y})}{\\displaystyle\\sum_{i=1}^n x_i^2-n \\overline {x}^2}$, $\\hat{b}=\\overline {y}-\\hat{a}\\overline{x}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题19", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040441": { + "id": "040441", + "content": "己知椭圆$C_1: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的离心率为$\\dfrac{\\sqrt{2}}{2}$, 且点$(-2, \\sqrt{2})$在椭圆$C_1$上.\\\\\n(1) 求椭圆$C_1$的方程;\\\\\n(2) 过点$Q(0,1)$的直线$l$与椭圆$C_1$交于$D$、$E$两点, 已知$\\overrightarrow{DQ}=2 \\overrightarrow{QE}$, 求直线$l$的方程;\\\\\n(3) 点$P$为椭圆$C_1$上任意一点, 过点$P$作$C_1$的切线与圆$C_2: x^2+y^2=12$交于$A$、$B$两点, 设直线$OA$、$OB$的斜率分别为$k_1$、$k_2$, 证明: $k_1 k_2$为定值, 并求该定值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题20", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040442": { + "id": "040442", + "content": "设$f(x)=\\mathrm{e}^x+a \\sin x-1$.\\\\\n(1) 求曲线$y=f(x)$在点$(0, f(0))$处的切线方程;\\\\\n(2) 若函数$y=f(x)$在$x=0$处取得极小值, 求$a$的值;\\\\\n(3) 若存在正实数$m$, 使得对任意的$x \\in(0, m)$, 都有$f(x)<0$, 求$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届三校联考试题21", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040443": { + "id": "040443", + "content": "已知集合$A=\\{1,2\\}$, $B=\\{2,3\\}$, 则$A \\cup B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题1", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040444": { + "id": "040444", + "content": "若复数$z$满足$z=\\dfrac{3+\\mathrm{i}}{\\mathrm{i}}$(其中$\\mathrm{i}$是虚数单位), 则$|\\overline {z}|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题2", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040445": { + "id": "040445", + "content": "轴截面是边长为$2$的正三角形的圆锥的侧面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题3", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040446": { + "id": "040446", + "content": "若$\\sin \\alpha=\\dfrac{1}{3}$, 则$\\cos (\\alpha+\\dfrac{\\pi}{2})=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题4", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040447": { + "id": "040447", + "content": "在$(x+2)^4$的展开式中, 含有$x^2$项的系数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题5", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040448": { + "id": "040448", + "content": "$f(x)=x^3+a x^2+3 x-9$, 已知$f(x)$在$x=3$时取得极值, 则$a$等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题6", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040449": { + "id": "040449", + "content": "在空间直角坐标系中, 点$A(1,0,0)$, 点$B(5,-4,3)$, 点$C(2,0,1)$, 则$\\overrightarrow{AB}$在$\\overrightarrow{CA}$方向上的投影向量的坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题7", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040450": { + "id": "040450", + "content": "已知函数$f(x)=x^{\\frac{1}{3}}$, 则关于$t$的表达式$f(t^2-2 t)+f(2 t^2-1)<0$的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题8", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040451": { + "id": "040451", + "content": "已知数列$\\{a_n\\}$的通项公式为$a_n=(20-n) \\cdot(\\dfrac{3}{2})^n$, 则$a_n$取最大值时, $n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题9", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040452": { + "id": "040452", + "content": "一项研究同年龄段的男、女生的注意力差别的脑功能实验, 实验数据如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline & 注意力稳定 & 注意力不稳定 \\\\\n\\hline 男生 & 29 & 7 \\\\\n\\hline 女生 & 33 & 5 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n依据$P(\\chi^2 \\geq 3.841) \\approx 0.05$, 该实验\\blank{50}该年龄段的学生在注意力的稳定性上对于性别没有显著差异(填拒绝或支持).\n参考公式: $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$, 其中$n=a+b+c+d$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题10", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040453": { + "id": "040453", + "content": "已知$F_1$、$F_2$是椭圆$\\Gamma$的两个焦点, 点$A$在$\\Gamma$上, 且$\\angle F_1AF_2=90^{\\circ}$, 延长$AF_1$交$\\Gamma$于点$B$, 若$|AB|=|AF_2|$, 则椭圆$\\Gamma$的离心率$e=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题11", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040454": { + "id": "040454", + "content": "已知等差数列共有$n$($n \\geq 4$)项, 各项与公差$d$均不为零, 若将此数列删去某一项后, 得到的数列 (按原来顺序) 是等比数列, 则所有数列$(n, \\dfrac{a_1}{d})$组成的集合为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题12", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040455": { + "id": "040455", + "content": "已知$P(B | A)=\\dfrac{1}{2}$, $P(AB)=\\dfrac{3}{8}$, 则$P(A)=$\\bracket{20}.\n\\fourch{$\\dfrac{3}{16}$}{$\\dfrac{13}{16}$}{$\\dfrac{3}{4}$}{$\\dfrac{1}{4}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题13", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040456": { + "id": "040456", + "content": "``$x=2 k \\pi+\\dfrac{\\pi}{2}$($k \\in \\mathbf{Z}$)''是``$|\\sin x|=1$''的\\bracket{20}条件.\n\\fourch{充分不必要}{必要不充分}{充要}{既不充分也不必要}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题14", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040457": { + "id": "040457", + "content": "对于某一集合$A$, 若满足$a$、$b$、$c \\in A$, 任取$a$、$b$、$c \\in A$都有``$a$、$b$、$c$为某一三角形的三边长'', 则称集合$A$为``三角集'', 下列集合中为三角集的是\\bracket{20}.\n\\twoch{$\\{x | x$是$\\triangle ABC$的高的长度$\\}$}{$\\{x | \\dfrac{x-1}{x-2} \\leq 0\\}$}{$\\{x|| x-1|+| x-3 |=2\\}$}{$\\{x | y=\\log _2(3 x-2)\\}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题15", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040458": { + "id": "040458", + "content": "若存在实常数$k$和$b$, 使得函数$F(x)$和$G(x)$对其公共定义域上的任意实数$x$都满足: $F(x) \\geq k x+b$和$G(x) \\leq k x+b$恒成立, 则称此直线$y=k x+b$为$F(x)$和$G(x)$的``隔离直线'', 已知函数$f(x)=x^2$($x \\in \\mathbf{R}$), $g(x)=\\dfrac{1}{x}$($x<0$), $h(x)=2 \\mathrm{e} \\ln x$($x>0$), 有下列两个命题:\\\\\n命题$\\alpha: f(x)$和$h(x)$之间存在唯一的``隔离直线''$y=2 \\sqrt{\\mathrm{e}} x-\\mathrm{e}$;\\\\\n命题$\\beta: f(x)$和$g(x)$之间存在``隔离直线'', 且$b$的最小值为$-1$. 则下列说法正确的是\\bracket{20}.\n\\twoch{命题$\\alpha$、命题$\\beta$都是真命题}{命题$\\alpha$为真命题, 命题$\\beta$为假命题}{命题$\\alpha$为假命题, 命题$\\beta$为真命题}{命题$\\alpha$、命题$\\beta$都是假命题}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题16", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040459": { + "id": "040459", + "content": "已知函数$f(x)=\\cos ^2 x-\\sin ^2 x+\\dfrac{1}{2}$.\\\\\n(1) 求$f(x)$的单调增区间;\\\\\n(2) 设$\\triangle ABC$为锐角三角形, 角$A$、$B$、$C$所对的边分别是$a$、$b$、$c$, $a=\\sqrt{19}$, $b=5$, 若$f(A)=0$, 求$\\triangle ABC$的面积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题17", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040460": { + "id": "040460", + "content": "如图所示, 在四棱锥$P-ABCD$中, $AB \\perp$平面$PAD$, $AB\\parallel CD$且$2AB=CD$, $PD=PA$, 点$H$为线段$AD$的中点, 若$PH=1$, $AD=\\sqrt{2}$, $PB$与平面$ABCD$所成角的大小为$45^{\\circ}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 2.5]\n\\draw (0,0,0) node [right] {$H$} coordinate (H);\n\\draw (0,0,{sqrt(2)/2}) node [left] {$A$} coordinate (A);\n\\draw ({sqrt(2)/2},0,{sqrt(2)/2}) node [below] {$B$} coordinate (B);\n\\draw (0,0,{-sqrt(2)/2}) node [above right] {$D$} coordinate (D);\n\\draw (D) ++ ({sqrt(2)},0,0) node [right] {$C$} coordinate (C);\n\\draw (0,1,0) node [above] {$P$} coordinate (P);\n\\draw (P)--(A)--(B)--(C)--cycle(P)--(B);\n\\draw [dashed] (P)--(H)(P)--(D)--(C)(A)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $PH \\perp$平面$ABCD$;\\\\\n(2) 求四棱锥$P-ABCD$的体积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题18", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040461": { + "id": "040461", + "content": "某校举行知识竞赛, 最后一个名额要在$A$、$B$两名同学中产生, 测试方案如下: $A$、$B$两名学生各自从给定的$4$个问题中随机抽取$3$个问题作答, 在这$4$个问题中, 已知$A$能正确作答其中的$3$个, $B$能正确作答每个问题的概率是$\\dfrac{3}{4}$, $A$、$B$两名同学作答问题相互独立.\\\\\n(1) 求$A$、$B$恰好答对$2$个问题的概率;\\\\\n(2) 设$A$答对的题数为$X, B$答对的题数为$Y$, 若让你投票决定参赛选手, 你会选择哪名学生, 说明理由?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题19", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040462": { + "id": "040462", + "content": "已知点$F_1$、$F_2$分别为双曲线$\\Gamma: \\dfrac{x^2}{2}-y^2=1$的左、右焦点, 直线$l: y=k x+1$与$\\Gamma$有两个不同的交点$A$、$B$.\\\\\n(1) 当$F_1 \\in l$时, 求$F_2$到$l$的距离;\\\\\n(2) 若$O$为原点, 直线$l$与$\\Gamma$的两条渐近线在一、二象限的交点分别为$C$、$D$, 证明: 当$\\triangle COD$的面积最小时, 直线$CD$平行于$x$轴;\\\\\n(3) 设$P$为$x$轴上一点, 是否存在实数$k$($k>0$), 使得$\\triangle PAB$是点$P$为直角顶点的等腰直角三角形? 若存在, 求出$k$的值及点$P$的坐标; 若不存在, 说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题20", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040463": { + "id": "040463", + "content": "已知函数$g(x)=a \\mathrm{e}^x-2 x-a \\mathrm{e}^{-x}$.\\\\\n(1) 若$a=2$, 求曲线$y=g(x)$在点$(0, g(0))$处的切线方程;\\\\\n(2) 若函数$y=g(x)$在$\\mathbf{R}$上是单调函数, 求实数$a$的取值范围;\\\\\n(3) 设函数$h(x)=a \\mathrm{e}^x$, 若在$\\mathbf{R}$上至少存在一点$x_1$, 使得$g(x_1)>h(x_1)$成立, 求实数$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届六校联考试题21", + "edit": [ + "20230401\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" } } \ No newline at end of file