diff --git a/工具/latex界面修改题目内容.py b/工具/latex界面修改题目内容.py index 67d9b807..c5aa0a96 100644 --- a/工具/latex界面修改题目内容.py +++ b/工具/latex界面修改题目内容.py @@ -1,6 +1,6 @@ import os,re,json """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭""" -problems = "40399" +problems = "18081" editor = "王伟叶" def generate_number_set(string,dict): diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index 85fb0476..670427a8 100644 --- a/工具/批量收录题目.py +++ b/工具/批量收录题目.py @@ -1,8 +1,8 @@ #修改起始id,出处,文件名 -starting_id = 17865 -raworigin = "高中数学质量测试综合测试" -filename = r"C:\Users\weiye\Documents\wwy sync\待整理word题目\质量测试与监控第二部分.tex" -editor = "20230606\t王伟叶" +starting_id = 18061 +raworigin = "" +filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex" +editor = "20230608\t王伟叶" indexed = True IndexDescription = "试题" diff --git a/工具/文本文件/批量题目分类号记录.txt b/工具/文本文件/批量题目分类号记录.txt index 3f7a7592..0171bf27 100644 --- a/工具/文本文件/批量题目分类号记录.txt +++ b/工具/文本文件/批量题目分类号记录.txt @@ -57,8 +57,8 @@ problems_dict = { "2019年秋考":"003631:003651", "2020年秋考":"003610:003630", "2021年秋考":"003589:003609", -"2022年秋考":"009984:010004" - +"2022年秋考":"009984:010004", +"2023年秋考":"018061:018081" } 20230427 2023届一模中档题汇编 diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index b6886c58..523cf9a0 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -463218,6 +463218,427 @@ "space": "4em", "unrelated": [] }, + "018061": { + "id": "018061", + "content": "不等式$|x-2|<1$的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题1", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018062": { + "id": "018062", + "content": "已知$\\overrightarrow {a}=(-2,3)$, $\\overrightarrow {b}=(1,2)$, 则$\\overrightarrow {a} \\cdot \\overrightarrow {b}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题2", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018063": { + "id": "018063", + "content": "已知$\\{a_n\\}$为等比数列, 且$a_1=3$, $q=2$, 则$s_6=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题3", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018064": { + "id": "018064", + "content": "已知$\\tan \\alpha=3$, 则$\\tan 2 \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题4", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018065": { + "id": "018065", + "content": "已知$f(x)=\\begin{cases}2^x, & x>0 \\\\ 1, & x \\leq 0\\end{cases}$, 则$f(x)$的值域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题5", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018066": { + "id": "018066", + "content": "已知当$z=1+\\mathrm{i}$, 则$|1-\\mathrm{i} \\cdot z|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题6", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018067": { + "id": "018067", + "content": "已知$x^2+y^2-4 y-m=0$的面积为$\\pi$, 则实数$m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题7", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018068": { + "id": "018068", + "content": "在$\\triangle ABC$中, $a=4$, $b=5$, $c=6$, 则$\\sin A=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题8", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018069": { + "id": "018069", + "content": "国内生产总值 (GDP) 是衡量地区经济状况的最佳指标, 根据统计数据显示, 某市在$2020$年间经济高质量增长, GDP 稳步增长, 第一季度和第四季度的 GDP 分别为$231$百亿元和$242$百亿元, 且四个季度 GDP 的中位数与平均数相等, 则$2020$年 GDP 总额为\\blank{50}百亿元.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题9", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018070": { + "id": "018070", + "content": "已知$(1+2023 x)^{100}+(2023-x)^{100}=a_0+a_1 x+a_2 x^2+\\cdots+a_{100} x^{100}$, 其中$a_0, a_1, a_2 \\cdots a_{100} \\in \\mathbf{R}$, 若$0 \\leq k \\leq 100$, $k \\in \\mathbf{N}$, 且$a_k<0$时, $k$的最大值是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题10", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018071": { + "id": "018071", + "content": "公园修建斜坡, 假设斜坡起点在水平面上, 斜坡与水平面的夹角为$\\theta$, 斜坡终点距离水平面的垂直高度为$4$米, 游客每走一米消耗的体能为$(1.025-\\cos \\theta)$, 要使游客从斜坡底走到斜坡顶端所消耗的总体能最少, 则$\\theta=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题11", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018072": { + "id": "018072", + "content": "空间内存在三点$A$、$B$、$C$, 满足$AB=AC=BC=1$, 在空间内取不同两点(不计顺序), 使得这两点与$A$、$B$、$C$可以构成正四棱锥的五个顶点, 不同的方案数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题12", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018073": { + "id": "018073", + "content": "已知$P=\\{1,2\\}$, $Q=\\{2,3\\}$, 若$M=\\{x | x \\in P$且$x \\notin Q\\}$, 则$M=$\\bracket{20}.\n\\fourch{$\\{1\\}$}{$\\{2\\}$}{$\\{1,2\\}$}{$\\{1,2,3\\}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题13", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018074": { + "id": "018074", + "content": "根据如下身高和体重散点图, 下列说法正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.1, yscale = 0.05]\n\\foreach \\i in {140,150,...,190,200}\n{\\draw [gray] (\\i,40) -- (\\i,120);\n\\draw (\\i,40) node [below] {$\\i$};};\n\\foreach \\j in {40,50,...,120}\n{\\draw [gray] (140,\\j) -- (200,\\j);\n\\draw (140,\\j) node [left] {$\\j$};};\n\\draw (170,25) node {身高/cm};\n\\draw (130,80) node [rotate = 90] {体重/kg};\n\\foreach \\i/\\j in {162.7541947/51.35667837,155.5904334/50.43458716,182.6281063/66.42520322,194.5162186/73.26691491,167.0109575/64.85837148,186.1664161/56.42752272,155.3201017/41.01812489,164.8129716/63.14035077,149.9758607/50.66177296,182.1245727/61.56063672,167.7164262/63.36603393,188.1316785/62.07889087,168.181048/56.74601718,169.0289674/48.2316275,165.9568328/45.69465675,158.6475788/59.43511492,177.9581592/65.94572529,149.8883543/42.89574403,154.1762601/52.35704594,177.5744725/64.40559165,147.8675451/36.73642194,158.874746/50.18512684,169.9543832/56.11235339,178.5879736/72.65914687,164.7971686/64.1538182,148.9397741/40.05063508,169.2046131/56.68262717,161.8658622/50.29256194,183.4761935/65.62962727,172.6295456/56.89824375,145.9413914/42.71276268,165.7868326/48.24900293,144.8721261/43.65404209,154.2605136/48.46520756,164.9177355/56.03416046,152.6628467/51.99903484,162.0341495/49.92958441,198.8067301/88.7414868,191.9745755/65.53331829,176.9590713/61.41886794}\n{\\filldraw (\\i,\\j*1.2) ellipse (0.3 and 0.6);};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{身高越高, 体重越重}{身高越高, 体重越轻}{身高与体重成正相关}{身高与体重成负相关}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题14", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018075": { + "id": "018075", + "content": "设$a>0$, 函数$y=\\sin x$在区间$[a, 2 a]$上的最小值为$s_a$, 在$[2 a, 3 a]$上的最小值为$t_a$, 当$a$变化时, 以下不可能的情形是\\bracket{20}.\n\\fourch{$s_a>0$且$t_a>0$}{$s_a<0$且$t_a<0$}{$s_a>0$且$t_a<0$}{$s_a<0$且$t_a>0$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题15", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018076": { + "id": "018076", + "content": "在平面上, 若曲线$\\Gamma$具有如下性质: 存在点$M$, 使得对于任意点$P \\in \\Gamma$, 都有$Q \\in \\Gamma$使得$|PM| \\cdot|QM|=1$.则称这条曲线为\"自相关曲线\".\n下列两个命题:\\\\\n\\textcircled{1} 所有椭圆都是``自相关曲线'';\\\\\n\\textcircled{2} 存在是``自相关曲线''的双曲线.\\\\\n的真假情况为\\bracket{20}.\n\\fourch{\\textcircled{1}为假命题, \\textcircled{2}为真命题}{\\textcircled{1}为真命题, \\textcircled{2}为假命题}{\\textcircled{1}为真命题, \\textcircled{2}为真命题}{\\textcircled{1}为假命题, \\textcircled{2}为假命题}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题16", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "018077": { + "id": "018077", + "content": "直四棱柱$ABCD-A_1B_1C_1D_1$中, $AB\\parallel DC$, $AB \\perp AD$, $AB=2$, $AD=3$, $DC=4$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (2,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (4,0,-3) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-3) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,4,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,4,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,4,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,4,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw (A_1)--(B);\n\\draw [dashed] (B)--(D)--(A)(D)--(A_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $A_1B \\parallel$面$DCC_1D$;\\\\\n(2) 若四棱柱体积为$36$, 求二面角$A_1-BD-A$的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题17", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018078": { + "id": "018078", + "content": "函数$f(x)=\\dfrac{x^2+(3 a+1) x+c}{x+a}$($a, c \\in \\mathbf{R}$).\\\\\n(1) 当$a=0$时, 是否存在实数$c$, 使得$f(x)$为奇函数? 说明理由;\\\\\n(2) 函数$f(x)$的图像过点$(1,3)$, 且$f(x)$的图像$x$轴负半轴有两个交点, 求实数$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题18", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018079": { + "id": "018079", + "content": "21 世纪汽车博览会于 2023年 6 月 7 日在上海举行, 某汽车模型公司展示了$25$个汽车模型, 其外观和内饰的颜色分布如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline \\backslashbox{内饰}{外观} & 红色外观 & 蓝色外观 \\\\\n\\hline 棕色内饰 & 12 & 8 \\\\\n\\hline 米色内饰 & 2 & 3 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 若小明从这些模型中随机拿一个模型, 记事件$A$为小明取到的模型为红色外观, 事件$B$为取到模型有棕色内饰. 求$P(B)$、$P(B|A)$, 并据此判断事件$A$和事件$B$是否独立;\\\\\n(2) 该公司举行了一个抽奖活动, 规定在一次抽奖中, 每人可以一次性从这些模型中拿两个汽车模型, 给出以下假设: \\textcircled{1} 拿到的两个模型会出现三种结果, 即外观和内饰均为同色、 外观内饰都异色、以及仅外观或仅内饰同色; \\textcircled{2} 按结果的可能性大小, 概率越小奖项越高; \\textcircled{3} 奖金额为一等奖$600$元, 二等奖$300$元, 三等奖$150$元, 请你分析奖项对应的结果. 设$X$为一次抽奖获得的奖金额, 写出$X$的分布列并求出$X$的期望.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题19", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018080": { + "id": "018080", + "content": "曲线$\\Gamma: y^2=4 x$, 第一象限内点$A$在$\\Gamma$上, $A$的纵坐标是$a$.\\\\\n(1) 若$A$到准线的距离为$3$, 求$a$;\n(2) 若$a=4$, $B$在$x$轴上, $AB$中点在$\\Gamma$上, 求点$B$坐标和坐标原点$O$到$AB$距离;\\\\\n(3) 直线$l: x=-3$, 令$P$是第一象限$\\Gamma$上异于$A$的一点, 直线$PA$交$l$于$Q$, $H$是$P$在$l$上的投影, 若点$A$满足``对于任意$P$都有$|HQ|>4$'', 求$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题20", + "edit": [ + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "018081": { + "id": "018081", + "content": "令$f(x)=\\ln x$, 取点$(a_1, f(a_1))$, 过该点作曲线$y=f(x)$的切线交$y$轴于点$(0, a_2)$, 取点$(a_{2},f(a_2))$, 过该点作切线交$y$轴于$(0, a_3)$, 以此类推, 期间若$a_k\\le 0$则停止, 得到数列$\\{a_n\\}$.\\\\\n(1) 若正整数$m \\geq 2$, 证明$a_m=\\ln a_{m-1}-1$;\\\\\n(2) 若正整数$m \\geq 2$, 试比较$a_m$与$a_{m-1}-2$大小;\\\\\n(3) 若正整数$k \\geq 3$, 是否存在$k$使得$a_1, a_2 \\cdots a_k$依次成等差数列? 若存在, 求出$k$的所有取值, 若不存在, 试说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023年秋考试题21", + "edit": [ + "20230608\t王伟叶", + "20230608\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "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.",