From ff0f115dff35985581c0747434d185dc6b87aef6 Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Thu, 13 Apr 2023 18:35:34 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=952023=E5=B1=8A=E9=87=91?= =?UTF-8?q?=E5=B1=B1=E5=8C=BA=E4=BA=8C=E6=A8=A1=E8=AF=95=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/批量收录题目.py | 2 +- 题库0.3/Problems.json | 399 ++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 400 insertions(+), 1 deletion(-) diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index 643fa873..4c5e37ac 100644 --- a/工具/批量收录题目.py +++ b/工具/批量收录题目.py @@ -1,5 +1,5 @@ #修改起始id,出处,文件名 -starting_id = 15017 +starting_id = 15038 raworigin = "" filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex" editor = "202304012\t王伟叶" diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 13c11ea0..0496df2b 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -369604,6 +369604,405 @@ "remark": "", "space": "12ex" }, + "015038": { + "id": "015038", + "content": "已知集合$A=\\{-1,0\\}$, 集合$B=\\{2, a\\}$, 若$A \\cap B=\\{0\\}$, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题1", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015039": { + "id": "015039", + "content": "若实数$x$满足不等式$x^2-3 x+2<0$, 则$x$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题2", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015040": { + "id": "015040", + "content": "双曲线$\\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$的渐近线方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题3", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015041": { + "id": "015041", + "content": "已知向量$\\overrightarrow {a}=(0,1,0)$, 向量$\\overrightarrow {b}=(1,1,0)$, 则$\\overrightarrow {a}$与$\\overrightarrow {b}$的夹角的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题4", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015042": { + "id": "015042", + "content": "在$(2+x)^5$的二项展开式中, $x^4$项的系数为\\blank{50}(结果用数值表示).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题5", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015043": { + "id": "015043", + "content": "若复数$z=2+\\mathrm{i}$($\\mathrm{i}$是虚数单位), 则$z \\cdot \\overline {z}-z=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题6", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015044": { + "id": "015044", + "content": "已知$y=f(x)$是定义域为$\\mathbf{R}$的奇函数, 当$x \\geq 0$时, $f(x)=2 x^3+2^x-1$, 则$f(-2)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题7", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015045": { + "id": "015045", + "content": "掷一颗骰子, 令事件$A=\\{1,2,3\\}$, $B=\\{1,2,5,6\\}$, 则$P(A | B)=$\\blank{50}(结果用数值表示).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题8", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015046": { + "id": "015046", + "content": "已知正实数$a$、$b$满足$\\dfrac{1}{a}+\\dfrac{2}{b}=1$, 则$2 a+b$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题9", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015047": { + "id": "015047", + "content": "若函数$y=\\sin (\\omega x-\\dfrac{\\pi}{3})$(常数$\\omega>0$)在区间$(0, \\pi)$没有最值, 则$\\omega$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题10", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015048": { + "id": "015048", + "content": "已知函数$y=f(x)$和$y=g(x)$的表达式分别为$f(x)=\\sqrt{-x^2-4 x}$, $g(x)=x|x^2-a|$, 若对任意$x_1 \\in[1, \\sqrt{2}]$, 总存在$x_2 \\in[-3,0]$, 使得$g(x_1)b^2>0$, 则下列不等式中成立的是\\bracket{20}.\n\\fourch{$a>b$}{$2^a>2^b$}{$a>|b|$}{$\\log _2 a^2>\\log _2 b^2$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题13", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015051": { + "id": "015051", + "content": "某社区通过公益讲座宣传交通法规. 为了解讲座效果, 随机抽取$10$位居民, 分别在讲座前、\n后各回答一份交通法规知识问卷, 满分为$100$分. 他们得分的茎叶图如图所示 (``叶''是个位数字), 则下列选项叙述错误的是\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{ccc|c|cccc} \n\\multicolumn{3}{r|}{讲座前} & & \\multicolumn{4}{l}{讲座后} \\\\\n& 5 & 0 & 5 & & & & \\\\\n5 & 0 & 0 & 6 & & & & \\\\\n5 & 0 & 0 & 7 & & & & \\\\\n& & 0 & 8 & 0 & 5 & 5 & 5 \\\\\n& & 0 & 9 & 0 & 0 & 5 & 5 \\\\\n& & & 10 & 0 & 0 & &\n\\end{tabular}\n\\end{center}\n\\twoch{讲座后的答卷得分整体上高于讲座前的得分}{讲座前的答卷得分分布较讲座后分散}{讲座后答卷得分的第$80$百分位数为$95$}{讲座前答卷得分的极差大于讲座后得分的极差}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题14", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015052": { + "id": "015052", + "content": "如图, 在矩形$ABCD$中, $E$、$F$分别为边$AD$、$BC$上的点, 且$AD=3AE$, $BC=3BF$, 设$P$、$Q$分别为线段$AF$、$CE$的中点, 将四边形$ABFE$沿着直线$EF$进行翻折, 使得点$A$不在平面$CDEF$上, 在这一过程中, 下列关系不能恒成立的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (1,0) node [below] {$F$} coordinate (F);\n\\draw (3,0) node [right] {$C$} coordinate (C);\n\\draw (3,2) node [right] {$D$} coordinate (D);\n\\draw (1,2) node [above] {$E$} coordinate (E);\n\\draw (0,2) node [left] {$A$} coordinate (A);\n\\draw (B) rectangle (D) (E)--(F)(A)--(F)(E)--(C);\n\\filldraw ($(A)!0.5!(F)$) node [left] {$P$} coordinate (P) circle (0.03);\n\\filldraw ($(C)!0.5!(E)$) node [left] {$Q$} coordinate (Q) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n\\twoch{直线$AB\\parallel$直线$CD$}{直线$PQ\\parallel$直线$ED$}{直线$AB \\perp$直线$PQ$}{直线$PQ\\parallel$平面$ADE$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题15", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015053": { + "id": "015053", + "content": "设$\\{a_n\\}$是项数为$n_0$的有穷数列, 其中$n_0 \\geq 2$. 当$n \\leq \\dfrac{n_0}{2}$时, $a_n=\\dfrac{1}{2^n}$, 且对任意正整数$n \\leq n_0$都有$a_n+a_{n_0+1-n}=0$. 给出下列两个命题: \\textcircled{1} 若对任意正整数$n \\leq n_0$都有$\\displaystyle\\sum_{i=1}^n a_i \\leq \\dfrac{511}{512}$, 则$n_0$的最大值为$18$; \\textcircled{2} 对于任意满足$1 \\leq s=latex]\n\\def\\l{2}\n\\def\\h{2}\n\\draw ({-\\l/2},0,0) node [left] {$C$} coordinate (C);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$A$} coordinate (A);\n\\draw ({\\l/2},0,0) node [right] {$B$} coordinate (B);\n\\draw (C) ++ (0,\\h) node [left] {$C_1$} coordinate (C_1);\n\\draw (A) ++ (0,\\h) node [below right] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\h) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) -- (A) -- (B) (C) -- (C_1) (A) -- (A_1) (B) -- (B_1) (C_1) -- (A_1) -- (B_1) (C_1) -- (B_1);\n\\draw [dashed] (C) -- (B);\n\\draw ($(A)!0.5!(B)$) node [below] {$D$} coordinate (D);\n\\draw (D)--(B_1);\n\\draw [dashed] (D)--(C)--(B_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$CC_1$与$DB_1$所成的角的大小;\\\\\n(2) 求证: 平面$CDB_1 \\perp$平面$ABB_1A_1$, 并求点$B$到平面$CDB_1$的距离.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题18", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "015056": { + "id": "015056", + "content": "某网站计划$4$月份订购草莓在网络销售, 每天的进货量相同, 成本价为每盒$15$元. 决定每盒售价为$20$元, 未售出的草莓降价处理, 每盒$10$元. 假设当天进货能全部售完. 根据销售经验, 每天的购买量与网站每天的浏览量(单位: 万次) 有关. 为确定草莓的进货量, 相关人员统计了前两年$4$月份(共$60$天)网站每天的浏览量(单位: 万次)、购买草莓的数量(单位: 盒) 以及达到该流量的天数, 如下表所示:\n\\begin{center} \n\\begin{tabular}{|c|c|c|}\n\\hline 每天的浏览量 &$(0,1)$& {$[1,+\\infty)$} \\\\\n\\hline 每天的购买量 & 600 & 900 \\\\\n\\hline 天数 & 36 & 24 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n以每天的浏览量位于各区间的频率代替浏览量位于该区间的概率.\n(1) 求$4$月份草苺一天的购买量$X$(单位: 盒)的分布;\\\\\n(2) 设$4$月份销售草莓一天的利润为$Y$(单位: 元), 一天的进货量为$n$(单位: 盒), $n$为正整数且$n \\in[600,900]$, 当$n$为多少时, $Y$的期望达到最大值, 并求此最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2023届金山区高三二模试题19", + "edit": [ + "202304012\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "015057": { + "id": "015057", + "content": "已知椭圆$\\Gamma: \\dfrac{x^2}{4}+\\dfrac{y^2}{b^2}=1$($0