diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index b3c4a35f..ea9e4b9d 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -277,3 +277,15 @@ 20240131-153325 030615,030966,030760,024332:024334,031000,024335,030674,013417 +20240131-153954 +015017,030637,030839,024336:024338,030888,024339,030979,030652 + +20240131-154406 +024340:024348,004177 + +20240131-154704 +030597,030973,030850,024349,030999,024350:024351,030775,031106,030991 + +20240131-155337 +030618,024352:024353,031095,024354,031069,024355:024357,030944 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index e5ff473f..c460f678 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -114239,7 +114239,9 @@ "20220701\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024337" + ], "remark": "", "space": "", "unrelated": [] @@ -142092,7 +142094,9 @@ "20220709\t朱敏慧\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024338" + ], "remark": "", "space": "", "unrelated": [] @@ -278910,7 +278914,9 @@ "20220730\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024353" + ], "remark": "", "space": "4em", "unrelated": [] @@ -308908,7 +308914,8 @@ "004686", "004727", "004747", - "019960" + "019960", + "024349" ], "remark": "", "space": "", @@ -312656,7 +312663,8 @@ ], "related": [ "000576", - "000836" + "000836", + "024340" ], "remark": "", "space": "", @@ -320283,7 +320291,8 @@ "004686", "004727", "004747", - "024326" + "024326", + "024349" ], "remark": "", "space": "", @@ -322655,7 +322664,9 @@ "20220818\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024339" + ], "remark": "", "space": "", "unrelated": [] @@ -412097,7 +412108,9 @@ "20230314\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024337" + ], "remark": "", "space": "", "unrelated": [] @@ -420249,7 +420262,9 @@ "20230413\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024337" + ], "remark": "", "space": "", "unrelated": [] @@ -468749,7 +468764,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024338" + ], "remark": "", "space": "", "unrelated": [] @@ -468925,7 +468942,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024351" + ], "remark": "", "space": "", "unrelated": [] @@ -533358,7 +533377,9 @@ "20231028\t毛培菁" ], "same": [], - "related": [], + "related": [ + "024355" + ], "remark": "", "space": "", "unrelated": [] @@ -535289,7 +535310,8 @@ "same": [], "related": [ "000532", - "010990" + "010990", + "024349" ], "remark": "", "space": "", @@ -607593,7 +607615,9 @@ "20230905\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024342" + ], "remark": "", "space": "", "unrelated": [] @@ -659745,6 +659769,475 @@ "space": "", "unrelated": [] }, + "024336": { + "id": "024336", + "content": "函数 $f(x)=\\dfrac{1}{3}x^3-x$ 的单调增区间为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024337": { + "id": "024337", + "content": "在 $(2 x+1)^6$ 的展开式中, $x^2$ 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": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "003654", + "015042", + "014746" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024338": { + "id": "024338", + "content": "将两枚质地均匀的骰子各掷一次, 设事件 $A$ 表示两个点数互不相同, 事件 $B$ 表示至少出现一个 $4$ 点, 则 $P(B | A)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "017109", + "004575" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024339": { + "id": "024339", + "content": "从 $1 \\sim 9$ 这 $9$ 个数中任取 $4$ 个不同的数, 则这 $4$ 个不同的数的中位数为 $6$ 的概率为\\blank{50}.(结果用最简分数表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "011508" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024340": { + "id": "024340", + "content": "已知集合 $A=\\{1,2,3,4\\}$, 集合 $B=\\{2,3, m\\}$, 若 $A \\cap B=\\{2,3,4\\}$, 则 $m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "011112", + "030428" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024341": { + "id": "024341", + "content": "已知 $X$ 的分布是伯努利分布, 且 $P(X=1)-P(X=0)=0.2$, 则 $P(X=1)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024342": { + "id": "024342", + "content": "不等式 $\\dfrac{x}{1-x}\\geq 0$ 的解集为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "022314" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024343": { + "id": "024343", + "content": "函数 $f(x)=x^2 \\mathrm{e}^x$ 在 $[-1,1]$ 上的极小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024344": { + "id": "024344", + "content": "若 $\\dfrac{a+2 \\mathrm{i}}{\\mathrm{i}}=b+\\mathrm{i}$($a, b \\in \\mathbf{R}$, $\\mathrm{i}$ 为虚数单位 ), 则 $a+b=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024345": { + "id": "024345", + "content": "某圆锥的底面积为 $4 \\pi$, 侧面积为 $8 \\pi$, 则该圆锥的母线与底面所成角的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "031024" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024346": { + "id": "024346", + "content": "若正方形 $ABCD$ 的边长为 1 , 记 $\\overrightarrow{AB}=\\overrightarrow{a}$, $\\overrightarrow{BC}=\\overrightarrow{b}$, $\\overrightarrow{AC}=\\overrightarrow{c}$, 则 $|\\overrightarrow{a}+2 \\overrightarrow{b}-3 \\overrightarrow{c}|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024347": { + "id": "024347", + "content": "一个不透明的袋中装有 $5$ 个白球、$4$ 个红球 ($9$个球除颜色外其余完全相同), 经充分混合后, 从袋中随机摸出 $3$ 个球, 则摸出的 $3$ 个球中至少有一个是白球的概率为\\blank{50}. (结果用最简分数表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "031737" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024348": { + "id": "024348", + "content": "函数 $y=2 \\cos 2 x$($x \\in \\mathbf{R}$) 的最小正周期为\\bracket{20}.\n\\fourch{$\\dfrac{\\pi}{2}$}{$\\pi$}{$2 \\pi$}{$4 \\pi$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024349": { + "id": "024349", + "content": "$(1-2 x)^4$ 的二项展开式中 $x^3$ 项的系数为\\blank{50}. (结果用数字作答)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "010990", + "011415", + "019960" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024350": { + "id": "024350", + "content": "函数 $f(x)=x-\\ln x$ 的极小值点为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024351": { + "id": "024351", + "content": "随机变量 $X$ 的取值为 $0,1,2$, 若 $P(X=0)=\\dfrac{1}{5}$, $E[X]=1$, 则 $P(X=1)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "017117" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024352": { + "id": "024352", + "content": "直线 $l$ 的一个法向量 $\\overrightarrow{n}=(1,-1)$, 且经过圆 $(x-2)^2+(y-4)^2=4$ 的圆心, 则直线 $l$ 的方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024353": { + "id": "024353", + "content": "函数 $y=x^3-3 x$ 的单调减区间是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "009921", + "031589" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024354": { + "id": "024354", + "content": "指数方程 $2^{x+3}=8^{x^2-9}$ 的解为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024355": { + "id": "024355", + "content": "将一枚骰子先后抛两次, 则向上的点数之积为 12 的概率为\\blank{50}. (结果用最简分数表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [ + "019903" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024356": { + "id": "024356", + "content": "已知随机变量 $X$ 的分布为 $\\begin{pmatrix}0 & 1 & m \\\\ 0.2 & n & 0.3\\end{pmatrix}$, 且 $E[X]=1.1$, 则 $D[X]=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024357": { + "id": "024357", + "content": "2022 年 2 月 4 日至 2 月 20 日春节期间,第 24 届冬奥会在北京市和张家口市联合举行. 共有 3 个冬奥村供运动员和代表队官员入住, 其中北京冬奥村的容量约为 $2250$ 人, 延庆冬奥村的容量约 $1440$ 人, 张家口冬奥村的容量约 $2610$ 人. 为了解各冬奥村服务质量, 现共准备了 $140$ 份调查问卷, 采用分层抽样的方法, 则需在延庆冬奥村投放的问卷数量是\\bracket{20}.\n\\fourch{$58$ 份}{$50$ 份}{$32$ 份}{$19$ 份}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240131\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0