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 afedb069..60041838 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 @@ -157,3 +157,6 @@ 20240125-130946 024012,015714,024013:024018 +20240125-131414 +024019:024030 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 72673eb7..a2956d27 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -35144,7 +35144,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024020" + ], "remark": "", "space": "", "unrelated": [] @@ -148221,7 +148223,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024028" + ], "remark": "", "space": "", "unrelated": [] @@ -148363,7 +148367,9 @@ "same": [ "020039" ], - "related": [], + "related": [ + "024027" + ], "remark": "", "space": "", "unrelated": [] @@ -148387,7 +148393,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024020" + ], "remark": "", "space": "", "unrelated": [] @@ -329588,7 +329596,9 @@ "20220901\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024030" + ], "remark": "", "space": "4em", "unrelated": [] @@ -427596,7 +427606,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024028" + ], "remark": "", "space": "4em", "unrelated": [] @@ -533410,7 +533422,9 @@ "20220803\t伍杨超, 王伟叶" ], "same": [], - "related": [], + "related": [ + "024021" + ], "remark": "", "space": "4em", "unrelated": [] @@ -534346,7 +534360,9 @@ "same": [ "004794" ], - "related": [], + "related": [ + "024027" + ], "remark": "", "space": "", "unrelated": [] @@ -647121,6 +647137,259 @@ "space": "4em", "unrelated": [] }, + "024019": { + "id": "024019", + "content": "已知集合 $A=\\{1,2,3,4\\}$, 那么 $A$ 的真子集的个数是\\bracket{20}.\n\\fourch{$15$ 个}{$16$ 个}{$3$ 个}{$4$ 个}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024020": { + "id": "024020", + "content": "设集合 $M=\\{1,2,3\\}$, $N=\\{x | x \\subseteq M\\}$, 则 $M$ 与 $N$ 的关系是\\bracket{20}.\n\\fourch{$M \\subset N$}{$N \\subset M$}{$M \\in N$}{$M \\cap N=M$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "004795", + "000999" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024021": { + "id": "024021", + "content": "已知集合 $A=\\{1,2, a^2-2 a\\}$, 若 $3 \\in A$, 则实数 $a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "020012" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024022": { + "id": "024022", + "content": "已知集合 $M=\\{-1,0,1\\}$, $N=\\{y | y=\\cos x, x \\in M\\}$, 则 $M \\cap N=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024023": { + "id": "024023", + "content": "设 $a$、$b \\in R$, 若集合 $\\{1, a+b, a\\}=\\{0, b, \\dfrac{b}{a}\\}$, 则 $a^{2023}+b^{2023}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024024": { + "id": "024024", + "content": "已知函数 $f(x)=a x^2+b x+c(a \\neq 0)$, $a$、$b$、$c \\in \\mathbf{R}$, 集合 $A=\\{x | f(x)=x\\}$, 当 $A=\\{2\\}$ 时, $a: c=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024025": { + "id": "024025", + "content": "已知集合 $A=\\{1,2\\}$, $B=\\{x | x^2+m x+1=0, x \\in \\mathbf{R}\\}$, 若 $B \\subseteq A$, 则实数 $m$ 的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024026": { + "id": "024026", + "content": "设集合 $A=\\{x|| x |<3\\}$, $B=\\{x | x^2-3 x+2>0\\}$, 集合 $P=\\{x | x \\in A, x \\notin A \\cap B\\}$, 集合 $P$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024027": { + "id": "024027", + "content": "同时满足条件: \\textcircled{1} $M \\subseteq\\{1,2,3,4,5\\}$; \\textcircled{2} 若 $a \\in M$, 则 $6-a \\in M$, 所有这样的非空集合 $M$为\\blank{50}(试列举出这些集合).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "020039", + "004794" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024028": { + "id": "024028", + "content": "已知集合 $A=\\{x | x^2+x-6=0\\}$, $B=\\{x | a x+1=0\\}$, 且 $B \\subseteq A$, 则实数 $a$ 的取值集合为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "004789", + "015358" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024029": { + "id": "024029", + "content": "已知集合 $A=\\{1, a, b\\}$, $B=\\{a, a^2, a b\\}$, 若 $A=B$, 则实数 $a$、$b$ 的值分别为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024030": { + "id": "024030", + "content": "已知集合 $A=\\{x | \\dfrac{a x-1}{x-a}<0\\}$, 且 $2 \\in A$, $3 \\notin A$, 求实数 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "011833" + ], + "remark": "", + "space": "4em", + "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