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 6979709d..ece6536f 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 @@ -166,3 +166,6 @@ 20240125-134803 024040:024048 +20240125-135214 +024049:024057 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 0585c16a..871cf3c5 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -144958,7 +144958,9 @@ "same": [ "012021" ], - "related": [], + "related": [ + "024056" + ], "remark": "", "space": "", "unrelated": [] @@ -155556,7 +155558,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024052" + ], "remark": "", "space": "4em", "unrelated": [] @@ -430562,7 +430566,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024051" + ], "remark": "", "space": "4em", "unrelated": [] @@ -432410,7 +432416,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024052" + ], "remark": "", "space": "", "unrelated": [] @@ -537335,7 +537343,8 @@ "same": [], "related": [ "004908", - "011834" + "011834", + "024057" ], "remark": "", "space": "4em", @@ -541087,7 +541096,9 @@ "20221223\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024057" + ], "remark": "", "space": "4em", "unrelated": [] @@ -647780,6 +647791,196 @@ "space": "4em", "unrelated": [] }, + "024049": { + "id": "024049", + "content": "若 $a$、$b$、$c \\in \\mathbf{R}$, 且 $a>b$, 则下列不等式中一定成立的序号为\\blank{50}.\\\\\n\\textcircled{1} $a+c \\geq b+c$; \\textcircled{2} $a c \\geq b c$; \\textcircled{3} $\\dfrac{c^2}{a-b}>0$; \\textcircled{4} $(a-b) c^2\\geq 0$; \\textcircled{5} $\\sqrt[3]{a}>\\sqrt[3]{b}$\\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": [] + }, + "024050": { + "id": "024050", + "content": "若方程 $x^2+p x+q=0$ 的两根均为正整数, 且 $p+q=28$, 则该方程两根为\\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": [] + }, + "024051": { + "id": "024051", + "content": "已知三个不等式: \\textcircled{1} $a b>0 ;\\textcircled{2}-\\dfrac{c}{a}<-\\dfrac{d}{b}$; \\textcircled{3} $b c>a d$. 以其中两个作为条件, 余下一个作为结论, 则可以组成\\blank{50}个真命题.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "015492" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024052": { + "id": "024052", + "content": "已知 $m>1$, 设 $A=\\sqrt{m+1}-\\sqrt{m}$, $B=\\sqrt{m}-\\sqrt{m-1}$, 则 $A$、$B$ 之间的大小关系为\\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": [ + "005074", + "015576" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024053": { + "id": "024053", + "content": "设角 $\\alpha$、$\\beta$ 满足 $-\\dfrac{\\pi}{2}<\\alpha<\\beta<\\dfrac{\\pi}{2}$, 则 $\\alpha-\\beta$ 的取值范围是\\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": [] + }, + "024054": { + "id": "024054", + "content": "实验室原有两瓶酒精溶液分别为 $a_1$、$a_2$ (单位: g), 其中对应含有酒精 $b_1, b_2$ (单位: g),\n且两瓶酒精浓度满足 $\\dfrac{b_1}{a_1}<\\dfrac{b_2}{a_2}$, 小明将两瓶酒精溶液全都倒下一个新容器中后, 新溶液的浓度发生变化. 请根据以上事实, 提炼出关于不等式的命题:\\blank{100}.", + "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": [] + }, + "024055": { + "id": "024055", + "content": "若 $a\\dfrac{1}{b}$}{$\\dfrac{1}{a-b}>\\dfrac{1}{a}$}{$|a|>|b|$}{$a^2>b^2$}", + "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": [] + }, + "024056": { + "id": "024056", + "content": "下面四个条件中, 使 $a>b$ 成立的充分非必要条件是\\bracket{20}.\n\\fourch{$a>b+1$}{$a>b-1$}{$a^2>b^2$}{$a^3>b^3$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "004673" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024057": { + "id": "024057", + "content": "已知 $a \\neq 1$ 且 $a \\in \\mathbf{R}$, 试比较 $\\dfrac{1}{1-a}$ 与 $1+a$ 的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "020251", + "020123" + ], + "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