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 eb5bb7d6..82ff293c 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 @@ -79,3 +79,6 @@ 20240125-111717 023828:023834 +20240125-112043 +023835:023841,013014,023842:023843 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 373a967d..c050d593 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -22252,7 +22252,9 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [], + "related": [ + "023843" + ], "remark": "", "space": "", "unrelated": [] @@ -187377,7 +187379,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023836" + ], "remark": "", "space": "", "unrelated": [] @@ -233634,7 +233638,9 @@ "same": [ "010266" ], - "related": [], + "related": [ + "023837" + ], "remark": "", "space": "4em", "unrelated": [] @@ -580255,7 +580261,9 @@ "20230209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023841" + ], "remark": "", "space": "", "unrelated": [] @@ -643196,6 +643204,194 @@ "space": "4em", "unrelated": [] }, + "023835": { + "id": "023835", + "content": "在 $\\triangle ABC$ 中, 若 $a=10$, $b=20$, $C=120^{\\circ}$, 则边 $c=$\\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": [] + }, + "023836": { + "id": "023836", + "content": "在 $\\triangle ABC$ 中, 若 $B=45^{\\circ}$, $c=2 \\sqrt{2}$, $b=\\dfrac{4 \\sqrt{3}}{3}$, 则 $A=$\\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": [ + "006348" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023837": { + "id": "023837", + "content": "在 $\\triangle ABC$ 中, 若 $a=2$, $b=3$, $c=4$, 则角 $C=$\\blank{50}, $S_{\\triangle ABC}=$\\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": [ + "008197" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023838": { + "id": "023838", + "content": "在 $\\triangle ABC$ 中, 若 $2R(\\sin ^2A-\\sin ^2C)=(a-b) \\sin B$, $R$ 为 $\\triangle ABC$ 外接圆的半径, 则角 $C=$\\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": [] + }, + "023839": { + "id": "023839", + "content": "在 $\\triangle ABC$ 中, 若 $A(-4,0)$, $C(4,0)$, $B$ 在椭圆 $\\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$ 上, 则 $\\dfrac{\\sin A+\\sin C}{\\sin B}=$\\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": [] + }, + "023840": { + "id": "023840", + "content": "在 $\\triangle ABC$ 中, 角 $A$、$B$、$C$ 所对边的长分别为 $a$、$b$、$c$, $S$ 表示 $\\triangle ABC$ 的面积. 若 $a \\cos B+b \\cos A=c \\sin C$, $S=\\dfrac{1}{4}(b^2+c^2-a^2)$, 则 $\\triangle ABC$ 的形状是\\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": [] + }, + "023841": { + "id": "023841", + "content": "在 $\\triangle ABC$ 中, 若 $\\cos A \\cos B>\\sin A \\sin B$, 则 $\\triangle ABC$ 的形状为\\blank{50}三角形.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "021556" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023842": { + "id": "023842", + "content": "在 $\\triangle ABC$ 中, 已知 $a^2 \\tan B=b^2 \\tan A$, 试判断三角形的形状.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023843": { + "id": "023843", + "content": "在 $\\triangle ABC$ 中, 角 $A$、$B$、$C$ 所对边的长分别为 $a$、$b$、$c$, 且 $(a+b-c)(a+b+c)=a b$.\\\\\n(1) 求角 $C$ 的大小;\\\\\n(2) 若 $c=2 a \\cos B$, $b=2$, 求 $\\triangle ABC$ 的面积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "000592" + ], + "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