diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index dd280374..570cd5e2 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -618052,6 +618052,206 @@ "space": "", "unrelated": [] }, + "023072": { + "id": "023072", + "content": "已知全集 $U=\\mathbf{R}$, 集合 $A=$($-\\infty, 1]\\cup [2,+\\infty$), 则 $\\overline{A}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023073": { + "id": "023073", + "content": "函数 $y=\\lg \\dfrac{x}{x-3}$ 的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023074": { + "id": "023074", + "content": "若复数 $z$ 满足 $(3-4 \\mathrm{i}) z=8+6 \\mathrm{i}$, 则 $|z|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023075": { + "id": "023075", + "content": "已知等差数列 $\\{a_n\\}$ 的前 10 项和为 30 , 则 $a_1+a_4+a_7+a_{10}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023076": { + "id": "023076", + "content": "已知直线 $m$ 垂直于直线 $n: x+2 y+1=0$, 则 $m$ 的倾斜角大小为等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023077": { + "id": "023077", + "content": "若圆 $C$ 的方程为 $x^2+y^2-2 x+4 y=0$, 则圆 $C$ 的面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023078": { + "id": "023078", + "content": "已知双曲线 $\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$) 的一条渐近线方程是 $y=2 x$, 一个焦点为 $(5,0)$,则此双曲线的方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023079": { + "id": "023079", + "content": "若向量 $\\overrightarrow{a}, \\overrightarrow{b}$ 满足 $\\overrightarrow{b}\\cdot(\\overrightarrow{a}+\\overrightarrow{b})=7$, 且 $|\\overrightarrow{a}|=\\sqrt{3}$, $|\\overrightarrow{b}|=2$, 则 $\\langle\\overrightarrow{a}, \\overrightarrow{b}\\rangle$ 的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023080": { + "id": "023080", + "content": "若 $a \\in \\mathbf{R}$, 则``$a \\geq 0$''是``$a=0$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023081": { + "id": "023081", + "content": "上海市普通高中学业水平等级考成绩共分为五等十一级, 各等级换算成分数如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline 等级 & A$+$ & A & B$+$ & B & B$-$ & C$+$ & C & C$-$ & D$+$ & D & E \\\\\n\\hline 分数 & 70 & 67 & 64 & 61 & 58 & 55 & 52 & 49 & 46 & 43 & 40 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n某班级选考物理学业水平等级考的学生中, 所有人得了 A$+$、A、B$+$ 这三个等级之一, 平均分是 $68$ 分. 在这些人中, 恰有 5 人取得 A$+$ 成绩, 那么 B$+$ 的人数的最大可能值为\\bracket{20}.\n\\fourch{1}{2}{3}{4}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "24届赋能补充题目", + "edit": [ + "20240105\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