From 4044dc213cc039cbf4966e94f8dab3c3cad35bee Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Fri, 5 Jan 2024 09:52:19 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A524=E5=B1=8A=E8=B5=8B=E8=83=BD?= =?UTF-8?q?=E8=A1=A5=E5=85=85=E9=A2=98=E8=87=B39B?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 160 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 160 insertions(+) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c820a363..cd98e83a 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -617592,6 +617592,166 @@ "space": "", "unrelated": [] }, + "023049": { + "id": "023049", + "content": "设集合 $A=\\{2,3,4,12\\}$, $B=\\{0,1,2,3\\}$, 则 $A \\cup B=$\\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": [] + }, + "023050": { + "id": "023050", + "content": "双曲线 $x^2-\\dfrac{y^2}{2}=1$ 的渐近线方程为\\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": [] + }, + "023051": { + "id": "023051", + "content": "若复数 $z=1-\\mathrm{i}$ ($\\mathrm{i}$ 为虚数单位), 则 $z^2$ 的共轭复数为\\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": [] + }, + "023052": { + "id": "023052", + "content": "记等差数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n$. 若 $a_5=1$, 则 $S_9=$\\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": [] + }, + "023053": { + "id": "023053", + "content": "已知实数 $a>0$, $b>0$, 且 $a+b=4$, 则 $a^2+b^2$ 的最小值为\\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": [] + }, + "023054": { + "id": "023054", + "content": "已知圆锥的体积为 $\\dfrac{\\sqrt{3}}{3}\\pi$, 且母线与底面所成角为 $\\dfrac{\\pi}{3}$, 则该圆锥的表面积为\\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": [] + }, + "023055": { + "id": "023055", + "content": "设 $a \\in \\mathbf{R}$, 若 $(2+\\dfrac{a}{x})(1+x)^5$ 展开式中 $x^2$ 的系数为 $10$, 则 $a=$\\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": [] + }, + "023056": { + "id": "023056", + "content": "下列命题正确的是\\bracket{20} .\n\\onech{如果两条直线垂直于同一条直线, 那么这两条直线互相平行}{如果一条直线垂直于一个平面内的两条直线, 那么这条直线垂直于这个平面}{如果一条直线平行于一个平面内的一条直线, 那么这条直线平行于这个平面}{如果一个平面内的两条相交直线与另一个平面平行, 那么这两个平面互相平行}", + "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