From f762155aa89243986804554dccfcb534ebff4661 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 7 Jan 2024 18:39:40 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A525=E5=B1=8A=E6=9F=B1=E4=BD=93?= =?UTF-8?q?=E9=94=A5=E4=BD=93=E8=A1=A5=E5=85=85=E4=BD=9C=E4=B8=9A=E5=B9=B6?= =?UTF-8?q?=E5=85=B3=E8=81=94=E7=9B=B8=E4=BC=BC?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 127 ++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 122 insertions(+), 5 deletions(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 42144243..e200abb3 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -54646,7 +54646,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023357" + ], "remark": "", "space": "", "unrelated": [] @@ -54696,7 +54698,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023356" + ], "remark": "", "space": "4em", "unrelated": [] @@ -54989,7 +54993,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023357" + ], "remark": "", "space": "", "unrelated": [] @@ -558859,7 +558865,9 @@ "20230101\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023356" + ], "remark": "", "space": "", "unrelated": [] @@ -624697,6 +624705,113 @@ "space": "4em", "unrelated": [] }, + "023356": { + "id": "023356", + "content": "已知$A$是所有正方体组成的集合, $B$是所有长方体组成的集合, $C$是所有正四棱柱组成的集合, $D$是所有直四棱柱组成的集合, $E$是所有直平行六面体组成的集合, $F$是所有平行六面体组成的集合, $G$是所有四棱柱组成的集合. 判断这些集合相互间的关系. (也许需要两组包含关系)", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240107\t杨懿荔" + ], + "same": [], + "related": [ + "001684", + "030133", + "020973" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023357": { + "id": "023357", + "content": "判断题(``T''或``F''):\\\\\n\\blank{20}(1) 有两个面互相平行, 其余的面都是四边形的多面体是棱柱; \\\\\n\\blank{20}(2) 有两个面互相平行, 其余的面都是平行四边形的多面体是棱柱; \\\\\n\\blank{20}(3) 棱柱中互相平行的两个平面叫做棱柱的底面; \\\\\n\\blank{20}(4) 有一侧棱与底面的两条棱互相垂直的棱柱是直棱柱; \\\\\n\\blank{20}(5) 有两个侧面是矩形的棱柱是直棱柱; \\\\\n\\blank{20}(6) 有两个侧面与底面垂直的棱柱是直棱柱; \\\\\n\\blank{20}(7) 所有侧面都是全等的矩形的四棱柱一定是正四棱柱; \\\\\n\\blank{20}(8) 对角线相等的平行六面体是长方体.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240107\t杨懿荔" + ], + "same": [], + "related": [ + "001682", + "001695" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023358": { + "id": "023358", + "content": "已知正三棱锥 $P-ABC$ 的底面边长为 $12 \\mathrm{cm}$,高 $PO=8 \\mathrm{cm}, Q$ 为 $PA$ 上一点, 求截面 $\\triangle QBC$ 面积的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240107\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023359": { + "id": "023359", + "content": "正方体 $ABCD-A_1B_1C_1D_1$ 的棱长为 1 ,\\\\\n(1) 若 $S, T$ 分别是 $AA_1, CC_1$ 的中点, 求四棱锥 $A_1-SBTD_1$ 的体积.\\\\\n(2) 若 $P, Q$ 分别是 $BC, DD_1$ 的中点, 求四面体 $AB_1PQ$ 的体积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240107\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023360": { + "id": "023360", + "content": "斜三棱柱 $ABC-A_1B_1C_1$ 的底面是直角三角形, $\\angle BAC= 90^{\\circ}$, 且 $BC_1 \\perp AC$, $AB=AC=2$, $BC_1=2 \\sqrt{6}$, 侧棱与底面成 $60^{\\circ}$,求三棱柱 $ABC-A_1B_1C_1$ 的体积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240107\t杨懿荔" + ], + "same": [], + "related": [], + "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