From 7ca1f94344a035b3bc724b69ef29c525c59f60fe Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 12:08:20 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A39=E6=96=B0=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 ++ 题库0.3/Problems.json | 80 ++++++++++++++++++++++++++++++++ 2 files changed, 83 insertions(+) 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 4e6b98e9..4666d7e9 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 @@ -115,3 +115,6 @@ 20240125-120516 023917:023924 +20240125-120800 +023925:023926,014924,016867,023927,020917,023159,023928 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index ebe132b4..cdbd096d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -645121,6 +645121,86 @@ "space": "4em", "unrelated": [] }, + "023925": { + "id": "023925", + "content": "如图, 已知 $\\angle BAC=90^{\\circ}$, $PC \\perp$ 平面 $ABC$, 则在 $\\triangle ABC$、$\\triangle PAC$ 的边所在的直线中, 与 $PC$垂直的直线有\\blank{50}; 与 $AP$ 垂直的直线有\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0) node [right] {$B$} coordinate (B);\n\\draw (0,0,-2) node [above right] {$C$} coordinate (C);\n\\draw (C) ++ (0,1,0) node [above] {$P$} coordinate (P);\n\\draw (A)--(B)--(C)--(P)--cycle(A)--(C);\n\\end{tikzpicture}\n\\end{center}", + "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": [] + }, + "023926": { + "id": "023926", + "content": "给出下列四个命题:\\\\\n\\textcircled{1} 垂直于同一直线的两条直线互相平行;\\\\\n\\textcircled{2} 垂直于同一平面的两个平面互相平行;\\\\\n\\textcircled{3} 若直线 $l_1$、$l_2$ 与同一平面所成的角相等, 则 $l_1, l_2$ 互相平行;\\\\\n\\textcircled{4} 若直线 $l_1$、$l_2$ 是异面直线, 则与 $l_1$、$l_2$ 都相交的两条直线是异面直线.\n其中假命题的个数是\\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": [] + }, + "023927": { + "id": "023927", + "content": "在正三棱柱 $ABC-A_1B_1C_1$ 中, 所有棱长均为 $1$ , 则点 $B_1$ 到平面 $ABC_1$ 的距离为\\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": [] + }, + "023928": { + "id": "023928", + "content": "如图, 在四棱锥 $P-ABCD$ 中, $AD \\perp$ 平面 $PDC, AD \\parallel BC$, $PD \\perp PB$, $AD=1$, $BC=3$, $CD=4$, $PD=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [below] {$D$} coordinate (D);\n\\draw (1,0,0) node [below] {$A$} coordinate (A);\n\\draw (0,0,-4) node [below] {$C$} coordinate (C);\n\\draw (3,0,-4) node [right] {$B$} coordinate (B);\n\\draw (0,{sqrt(3)},-1) node [above] {$P$} coordinate (P);\n\\draw (D)--(A)--(B)--(P)--cycle(P)--(A);\n\\draw [dashed] (D)--(C)--(B)(C)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 求异面直线 $AP$ 与 $BC$ 所成角的余弦值;\\\\\n(2) 求证: $PD \\perp$ 平面 $PBC$;\\\\\n(3) 求直线 $AB$ 与平面 $PBC$ 所成角的正弦值.", + "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": [] + }, "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