From 769394e5a3639dfc5348e32764c7445691be8a26 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 11:27:01 +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=9A28=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 | 86 +++++++++++++++++++++++++++++++- 2 files changed, 88 insertions(+), 1 deletion(-) 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 82ff293c..b3651951 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 @@ -82,3 +82,6 @@ 20240125-112043 023835:023841,013014,023842:023843 +20240125-112538 +023844:023847 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c050d593..25143ab3 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -131433,7 +131433,9 @@ "20220705\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023847" + ], "remark": "", "space": "4em", "unrelated": [] @@ -643392,6 +643394,88 @@ "space": "4em", "unrelated": [] }, + "023844": { + "id": "023844", + "content": "选择正确的序号填空: (\\textcircled{1} 充要; \\textcircled{2} 充分非必要; \\textcircled{3} 必要非充分; \\textcircled{4} 既非充分又非必要)\\\\\n(1) 在 $\\triangle ABC$ 中, ``$A>B$''是``$\\sin A>\\sin B$''的\\blank{50}条件;\\\\\n(2) 在 $\\triangle ABC$ 中, ``$A>B$''是``$\\tan A>\\tan B$''的\\blank{50}条件;\\\\\n(3) 在 $\\triangle ABC$ 中, ``$A>B$''是``$\\cos A<\\cos B$''的\\blank{50}条件.", + "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": [] + }, + "023845": { + "id": "023845", + "content": "甲船在 $A$ 处测得乙船在北偏东 $70^{\\circ}$ 方向, 两船相距 $10$ 海里, 且乙船正沿着南偏东 $40^{\\circ}$ 方向以每小时 $12$ 海里的速度航行, 经过半小时, 甲船追上乙船, 则甲船的航行速度是每小时\\blank{50}海里(精确到 $0.1$).", + "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": [] + }, + "023846": { + "id": "023846", + "content": "$\\triangle ABC$ 的内角 $A$、$B$、$C$ 所对边的长分别为 $a$、$b$、$c$. 已知 $2 \\cos C(a \\cos B+b \\cos A)=c$.\\\\\n(1) 求 $C$;\\\\\n(2) 若 $c=\\sqrt{7}, \\triangle ABC$ 的面积为 $\\dfrac{3 \\sqrt{3}}{2}$, 求 $\\triangle ABC$ 的周长.", + "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": [] + }, + "023847": { + "id": "023847", + "content": "某动物园喜迎虎年的到来, 拟用一块形如直角三角形 $ABC$ 的地块建造小老虎的休息区和活动区. 如图, $\\angle BAC=90^{\\circ}$, $AB=AC=20$ (单位: 米), $E$、$F$ 为 $BC$ 上的两点, 且 $\\angle EAF=45^{\\circ}, \\triangle AEF$ 区域为休息区, $\\triangle ABE$ 和 $\\triangle ACF$ 区域均为活动区. 设 $\\angle EAB=\\alpha$($0<\\alpha<\\dfrac{\\pi}{4}$).\\\\\n\\begin{center}\n\\begin{tikzpicture}\n\\path (0,0) node [below left] {$A$} coordinate (A)-- (3,0) node [below right] {$B$} coordinate (B)-- (0,3) node [above left] {$C$} coordinate (C)-- cycle;\n\\path [name path = lineBC] (3,0) -- (0,3);\n\\path [name path = lineAE] (0,0) -- (15:3);\n\\path [name path = lineAF] (0,0) -- (60:3);\n\\path [name intersections = {of = lineBC and lineAE, by = E}];\n\\path [name intersections = {of = lineBC and lineAF, by = F}];\n\\filldraw [gray!30] (A) -- (B) -- (E) -- cycle;\n\\filldraw [gray!30] (A) -- (F) -- (C) -- cycle;\n\\draw (0,0) -- (E) node [above right] {$E$};\n\\draw (0,0) -- (F) node [above right] {$F$};\n\\draw (A) -- (B) -- (C) -- cycle;\n\\draw (2,0) node [above] {\\tiny{活动区}};\n\\draw (0,2) node [right] {\\tiny{活动区}};\n\\draw (1.2,1) node {\\small{休息区}};\n\\end{tikzpicture}\n\\end{center}\n(1) 求 $AE$ 的长 (用 $\\alpha$ 的代数式表示);\\\\\n(2) 为了使小老虎能健康成长, 要求所建造的活动区面积尽可能大 (即休息区尽可能小), 当 $\\alpha$ 为多少时, 活动区的面积最大? 最大面积为多少?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "004266" + ], + "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