From 0acaf29a1a4e0ce00d801e82bb8c306f0e9d2e64 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 10:57:48 +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=9A23=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 | 230 +++++++++++++++++++++++++++++-- 2 files changed, 224 insertions(+), 9 deletions(-) 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 6151de94..051c482f 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 @@ -67,3 +67,6 @@ 20240125-105348 023789:023798 +20240125-105739 +023799:023805,003102,023806:023807 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 8b09236f..db06a27b 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -48008,7 +48008,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023803" + ], "remark": "", "space": "", "unrelated": [] @@ -233127,7 +233129,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023807" + ], "remark": "", "space": "4em", "unrelated": [] @@ -335545,7 +335549,9 @@ "20221117\t朱敏慧\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023805" + ], "remark": "", "space": "", "unrelated": [] @@ -581539,7 +581545,9 @@ "20230209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023800" + ], "remark": "", "space": "4em", "unrelated": [] @@ -642405,6 +642413,200 @@ "space": "4em", "unrelated": [] }, + "023799": { + "id": "023799", + "content": "若 $\\cot (\\pi-\\alpha)=2$, 则 $\\cos (\\dfrac{3 \\pi}{2}+2 \\alpha)=$\\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": [] + }, + "023800": { + "id": "023800", + "content": "若 $\\dfrac{3}{2}\\pi<\\alpha<\\dfrac{5}{2}\\pi$, 则 $\\sqrt{\\dfrac{1}{2}+\\dfrac{1}{2}\\sqrt{\\dfrac{1}{2}+\\dfrac{1}{2}\\cos \\alpha}}=$\\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": [ + "040122", + "040232", + "021598" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023801": { + "id": "023801", + "content": "已知 $\\sin \\alpha=\\dfrac{4}{5}$, $\\cos (\\alpha+\\beta)=-\\dfrac{3}{5}$, 若 $\\alpha$、$\\beta$ 都是第一象限的角, 则 $\\sin \\beta=$\\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": [ + "040091" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023802": { + "id": "023802", + "content": "若 $\\sin \\theta, \\cos \\theta$ 是二次方程 $2 x^2-(\\sqrt{3}+1) x+m=0$ 的两个根, 则 $\\dfrac{\\sin \\theta}{1-\\cot \\theta}+\\dfrac{\\cos \\theta}{1-\\tan \\theta}$ 的值为\\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": [] + }, + "023803": { + "id": "023803", + "content": "若 $\\alpha+\\beta=\\dfrac{\\pi}{3}$, 则 $\\tan \\alpha+\\tan \\beta+\\sqrt{3}\\tan \\alpha \\tan \\beta=$\\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": [ + "001435" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023804": { + "id": "023804", + "content": "化简: $\\cos (20^{\\circ}+x) \\cos (25^{\\circ}-x)-\\cos (70^{\\circ}-x) \\sin (25^{\\circ}-x)=$\\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": [] + }, + "023805": { + "id": "023805", + "content": "已知 $\\tan (\\dfrac{\\pi}{4}+\\theta)=3$, 则 $\\sin 2 \\theta-2 \\cos ^2 \\theta$ 的值为\\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": [ + "012059", + "040353" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023806": { + "id": "023806", + "content": "若表达式 $3 \\sin ^2 \\theta+\\sqrt{3}\\sin \\theta \\cos \\theta+4 \\cos ^2 \\theta+k$ 可化为 $\\sin (2 \\theta+\\varphi)$, $0 \\leq \\varphi<2 \\pi$ 的形式, 则 $k$ 的值为\\blank{50}, $\\varphi$ 的值为\\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": [] + }, + "023807": { + "id": "023807", + "content": "已知 $\\tan \\alpha, \\tan \\beta$ 是方程 $x^2+a x+a+1=0$ 的两个实根, 求证: $\\sin (\\alpha+\\beta)=\\cos (\\alpha+\\beta)$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "008176", + "040340" + ], + "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