From 2fbd328f12ce13a7166d4ce41151808e548d2dfb Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 11:01:57 +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=9A24=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 | 239 ++++++++++++++++++++++++++++++- 2 files changed, 235 insertions(+), 7 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 051c482f..423f9b28 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 @@ -70,3 +70,6 @@ 20240125-105739 023799:023805,003102,023806:023807 +20240125-110148 +023808:023810,015997,023811:023817 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index db06a27b..923c7ff2 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -4060,7 +4060,9 @@ "same": [ "008382" ], - "related": [], + "related": [ + "023814" + ], "remark": "", "space": "4em", "unrelated": [] @@ -48009,7 +48011,8 @@ ], "same": [], "related": [ - "023803" + "023803", + "023813" ], "remark": "", "space": "", @@ -181719,7 +181722,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023810" + ], "remark": "", "space": "", "unrelated": [] @@ -182727,7 +182732,9 @@ "20220720\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023813" + ], "remark": "", "space": "", "unrelated": [] @@ -364485,7 +364492,9 @@ "20230118\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023810" + ], "remark": "", "space": "", "unrelated": [] @@ -441138,7 +441147,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023811" + ], "remark": "", "space": "", "unrelated": [] @@ -642607,6 +642618,218 @@ "space": "4em", "unrelated": [] }, + "023808": { + "id": "023808", + "content": "若 $180^{\\circ}<\\alpha<360^{\\circ}$, 则 $\\cos \\dfrac{\\alpha}{2}$ 的值等于\\bracket{20}.\n\\fourch{$-\\sqrt{\\dfrac{1-\\cos \\alpha}{2}}$}{$\\sqrt{\\dfrac{1-\\cos \\alpha}{2}}$}{$-\\sqrt{\\dfrac{1+\\cos \\alpha}{2}}$}{$\\sqrt{\\dfrac{1+\\cos \\alpha}{2}}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023809": { + "id": "023809", + "content": "若 $\\dfrac{\\sin \\alpha-\\cos \\alpha}{\\sin \\alpha+\\cos \\alpha}=\\dfrac{1}{2}$, 则 $\\tan 2 \\alpha=$\\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": [ + "031555" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023810": { + "id": "023810", + "content": "若 $\\alpha$、$\\beta \\in(0, \\dfrac{\\pi}{2})$, 且 $\\cos \\alpha=\\dfrac{5}{13}$, $\\sin (\\alpha+\\beta)=\\dfrac{3}{5}$, 则 $\\cos \\beta=$\\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": [ + "013024", + "006115" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023811": { + "id": "023811", + "content": "若 $\\sin (\\dfrac{\\pi}{6}-\\alpha)=\\dfrac{1}{3}$, 则 $\\cos (\\dfrac{2 \\pi}{3}+2 \\alpha)=$\\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": [ + "015977" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023812": { + "id": "023812", + "content": "若 $\\tan (\\alpha+\\dfrac{\\pi}{6})=\\dfrac{3}{2}$, 则 $\\cos (2 \\alpha-\\dfrac{\\pi}{6})=$\\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": [] + }, + "023813": { + "id": "023813", + "content": "已知 $\\alpha+\\beta=\\dfrac{\\pi}{4}$, 则 $(1+\\tan \\alpha)(1+\\tan \\beta)$ 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": [ + "006154", + "001435" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023814": { + "id": "023814", + "content": "已知 $0<\\alpha<\\dfrac{\\pi}{2}$, $\\cos \\alpha=\\dfrac{4}{5}$. 若 $0<\\beta<\\dfrac{\\pi}{2}$ 且 $\\cos (\\alpha+\\beta)=-\\dfrac{1}{2}$, 则 $\\sin \\beta$ 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": [ + "000108" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023815": { + "id": "023815", + "content": "若 $\\sin \\alpha+\\sin \\beta=\\dfrac{1}{4}$, $\\cos \\alpha+\\cos \\beta=\\dfrac{1}{3}$, 则 $\\tan (\\alpha+\\beta)$ 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": [] + }, + "023816": { + "id": "023816", + "content": "已知 $\\alpha$ 与 $\\beta$ 都是锐角, 且 $\\sin (\\alpha-\\beta)=\\dfrac{1}{3}$, $\\cos (\\alpha+\\beta)=\\dfrac{\\sqrt{3}}{2}$.\\\\\n(1) 求 $\\sin 2 \\alpha$ 的值;\\\\\n(2) 求证: $\\sin \\alpha \\cos \\beta=5 \\cos \\alpha \\sin \\beta$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "023817": { + "id": "023817", + "content": "如图, 已知面积为 $\\dfrac{\\pi}{6}$ 的扇形 $AOB$, 半径为 $1$, $C$ 是弧 $AB$ 上任意一点, 作矩形 $CDEF$ 内接于该扇形.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\t{35}\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (2,0) node [below] {$A$} coordinate (A);\n\\draw (60:2) node [above] {$B$} coordinate (B);\n\\draw (\\t:2) node [above right] {$C$} coordinate (C);\n\\draw (C) ++ ({-2/sin(120)*sin(60-\\t)},0) node [above left] {$D$} coordinate (D);\n\\draw ($(O)!(D)!(A)$) node [below] {$E$} coordinate (E);\n\\draw ($(O)!(C)!(A)$) node [below] {$F$} coordinate (F);\n\\draw (E)--(D)--(C)--(F)(A)--(O)--(B) arc (60:0:2);\n\\end{tikzpicture}\n\\end{center}\n(1) 求扇形圆心角 $\\angle AOB$ 的大小;\\\\\n(2) 点 $C$ 在什么位置时, 矩形 $CDEF$ 的面积最大?并说明理由.", + "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