From d461bff315b9ed1f1a1156b7a6e43af4ce8a92e4 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 12:23:57 +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=9A41=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 | 163 ++++++++++++++++++++++++++++++- 2 files changed, 162 insertions(+), 4 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 479a4de1..4a0281c0 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 @@ -121,3 +121,6 @@ 20240125-122103 023929:023933,016750,023934:023935 +20240125-122347 +023936:023942 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 3ee84d7e..c83bd9a9 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -341767,7 +341767,9 @@ "20221209\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023938" + ], "remark": "", "space": "", "unrelated": [] @@ -458708,7 +458710,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023938" + ], "remark": "", "space": "", "unrelated": [] @@ -563404,7 +563408,9 @@ "20230101\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023939" + ], "remark": "", "space": "4em", "unrelated": [] @@ -614491,7 +614497,9 @@ "20231109\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023936" + ], "remark": "", "space": "", "unrelated": [] @@ -645353,6 +645361,153 @@ "space": "4em", "unrelated": [] }, + "023936": { + "id": "023936", + "content": "若正三棱柱 $ABC-A_1B_1C_1$ 的侧棱长与底面边长相等, 则 $AB_1$ 与侧面 $ACC_1A_1$ 所成角的正弦值等于\\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": [ + "022721" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023937": { + "id": "023937", + "content": "如图, 正方体 $ABCD-A_1B_1C_1D_1$ 的棱长为 $1$ , 将该正方体沿对角面 $BB_1D_1D$ 切成两块, 再将这两块拼接成一个不是正方体的四棱柱, 那么所得四棱柱的全面积为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\fill [pattern = north east lines] (B)--(D)--(D_1)--(B_1)--cycle;\n\\draw (B_1)--(D_1);\n\\draw [dashed] (B)--(D);\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": [] + }, + "023938": { + "id": "023938", + "content": "若某圆柱底面的半径为 $1$, 高为 $2$, 则该圆柱的表面积为\\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": [ + "012247", + "016770" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023939": { + "id": "023939", + "content": "已知一个正方体与一个圆柱等高, 若侧面积相等, 则这个正方体和圆柱的体积之比为\\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": [ + "020995" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023940": { + "id": "023940", + "content": "正三棱柱 $ABC-A_1B_1C_1$ 的各棱长都 $2$, 若 $E$、$F$ 分别是 $AB$、$A_1C_1$ 的中点, 则 $EF$ 的长是\\bracket{20}.\n\\fourch{$2$}{$\\sqrt{3}$}{$\\sqrt{5}$}{$\\sqrt{7}$}", + "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": [] + }, + "023941": { + "id": "023941", + "content": "如图, 在正方体 $ABCD-A_1B_1C_1D_1$ 中, 点 $P$ 是线段 $BC_1$ 上的一个动点, 有下列三个结论: \\textcircled{1} $A_1P \\parallel $ 平面 $ACD_1$; \\textcircled{2} $B_1D \\perp A_1P$; \\textcircled{3} 平面 $A_1PB \\perp$ 平面 $B_1CD$. 其中所有正确结论的序号是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw (B)--(C_1);\n\\draw ($(B)!0.6!(C_1)$) node [right] {$P$} coordinate (P);\n\\draw [dashed] (A_1)--(P);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{\\textcircled{1}\\textcircled{2}\\textcircled{3}}{\\textcircled{2}\\textcircled{3}}{\\textcircled{1}\\textcircled{3}}{\\textcircled{1}\\textcircled{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": [] + }, + "023942": { + "id": "023942", + "content": "如图, $AA_1$ 是圆柱的一条母线, $AB$ 是圆柱的底面直径, $C$ 在圆柱下底面圆周上, $M$ 是线段 $A_1C$ 的中点. 已知 $AA_1=AC=4$, $BC=3$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (-2.5,0) node [left] {$A$} coordinate (A);\n\\draw (2.5,0) node [right] {$B$} coordinate (B);\n\\draw (A) ++ (0,4) node [left] {$A_1$} coordinate (A_1);\n\\draw (-70:2.5 and {2.5/4}) node [below] {$C$} coordinate (C);\n\\draw ($(A_1)!0.5!(C)$) node [above right] {$M$} coordinate (M);\n\\draw [dashed] (A)--(C)--(B)--cycle(A_1)--(C)(A)--(M);\n\\draw [dashed] (A) arc (180:0:2.5 and {2.5/4});\n\\draw (A)--++(0,4)(B)--++(0,4)(A_1)arc (180:-180:2.5 and {2.5/4})(A) arc (180:360:2.5 and {2.5/4});\n\\end{tikzpicture}\n\\end{center}\n(1) 求圆柱的侧面积;\\\\\n(2) 求证: $BC \\perp AM$.", + "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