From ea5b382bcb68673c939f48c92d869aa29f1a1344 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 11:53:21 +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=9A34=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 | 184 ++++++++++++++++++++++++++++++- 2 files changed, 183 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 b1e72e11..87332be5 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 @@ -100,3 +100,6 @@ 20240125-115018 023883:023888 +20240125-115315 +023889:023896 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 1f864251..751c8633 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -299526,7 +299526,9 @@ "20221111\t周双" ], "same": [], - "related": [], + "related": [ + "023889" + ], "remark": "", "space": "4em", "unrelated": [] @@ -368312,7 +368314,9 @@ "20230118\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023891" + ], "remark": "", "space": "", "unrelated": [] @@ -485989,7 +485993,9 @@ "20230606\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023896" + ], "remark": "", "space": "4em", "unrelated": [] @@ -644368,6 +644374,174 @@ "space": "4em", "unrelated": [] }, + "023889": { + "id": "023889", + "content": "平行六面体 $ABCD-A_1B_1C_1D_1$ 中, $M$ 为 $AC$ 与 $BD$ 的交点, 设 $\\overrightarrow{A_1B_1}=\\overrightarrow{a}$, $\\overrightarrow{A_1D_1}=\\overrightarrow{b}$,\n$\\overrightarrow{AA_1}=\\overrightarrow{c}$, 则 $\\overrightarrow{B_1M}=$\\blank{50}. (用 $\\overrightarrow{a}$、$\\overrightarrow{b}$、$\\overrightarrow{c}$ 表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "010715" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023890": { + "id": "023890", + "content": "下列所有命题中正确的命题序号是\\blank{50}.\\\\\n\\textcircled{1} 若 $|\\overrightarrow{a}|=|\\overrightarrow{b}|$, 则 $\\overrightarrow{a}, \\overrightarrow{b}$ 的长度相同, 方向相反或相同; \\textcircled{2} 若 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 是互为负向量, 则 $|\\overrightarrow{a}|=|\\overrightarrow{b}|$; \\textcircled{3} 空间向量的加法满足结合律; \\textcircled{4} 在四边形 $ABCD$ 中, 一定有 $\\overrightarrow{AB}+\\overrightarrow{AD}=\\overrightarrow{AC}$.", + "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": [] + }, + "023891": { + "id": "023891", + "content": "在正四面体 $O-ABC$ 中, $\\overrightarrow{OA}=\\overrightarrow{a}$, $\\overrightarrow{OB}=\\overrightarrow{b}$, $\\overrightarrow{OC}=\\overrightarrow{c}, D$ 为 $BC$ 的中点, $E$ 为 $AD$ 的中点, 则 $\\overrightarrow{OE}=$\\blank{50}. (用 $\\overrightarrow{a}$、$\\overrightarrow{b}$、$\\overrightarrow{c}$ 表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "013151" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023892": { + "id": "023892", + "content": "给出下列命题: \\textcircled{1} 空间任意两个向量 $\\overrightarrow{a}$、$\\overrightarrow{b}$ 一定是共面的; \\textcircled{2} $\\overrightarrow{a}$、$\\overrightarrow{b}$ 为空间两个向量, 则 $|\\overrightarrow{a}|=|\\overrightarrow{b}| \\Leftrightarrow \\overrightarrow{a}=\\overrightarrow{b}$; \\textcircled{3} 若 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$, 则 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 所在直线平行; \\textcircled{4} 如果 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$、$\\overrightarrow{b}\\parallel \\overrightarrow{c}$, 那么 $\\overrightarrow{a}\\parallel \\overrightarrow{c}$. 其中假命题的序号是\\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": [] + }, + "023893": { + "id": "023893", + "content": "已知向量 $\\overrightarrow{AB}$、$\\overrightarrow{AC}$、$\\overrightarrow{BC}$ 满足 $|\\overrightarrow{AB}|=|\\overrightarrow{AC}|+|\\overrightarrow{BC}|$, 则有\\bracket{20}.\n\\fourch{$\\overrightarrow{AB}=\\overrightarrow{AC}+\\overrightarrow{BC}$}{$\\overrightarrow{AB}=-\\overrightarrow{AC}-\\overrightarrow{BC}$}{$\\overrightarrow{AC}$ 与 $\\overrightarrow{BC}$ 同向}{$\\overrightarrow{AC}$ 与 $\\overrightarrow{CB}$ 同向}", + "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": [] + }, + "023894": { + "id": "023894", + "content": "已知向量 $\\overrightarrow{a}=\\overrightarrow{x}+2 \\overrightarrow{y}-\\overrightarrow{z}$, 且 $|\\overrightarrow{x}|=|\\overrightarrow{y}|=|\\overrightarrow{z}|=1$, 若向量 $\\overrightarrow{x}$、$\\overrightarrow{y}$、$\\overrightarrow{z}$ 两两垂直, 则 $|\\overrightarrow{a}|=$\\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": [] + }, + "023895": { + "id": "023895", + "content": "已知平行六面体 $ABCD-A' B' C' D'$ 中, $AB=4$, $AD=3$, $AA'=5$, $\\angle BAD=90^{\\circ}$, $\\angle BAA'=\\angle DAA'=60^{\\circ}$, 则$|AC'|=$\\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": [ + "040598" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023896": { + "id": "023896", + "content": "如图, 已知 $M$、$N$ 分别为四面体 $A-BCD$ 的面 $BCD$ 与面 $ACD$ 的重心, $G$ 为 $AM$ 上一点, 且 $GM: GA=1: 3$. 求证: $B$、$G$、$N$ 三点共线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$B$} coordinate (B);\n\\draw (2,0,0) node [right] {$D$} coordinate (D);\n\\draw (1,0,{sqrt(3)}) node [below] {$C$} coordinate (C);\n\\draw ($1/3*(D)+1/3*(B)+1/3*(C)$) ++ (0,{2*sqrt(6)/3},0) node [above] {$A$} coordinate (A);\n\\draw (A)--(B)(A)--(C)(A)--(D)(B)--(C)--(D);\n\\draw [dashed] (B)--(D);\n\\draw (A)--(B)--(C)--(D)--cycle(A)--(C);\n\\draw [dashed] (B)--(D);\n\\filldraw ($1/3*(D)+1/3*(B)+1/3*(C)$) node [below] {$M$} coordinate (M) circle (0.03);\n\\filldraw ($1/3*(D)+1/3*(A)+1/3*(C)$) node [below] {$N$} coordinate (N) circle (0.03);\n\\filldraw ($(A)!0.75!(M)$) node [left] {$G$} coordinate (G) circle (0.03);\n\\draw [dashed] (A)--(M);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "017992" + ], + "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