From 279f845f050ebd61b7ac34cd8423d827e014c1a7 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 12:38:10 +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=9A45=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 | 120 +++++++++++++++++++++++++++++++ 2 files changed, 123 insertions(+) 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 2ce3cb29..60201c10 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 @@ -133,3 +133,6 @@ 20240125-123201 023954:023956,016816,023957:023959 +20240125-123757 +023960:023965 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 0b5357d3..727fac57 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -645864,6 +645864,126 @@ "space": "4em", "unrelated": [] }, + "023960": { + "id": "023960", + "content": "函数 $f(x)=\\sqrt{x+3}+\\log _2(6-x)$ 的定义域是\\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": [] + }, + "023961": { + "id": "023961", + "content": "已知函数 $f(x)=\\sqrt{-x^2+2 x+3}$, 则函数 $f(3 x-2)$ 的定义域为\\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": [] + }, + "023962": { + "id": "023962", + "content": "已知 $f(\\dfrac{1}{2}x-1)=2 x-5$, 且 $f(a)=6$, 则 $a=$\\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": [] + }, + "023963": { + "id": "023963", + "content": "已知 $f(2 x+1)=x^2-2 x$, 则 $f(3)=$\\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": [] + }, + "023964": { + "id": "023964", + "content": "高斯是德国著名的数学家, 近代数学奠基者之一, 享有``数学王子''的称号, 用其名字命名的``高斯函数''为设 $x \\in \\mathbf{R}$, 用 $[x]$ 表示不超过 $x$ 的最大整数, 则 $y=[x]$ 称为高斯函数.例如: $[-2.1]=-3$, $[3.1]=3$, 已知函数 $f(x)=\\dfrac{2^x+3}{2^x+1}$, 则函数 $y=[f(x)]$ 的值域为\\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": [] + }, + "023965": { + "id": "023965", + "content": "行驶中的汽车在刹车时由于惯性作用, 要继续往前滑行一段距离才能停下, 这段距离叫做刹车距离. 在某种路面上, 某种型号汽车的刹车距离 $y(\\mathrm{m})$ 与汽车的车速 $x(\\mathrm{km}/ \\mathrm{h})$ 满足下列关系: $y=\\dfrac{x^2}{200}+m x+n(m$、$n$ 是常数 $)$. 下图是根据多次实验数据绘制的刹车距离 $y(m)$ 与汽车的车速 $x(\\mathrm{km}/ \\mathrm{h})$ 的关系图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.05, yscale = 0.05]\n\\draw [->] (-10,0) -- (100,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,50) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:100, samples = 100] plot (\\x,{\\x*\\x/200+\\x/100});\n\\foreach \\i/\\j in {40/8.4,60/18.6,80/32.8}\n{\\draw [dashed] (\\i,0) node [below] {$\\i$} -- (\\i,\\j) -- (0,\\j) node [left] {$\\j$};}; \n\\end{tikzpicture}\n\\end{center}\n(1) 求出 $y$ 关于 $x$ 的函数表达式;\\\\\n(2) 如果要求刹车距离不超过 $25.2 m$, 求行驶的最大速度.", + "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