From 2a9d1fd31916ce3d5224cf450a2e2022596af8a7 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 11:17:23 +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=9A26=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 | 156 ++++++++++++++++++++++++++++++- 2 files changed, 156 insertions(+), 3 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 e6843e16..eb5bb7d6 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 @@ -76,3 +76,6 @@ 20240125-111402 023818:023827 +20240125-111717 +023828:023834 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index d69ae2c5..373a967d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -237499,7 +237499,8 @@ ], "same": [], "related": [ - "003166" + "003166", + "023828" ], "remark": "", "space": "", @@ -443643,7 +443644,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023830" + ], "remark": "", "space": "", "unrelated": [] @@ -643048,6 +643051,151 @@ "space": "4em", "unrelated": [] }, + "023828": { + "id": "023828", + "content": "函数 $y=\\sin (2 x+\\dfrac{\\pi}{4})$ 的对称轴方程为\\blank{50}, 对称中心为\\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": [ + "008354" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023829": { + "id": "023829", + "content": "若函数 $f(x)=\\sin (\\omega x+\\dfrac{\\pi}{6})$($\\omega>0$) 的最小正周期为 $\\pi$, 则 $f(\\dfrac{\\pi}{3})$ 的值是\\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": [] + }, + "023830": { + "id": "023830", + "content": "把函数 $y=\\cos x-\\sqrt{3}\\sin x$ 的图像向左平移 $m$($m>0$) 个单位所得图像关于 $y$ 轴对称, 则实数 $m$ 的最小值是\\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": [ + "030014", + "016090" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023831": { + "id": "023831", + "content": "电流强度 $I$(A) 随时间 $t$(s) 变化的函数 $I=A \\sin (\\omega t+\\varphi) $($A>0$, $\\omega>0$, $0<\\varphi<\\dfrac{\\pi}{2}$) 的部分图像如图所示, 则当 $t=\\dfrac{1}{100}$s时, 电流强度是\\blank{50}A.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 1.5, yscale = 0.1]\n\\draw [->] (0,0) -- ({7/3},0) node [below] {$x$};\n\\draw [->] (0,-15) -- (0,15) node [left] {$y$};\n\\draw (0,0) node [left] {$O$};\n\\draw [domain = 0:{11/6}, samples = 100] plot (\\x,{10*sin(180*\\x+30)});\n\\foreach \\i in {-10,-5,5,10}\n{\\draw (0.04,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw [dashed] ({4/3},0) --++ (0,-10) -- (0,-10) ({1/3},0)--++ (0,10) -- (0,10);\n\\draw ({1/3},0) node [below] {$\\dfrac{1}{300}$};\n\\draw ({4/3},0) node [above] {$\\dfrac{4}{300}$};\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": [] + }, + "023832": { + "id": "023832", + "content": "若函数 $f(x)=A \\sin (\\omega x+\\varphi)+k$($A>0$, $\\omega>0$, $|\\varphi|<\\dfrac{\\pi}{2}$)的图像如图所示, 则 $f(x)$ 的表达式是 $f(x)=$\\blank{50}.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1.5,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [domain = -1.5:2.5, samples = 100] plot (\\x,{1.5*sin(\\x*360/pi+60)+1});\n\\draw [dashed] ({7*pi/12},0) --++ (0,-0.5) -- (0,-0.5);\n\\draw [dashed] ({pi/12},0) --++ (0,2.5) -- (0,2.5);\n\\draw (0,-0.5) node [left] {$-\\frac{1}{2}$} (0,2.5) node [left] {$\\frac{5}{2}$};\n\\draw ({pi/12},0) node [below] {$\\frac{\\pi}{12}$} ({7*pi/12},0) node [above] {$\\frac{7\\pi}{12}$};\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": [] + }, + "023833": { + "id": "023833", + "content": "若函数 $f(x)=2 \\sin (\\dfrac{\\pi}{3}x+\\varphi)$($|\\varphi|<\\dfrac{\\pi}{2}$) 的图像经过点 $(0,1)$, 则其最小正周期 $T=$\\blank{50}, 初始相位 $\\varphi=$\\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": [] + }, + "023834": { + "id": "023834", + "content": "设 $\\omega \\in \\mathbf{R}$. 已知向量 $\\overrightarrow{m}=(\\cos \\omega x, \\sin \\omega x)$, $\\overrightarrow{n}=(\\cos \\omega x, \\sqrt{3}\\cos \\omega x)$, 函数 $y=f(x)$, 其中 $f(x)=\\overrightarrow{m}\\cdot \\overrightarrow{n}$.\\\\\n(1) 若 $f(x)$ 的最小正周期是 $2 \\pi$, 求 $f(x)$ 的单调增区间;\\\\\n(2) 若 $f(x)$ 的图像的一条对称轴是 $x=\\dfrac{\\pi}{6}$($0<\\omega<2$), 求 $f(x)$ 的最小正周期和值域.", + "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