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 97dc1de0..8cee0c60 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 @@ -145,3 +145,6 @@ 20240125-125651 023979:023984,012842,023985 +20240125-125941 +000498,023986:023993 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 75f73fb3..fbdb3ab7 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -3412,7 +3412,8 @@ ], "same": [], "related": [ - "030052" + "030052", + "023993" ], "remark": "", "space": "4em", @@ -226882,7 +226883,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023993" + ], "remark": "", "space": "4em", "unrelated": [] @@ -646407,6 +646410,169 @@ "space": "4em", "unrelated": [] }, + "023986": { + "id": "023986", + "content": "若函数 $h(x)=4 x^2-k x-8$ 在 $[5,20]$ 上是单调函数, 则实数 $k$ 的取值范围是\\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": [] + }, + "023987": { + "id": "023987", + "content": "若幂函数 $f(x)=(m^2-3 m+3) x^{m+1}$ 为偶函数, 则实数 $m$ 的值等于\\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": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023988": { + "id": "023988", + "content": "已知函数 $f(x)=x^2-6 x+8$, $x \\in[1, a]$, 若函数 $f(x)$ 的最小值为 $f(a)$, 则实数 $a$ 的取值范围是\\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": [] + }, + "023989": { + "id": "023989", + "content": "若 $f(x)=x^{\\frac{1}{4}}$, 则不等式 $f(x)>f(8 x-16)$ 的解集是\\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": [] + }, + "023990": { + "id": "023990", + "content": "若对于任意实数 $x$, 函数 $f(x)=(5-a) x^2-6 x+a+5$ 恒为正值, 则实数 $a$ 的取值范围是\\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": [] + }, + "023991": { + "id": "023991", + "content": "下图给出四个幂函数的图像, 则图像与函数表达式对应是\\bracket{20}.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {-exp(1/3*ln(2))}:{exp(1/3*ln(2))}, samples = 100] plot (\\x,{\\x*\\x*\\x});\n\\draw (0,-2) node [below] {\\textcircled{1}};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {-exp(1/2*ln(2))}:{exp(1/2*ln(2))}, samples = 100] plot (\\x,{\\x*\\x});\n\\draw (0,-2) node [below] {\\textcircled{2}};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:2, samples = 100] plot (\\x,{sqrt(\\x)});\n\\draw (0,-2) node [below] {\\textcircled{3}};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.5:2, samples = 100] plot (\\x,{1/\\x});\n\\draw [domain = -2:-0.5, samples = 100] plot (\\x,{1/\\x});\n\\draw (0,-2) node [below] {\\textcircled{4}};\n\\end{tikzpicture}\n\\end{center}\n\\onech{\\textcircled{1} $y=x^{\\frac{1}{3}}$, \\textcircled{2} $y=x^2$, \\textcircled{3} $y=x^{\\frac{1}{2}}$, \\textcircled{4} $y=x^{-1}$}{\\textcircled{1} $y=x^3$, \\textcircled{2} $y=x^2$, \\textcircled{3} $y=x^{\\frac{1}{2}}$, \\textcircled{4} $y=x^{-1}$}{\\textcircled{1} $y=x^2$, \\textcircled{2} $y=x^3$, \\textcircled{3} $y=x^{-1}$, \\textcircled{4} $y=x^{\\frac{1}{2}}$}{\\textcircled{1} $y=x^{\\frac{1}{3}}$, \\textcircled{2} $y=x^{\\frac{1}{2}}$, \\textcircled{3} $y=x^2$, \\textcircled{4} $y=x^{-1}$}", + "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": [] + }, + "023992": { + "id": "023992", + "content": "已知函数 $y=f(x)$ 是偶函数, 当 $x>0$ 时, $f(x)=(x-1)^2$, 若当 $x \\in[-2,-\\dfrac{1}{2}]$时, $n \\leq f(x) \\leq m$ 恒成立, 则 $m-n$ 的最小值为\\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": [] + }, + "023993": { + "id": "023993", + "content": "已知函数 $f(x)=x^2+(2 a-1) x-3$. 若函数 $f(x)$ 在 $[-1,3]$ 上最大值为 $1$, 求实数 $a$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "007938", + "000087" + ], + "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