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 8cee0c60..55eccd17 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 @@ -148,3 +148,6 @@ 20240125-125941 000498,023986:023993 +20240125-130257 +023994:024001 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 52a7c0eb..62de90fd 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -135551,7 +135551,9 @@ "same": [ "012124" ], - "related": [], + "related": [ + "023998" + ], "remark": "", "space": "", "unrelated": [] @@ -168137,7 +168139,9 @@ "20240125\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023994" + ], "remark": "", "space": "", "unrelated": [] @@ -338246,7 +338250,9 @@ "same": [ "004395" ], - "related": [], + "related": [ + "023998" + ], "remark": "", "space": "", "unrelated": [] @@ -646574,6 +646580,171 @@ "space": "4em", "unrelated": [] }, + "023994": { + "id": "023994", + "content": "若函数 $f(x)=4+2 a^{x-1}$ 的图像过定点 $P$, 则点 $P$ 的坐标是\\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": [ + "005563" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023995": { + "id": "023995", + "content": "若函数 $f(x)=a^x+b$($a>0$, 且 $a \\neq 1$) 的定义域和值域都是 $[-1,0]$, 则 $a+b=$\\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": [] + }, + "023996": { + "id": "023996", + "content": "若函数 $y=|2^x-1|$ 的图像与直线 $y=b$ 有两个公共点, 则实数 $b$ 的取值范围为\\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": [] + }, + "023997": { + "id": "023997", + "content": "已知实数 $a \\neq 1$, 函数 $f(x)=\\begin{cases}4^x,& x \\geq 0,\\\\2^{a-x},& x<0,\\end{cases}$ 若 $f(1-a)=f(a-1)$, 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": [] + }, + "023998": { + "id": "023998", + "content": "若偶函数 $f(x)$ 满足 $f(x)=2^x-4$($x \\geq 0$), 则不等式 $f(x-2)>0$ 的解集为\\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": [ + "004395", + "012124" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023999": { + "id": "023999", + "content": "若函数 $f(x)=a^{x-b}$ 的图像如图所示, 其中 $a$、$b$ 为实常数, 则下列结论中正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:2, samples = 100] plot (\\x,{exp((\\x+0.8)*ln(0.6))});\n\\draw (0,1) -- (0.1,1) node [right] {$1$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$a>1$, $b<0$}{$a>1$, $b>0$}{$0K.\\end{cases}$ 给出函数 $f(x)=2^{x+1}-4^x$, 若对于任意$x\\in (-\\infty,1]$, 恒有 $f_K(x)=f(x)$, 则\\bracket{20}.\n\\fourch{$K$ 的最大值为 $0$}{$K$ 的最小值为 $0$}{$K$ 的最大值为 $1$}{$K$ 的最小值为 $1$}", + "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": [] + }, + "024001": { + "id": "024001", + "content": "已知函数 $f(x)=\\dfrac{3^x+a}{3^x+1}$($a \\in \\mathbf{R}$) 为奇函数.\\\\\n(1) 求 $a$ 的值;\\\\\n(2) 判断函数 $f(x)$ 的单调性, 并用定义证明.", + "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