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 5474c60a..9a9ee3f4 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 @@ -340,3 +340,6 @@ 20240204-141708 高二寒假作业7 024501:024502,022875,024503:024512,008994,009009,024513:024514,009070 +20240204-142554 高二寒假作业8 +002910,024515:024516,022377,022367,024517,003025,024518:024521,020568,024522,014665,024523:024526 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 8540ee50..16f09e26 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -93582,7 +93582,9 @@ "20220701\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024521" + ], "remark": "", "space": "", "unrelated": [] @@ -169362,7 +169364,9 @@ "007972", "017589" ], - "related": [], + "related": [ + "024522" + ], "remark": "", "space": "", "unrelated": [] @@ -228455,7 +228459,9 @@ "005590", "017589" ], - "related": [], + "related": [ + "024522" + ], "remark": "", "space": "", "unrelated": [] @@ -362014,7 +362020,9 @@ "20230118\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024524" + ], "remark": "", "space": "", "unrelated": [] @@ -479966,7 +479974,9 @@ "007972", "005590" ], - "related": [], + "related": [ + "024522" + ], "remark": "", "space": "", "unrelated": [] @@ -609588,7 +609598,9 @@ "20230905\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024523" + ], "remark": "", "space": "4em", "unrelated": [] @@ -663844,6 +663856,256 @@ "space": "4em", "unrelated": [] }, + "024515": { + "id": "024515", + "content": "已知 $f(x)=\\ln \\dfrac{x+1}{x-1}$, 则 $f^{-1}(2)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024516": { + "id": "024516", + "content": "函数 $f(x)=\\ln (x-2)+\\ln (x+2)$ 的奇偶性是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024517": { + "id": "024517", + "content": "函数 $y=\\log _{(x+1)}(16-4^x)$ 的定义域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024518": { + "id": "024518", + "content": "函数 $y=4^x-2^{x+1}-1$, $x \\in[-1,2)$ 的值域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024519": { + "id": "024519", + "content": "若函数 $f(x)=2^{-|x|}-m$ 与 $x$ 轴有交点, 则实数 $m$ 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": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024520": { + "id": "024520", + "content": "将函数 $y=f(x)$ 的图像沿 $x$ 轴向左平移一个单位, 再沿 $y$ 轴翻折, 得到 $y=\\lg x$ 的图像, 则 $y=f(x)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024521": { + "id": "024521", + "content": "已知集合 $A=\\{y | y=(\\dfrac{1}{3})^{|x|}\\}$, $B=\\{a | \\log _a(3 a-1)>0\\}$, 则 $A \\cap \\overline{B}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "002956" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024522": { + "id": "024522", + "content": "关于 $x$ 方程 $(\\dfrac{1}{2})^x=\\dfrac{2 a+3}{a-5}$ 有负根, 则实数 $a$ 取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "007972", + "005590", + "017589" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024523": { + "id": "024523", + "content": "设函数 $f(x)=\\dfrac{x^2+4 x+5}{x^2+4 x+4}$, 作出 $y=f(x)$ 的大致图像, 讨论 $y=f(x)$ 的性质, 并利用性质比较 $f(-\\pi)$ 与 $f(-\\dfrac{\\sqrt{2}}{2})$ 的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "022376" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024524": { + "id": "024524", + "content": "(1) 已知关于 $x$ 的方程 $\\lg ^2 x+(m+4) \\lg x+4=0$ 有实数解, 求实数 $m$ 的取值范围;\\\\\n(2) 已知关于 $x$ 的方程 $9^x+(k+4) \\cdot 3^x+4=0$ 有实数解, 求实数 $k$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "012874" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024525": { + "id": "024525", + "content": "已知 $f(x)=\\lg (x+1)$, $g(x)=2 \\lg (2 x+t)$.\\\\\n(1) 若 $t=-1$, 解不等式 $f(x) \\leq g(x)$;\\\\\n(2) 若对任意 $x \\in[0,1)$, 不等式 $f(x) \\leq g(x)$ 恒成立, 求实数 $t$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024526": { + "id": "024526", + "content": "设函数 $f(x)=\\log _a(x-3 a)$($a>0$, $a \\neq 1$), 当且仅当点 $P(x, y)$ 是函数 $y=f(x)$ 图像上的点时,点 $Q(x-2 a,-y)$ 是函数 $y=g(x)$ 的图像上的点.\\\\\n(1) 写出函数 $y=g(x)$ 的解析式;\\\\\n(2) 若当 $x \\in[a+2, a+3]$ 时, 恒有 $|f(x)-g(x)| \\leq 1$, 试确定 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "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