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 1c5a31d9..f05a3672 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 @@ -406,3 +406,6 @@ 20240307-095910 高一下学期统考复习卷01 024622:024640 +20240307-121505 高一下学期统考复习卷02 +024641:024659 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index e6e236d4..17f1c46a 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -88837,7 +88837,8 @@ ], "same": [], "related": [ - "030040" + "030040", + "024650" ], "remark": "", "space": "", @@ -89753,7 +89754,9 @@ "same": [ "015601" ], - "related": [], + "related": [ + "024649" + ], "remark": "", "space": "", "unrelated": [] @@ -329325,7 +329328,9 @@ "20220819\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024659" + ], "remark": "", "space": "4em", "unrelated": [] @@ -360414,7 +360419,8 @@ "same": [], "related": [ "022803", - "023395" + "023395", + "024648" ], "remark": "", "space": "", @@ -388780,7 +388786,9 @@ "20230123\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024653" + ], "remark": "", "space": "", "unrelated": [] @@ -442354,7 +442362,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024659" + ], "remark": "", "space": "4em", "unrelated": [] @@ -442825,7 +442835,9 @@ "same": [ "002806" ], - "related": [], + "related": [ + "024649" + ], "remark": "", "space": "", "unrelated": [] @@ -527626,7 +527638,9 @@ "20230726\t赵琍琍" ], "same": [], - "related": [], + "related": [ + "024647" + ], "remark": "", "space": "4em", "unrelated": [] @@ -553062,7 +553076,8 @@ "020319" ], "related": [ - "024070" + "024070", + "024653" ], "remark": "", "space": "", @@ -553424,7 +553439,9 @@ "same": [ "020329" ], - "related": [], + "related": [ + "024648" + ], "remark": "", "space": "", "unrelated": [] @@ -557374,7 +557391,9 @@ "same": [ "020192" ], - "related": [], + "related": [ + "024653" + ], "remark": "", "space": "", "unrelated": [] @@ -557693,7 +557712,9 @@ "same": [ "020202" ], - "related": [], + "related": [ + "024648" + ], "remark": "", "space": "", "unrelated": [] @@ -620499,7 +620520,9 @@ "20230905\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024653" + ], "remark": "", "space": "", "unrelated": [] @@ -629124,7 +629147,9 @@ "20230905\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024642" + ], "remark": "", "space": "", "unrelated": [] @@ -629290,7 +629315,9 @@ "20230905\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024648" + ], "remark": "", "space": "", "unrelated": [] @@ -631512,7 +631539,9 @@ "20230925\t严捷" ], "same": [], - "related": [], + "related": [ + "024645" + ], "remark": "", "space": "", "unrelated": [] @@ -631618,7 +631647,9 @@ "20230925\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024650" + ], "remark": "", "space": "", "unrelated": [] @@ -667845,7 +667876,8 @@ "same": [], "related": [ "005103", - "020192" + "020192", + "024653" ], "remark": "", "space": "", @@ -681424,6 +681456,413 @@ "space": "4em", "unrelated": [] }, + "024641": { + "id": "024641", + "content": "用不等号连结: 若 $00$ 的解集为\\blank{50}. (用区间表示)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题2", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "022608" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024643": { + "id": "024643", + "content": "设 $a$、$b$、$c$、$d \\in \\mathbf{R}$, ``$a+c2+\\sqrt{x-3}$ 的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题4", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024645": { + "id": "024645", + "content": "若关于 $x$ 的方程 $3(x+1)=k(x-2)$ 的解为非正数, 则实数 $k$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题5", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "022689" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024646": { + "id": "024646", + "content": "若 $x \\in \\mathbf{N}$,则不等式 $|\\dfrac{2}{x-13}|>\\dfrac{8}{9}$ 的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题6", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024647": { + "id": "024647", + "content": "若关于 $x$ 的不等式 $|a x+2|<6$ 的解集为 $(-1,2)$, 则实数 $a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题7", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "019296" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024648": { + "id": "024648", + "content": "若 $x<1$, 则 $x+\\dfrac{1}{x-1}$ 的最大值是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题8", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "022613", + "012658", + "020202", + "020329" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024649": { + "id": "024649", + "content": "若不等式 $|3 x-b|<4$ 的解集中的整数有且仅有 $2$、$3$, 则实数 $b$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题9", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "015601", + "002806" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024650": { + "id": "024650", + "content": "关于 $x$ 的不等式 $a x^2+b x+c>0$ 的解集为 $(-2,1)$, 对于实系数 $a$、$b$、$c$, 有如下结论:\\\\\n\\textcircled{1} $a>0$; \\textcircled{2} $b>0$; \\textcircled{3} $c>0$; \\textcircled{4} $a+b+c>0$; \\textcircled{5} $a-b+c>0$.\\\\\n其中所有正确的结论的序号是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题10", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "002775", + "030040", + "022692" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024651": { + "id": "024651", + "content": "若不等式 $a x^2+b x+1>0$ 的解集是 $(-\\dfrac{1}{2}, 1)$, 则实数 $a$、$b$ 的值分别是\\bracket{20}.\n\\fourch{$a=2$, $b=-1$}{$a=2$, $b=1$}{$a=-2$, $b=-1$}{$a=-2$, $b=1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题11", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024652": { + "id": "024652", + "content": "如果 $0\\dfrac{1}{b}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题12", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024653": { + "id": "024653", + "content": "下列式子中最小值为 $2$ 的是\\bracket{20}.\n\\fourch{$x+\\dfrac{1}{x}$}{$\\sqrt{x^2+2}+\\dfrac{1}{\\sqrt{x^2+2}}$}{$x^2+\\dfrac{2}{x^2}$}{$\\dfrac{x^2+2}{\\sqrt{x^2+1}}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题13", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "013643", + "024070", + "020192", + "020319", + "022300" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024654": { + "id": "024654", + "content": "设 $a$ 为实数, ``$a=1$''是``对任意的正数 $x$, $2 x+\\dfrac{a}{x}>1$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题14", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024655": { + "id": "024655", + "content": "解关于 $x$ 的不等式: $0<|\\dfrac{x}{x+1}| \\leq 1$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题15", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024656": { + "id": "024656", + "content": "已知集合 $A=\\{x | \\dfrac{x-2}{x-3}\\geq 0, x \\in \\mathbf{R}\\}$, $B=\\{x|| x-2 a | \\leq 2, x \\in \\mathbf{R}\\}$, 若 $A \\cup B=\\mathbf{R}$, 求实数 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题16", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024657": { + "id": "024657", + "content": "当 $0 \\leq m<\\dfrac{12}{5}$ 时, 关于 $x$ 的不等式 $m x^2+3 m x+m+3>0$ 对一切实数 $x$ 恒成立吗? 若成立, 请给出证明; 若不成立, 请举出反例.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题17", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024658": { + "id": "024658", + "content": "如图,设计一幅矩形宣传画, 要求画面面积为 $4840 \\mathrm{cm}^2$, 画面上下边要留 $8 \\mathrm{cm}$ 空白, 左右要留 $5 \\mathrm{cm}$ 空白, 怎样确定画面的高与宽的尺寸,才能使宣传画面所用纸张面积最小?\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.03]\n\\draw (0,0) rectangle (65,104);\n\\filldraw [pattern = north east lines] (5,8) rectangle ++ (55,88);\n\\draw (-12,0) -- (-1,0) (-12,8) -- (-1,8);\n\\draw [->] (-11,-10) -- (-11,0);\n\\draw [->] (-11,18) -- (-11,8);\n\\draw (-11,4) node [left] {$8$cm};\n\\draw (0,-12) -- (0,-1) (5,-12) -- (5,-1);\n\\draw [->] (-10,-11) -- (0,-11);\n\\draw [->] (15,-11) -- (5,-11);\n\\draw (2.5,-11) node [below] {$5$cm};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题18", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024659": { + "id": "024659", + "content": "若实数 $x$、$y$、$m$ 满足 $|x-m|>|y-m|$, 则称 $x$ 比 $y$ 远离 $m$.\\\\\n(1) 若 $x^2-1$ 比 $3$ 远离 $0$, 求 $x$ 的取值范围;\\\\\n(2) 对任意两个不相等的正数 $a$、$b$, 证明: $a^3+b^3$ 比 $a^2 b+a b^2$ 远离 $2 a b \\sqrt{a b}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "导学先锋必修第一册第二章测验卷试题19", + "edit": [ + "20240307\t朱敏慧" + ], + "same": [], + "related": [ + "015580", + "011599" + ], + "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