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3
工具v2/文本文件/新题收录列表.txt
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@ -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

478
题库0.3/Problems.json
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@ -88837,7 +88837,8 @@
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"20220819\t王伟叶"
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"20230123\t王伟叶"
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"20230726\t赵琍琍"
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"20230925\t严捷"
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@ -681424,6 +681456,413 @@
"space": "4em",
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"024641": {
"id": "024641",
"content": "用不等号连结: 若 $0<a<b$, 则 $a^2$\\blank{50}$ab$.",
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"genre": "填空题",
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"origin": "导学先锋必修第一册第二章测验卷试题1",
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"024642": {
"id": "024642",
"content": "不等式 $-35 x^2+2 x+1>0$ 的解集为\\blank{50}. (用区间表示)",
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"genre": "填空题",
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"origin": "导学先锋必修第一册第二章测验卷试题2",
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"024643": {
"id": "024643",
"content": "设 $a$、$b$、$c$、$d \\in \\mathbf{R}$, ``$a+c<b+d$''是``$a<b$ 且 $c<d$''的\\blank{50}条件.",
"objs": [],
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"origin": "导学先锋必修第一册第二章测验卷试题3",
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"024644": {
"id": "024644",
"content": "不等式 $x+\\sqrt{x-3}>2+\\sqrt{x-3}$ 的解集是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
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"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": [],
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"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
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"origin": "导学先锋必修第一册第二章测验卷试题5",
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"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",
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"024647": {
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"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": "",
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"024648": {
"id": "024648",
"content": "若 $x<1$, 则 $x+\\dfrac{1}{x-1}$ 的最大值是\\blank{50}.",
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"tags": [],
"genre": "填空题",
"ans": "",
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"duration": -1,
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"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": [],
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"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
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"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}.",
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"tags": [],
"genre": "填空题",
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"solution": "",
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"origin": "导学先锋必修第一册第二章测验卷试题10",
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"20240307\t朱敏慧"
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"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{$a=2$, $b=-1$}{$a=2$, $b=1$}{$a=-2$, $b=-1$}{$a=-2$, $b=1$}",
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"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",
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],
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"024652": {
"id": "024652",
"content": "如果 $0<a<b$, 那么下列不等式中错误的是\\bracket{20}.\n\\fourch{$a+c<b+c$}{$\\sqrt{a}<\\sqrt{b}$}{$a c^2<b c^2$}{$\\dfrac{1}{a}>\\dfrac{1}{b}$}",
"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"
],
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"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"
],
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"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": "",
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"duration": -1,
"usages": [],
"origin": "导学先锋必修第一册第二章测验卷试题14",
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},
"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": [],
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"space": "4em",
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"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": [],
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"remark": "",
"space": "4em",
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"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.",
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"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"
],
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"space": "4em",
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"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"
],
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"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": [],
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"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "导学先锋必修第一册第二章测验卷试题19",
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"20240307\t朱敏慧"
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"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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
@ -682845,7 +683284,8 @@
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