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收录高三寒假作业57新题

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wangweiye7840 2024-01-25 13:56:58 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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@ -169,3 +169,6 @@
20240125-135214
024049:024057
20240125-135645
024058:024066

192
题库0.3/Problems.json
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@ -157599,7 +157599,9 @@
"20220720\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024058"
],
"remark": "",
"space": "",
"unrelated": []
@ -476403,7 +476405,9 @@
"20230606\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024063"
],
"remark": "",
"space": "",
"unrelated": []
@ -647981,6 +647985,190 @@
"space": "4em",
"unrelated": []
},
"024058": {
"id": "024058",
"content": "若不等式 $a x^2+b x+c>0$($a$、$b$、$c \\in \\mathbf{R}$) 的解集是 $\\{x | 2<x<5\\}$, 则不等式 $c x^2+b x+a<0$ 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": [
"005153"
],
"remark": "",
"space": "",
"unrelated": []
},
"024059": {
"id": "024059",
"content": "若不等式 $x^2-a x+1 \\leq 1$ 有唯一解, 则实数 $a$ 的取值集合为\\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": []
},
"024060": {
"id": "024060",
"content": "不等式 $\\dfrac{3-2 x}{2-3 x}\\leq 1$ 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": [],
"remark": "",
"space": "",
"unrelated": []
},
"024061": {
"id": "024061",
"content": "关于 $x$ 的方程 $5 x-2 k=k x-x-4$ 的解集在区间 $(0,6)$ 内, 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": []
},
"024062": {
"id": "024062",
"content": "问题``求不等式 $3^x+4^x\\leq 5^x$ 的解''有如下的思路: 不等式 $3^x+4^x\\leq 5^x$ 可变为 $(\\dfrac{3}{5})^x+(\\dfrac{4}{5})^x\\leq 1$, 考察函数 $f(x)=(\\dfrac{3}{5})^x+(\\dfrac{4}{5})^x$ 可知, 函数 $f(x)$ 在 $\\mathbf{R}$ 上是严格减函数, 且 $f(2)=1$, 所以原不等式的解集是 $[2,+\\infty)$. 仿照此解法可得到不等式: $x^3-(2 x+3)>(2 x+3)^3-x$ 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": []
},
"024063": {
"id": "024063",
"content": "若全集 $U=\\mathbf{R}$, $f(x)$、$g(x)$ 均为 $x$ 的二次函数, $P=\\{x | f(x)<0\\}$, $Q=\\{x | g(x) \\geq 0\\}$, 则不等式组 $\\begin{cases}f(x)<0,\\\\g(x)<0\\end{cases}$ 的解集可用 $P$、$Q$ 表示为 \\bracket{20}.\n\\fourch{$P \\cap Q$}{$P \\cap \\overline{Q}$}{$P \\cup Q$}{$P \\cup \\overline{Q}$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"017555"
],
"remark": "",
"space": "",
"unrelated": []
},
"024064": {
"id": "024064",
"content": "若 $a$、$b$、$c$ 是实常数, 则``$a>0$ 且 $b^2-4 a c<0$''是``对任意 $x \\in \\mathbf{R}$, 有 $a x^2+b x+c>0$''的\\bracket{20};\n\\twoch{充分非必要条件}{必要非充分条件 }{充要条件}{既非充分又非必要条件}",
"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": []
},
"024065": {
"id": "024065",
"content": "不等式组 $\\begin{cases}|1-2 x|>3,\\\\x^2+x-6 \\leq 0\\end{cases}$ 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": []
},
"024066": {
"id": "024066",
"content": "解关于 $x$ 的不等式: $x^2-(a+a^2) x+a^3>0$($a \\in \\mathbf{R}$).",
"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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",