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收录高三寒假作业试卷06新题

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wangweiye7840 2024-01-25 15:32:03 +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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@ -226,3 +226,6 @@
20240125-152725
024211:024215,011270,024216,011102,024217:024218,004157,024219:024222
20240125-153148
024223:024238

348
题库0.3/Problems.json
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@ -87017,7 +87017,9 @@
"20220701\t王伟叶"
],
"same": [],
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"related": [
"024230"
],
"remark": "",
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@ -222072,7 +222074,9 @@
"20220726\t王伟叶"
],
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"024230"
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@ -431000,7 +431004,9 @@
"20230503\t王伟叶"
],
"same": [],
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"related": [
"024226"
],
"remark": "",
"space": "",
"unrelated": []
@ -535820,7 +535826,9 @@
"same": [
"007736"
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"related": [
"024230"
],
"remark": "",
"space": "",
"unrelated": []
@ -632898,7 +632906,9 @@
"20240108\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024228"
],
"remark": "",
"space": "4em",
"unrelated": []
@ -651468,6 +651478,334 @@
"space": "4em",
"unrelated": []
},
"024223": {
"id": "024223",
"content": "不等式 $(\\dfrac{1}{3})^{x^2-3 x-4}>(\\dfrac{1}{3})^{2 x+10}$ 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": []
},
"024224": {
"id": "024224",
"content": "已知集合 $A=\\{1,2\\}$, $B=\\{1,2,3,4\\}$, 满足 $A \\cup C=B \\cap C$ 的集合 $C$ 的个数为\\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": []
},
"024225": {
"id": "024225",
"content": "已知不等式 $|x-m|<1$ 成立的充分不必要条件是 $\\dfrac{1}{3}<x<\\dfrac{1}{2}$, 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": [
"20240125\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024226": {
"id": "024226",
"content": "若在关于 $x$ 的不等式 $x^2-(a+1) x+a<0$ 的解集中至多包含 $2$ 个整数, 则实数 $a$ 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": [
"015509"
],
"remark": "",
"space": "",
"unrelated": []
},
"024227": {
"id": "024227",
"content": "若 $a$、$b \\in \\mathbf{R}$ 且 $a+2 b=2$, 则 $2^a+4^b$ 的最小值为\\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": []
},
"024228": {
"id": "024228",
"content": "设集合 $A=\\{x | x^2-3 x+2=0\\}$, $B=\\{x | x^2-a x+a-1=0\\}$, $C=\\{x | x^2-m x+2=0\\}$, 若 $A \\cup B=A$、$A \\cap C=C$, 则实数 $a$ 的值为\\blank{50}, 实数 $m$ 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": [
"023383"
],
"remark": "",
"space": "",
"unrelated": []
},
"024229": {
"id": "024229",
"content": "已知函数 $f(x)=\\dfrac{x^2+a x+11}{x+1}$($a \\in \\mathbf{R}$), 若对于任意 $x \\in \\mathbf{N}$, $x \\geq 1$, $f(x) \\geq 3$ 恒成立, 则实数 $a$ 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": []
},
"024230": {
"id": "024230",
"content": "若 $A$ 是 $B$ 成立的充分条件, $D$ 是 $C$ 成立的必要条件, $C$ 是 $B$ 成立的充要条件, 则 $D$ 是 $A$成立的\\bracket{20}.\n\\fourch{充分非必要条件}{必要非充分条件}{充要条件}{非充分非必要条件}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"007758",
"002733",
"020077"
],
"remark": "",
"space": "",
"unrelated": []
},
"024231": {
"id": "024231",
"content": "用反证法证明``若 $a$、$b \\in \\mathbf{R}$, $a^2+b^2\\neq 0$, 则 $a$、$b$ 不全为 $0$''时, 假设正确的是\\bracket{20}.\n\\fourch{$a$、$b$ 中只有一个为 $0$}{$a$、$b$ 至少一个不为 $0$}{$a$、$b$ 至少有一个为 $0$}{$a$、$b$ 全为 $0$}",
"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": []
},
"024232": {
"id": "024232",
"content": "非零实数 $x, y$ 满足 $|x+y|+|x y|=|x+y-x y|$ 的充要条件是\\bracket{20}.\n\\fourch{$x+y=0$}{$x y<0$}{$(x+y) x y>0$}{$(x+y) x y \\leq 0$}",
"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": []
},
"024233": {
"id": "024233",
"content": "若 $a<b$, 则下列不等式: \\textcircled{1} $b^2>a^2$; \\textcircled{2} $\\dfrac{1}{b}<\\dfrac{1}{a}$; \\textcircled{3} $3^b>3^a$; \\textcircled{4} $\\lg \\dfrac{a}{b}<0$; \\textcircled{5} $a^{\\frac{1}{5}}<b^{\\frac{1}{5}}$, 其中总成立的是\\bracket{20}.\n\\fourch{\\textcircled{1} 和 \\textcircled{3}}{\\textcircled{2} 和 \\textcircled{4}}{\\textcircled{1} 和 \\textcircled{4}}{\\textcircled{3} 和 \\textcircled{5}}",
"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": []
},
"024234": {
"id": "024234",
"content": "已知 $x=\\dfrac{9}{4}$ 是不等式 $\\log _a(x^2-x-2)>\\log _a(-x^2+2 x+3)$ 的解, 求此不等式的解集.",
"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": []
},
"024235": {
"id": "024235",
"content": "已知集合 $A=\\{x | x^2+x-6 \\leq 0\\}$, $B=\\{x|| x-a |<1\\}$.\\\\\n(1) 若 $B \\subseteq A$, 求实数 $a$ 的取值范围;\\\\\n(2) 若 $A \\cap B=\\varnothing$, 求实数 $a$ 的取值范围.",
"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": []
},
"024236": {
"id": "024236",
"content": "某商场对全年购销某种品牌电脑的策略调整如下: 分批购入价值 $4000$ 元的电脑共 $1800$ 台, 每批都购入 $x$ 台 ($x \\in \\mathbf{Z}$), 且每批均需支付运费 $400 $元, 储存购入的电脑全年保管费与每批购入的电脑的总价值 (不含运费) 成正比, 若每批购 $200$ 台, 则全年需要用去运费和保管费 $43600$ 元.\\\\\n(1) 试将全年所需运费和保管费 $y($ 元 $)$ 表示为每批购人台数 $x$ 的函数;\\\\\n(2) 现全年只有 $24000$ 元资金可用于支付运费和保管费, 试分析是否能够恰当安排每批进货数量, 使资金够用?",
"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": []
},
"024237": {
"id": "024237",
"content": "已知非空集合 $S \\subset\\{x | x \\in \\mathbf{N}, x \\geq 1\\}$, 且若 $x \\in S$, 则 $\\dfrac{36}{x}\\in S$.\\\\\n(1) 写出所有只含三个元素的集合 $S$;\\\\\n(2) 写出所有只含四个元素的集合 $S$;\\\\\n(3) 满足题设条件的集合 $S$ 共有几个?",
"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": []
},
"024238": {
"id": "024238",
"content": "已知 $a$ 和 $b$ 是任意非零实数.\\\\\n(1) 求 $\\dfrac{|2 a+b|+|2 a-b|}{|a|}$ 的最小值;\\\\\n(2) 若不等式 $|2 a+b|+|2 a-b| \\geq|a|(|2+x|+|2-x|)$ 恒成立, 求实数 $x$ 的取值范围.",
"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.",