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收录高三寒假作业55新题

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wangweiye7840 2024-01-25 13:48:12 +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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@ -163,3 +163,6 @@
20240125-134138
015380,024031:024039
20240125-134803
024040:024048

203
题库0.3/Problems.json
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@ -87437,7 +87437,9 @@
"20220701\t王伟叶"
],
"same": [],
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"024047"
],
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"space": "4em",
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@ -476507,7 +476509,9 @@
"20230606\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024046"
],
"remark": "",
"space": "",
"unrelated": []
@ -599897,7 +599901,9 @@
"edit": [
"20230905\t王伟叶"
],
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"same": [
"024043"
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@ -600199,7 +600205,9 @@
"edit": [
"20230905\t王伟叶"
],
"same": [],
"same": [
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@ -647585,6 +647593,193 @@
"space": "",
"unrelated": []
},
"024040": {
"id": "024040",
"content": "命题 $p$: 若 $a$、$b \\in \\mathbf{R}$, 则 $|a|+|b|>1$ 是 $|a+b|>1$ 的充分非必要条件; \n命题 $q$: 函数 $y=\\sqrt{|x-1|-2}$ 的定义域是 $(-\\infty,-1] \\cup[3,+\\infty)$, 则\\bracket{20}.\n\\fourch{``$p$ 或 $q$''为假}{``$p$ 且 $q$''为真}{$p$ 真 $q$ 假}{$p$ 假 $q$ 真}",
"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": []
},
"024041": {
"id": "024041",
"content": "设 $x \\in \\mathbf{R}$, 则``$|x+1|<2$''是``$\\lg x<0$''的条件\\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": "",
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},
"024042": {
"id": "024042",
"content": "设 $a$、$b \\in R$, 用 $\\alpha \\Rightarrow \\beta, \\beta \\Rightarrow \\alpha, \\alpha \\Leftrightarrow \\beta$ 这三种符号中的一种填空:\\\\\n(1) $\\alpha: $ 方程 $x^2+a x+b=0$ 有两相异实数根; $\\beta: b<0$. 则\\blank{50};\\\\\n(2) $\\alpha: a^2+b^2=0 ; \\beta: a=b=0$. 则\\blank{50};\\\\\n(3) $\\alpha: a b>0 ; \\beta:|a+b|=|a|+|b|$. 则\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"edit": [
"20240125\t毛培菁"
],
"same": [],
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"space": "",
"unrelated": []
},
"024043": {
"id": "024043",
"content": "已知集合 $M=\\{x | x>2\\}$, $P=\\{x | x<3\\}$, 那么``$x \\in M$ 或 $x \\in P$''是``$x \\in M \\cap P$''的条件. (填入``充要''、``充分非必要''、``必要非充分''、``非充分非必要''之一)",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
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"022195",
"022208"
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"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"024044": {
"id": "024044",
"content": "设 $x$、$y \\in \\mathbf{R}$, 用反证法证明命题``如果 $x^2+y^2<4$, 那么 $|x|<2$ 且 $|y|<2$''时, 应先假设\\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": [],
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"remark": "",
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},
"024045": {
"id": "024045",
"content": "设 $n \\in \\mathbf{N}$ 且 $n \\geq 1$, 一元二次方程 $x^2-4 x+n=0$ 有整数根的一个充要条件是\\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": "",
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},
"024046": {
"id": "024046",
"content": "函数 $f(x)=x^2+m x+1$ 的图像关于直线 $x=1$ 对称的一个充要条件是\\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": [
"017560"
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"remark": "",
"space": "",
"unrelated": []
},
"024047": {
"id": "024047",
"content": "已知 $P=\\{x | x^2-8 x-20 \\leq 0\\}$, 非空集合 $S=\\{x | 1-m \\leq x \\leq 1+m\\}$, 若 $x \\in P$ 是 $x \\in S$ 的必要条件, 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": [
"002748"
],
"remark": "",
"space": "",
"unrelated": []
},
"024048": {
"id": "024048",
"content": "设 $a$、$b$、$c \\in(0,1)$, 用反证法证明: 下列三个关于 $x$ 的方程$a x^2+x+1-b=0$、$b x^2+x+1-c=0$、$c x^2+x+1-a=0$ 中至少有一个有实数根.",
"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.",