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收录高三寒假作业52新题

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wangweiye7840 2024-01-25 13:09:56 +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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@ -154,3 +154,6 @@
20240125-130554
024002:024011
20240125-130946
024012,015714,024013:024018

185
题库0.3/Problems.json
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@ -25325,7 +25325,9 @@
"same": [
"004067"
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"related": [],
"related": [
"024017"
],
"remark": "",
"space": "",
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@ -91282,7 +91284,9 @@
"20220701\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024016"
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"remark": "",
"space": "",
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@ -124964,7 +124968,9 @@
"same": [
"000675"
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"related": [
"024017"
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"remark": "",
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@ -226252,7 +226258,9 @@
"20220726\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024012"
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"remark": "",
"space": "4em",
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@ -313570,7 +313578,9 @@
"20220817\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024016"
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"remark": "",
"space": "",
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@ -517184,7 +517194,9 @@
"20230730\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024018"
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"remark": "",
"space": "4em",
"unrelated": []
@ -549239,7 +549251,9 @@
"20221231\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024012"
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"remark": "",
"space": "4em",
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@ -550377,7 +550391,9 @@
"20221231\t王伟叶"
],
"same": [],
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"related": [
"024014"
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"remark": "",
"space": "4em",
"unrelated": []
@ -646952,6 +646968,159 @@
"space": "4em",
"unrelated": []
},
"024012": {
"id": "024012",
"content": "若函数 $f(x)=a x^2+b x-3 a$($x \\in[a, 2 a+1]$) 是偶函数, 则 $f(1)$ 的值为\\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": [
"007914",
"020531"
],
"remark": "",
"space": "",
"unrelated": []
},
"024013": {
"id": "024013",
"content": "函数 $f(x)=|x|(2-x)$ 的单调增区间是\\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": []
},
"024014": {
"id": "024014",
"content": "若函数 $y=\\log _{\\frac{1}{3}}(x^2-a x+a)$ 在区间 $(-\\infty, \\sqrt{2})$ 上是严格增函数, 则实数 $a$ 的取值范围为\\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": [
"020568"
],
"remark": "",
"space": "",
"unrelated": []
},
"024015": {
"id": "024015",
"content": "若关于 $x$ 的方程 $2^x+3 x=k$ 的解在 $[1,2)$ 内, 则实数 $k$ 的取值范围为\\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": []
},
"024016": {
"id": "024016",
"content": "若函数 $y=f(x)$ 是定义在 $\\mathbf{R}$ 上的以 $3$ 为周期的奇函数, 且 $f(2)=0$, 则方程 $f(x)=0$ 在区间 $(0,6)$ 内零点的个数的最小值是\\blank{50}个.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"011190",
"002882"
],
"remark": "",
"space": "",
"unrelated": []
},
"024017": {
"id": "024017",
"content": "若定义在 $\\mathbf{R}$ 上的函数 $f(x)$ 满足: \\textcircled{1} $f(x)+f(2-x)=0$; \\textcircled{2} $f(x-2)=f(-x)$; \\textcircled{3} 当 $x \\in[-1,1]$ 时, $f(x)=\\begin{cases}\\sqrt{1-x^2},& x \\in[-1,0],\\\\ \\cos \\dfrac{\\pi}{2}x,& x \\in(0,1].\\end{cases}$ 则函数 $y=f(x)-(\\dfrac{1}{2})^{|x|}$ 在区间 $[-3,3]$ 上的零点个数为\\blank{50}个.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"004067",
"000675"
],
"remark": "",
"space": "",
"unrelated": []
},
"024018": {
"id": "024018",
"content": "设 $f(x)=x^3+a x^2-2 x$($x \\in \\mathbf{R}$), 其中常数 $a \\in \\mathbf{R}$.\\\\\n(1) 判断函数 $y=f(x)$ 的奇偶性, 并说明理由;\\\\\n(2) 若不等式 $f(x)>\\dfrac{3}{2}x^3$ 在区间 $[\\dfrac{1}{2}, 1]$ 上有解, 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": [
"019381"
],
"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.",