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收录高三寒假作业48新题

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wangweiye7840 2024-01-25 12:57:00 +08:00
parent d6452a5c67
commit 74cf7134a3
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3
工具v2/文本文件/新题收录列表.txt
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@ -142,3 +142,6 @@
20240125-125411
023971:023978
20240125-125651
023979:023984,012842,023985

152
题库0.3/Problems.json
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@ -90255,7 +90255,9 @@
"20240124\t王伟叶"
],
"same": [],
"related": [],
"related": [
"023981"
],
"remark": "",
"space": "",
"unrelated": []
@ -175318,7 +175320,9 @@
"20220720\t王伟叶"
],
"same": [],
"related": [],
"related": [
"023979"
],
"remark": "",
"space": "4em",
"unrelated": []
@ -646259,6 +646263,150 @@
"space": "4em",
"unrelated": []
},
"023979": {
"id": "023979",
"content": "若函数 $f(x+1)$ 是偶函数, 则 $f(x)$ 的图像的对称轴方程是\\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": [
"005847"
],
"remark": "",
"space": "",
"unrelated": []
},
"023980": {
"id": "023980",
"content": "若 $f(x)=x^2+2 x-3$, 则 $y=|f(x)|$ 的严格增区间是\\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": []
},
"023981": {
"id": "023981",
"content": "若奇函数 $f(x)$ 的定义域为 $[-5,5]$, 当 $x \\in[0,5]$ 时, $f(x)$ 的图像如图所示, 则不等式 $f(x)<0$ 的解是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, yscale = 0.5]\n\\draw [->] (-1,0) -- (6,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (2,0) node [below] {$2$};\n\\draw (5,0) node [above] {$5$};\n\\draw [domain = 0:2,samples = 100] plot (\\x,-\\x*\\x+2*\\x);\n\\draw [domain = 2:5,samples = 100] plot (\\x, \\x*\\x/2-4*\\x+6);\n\\draw [dashed] (5,0) -- (5,-1.5);\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"002848"
],
"remark": "",
"space": "",
"unrelated": []
},
"023982": {
"id": "023982",
"content": "若函数 $f(x)=\\dfrac{x-a}{x-a-1}$ 图像的对称中心是 $(4,1)$, 则实数 $a$ 的值等于\\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": []
},
"023983": {
"id": "023983",
"content": "若定义域为 $\\mathbf{R}$ 的函数 $f(x)=\\begin{cases}|\\lg x|,& x>0,\\\\-x^2-2 x,& x \\leq 0,\\end{cases}$ 则函数 $f(x)$ 的零点为\\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": []
},
"023984": {
"id": "023984",
"content": "若直线 $y=1$ 与曲线 $y=x^2-|x|+a$ 有四个交点, 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": []
},
"023985": {
"id": "023985",
"content": "讨论关于 $x$ 的方程 $|x^2-2 x-3|-a=0$($a \\in \\mathbf{R}$) 的实数解的个数.",
"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.",