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收录高三寒假作业51新题

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wangweiye7840 2024-01-25 13:06:07 +08:00
parent a504bb9ff5
commit 8ff685a477
2 changed files with 215 additions and 3 deletions
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3
工具v2/文本文件/新题收录列表.txt
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@ -151,3 +151,6 @@
20240125-130257
023994:024001
20240125-130554
024002:024011

215
题库0.3/Problems.json
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@ -169348,7 +169348,9 @@
"20220720\t王伟叶"
],
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@ -170058,7 +170060,8 @@
],
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"005636"
"005636",
"024004"
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"space": "",
@ -646745,6 +646748,210 @@
"space": "4em",
"unrelated": []
},
"024002": {
"id": "024002",
"content": "函数 $y=\\sqrt{\\log _3(2 x-1)+1}$ 的定义域是\\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": []
},
"024003": {
"id": "024003",
"content": "计算: $\\lg \\dfrac{5}{2}+2 \\lg 2-(\\dfrac{1}{2})^{-1}=$\\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": []
},
"024004": {
"id": "024004",
"content": "若 $2^a=5^b=m$, 且 $\\dfrac{1}{a}+\\dfrac{1}{b}=2$, 则 $m=$\\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": [
"031316",
"005609",
"005637"
],
"remark": "",
"space": "",
"unrelated": []
},
"024005": {
"id": "024005",
"content": "若函数 $f(x)=\\begin{cases}-x+6,& x \\geq 2,\\\\3+\\log _ax,& x>2\\end{cases}$($a>0$, $a \\neq 1$) 的值域是 $[4,+\\infty)$, 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": []
},
"024006": {
"id": "024006",
"content": "已知 $a>0$, 且 $a \\neq 1$, 函数 $y=\\log _a(2 x-3)+\\sqrt{2}$ 的图像恒过点 $P$. 若点 $P$ 也在幂函数 $f(x)$ 的图像上, 则 $f(x)=$\\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": []
},
"024007": {
"id": "024007",
"content": "若函数 $f(x)=\\log _2(x^2-a x-3 a)$ 在区间 $(-\\infty,-2]$ 上是严格减函数, 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": [],
"remark": "",
"space": "",
"unrelated": []
},
"024008": {
"id": "024008",
"content": "若函数 $f(x)=\\lg (x^2-4 x-5)$ 在 $(a,+\\infty)$ 上是严格增函数, 则 $a$ 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": []
},
"024009": {
"id": "024009",
"content": "已知 $f(x)$ 是定义在 $\\mathbf{R}$ 上的奇函数, $f(x-2)$ 为偶函数, 若当 $0<x \\leq 2$\n时, $f(x)=\\log _22 x$, 则 $f(201)+f(202)$ 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": [],
"remark": "",
"space": "",
"unrelated": []
},
"024010": {
"id": "024010",
"content": "已知函数 $f(x)$ 是定义在 $\\mathbf{R}$ 上的偶函数, 若 $f(0)=0$, 当 $x>0$ 时, $f(x)=\\log _{\\frac{1}{2}}x$, 则不等式 $f(x^2-1)>-2$ 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": []
},
"024011": {
"id": "024011",
"content": "已知函数 $f(x)=\\lg (x+\\dfrac{a}{x}-2)$, 其中 $a$ 是大于 $0$ 的常数. 若对任意 $x \\in[2,+\\infty)$ 恒有 $f(x)>0$, 试确定实数 $a$ 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": []
},
"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.",
@ -683871,7 +684078,9 @@
"20230315\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024004"
],
"remark": "",
"space": "",
"unrelated": []