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收录赋能题目若干

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wangweiye7840 2024-01-31 14:35:46 +08:00
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6
工具v2/文本文件/新题收录列表.txt
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@ -238,3 +238,9 @@
20240129-083516
024272
20240131-142137
024274:024276,017614,024277:024279,011354,024217,024280
20240131-143522
024281:024284,019976,014717,024285:024288

350
题库0.3/Problems.json
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@ -113594,7 +113594,9 @@
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@ -354616,7 +354618,9 @@
"20221217\t周双"
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@ -396365,7 +396369,9 @@
"20230131\t王伟叶"
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@ -434992,7 +434998,9 @@
"20230503\t王伟叶"
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@ -521701,7 +521709,9 @@
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@ -524433,7 +524443,9 @@
"20230730\t王伟叶"
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@ -657912,7 +657924,9 @@
"20240127\t王伟叶"
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@ -658411,6 +658425,320 @@
"space": "",
"unrelated": []
},
"024274": {
"id": "024274",
"content": "设集合 $A=\\{x | x^2-3 x-4<0\\}$, $B=\\{x |-2<x<2\\}$, 则 $A \\cap B=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
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"space": "",
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},
"024275": {
"id": "024275",
"content": "复数 $z=\\dfrac{1+2 \\mathrm{i}}{\\mathrm{i}}$ ($\\mathrm{i}$ 为虚数单位) 的共轭复数为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
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},
"024276": {
"id": "024276",
"content": "在无穷等比数列 $\\{a_n\\}$ 中, $a_2=1$, $a_5=\\dfrac{1}{27}$, 则 $\\displaystyle\\lim _{n \\to \\infty}(a_1+a_2+\\cdots+a_n)=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024277": {
"id": "024277",
"content": "已知随机变量 $X$ 的分布是 $\\begin{pmatrix}1 & 2 & 3 \\\\ \\dfrac{1}{2}& \\dfrac{1}{3}& a\\end{pmatrix}$, 则 $E[2X+a]=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024278": {
"id": "024278",
"content": "函数 $f(x)=x^2 \\ln x$ 的最小值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024279": {
"id": "024279",
"content": "在 $(1-\\dfrac{2}{x})^6$ 的二项展开式中, 中间一项的系数为\\blank{50}. (用数字作答)",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024280": {
"id": "024280",
"content": "如图是函数 $f(x)=\\sin (\\pi x+\\dfrac{\\pi}{6})$ 在一个周期内的图像, 该图像分别与 $x$ 轴、 $y$ 轴相交于 $A$、$B$ 两点, 与过点 $A$ 的直线相交于另外两点 $C$、$D$, $\\overrightarrow{i}$ 为 $x$ 轴上的基本单位向量, 则 $(\\overrightarrow{BC}+\\overrightarrow{BD}) \\cdot \\overrightarrow{i}=$\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.5,0) -0 (2.5,0) node [below] {$x$};\n\\draw [->] (0,-1.1) -- (0,1.1) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {-1/6}:{11/6}, samples = 100] plot (\\x,{sin(180*\\x+30)});\n\\draw (0,0.5) node [above left] {$B$} coordinate (B);\n\\draw ({5/6},0) node [below left] {$A$} coordinate (A);\n\\draw ({-1/12},{sin(15)}) node [left] {$D$} coordinate (D);\n\\draw ($(D)!2!(A)$) node [right] {$C$} coordinate (C);\n\\draw (B)--(C)(D)--(C);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$-1$}{$-\\dfrac{5}{6}$}{$\\dfrac{5}{6}$}{$\\dfrac{5}{3}$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024281": {
"id": "024281",
"content": "设集合 $A=(-1,3)$, $B=[0,4)$, 则 $A \\cup B=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024282": {
"id": "024282",
"content": "复数 $z$ 满足 $\\overline{z}=\\dfrac{1}{1+\\mathrm{i}}$ ($\\mathrm{i}$ 为虚数单位), 则 $|z|=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [
"024252"
],
"remark": "",
"space": "",
"unrelated": []
},
"024283": {
"id": "024283",
"content": "已知一组数据 $6,7,8,8,9,10$, 则该组数据的标准差是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024284": {
"id": "024284",
"content": "若向量 $\\overrightarrow{a}=(1,0,1)$, $\\overrightarrow{b}=(0,1,-1)$ , 则向量 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 的夹角为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [
"019567",
"031957",
"003633"
],
"remark": "",
"space": "",
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},
"024285": {
"id": "024285",
"content": "在公差不为零的等差数列 $\\{a_n\\}$ 中, $a_3$ 是 $a_1$ 与 $a_9$ 的等比中项, 则 $\\dfrac{a_1+a_2+\\cdots+a_9}{a_9}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024286": {
"id": "024286",
"content": "设函数 $f(x)=\\sin \\omega x $($0<\\omega<2$), 将 $f(x)$ 图像向左平移 $\\dfrac{2 \\pi}{3}$ 单位后所得函数图像与原函数图像的对称轴重合, 则 $\\omega=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [
"019447",
"030777"
],
"remark": "",
"space": "",
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},
"024287": {
"id": "024287",
"content": "设 $f(x)=x^\\alpha $($\\alpha \\in\\{-2,-1, \\dfrac{1}{3}, \\dfrac{1}{2}, 1,2\\}$), 则``$y=f(x)$ 图像经过点 $(-1,1)$''是``$y=f(x)$ 是偶函数''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件 }{充要条件}{既非充分又非必要条件}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
"related": [
"012626",
"014169"
],
"remark": "",
"space": "",
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},
"024288": {
"id": "024288",
"content": "若曲线 $y=\\mathrm{e}^x-1$ 在 $x=x_0$ 处的切线方程为 $\\mathrm{e} x-y+t=0$, 则\\bracket{20}.\n\\fourch{$x_0=1$, $t=-1$}{$x_0=1$, $t=-\\mathrm{e}$}{$x_0=-1$, $t=-1$}{$x_0=-1$, $t=-\\mathrm{e}$}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240131\t毛培菁"
],
"same": [],
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"remark": "",
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},
"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.",
@ -682198,7 +682526,9 @@
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@ -711234,7 +711564,9 @@
"20230730\t王伟叶"
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