录入24届赋能补充题至11B
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acedea4ec1
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@ -617872,6 +617872,186 @@
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"space": "",
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"unrelated": []
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},
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"023063": {
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"id": "023063",
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"content": "不等式 $\\overrightarrow{a}=(2,1)$, $\\overrightarrow{b}=(3,-2)$, 则 $\\overrightarrow{a}\\cdot \\overrightarrow{b}=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023064": {
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"id": "023064",
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"content": "已知集合 $A=\\{x | 3^x<1, x \\in \\mathbf{R}\\}$, $B=\\{x|| x |<1, x \\in \\mathbf{R}\\}$, 则 $AB=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023065": {
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"id": "023065",
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"content": "若实数 $x, y$ 满足 $x y=1$, 则 $2 x^2+y^2$ 的最小值为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023066": {
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"id": "023066",
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"content": "设 $a \\in \\mathbf{R}, \\mathrm{i}$ 是虚数单位. 若复数 $(a+\\mathrm{i})(3+4 \\mathrm{i})$ 的实部、虚部相等, 则 $a=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023067": {
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"id": "023067",
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"content": "设 $m \\in \\mathbf{R}$, 直线 $l$ 经过原点 $O$ 以及点 $A(m, 9)$, 且 $(3,1)$ 是 $l$ 的一个法向量, 则 $m=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023068": {
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"id": "023068",
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"content": "设 $n$ 是正整数, $(2 x^2+x^{-1})^n$ 的二项展开式的各项的系数之和为 243 , 则该二项展开式中 $x^{-2}$ 的系数是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023069": {
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"id": "023069",
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"content": "在 $\\triangle ABC$ 中, 角 $A$、$B$、$C$ 所对的边分别是 $a$、$b$、$c$. 若 $c^2=(a-b)^2+4$, $C=\\dfrac{\\pi}{3}$, 则 $\\triangle ABC$ 的面积为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023070": {
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"id": "023070",
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"content": "设 $\\theta \\in \\mathbf{R}$, 则``$\\theta=\\dfrac{\\pi}{6}$''是``$\\sin \\theta=\\dfrac{1}{2}$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023071": {
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"id": "023071",
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"content": "如图, 与复平面中的阴影部分 (含边界) 对应的复数集合是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\fill [pattern = north east lines] (30:1) arc (30:150:1) -- cycle;\n\\draw (30:1) -- (150:1);\n\\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) circle (1);\n\\draw (1,0) node [below right] {$1$} (-1,0) node [below left] {$-1$};\n\\draw (0,0.5) node [below left] {$0.5$};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$\\{z|| z |=1, \\mathrm{Re}z \\geq \\dfrac{1}{2}, z \\in \\mathbf{C}\\}$}{$\\{z|| z | \\leq 1, \\mathrm{Re}z \\geq \\dfrac{1}{2}, z \\in \\mathbf{C}\\}$}{$\\{z|| z |=1, \\mathrm{Im}z \\geq \\dfrac{1}{2}, z \\in \\mathbf{C}\\}$}{$\\{z|| z | \\leq 1, \\mathrm{Im}z \\geq \\dfrac{1}{2}, z \\in \\mathbf{C}\\}$}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "24届赋能补充题目",
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"edit": [
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"20240105\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"030001": {
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"id": "030001",
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"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.",
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